%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEU938^5 : 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 : n012.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 08:29:37 AM UTC 2026
% Result : Theorem 32.42s 8.93s
% Output : Refutation 32.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 4
% Syntax : Number of formulae : 87 ( 24 unt; 0 typ; 3 def)
% Number of atoms : 261 ( 140 equ; 9 cnn)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 1000 ( 161 ~; 153 |; 20 &; 642 @)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 201 ( 201 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 8 usr; 7 con; 0-4 aty)
% Number of variables : 362 ( 195 ^; 164 !; 0 ?; 362 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(h_decl,type,
h: $i > $i ).
thf(sk1_decl,type,
sk1: ( $i > $i ) > ( $i > $i ) > $i ).
thf(sk2_decl,type,
sk2: ( $i > $i ) > ( $i > $i ) > $o ).
thf(sk3_decl,type,
sk3: ( $i > $i ) > ( $i > $i ) > ( $i > $i ) > $o ).
thf(sk4_decl,type,
sk4: ( ( $i > $i ) > $o ) > ( $i > $i ) > ( $i > $i ) > $i > $i ).
thf(sk8_decl,type,
sk8: $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i > $i,B: $i > $i] :
@+[C: $i] :
( ( B @ C )
!= ( A @ C ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i > $i,B: $i > $i] :
@+[C: ( $i > $i ) > $o] :
~ ( ( ( C @ B )
& ! [D: $i > $i] :
( ( C @ D )
=> ( C
@ ^ [E: $i] : ( B @ ( D @ E ) ) ) ) )
=> ( C
@ ^ [D: $i] : ( A @ ( B @ D ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: ( $i > $i ) > $o,B: $i > $i,C: $i > $i] :
@+[D: $i > $i] :
~ ( ( A @ D )
=> ( A
@ ^ [E: $i] : ( C @ ( D @ E ) ) ) ) ) ) ).
thf(1,conjecture,
( ( ( ( h @ a )
= a )
& ( ( h @ b )
!= a )
& ! [A: $i > $i,B: $i > $i] :
( ! [C: $i] :
( ( A @ C )
= ( B @ C ) )
=> ( A = B ) ) )
=> ~ ! [A: $i > $i,B: $i > $i] :
( ! [C: ( $i > $i ) > $o] :
( ( ( C @ A )
& ! [D: $i > $i] :
( ( C @ D )
=> ( C
@ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
=> ( C
@ ^ [D: $i] : ( B @ ( A @ D ) ) ) )
=> ! [C: ( $i > $i ) > $o] :
( ( ( C @ A )
& ! [D: $i > $i] :
( ( C @ D )
=> ( C
@ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM196_pme) ).
thf(2,negated_conjecture,
~ ( ( ( ( h @ a )
= a )
& ( ( h @ b )
!= a )
& ! [A: $i > $i,B: $i > $i] :
( ! [C: $i] :
( ( A @ C )
= ( B @ C ) )
=> ( A = B ) ) )
=> ~ ! [A: $i > $i,B: $i > $i] :
( ! [C: ( $i > $i ) > $o] :
( ( ( C @ A )
& ! [D: $i > $i] :
( ( C @ D )
=> ( C
@ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
=> ( C
@ ^ [D: $i] : ( B @ ( A @ D ) ) ) )
=> ! [C: ( $i > $i ) > $o] :
( ( ( C @ A )
& ! [D: $i > $i] :
( ( C @ D )
=> ( C
@ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ( ( ( ( h @ a )
= a )
& ( ( h @ b )
!= a )
& ! [A: $i > $i,B: $i > $i] :
( ! [C: $i] :
( ( A @ C )
= ( B @ C ) )
=> ( A = B ) ) )
=> ~ ! [A: $i > $i,B: $i > $i] :
( ! [C: ( $i > $i ) > $o] :
( ( ( C @ A )
& ! [D: $i > $i] :
( ( C @ D )
=> ( C
@ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
=> ( C
@ ^ [D: $i] : ( B @ ( A @ D ) ) ) )
=> ! [C: ( $i > $i ) > $o] :
( ( ( C @ A )
& ! [D: $i > $i] :
( ( C @ D )
=> ( C
@ ^ [E: $i] : ( A @ ( D @ E ) ) ) ) )
