TSTP Solution File: SEV195^5 by Leo-III---1.7.15
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : SEV195^5 : TPTP v8.2.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 15:58:28 EDT 2024
% Result : Theorem 43.35s 11.10s
% Output : Refutation 43.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 3
% Syntax : Number of formulae : 140 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 499 ( 491 equ; 141 cnn)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 2358 ( 429 ~; 420 |; 20 &;1473 @)
% ( 0 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 9 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 129 ( 129 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 527 ( 168 ^ 349 !; 10 ?; 527 :)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(cP_type,type,
cP: a > a > a ).
thf(cZ_type,type,
cZ: a ).
thf(sk1_type,type,
sk1: ( a > $o ) > a ).
thf(sk2_type,type,
sk2: ( a > $o ) > a ).
thf(sk3_type,type,
sk3: a ).
thf(sk4_type,type,
sk4: a > a > a ).
thf(sk5_type,type,
sk5: a > a > a ).
thf(1,conjecture,
( ( ! [A: a,B: a] :
( ( cP @ A @ B )
!= cZ )
& ! [A: a,B: a,C: a,D: a] :
( ( ( cP @ A @ C )
= ( cP @ B @ D ) )
=> ( ( A = B )
& ( C = D ) ) )
& ! [A: a > $o] :
( ( ( A @ cZ )
& ! [B: a,C: a] :
( ( ( A @ B )
& ( A @ C ) )
=> ( A @ ( cP @ B @ C ) ) ) )
=> ! [B: a] : ( A @ B ) ) )
=> ! [A: a] :
( ( A = cZ )
| ? [B: a,C: a] :
( A
= ( cP @ B @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cS_LEM1D_pme) ).
thf(2,negated_conjecture,
~ ( ( ! [A: a,B: a] :
( ( cP @ A @ B )
!= cZ )
& ! [A: a,B: a,C: a,D: a] :
( ( ( cP @ A @ C )
= ( cP @ B @ D ) )
=> ( ( A = B )
& ( C = D ) ) )
& ! [A: a > $o] :
( ( ( A @ cZ )
& ! [B: a,C: a] :
( ( ( A @ B )
& ( A @ C ) )
=> ( A @ ( cP @ B @ C ) ) ) )
=> ! [B: a] : ( A @ B ) ) )
=> ! [A: a] :
( ( A = cZ )
| ? [B: a,C: a] :
( A
= ( cP @ B @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ! [A: a,B: a] :
( ( cP @ A @ B )
!= cZ )
& ! [A: a,B: a,C: a,D: a] :
( ( ( cP @ A @ C )
= ( cP @ B @ D ) )
=> ( ( A = B )
& ( C = D ) ) )
& ! [A: a > $o] :
( ( ( A @ cZ )
& ! [B: a,C: a] :
( ( ( A @ B )
& ( A @ C ) )
=> ( A @ ( cP @ B @ C ) ) ) )
=> ! [B: a] : ( A @ B ) ) )
=> ! [A: a] :
( ( A = cZ )
| ? [B: a,C: a] :
( A
= ( cP @ B @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
~ ( ( ~ ? [A: a,B: a] :
( ( cP @ A @ B )
= cZ )
& ! [A: a,B: a,C: a,D: a] :
( ( ( cP @ A @ C )
= ( cP @ B @ D ) )
=> ( ( A = B )
& ( C = D ) ) )
& ! [A: a > $o] :
( ( ( A @ cZ )
& ! [B: a,C: a] :
( ( ( A @ B )
& ( A @ C ) )
=> ( A @ ( cP @ B @ C ) ) ) )
=> ! [B: a] : ( A @ B ) ) )
=> ! [A: a] :
( ( A = cZ )
| ? [B: a,C: a] :
( A
= ( cP @ B @ C ) ) ) ),
inference(miniscope,[status(thm)],[3]) ).
thf(8,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(32,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( A @ B ) ),
inference(simp,[status(thm)],[8]) ).
thf(39,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ cZ ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[32]) ).
thf(54,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ cZ ) ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(79,plain,
! [D: a,C: a > $o,B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( C @ cZ )
| ( ( C @ D )
!= ( ~ ( C @ cZ ) ) )
| ( ( A @ B )
!= ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,54]) ).
thf(101,plain,
! [D: a,C: a > $o,B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( C @ cZ )
| ( ( C @ D )
!= ( ~ ( C @ cZ ) ) )
| ( ( A @ B )
!= ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[79:[]]) ).
thf(35,plain,
! [D: a,C: a > $o,B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
| ( C @ D )
| ( ( A @ B )
!= ( C @ cZ ) ) ),
inference(paramod_ordered,[status(thm)],[32,32]) ).
thf(55,plain,
! [D: a,C: a > $o,B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
| ( C @ D )
| ( ( A @ B )
!= ( C @ cZ ) ) ),
inference(pre_uni,[status(thm)],[35:[]]) ).
