%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV248^5 : 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 : 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 08:37:04 AM UTC 2026
% Result : Theorem 13.24s 3.36s
% Output : Refutation 11.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 71
% Number of leaves : 9
% Syntax : Number of formulae : 91 ( 22 unt; 0 typ; 8 def)
% Number of atoms : 788 ( 760 equ; 104 cnn)
% Maximal formula atoms : 20 ( 8 avg)
% Number of connectives : 808 ( 105 ~; 335 |; 21 &; 347 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 200 ( 35 ^; 157 !; 0 ?; 200 :)
% ( 0 !>; 0 ?*; 0 @-; 8 @+)
% Comments :
%------------------------------------------------------------------------------
thf(a_type,type,
a: $tType ).
thf(sk1_decl,type,
sk1: a ).
thf(sk2_decl,type,
sk2: a ).
thf(sk3_decl,type,
sk3: a ).
thf(sk4_decl,type,
sk4: a ).
thf(sk5_decl,type,
sk5: a > $o ).
thf(sk6_decl,type,
sk6: a > ( a > $o ) > a ).
thf(sk9_decl,type,
sk9: a > ( a > $o ) > a ).
thf(sk31_decl,type,
sk31: ( a > $o ) > a ).
thf(sk1_def,definition,
( sk1
= ( @+[A: a] :
~ ! [B: a,C: a,D: a] :
( ( ! [E: a > $o] :
( ( ( E
= ( (=) @ a @ A ) )
| ! [F: a] :
( ( E @ F )
= ( ( F = A )
| ( F = B ) ) ) )
= ( ( E
= ( (=) @ a @ C ) )
| ! [F: a] :
( ( E @ F )
= ( ( F = C )
| ( F = D ) ) ) ) ) )
= ( ( A = C )
& ( B = D ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: a] :
~ ! [B: a,C: a] :
( ( ! [D: a > $o] :
( ( ( D
= ( (=) @ a @ sk1 ) )
| ! [E: a] :
( ( D @ E )
= ( ( E = sk1 )
| ( E = A ) ) ) )
= ( ( D
= ( (=) @ a @ B ) )
| ! [E: a] :
( ( D @ E )
= ( ( E = B )
| ( E = C ) ) ) ) ) )
= ( ( sk1 = B )
& ( A = C ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: a] :
~ ! [B: a] :
( ( ! [C: a > $o] :
( ( ( C
= ( (=) @ a @ sk1 ) )
| ! [D: a] :
( ( C @ D )
= ( ( D = sk1 )
| ( D = sk2 ) ) ) )
= ( ( C
= ( (=) @ a @ A ) )
| ! [D: a] :
( ( C @ D )
= ( ( D = A )
| ( D = B ) ) ) ) ) )
= ( ( sk1 = A )
& ( sk2 = B ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: a] :
( ( ! [B: a > $o] :
( ( ( B
= ( (=) @ a @ sk1 ) )
| ! [C: a] :
( ( B @ C )
= ( ( C = sk1 )
| ( C = sk2 ) ) ) )
= ( ( B
= ( (=) @ a @ sk3 ) )
| ! [C: a] :
( ( B @ C )
= ( ( C = sk3 )
| ( C = A ) ) ) ) ) )
!= ( ( sk1 = sk3 )
& ( sk2 = A ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: a > $o] :
( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) )
!= ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: a,B: a > $o] :
@+[C: a] :
( ( B @ C )
!= ( ( C = sk1 )
| ( C = sk2 ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: a,B: a > $o] :
@+[C: a] :
( ( B @ C )
!= ( ( C = sk1 )
| ( C = sk2 ) ) ) ) ) ).
thf(sk31_def,definition,
( sk31
= ( ^ [A: a > $o] :
@+[B: a] :
( ( A @ B )
!= ( ( B = sk1 )
| ( B = sk4 ) ) ) ) ) ).
thf(1,conjecture,
! [A: a,B: a,C: a,D: a] :
( ( ! [E: a > $o] :
( ( ( E
= ( (=) @ a @ A ) )
| ! [F: a] :
( ( E @ F )
= ( ( F = A )
| ( F = B ) ) ) )
= ( ( E
= ( (=) @ a @ C ) )
| ! [F: a] :
( ( E @ F )
= ( ( F = C )
| ( F = D ) ) ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM103_pme) ).
