%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU897^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n004.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 08:29:33 AM UTC 2026
% Result : Theorem 14.15s 4.61s
% Output : Refutation 14.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 6
% Syntax : Number of formulae : 112 ( 14 unt; 0 typ; 5 def)
% Number of atoms : 517 ( 96 equ; 0 cnn)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 1217 ( 230 ~; 293 |; 24 &; 655 @)
% ( 0 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 58 ( 58 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 7 usr; 6 con; 0-3 aty)
% Number of variables : 182 ( 3 ^; 158 !; 16 ?; 182 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(cS_decl,type,
cS: a > $o ).
thf(cR_decl,type,
cR: a > $o ).
thf(sk1_decl,type,
sk1: a ).
thf(sk2_decl,type,
sk2: a > a ).
thf(sk3_decl,type,
sk3: a ).
thf(sk4_decl,type,
sk4: a ).
thf(sk5_decl,type,
sk5: a > ( a > a ) > a > a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a] :
~ ( ( cR @ A )
=> ( cS @ A ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a > a] :
~ ! [B: a] :
( ? [C: a] :
( ( cR @ C )
& ( B
= ( A @ C ) ) )
=> ? [C: a] :
( ( cS @ C )
& ( B
= ( A @ C ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a] :
~ ( ? [B: a] :
( ( cR @ B )
& ( A
= ( sk2 @ B ) ) )
=> ? [B: a] :
( ( cS @ B )
& ( A
= ( sk2 @ B ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: a] :
( ( cR @ A )
& ( sk3
= ( sk2 @ A ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: a,B: a > a,C: a] :
@+[D: a] :
( ( cS @ D )
& ( A
= ( B @ D ) ) ) ) ) ).
thf(1,conjecture,
( ( ! [A: a] :
( ( cR @ A )
=> ( cS @ A ) ) )
= ( ! [A: a > a,B: a] :
( ? [C: a] :
( ( cR @ C )
& ( B
= ( A @ C ) ) )
=> ? [C: a] :
( ( cS @ C )
& ( B
= ( A @ C ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM30_pme) ).
thf(2,negated_conjecture,
( ( ! [A: a] :
( ( cR @ A )
=> ( cS @ A ) ) )
!= ( ! [A: a > a,B: a] :
( ? [C: a] :
( ( cR @ C )
& ( B
= ( A @ C ) ) )
=> ? [C: a] :
( ( cS @ C )
& ( B
= ( A @ C ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
( ( ! [A: a] :
( ( cR @ A )
=> ( cS @ A ) ) )
!= ( ! [A: a > a,B: a] :
( ? [C: a] :
( ( cR @ C )
& ( B
= ( A @ C ) ) )
=> ? [C: a] :
( ( cS @ C )
& ( B
= ( A @ C ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [A: a] :
( ( cR @ A )
=> ( cS @ A ) ) )
!= ( ! [A: a > a,B: a] :
( ? [C: a] :
( ( cR @ C )
& ( B
= ( A @ C ) ) )
=> ? [C: a] :
( ( cS @ C )
& ( B
= ( A @ C ) ) ) ) ) ),
inference(lifteq,[status(thm)],[3]) ).
thf(6,plain,
( ! [A: a] :
( ( cR @ A )
=> ( cS @ A ) )
| ! [A: a > a,B: a] :
( ? [C: a] :
( ( cR @ C )
& ( B
= ( A @ C ) ) )
=> ? [C: a] :
( ( cS @ C )
& ( B
= ( A @ C ) ) ) ) ),
inference(bool_ext,[status(thm)],[4]) ).
