%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SET752^4 : TPTP v9.3.1. Released v3.6.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n010.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 08:23:07 AM UTC 2026
% Result : Theorem 9.06s 2.31s
% Output : Refutation 9.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 9
% Syntax : Number of formulae : 107 ( 15 unt; 0 typ; 8 def)
% Number of atoms : 500 ( 219 equ; 0 cnn)
% Maximal formula atoms : 28 ( 4 avg)
% Number of connectives : 1070 ( 250 ~; 305 |; 41 &; 474 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-3 aty)
% Number of variables : 123 ( 18 ^; 71 !; 28 ?; 123 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(union_decl,type,
union: ( $i > $o ) > ( $i > $o ) > $i > $o ).
thf(fun_image_decl,type,
fun_image: ( $i > $i ) > ( $i > $o ) > $i > $o ).
thf(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: $i > $o ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk7_decl,type,
sk7: $i ).
thf(union_def,definition,
( union
= ( ^ [A: $i > $o,B: $i > $o,C: $i] :
( ( A @ C )
| ( B @ C ) ) ) ) ).
thf(fun_image_def,definition,
( fun_image
= ( ^ [A: $i > $i,B: $i > $o,C: $i] :
? [D: $i] :
( ( B @ D )
& ( C
= ( A @ D ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i > $o] :
~ ! [B: $i > $o,C: $i > $i] :
( ( ^ [D: $i] :
? [E: $i] :
( ( ( A @ E )
| ( B @ E ) )
& ( D
= ( C @ E ) ) ) )
= ( ^ [D: $i] :
( ? [E: $i] :
( ( A @ E )
& ( D
= ( C @ E ) ) )
| ? [E: $i] :
( ( B @ E )
& ( D
= ( C @ E ) ) ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $o] :
~ ! [B: $i > $i] :
( ( ^ [C: $i] :
? [D: $i] :
( ( ( sk1 @ D )
| ( A @ D ) )
& ( C
= ( B @ D ) ) ) )
= ( ^ [C: $i] :
( ? [D: $i] :
( ( sk1 @ D )
& ( C
= ( B @ D ) ) )
| ? [D: $i] :
( ( A @ D )
& ( C
= ( B @ D ) ) ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $i] :
( ( ^ [B: $i] :
? [C: $i] :
( ( ( sk1 @ C )
| ( sk2 @ C ) )
& ( B
= ( A @ C ) ) ) )
!= ( ^ [B: $i] :
( ? [C: $i] :
( ( sk1 @ C )
& ( B
= ( A @ C ) ) )
| ? [C: $i] :
( ( sk2 @ C )
& ( B
= ( A @ C ) ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] :
( ( ( sk1 @ A )
| ( sk2 @ A ) )
& ( sk4
= ( sk3 @ A ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( @+[A: $i] :
( ( sk1 @ A )
& ( sk4
= ( sk3 @ A ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( @+[A: $i] :
( ( sk2 @ A )
& ( sk4
= ( sk3 @ A ) ) ) ) ) ).
thf(1,conjecture,
! [A: $i > $o,B: $i > $o,C: $i > $i] :
( ( fun_image @ C @ ( union @ A @ B ) )
= ( union @ ( fun_image @ C @ A ) @ ( fun_image @ C @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',thm) ).