=> ( C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
! [F: ( $i > $i ) > $o,E: $i > $i,D: $i > $i,C: $i > $i,B: $i > $i,A: $i > $i] :
( ( ( h @ a )
= a )
& ( ( h @ b )
!= a )
& ( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( A = B ) )
& ( ( sk3 @ D @ C @ C )
| ( sk2 @ C @ D ) )
& ( ~ ( sk3 @ D @ C @ E )
| ( sk3 @ D @ C
@ ^ [G: $i] : ( C @ ( E @ G ) ) )
| ( sk2 @ C @ D ) )
& ( ~ ( sk3 @ D @ C
@ ^ [G: $i] : ( D @ ( C @ G ) ) )
| ( sk2 @ C @ D ) )
& ( ~ ( sk2 @ C @ D )
| ~ ( F @ C )
| ( F @ ( sk4 @ F @ D @ C ) )
| ( F @ D ) )
& ( ~ ( sk2 @ C @ D )
| ~ ( F @ C )
| ~ ( F
@ ^ [G: $i] : ( C @ ( sk4 @ F @ D @ C @ G ) ) )
| ( F @ D ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
! [B: $i > $i,A: $i > $i] :
( ( sk3 @ B @ A @ A )
| ( sk2 @ A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(15,plain,
! [B: $i > $i,A: $i > $i] :
( ( sk3 @ B @ A @ A )
| ( sk2 @ A @ B ) ),
inference(simp,[status(thm)],[5]) ).
thf(8,plain,
! [C: ( $i > $i ) > $o,B: $i > $i,A: $i > $i] :
( ~ ( sk2 @ A @ B )
| ~ ( C @ A )
| ( C @ ( sk4 @ C @ B @ A ) )
| ( C @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(14,plain,
! [B: $i > $i,A: $i > $i] :
( ~ ( sk2 @ A @ B )
| ( A != A )
| ( A
= ( sk4 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A ) )
| ( A = B ) ),
inference(replace_leibeq,[status(thm)],[8:[bind(A,$thf( (@) )),bind(B,$thf( A )),bind(C,$thf( (=) @ ( $i > $i ) @ (@) ))]]) ).
thf(17,plain,
! [B: $i > $i,A: $i > $i] :
( ( A != A )
| ( A
= ( sk4 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A ) )
| ( A = B )
| ~ ( sk2 @ A @ B ) ),
inference(lifteq,[status(thm)],[14]) ).
thf(18,plain,
! [B: $i > $i,A: $i > $i] :
( ( A
= ( sk4 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A ) )
| ( A = B )
| ~ ( sk2 @ A @ B ) ),
inference(simp,[status(thm)],[17]) ).
thf(12,plain,
! [C: ( $i > $i ) > $o,B: $i > $i,A: $i > $i] :
( ~ ( sk2 @ A @ B )
| ~ ( C @ A )
| ~ ( C
@ ^ [D: $i] : ( A @ ( sk4 @ C @ B @ A @ D ) ) )
| ( C @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(23,plain,
! [C: ( $i > $i ) > $o,B: $i > $i,A: $i > $i] :
( ~ ( sk2 @ A @ B )
| ~ ( C @ A )
| ~ ( C
@ ^ [D: $i] : ( A @ ( sk4 @ C @ B @ A @ D ) ) )
| ( C @ B ) ),
inference(simp,[status(thm)],[12]) ).
thf(170,plain,
! [E: ( $i > $i ) > $o,D: $i > $i,C: $i > $i,B: $i > $i,A: $i > $i] :
( ( A = B )
| ~ ( sk2 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( E @ C )
| ~ ( E @ A )
| ( E @ D )
| ( ( sk4 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A )
!= ( ^ [F: $i] : ( C @ ( sk4 @ E @ D @ C @ F ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[18,23]) ).
thf(190,plain,
! [B: $i > $i,A: $i > $i] :
( ( ( ^ [C: $i] : C )
= A )
| ~ ( sk2
@ ^ [C: $i] : C
@ A )
| ~ ( sk2
@ ^ [C: $i] : C
@ B )
| ( ( ^ [C: $i] : C )
!= ( ^ [C: $i] : C ) )
| ( ( ^ [C: $i] : C )
!= ( ^ [C: $i] : C ) )
| ( ( ^ [C: $i] : C )
= B )
| ( ( ^ [C: $i] : A )
!= ( ^ [C: $i] : B ) ) ),
inference(pre_uni,[status(thm)],[170:[bind(A,$thf( ^ [F: $i] : F )),bind(B,$thf( B )),bind(C,$thf( ^ [F: $i] : F )),bind(D,$thf( D )),bind(E,$thf( (=) @ ( $i > $i ) @ ^ [F: $i] : F ))]]) ).