thf(56,plain,
! [D: a,C: a > $o,B: a,A: a > $o] :
( ( C @ D )
| ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( A @ cZ )
| ( ( A @ B )
!= ( C @ cZ ) ) ),
inference(pre_uni,[status(thm)],[55:[]]) ).
thf(37,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ( A @ B )
| ( ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( A @ cZ ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[32]) ).
thf(51,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ( A @ B )
| ( ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( A @ cZ ) ) ),
inference(pre_uni,[status(thm)],[37:[]]) ).
thf(52,plain,
! [B: a,A: a > $o] :
( ( A @ B )
| ~ ( A @ cZ )
| ( ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( A @ cZ ) ) ),
inference(pre_uni,[status(thm)],[51:[]]) ).
thf(90,plain,
! [C: a > $o,B: a > $o,A: a] :
( ~ ( ( B @ cZ )
| ( C @ cZ ) )
| ~ ( ( B
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( C
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) ) )
| ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) ) ),
inference(prim_subst,[status(thm)],[54:[bind(A,$thf( ^ [E: a] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(117,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ cZ ) ),
inference(cnf,[status(esa)],[90]) ).
thf(121,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ cZ ) ),
inference(simp,[status(thm)],[117]) ).
thf(12,plain,
sk3 != cZ,
inference(cnf,[status(esa)],[4]) ).
thf(28,plain,
sk3 != cZ,
inference(lifteq,[status(thm)],[12]) ).
thf(10,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ( A @ ( sk2 @ A ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(13,plain,
! [A: a] :
( ( cZ != cZ )
| ( cZ
= ( sk2 @ ( (=) @ a @ cZ ) ) )
| ( cZ = A ) ),
inference(replace_leibeq,[status(thm)],[10:[bind(A,$thf( (=) @ a @ cZ ))]]) ).
thf(26,plain,
! [A: a] :
( ( cZ != cZ )
| ( ( sk2 @ ( (=) @ a @ cZ ) )
= cZ )
| ( cZ = A ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(27,plain,
! [A: a] :
( ( ( sk2 @ ( (=) @ a @ cZ ) )
= cZ )
| ( cZ = A ) ),
inference(simp,[status(thm)],[26]) ).
thf(11,plain,
! [B: a,A: a] :
( ( cP @ A @ B )
!= cZ ),
inference(cnf,[status(esa)],[4]) ).
thf(31,plain,
! [B: a,A: a] :
( ( cP @ A @ B )
!= cZ ),
inference(lifteq,[status(thm)],[11]) ).
thf(238,plain,
! [C: a,B: a,A: a] :
( ( ( sk2 @ ( (=) @ a @ cZ ) )
= cZ )
| ( A
!= ( cP @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27,31]) ).
thf(239,plain,
( ( sk2 @ ( (=) @ a @ cZ ) )
= cZ ),
inference(pattern_uni,[status(thm)],[238:[bind(A,$thf( cP @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(19,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ( A @ ( sk2 @ A ) )
| ( A @ B ) ),
inference(simp,[status(thm)],[10]) ).
thf(448,plain,
! [D: a,C: a > $o,B: a,A: a > $o] :
( ~ ( A @ cZ )
| ( A @ B )
| ( C @ ( sk2 @ C ) )
| ( C @ D )
| ( ( A @ ( sk2 @ A ) )
!= ( C @ cZ ) ) ),
inference(paramod_ordered,[status(thm)],[19,19]) ).
thf(467,plain,
! [C: a,B: a > $o,A: a] :
( ( cZ != cZ )
| ( cZ = A )
| ( B @ ( sk2 @ B ) )
| ( B @ C )
| ( ( cZ
= ( sk2 @ ( (=) @ a @ cZ ) ) )
!= ( B @ cZ ) ) ),
inference(replace_leibeq,[status(thm)],[448:[bind(A,$thf( (=) @ a @ cZ ))]]) ).
thf(489,plain,
! [C: a,B: a > $o,A: a] :
( ( cZ != cZ )
| ( cZ = A )
| ( B @ ( sk2 @ B ) )
| ( B @ C )
| ( ( cZ
= ( sk2 @ ( (=) @ a @ cZ ) ) )
!= ( B @ cZ ) ) ),
inference(lifteq,[status(thm)],[467]) ).
thf(534,plain,
! [B: a,A: a] :
( ( cZ
= ( sk2 @ ( (=) @ a @ B ) ) )
| ( cZ
= ( sk2
@ ( (=) @ a
@ ( sk2
@ ^ [C: a] :
( cZ
= ( sk2 @ ( (=) @ a @ C ) ) ) ) ) ) )
| ( cZ = A ) ),
inference(pre_uni,[status(thm)],[489:[bind(A,$thf( A )),bind(B,$thf( ^ [D: a] : ( cZ = ( sk2 @ ( (=) @ a @ D ) ) ) )),bind(C,$thf( C ))]]) ).