thf(2,negated_conjecture,
~ ! [A: $i > $o,B: $i > $o,C: $i > $i] :
( ( fun_image @ C @ ( union @ A @ B ) )
= ( union @ ( fun_image @ C @ A ) @ ( fun_image @ C @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: $i > $o,B: $i > $o,C: $i > $i] :
( ( ^ [D: $i] :
? [E: $i] :
( ( ( A @ E )
| ( B @ E ) )
& ( D
= ( C @ E ) ) ) )
= ( ^ [D: $i] :
( ? [E: $i] :
( ( A @ E )
& ( D
= ( C @ E ) ) )
| ? [E: $i] :
( ( B @ E )
& ( D
= ( C @ E ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ^ [A: $i] :
? [B: $i] :
( ( ( sk1 @ B )
| ( sk2 @ B ) )
& ( A
= ( sk3 @ B ) ) ) )
!= ( ^ [A: $i] :
( ? [B: $i] :
( ( sk1 @ B )
& ( A
= ( sk3 @ B ) ) )
| ? [B: $i] :
( ( sk2 @ B )
& ( A
= ( sk3 @ B ) ) ) ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ^ [A: $i] :
? [B: $i] :
( ( ( sk1 @ B )
| ( sk2 @ B ) )
& ( A
= ( sk3 @ B ) ) ) )
!= ( ^ [A: $i] :
( ? [B: $i] :
( ( sk1 @ B )
& ( A
= ( sk3 @ B ) ) )
| ? [B: $i] :
( ( sk2 @ B )
& ( A
= ( sk3 @ B ) ) ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(6,plain,
( ( ? [A: $i] :
( ( ( sk1 @ A )
| ( sk2 @ A ) )
& ( sk4
= ( sk3 @ A ) ) ) )
!= ( ? [A: $i] :
( ( sk1 @ A )
& ( sk4
= ( sk3 @ A ) ) )
| ? [A: $i] :
( ( sk2 @ A )
& ( sk4
= ( sk3 @ A ) ) ) ) ),
inference(func_ext,[status(esa)],[5]) ).
thf(8,plain,
( ? [A: $i] :
( ( ( sk1 @ A )
| ( sk2 @ A ) )
& ( sk4
= ( sk3 @ A ) ) )
| ? [A: $i] :
( ( sk1 @ A )
& ( sk4
= ( sk3 @ A ) ) )
| ? [A: $i] :
( ( sk2 @ A )
& ( sk4
= ( sk3 @ A ) ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(20,plain,
( ( ( sk1 @ sk5 )
| ( sk2 @ sk5 )
| ( sk1 @ sk6 )
| ( sk2 @ sk7 ) )
& ( ( sk1 @ sk5 )
| ( sk2 @ sk5 )
| ( sk1 @ sk6 )
| ( sk4
= ( sk3 @ sk7 ) ) )
& ( ( sk1 @ sk5 )
| ( sk2 @ sk5 )
| ( sk4
= ( sk3 @ sk6 ) )
| ( sk2 @ sk7 ) )
& ( ( sk1 @ sk5 )
| ( sk2 @ sk5 )
| ( sk4
= ( sk3 @ sk6 ) )
| ( sk4
= ( sk3 @ sk7 ) ) )
& ( ( sk4
= ( sk3 @ sk5 ) )
| ( sk1 @ sk6 )
| ( sk2 @ sk7 ) )
& ( ( sk4
= ( sk3 @ sk5 ) )
| ( sk1 @ sk6 )
| ( sk4
= ( sk3 @ sk7 ) ) )
& ( ( sk4
= ( sk3 @ sk5 ) )
| ( sk4
= ( sk3 @ sk6 ) )
| ( sk2 @ sk7 ) )
& ( ( sk4
= ( sk3 @ sk5 ) )
| ( sk4
= ( sk3 @ sk6 ) )
| ( sk4
= ( sk3 @ sk7 ) ) ) ),
inference(cnf,[status(esa)],[8]) ).
thf(23,plain,
( ( sk4
= ( sk3 @ sk5 ) )
| ( sk4
= ( sk3 @ sk6 ) )
| ( sk2 @ sk7 ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(35,plain,
( ( ( sk3 @ sk5 )
= sk4 )
| ( ( sk3 @ sk6 )
= sk4 )
| ( sk2 @ sk7 ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(7,plain,
( ~ ? [A: $i] :
( ( ( sk1 @ A )
| ( sk2 @ A ) )
& ( sk4
= ( sk3 @ A ) ) )
| ~ ( ? [A: $i] :
( ( sk1 @ A )
& ( sk4
= ( sk3 @ A ) ) )
| ? [A: $i] :
( ( sk2 @ A )
& ( sk4
= ( sk3 @ A ) ) ) ) ),
inference(bool_ext,[status(thm)],[6]) ).
