Proof Step: c_0_9

name: c_0_9 syntax: thf role: negated_conjecture inference: distribute

Proof State Overview

proof_step c_0_1 c_0_1 c_0_7 c_0_7 c_0_1->c_0_7 c_0_9 c_0_9 c_0_7->c_0_9 c_0_12 ⊕ member_msg y synth analz h ⊕ member_msg mPair x y synth analz h c_0_9->c_0_12 c_0_18 ⊖ member_msg mPair x y synth analz h ⊖ member_msg x synth analz h ⊖ member_msg y synth analz h c_0_9->c_0_18 c_0_30 ⊕ member_msg x synth analz h ⊕ member_msg mPair x y synth analz h c_0_9->c_0_30

Input Dependencies

c_0_1

Assumptions

c_0_7

Conclusion

c_0_9

Dependents

c_0_12 c_0_18 c_0_30

Formula

( ( ~ ( member_msg @ ( mPair @ x @ y ) @ ( synth @ ( analz @ h ) ) )
  | ~ ( member_msg @ x @ ( synth @ ( analz @ h ) ) )
  | ~ ( member_msg @ y @ ( synth @ ( analz @ h ) ) ) )
& ( ( member_msg @ x @ ( synth @ ( analz @ h ) ) )
  | ( member_msg @ ( mPair @ x @ y ) @ ( synth @ ( analz @ h ) ) ) )
& ( ( member_msg @ y @ ( synth @ ( analz @ h ) ) )
  | ( member_msg @ ( mPair @ x @ y ) @ ( synth @ ( analz @ h ) ) ) ) )

Source

inference(distribute,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_7])])