%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV106^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:36:51 AM UTC 2026
% Result : Theorem 30.86s 7.61s
% Output : Refutation 28.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 11
% Syntax : Number of formulae : 156 ( 38 unt; 0 typ; 10 def)
% Number of atoms : 628 ( 192 equ; 0 cnn)
% Maximal formula atoms : 38 ( 4 avg)
% Number of connectives : 1870 ( 241 ~; 219 |; 109 &;1229 @)
% ( 0 <=>; 72 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 107 ( 107 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 483 ( 213 ^; 221 !; 39 ?; 483 :)
% ( 0 !>; 0 ?*; 0 @-; 10 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a > $o ).
thf(sk2_decl,type,
sk2: a > $o ).
thf(sk3_decl,type,
sk3: a > $o ).
thf(sk4_decl,type,
sk4: a > a ).
thf(sk5_decl,type,
sk5: a > a ).
thf(sk6_decl,type,
sk6: a > a ).
thf(sk7_decl,type,
sk7: a > a ).
thf(sk8_decl,type,
sk8: ( a > a ) > $o ).
thf(sk9_decl,type,
sk9: ( a > a ) > a ).
thf(sk10_decl,type,
sk10: ( a > a ) > a ).
thf(sk11_decl,type,
sk11: a > ( a > a ) > a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a > $o] :
~ ! [B: a > $o,C: a > $o] :
( ( ? [D: a > a] :
( ! [E: a] :
( ( A @ E )
=> ( B @ ( D @ E ) ) )
& ! [E: a] :
( ( B @ E )
=> ? [F: a] :
( ( A @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( A @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) )
& ? [D: a > a] :
( ! [E: a] :
( ( B @ E )
=> ( C @ ( D @ E ) ) )
& ! [E: a] :
( ( C @ E )
=> ? [F: a] :
( ( B @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( B @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) ) )
=> ? [D: a > a] :
( ! [E: a] :
( ( A @ E )
=> ( C @ ( D @ E ) ) )
& ! [E: a] :
( ( C @ E )
=> ? [F: a] :
( ( A @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( A @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > $o] :
~ ! [B: a > $o] :
( ( ? [C: a > a] :
( ! [D: a] :
( ( sk1 @ D )
=> ( A @ ( C @ D ) ) )
& ! [D: a] :
( ( A @ D )
=> ? [E: a] :
( ( sk1 @ E )
& ( D
= ( C @ E ) )
& ! [F: a] :
( ( ( sk1 @ F )
& ( D
= ( C @ F ) ) )
=> ( F = E ) ) ) ) )
& ? [C: a > a] :
( ! [D: a] :
( ( A @ D )
=> ( B @ ( C @ D ) ) )
& ! [D: a] :
( ( B @ D )
=> ? [E: a] :
( ( A @ E )
& ( D
= ( C @ E ) )
& ! [F: a] :
( ( ( A @ F )
& ( D
= ( C @ F ) ) )
=> ( F = E ) ) ) ) ) )
=> ? [C: a > a] :
( ! [D: a] :
( ( sk1 @ D )
=> ( B @ ( C @ D ) ) )
& ! [D: a] :
( ( B @ D )
=> ? [E: a] :
( ( sk1 @ E )
& ( D
= ( C @ E ) )
& ! [F: a] :
( ( ( sk1 @ F )
& ( D
= ( C @ F ) ) )
=> ( F = E ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a > $o] :
~ ( ( ? [B: a > a] :
( ! [C: a] :
( ( sk1 @ C )
=> ( sk2 @ ( B @ C ) ) )
& ! [C: a] :
( ( sk2 @ C )
=> ? [D: a] :
( ( sk1 @ D )
& ( C
= ( B @ D ) )
& ! [E: a] :
( ( ( sk1 @ E )
& ( C
= ( B @ E ) ) )
=> ( E = D ) ) ) ) )
& ? [B: a > a] :
( ! [C: a] :
( ( sk2 @ C )
=> ( A @ ( B @ C ) ) )
& ! [C: a] :
( ( A @ C )
=> ? [D: a] :
( ( sk2 @ D )
& ( C
= ( B @ D ) )
& ! [E: a] :
( ( ( sk2 @ E )
& ( C
= ( B @ E ) ) )
=> ( E = D ) ) ) ) ) )
=> ? [B: a > a] :
( ! [C: a] :
( ( sk1 @ C )
=> ( A @ ( B @ C ) ) )
& ! [C: a] :
( ( A @ C )
=> ? [D: a] :
( ( sk1 @ D )
& ( C
= ( B @ D ) )
& ! [E: a] :
( ( ( sk1 @ E )
& ( C
= ( B @ E ) ) )
=> ( E = D ) ) ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: a > a] :