thf(9,plain,
! [C: $i,B: $i,A: $i] :
( ( ~ ( sk1 @ A )
| ( sk4
!= ( sk3 @ A ) )
| ~ ( sk1 @ B )
| ( sk4
!= ( sk3 @ B ) ) )
& ( ~ ( sk1 @ A )
| ( sk4
!= ( sk3 @ A ) )
| ~ ( sk2 @ C )
| ( sk4
!= ( sk3 @ C ) ) )
& ( ~ ( sk2 @ A )
| ( sk4
!= ( sk3 @ A ) )
| ~ ( sk1 @ B )
| ( sk4
!= ( sk3 @ B ) ) )
& ( ~ ( sk2 @ A )
| ( sk4
!= ( sk3 @ A ) )
| ~ ( sk2 @ C )
| ( sk4
!= ( sk3 @ C ) ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(10,plain,
! [B: $i,A: $i] :
( ~ ( sk1 @ A )
| ( sk4
!= ( sk3 @ A ) )
| ~ ( sk1 @ B )
| ( sk4
!= ( sk3 @ B ) ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(14,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ A )
!= sk4 )
| ( ( sk3 @ B )
!= sk4 )
| ~ ( sk1 @ A )
| ~ ( sk1 @ B ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ A )
!= sk4 )
| ~ ( sk1 @ A )
| ~ ( sk1 @ B )
| ( ( sk3 @ B )
!= ( sk3 @ A ) )
| ( sk4 != sk4 ) ),
inference(eqfactor_ordered,[status(thm)],[14]) ).
thf(56,plain,
! [A: $i] :
( ( ( sk3 @ A )
!= sk4 )
| ~ ( sk1 @ A )
| ~ ( sk1 @ A ) ),
inference(pattern_uni,[status(thm)],[55:[bind(A,$thf( B ))]]) ).
thf(58,plain,
! [A: $i] :
( ( ( sk3 @ A )
!= sk4 )
| ~ ( sk1 @ A ) ),
inference(simp,[status(thm)],[56]) ).
thf(141,plain,
! [A: $i] :
( ( ( sk3 @ sk5 )
= sk4 )
| ( sk2 @ sk7 )
| ( sk4 != sk4 )
| ~ ( sk1 @ A )
| ( ( sk3 @ sk6 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[35,58]) ).
thf(142,plain,
! [A: $i] :
( ( ( sk3 @ sk5 )
= sk4 )
| ( sk2 @ sk7 )
| ~ ( sk1 @ A )
| ( ( sk3 @ sk6 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(143,plain,
( ( ( sk3 @ sk5 )
= sk4 )
| ( sk2 @ sk7 )
| ~ ( sk1 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[142:[bind(A,$thf( sk6 ))]]) ).
thf(175,plain,
! [A: $i] :
( ( sk2 @ sk7 )
| ~ ( sk1 @ sk6 )
| ( sk4 != sk4 )
| ~ ( sk1 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[143,58]) ).
thf(176,plain,
! [A: $i] :
( ( sk2 @ sk7 )
| ~ ( sk1 @ sk6 )
| ~ ( sk1 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(177,plain,
( ( sk2 @ sk7 )
| ~ ( sk1 @ sk6 )
| ~ ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[176:[bind(A,$thf( sk5 ))]]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ~ ( sk2 @ A )
| ( sk4
!= ( sk3 @ A ) )
| ~ ( sk2 @ B )
| ( sk4
!= ( sk3 @ B ) ) ),
inference(cnfConj,[status(thm)],[9]) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ A )
!= sk4 )
| ( ( sk3 @ B )
!= sk4 )
| ~ ( sk2 @ A )
| ~ ( sk2 @ B ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ A )
!= sk4 )
| ( ( sk3 @ B )
!= sk4 )
| ~ ( sk2 @ A )
| ~ ( sk2 @ B ) ),
inference(simp,[status(thm)],[18]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ A )
!= sk4 )
| ~ ( sk2 @ A )
| ~ ( sk2 @ B )
| ( ( sk3 @ B )
!= ( sk3 @ A ) )
| ( sk4 != sk4 ) ),
inference(eqfactor_ordered,[status(thm)],[19]) ).
thf(258,plain,
! [A: $i] :
( ( ( sk3 @ A )
!= sk4 )
| ~ ( sk2 @ A )
| ~ ( sk2 @ A ) ),
inference(pattern_uni,[status(thm)],[257:[bind(A,$thf( B ))]]) ).