thf(191,plain,
! [A: $i > $i] :
( ( ( ^ [B: $i] : B )
= A )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : B ) )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : B ) )
| ~ ( sk2
@ ^ [B: $i] : B
@ A )
| ~ ( sk2
@ ^ [B: $i] : B
@ A )
| ( ( ^ [B: $i] : B )
= A ) ),
inference(pattern_uni,[status(thm)],[190:[bind(A,$thf( (@) )),bind(B,$thf( (@) ))]]) ).
thf(249,plain,
! [A: $i > $i] :
( ( ( ^ [B: $i] : B )
= A )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : B ) )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : B ) )
| ~ ( sk2
@ ^ [B: $i] : B
@ A )
| ~ ( sk2
@ ^ [B: $i] : B
@ A )
| ( ( ^ [B: $i] : B )
= A ) ),
inference(lifteq,[status(thm)],[191]) ).
thf(250,plain,
! [A: $i > $i] :
( ( ( ^ [B: $i] : B )
= A )
| ~ ( sk2
@ ^ [B: $i] : B
@ A ) ),
inference(simp,[status(thm)],[249]) ).
thf(265,plain,
! [C: $i > $i,B: $i > $i,A: $i > $i] :
( ( sk3 @ B @ A @ A )
| ( ( ^ [D: $i] : D )
= C )
| ~ $true
| ( ( sk2 @ A @ B )
!= ( sk2
@ ^ [D: $i] : D
@ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,250]) ).
thf(266,plain,
! [C: $i > $i,B: $i > $i,A: $i > $i] :
( ( sk3 @ B @ A @ A )
| ( ( ^ [D: $i] : D )
= C )
| ( ( sk2 @ A @ B )
!= ( sk2
@ ^ [D: $i] : D
@ C ) ) ),
inference(simp,[status(thm)],[265]) ).
thf(267,plain,
! [A: $i > $i] :
( ( sk3 @ A
@ ^ [B: $i] : B
@ ^ [B: $i] : B )
| ( ( ^ [B: $i] : B )
= A ) ),
inference(pattern_uni,[status(thm)],[266:[bind(A,$thf( ^ [D: $i] : D )),bind(B,$thf( B )),bind(C,$thf( B ))]]) ).
thf(326,plain,
! [A: $i > $i] :
( ( sk3 @ A
@ ^ [B: $i] : B
@ ^ [B: $i] : B )
| ( ( ^ [B: $i] : B )
= A ) ),
inference(simp,[status(thm)],[267]) ).
thf(351,plain,
! [B: $i,A: $i > $i] :
( ( ( A @ B )
= B )
| ( sk3 @ A
@ ^ [C: $i] : C
@ ^ [C: $i] : C ) ),
inference(func_ext,[status(esa)],[326]) ).
thf(7,plain,
( ( h @ a )
= a ),
inference(cnfConj,[status(thm)],[4]) ).
thf(24,plain,
( ( h @ a )
= a ),
inference(lifteq,[status(thm)],[7]) ).
thf(6,plain,
( ( h @ b )
!= a ),
inference(cnfConj,[status(thm)],[4]) ).
thf(19,plain,
( ( h @ b )
!= a ),
inference(lifteq,[status(thm)],[6]) ).
thf(27,plain,
( ( a != a )
| ( ( h @ b )
!= ( h @ a ) ) ),
inference(paramod_ordered,[status(thm)],[24,19]) ).
thf(28,plain,
( ( h @ b )
!= ( h @ a ) ),
inference(simp,[status(thm)],[27]) ).
thf(29,plain,
b != a,
inference(simp,[status(thm)],[28]) ).
thf(1116,plain,
! [B: $i,A: $i > $i] :
( ( sk3 @ A
@ ^ [C: $i] : C
@ ^ [C: $i] : C )
| ( B != a )
| ( ( A @ B )
!= b ) ),
inference(paramod_ordered,[status(thm)],[351,29]) ).