( ! [B: a] :
( ( sk1 @ B )
=> ( sk2 @ ( A @ B ) ) )
& ! [B: a] :
( ( sk2 @ B )
=> ? [C: a] :
( ( sk1 @ C )
& ( B
= ( A @ C ) )
& ! [D: a] :
( ( ( sk1 @ D )
& ( B
= ( A @ D ) ) )
=> ( D = C ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: a] :
@+[B: a] :
( ( sk1 @ B )
& ( A
= ( sk4 @ B ) )
& ! [C: a] :
( ( ( sk1 @ C )
& ( A
= ( sk4 @ C ) ) )
=> ( C = B ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: a > a] :
( ! [B: a] :
( ( sk2 @ B )
=> ( sk3 @ ( A @ B ) ) )
& ! [B: a] :
( ( sk3 @ B )
=> ? [C: a] :
( ( sk2 @ C )
& ( B
= ( A @ C ) )
& ! [D: a] :
( ( ( sk2 @ D )
& ( B
= ( A @ D ) ) )
=> ( D = C ) ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: a] :
@+[B: a] :
( ( sk2 @ B )
& ( A
= ( sk6 @ B ) )
& ! [C: a] :
( ( ( sk2 @ C )
& ( A
= ( sk6 @ C ) ) )
=> ( C = B ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: a > a] :
@+[B: a] :
~ ( ( sk1 @ B )
=> ( sk3 @ ( A @ B ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: a > a] :
@+[B: a] :
~ ( ( sk3 @ B )
=> ? [C: a] :
( ( sk1 @ C )
& ( B
= ( A @ C ) )
& ! [D: a] :
( ( ( sk1 @ D )
& ( B
= ( A @ D ) ) )
=> ( D = C ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: a,B: a > a] :
@+[C: a] :
~ ( ( ( sk1 @ C )
& ( ( sk10 @ B )
= ( B @ C ) ) )
=> ( C = A ) ) ) ) ).
thf(1,conjecture,
! [A: a > $o,B: a > $o,C: a > $o] :
( ( ? [D: a > a] :
( ! [E: a] :
( ( A @ E )
=> ( B @ ( D @ E ) ) )
& ! [E: a] :
( ( B @ E )
=> ? [F: a] :
( ( A @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( A @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) )
& ? [D: a > a] :
( ! [E: a] :
( ( B @ E )
=> ( C @ ( D @ E ) ) )
& ! [E: a] :
( ( C @ E )
=> ? [F: a] :
( ( B @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( B @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) ) )
=> ? [D: a > a] :
( ! [E: a] :
( ( A @ E )
=> ( C @ ( D @ E ) ) )
& ! [E: a] :
( ( C @ E )
=> ? [F: a] :
( ( A @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( A @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cEQP1_1C_pme) ).
thf(2,negated_conjecture,
~ ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ? [D: a > a] :
( ! [E: a] :
( ( A @ E )
=> ( B @ ( D @ E ) ) )
& ! [E: a] :
( ( B @ E )
=> ? [F: a] :
( ( A @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( A @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) )
& ? [D: a > a] :
( ! [E: a] :
( ( B @ E )
=> ( C @ ( D @ E ) ) )
& ! [E: a] :
( ( C @ E )
=> ? [F: a] :
( ( B @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( B @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) ) )
=> ? [D: a > a] :
( ! [E: a] :
( ( A @ E )
=> ( C @ ( D @ E ) ) )
& ! [E: a] :
( ( C @ E )
=> ? [F: a] :
( ( A @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( A @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a > $o,B: a > $o,C: a > $o] :
( ( ? [D: a > a] :
( ! [E: a] :
( ( A @ E )
=> ( B @ ( D @ E ) ) )
& ! [E: a] :
( ( B @ E )
=> ? [F: a] :
( ( A @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( A @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) )
& ? [D: a > a] :
( ! [E: a] :
( ( B @ E )
=> ( C @ ( D @ E ) ) )
& ! [E: a] :
( ( C @ E )
=> ? [F: a] :
( ( B @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( B @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) ) )