thf(259,plain,
! [A: $i] :
( ( ( sk3 @ A )
!= sk4 )
| ~ ( sk2 @ A ) ),
inference(simp,[status(thm)],[258]) ).
thf(278,plain,
! [A: $i] :
( ~ ( sk1 @ sk6 )
| ~ ( sk1 @ sk5 )
| ( ( sk3 @ A )
!= sk4 )
| ~ $true
| ( ( sk2 @ sk7 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[177,259]) ).
thf(279,plain,
! [A: $i] :
( ~ ( sk1 @ sk6 )
| ~ ( sk1 @ sk5 )
| ( ( sk3 @ A )
!= sk4 )
| ( ( sk2 @ sk7 )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[278]) ).
thf(280,plain,
( ~ ( sk1 @ sk6 )
| ~ ( sk1 @ sk5 )
| ( ( sk3 @ sk7 )
!= sk4 ) ),
inference(pattern_uni,[status(thm)],[279:[bind(A,$thf( sk7 ))]]) ).
thf(27,plain,
( ( sk4
= ( sk3 @ sk5 ) )
| ( sk1 @ sk6 )
| ( sk2 @ sk7 ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(34,plain,
( ( ( sk3 @ sk5 )
= sk4 )
| ( sk1 @ sk6 )
| ( sk2 @ sk7 ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(63,plain,
! [A: $i] :
( ( sk1 @ sk6 )
| ( sk2 @ sk7 )
| ( sk4 != sk4 )
| ~ ( sk1 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,58]) ).
thf(64,plain,
! [A: $i] :
( ( sk1 @ sk6 )
| ( sk2 @ sk7 )
| ~ ( sk1 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(65,plain,
( ( sk1 @ sk6 )
| ( sk2 @ sk7 )
| ~ ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[64:[bind(A,$thf( sk5 ))]]) ).
thf(21,plain,
( ( sk4
= ( sk3 @ sk5 ) )
| ( sk1 @ sk6 )
| ( sk4
= ( sk3 @ sk7 ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(32,plain,
( ( ( sk3 @ sk5 )
= sk4 )
| ( ( sk3 @ sk7 )
= sk4 )
| ( sk1 @ sk6 ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(40,plain,
( ( ( sk3 @ sk5 )
= sk4 )
| ( sk1 @ sk6 )
| ( ( sk3 @ sk7 )
!= ( sk3 @ sk5 ) )
| ( sk4 != sk4 ) ),
inference(eqfactor_ordered,[status(thm)],[32]) ).
thf(42,plain,
( ( ( sk3 @ sk5 )
= sk4 )
| ( sk1 @ sk6 )
| ( sk7 != sk5 ) ),
inference(simp,[status(thm)],[40]) ).
thf(69,plain,
! [A: $i] :
( ( sk1 @ sk6 )
| ( sk7 != sk5 )
| ( sk4 != sk4 )
| ~ ( sk1 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42,58]) ).
thf(70,plain,
! [A: $i] :
( ( sk1 @ sk6 )
| ( sk7 != sk5 )
| ~ ( sk1 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(71,plain,
( ( sk1 @ sk6 )
| ( sk7 != sk5 )
| ~ ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( sk5 ))]]) ).
thf(293,plain,
! [A: $i] :
( ( sk1 @ sk6 )
| ( sk2 @ sk7 )
| ( sk4 != sk4 )
| ~ ( sk2 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[34,259]) ).
thf(294,plain,
! [A: $i] :
( ( sk1 @ sk6 )
| ( sk2 @ sk7 )
| ~ ( sk2 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[293]) ).
thf(295,plain,
( ( sk1 @ sk6 )
| ( sk2 @ sk7 )
| ~ ( sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[294:[bind(A,$thf( sk5 ))]]) ).
thf(26,plain,
( ( sk1 @ sk5 )
| ( sk2 @ sk5 )
| ( sk1 @ sk6 )
| ( sk2 @ sk7 ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(25,plain,
( ( sk1 @ sk5 )
| ( sk2 @ sk5 )
| ( sk4
= ( sk3 @ sk6 ) )
| ( sk4
= ( sk3 @ sk7 ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(30,plain,
( ( ( sk3 @ sk6 )
= sk4 )
| ( ( sk3 @ sk7 )
= sk4 )
| ( sk1 @ sk5 )
| ( sk2 @ sk5 ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(281,plain,
! [A: $i] :
( ( sk2 @ sk7 )
| ~ ( sk1 @ sk6 )
| ( sk4 != sk4 )
| ~ ( sk2 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[143,259]) ).