thf(578,plain,
! [B: a,A: a] :
( ( ( sk2 @ ( (=) @ a @ B ) )
= cZ )
| ( ( sk2
@ ( (=) @ a
@ ( sk2
@ ^ [C: a] :
( cZ
= ( sk2 @ ( (=) @ a @ C ) ) ) ) ) )
= cZ )
| ( cZ = A ) ),
inference(lifteq,[status(thm)],[534]) ).
thf(579,plain,
! [B: a,A: a] :
( ( ( sk2 @ ( (=) @ a @ B ) )
= cZ )
| ( ( sk2
@ ( (=) @ a
@ ( sk2
@ ^ [C: a] :
( cZ
= ( sk2 @ ( (=) @ a @ C ) ) ) ) ) )
= cZ )
| ( cZ = A ) ),
inference(simp,[status(thm)],[578]) ).
thf(7026,plain,
! [B: a,A: a] :
( ( ( sk2 @ ( (=) @ a @ B ) )
= cZ )
| ( cZ = A )
| ( ( sk2
@ ( (=) @ a
@ ( sk2
@ ^ [C: a] :
( cZ
= ( sk2 @ ( (=) @ a @ C ) ) ) ) ) )
!= ( sk2 @ ( (=) @ a @ B ) ) )
| ( cZ != cZ ) ),
inference(eqfactor_ordered,[status(thm)],[579]) ).
thf(7116,plain,
! [A: a] :
( ( ( sk2
@ ( (=) @ a
@ ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) )
= cZ )
| ( cZ = A ) ),
inference(pattern_uni,[status(thm)],[7026:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ^ [C: a] : ( cZ = ( sk2 @ ( (=) @ a @ C ) ) ) ))]]) ).
thf(15384,plain,
! [C: a,B: a,A: a] :
( ( ( sk2
@ ( (=) @ a
@ ( sk2
@ ^ [D: a] :
( cZ
= ( sk2 @ ( (=) @ a @ D ) ) ) ) ) )
= cZ )
| ( A
!= ( cP @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[7116,31]) ).
thf(15385,plain,
( ( sk2
@ ( (=) @ a
@ ( sk2
@ ^ [A: a] :
( cZ
= ( sk2 @ ( (=) @ a @ A ) ) ) ) ) )
= cZ ),
inference(pattern_uni,[status(thm)],[15384:[bind(A,$thf( cP @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(15939,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ cZ ) )
| ( ( A @ B )
!= ( ~ ( A @ cZ ) ) )
| ( ( sk2
@ ( (=) @ a
@ ( sk2
@ ^ [C: a] :
( cZ
= ( sk2 @ ( (=) @ a @ C ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[15385,54]) ).
thf(15940,plain,
! [A: a] :
( ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ )
| ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= ( cP
@ ( sk1
@ ( (=) @ a
@ ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) )
@ cZ ) )
| ( ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
= A )
!= ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ ) ) ),
inference(pattern_uni,[status(thm)],[15939:[bind(A,$thf( (=) @ a @ ( sk2 @ ^ [C: a] : ( cZ = ( sk2 @ ( (=) @ a @ C ) ) ) ) )),bind(B,$thf( B ))]]) ).
thf(15955,plain,
! [A: a] :
( ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ )
| ( ( cP
@ ( sk1
@ ( (=) @ a
@ ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) )
@ cZ )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
= A )
!= ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ ) ) ),
inference(lifteq,[status(thm)],[15940]) ).
thf(15983,plain,
! [A: a] :
( ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ )
| ( ( cP
@ ( sk1
@ ( (=) @ a
@ ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) )
@ cZ )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
= A )
!= ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ ) ) ),
inference(simp,[status(thm)],[15955]) ).
thf(17272,plain,
! [A: a] :
( ( ( cP
@ ( sk1
@ ( (=) @ a
@ ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) )
@ cZ )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
= A )
!= ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ ) )
| ( ( sk2 @ ( (=) @ a @ cZ ) )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[239,15983]) ).
thf(17402,plain,
! [A: a] :
( ( ( cP
@ ( sk1
@ ( (=) @ a
@ ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) )
@ cZ )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
= A )
!= ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ ) )
| ( ( (=) @ a @ cZ )
!= ( ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[17272]) ).
thf(9,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ( A @ ( sk1 @ A ) )
| ( A @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(25,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ( A @ ( sk1 @ A ) )
| ( A @ B ) ),
inference(simp,[status(thm)],[9]) ).
thf(678,plain,
! [B: a > $o,A: a] :
( ~ ~ ( B @ cZ )
| ~ ( B
@ ( sk1
@ ^ [C: a] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[25:[bind(A,$thf( ^ [D: a] : ~ ( C @ D ) ))]]) ).