thf(18,plain,
! [D: a,C: a,B: a > a,A: a] :
( ( ~ ( cR @ A )
| ( cS @ A )
| ~ ( cR @ D )
| ( C
!= ( B @ D ) )
| ( cS @ ( sk5 @ C @ B @ A ) ) )
& ( ~ ( cR @ A )
| ( cS @ A )
| ~ ( cR @ D )
| ( C
!= ( B @ D ) )
| ( C
= ( B @ ( sk5 @ C @ B @ A ) ) ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(20,plain,
! [D: a,C: a,B: a > a,A: a] :
( ~ ( cR @ A )
| ( cS @ A )
| ~ ( cR @ D )
| ( C
!= ( B @ D ) )
| ( C
= ( B @ ( sk5 @ C @ B @ A ) ) ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(23,plain,
! [D: a,C: a,B: a > a,A: a] :
( ( C
!= ( B @ D ) )
| ( ( B @ ( sk5 @ C @ B @ A ) )
= C )
| ~ ( cR @ A )
| ( cS @ A )
| ~ ( cR @ D ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(24,plain,
! [C: a,B: a > a,A: a] :
( ( ( B @ ( sk5 @ ( B @ C ) @ B @ A ) )
= ( B @ C ) )
| ~ ( cR @ A )
| ( cS @ A )
| ~ ( cR @ C ) ),
inference(simp,[status(thm)],[23]) ).
thf(5,plain,
( ~ ! [A: a] :
( ( cR @ A )
=> ( cS @ A ) )
| ~ ! [A: a > a,B: a] :
( ? [C: a] :
( ( cR @ C )
& ( B
= ( A @ C ) ) )
=> ? [C: a] :
( ( cS @ C )
& ( B
= ( A @ C ) ) ) ) ),
inference(bool_ext,[status(thm)],[4]) ).
thf(7,plain,
! [A: a] :
( ( ( cR @ sk1 )
| ( cR @ sk4 ) )
& ( ( cR @ sk1 )
| ( sk3
= ( sk2 @ sk4 ) ) )
& ( ( cR @ sk1 )
| ~ ( cS @ A )
| ( sk3
!= ( sk2 @ A ) ) )
& ( ~ ( cS @ sk1 )
| ( cR @ sk4 ) )
& ( ~ ( cS @ sk1 )
| ( sk3
= ( sk2 @ sk4 ) ) )
& ( ~ ( cS @ sk1 )
| ~ ( cS @ A )
| ( sk3
!= ( sk2 @ A ) ) ) ),
inference(cnf,[status(esa)],[5]) ).
thf(10,plain,
( ( cR @ sk1 )
| ( cR @ sk4 ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(19,plain,
! [D: a,C: a,B: a > a,A: a] :
( ~ ( cR @ A )
| ( cS @ A )
| ~ ( cR @ D )
| ( C
!= ( B @ D ) )
| ( cS @ ( sk5 @ C @ B @ A ) ) ),
inference(cnfConj,[status(thm)],[18]) ).
thf(21,plain,
! [D: a,C: a,B: a > a,A: a] :
( ( C
!= ( B @ D ) )
| ~ ( cR @ A )
| ( cS @ A )
| ~ ( cR @ D )
| ( cS @ ( sk5 @ C @ B @ A ) ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(22,plain,
! [C: a,B: a > a,A: a] :
( ~ ( cR @ A )
| ( cS @ A )
| ~ ( cR @ C )
| ( cS @ ( sk5 @ ( B @ C ) @ B @ A ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(46,plain,
! [C: a,B: a > a,A: a] :
( ( cR @ sk1 )
| ~ $true
| ( cS @ A )
| ~ ( cR @ C )
| ( cS @ ( sk5 @ ( B @ C ) @ B @ A ) )
| ( ( cR @ sk4 )
!= ( cR @ A ) ) ),
inference(paramod_ordered,[status(thm)],[10,22]) ).
thf(47,plain,
! [C: a,B: a > a,A: a] :
( ( cR @ sk1 )
| ( cS @ A )
| ~ ( cR @ C )
| ( cS @ ( sk5 @ ( B @ C ) @ B @ A ) )
| ( ( cR @ sk4 )
!= ( cR @ A ) ) ),
inference(simp,[status(thm)],[46]) ).
thf(48,plain,
! [B: a,A: a > a] :
( ( cR @ sk1 )
| ( cS @ sk4 )
| ~ ( cR @ B )
| ( cS @ ( sk5 @ ( A @ B ) @ A @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( sk4 ))]]) ).