thf(282,plain,
! [A: $i] :
( ( sk2 @ sk7 )
| ~ ( sk1 @ sk6 )
| ~ ( sk2 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[281]) ).
thf(283,plain,
( ( sk2 @ sk7 )
| ~ ( sk1 @ sk6 )
| ~ ( sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[282:[bind(A,$thf( sk5 ))]]) ).
thf(60,plain,
! [A: $i] :
( ( ( sk3 @ sk5 )
= sk4 )
| ( sk1 @ sk6 )
| ( sk4 != sk4 )
| ~ ( sk1 @ A )
| ( ( sk3 @ sk7 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[32,58]) ).
thf(61,plain,
! [A: $i] :
( ( ( sk3 @ sk5 )
= sk4 )
| ( sk1 @ sk6 )
| ~ ( sk1 @ A )
| ( ( sk3 @ sk7 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[60]) ).
thf(62,plain,
( ( ( sk3 @ sk5 )
= sk4 )
| ( sk1 @ sk6 )
| ~ ( sk1 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[61:[bind(A,$thf( sk7 ))]]) ).
thf(99,plain,
! [A: $i] :
( ( sk1 @ sk6 )
| ~ ( sk1 @ sk7 )
| ( sk4 != sk4 )
| ~ ( sk1 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[62,58]) ).
thf(100,plain,
! [A: $i] :
( ( sk1 @ sk6 )
| ~ ( sk1 @ sk7 )
| ~ ( sk1 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(101,plain,
( ( sk1 @ sk6 )
| ~ ( sk1 @ sk7 )
| ~ ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[100:[bind(A,$thf( sk5 ))]]) ).
thf(86,plain,
! [A: $i] :
( ( sk7 != sk5 )
| ~ ( sk1 @ sk5 )
| ( ( sk3 @ A )
!= sk4 )
| ~ $true
| ( ( sk1 @ sk6 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[71,58]) ).
thf(87,plain,
! [A: $i] :
( ( sk7 != sk5 )
| ~ ( sk1 @ sk5 )
| ( ( sk3 @ A )
!= sk4 )
| ( ( sk1 @ sk6 )
!= ( sk1 @ A ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(88,plain,
( ( sk7 != sk5 )
| ~ ( sk1 @ sk5 )
| ( ( sk3 @ sk6 )
!= sk4 ) ),
inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( sk6 ))]]) ).
thf(318,plain,
! [A: $i] :
( ~ ( sk1 @ sk6 )
| ~ ( sk2 @ sk5 )
| ( ( sk3 @ A )
!= sk4 )
| ~ $true
| ( ( sk2 @ sk7 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[283,259]) ).
thf(319,plain,
! [A: $i] :
( ~ ( sk1 @ sk6 )
| ~ ( sk2 @ sk5 )
| ( ( sk3 @ A )
!= sk4 )
| ( ( sk2 @ sk7 )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[318]) ).
thf(320,plain,
( ~ ( sk1 @ sk6 )
| ~ ( sk2 @ sk5 )
| ( ( sk3 @ sk7 )
!= sk4 ) ),
inference(pattern_uni,[status(thm)],[319:[bind(A,$thf( sk7 ))]]) ).
thf(287,plain,
! [A: $i] :
( ( sk1 @ sk6 )
| ~ ( sk1 @ sk7 )
| ( sk4 != sk4 )
| ~ ( sk2 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[62,259]) ).
thf(288,plain,
! [A: $i] :
( ( sk1 @ sk6 )
| ~ ( sk1 @ sk7 )
| ~ ( sk2 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[287]) ).
thf(289,plain,
( ( sk1 @ sk6 )
| ~ ( sk1 @ sk7 )
| ~ ( sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( sk5 ))]]) ).
