%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV181^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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 : n006.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 08:36:57 AM UTC 2026
% Result : Theorem 21.85s 5.57s
% Output : Refutation 19.55s
% Verified :
% SZS Type : Refutation
% Derivation depth : 23
% Number of leaves : 5
% Syntax : Number of formulae : 70 ( 16 unt; 0 typ; 4 def)
% Number of atoms : 298 ( 90 equ; 0 cnn)
% Maximal formula atoms : 5 ( 4 avg)
% Number of connectives : 656 ( 110 ~; 35 |; 25 &; 478 @)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 76 ( 76 >; 0 *; 0 +; 0 <<)
% Number of symbols : 8 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 180 ( 93 ^; 61 !; 23 ?; 180 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(cD_FOR_X5309_decl,type,
cD_FOR_X5309: ( ( $i > $o ) > $i ) > $i > $o ).
thf(sk1_decl,type,
sk1: ( $i > $o ) > $i ).
thf(sk2_decl,type,
sk2: $i > $o ).
thf(sk3_decl,type,
sk3: $i > $i > $o ).
thf(sk6_decl,type,
sk6: $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(cD_FOR_X5309_def,definition,
( cD_FOR_X5309
= ( ^ [A: ( $i > $o ) > $i,B: $i] :
? [C: $i > $o] :
( ~ ( C @ ( A @ C ) )
& ( B
= ( A @ C ) ) ) ) ) ).
thf(sk1_def,definition,
( sk1
= ( @+[A: ( $i > $o ) > $i] :
~ ( ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ~ ? [B: $i > $o] :
( ~ ( B @ ( A @ B ) )
& ( ( A
@ ^ [C: $i] :
? [D: $i > $o] :
( ~ ( D @ ( A @ D ) )
& ( C
= ( A @ D ) ) ) )
= ( A @ B ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i > $o] :
( ~ ( A @ ( sk1 @ A ) )
& ( ( sk1
@ ^ [B: $i] :
? [C: $i > $o] :
( ~ ( C @ ( sk1 @ C ) )
& ( B
= ( sk1 @ C ) ) ) )
= ( sk1 @ A ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i > $i > $o] :
! [B: $i > $o] :
( ( A @ ( sk1 @ B ) )
= B ) ) ) ).
thf(1,conjecture,
! [A: ( $i > $o ) > $i] :
( ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ~ ( cD_FOR_X5309 @ A @ ( A @ ( cD_FOR_X5309 @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM143C_pme) ).
thf(2,negated_conjecture,
~ ! [A: ( $i > $o ) > $i] :
( ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ~ ( cD_FOR_X5309 @ A @ ( A @ ( cD_FOR_X5309 @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: ( $i > $o ) > $i] :
( ! [B: $i > $o,C: $i > $o] :
( ( ( A @ B )
= ( A @ C ) )
=> ( B = C ) )
=> ~ ? [B: $i > $o] :
( ~ ( B @ ( A @ B ) )
& ( ( A
@ ^ [C: $i] :
? [D: $i > $o] :
( ~ ( D @ ( A @ D ) )
& ( C
= ( A @ D ) ) ) )
= ( A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( ( sk1 @ A )
!= ( sk1 @ B ) )
| ( A = B ) )
& ~ ( sk2 @ ( sk1 @ sk2 ) )
& ( ( sk1
@ ^ [C: $i] :
? [D: $i > $o] :
( ~ ( D @ ( sk1 @ D ) )
& ( C
= ( sk1 @ D ) ) ) )
= ( sk1 @ sk2 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( sk1 @ A )
!= ( sk1 @ B ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(8,plain,
! [B: $i > $o,A: $i > $o] :
( ( ( sk1 @ A )
!= ( sk1 @ B ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[5]) ).
thf(9,plain,
? [A: $i > $i > $o] :
! [B: $i > $o] :
( ( A @ ( sk1 @ B ) )
= B ),
inference(detectInverse,[status(thm)],[8]) ).
thf(10,plain,
! [A: $i > $o] :
( ( sk3 @ ( sk1 @ A ) )
= A ),
inference(cnf,[status(esa)],[9]) ).