thf(2,negated_conjecture,
~ ! [A: a,B: a,C: a,D: a] :
( ( ! [E: a > $o] :
( ( ( E
= ( (=) @ a @ A ) )
| ! [F: a] :
( ( E @ F )
= ( ( F = A )
| ( F = B ) ) ) )
= ( ( E
= ( (=) @ a @ C ) )
| ! [F: a] :
( ( E @ F )
= ( ( F = C )
| ( F = D ) ) ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(3,plain,
~ ! [A: a,B: a,C: a,D: a] :
( ( ! [E: a > $o] :
( ( ( E
= ( (=) @ a @ A ) )
| ! [F: a] :
( ( E @ F )
= ( ( F = A )
| ( F = B ) ) ) )
= ( ( E
= ( (=) @ a @ C ) )
| ! [F: a] :
( ( E @ F )
= ( ( F = C )
| ( F = D ) ) ) ) ) )
= ( ( A = C )
& ( B = D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(4,plain,
( ( ! [A: a > $o] :
( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) )
= ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) ) ) )
!= ( ( sk1 = sk3 )
& ( sk2 = sk4 ) ) ),
inference(cnf,[status(esa)],[3]) ).
thf(5,plain,
( ( ( sk1 = sk3 )
& ( sk2 = sk4 ) )
!= ( ! [A: a > $o] :
( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) )
= ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) ) ) ) ),
inference(lifteq,[status(thm)],[4]) ).
thf(7,plain,
( ( ( sk1 = sk3 )
& ( sk2 = sk4 ) )
| ! [A: a > $o] :
( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) )
= ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(10,plain,
! [A: a > $o] :
( ( ( sk1 = sk3 )
| ( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) )
= ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) ) ) )
& ( ( sk2 = sk4 )
| ( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) )
= ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) ) ) ) ),
inference(cnf,[status(esa)],[7]) ).
thf(12,plain,
! [A: a > $o] :
( ( sk2 = sk4 )
| ( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) )
= ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) ) ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(14,plain,
! [A: a > $o] :
( ( sk4 = sk2 )
| ( ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) )
= ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) ) ) ),
inference(lifteq,[status(thm)],[12]) ).
thf(37,plain,
! [A: a > $o] :
( ( sk4 = sk2 )
| ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) )
| ~ ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) ) ),
inference(bool_ext,[status(thm)],[14]) ).
thf(59,plain,
! [B: a,A: a > $o] :
( ( ( sk4 = sk2 )
| ( A
= ( (=) @ a @ sk3 ) )
| ( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) )
| ( A
!= ( (=) @ a @ sk1 ) ) )
& ( ( sk4 = sk2 )
| ( A
= ( (=) @ a @ sk3 ) )
| ( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) )
| ( ( A @ ( sk9 @ B @ A ) )
!= ( ( ( sk9 @ B @ A )
= sk1 )
| ( ( sk9 @ B @ A )
= sk2 ) ) ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(61,plain,
! [B: a,A: a > $o] :
( ( sk4 = sk2 )
| ( A
= ( (=) @ a @ sk3 ) )
| ( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) )
| ( ( A @ ( sk9 @ B @ A ) )
!= ( ( ( sk9 @ B @ A )
= sk1 )
| ( ( sk9 @ B @ A )
= sk2 ) ) ) ),
inference(cnfConj,[status(thm)],[59]) ).
thf(64,plain,
! [B: a,A: a > $o] :
( ( A
= ( (=) @ a @ sk3 ) )
| ( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) )
| ( ( A @ ( sk9 @ B @ A ) )
!= ( ( ( sk9 @ B @ A )
= sk1 )
| ( ( sk9 @ B @ A )
= sk2 ) ) )
| ( sk4 = sk2 ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(11,plain,
! [A: a > $o] :
( ( sk1 = sk3 )
| ( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) )
= ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) ) ) ),
inference(cnfConj,[status(thm)],[10]) ).
thf(13,plain,
! [A: a > $o] :
( ( sk3 = sk1 )
| ( ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) )
= ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) ) ) ),
inference(lifteq,[status(thm)],[11]) ).
thf(16,plain,
! [A: a > $o] :
( ( sk3 = sk1 )
| ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) )
| ~ ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) ) ),
inference(bool_ext,[status(thm)],[13]) ).
thf(24,plain,
! [B: a,A: a > $o] :
( ( ( sk3 = sk1 )
| ( A
= ( (=) @ a @ sk3 ) )
| ( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) )
| ( A
!= ( (=) @ a @ sk1 ) ) )
& ( ( sk3 = sk1 )
| ( A
= ( (=) @ a @ sk3 ) )
| ( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) )
| ( ( A @ ( sk6 @ B @ A ) )
!= ( ( ( sk6 @ B @ A )
= sk1 )
| ( ( sk6 @ B @ A )
= sk2 ) ) ) ) ),
inference(cnf,[status(esa)],[16]) ).