thf(832,plain,
! [B: a > $o,A: a] :
( ~ ( B @ A )
| ~ ( B
@ ( sk1
@ ^ [C: a] :
~ ( B @ C ) ) )
| ( B @ cZ ) ),
inference(cnf,[status(esa)],[678]) ).
thf(833,plain,
! [B: a > $o,A: a] :
( ~ ( B @ A )
| ~ ( B
@ ( sk1
@ ^ [C: a] :
~ ( B @ C ) ) )
| ( B @ cZ ) ),
inference(simp,[status(thm)],[832]) ).
thf(3153,plain,
! [B: a > $o,A: a] :
( ~ ~ ( B @ A )
| ~ ~ ( B
@ ( sk1
@ ^ [C: a] :
~ ~ ( B @ C ) ) )
| ~ ( B @ cZ ) ),
inference(prim_subst,[status(thm)],[833:[bind(A,$thf( A )),bind(B,$thf( ^ [D: a] : ~ ( C @ D ) ))]]) ).
thf(3233,plain,
! [B: a > $o,A: a] :
( ~ ( B @ cZ )
| ( B
@ ( sk1
@ ^ [C: a] :
~ ~ ( B @ C ) ) )
| ( B @ A ) ),
inference(cnf,[status(esa)],[3153]) ).
thf(3234,plain,
! [B: a > $o,A: a] :
( ~ ( B @ cZ )
| ( B @ ( sk1 @ B ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[3233]) ).
thf(44,plain,
! [C: a > $o,B: a > $o,A: a] :
( ~ ( ( B @ cZ )
| ( C @ cZ ) )
| ~ ( ( B
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ( C
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) ) )
| ( B @ A )
| ( C @ A ) ),
inference(prim_subst,[status(thm)],[32:[bind(A,$thf( ^ [E: a] : ( ( C @ E ) | ( D @ E ) ) ))]]) ).
thf(68,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( B @ A )
| ( C @ A )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ cZ ) ),
inference(cnf,[status(esa)],[44]) ).
thf(72,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( B @ A )
| ( C @ A )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ cZ ) ),
inference(simp,[status(thm)],[68]) ).
thf(83,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ( ( A @ B )
!= ( ~ ( A @ cZ ) ) )
| ( ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( A @ cZ ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[54]) ).
thf(104,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ( ( A @ B )
!= ( ~ ( A @ cZ ) ) )
| ( ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( A @ cZ ) ) ),
inference(pre_uni,[status(thm)],[83:[]]) ).
thf(14,plain,
! [A: a] :
( ( cZ != cZ )
| ( cZ
= ( sk1 @ ( (=) @ a @ cZ ) ) )
| ( cZ = A ) ),
inference(replace_leibeq,[status(thm)],[9:[bind(A,$thf( (=) @ a @ cZ ))]]) ).
thf(20,plain,
! [A: a] :
( ( cZ != cZ )
| ( ( sk1 @ ( (=) @ a @ cZ ) )
= cZ )
| ( cZ = A ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(21,plain,
! [A: a] :
( ( ( sk1 @ ( (=) @ a @ cZ ) )
= cZ )
| ( cZ = A ) ),
inference(simp,[status(thm)],[20]) ).
thf(155,plain,
! [C: a,B: a,A: a] :
( ( ( sk1 @ ( (=) @ a @ cZ ) )
= cZ )
| ( A
!= ( cP @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21,31]) ).
thf(156,plain,
( ( sk1 @ ( (=) @ a @ cZ ) )
= cZ ),
inference(pattern_uni,[status(thm)],[155:[bind(A,$thf( cP @ D @ E )),bind(B,$thf( D )),bind(C,$thf( E ))]]) ).
thf(115,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ cZ ) ),
inference(cnf,[status(esa)],[90]) ).
thf(119,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ cZ ) ),
inference(simp,[status(thm)],[115]) ).
thf(906,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( C
@ ( cP @ cZ
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ cZ )
| ( ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
!= ( sk1 @ ( (=) @ a @ cZ ) ) ) ),
inference(paramod_ordered,[status(thm)],[156,119]) ).
thf(1005,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( C
@ ( cP @ cZ
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ cZ )
| ( ( ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
!= ( (=) @ a @ cZ ) ) ),
inference(simp,[status(thm)],[906]) ).
thf(116,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ cZ ) ),
inference(cnf,[status(esa)],[90]) ).
thf(120,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ cZ ) ),
inference(simp,[status(thm)],[116]) ).
thf(454,plain,
! [B: a > $o,A: a] :
( ~ ~ ( B @ cZ )
| ~ ( B
@ ( sk2
@ ^ [C: a] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[19:[bind(A,$thf( ^ [D: a] : ~ ( C @ D ) ))]]) ).