thf(20,plain,
! [A: $i > $o] :
( ( sk3 @ ( sk1 @ A ) )
= A ),
inference(lifteq,[status(thm)],[10]) ).
thf(6,plain,
~ ( sk2 @ ( sk1 @ sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(21,plain,
! [B: $i,A: $i > $o] :
( ( sk3 @ ( sk1 @ A ) @ B )
= ( A @ B ) ),
inference(func_ext,[status(esa)],[20]) ).
thf(280,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk3 @ ( sk1 @ A ) @ B )
| ( ( A @ B )
!= ( sk2 @ ( sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,6]) ).
thf(285,plain,
~ ( sk3 @ ( sk1 @ sk2 ) @ ( sk1 @ sk2 ) ),
inference(pre_uni,[status(thm)],[280:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 @ sk2 ))]]) ).
thf(286,plain,
! [A: $i] :
~ ( sk3
@ ( sk1
@ ^ [B: $i] : ( sk2 @ ( sk1 @ sk2 ) ) )
@ A ),
inference(pre_uni,[status(thm)],[280:[bind(A,$thf( ^ [C: $i] : ( sk2 @ ( sk1 @ sk2 ) ) )),bind(B,$thf( B ))]]) ).
thf(290,plain,
! [A: $i] :
~ ( sk3
@ ( sk1
@ ^ [B: $i] : ( sk2 @ ( sk1 @ sk2 ) ) )
@ A ),
inference(simp,[status(thm)],[286]) ).
thf(513,plain,
! [A: $i] :
~ ( sk3
@ ( sk1
@ ^ [B: $i] : $false )
@ A ),
inference(rewrite,[status(thm)],[290,6]) ).
thf(517,plain,
! [C: $i,B: $i,A: $i > $o] :
( ~ ( sk3 @ ( sk1 @ A ) @ B )
| ( ( A @ B )
!= ( sk3
@ ( sk1
@ ^ [D: $i] : $false )
@ C ) ) ),
inference(paramod_ordered,[status(thm)],[21,513]) ).
thf(528,plain,
! [A: $i > $i] :
~ ( sk3
@ ( sk1
@ ^ [B: $i] : ( sk3 @ B @ ( A @ B ) ) )
@ ( sk1
@ ^ [B: $i] : $false ) ),
inference(pre_uni,[status(thm)],[517:[bind(A,$thf( ^ [E: $i] : ( sk3 @ E @ ( E @ E ) ) )),bind(B,$thf( sk1 @ ^ [D: $i] : $false )),bind(C,$thf( E @ ( sk1 @ ^ [E: $i] : $false ) ))]]) ).
thf(530,plain,
! [A: $i > $i] :
~ ( sk3
@ ( sk1
@ ^ [B: $i] : ( sk3 @ B @ ( A @ B ) ) )
@ ( sk1
@ ^ [B: $i] : $false ) ),
inference(simp,[status(thm)],[528]) ).
thf(7,plain,
( ( sk1
@ ^ [A: $i] :
? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) )
= ( sk1 @ sk2 ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(11,plain,
( ( sk1
@ ^ [A: $i] :
? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) )
= ( sk1 @ sk2 ) ),
inference(lifteq,[status(thm)],[7]) ).
thf(25,plain,
! [A: $i > $o] :
( ( ( sk3 @ ( sk1 @ sk2 ) )
= A )
| ( ( sk1
@ ^ [B: $i] :
? [C: $i > $o] :
( ~ ( C @ ( sk1 @ C ) )
& ( B
= ( sk1 @ C ) ) ) )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11,20]) ).
thf(26,plain,
( ( sk3 @ ( sk1 @ sk2 ) )
= ( ^ [A: $i] :
? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[25:[bind(A,$thf( ^ [B: $i] : ? [C: $i > $o] : ( ~ ( C @ ( sk1 @ C ) ) & ( B = ( sk1 @ C ) ) ) ))]]) ).