thf(1166,plain,
! [A: $i] :
( ( sk3
@ ^ [B: $i] : b
@ ^ [B: $i] : B
@ ^ [B: $i] : B )
| ( A != a ) ),
inference(pre_uni,[status(thm)],[1116:[bind(A,$thf( ^ [C: $i] : b ))]]) ).
thf(1168,plain,
( sk3
@ ^ [A: $i] : b
@ ^ [A: $i] : A
@ ^ [A: $i] : A ),
inference(pattern_uni,[status(thm)],[1166:[bind(A,$thf( a ))]]) ).
thf(9,plain,
! [B: $i > $i,A: $i > $i] :
( ~ ( sk3 @ B @ A
@ ^ [C: $i] : ( B @ ( A @ C ) ) )
| ( sk2 @ A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(20,plain,
! [B: $i > $i,A: $i > $i] :
( ~ ( sk3 @ B @ A
@ ^ [C: $i] : ( B @ ( A @ C ) ) )
| ( sk2 @ A @ B ) ),
inference(simp,[status(thm)],[9]) ).
thf(1233,plain,
! [B: $i > $i,A: $i > $i] :
( ~ $true
| ( sk2 @ A @ B )
| ( ( sk3
@ ^ [C: $i] : b
@ ^ [C: $i] : C
@ ^ [C: $i] : C )
!= ( sk3 @ B @ A
@ ^ [C: $i] : ( B @ ( A @ C ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[1168,20]) ).
thf(1234,plain,
! [B: $i > $i,A: $i > $i] :
( ( sk2 @ A @ B )
| ( ( sk3
@ ^ [C: $i] : b
@ ^ [C: $i] : C
@ ^ [C: $i] : C )
!= ( sk3 @ B @ A
@ ^ [C: $i] : ( B @ ( A @ C ) ) ) ) ),
inference(simp,[status(thm)],[1233]) ).
thf(1249,plain,
! [B: $i > $i,A: $i > $i] :
( ( sk2 @ A @ B )
| ( ( ^ [C: $i] : b )
!= B )
| ( ( ^ [C: $i] : C )
!= A )
| ( ( ^ [C: $i] : ( B @ ( A @ C ) ) )
!= ( ^ [C: $i] : C ) ) ),
inference(simp,[status(thm)],[1234]) ).
thf(1260,plain,
( ( sk2
@ ^ [A: $i] : A
@ ^ [A: $i] : b )
| ( ( ^ [A: $i] : b )
!= ( ^ [A: $i] : A ) ) ),
inference(simp,[status(thm)],[1249]) ).
thf(251,plain,
! [B: $i,A: $i > $i] :
( ( ( A @ B )
= B )
| ~ ( sk2
@ ^ [C: $i] : C
@ A ) ),
inference(func_ext,[status(esa)],[250]) ).
thf(594,plain,
! [B: $i,A: $i > $i] :
( ~ ( sk2
@ ^ [C: $i] : C
@ A )
| ( B != a )
| ( ( A @ B )
!= b ) ),
inference(paramod_ordered,[status(thm)],[251,29]) ).
thf(607,plain,
! [A: $i] :
( ~ ( sk2
@ ^ [B: $i] : B
@ ^ [B: $i] : b )
| ( A != a ) ),
inference(pre_uni,[status(thm)],[594:[bind(A,$thf( ^ [C: $i] : b ))]]) ).
thf(609,plain,
~ ( sk2
@ ^ [A: $i] : A
@ ^ [A: $i] : b ),
inference(pattern_uni,[status(thm)],[607:[bind(A,$thf( a ))]]) ).
thf(1776,plain,
( $false
| ( ( ^ [A: $i] : b )
!= ( ^ [A: $i] : A ) ) ),
inference(rewrite,[status(thm)],[1260,609]) ).
thf(1777,plain,
( ( ^ [A: $i] : b )
!= ( ^ [A: $i] : A ) ),
inference(simp,[status(thm)],[1776]) ).
thf(1795,plain,
! [A: $i > $i] :
( ~ ( sk2
@ ^ [B: $i] : B
@ A )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : b ) )
| ( A
!= ( ^ [B: $i] : B ) ) ),
inference(paramod_ordered,[status(thm)],[250,1777]) ).