thf(596,plain,
! [B: a > $o,A: a] :
( ~ ( B @ A )
| ~ ( B
@ ( sk2
@ ^ [C: a] :
~ ( B @ C ) ) )
| ( B @ cZ ) ),
inference(cnf,[status(esa)],[454]) ).
thf(597,plain,
! [B: a > $o,A: a] :
( ~ ( B @ A )
| ~ ( B
@ ( sk2
@ ^ [C: a] :
~ ( B @ C ) ) )
| ( B @ cZ ) ),
inference(simp,[status(thm)],[596]) ).
thf(6,plain,
! [D: a,C: a,B: a,A: a] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( C = D ) ),
inference(cnf,[status(esa)],[4]) ).
thf(22,plain,
! [D: a,C: a,B: a,A: a] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( C = D ) ),
inference(lifteq,[status(thm)],[6]) ).
thf(23,plain,
! [D: a,C: a,B: a,A: a] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( C = D ) ),
inference(simp,[status(thm)],[22]) ).
thf(24,plain,
! [B: a,A: a] :
( ( sk5 @ A @ ( cP @ A @ B ) )
= B ),
introduced(tautology,[new_symbols(inverse(cP),[sk5])]) ).
thf(9414,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( C @ ( cP @ cZ @ cZ ) )
| ~ ( B @ cZ )
| ( ( ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
!= ( (=) @ a @ cZ ) )
| ( ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
!= ( sk2 @ ( (=) @ a @ cZ ) ) ) ),
inference(paramod_ordered,[status(thm)],[239,1005]) ).
thf(9743,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( C @ ( cP @ cZ @ cZ ) )
| ~ ( B @ cZ )
| ( ( ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
!= ( (=) @ a @ cZ ) )
| ( ( ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
!= ( (=) @ a @ cZ ) ) ),
inference(simp,[status(thm)],[9414]) ).
thf(9789,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( C @ ( cP @ cZ @ cZ ) )
| ~ ( B @ cZ )
| ( ( ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
!= ( (=) @ a @ cZ ) ) ),
inference(simp,[status(thm)],[9743]) ).
thf(11373,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( B @ cZ )
| ( ( ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
!= ( (=) @ a @ cZ ) )
| ( ( C @ ( cP @ cZ @ cZ ) )
!= ( B @ cZ ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[9789]) ).
thf(11609,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( B @ cZ )
| ( ( ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
!= ( (=) @ a @ cZ ) )
| ( ( C @ ( cP @ cZ @ cZ ) )
!= ( B @ cZ ) ) ),
inference(pre_uni,[status(thm)],[11373:[]]) ).
thf(78,plain,
! [D: a,C: a > $o,B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
| ( ( C @ D )
!= ( ~ ( C @ cZ ) ) )
| ( ( A @ B )
!= ( C @ cZ ) ) ),
inference(paramod_ordered,[status(thm)],[32,54]) ).
thf(97,plain,
! [D: a,C: a > $o,B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
| ( ( C @ D )
!= ( ~ ( C @ cZ ) ) )
| ( ( A @ B )
!= ( C @ cZ ) ) ),
inference(pre_uni,[status(thm)],[78:[]]) ).
thf(3910,plain,
! [D: a,C: a > $o,B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
| ( ( C @ D )
!= ( ~ ( C @ cZ ) ) )
| ~ ( A @ B )
| ( ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
!= ( C @ cZ ) ) ),
inference(eqfactor_ordered,[status(thm)],[97]) ).
thf(3965,plain,
! [B: a,A: a > $o] :
( ~ $true
| ~ $true
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ cZ ) ) )
| ( ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( A @ cZ ) ) ),
inference(pre_uni,[status(thm)],[3910:[bind(A,$thf( ^ [E: a] : $true ))]]) ).
thf(4141,plain,
! [B: a,A: a > $o] :
( ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ cZ ) ) )
| ( ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
!= ( A @ cZ ) ) ),
inference(simp,[status(thm)],[3965]) ).
thf(17470,plain,
! [A: a] :
( ( ( cP
@ ( sk1
@ ( (=) @ a
@ ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) )
@ cZ )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( cZ = A )
!= ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ ) )
| ( ( (=) @ a @ cZ )
!= ( ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( sk2 @ ( (=) @ a @ cZ ) )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[239,17402]) ).
thf(17598,plain,
! [A: a] :
( ( ( cP
@ ( sk1
@ ( (=) @ a
@ ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) )
@ cZ )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( cZ = A )
!= ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ ) )
| ( ( (=) @ a @ cZ )
!= ( ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( (=) @ a @ cZ )
!= ( ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[17470]) ).