thf(25,plain,
! [B: a,A: a > $o] :
( ( sk3 = sk1 )
| ( A
= ( (=) @ a @ sk3 ) )
| ( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) )
| ( A
!= ( (=) @ a @ sk1 ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(27,plain,
! [B: a,A: a > $o] :
( ( A
= ( (=) @ a @ sk3 ) )
| ( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) )
| ( A
!= ( (=) @ a @ sk1 ) )
| ( sk3 = sk1 ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(28,plain,
! [A: a] :
( ( ( (=) @ a @ sk3 )
= ( (=) @ a @ sk1 ) )
| ( ( ( A = sk3 )
| ( A = sk4 ) )
= ( sk1 = A ) )
| ( sk3 = sk1 ) ),
inference(simp,[status(thm)],[27]) ).
thf(161,plain,
! [A: a] :
( ( ( (=) @ a @ sk3 )
= ( (=) @ a @ sk1 ) )
| ( sk3 = sk1 )
| ~ ( ( A = sk3 )
| ( A = sk4 ) )
| ( sk1 = A ) ),
inference(bool_ext,[status(thm)],[28]) ).
thf(230,plain,
! [A: a] :
( ( sk1 = A )
| ( ( (=) @ a @ sk3 )
= ( (=) @ a @ sk1 ) )
| ( sk3 = sk1 )
| ~ ( ( A = sk3 )
| ( A = sk4 ) ) ),
inference(lifteq,[status(thm)],[161]) ).
thf(238,plain,
! [A: a] :
( ( ( sk1 = A )
| ( ( (=) @ a @ sk3 )
= ( (=) @ a @ sk1 ) )
| ( sk3 = sk1 )
| ( A != sk3 ) )
& ( ( sk1 = A )
| ( ( (=) @ a @ sk3 )
= ( (=) @ a @ sk1 ) )
| ( sk3 = sk1 )
| ( A != sk4 ) ) ),
inference(cnf,[status(esa)],[230]) ).
thf(239,plain,
! [A: a] :
( ( sk1 = A )
| ( ( (=) @ a @ sk3 )
= ( (=) @ a @ sk1 ) )
| ( sk3 = sk1 )
| ( A != sk3 ) ),
inference(cnfConj,[status(thm)],[238]) ).
thf(241,plain,
! [A: a] :
( ( A != sk3 )
| ( sk1 = A )
| ( ( (=) @ a @ sk3 )
= ( (=) @ a @ sk1 ) )
| ( sk3 = sk1 ) ),
inference(lifteq,[status(thm)],[239]) ).
thf(242,plain,
( ( sk3 = sk1 )
| ( ( (=) @ a @ sk3 )
= ( (=) @ a @ sk1 ) ) ),
inference(simp,[status(thm)],[241]) ).
thf(248,plain,
! [A: a] :
( ( ( sk3 = A )
= ( sk1 = A ) )
| ( sk3 = sk1 ) ),
inference(func_ext,[status(esa)],[242]) ).
thf(300,plain,
! [A: a] :
( ( sk3 = sk1 )
| ( sk3 != A )
| ( sk1 = A ) ),
inference(bool_ext,[status(thm)],[248]) ).
thf(360,plain,
! [A: a] :
( ( sk3 != A )
| ( sk1 = A )
| ( sk3 = sk1 ) ),
inference(lifteq,[status(thm)],[300]) ).
thf(365,plain,
sk3 = sk1,
inference(simp,[status(thm)],[360]) ).
thf(373,plain,
! [A: a > $o] :
( ( sk4 = sk2 )
| ( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk4 ) ) ) )
= ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) ) ) ),
inference(rewrite,[status(thm)],[14,365]) ).
thf(6,plain,
( ~ ( ( sk1 = sk3 )
& ( sk2 = sk4 ) )
| ~ ! [A: a > $o] :
( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) )
= ( ( A
= ( (=) @ a @ sk3 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk3 )
| ( B = sk4 ) ) ) ) ) ),
inference(bool_ext,[status(thm)],[5]) ).