thf(103,plain,
! [B: a,A: a > a] :
( ( cR @ sk1 )
| ( cS @ sk4 )
| ~ ( cR @ B )
| ( cS @ ( sk5 @ ( A @ B ) @ A @ sk4 ) ) ),
inference(simp,[status(thm)],[48]) ).
thf(199,plain,
! [B: a,A: a > a] :
( ( cR @ sk1 )
| ( cR @ sk1 )
| ( cS @ sk4 )
| ~ $true
| ( cS @ ( sk5 @ ( A @ B ) @ A @ sk4 ) )
| ( ( cR @ sk4 )
!= ( cR @ B ) ) ),
inference(paramod_ordered,[status(thm)],[10,103]) ).
thf(200,plain,
! [B: a,A: a > a] :
( ( cR @ sk1 )
| ( cS @ sk4 )
| ( cS @ ( sk5 @ ( A @ B ) @ A @ sk4 ) )
| ( ( cR @ sk4 )
!= ( cR @ B ) ) ),
inference(simp,[status(thm)],[199]) ).
thf(201,plain,
! [A: a > a] :
( ( cR @ sk1 )
| ( cS @ sk4 )
| ( cS @ ( sk5 @ ( A @ sk4 ) @ A @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( A )),bind(B,$thf( sk4 ))]]) ).
thf(471,plain,
! [D: a > a,C: a,B: a > a,A: a] :
( ~ ( cR @ A )
| ( cS @ A )
| ~ ( cR @ C )
| ( cR @ sk1 )
| ( cS @ sk4 )
| ( cS @ ( B @ C ) )
| ( ( B @ ( sk5 @ ( B @ C ) @ B @ A ) )
!= ( sk5 @ ( D @ sk4 ) @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[24,201]) ).
thf(510,plain,
( ~ ( cR @ sk4 )
| ( cS @ sk4 )
| ~ ( cR @ sk4 )
| ( cR @ sk1 )
| ( cS @ sk4 )
| ( cS @ sk4 ) ),
inference(pre_uni,[status(thm)],[471:[bind(A,$thf( sk4 )),bind(B,$thf( ^ [E: a] : E )),bind(C,$thf( sk4 )),bind(D,$thf( ^ [E: a] : E ))]]) ).
thf(527,plain,
( ~ ( cR @ sk4 )
| ( cS @ sk4 )
| ( cR @ sk1 ) ),
inference(simp,[status(thm)],[510]) ).
thf(528,plain,
( ( cR @ sk1 )
| ~ $true
| ( cS @ sk4 )
| ( cR @ sk1 )
| ( ( cR @ sk4 )
!= ( cR @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[10,527]) ).
thf(529,plain,
( ( cR @ sk1 )
| ( cS @ sk4 )
| ( ( cR @ sk4 )
!= ( cR @ sk4 ) ) ),
inference(simp,[status(thm)],[528]) ).
thf(530,plain,
( ( cR @ sk1 )
| ( cS @ sk4 ) ),
inference(pattern_uni,[status(thm)],[529:[]]) ).
thf(9,plain,
( ( cR @ sk1 )
| ( sk3
= ( sk2 @ sk4 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(14,plain,
( ( ( sk2 @ sk4 )
= sk3 )
| ( cR @ sk1 ) ),
inference(lifteq,[status(thm)],[9]) ).
thf(13,plain,
! [A: a] :
( ( cR @ sk1 )
| ~ ( cS @ A )
| ( sk3
!= ( sk2 @ A ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(15,plain,
! [A: a] :
( ( ( sk2 @ A )
!= sk3 )
| ( cR @ sk1 )
| ~ ( cS @ A ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(31,plain,
! [A: a] :
( ( cR @ sk1 )
| ( sk3 != sk3 )
| ( cR @ sk1 )
| ~ ( cS @ A )
| ( ( sk2 @ sk4 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[14,15]) ).
thf(32,plain,
! [A: a] :
( ( cR @ sk1 )
| ~ ( cS @ A )
| ( ( sk2 @ sk4 )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[31]) ).