thf(17646,plain,
! [A: a] :
( ( ( cP
@ ( sk1
@ ( (=) @ a
@ ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) )
@ cZ )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( cZ = A )
!= ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ ) )
| ( ( (=) @ a @ cZ )
!= ( ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[17598]) ).
thf(18813,plain,
! [A: a] :
( ( ( cP @ ( sk1 @ ( (=) @ a @ cZ ) ) @ cZ )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( cZ = A )
!= ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ ) )
| ( ( (=) @ a @ cZ )
!= ( ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( sk2 @ ( (=) @ a @ cZ ) )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[239,17646]) ).
thf(18947,plain,
! [A: a] :
( ( ( cP @ ( sk1 @ ( (=) @ a @ cZ ) ) @ cZ )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( cZ = A )
!= ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ ) )
| ( ( (=) @ a @ cZ )
!= ( ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( (=) @ a @ cZ )
!= ( ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[18813]) ).
thf(18960,plain,
! [A: a] :
( ( ( cP @ ( sk1 @ ( (=) @ a @ cZ ) ) @ cZ )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( cZ = A )
!= ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ ) )
| ( ( (=) @ a @ cZ )
!= ( ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) ),
inference(simp,[status(thm)],[18947]) ).
thf(20619,plain,
! [A: a] :
( ( ( cP @ cZ @ cZ )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( cZ = A )
!= ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ ) )
| ( ( (=) @ a @ cZ )
!= ( ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) ),
inference(rewrite,[status(thm)],[18960,156]) ).
thf(70,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( B @ A )
| ( C @ A )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ cZ ) ),
inference(cnf,[status(esa)],[44]) ).
thf(74,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( B @ A )
| ( C @ A )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ cZ ) ),
inference(simp,[status(thm)],[70]) ).
thf(3018,plain,
! [B: a > $o,A: a] :
( ~ ~ ( B @ A )
| ~ ~ ( B
@ ( sk2
@ ^ [C: a] :
~ ~ ( B @ C ) ) )
| ~ ( B @ cZ ) ),
inference(prim_subst,[status(thm)],[597:[bind(A,$thf( A )),bind(B,$thf( ^ [D: a] : ~ ( C @ D ) ))]]) ).
thf(3096,plain,
! [B: a > $o,A: a] :
( ~ ( B @ cZ )
| ( B
@ ( sk2
@ ^ [C: a] :
~ ~ ( B @ C ) ) )
| ( B @ A ) ),
inference(cnf,[status(esa)],[3018]) ).
thf(3097,plain,
! [B: a > $o,A: a] :
( ~ ( B @ cZ )
| ( B @ ( sk2 @ B ) )
| ( B @ A ) ),
inference(simp,[status(thm)],[3096]) ).
thf(36,plain,
! [D: a,C: a > $o,B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( C @ cZ )
| ( C @ D )
| ( ( A @ B )
!= ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[32,32]) ).
thf(59,plain,
! [D: a,C: a > $o,B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( C @ cZ )
| ( C @ D )
| ( ( A @ B )
!= ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[36:[]]) ).
thf(60,plain,
! [D: a,C: a > $o,B: a,A: a > $o] :
( ( C @ D )
| ~ ( C @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( A @ cZ )
| ( ( A @ B )
!= ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[59:[]]) ).
thf(41,plain,
! [B: a > $o,A: a] :
( ~ ~ ( B @ cZ )
| ~ ~ ( B
@ ( cP
@ ( sk1
@ ^ [C: a] :
~ ( B @ C ) )
@ ( sk2
@ ^ [C: a] :
~ ( B @ C ) ) ) )
| ~ ( B @ A ) ),
inference(prim_subst,[status(thm)],[32:[bind(A,$thf( ^ [D: a] : ~ ( C @ D ) ))]]) ).
thf(64,plain,
! [B: a > $o,A: a] :
( ~ ( B @ A )
| ( B
@ ( cP
@ ( sk1
@ ^ [C: a] :
~ ( B @ C ) )
@ ( sk2
@ ^ [C: a] :
~ ( B @ C ) ) ) )
| ( B @ cZ ) ),
inference(cnf,[status(esa)],[41]) ).
thf(65,plain,
! [B: a > $o,A: a] :
( ~ ( B @ A )
| ( B
@ ( cP
@ ( sk1
@ ^ [C: a] :
~ ( B @ C ) )
@ ( sk2
@ ^ [C: a] :
~ ( B @ C ) ) ) )
| ( B @ cZ ) ),
inference(simp,[status(thm)],[64]) ).
thf(1358,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ cZ ) )
| ~ ( C @ cZ )
| ( ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
!= ( sk2 @ ( (=) @ a @ cZ ) ) ) ),
inference(paramod_ordered,[status(thm)],[239,120]) ).
thf(1541,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ cZ ) )
| ~ ( C @ cZ )
| ( ( ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
!= ( (=) @ a @ cZ ) ) ),
inference(simp,[status(thm)],[1358]) ).