=> ? [D: a > a] :
( ! [E: a] :
( ( A @ E )
=> ( C @ ( D @ E ) ) )
& ! [E: a] :
( ( C @ E )
=> ? [F: a] :
( ( A @ F )
& ( E
= ( D @ F ) )
& ! [G: a] :
( ( ( A @ G )
& ( E
= ( D @ G ) ) )
=> ( G = F ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [H: a,G: a > a,F: a,E: a,D: a,C: a,B: a,A: a] :
( ( ~ ( sk1 @ A )
| ( sk2 @ ( sk4 @ A ) ) )
& ( ~ ( sk2 @ B )
| ( sk1 @ ( sk5 @ B ) ) )
& ( ~ ( sk2 @ B )
| ( B
= ( sk4 @ ( sk5 @ B ) ) ) )
& ( ~ ( sk2 @ B )
| ~ ( sk1 @ C )
| ( B
!= ( sk4 @ C ) )
| ( C
= ( sk5 @ B ) ) )
& ( ~ ( sk2 @ D )
| ( sk3 @ ( sk6 @ D ) ) )
& ( ~ ( sk3 @ E )
| ( sk2 @ ( sk7 @ E ) ) )
& ( ~ ( sk3 @ E )
| ( E
= ( sk6 @ ( sk7 @ E ) ) ) )
& ( ~ ( sk3 @ E )
| ~ ( sk2 @ F )
| ( E
!= ( sk6 @ F ) )
| ( F
= ( sk7 @ E ) ) )
& ( ( sk1 @ ( sk9 @ G ) )
| ~ ( sk8 @ G ) )
& ( ~ ( sk3 @ ( G @ ( sk9 @ G ) ) )
| ~ ( sk8 @ G ) )
& ( ( sk8 @ G )
| ( sk3 @ ( sk10 @ G ) ) )
& ( ( sk8 @ G )
| ~ ( sk1 @ H )
| ( ( sk10 @ G )
!= ( G @ H ) )
| ( sk1 @ ( sk11 @ H @ G ) ) )
& ( ( sk8 @ G )
| ~ ( sk1 @ H )
| ( ( sk10 @ G )
!= ( G @ H ) )
| ( ( sk10 @ G )
= ( G @ ( sk11 @ H @ G ) ) ) )
& ( ( sk8 @ G )
| ~ ( sk1 @ H )
| ( ( sk10 @ G )
!= ( G @ H ) )
| ( ( sk11 @ H @ G )
!= H ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(17,plain,
! [A: a > a] :
( ( sk8 @ A )
| ( sk3 @ ( sk10 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(26,plain,
! [A: a > a] :
( ( sk8 @ A )
| ( sk3 @ ( sk10 @ A ) ) ),
inference(simp,[status(thm)],[17]) ).
thf(10,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( sk2 @ ( sk7 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(21,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( sk2 @ ( sk7 @ A ) ) ),
inference(simp,[status(thm)],[10]) ).
thf(43,plain,
! [B: a,A: a > a] :
( ( sk8 @ A )
| ~ $true
| ( sk2 @ ( sk7 @ B ) )
| ( ( sk3 @ ( sk10 @ A ) )
!= ( sk3 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[26,21]) ).
thf(44,plain,
! [B: a,A: a > a] :
( ( sk8 @ A )
| ( sk2 @ ( sk7 @ B ) )
| ( ( sk3 @ ( sk10 @ A ) )
!= ( sk3 @ B ) ) ),
inference(simp,[status(thm)],[43]) ).
thf(45,plain,
! [A: a > a] :
( ( sk8 @ A )
| ( sk2 @ ( sk7 @ ( sk10 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[44:[bind(A,$thf( C )),bind(B,$thf( sk10 @ C ))]]) ).
thf(49,plain,
! [A: a > a] :
( ( sk8 @ A )
| ( sk2 @ ( sk7 @ ( sk10 @ A ) ) ) ),
inference(simp,[status(thm)],[45]) ).
thf(14,plain,
! [A: a > a] :
( ( sk1 @ ( sk9 @ A ) )
| ~ ( sk8 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(22,plain,
! [A: a > a] :
( ( sk1 @ ( sk9 @ A ) )
| ~ ( sk8 @ A ) ),
inference(simp,[status(thm)],[14]) ).
thf(9,plain,
! [A: a] :
( ~ ( sk1 @ A )
| ( sk2 @ ( sk4 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(39,plain,
! [B: a,A: a > a] :
( ~ ( sk8 @ A )
| ~ $true
| ( sk2 @ ( sk4 @ B ) )
| ( ( sk1 @ ( sk9 @ A ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[22,9]) ).
thf(40,plain,
! [B: a,A: a > a] :
( ~ ( sk8 @ A )
| ( sk2 @ ( sk4 @ B ) )
| ( ( sk1 @ ( sk9 @ A ) )
!= ( sk1 @ B ) ) ),
inference(simp,[status(thm)],[39]) ).
thf(41,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ( sk2 @ ( sk4 @ ( sk9 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[40:[bind(A,$thf( C )),bind(B,$thf( sk9 @ C ))]]) ).