thf(33,plain,
( ( cR @ sk1 )
| ~ ( cS @ sk4 ) ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( sk4 ))]]) ).
thf(58,plain,
! [C: a,B: a > a,A: a] :
( ~ ( cS @ sk4 )
| ~ ( cR @ A )
| ( cS @ A )
| ~ $true
| ( cS @ ( sk5 @ ( B @ C ) @ B @ A ) )
| ( ( cR @ sk1 )
!= ( cR @ C ) ) ),
inference(paramod_ordered,[status(thm)],[33,22]) ).
thf(59,plain,
! [C: a,B: a > a,A: a] :
( ~ ( cS @ sk4 )
| ~ ( cR @ A )
| ( cS @ A )
| ( cS @ ( sk5 @ ( B @ C ) @ B @ A ) )
| ( ( cR @ sk1 )
!= ( cR @ C ) ) ),
inference(simp,[status(thm)],[58]) ).
thf(60,plain,
! [B: a > a,A: a] :
( ~ ( cS @ sk4 )
| ~ ( cR @ A )
| ( cS @ A )
| ( cS @ ( sk5 @ ( B @ sk1 ) @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[59:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(699,plain,
! [B: a > a,A: a] :
( ~ ( cS @ sk4 )
| ~ ( cS @ sk4 )
| ~ $true
| ( cS @ A )
| ( cS @ ( sk5 @ ( B @ sk1 ) @ B @ A ) )
| ( ( cR @ sk1 )
!= ( cR @ A ) ) ),
inference(paramod_ordered,[status(thm)],[33,60]) ).
thf(700,plain,
! [B: a > a,A: a] :
( ~ ( cS @ sk4 )
| ( cS @ A )
| ( cS @ ( sk5 @ ( B @ sk1 ) @ B @ A ) )
| ( ( cR @ sk1 )
!= ( cR @ A ) ) ),
inference(simp,[status(thm)],[699]) ).
thf(701,plain,
! [A: a > a] :
( ~ ( cS @ sk4 )
| ( cS @ sk1 )
| ( cS @ ( sk5 @ ( A @ sk1 ) @ A @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[700:[bind(A,$thf( sk1 ))]]) ).
thf(774,plain,
! [A: a > a] :
( ~ ( cS @ sk4 )
| ( cS @ sk1 )
| ( cS @ ( sk5 @ ( A @ sk1 ) @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[701]) ).
thf(809,plain,
! [D: a > a,C: a,B: a > a,A: a] :
( ~ ( cR @ A )
| ( cS @ A )
| ~ ( cR @ C )
| ~ ( cS @ sk4 )
| ( cS @ sk1 )
| ( cS @ ( B @ C ) )
| ( ( B @ ( sk5 @ ( B @ C ) @ B @ A ) )
!= ( sk5 @ ( D @ sk1 ) @ D @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[24,774]) ).
thf(817,plain,
( ~ ( cR @ sk1 )
| ( cS @ sk1 )
| ~ ( cR @ sk1 )
| ~ ( cS @ sk4 )
| ( cS @ sk1 )
| ( cS @ sk1 ) ),
inference(pre_uni,[status(thm)],[809:[bind(A,$thf( sk1 )),bind(B,$thf( ^ [E: a] : E )),bind(C,$thf( sk1 )),bind(D,$thf( ^ [E: a] : E ))]]) ).
thf(846,plain,
( ~ ( cR @ sk1 )
| ( cS @ sk1 )
| ~ ( cS @ sk4 ) ),
inference(simp,[status(thm)],[817]) ).
thf(853,plain,
( ~ ( cS @ sk4 )
| ~ $true
| ( cS @ sk1 )
| ~ ( cS @ sk4 )
| ( ( cR @ sk1 )
!= ( cR @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[33,846]) ).
thf(854,plain,
( ~ ( cS @ sk4 )
| ( cS @ sk1 )
| ( ( cR @ sk1 )
!= ( cR @ sk1 ) ) ),
inference(simp,[status(thm)],[853]) ).
thf(855,plain,
( ~ ( cS @ sk4 )
| ( cS @ sk1 ) ),
inference(pattern_uni,[status(thm)],[854:[]]) ).