thf(69,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( B @ A )
| ( C @ A )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ cZ ) ),
inference(cnf,[status(esa)],[44]) ).
thf(73,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( B @ A )
| ( C @ A )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ cZ ) ),
inference(simp,[status(thm)],[69]) ).
thf(3151,plain,
! [B: a > $o,A: a] :
( ~ ( B @ A )
| ( B @ cZ )
| ~ ( B
@ ( sk1
@ ^ [C: a] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(eqfactor_ordered,[status(thm)],[833]) ).
thf(3160,plain,
! [A: a] :
( ( A != A )
| ( A = cZ )
| ( A
!= ( sk1
@ ^ [B: a] : ( A != B ) ) )
| ( A != A ) ),
inference(replace_leibeq,[status(thm)],[3151:[bind(A,$thf( A )),bind(B,$thf( (=) @ a @ A ))]]) ).
thf(3176,plain,
! [A: a] :
( ( A != A )
| ( A = cZ )
| ( A
!= ( sk1
@ ^ [B: a] : ( A != B ) ) )
| ( A != A ) ),
inference(lifteq,[status(thm)],[3160]) ).
thf(3257,plain,
! [A: a] :
( ( A = cZ )
| ( A
!= ( sk1
@ ^ [B: a] : ( A != B ) ) ) ),
inference(simp,[status(thm)],[3176]) ).
thf(5,plain,
! [D: a,C: a,B: a,A: a] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( A = B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(16,plain,
! [D: a,C: a,B: a,A: a] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(17,plain,
! [D: a,C: a,B: a,A: a] :
( ( ( cP @ A @ C )
!= ( cP @ B @ D ) )
| ( A = B ) ),
inference(simp,[status(thm)],[16]) ).
thf(907,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ cZ ) )
| ~ ( B @ cZ )
| ( ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
!= ( sk2 @ ( (=) @ a @ cZ ) ) ) ),
inference(paramod_ordered,[status(thm)],[239,119]) ).
thf(1092,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ cZ ) )
| ~ ( B @ cZ )
| ( ( ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
!= ( (=) @ a @ cZ ) ) ),
inference(simp,[status(thm)],[907]) ).
thf(18,plain,
! [B: a,A: a] :
( ( sk4 @ A @ ( cP @ B @ A ) )
= B ),
introduced(tautology,[new_symbols(inverse(cP),[sk4])]) ).
thf(3016,plain,
! [B: a > $o,A: a] :
( ~ ( B @ A )
| ( B @ cZ )
| ~ ( B
@ ( sk2
@ ^ [C: a] :
~ ( B @ C ) ) )
| ~ ( B @ A ) ),
inference(eqfactor_ordered,[status(thm)],[597]) ).
thf(3026,plain,
! [A: a] :
( ( A != A )
| ( A = cZ )
| ( A
!= ( sk2
@ ^ [B: a] : ( A != B ) ) )
| ( A != A ) ),
inference(replace_leibeq,[status(thm)],[3016:[bind(A,$thf( A )),bind(B,$thf( (=) @ a @ A ))]]) ).
thf(3042,plain,
! [A: a] :
( ( A != A )
| ( A = cZ )
| ( A
!= ( sk2
@ ^ [B: a] : ( A != B ) ) )
| ( A != A ) ),
inference(lifteq,[status(thm)],[3026]) ).
thf(3112,plain,
! [A: a] :
( ( A = cZ )
| ( A
!= ( sk2
@ ^ [B: a] : ( A != B ) ) ) ),
inference(simp,[status(thm)],[3042]) ).
thf(20620,plain,
! [A: a] :
( ( ( cP @ cZ @ cZ )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( cZ = A )
!= ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ ) )
| ( ( ^ [B: a] : cZ )
!= ( ^ [B: a] : cZ ) )
| ( ( ^ [B: a] : B )
!= ( ^ [B: a] : ( sk2 @ ( (=) @ a @ B ) ) ) ) ),
inference(simp,[status(thm)],[20619]) ).
thf(20785,plain,
! [A: a] :
( ( ( cP @ cZ @ cZ )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( cZ = A )
!= ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ ) )
| ( ( ^ [B: a] : B )
!= ( ^ [B: a] : ( sk2 @ ( (=) @ a @ B ) ) ) ) ),
inference(simp,[status(thm)],[20620]) ).
thf(71,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( B @ A )
| ( C @ A )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ cZ ) ),
inference(cnf,[status(esa)],[44]) ).
thf(75,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( B @ A )
| ( C @ A )
| ~ ( C
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( B @ cZ ) ),
inference(simp,[status(thm)],[71]) ).
thf(40,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[32]) ).