thf(42,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ( sk2 @ ( sk4 @ ( sk9 @ A ) ) ) ),
inference(simp,[status(thm)],[41]) ).
thf(8,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk3 @ ( sk6 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(36,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk3 @ ( sk6 @ A ) ) ),
inference(simp,[status(thm)],[8]) ).
thf(6,plain,
! [A: a > a] :
( ~ ( sk3 @ ( A @ ( sk9 @ A ) ) )
| ~ ( sk8 @ A ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(23,plain,
! [A: a > a] :
( ~ ( sk3 @ ( A @ ( sk9 @ A ) ) )
| ~ ( sk8 @ A ) ),
inference(simp,[status(thm)],[6]) ).
thf(110,plain,
! [B: a > a,A: a] :
( ~ ( sk2 @ A )
| ~ $true
| ~ ( sk8 @ B )
| ( ( sk3 @ ( sk6 @ A ) )
!= ( sk3 @ ( B @ ( sk9 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,23]) ).
thf(111,plain,
! [B: a > a,A: a] :
( ~ ( sk2 @ A )
| ~ ( sk8 @ B )
| ( ( sk3 @ ( sk6 @ A ) )
!= ( sk3 @ ( B @ ( sk9 @ B ) ) ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(112,plain,
! [A: a > a] :
( ~ ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) )
| ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ),
inference(pre_uni,[status(thm)],[111:[bind(A,$thf( C @ ( sk9 @ ^ [D: a] : ( sk6 @ ( C @ D ) ) ) )),bind(B,$thf( ^ [D: a] : ( sk6 @ ( C @ D ) ) ))]]) ).
thf(113,plain,
! [A: a > a] :
( ~ ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) )
| ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(221,plain,
! [B: a > a,A: a > a] :
( ~ ( sk8 @ A )
| ~ $true
| ~ ( sk8
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) )
| ( ( sk2 @ ( sk4 @ ( sk9 @ A ) ) )
!= ( sk2
@ ( B
@ ( sk9
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[42,113]) ).
thf(222,plain,
! [B: a > a,A: a > a] :
( ~ ( sk8 @ A )
| ~ ( sk8
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) )
| ( ( sk2 @ ( sk4 @ ( sk9 @ A ) ) )
!= ( sk2
@ ( B
@ ( sk9
@ ^ [C: a] : ( sk6 @ ( B @ C ) ) ) ) ) ) ),
inference(simp,[status(thm)],[221]) ).
thf(245,plain,
( ~ ( sk8
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) )
| ~ ( sk8
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ),
inference(pre_uni,[status(thm)],[222:[bind(A,$thf( ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) )),bind(B,$thf( sk4 ))]]) ).
thf(253,plain,
~ ( sk8
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ),
inference(simp,[status(thm)],[245]) ).
thf(261,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ~ $true
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,253]) ).
thf(262,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ),
inference(simp,[status(thm)],[261]) ).
thf(263,plain,
( sk3
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[262:[bind(A,$thf( ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ))]]) ).
thf(273,plain,
! [A: a > a] :
( ~ $true
| ~ ( sk8 @ A )
| ( ( sk3
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) )
!= ( sk3 @ ( A @ ( sk9 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[263,23]) ).
thf(274,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ( ( sk3
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) )
!= ( sk3 @ ( A @ ( sk9 @ A ) ) ) ) ),
inference(simp,[status(thm)],[273]) ).
thf(275,plain,
~ ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ),
inference(pre_uni,[status(thm)],[274:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ))]]) ).
thf(281,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ~ $true
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,275]) ).
thf(282,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(283,plain,
( sk3
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ))]]) ).
thf(348,plain,
! [A: a > a] :
( ~ $true
| ~ ( sk8 @ A )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) )
!= ( sk3 @ ( A @ ( sk9 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[283,23]) ).
thf(349,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) )
!= ( sk3 @ ( A @ ( sk9 @ A ) ) ) ) ),
inference(simp,[status(thm)],[348]) ).
thf(350,plain,
~ ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ),
inference(pre_uni,[status(thm)],[349:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ))]]) ).
thf(353,plain,
! [A: a > a] :
( ( sk2 @ ( sk7 @ ( sk10 @ A ) ) )
| ~ $true
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,350]) ).
thf(354,plain,
! [A: a > a] :
( ( sk2 @ ( sk7 @ ( sk10 @ A ) ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ),
inference(simp,[status(thm)],[353]) ).
thf(355,plain,
( sk2
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[354:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ))]]) ).
thf(567,plain,
! [A: a > a] :
( ~ $true
| ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) )
!= ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[355,113]) ).