thf(8,plain,
( ~ ( cS @ sk1 )
| ( cR @ sk4 ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(73,plain,
! [C: a,B: a > a,A: a] :
( ~ ( cS @ sk1 )
| ~ ( cR @ A )
| ( cS @ A )
| ~ $true
| ( cS @ ( sk5 @ ( B @ C ) @ B @ A ) )
| ( ( cR @ sk4 )
!= ( cR @ C ) ) ),
inference(paramod_ordered,[status(thm)],[8,22]) ).
thf(74,plain,
! [C: a,B: a > a,A: a] :
( ~ ( cS @ sk1 )
| ~ ( cR @ A )
| ( cS @ A )
| ( cS @ ( sk5 @ ( B @ C ) @ B @ A ) )
| ( ( cR @ sk4 )
!= ( cR @ C ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(75,plain,
! [B: a > a,A: a] :
( ~ ( cS @ sk1 )
| ~ ( cR @ A )
| ( cS @ A )
| ( cS @ ( sk5 @ ( B @ sk4 ) @ B @ A ) ) ),
inference(pattern_uni,[status(thm)],[74:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk4 ))]]) ).
thf(1052,plain,
! [B: a > a,A: a] :
( ~ ( cS @ sk1 )
| ~ ( cS @ sk1 )
| ~ $true
| ( cS @ A )
| ( cS @ ( sk5 @ ( B @ sk4 ) @ B @ A ) )
| ( ( cR @ sk4 )
!= ( cR @ A ) ) ),
inference(paramod_ordered,[status(thm)],[8,75]) ).
thf(1053,plain,
! [B: a > a,A: a] :
( ~ ( cS @ sk1 )
| ( cS @ A )
| ( cS @ ( sk5 @ ( B @ sk4 ) @ B @ A ) )
| ( ( cR @ sk4 )
!= ( cR @ A ) ) ),
inference(simp,[status(thm)],[1052]) ).
thf(1054,plain,
! [A: a > a] :
( ~ ( cS @ sk1 )
| ( cS @ sk4 )
| ( cS @ ( sk5 @ ( A @ sk4 ) @ A @ sk4 ) ) ),
inference(pattern_uni,[status(thm)],[1053:[bind(A,$thf( sk4 ))]]) ).
thf(1097,plain,
! [A: a > a] :
( ~ ( cS @ sk1 )
| ( cS @ sk4 )
| ( cS @ ( sk5 @ ( A @ sk4 ) @ A @ sk4 ) ) ),
inference(simp,[status(thm)],[1054]) ).
thf(1134,plain,
! [D: a > a,C: a,B: a > a,A: a] :
( ~ ( cR @ A )
| ( cS @ A )
| ~ ( cR @ C )
| ~ ( cS @ sk1 )
| ( cS @ sk4 )
| ( cS @ ( B @ C ) )
| ( ( B @ ( sk5 @ ( B @ C ) @ B @ A ) )
!= ( sk5 @ ( D @ sk4 ) @ D @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[24,1097]) ).
thf(1168,plain,
( ~ ( cR @ sk4 )
| ( cS @ sk4 )
| ~ ( cR @ sk4 )
| ~ ( cS @ sk1 )
| ( cS @ sk4 )
| ( cS @ sk4 ) ),
inference(pre_uni,[status(thm)],[1134:[bind(A,$thf( sk4 )),bind(B,$thf( ^ [E: a] : E )),bind(C,$thf( sk4 )),bind(D,$thf( ^ [E: a] : E ))]]) ).
thf(1190,plain,
( ~ ( cR @ sk4 )
| ( cS @ sk4 )
| ~ ( cS @ sk1 ) ),
inference(simp,[status(thm)],[1168]) ).
thf(1209,plain,
( ~ ( cS @ sk1 )
| ~ $true
| ( cS @ sk4 )
| ~ ( cS @ sk1 )
| ( ( cR @ sk4 )
!= ( cR @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[8,1190]) ).