thf(1796,plain,
( ~ ( sk2
@ ^ [A: $i] : A
@ ^ [A: $i] : A )
| ( ( ^ [A: $i] : A )
!= ( ^ [A: $i] : b ) ) ),
inference(pattern_uni,[status(thm)],[1795:[bind(A,$thf( ^ [B: $i] : B ))]]) ).
thf(1104,plain,
! [B: $i,A: $i > $i] :
( ( sk3 @ A
@ ^ [C: $i] : C
@ ^ [C: $i] : C )
| ( B != a )
| ( ( A @ B )
!= ( h @ b ) ) ),
inference(paramod_ordered,[status(thm)],[351,19]) ).
thf(1151,plain,
! [A: $i] :
( ( sk3
@ ^ [B: $i] : ( h @ b )
@ ^ [B: $i] : B
@ ^ [B: $i] : B )
| ( A != a ) ),
inference(pre_uni,[status(thm)],[1104:[bind(A,$thf( ^ [C: $i] : ( h @ b ) )),bind(B,$thf( B ))]]) ).
thf(1153,plain,
( sk3
@ ^ [A: $i] : ( h @ b )
@ ^ [A: $i] : A
@ ^ [A: $i] : A ),
inference(pattern_uni,[status(thm)],[1151:[bind(A,$thf( a ))]]) ).
thf(1778,plain,
sk8 != b,
inference(func_ext,[status(esa)],[1777]) ).
thf(1820,plain,
! [B: $i,A: $i > $i] :
( ~ ( sk2
@ ^ [C: $i] : C
@ A )
| ( B != b )
| ( ( A @ B )
!= sk8 ) ),
inference(paramod_ordered,[status(thm)],[251,1778]) ).
thf(1822,plain,
! [A: $i] :
( ~ ( sk2
@ ^ [B: $i] : B
@ ^ [B: $i] : sk8 )
| ( A != b ) ),
inference(pre_uni,[status(thm)],[1820:[bind(A,$thf( ^ [C: $i] : sk8 ))]]) ).
thf(1824,plain,
~ ( sk2
@ ^ [A: $i] : A
@ ^ [A: $i] : sk8 ),
inference(pattern_uni,[status(thm)],[1822:[bind(A,$thf( b ))]]) ).
thf(583,plain,
! [B: $i,A: $i > $i] :
( ~ ( sk2
@ ^ [C: $i] : C
@ A )
| ( B != a )
| ( ( A @ B )
!= ( h @ b ) ) ),
inference(paramod_ordered,[status(thm)],[251,19]) ).
thf(599,plain,
! [A: $i] :
( ~ ( sk2
@ ^ [B: $i] : B
@ ^ [B: $i] : ( h @ b ) )
| ( A != a ) ),
inference(pre_uni,[status(thm)],[583:[bind(A,$thf( ^ [C: $i] : ( h @ b ) )),bind(B,$thf( B ))]]) ).
thf(601,plain,
~ ( sk2
@ ^ [A: $i] : A
@ ^ [A: $i] : ( h @ b ) ),
inference(pattern_uni,[status(thm)],[599:[bind(A,$thf( a ))]]) ).
thf(13,plain,
! [B: $i > $i,A: $i > $i] :
( ~ ( sk2 @ A @ B )
| ( A != A )
| ( A
!= ( ^ [C: $i] : ( A @ ( sk4 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A @ C ) ) ) )
| ( A = B ) ),
inference(replace_leibeq,[status(thm)],[12:[bind(A,$thf( (@) )),bind(B,$thf( A )),bind(C,$thf( (=) @ ( $i > $i ) @ (@) ))]]) ).
thf(21,plain,
! [B: $i > $i,A: $i > $i] :
( ( A != A )
| ( ( ^ [C: $i] : ( A @ ( sk4 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A @ C ) ) )
!= A )
| ( A = B )
| ~ ( sk2 @ A @ B ) ),
inference(lifteq,[status(thm)],[13]) ).
thf(22,plain,
! [B: $i > $i,A: $i > $i] :
( ( ( ^ [C: $i] : ( A @ ( sk4 @ ( (=) @ ( $i > $i ) @ A ) @ B @ A @ C ) ) )
!= A )
| ( A = B )
| ~ ( sk2 @ A @ B ) ),
inference(simp,[status(thm)],[21]) ).
thf(10,plain,
! [B: $i > $i,A: $i > $i] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( A = B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(16,plain,
! [B: $i > $i,A: $i > $i] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[10]) ).