thf(568,plain,
! [A: a > a] :
( ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) )
!= ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ),
inference(simp,[status(thm)],[567]) ).
thf(570,plain,
~ ( sk8
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[568:[bind(A,$thf( ^ [B: a] : ( sk7 @ ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ))]]) ).
thf(356,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ~ $true
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,350]) ).
thf(357,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ),
inference(simp,[status(thm)],[356]) ).
thf(358,plain,
( sk3
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ))]]) ).
thf(487,plain,
! [A: a > a] :
( ~ $true
| ~ ( sk8 @ A )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) )
!= ( sk3 @ ( A @ ( sk9 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[358,23]) ).
thf(488,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) )
!= ( sk3 @ ( A @ ( sk9 @ A ) ) ) ) ),
inference(simp,[status(thm)],[487]) ).
thf(489,plain,
~ ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[488:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ))]]) ).
thf(11,plain,
! [B: a,A: a > a] :
( ( sk8 @ A )
| ~ ( sk1 @ B )
| ( ( sk10 @ A )
!= ( A @ B ) )
| ( sk1 @ ( sk11 @ B @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(34,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( sk8 @ A )
| ~ ( sk1 @ B )
| ( sk1 @ ( sk11 @ B @ A ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(35,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( sk8 @ A )
| ~ ( sk1 @ B )
| ( sk1 @ ( sk11 @ B @ A ) ) ),
inference(simp,[status(thm)],[34]) ).
thf(783,plain,
( ( sk1
@ ( sk11
@ ( sk10
@ ^ [A: a] : A )
@ ^ [A: a] : A ) )
| ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( sk8
@ ^ [A: a] : A ) ),
inference(pre_uni,[status(thm)],[35:[bind(A,$thf( ^ [C: a] : C )),bind(B,$thf( sk10 @ ^ [C: a] : C ))]]) ).
thf(995,plain,
! [A: a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( sk8
@ ^ [B: a] : B )
| ~ $true
| ( sk2 @ ( sk4 @ A ) )
| ( ( sk1
@ ( sk11
@ ( sk10
@ ^ [B: a] : B )
@ ^ [B: a] : B ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[783,9]) ).
thf(996,plain,
! [A: a] :
( ~ ( sk1
@ ( sk10
@ ^ [B: a] : B ) )
| ( sk8
@ ^ [B: a] : B )
| ( sk2 @ ( sk4 @ A ) )
| ( ( sk1
@ ( sk11
@ ( sk10
@ ^ [B: a] : B )
@ ^ [B: a] : B ) )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[995]) ).
thf(997,plain,
( ~ ( sk1
@ ( sk10
@ ^ [A: a] : A ) )
| ( sk8
@ ^ [A: a] : A )
| ( sk2
@ ( sk4
@ ( sk11
@ ( sk10
@ ^ [A: a] : A )
@ ^ [A: a] : A ) ) ) ),
inference(pattern_uni,[status(thm)],[996:[bind(A,$thf( sk11 @ ( sk10 @ ^ [B: a] : B ) @ ^ [B: a] : B ))]]) ).
thf(495,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ~ $true
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,489]) ).
thf(496,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[495]) ).
thf(497,plain,
( sk3
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[496:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ))]]) ).
thf(771,plain,
! [A: a > a] :
( ~ $true
| ~ ( sk8 @ A )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) )
!= ( sk3 @ ( A @ ( sk9 @ A ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[497,23]) ).
thf(772,plain,
! [A: a > a] :
( ~ ( sk8 @ A )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) )
!= ( sk3 @ ( A @ ( sk9 @ A ) ) ) ) ),
inference(simp,[status(thm)],[771]) ).
thf(773,plain,
~ ( sk8
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[772:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk10 @ ^ [F: a] : ( sk6 @ ( sk4 @ F ) ) ) ) ) ) ))]]) ).
thf(492,plain,
! [A: a > a] :
( ( sk2 @ ( sk7 @ ( sk10 @ A ) ) )
| ~ $true
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,489]) ).
thf(493,plain,
! [A: a > a] :
( ( sk2 @ ( sk7 @ ( sk10 @ A ) ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] :
( sk10
@ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ) ) ),
inference(simp,[status(thm)],[492]) ).
thf(494,plain,
( sk2
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[493:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk10 @ ^ [E: a] : ( sk6 @ ( sk4 @ E ) ) ) ) ) ))]]) ).
thf(7,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ ( sk5 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(29,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk1 @ ( sk5 @ A ) ) ),
inference(simp,[status(thm)],[7]) ).
thf(88,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ~ $true
| ( sk2 @ ( sk4 @ B ) )
| ( ( sk1 @ ( sk5 @ A ) )
!= ( sk1 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29,9]) ).