thf(24,plain,
( ( sk4
= ( sk3 @ sk5 ) )
| ( sk4
= ( sk3 @ sk6 ) )
| ( sk4
= ( sk3 @ sk7 ) ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(29,plain,
( ( ( sk3 @ sk5 )
= sk4 )
| ( ( sk3 @ sk6 )
= sk4 )
| ( ( sk3 @ sk7 )
= sk4 ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(197,plain,
( ( sk7 != sk5 )
| ~ ( sk1 @ sk5 )
| ( sk2 @ sk7 )
| ~ $true
| ~ ( sk1 @ sk5 )
| ( ( sk1 @ sk6 )
!= ( sk1 @ sk6 ) ) ),
inference(paramod_ordered,[status(thm)],[71,177]) ).
thf(198,plain,
( ( sk7 != sk5 )
| ~ ( sk1 @ sk5 )
| ( sk2 @ sk7 )
| ( ( sk1 @ sk6 )
!= ( sk1 @ sk6 ) ) ),
inference(simp,[status(thm)],[197]) ).
thf(199,plain,
( ( sk7 != sk5 )
| ~ ( sk1 @ sk5 )
| ( sk2 @ sk7 ) ),
inference(pattern_uni,[status(thm)],[198:[]]) ).
thf(296,plain,
! [A: $i] :
( ( sk7 != sk5 )
| ~ ( sk1 @ sk5 )
| ( ( sk3 @ A )
!= sk4 )
| ~ $true
| ( ( sk2 @ sk7 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[199,259]) ).
thf(297,plain,
! [A: $i] :
( ( sk7 != sk5 )
| ~ ( sk1 @ sk5 )
| ( ( sk3 @ A )
!= sk4 )
| ( ( sk2 @ sk7 )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(298,plain,
( ( sk7 != sk5 )
| ~ ( sk1 @ sk5 )
| ( ( sk3 @ sk7 )
!= sk4 ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( sk7 ))]]) ).
thf(159,plain,
( ( ( sk3 @ sk5 )
= sk4 )
| ( sk2 @ sk7 )
| ( ( sk3 @ sk6 )
!= ( sk3 @ sk5 ) )
| ( sk4 != sk4 ) ),
inference(eqfactor_ordered,[status(thm)],[35]) ).
thf(161,plain,
( ( ( sk3 @ sk5 )
= sk4 )
| ( sk2 @ sk7 )
| ( sk6 != sk5 ) ),
inference(simp,[status(thm)],[159]) ).
thf(272,plain,
! [A: $i] :
( ( sk1 @ sk6 )
| ~ ( sk1 @ sk5 )
| ( ( sk3 @ A )
!= sk4 )
| ~ $true
| ( ( sk2 @ sk7 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[65,259]) ).
thf(273,plain,
! [A: $i] :
( ( sk1 @ sk6 )
| ~ ( sk1 @ sk5 )
| ( ( sk3 @ A )
!= sk4 )
| ( ( sk2 @ sk7 )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[272]) ).
thf(274,plain,
( ( sk1 @ sk6 )
| ~ ( sk1 @ sk5 )
| ( ( sk3 @ sk7 )
!= sk4 ) ),
inference(pattern_uni,[status(thm)],[273:[bind(A,$thf( sk7 ))]]) ).
thf(275,plain,
! [A: $i] :
( ( ( sk3 @ sk5 )
= sk4 )
| ( sk2 @ sk7 )
| ( sk4 != sk4 )
| ~ ( sk2 @ A )
| ( ( sk3 @ sk6 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[35,259]) ).
thf(276,plain,
! [A: $i] :
( ( ( sk3 @ sk5 )
= sk4 )
| ( sk2 @ sk7 )
| ~ ( sk2 @ A )
| ( ( sk3 @ sk6 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[275]) ).
thf(277,plain,
( ( ( sk3 @ sk5 )
= sk4 )
| ( sk2 @ sk7 )
| ~ ( sk2 @ sk6 ) ),
inference(pattern_uni,[status(thm)],[276:[bind(A,$thf( sk6 ))]]) ).
thf(782,plain,
! [A: $i] :
( ( sk2 @ sk7 )
| ~ ( sk2 @ sk6 )
| ( sk4 != sk4 )
| ~ ( sk2 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[277,259]) ).