thf(58,plain,
! [B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ( ( A @ B )
!= ( ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) ) ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(7,plain,
! [B: a,A: a] :
( sk3
!= ( cP @ A @ B ) ),
inference(cnf,[status(esa)],[4]) ).
thf(29,plain,
! [B: a,A: a] :
( ( cP @ A @ B )
!= sk3 ),
inference(lifteq,[status(thm)],[7]) ).
thf(30,plain,
! [B: a,A: a] :
( ( cP @ A @ B )
!= sk3 ),
inference(simp,[status(thm)],[29]) ).
thf(17441,plain,
! [A: a] :
( ( ( cP
@ ( sk1
@ ( (=) @ a
@ ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) )
@ cZ )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
= A )
!= ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ ) )
| ( ( ^ [B: a] : cZ )
!= ( ^ [B: a] : cZ ) )
| ( ( ^ [B: a] : B )
!= ( ^ [B: a] : ( sk2 @ ( (=) @ a @ B ) ) ) ) ),
inference(simp,[status(thm)],[17402]) ).
thf(17626,plain,
! [A: a] :
( ( ( cP
@ ( sk1
@ ( (=) @ a
@ ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) ) )
@ cZ )
!= ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) ) )
| ( ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
= A )
!= ( ( sk2
@ ^ [B: a] :
( cZ
= ( sk2 @ ( (=) @ a @ B ) ) ) )
!= cZ ) )
| ( ( ^ [B: a] : B )
!= ( ^ [B: a] : ( sk2 @ ( (=) @ a @ B ) ) ) ) ),
inference(simp,[status(thm)],[17441]) ).
thf(118,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ cZ ) ),
inference(cnf,[status(esa)],[90]) ).
thf(122,plain,
! [C: a > $o,B: a > $o,A: a] :
( ( ( ( B @ A )
| ( C @ A ) )
!= ( ~ ( ( B @ cZ )
| ( C @ cZ ) ) ) )
| ~ ( B
@ ( cP
@ ( sk1
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) )
@ ( sk2
@ ^ [D: a] :
( ( B @ D )
| ( C @ D ) ) ) ) )
| ~ ( C @ cZ ) ),
inference(simp,[status(thm)],[118]) ).
thf(82,plain,
! [D: a,C: a > $o,B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( C @ cZ )
| ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
| ( C @ D )
| ( ( A @ B )
!= ( C @ cZ ) ) ),
inference(paramod_ordered,[status(thm)],[32,54]) ).
thf(99,plain,
! [D: a,C: a > $o,B: a,A: a > $o] :
( ~ ( A @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( C @ cZ )
| ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
| ( C @ D )
| ( ( A @ B )
!= ( C @ cZ ) ) ),
inference(pre_uni,[status(thm)],[82:[]]) ).
thf(100,plain,
! [D: a,C: a > $o,B: a,A: a > $o] :
( ( C @ D )
| ~ ( C @ ( cP @ ( sk1 @ C ) @ ( sk2 @ C ) ) )
| ~ ( C @ cZ )
| ~ ( A @ ( cP @ ( sk1 @ A ) @ ( sk2 @ A ) ) )
| ~ ( A @ cZ )
| ( ( A @ B )
!= ( C @ cZ ) ) ),
inference(pre_uni,[status(thm)],[99:[]]) ).
thf(21249,plain,
$false,
inference(e,[status(thm)],[101,56,52,121,28,17402,3234,3,15385,31,72,104,239,1005,120,597,24,25,11609,4141,20619,74,3097,60,65,97,1541,156,73,17646,3257,32,17,54,1092,15983,9789,18,3112,20785,23,75,119,58,833,30,17626,19,122,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13 % Problem : SEV195^5 : TPTP v8.2.0. Released v4.0.0.
% 0.08/0.13 % Command : run_Leo-III %s %d THM
% 0.13/0.35 % Computer : n020.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Fri Jun 21 18:29:55 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.90/0.84 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.95 % [INFO] Parsing done (106ms).
% 1.21/0.95 % [INFO] Running in sequential loop mode.
% 1.50/1.18 % [INFO] eprover registered as external prover.
% 1.66/1.18 % [INFO] Scanning for conjecture ...
% 1.66/1.24 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.66/1.26 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.66/1.27 % [INFO] Problem is higher-order (TPTP THF).
% 1.66/1.27 % [INFO] Type checking passed.
% 1.66/1.27 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 43.35/11.10 % External prover 'e' found a proof!
% 43.35/11.10 % [INFO] Killing All external provers ...
% 43.35/11.10 % Time passed: 10567ms (effective reasoning time: 10142ms)
% 43.35/11.10 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 43.35/11.10 % Axioms used in derivation (0):
% 43.35/11.10 % No. of inferences in proof: 140
% 43.35/11.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10567 ms resp. 10142 ms w/o parsing
% 43.35/11.19 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 43.35/11.19 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------