thf(89,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk4 @ B ) )
| ( ( sk1 @ ( sk5 @ A ) )
!= ( sk1 @ B ) ) ),
inference(simp,[status(thm)],[88]) ).
thf(90,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk4 @ ( sk5 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[89:[bind(A,$thf( C )),bind(B,$thf( sk5 @ C ))]]) ).
thf(99,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( sk2 @ ( sk4 @ ( sk5 @ A ) ) ) ),
inference(simp,[status(thm)],[90]) ).
thf(85,plain,
! [B: a,A: a] :
( ~ ( sk3 @ A )
| ~ $true
| ( sk1 @ ( sk5 @ B ) )
| ( ( sk2 @ ( sk7 @ A ) )
!= ( sk2 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[21,29]) ).
thf(86,plain,
! [B: a,A: a] :
( ~ ( sk3 @ A )
| ( sk1 @ ( sk5 @ B ) )
| ( ( sk2 @ ( sk7 @ A ) )
!= ( sk2 @ B ) ) ),
inference(simp,[status(thm)],[85]) ).
thf(87,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( sk1 @ ( sk5 @ ( sk7 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( C )),bind(B,$thf( sk7 @ C ))]]) ).
thf(98,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( sk1 @ ( sk5 @ ( sk7 @ A ) ) ) ),
inference(simp,[status(thm)],[87]) ).
thf(270,plain,
! [A: a] :
( ~ $true
| ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[263,98]) ).
thf(271,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[270]) ).
thf(272,plain,
( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[271:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ))]]) ).
thf(484,plain,
! [A: a] :
( ~ $true
| ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[358,98]) ).
thf(485,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] :
( sk10
@ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[484]) ).
thf(486,plain,
( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[485:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ))]]) ).
thf(345,plain,
! [A: a] :
( ~ $true
| ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[283,98]) ).
thf(346,plain,
! [A: a] :
( ( sk1 @ ( sk5 @ ( sk7 @ A ) ) )
| ( ( sk3
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[345]) ).
thf(347,plain,
( sk1
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[346:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ))]]) ).
thf(256,plain,
! [A: a > a] :
( ( sk2 @ ( sk7 @ ( sk10 @ A ) ) )
| ~ $true
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,253]) ).
thf(257,plain,
! [A: a > a] :
( ( sk2 @ ( sk7 @ ( sk10 @ A ) ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ),
inference(simp,[status(thm)],[256]) ).
thf(258,plain,
( sk2
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ),
inference(pattern_uni,[status(thm)],[257:[bind(A,$thf( ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ))]]) ).
thf(284,plain,
! [A: a] :
( ~ $true
| ( sk2 @ ( sk4 @ ( sk5 @ A ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[258,99]) ).
thf(285,plain,
! [A: a] :
( ( sk2 @ ( sk4 @ ( sk5 @ A ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[284]) ).
thf(286,plain,
( sk2
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[285:[bind(A,$thf( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ))]]) ).
thf(516,plain,
! [A: a > a] :
( ~ $true
| ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
| ( ( sk2
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) )
!= ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[286,113]) ).
thf(517,plain,
! [A: a > a] :
( ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
| ( ( sk2
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) )
!= ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ),
inference(simp,[status(thm)],[516]) ).
thf(518,plain,
~ ( sk8
@ ^ [A: a] :
( sk6
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[517:[bind(A,$thf( ^ [B: a] : ( sk4 @ ( sk5 @ ( sk7 @ ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ))]]) ).
thf(276,plain,
! [A: a > a] :
( ( sk2 @ ( sk7 @ ( sk10 @ A ) ) )
| ~ $true
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[49,275]) ).
thf(277,plain,
! [A: a > a] :
( ( sk2 @ ( sk7 @ ( sk10 @ A ) ) )
| ( ( sk8 @ A )
!= ( sk8
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ),
inference(simp,[status(thm)],[276]) ).
thf(278,plain,
( sk2
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[277:[bind(A,$thf( ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ))]]) ).
thf(377,plain,
! [A: a] :
( ~ $true
| ( sk2 @ ( sk4 @ ( sk5 @ A ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[278,99]) ).
thf(378,plain,
! [A: a] :
( ( sk2 @ ( sk4 @ ( sk5 @ A ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[377]) ).
thf(379,plain,
( sk2
@ ( sk4
@ ( sk5
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[378:[bind(A,$thf( sk7 @ ( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ))]]) ).