thf(783,plain,
! [A: $i] :
( ( sk2 @ sk7 )
| ~ ( sk2 @ sk6 )
| ~ ( sk2 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[782]) ).
thf(784,plain,
( ( sk2 @ sk7 )
| ~ ( sk2 @ sk6 )
| ~ ( sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[783:[bind(A,$thf( sk5 ))]]) ).
thf(269,plain,
! [A: $i] :
( ( sk1 @ sk6 )
| ( sk7 != sk5 )
| ( sk4 != sk4 )
| ~ ( sk2 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[42,259]) ).
thf(270,plain,
! [A: $i] :
( ( sk1 @ sk6 )
| ( sk7 != sk5 )
| ~ ( sk2 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[269]) ).
thf(271,plain,
( ( sk1 @ sk6 )
| ( sk7 != sk5 )
| ~ ( sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[270:[bind(A,$thf( sk5 ))]]) ).
thf(28,plain,
( ( sk1 @ sk5 )
| ( sk2 @ sk5 )
| ( sk4
= ( sk3 @ sk6 ) )
| ( sk2 @ sk7 ) ),
inference(cnfConj,[status(thm)],[20]) ).
thf(31,plain,
( ( ( sk3 @ sk6 )
= sk4 )
| ( sk1 @ sk5 )
| ( sk2 @ sk5 )
| ( sk2 @ sk7 ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(547,plain,
! [A: $i] :
( ( sk2 @ sk7 )
| ( sk6 != sk5 )
| ( sk4 != sk4 )
| ~ ( sk1 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[161,58]) ).
thf(548,plain,
! [A: $i] :
( ( sk2 @ sk7 )
| ( sk6 != sk5 )
| ~ ( sk1 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[547]) ).
thf(549,plain,
( ( sk2 @ sk7 )
| ( sk6 != sk5 )
| ~ ( sk1 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[548:[bind(A,$thf( sk5 ))]]) ).
thf(534,plain,
! [A: $i] :
( ( sk2 @ sk7 )
| ( sk6 != sk5 )
| ( sk4 != sk4 )
| ~ ( sk2 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[161,259]) ).
thf(535,plain,
! [A: $i] :
( ( sk2 @ sk7 )
| ( sk6 != sk5 )
| ~ ( sk2 @ A )
| ( ( sk3 @ sk5 )
!= ( sk3 @ A ) ) ),
inference(simp,[status(thm)],[534]) ).
thf(536,plain,
( ( sk2 @ sk7 )
| ( sk6 != sk5 )
| ~ ( sk2 @ sk5 ) ),
inference(pattern_uni,[status(thm)],[535:[bind(A,$thf( sk5 ))]]) ).
thf(1351,plain,
$false,
inference(e,[status(thm)],[5,280,6,65,259,71,295,143,26,30,283,101,88,42,320,289,29,298,161,32,34,274,784,271,3,35,199,177,31,58,549,536,62,277]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET752^4 : TPTP v9.3.1. Released v3.6.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.10/0.22 % Computer : n010.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 13:41:18 UTC 2026
% 0.10/0.22 % CPUTime :
% 0.10/0.22 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.67/0.54 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.01/0.67 % [INFO] Parsing done (129ms).
% 1.01/0.68 % [INFO] Running in sequential loop mode.
% 1.56/0.88 % [INFO] eprover registered as external prover.
% 1.56/0.88 % [INFO] Scanning for conjecture ...
% 1.79/0.96 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.79/0.97 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.79/0.97 % [INFO] Problem is higher-order (TPTP THF).
% 1.79/0.98 % [INFO] Type checking passed.
% 1.79/0.98 % [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 ...
% 9.06/2.31 % External prover 'e' found a proof!
% 9.06/2.31 % [INFO] Killing All external provers ...
% 9.06/2.31 % Time passed: 1995ms (effective reasoning time: 1628ms)
% 9.06/2.31 % 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)>
% 9.06/2.31 % Axioms used in derivation (0):
% 9.06/2.31 % No. of inferences in proof: 99
% 9.06/2.31 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 1995 ms resp. 1628 ms w/o parsing
% 9.06/2.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.06/2.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------