thf(1210,plain,
( ~ ( cS @ sk1 )
| ( cS @ sk4 )
| ( ( cR @ sk4 )
!= ( cR @ sk4 ) ) ),
inference(simp,[status(thm)],[1209]) ).
thf(1211,plain,
( ~ ( cS @ sk1 )
| ( cS @ sk4 ) ),
inference(pattern_uni,[status(thm)],[1210:[]]) ).
thf(11,plain,
( ~ ( cS @ sk1 )
| ( sk3
= ( sk2 @ sk4 ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(17,plain,
( ( ( sk2 @ sk4 )
= sk3 )
| ~ ( cS @ sk1 ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(12,plain,
! [A: a] :
( ~ ( cS @ sk1 )
| ~ ( cS @ A )
| ( sk3
!= ( sk2 @ A ) ) ),
inference(cnfConj,[status(thm)],[7]) ).
thf(16,plain,
! [A: a] :
( ( ( sk2 @ A )
!= sk3 )
| ~ ( cS @ sk1 )
| ~ ( cS @ A ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(40,plain,
! [A: a] :
( ~ ( cS @ sk1 )
| ( sk3 != sk3 )
| ~ ( cS @ sk1 )
| ~ ( cS @ A )
| ( ( sk2 @ sk4 )
!= ( sk2 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[17,16]) ).
thf(41,plain,
! [A: a] :
( ~ ( cS @ sk1 )
| ~ ( cS @ A )
| ( ( sk2 @ sk4 )
!= ( sk2 @ A ) ) ),
inference(simp,[status(thm)],[40]) ).
thf(42,plain,
( ~ ( cS @ sk1 )
| ~ ( cS @ sk4 ) ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( sk4 ))]]) ).
thf(112,plain,
( ~ ( cS @ sk1 )
| ( ( cS @ sk4 )
!= ( cS @ sk1 ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[42]) ).
thf(115,plain,
( ~ ( cS @ sk1 )
| ( ( cS @ sk4 )
!= ( cS @ sk1 ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(1500,plain,
( ~ ( cS @ sk1 )
| ~ ( cS @ sk1 )
| ~ ( cS @ sk1 )
| ( ( cS @ sk4 )
!= ( cS @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[1211,115]) ).
thf(1501,plain,
( ~ ( cS @ sk1 )
| ( ( cS @ sk4 )
!= ( cS @ sk4 ) ) ),
inference(simp,[status(thm)],[1500]) ).
thf(1502,plain,
~ ( cS @ sk1 ),
inference(pattern_uni,[status(thm)],[1501:[]]) ).
thf(1552,plain,
( ~ ( cS @ sk4 )
| $false ),
inference(rewrite,[status(thm)],[855,1502]) ).
thf(1553,plain,
~ ( cS @ sk4 ),
inference(simp,[status(thm)],[1552]) ).
thf(1624,plain,
( ( cR @ sk1 )
| $false ),
inference(rewrite,[status(thm)],[530,1553]) ).
thf(1625,plain,
cR @ sk1,
inference(simp,[status(thm)],[1624]) ).
thf(1645,plain,
! [C: a,B: a > a,A: a] :
( ~ $true
| ( cS @ A )
| ~ ( cR @ C )
| ( cS @ ( sk5 @ ( B @ C ) @ B @ A ) )
| ( ( cR @ sk1 )
!= ( cR @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1625,22]) ).
thf(1646,plain,
! [C: a,B: a > a,A: a] :
( ( cS @ A )
| ~ ( cR @ C )
| ( cS @ ( sk5 @ ( B @ C ) @ B @ A ) )
| ( ( cR @ sk1 )
!= ( cR @ A ) ) ),
inference(simp,[status(thm)],[1645]) ).
thf(1647,plain,
! [B: a,A: a > a] :
( ( cS @ sk1 )
| ~ ( cR @ B )
| ( cS @ ( sk5 @ ( A @ B ) @ A @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[1646:[bind(A,$thf( sk1 ))]]) ).
thf(1666,plain,
! [B: a,A: a > a] :
( ( cS @ sk1 )
| ~ ( cR @ B )
| ( cS @ ( sk5 @ ( A @ B ) @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[1647]) ).