thf(35,plain,
! [A: $i > $o] :
( ( ( ^ [B: $i] :
? [C: $i > $o] :
( ~ ( C @ ( sk1 @ C ) )
& ( B
= ( sk1 @ C ) ) ) )
= A )
| ( ( sk3 @ ( sk1 @ sk2 ) )
!= ( sk3 @ ( sk1 @ A ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,20]) ).
thf(36,plain,
( ( ^ [A: $i] :
? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[35:[bind(A,$thf( sk2 ))]]) ).
thf(166,plain,
( ( ( sk3 @ ( sk1 @ sk2 ) )
= sk2 )
| ( ( ^ [A: $i] :
? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) )
!= ( ^ [A: $i] :
? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,26]) ).
thf(167,plain,
( ( sk3 @ ( sk1 @ sk2 ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[166:[]]) ).
thf(313,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk3 @ ( sk1 @ A ) @ B )
| ( ( A @ B )
!= ( sk3 @ ( sk1 @ sk2 ) @ ( sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,285]) ).
thf(314,plain,
~ ( sk3
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ A ) )
@ ( sk1 @ sk2 ) ),
inference(pre_uni,[status(thm)],[313:[bind(A,$thf( ^ [C: $i] : ( sk3 @ C @ C ) )),bind(B,$thf( sk1 @ sk2 ))]]) ).
thf(340,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk3 @ ( sk1 @ A ) @ B )
| ( ( A @ B )
!= ( sk3
@ ( sk1
@ ^ [C: $i] : ( sk3 @ C @ C ) )
@ ( sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,314]) ).
thf(346,plain,
~ ( sk3
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ ( sk1 @ sk2 ) ) )
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ A ) ) ),
inference(pre_uni,[status(thm)],[340:[bind(A,$thf( ^ [C: $i] : ( sk3 @ C @ ( sk1 @ sk2 ) ) )),bind(B,$thf( sk1 @ ^ [C: $i] : ( sk3 @ C @ C ) ))]]) ).
thf(412,plain,
( ~ ( sk3 @ ( sk1 @ sk2 )
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ A ) ) )
| ( ( sk3 @ ( sk1 @ sk2 ) )
!= ( ^ [A: $i] : ( sk3 @ A @ ( sk1 @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[167,346]) ).
thf(446,plain,
( ~ ( sk3 @ ( sk1 @ sk2 )
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ A ) ) )
| ( ( ^ [A: $i] : ( sk1 @ sk2 ) )
!= ( ^ [A: $i] : A ) )
| ( ( ^ [A: $i] : A )
!= ( ^ [A: $i] : ( sk1 @ sk2 ) ) ) ),
inference(simp,[status(thm)],[412]) ).
thf(457,plain,
( ~ ( sk3 @ ( sk1 @ sk2 )
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ A ) ) )
| ( ( ^ [A: $i] : ( sk1 @ sk2 ) )
!= ( ^ [A: $i] : A ) ) ),
inference(simp,[status(thm)],[446]) ).
thf(706,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ B )
| ( ( ^ [C: $i] : ( sk1 @ sk2 ) )
!= ( ^ [C: $i] : C ) )
| ( ( sk3 @ ( sk1 @ A ) @ B )
!= ( sk3 @ ( sk1 @ sk2 )
@ ( sk1
@ ^ [C: $i] : ( sk3 @ C @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,457]) ).
thf(707,plain,
( ~ ( sk2
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ A ) ) )
| ( ( ^ [A: $i] : ( sk1 @ sk2 ) )
!= ( ^ [A: $i] : A ) ) ),
inference(pattern_uni,[status(thm)],[706:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 @ ^ [C: $i] : ( sk3 @ C @ C ) ))]]) ).
thf(754,plain,
( ( ( sk1 @ sk2 )
!= sk6 )
| ~ ( sk2
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ A ) ) ) ),
inference(func_ext,[status(esa)],[707]) ).
thf(347,plain,
~ ( sk3
@ ( sk1
@ ( sk3
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ A ) ) ) )
@ ( sk1 @ sk2 ) ),
inference(pre_uni,[status(thm)],[340:[bind(A,$thf( sk3 @ ( sk1 @ ^ [C: $i] : ( sk3 @ C @ C ) ) )),bind(B,$thf( sk1 @ sk2 ))]]) ).