thf(5,plain,
! [A: a] :
( ~ ( sk3 @ A )
| ( A
= ( sk6 @ ( sk7 @ A ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(19,plain,
! [A: a] :
( ( ( sk6 @ ( sk7 @ A ) )
= A )
| ~ ( sk3 @ A ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(20,plain,
! [A: a] :
( ( ( sk6 @ ( sk7 @ A ) )
= A )
| ~ ( sk3 @ A ) ),
inference(simp,[status(thm)],[19]) ).
thf(267,plain,
! [A: a] :
( ( ( sk6 @ ( sk7 @ A ) )
= A )
| ~ $true
| ( ( sk3
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[263,20]) ).
thf(268,plain,
! [A: a] :
( ( ( sk6 @ ( sk7 @ A ) )
= A )
| ( ( sk3
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(269,plain,
( ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) )
= ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ),
inference(pattern_uni,[status(thm)],[268:[bind(A,$thf( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ))]]) ).
thf(13,plain,
! [A: a] :
( ~ ( sk2 @ A )
| ( A
= ( sk4 @ ( sk5 @ A ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(24,plain,
! [A: a] :
( ( ( sk4 @ ( sk5 @ A ) )
= A )
| ~ ( sk2 @ A ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(25,plain,
! [A: a] :
( ( ( sk4 @ ( sk5 @ A ) )
= A )
| ~ ( sk2 @ A ) ),
inference(simp,[status(thm)],[24]) ).
thf(16,plain,
! [B: a,A: a] :
( ~ ( sk3 @ A )
| ~ ( sk2 @ B )
| ( A
!= ( sk6 @ B ) )
| ( B
= ( sk7 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(32,plain,
! [B: a,A: a] :
( ( A
!= ( sk6 @ B ) )
| ( B
= ( sk7 @ A ) )
| ~ ( sk3 @ A )
| ~ ( sk2 @ B ) ),
inference(lifteq,[status(thm)],[16]) ).
thf(33,plain,
! [A: a] :
( ( ( sk7 @ ( sk6 @ A ) )
= A )
| ~ ( sk3 @ ( sk6 @ A ) )
| ~ ( sk2 @ A ) ),
inference(simp,[status(thm)],[32]) ).
thf(12,plain,
! [B: a,A: a] :
( ~ ( sk2 @ A )
| ~ ( sk1 @ B )
| ( A
!= ( sk4 @ B ) )
| ( B
= ( sk5 @ A ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(27,plain,
! [B: a,A: a] :
( ( A
!= ( sk4 @ B ) )
| ( B
= ( sk5 @ A ) )
| ~ ( sk2 @ A )
| ~ ( sk1 @ B ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(28,plain,
! [A: a] :
( ( ( sk5 @ ( sk4 @ A ) )
= A )
| ~ ( sk2 @ ( sk4 @ A ) )
| ~ ( sk1 @ A ) ),
inference(simp,[status(thm)],[27]) ).
thf(15,plain,
! [B: a,A: a > a] :
( ( sk8 @ A )
| ~ ( sk1 @ B )
| ( ( sk10 @ A )
!= ( A @ B ) )
| ( ( sk10 @ A )
= ( A @ ( sk11 @ B @ A ) ) ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(37,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( ( A @ ( sk11 @ B @ A ) )
= ( sk10 @ A ) )
| ( sk8 @ A )
| ~ ( sk1 @ B ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(38,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( ( A @ ( sk11 @ B @ A ) )
= ( sk10 @ A ) )
| ( sk8 @ A )
| ~ ( sk1 @ B ) ),
inference(simp,[status(thm)],[37]) ).
thf(389,plain,
! [A: a > a] :
( ~ $true
| ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) )
!= ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[278,113]) ).
thf(390,plain,
! [A: a > a] :
( ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) )
!= ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ),
inference(simp,[status(thm)],[389]) ).
thf(391,plain,
~ ( sk8
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[390:[bind(A,$thf( ^ [B: a] : ( sk7 @ ( sk10 @ ^ [C: a] : ( sk10 @ ^ [D: a] : ( sk6 @ ( sk4 @ D ) ) ) ) ) ))]]) ).
thf(380,plain,
! [A: a] :
( ~ $true
| ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[278,36]) ).
thf(381,plain,
! [A: a] :
( ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] :
( sk10
@ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[380]) ).
thf(382,plain,
( sk3
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] :
( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[381:[bind(A,$thf( sk7 @ ( sk10 @ ^ [B: a] : ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ))]]) ).
thf(46,plain,
! [B: a > a,A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( sk1 @ ( sk9 @ B ) )
| ~ $true
| ( ( sk8 @ A )
!= ( sk8 @ B ) ) ),
inference(paramod_ordered,[status(thm)],[26,22]) ).