thf(1920,plain,
! [B: a,A: a > a] :
( $false
| ~ ( cR @ B )
| ( cS @ ( sk5 @ ( A @ B ) @ A @ sk1 ) ) ),
inference(rewrite,[status(thm)],[1666,1502]) ).
thf(1921,plain,
! [B: a,A: a > a] :
( ~ ( cR @ B )
| ( cS @ ( sk5 @ ( A @ B ) @ A @ sk1 ) ) ),
inference(simp,[status(thm)],[1920]) ).
thf(1929,plain,
! [B: a,A: a > a] :
( ~ ( cR @ B )
| ~ $true
| ( ( cS @ ( sk5 @ ( A @ B ) @ A @ sk1 ) )
!= ( cS @ sk4 ) ) ),
inference(paramod_ordered,[status(thm)],[1921,1553]) ).
thf(1930,plain,
! [B: a,A: a > a] :
( ~ ( cR @ B )
| ( ( cS @ ( sk5 @ ( A @ B ) @ A @ sk1 ) )
!= ( cS @ sk4 ) ) ),
inference(simp,[status(thm)],[1929]) ).
thf(1944,plain,
! [B: a,A: a > a] :
( ~ ( cR @ B )
| ( ( sk5 @ ( A @ B ) @ A @ sk1 )
!= sk4 ) ),
inference(simp,[status(thm)],[1930]) ).
thf(1956,plain,
! [E: a,D: a > a,C: a,B: a > a,A: a] :
( ~ ( cR @ A )
| ( cS @ A )
| ~ ( cR @ C )
| ~ ( cR @ E )
| ( ( B @ C )
!= sk4 )
| ( ( B @ ( sk5 @ ( B @ C ) @ B @ A ) )
!= ( sk5 @ ( D @ E ) @ D @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[24,1944]) ).
thf(1958,plain,
! [A: a] :
( ~ ( cR @ sk1 )
| ( cS @ sk1 )
| ~ ( cR @ A )
| ~ ( cR @ A )
| ( A != sk4 ) ),
inference(pre_uni,[status(thm)],[1956:[bind(A,$thf( sk1 )),bind(B,$thf( ^ [F: a] : F )),bind(C,$thf( E )),bind(D,$thf( ^ [F: a] : F ))]]) ).
thf(1960,plain,
( ~ ( cR @ sk4 )
| ~ ( cR @ sk4 )
| ( cS @ sk1 )
| ~ ( cR @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1958:[bind(A,$thf( sk4 ))]]) ).
thf(1964,plain,
( ~ ( cR @ sk4 )
| ( cS @ sk1 )
| ~ ( cR @ sk1 ) ),
inference(simp,[status(thm)],[1960]) ).
thf(68,plain,
! [C: a,B: a > a,A: a] :
( ~ ( cR @ A )
| ( cS @ A )
| ~ ( cR @ C )
| ~ $true
| ( cR @ sk4 )
| ( ( cS @ ( sk5 @ ( B @ C ) @ B @ A ) )
!= ( cS @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[22,8]) ).
thf(69,plain,
! [C: a,B: a > a,A: a] :
( ~ ( cR @ A )
| ( cS @ A )
| ~ ( cR @ C )
| ( cR @ sk4 )
| ( ( cS @ ( sk5 @ ( B @ C ) @ B @ A ) )
!= ( cS @ sk1 ) ) ),
inference(simp,[status(thm)],[68]) ).
thf(86,plain,
! [C: a,B: a > a,A: a] :
( ( cS @ A )
| ( cR @ sk4 )
| ~ ( cR @ A )
| ~ ( cR @ C )
| ( ( sk5 @ ( B @ C ) @ B @ A )
!= sk1 ) ),
inference(simp,[status(thm)],[69]) ).