thf(1782,plain,
! [B: $i > $i,A: $i > $i] :
( ( ( A @ ( sk1 @ B @ A ) )
!= ( B @ ( sk1 @ B @ A ) ) )
| ( B
!= ( ^ [C: $i] : C ) )
| ( A
!= ( ^ [C: $i] : b ) ) ),
inference(paramod_ordered,[status(thm)],[16,1777]) ).
thf(1783,plain,
! [A: $i > $i] :
( ( ( A
@ ( sk1 @ A
@ ^ [B: $i] : b ) )
!= b )
| ( A
!= ( ^ [B: $i] : B ) ) ),
inference(pattern_uni,[status(thm)],[1782:[bind(A,$thf( ^ [C: $i] : b ))]]) ).
thf(1815,plain,
( ( sk1
@ ^ [A: $i] : A
@ ^ [A: $i] : b )
!= b ),
inference(simp,[status(thm)],[1783]) ).
thf(2313,plain,
! [B: $i,A: $i > $i] :
( ( sk3 @ A
@ ^ [C: $i] : C
@ ^ [C: $i] : C )
| ( B != b )
| ( ( A @ B )
!= ( sk1
@ ^ [C: $i] : C
@ ^ [C: $i] : b ) ) ),
inference(paramod_ordered,[status(thm)],[351,1815]) ).
thf(2319,plain,
( ( sk3
@ ^ [A: $i] :
( sk1
@ ^ [B: $i] : B
@ ^ [B: $i] : A )
@ ^ [A: $i] : A
@ ^ [A: $i] : A )
| ( b != b ) ),
inference(pre_uni,[status(thm)],[2313:[bind(A,$thf( ^ [C: $i] : ( sk1 @ ^ [D: $i] : D @ ^ [D: $i] : C ) )),bind(B,$thf( b ))]]) ).
thf(2321,plain,
( sk3
@ ^ [A: $i] :
( sk1
@ ^ [B: $i] : B
@ ^ [B: $i] : A )
@ ^ [A: $i] : A
@ ^ [A: $i] : A ),
inference(pattern_uni,[status(thm)],[2319:[]]) ).
thf(1802,plain,
! [A: $i > $i] :
( ( sk3 @ A
@ ^ [B: $i] : B
@ ^ [B: $i] : B )
| ( ( ^ [B: $i] : B )
!= ( ^ [B: $i] : b ) )
| ( A
!= ( ^ [B: $i] : B ) ) ),
inference(paramod_ordered,[status(thm)],[326,1777]) ).
thf(1803,plain,
( ( sk3
@ ^ [A: $i] : A
@ ^ [A: $i] : A
@ ^ [A: $i] : A )
| ( ( ^ [A: $i] : A )
!= ( ^ [A: $i] : b ) ) ),
inference(pattern_uni,[status(thm)],[1802:[bind(A,$thf( ^ [B: $i] : B ))]]) ).
thf(11,plain,
! [C: $i > $i,B: $i > $i,A: $i > $i] :
( ~ ( sk3 @ B @ A @ C )
| ( sk3 @ B @ A
@ ^ [D: $i] : ( A @ ( C @ D ) ) )
| ( sk2 @ A @ B ) ),
inference(cnfConj,[status(thm)],[4]) ).
thf(25,plain,
! [C: $i > $i,B: $i > $i,A: $i > $i] :
( ~ ( sk3 @ B @ A @ C )
| ( sk3 @ B @ A
@ ^ [D: $i] : ( A @ ( C @ D ) ) )
| ( sk2 @ A @ B ) ),
inference(simp,[status(thm)],[11]) ).
thf(42,plain,
! [C: ( $i > $i ) > $o,B: $i > $i,A: $i > $i] :
( ~ ( sk2 @ A @ B )
| ~ ( C @ A )
| ( C @ B )
| ( ( C
@ ^ [D: $i] : ( A @ ( sk4 @ C @ B @ A @ D ) ) )
!= ( sk2 @ A @ B ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[23]) ).