thf(470,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk3 @ ( sk1 @ A ) @ B )
| ( ( A @ B )
!= ( sk3
@ ( sk1
@ ( sk3
@ ( sk1
@ ^ [C: $i] : ( sk3 @ C @ C ) ) ) )
@ ( sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,347]) ).
thf(495,plain,
~ ( sk3
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ ( sk1 @ sk2 ) ) )
@ ( sk1
@ ( sk3
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ A ) ) ) ) ),
inference(pre_uni,[status(thm)],[470:[bind(A,$thf( ^ [C: $i] : ( sk3 @ C @ ( sk1 @ sk2 ) ) )),bind(B,$thf( sk1 @ ( sk3 @ ( sk1 @ ^ [C: $i] : ( sk3 @ C @ C ) ) ) ))]]) ).
thf(417,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk3 @ ( sk1 @ A ) @ B )
| ( ( A @ B )
!= ( sk3
@ ( sk1
@ ^ [C: $i] : ( sk3 @ C @ ( sk1 @ sk2 ) ) )
@ ( sk1
@ ^ [C: $i] : ( sk3 @ C @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,346]) ).
thf(442,plain,
~ ( sk3
@ ( sk1
@ ^ [A: $i] :
( sk3 @ A
@ ( sk1
@ ^ [B: $i] : ( sk3 @ B @ B ) ) ) )
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ ( sk1 @ sk2 ) ) ) ),
inference(pre_uni,[status(thm)],[417:[bind(A,$thf( ^ [C: $i] : ( sk3 @ C @ ( sk1 @ ^ [D: $i] : ( sk3 @ D @ D ) ) ) )),bind(B,$thf( sk1 @ ^ [C: $i] : ( sk3 @ C @ ( sk1 @ sk2 ) ) ))]]) ).
thf(315,plain,
~ ( sk3
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ ( sk1 @ sk2 ) ) )
@ ( sk1 @ sk2 ) ),
inference(pre_uni,[status(thm)],[313:[bind(A,$thf( ^ [C: $i] : ( sk3 @ C @ ( sk1 @ sk2 ) ) )),bind(B,$thf( sk1 @ sk2 ))]]) ).
thf(379,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk3 @ ( sk1 @ A ) @ B )
| ( ( A @ B )
!= ( sk3
@ ( sk1
@ ^ [C: $i] : ( sk3 @ C @ ( sk1 @ sk2 ) ) )
@ ( sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,315]) ).
thf(393,plain,
~ ( sk3
@ ( sk1
@ ^ [A: $i] :
( sk3
@ ( sk1
@ ^ [B: $i] : ( sk3 @ B @ A ) )
@ A ) )
@ ( sk1 @ sk2 ) ),
inference(pre_uni,[status(thm)],[379:[bind(A,$thf( ^ [C: $i] : ( sk3 @ ( sk1 @ ^ [D: $i] : ( sk3 @ D @ C ) ) @ C ) )),bind(B,$thf( sk1 @ sk2 ))]]) ).
thf(611,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk3 @ ( sk1 @ A ) @ B )
| ( ( A @ B )
!= ( sk3
@ ( sk1
@ ^ [C: $i] :
( sk3
@ ( sk1
@ ^ [D: $i] : ( sk3 @ D @ C ) )
@ C ) )
@ ( sk1 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,393]) ).
thf(629,plain,
~ ( sk3
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ ( sk1 @ sk2 ) ) )
@ ( sk1
@ ^ [A: $i] :
( sk3
@ ( sk1
@ ^ [B: $i] : ( sk3 @ B @ A ) )
@ A ) ) ),
inference(pre_uni,[status(thm)],[611:[bind(A,$thf( ^ [C: $i] : ( sk3 @ C @ ( sk1 @ sk2 ) ) )),bind(B,$thf( sk1 @ ^ [C: $i] : ( sk3 @ ( sk1 @ ^ [D: $i] : ( sk3 @ D @ C ) ) @ C ) ))]]) ).