thf(8,plain,
( ( sk1 != sk3 )
| ( sk2 != sk4 )
| ( ( ( sk5
= ( (=) @ a @ sk1 ) )
| ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk2 ) ) ) )
!= ( ( sk5
= ( (=) @ a @ sk3 ) )
| ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk3 )
| ( A = sk4 ) ) ) ) ) ),
inference(cnf,[status(esa)],[6]) ).
thf(9,plain,
( ( sk3 != sk1 )
| ( sk4 != sk2 )
| ( ( ( sk5
= ( (=) @ a @ sk3 ) )
| ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk3 )
| ( A = sk4 ) ) ) )
!= ( ( sk5
= ( (=) @ a @ sk1 ) )
| ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk2 ) ) ) ) ) ),
inference(lifteq,[status(thm)],[8]) ).
thf(374,plain,
( ( sk1 != sk1 )
| ( sk4 != sk2 )
| ( ( ( sk5
= ( (=) @ a @ sk1 ) )
| ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk4 ) ) ) )
!= ( ( sk5
= ( (=) @ a @ sk1 ) )
| ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk2 ) ) ) ) ) ),
inference(rewrite,[status(thm)],[9,365]) ).
thf(375,plain,
( ( sk4 != sk2 )
| ( ( ( sk5
= ( (=) @ a @ sk1 ) )
| ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk4 ) ) ) )
!= ( ( sk5
= ( (=) @ a @ sk1 ) )
| ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk2 ) ) ) ) ) ),
inference(simp,[status(thm)],[374]) ).
thf(417,plain,
( ( sk4 != sk2 )
| ( ( sk5
= ( (=) @ a @ sk1 ) )
!= ( sk5
= ( (=) @ a @ sk1 ) ) )
| ( ( ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk4 ) ) ) )
!= ( ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk2 ) ) ) ) ) ),
inference(simp,[status(thm)],[375]) ).
thf(420,plain,
( ( sk4 != sk2 )
| ( ( ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk4 ) ) ) )
!= ( ! [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk2 ) ) ) ) ) ),
inference(simp,[status(thm)],[417]) ).
thf(434,plain,
( ( sk4 != sk2 )
| ( ( ^ [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk4 ) ) ) )
!= ( ^ [A: a] :
( ( sk5 @ A )
= ( ( A = sk1 )
| ( A = sk2 ) ) ) ) ) ),
inference(simp,[status(thm)],[420]) ).
thf(441,plain,
( ( sk4 != sk2 )
| ( sk5 != sk5 )
| ( ( ^ [A: a] :
( ( A = sk1 )
| ( A = sk4 ) ) )
!= ( ^ [A: a] :
( ( A = sk1 )
| ( A = sk2 ) ) ) ) ),
inference(simp,[status(thm)],[434]) ).
thf(443,plain,
( ( sk4 != sk2 )
| ( ( ^ [A: a] :
( ( A = sk1 )
| ( A = sk4 ) ) )
!= ( ^ [A: a] :
( ( A = sk1 )
| ( A = sk2 ) ) ) ) ),
inference(simp,[status(thm)],[441]) ).
thf(444,plain,
( ( sk4 != sk2 )
| ( ( ^ [A: a] : ( A = sk1 ) )
!= ( ^ [A: a] : ( A = sk1 ) ) )
| ( ( ^ [A: a] : ( A = sk4 ) )
!= ( ^ [A: a] : ( A = sk2 ) ) ) ),
inference(simp,[status(thm)],[443]) ).
thf(446,plain,
( ( sk4 != sk2 )
| ( ( ^ [A: a] : ( A = sk4 ) )
!= ( ^ [A: a] : ( A = sk2 ) ) ) ),
inference(simp,[status(thm)],[444]) ).
thf(447,plain,
( ( sk4 != sk2 )
| ( ( ^ [A: a] : A )
!= ( ^ [A: a] : A ) )
| ( ( ^ [A: a] : sk4 )
!= ( ^ [A: a] : sk2 ) ) ),
inference(simp,[status(thm)],[446]) ).
thf(449,plain,
( ( sk4 != sk2 )
| ( ( ^ [A: a] : sk4 )
!= ( ^ [A: a] : sk2 ) ) ),
inference(simp,[status(thm)],[447]) ).
thf(450,plain,
( ( sk4 != sk2 )
| ( sk4 != sk2 ) ),
inference(func_ext,[status(esa)],[449]) ).
thf(451,plain,
sk4 != sk2,
inference(simp,[status(thm)],[450]) ).
thf(469,plain,
! [A: a > $o] :
( ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk4 ) ) ) )
= ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) ) ),
inference(simplifyReflect,[status(thm)],[373,451]) ).