thf(47,plain,
! [B: a > a,A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( sk1 @ ( sk9 @ B ) )
| ( ( sk8 @ A )
!= ( sk8 @ B ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(48,plain,
! [A: a > a] :
( ( sk3 @ ( sk10 @ A ) )
| ( sk1 @ ( sk9 @ A ) ) ),
inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(287,plain,
! [A: a] :
( ~ $true
| ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[258,36]) ).
thf(288,plain,
! [A: a] :
( ( sk3 @ ( sk6 @ A ) )
| ( ( sk2
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[287]) ).
thf(289,plain,
( sk3
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ))]]) ).
thf(397,plain,
! [A: a] :
( ~ $true
| ( sk2 @ ( sk7 @ A ) )
| ( ( sk3
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[289,21]) ).
thf(398,plain,
! [A: a] :
( ( sk2 @ ( sk7 @ A ) )
| ( ( sk3
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[397]) ).
thf(399,plain,
( sk2
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [A: a] : ( sk6 @ ( sk4 @ A ) ) ) ) ) ) ),
inference(pattern_uni,[status(thm)],[398:[bind(A,$thf( sk6 @ ( sk7 @ ( sk10 @ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ))]]) ).
thf(730,plain,
! [A: a > a] :
( ~ $true
| ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
| ( ( sk2
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) )
!= ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[399,113]) ).
thf(731,plain,
! [A: a > a] :
( ~ ( sk8
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) )
| ( ( sk2
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) )
!= ( sk2
@ ( A
@ ( sk9
@ ^ [B: a] : ( sk6 @ ( A @ B ) ) ) ) ) ) ),
inference(simp,[status(thm)],[730]) ).
thf(733,plain,
~ ( sk8
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ) ) ),
inference(pre_uni,[status(thm)],[731:[bind(A,$thf( ^ [B: a] : ( sk7 @ ( sk6 @ ( sk7 @ ( sk10 @ ^ [C: a] : ( sk6 @ ( sk4 @ C ) ) ) ) ) ) ))]]) ).
thf(951,plain,
~ ( sk8
@ ^ [A: a] :
( sk6
@ ( sk7
@ ( sk10
@ ^ [B: a] : ( sk6 @ ( sk4 @ B ) ) ) ) ) ),
inference(rewrite,[status(thm)],[733,269]) ).
thf(18,plain,
! [B: a,A: a > a] :
( ( sk8 @ A )
| ~ ( sk1 @ B )
| ( ( sk10 @ A )
!= ( A @ B ) )
| ( ( sk11 @ B @ A )
!= B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(30,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( ( sk11 @ B @ A )
!= B )
| ( sk8 @ A )
| ~ ( sk1 @ B ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(31,plain,
! [B: a,A: a > a] :
( ( ( sk10 @ A )
!= ( A @ B ) )
| ( ( sk11 @ B @ A )
!= B )
| ( sk8 @ A )
| ~ ( sk1 @ B ) ),
inference(simp,[status(thm)],[30]) ).
thf(1784,plain,
$false,
inference(e,[status(thm)],[570,253,489,997,773,494,355,497,99,272,36,486,347,518,379,269,42,25,20,29,33,28,38,275,21,9,783,22,286,391,382,49,350,113,98,278,3,35,48,263,951,31,26,258,23,358,283]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV106^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.10/0.22 % Computer : n026.cluster.edu
% 0.10/0.22 % Model : x86_64 x86_64
% 0.10/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.22 % Memory : 8046.5625MB
% 0.10/0.22 % OS : Linux 6.8.0-71-generic
% 0.10/0.22 % CPULimit : 300
% 0.10/0.22 % WCLimit : 300
% 0.10/0.22 % DateTime : Tue Sep 29 15:13:27 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.04/0.80 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.01 % [INFO] Parsing done (204ms).
% 1.24/1.02 % [INFO] Running in sequential loop mode.
% 2.30/1.52 % [INFO] eprover registered as external prover.
% 2.30/1.53 % [INFO] Scanning for conjecture ...
% 2.57/1.64 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.57/1.69 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.57/1.69 % [INFO] Problem is higher-order (TPTP THF).
% 2.77/1.70 % [INFO] Type checking passed.
% 2.77/1.71 % [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 ...
% 30.86/7.60 % External prover 'e' found a proof!
% 30.86/7.61 % [INFO] Killing All external provers ...
% 30.86/7.61 % Time passed: 7250ms (effective reasoning time: 6576ms)
% 30.86/7.61 % 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)>
% 30.86/7.61 % Axioms used in derivation (0):
% 30.86/7.61 % No. of inferences in proof: 146
% 30.86/7.61 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 7250 ms resp. 6576 ms w/o parsing
% 28.08/7.88 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 28.08/7.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------