thf(392,plain,
~ ( sk3
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ ( sk1 @ sk2 ) ) )
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ ( sk1 @ sk2 ) ) ) ),
inference(pre_uni,[status(thm)],[379:[bind(A,$thf( ^ [C: $i] : ( sk3 @ C @ ( sk1 @ sk2 ) ) )),bind(B,$thf( sk1 @ ^ [C: $i] : ( sk3 @ C @ ( sk1 @ sk2 ) ) ))]]) ).
thf(804,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk3 @ ( sk1 @ A ) @ B )
| ( ( A @ B )
!= ( sk3
@ ( sk1
@ ^ [C: $i] : ( sk3 @ C @ ( sk1 @ sk2 ) ) )
@ ( sk1
@ ^ [C: $i] : ( sk3 @ C @ ( sk1 @ sk2 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,392]) ).
thf(838,plain,
~ ( sk3
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ A ) )
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ ( sk1 @ sk2 ) ) ) ),
inference(pre_uni,[status(thm)],[804:[bind(A,$thf( ^ [C: $i] : ( sk3 @ C @ C ) )),bind(B,$thf( sk1 @ ^ [C: $i] : ( sk3 @ C @ ( sk1 @ sk2 ) ) ))]]) ).
thf(870,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk3 @ ( sk1 @ A ) @ B )
| ( ( A @ B )
!= ( sk3
@ ( sk1
@ ^ [C: $i] : ( sk3 @ C @ C ) )
@ ( sk1
@ ^ [C: $i] : ( sk3 @ C @ ( sk1 @ sk2 ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,838]) ).
thf(893,plain,
~ ( sk3
@ ( sk1
@ ( sk3
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ A ) ) ) )
@ ( sk1
@ ^ [A: $i] : ( sk3 @ A @ ( sk1 @ sk2 ) ) ) ),
inference(pre_uni,[status(thm)],[870:[bind(A,$thf( sk3 @ ( sk1 @ ^ [C: $i] : ( sk3 @ C @ C ) ) )),bind(B,$thf( sk1 @ ^ [C: $i] : ( sk3 @ C @ ( sk1 @ sk2 ) ) ))]]) ).
thf(13,plain,
( ~ ( sk2
@ ( sk1
@ ^ [A: $i] :
? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) ) )
| ( ( sk1 @ sk2 )
!= ( sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[11,6]) ).
thf(14,plain,
~ ( sk2
@ ( sk1
@ ^ [A: $i] :
? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) ) ),
inference(pattern_uni,[status(thm)],[13:[]]) ).
thf(27,plain,
! [A: $i > $o] :
( ( ( sk3
@ ( sk1
@ ^ [B: $i] :
? [C: $i > $o] :
( ~ ( C @ ( sk1 @ C ) )
& ( B
= ( sk1 @ C ) ) ) ) )
= A )
| ( ( sk1 @ sk2 )
!= ( sk1 @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11,20]) ).
thf(28,plain,
( ( sk3
@ ( sk1
@ ^ [A: $i] :
? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( sk2 ))]]) ).
thf(648,plain,
! [A: $i > $i] :
( ~ ( sk3 @ ( sk1 @ sk2 )
@ ( sk1
@ ^ [B: $i] : $false ) )
| ( ( sk3 @ ( sk1 @ sk2 ) )
!= ( ^ [B: $i] : ( sk3 @ B @ ( A @ B ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[167,530]) ).
thf(669,plain,
! [A: $i > $i] :
( ~ ( sk3 @ ( sk1 @ sk2 )
@ ( sk1
@ ^ [B: $i] : $false ) )
| ( ( ^ [B: $i] : ( sk1 @ sk2 ) )
!= ( ^ [B: $i] : B ) )
| ( ( ^ [B: $i] : B )
!= A ) ),
inference(simp,[status(thm)],[648]) ).
thf(693,plain,
( ~ ( sk3 @ ( sk1 @ sk2 )
@ ( sk1
@ ^ [A: $i] : $false ) )
| ( ( ^ [A: $i] : ( sk1 @ sk2 ) )
!= ( ^ [A: $i] : A ) ) ),
inference(simp,[status(thm)],[669]) ).