thf(72,plain,
! [D: ( $i > $i ) > $i > $i,C: ( $i > $i ) > $i > $i,B: $i > $i,A: $i > $i] :
( ~ ( sk2 @ A @ B )
| ~ ( sk2 @ ( C @ A ) @ ( D @ A ) )
| ( sk2 @ ( C @ B ) @ ( D @ B ) )
| ( ( D
@ ^ [E: $i] :
( A
@ ( sk4
@ ^ [F: $i > $i] : ( sk2 @ ( C @ F ) @ ( D @ F ) )
@ B
@ A
@ E ) ) )
!= B )
| ( ( C
@ ^ [E: $i] :
( A
@ ( sk4
@ ^ [F: $i > $i] : ( sk2 @ ( C @ F ) @ ( D @ F ) )
@ B
@ A
@ E ) ) )
!= A ) ),
inference(pre_uni,[status(thm)],[42:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( ^ [F: $i > $i] : ( sk2 @ ( D @ F ) @ ( E @ F ) ) ))]]) ).
thf(73,plain,
! [D: ( $i > $i ) > $i > $i,C: ( $i > $i ) > $i > $i,B: $i > $i,A: $i > $i] :
( ( sk2 @ ( C @ B ) @ ( D @ B ) )
| ~ ( sk2 @ ( C @ A ) @ ( D @ A ) )
| ~ ( sk2 @ A @ B )
| ( ( D
@ ^ [E: $i] :
( A
@ ( sk4
@ ^ [F: $i > $i] : ( sk2 @ ( C @ F ) @ ( D @ F ) )
@ B
@ A
@ E ) ) )
!= B )
| ( ( C
@ ^ [E: $i] :
( A
@ ( sk4
@ ^ [F: $i > $i] : ( sk2 @ ( C @ F ) @ ( D @ F ) )
@ B
@ A
@ E ) ) )
!= A ) ),
inference(pre_uni,[status(thm)],[72:[]]) ).
thf(93,plain,
! [D: ( $i > $i ) > $i > $i,C: ( $i > $i ) > $i > $i,B: $i > $i,A: $i > $i] :
( ( sk2 @ ( C @ B ) @ ( D @ B ) )
| ~ ( sk2 @ ( C @ A ) @ ( D @ A ) )
| ~ ( sk2 @ A @ B )
| ( ( D
@ ^ [E: $i] :
( A
@ ( sk4
@ ^ [F: $i > $i] : ( sk2 @ ( C @ F ) @ ( D @ F ) )
@ B
@ A
@ E ) ) )
!= B )
| ( ( C
@ ^ [E: $i] :
( A
@ ( sk4
@ ^ [F: $i > $i] : ( sk2 @ ( C @ F ) @ ( D @ F ) )
@ B
@ A
@ E ) ) )
!= A ) ),
inference(simp,[status(thm)],[73]) ).
thf(30,plain,
! [E: ( $i > $i ) > $o,D: $i > $i,C: $i > $i,B: $i > $i,A: $i > $i] :
( ( sk2 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ $true
| ~ ( E
@ ^ [F: $i] : ( C @ ( sk4 @ E @ D @ C @ F ) ) )
| ( E @ D )
| ( ( sk3 @ B @ A @ A )
!= ( E @ C ) ) ),
inference(paramod_ordered,[status(thm)],[15,23]) ).
thf(31,plain,
! [E: ( $i > $i ) > $o,D: $i > $i,C: $i > $i,B: $i > $i,A: $i > $i] :
( ( sk2 @ A @ B )
| ~ ( sk2 @ C @ D )
| ~ ( E
@ ^ [F: $i] : ( C @ ( sk4 @ E @ D @ C @ F ) ) )
| ( E @ D )
| ( ( sk3 @ B @ A @ A )
!= ( E @ C ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(60,plain,
! [E: ( $i > $i ) > $o,D: $i > $i,C: $i > $i,B: $i > $i,A: $i > $i] :
( ( sk2 @ A @ B )
| ~ ( sk2 @ C @ D )
| ( ( ^ [F: $i] : ( C @ ( sk4 @ E @ D @ C @ F ) ) )
!= ( ^ [F: $i] :
( C
@ ( sk4
@ ( (=) @ ( $i > $i )
@ ^ [G: $i] : ( C @ ( sk4 @ E @ D @ C @ G ) ) )
@ D
@ C
@ F ) ) ) )
| ( ( ^ [F: $i] : ( C @ ( sk4 @ E @ D @ C @ F ) ) )
= D )
| ( ( sk3 @ B @ A @ A )
!= ( ( ^ [F: $i] : ( C @ ( sk4 @ E @ D @ C @ F ) ) )
= C ) ) ),
inference(replace_leibeq,[status(thm)],[31:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( (=) @ ( $i > $i ) @ ^ [F: $i] : ( C @ ( sk4 @ E @ D @ C @ F ) ) ))]]) ).