thf(1677,plain,
! [F: a,E: a > a,D: a,C: a,B: a > a,A: a] :
( ~ ( cR @ A )
| ( cS @ A )
| ~ ( cR @ C )
| ( cS @ D )
| ( cR @ sk4 )
| ~ ( cR @ D )
| ~ ( cR @ F )
| ( ( B @ C )
!= sk1 )
| ( ( B @ ( sk5 @ ( B @ C ) @ B @ A ) )
!= ( sk5 @ ( E @ F ) @ E @ D ) ) ),
inference(paramod_ordered,[status(thm)],[24,86]) ).
thf(1686,plain,
! [B: a,A: a] :
( ~ ( cR @ A )
| ( cS @ A )
| ~ ( cR @ B )
| ( cS @ A )
| ( cR @ sk4 )
| ~ ( cR @ A )
| ~ ( cR @ B )
| ( B != sk1 ) ),
inference(pre_uni,[status(thm)],[1677:[bind(A,$thf( D )),bind(B,$thf( ^ [G: a] : G )),bind(C,$thf( F )),bind(D,$thf( D )),bind(E,$thf( ^ [G: a] : G ))]]) ).
thf(1687,plain,
! [A: a] :
( ~ ( cR @ sk1 )
| ~ ( cR @ A )
| ( cR @ sk4 )
| ( cS @ A )
| ~ ( cR @ sk1 )
| ( cS @ A )
| ~ ( cR @ A ) ),
inference(pattern_uni,[status(thm)],[1686:[bind(A,$thf( (@) )),bind(B,$thf( sk1 ))]]) ).
thf(1691,plain,
! [A: a] :
( ~ ( cR @ sk1 )
| ~ ( cR @ A )
| ( cR @ sk4 )
| ( cS @ A ) ),
inference(simp,[status(thm)],[1687]) ).
thf(1733,plain,
! [A: a] :
( ~ $true
| ~ ( cR @ A )
| ( cR @ sk4 )
| ( cS @ A ) ),
inference(rewrite,[status(thm)],[1691,1625]) ).
thf(1734,plain,
! [A: a] :
( ~ ( cR @ A )
| ( cR @ sk4 )
| ( cS @ A ) ),
inference(simp,[status(thm)],[1733]) ).
thf(1754,plain,
! [A: a] :
( ~ $true
| ( cR @ sk4 )
| ( cS @ A )
| ( ( cR @ sk1 )
!= ( cR @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1625,1734]) ).
thf(1755,plain,
! [A: a] :
( ( cR @ sk4 )
| ( cS @ A )
| ( ( cR @ sk1 )
!= ( cR @ A ) ) ),
inference(simp,[status(thm)],[1754]) ).
thf(1756,plain,
( ( cR @ sk4 )
| ( cS @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1755:[bind(A,$thf( sk1 ))]]) ).
thf(1770,plain,
( ( cR @ sk4 )
| $false ),
inference(rewrite,[status(thm)],[1756,1502]) ).
thf(1771,plain,
cR @ sk4,
inference(simp,[status(thm)],[1770]) ).
thf(2002,plain,
( ~ $true
| $false
| ~ $true ),
inference(rewrite,[status(thm)],[1964,1625,1771,1502]) ).
thf(2003,plain,
$false,
inference(simp,[status(thm)],[2002]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU897^5 : TPTP v9.3.1. Released v4.0.0.
% 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 : n004.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 14:44:37 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
% 0.88/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/0.98 % [INFO] Parsing done (184ms).
% 1.18/1.00 % [INFO] Running in sequential loop mode.
% 1.74/1.39 % [INFO] eprover registered as external prover.
% 1.91/1.40 % [INFO] Scanning for conjecture ...
% 1.91/1.49 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.08/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.08/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.08/1.53 % [INFO] Type checking passed.
% 2.08/1.53 % [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 ...
% 14.15/4.61 % [INFO] Killing All external provers ...
% 14.15/4.61 % Time passed: 4248ms (effective reasoning time: 3609ms)
% 14.15/4.61 % 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)>
% 14.15/4.61 % Axioms used in derivation (0):
% 14.15/4.61 % No. of inferences in proof: 107
% 14.15/4.61 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4248 ms resp. 3609 ms w/o parsing
% 14.15/4.66 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.15/4.66 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------