thf(32,plain,
! [A: $i] :
( ( sk3 @ ( sk1 @ sk2 ) @ A )
= ( ? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) ) ),
inference(func_ext,[status(esa)],[26]) ).
thf(1101,plain,
! [B: $i,A: $i > $o] :
( ~ ( A @ B )
| ( ( ^ [C: $i] : ( sk1 @ sk2 ) )
!= ( ^ [C: $i] : C ) )
| ( ( sk3 @ ( sk1 @ A ) @ B )
!= ( sk3 @ ( sk1 @ sk2 )
@ ( sk1
@ ^ [C: $i] : $false ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,693]) ).
thf(1102,plain,
( ~ ( sk2
@ ( sk1
@ ^ [A: $i] : $false ) )
| ( ( ^ [A: $i] : ( sk1 @ sk2 ) )
!= ( ^ [A: $i] : A ) ) ),
inference(pattern_uni,[status(thm)],[1101:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 @ ^ [C: $i] : $false ))]]) ).
thf(279,plain,
! [B: $i,A: $i > $o] :
( ~ ( sk3 @ ( sk1 @ A ) @ B )
| ( ( A @ B )
!= ( sk2
@ ( sk1
@ ^ [C: $i] :
? [D: $i > $o] :
( ~ ( D @ ( sk1 @ D ) )
& ( C
= ( sk1 @ D ) ) ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[21,14]) ).
thf(287,plain,
~ ( sk3 @ ( sk1 @ sk2 )
@ ( sk1
@ ^ [A: $i] :
? [B: $i > $o] :
( ~ ( B @ ( sk1 @ B ) )
& ( A
= ( sk1 @ B ) ) ) ) ),
inference(pre_uni,[status(thm)],[279:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 @ ^ [C: $i] : ? [D: $i > $o] : ( ~ ( D @ ( sk1 @ D ) ) & ( C = ( sk1 @ D ) ) ) ))]]) ).
thf(1148,plain,
( ( ( sk1 @ sk2 )
!= sk8 )
| ~ ( sk2
@ ( sk1
@ ^ [A: $i] : $false ) ) ),
inference(func_ext,[status(esa)],[1102]) ).
thf(1408,plain,
$false,
inference(e,[status(thm)],[20,6,285,530,754,707,495,442,629,347,893,14,838,28,392,693,21,393,457,513,32,3,1102,167,11,314,8,346,287,315,36,1148]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV181^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 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
% 0.09/0.21 % Computer : n006.cluster.edu
% 0.09/0.21 % Model : x86_64 x86_64
% 0.09/0.21 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.21 % Memory : 8046.5625MB
% 0.09/0.21 % OS : Linux 6.8.0-71-generic
% 0.09/0.21 % CPULimit : 300
% 0.09/0.21 % WCLimit : 300
% 0.09/0.21 % DateTime : Tue Sep 29 15:18:39 UTC 2026
% 0.09/0.21 % CPUTime :
% 0.09/0.22 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
% 0.90/0.79 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/0.97 % [INFO] Parsing done (180ms).
% 1.23/0.98 % [INFO] Running in sequential loop mode.
% 1.83/1.37 % [INFO] eprover registered as external prover.
% 1.83/1.38 % [INFO] Scanning for conjecture ...
% 2.01/1.48 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 2.19/1.52 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 2.19/1.52 % [INFO] Problem is higher-order (TPTP THF).
% 2.19/1.52 % [INFO] Type checking passed.
% 2.19/1.53 % [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 ...
% 21.85/5.56 % External prover 'e' found a proof!
% 21.85/5.56 % [INFO] Killing All external provers ...
% 21.85/5.57 % Time passed: 5217ms (effective reasoning time: 4577ms)
% 21.85/5.57 % 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)>
% 21.85/5.57 % Axioms used in derivation (0):
% 21.85/5.57 % No. of inferences in proof: 66
% 21.85/5.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5217 ms resp. 4577 ms w/o parsing
% 19.55/5.70 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 19.55/5.70 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------