thf(63,plain,
! [E: ( $i > $i ) > $o,D: $i > $i,C: $i > $i,B: $i > $i,A: $i > $i] :
( ( ( ^ [F: $i] : ( C @ ( sk4 @ E @ D @ C @ F ) ) )
!= ( ^ [F: $i] :
( C
@ ( sk4
@ ( (=) @ ( $i > $i )
@ ^ [G: $i] : ( C @ ( sk4 @ E @ D @ C @ G ) ) )
@ D
@ C
@ F ) ) ) )
| ( ( ^ [F: $i] : ( C @ ( sk4 @ E @ D @ C @ F ) ) )
= D )
| ( sk2 @ A @ B )
| ~ ( sk2 @ C @ D )
| ( ( sk3 @ B @ A @ A )
!= ( ( ^ [F: $i] : ( C @ ( sk4 @ E @ D @ C @ F ) ) )
= C ) ) ),
inference(lifteq,[status(thm)],[60]) ).
thf(26,plain,
! [C: ( $i > $i ) > $o,B: $i > $i,A: $i > $i] :
( ~ ( sk2 @ A @ B )
| ~ ( C @ A )
| ( C @ ( sk4 @ C @ B @ A ) )
| ( C @ B ) ),
inference(simp,[status(thm)],[8]) ).
thf(1821,plain,
! [B: $i,A: $i > $i] :
( ( sk3 @ A
@ ^ [C: $i] : C
@ ^ [C: $i] : C )
| ( B != b )
| ( ( A @ B )
!= sk8 ) ),
inference(paramod_ordered,[status(thm)],[351,1778]) ).
thf(1825,plain,
! [A: $i] :
( ( sk3
@ ^ [B: $i] : sk8
@ ^ [B: $i] : B
@ ^ [B: $i] : B )
| ( A != b ) ),
inference(pre_uni,[status(thm)],[1821:[bind(A,$thf( ^ [C: $i] : sk8 ))]]) ).
thf(1827,plain,
( sk3
@ ^ [A: $i] : sk8
@ ^ [A: $i] : A
@ ^ [A: $i] : A ),
inference(pattern_uni,[status(thm)],[1825:[bind(A,$thf( b ))]]) ).
thf(2602,plain,
$false,
inference(e,[status(thm)],[1168,1796,1153,1824,601,22,3,16,250,1777,19,326,2321,24,1803,25,20,93,1815,1778,29,609,251,63,18,26,351,23,1827,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU938^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % 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
% 0.08/0.12 % Computer : n012.cluster.edu
% 0.08/0.12 % Model : x86_64 x86_64
% 0.08/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.12 % Memory : 8046.5625MB
% 0.08/0.12 % OS : Linux 6.8.0-71-generic
% 0.08/0.12 % CPULimit : 300
% 0.08/0.12 % WCLimit : 300
% 0.08/0.12 % DateTime : Tue Sep 29 14:46:48 UTC 2026
% 0.08/0.12 % CPUTime :
% 0.08/0.12 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
% 0.40/0.40 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.56/0.50 % [INFO] Parsing done (100ms).
% 0.56/0.51 % [INFO] Running in sequential loop mode.
% 1.03/0.74 % [INFO] eprover registered as external prover.
% 1.03/0.74 % [INFO] Scanning for conjecture ...
% 1.24/0.83 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.24/0.85 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.24/0.85 % [INFO] Problem is higher-order (TPTP THF).
% 1.24/0.85 % [INFO] Type checking passed.
% 1.24/0.86 % [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 ...
% 32.42/8.92 % External prover 'e' found a proof!
% 32.42/8.92 % [INFO] Killing All external provers ...
% 32.42/8.92 % Time passed: 8733ms (effective reasoning time: 8414ms)
% 32.42/8.92 % 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)>
% 32.42/8.93 % Axioms used in derivation (0):
% 32.42/8.93 % No. of inferences in proof: 84
% 32.42/8.93 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 8733 ms resp. 8414 ms w/o parsing
% 32.42/9.02 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 32.42/9.02 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------