thf(472,plain,
! [A: a > $o] :
( ~ ( ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk4 ) ) ) )
| ( A
= ( (=) @ a @ sk1 ) )
| ! [B: a] :
( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) ),
inference(bool_ext,[status(thm)],[469]) ).
thf(475,plain,
! [B: a,A: a > $o] :
( ( ( A
!= ( (=) @ a @ sk1 ) )
| ( A
= ( (=) @ a @ sk1 ) )
| ( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) )
& ( ( ( A @ ( sk31 @ A ) )
!= ( ( ( sk31 @ A )
= sk1 )
| ( ( sk31 @ A )
= sk4 ) ) )
| ( A
= ( (=) @ a @ sk1 ) )
| ( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) ) ),
inference(cnf,[status(esa)],[472]) ).
thf(477,plain,
! [B: a,A: a > $o] :
( ( ( A @ ( sk31 @ A ) )
!= ( ( ( sk31 @ A )
= sk1 )
| ( ( sk31 @ A )
= sk4 ) ) )
| ( A
= ( (=) @ a @ sk1 ) )
| ( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) ),
inference(cnfConj,[status(thm)],[475]) ).
thf(480,plain,
! [B: a,A: a > $o] :
( ( ( A @ ( sk31 @ A ) )
!= ( ( ( sk31 @ A )
= sk1 )
| ( ( sk31 @ A )
= sk4 ) ) )
| ( A
= ( (=) @ a @ sk1 ) )
| ( ( A @ B )
= ( ( B = sk1 )
| ( B = sk2 ) ) ) ),
inference(lifteq,[status(thm)],[477]) ).
thf(552,plain,
! [A: a] :
( ( ( ( A = sk1 )
| ( A = sk4 ) )
= ( ( A = sk1 )
| ( A = sk2 ) ) )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk4 ) ) )
= ( (=) @ a @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[480:[bind(A,$thf( ^ [C: a] : ( ( C = sk1 ) | ( C = sk4 ) ) )),bind(B,$thf( B ))]]) ).
thf(642,plain,
! [A: a] :
( ( ( ( A = sk1 )
| ( A = sk4 ) )
= ( ( A = sk1 )
| ( A = sk2 ) ) )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk4 ) ) )
= ( (=) @ a @ sk1 ) ) ),
inference(simp,[status(thm)],[552]) ).
thf(676,plain,
! [B: a,A: a] :
( ( ( ( B = sk1 )
| ( B = sk4 ) )
= ( sk1 = B ) )
| ( ( ( A = sk1 )
| ( A = sk4 ) )
= ( ( A = sk1 )
| ( A = sk2 ) ) ) ),
inference(func_ext,[status(esa)],[642]) ).
thf(696,plain,
! [B: a,A: a] :
( ~ ( ( B = sk1 )
| ( B = sk4 ) )
| ( sk1 = B )
| ~ ( ( A = sk1 )
| ( A = sk4 ) )
| ( A = sk1 )
| ( A = sk2 ) ),
inference(bool_ext,[status(thm)],[676]) ).
thf(729,plain,
! [B: a,A: a] :
( ( sk1 = B )
| ~ ( ( B = sk1 )
| ( B = sk4 ) )
| ~ ( ( A = sk1 )
| ( A = sk4 ) )
| ( A = sk1 )
| ( A = sk2 ) ),
inference(lifteq,[status(thm)],[696]) ).
thf(793,plain,
! [B: a,A: a] :
( ( ( sk1 = B )
| ( B != sk1 )
| ( A != sk1 )
| ( A = sk1 )
| ( A = sk2 ) )
& ( ( sk1 = B )
| ( B != sk1 )
| ( A != sk4 )
| ( A = sk1 )
| ( A = sk2 ) )
& ( ( sk1 = B )
| ( B != sk4 )
| ( A != sk1 )
| ( A = sk1 )
| ( A = sk2 ) )
& ( ( sk1 = B )
| ( B != sk4 )
| ( A != sk4 )
| ( A = sk1 )
| ( A = sk2 ) ) ),
inference(cnf,[status(esa)],[729]) ).
thf(797,plain,
! [B: a,A: a] :
( ( sk1 = B )
| ( B != sk4 )
| ( A != sk4 )
| ( A = sk1 )
| ( A = sk2 ) ),
inference(cnfConj,[status(thm)],[793]) ).
thf(804,plain,
! [B: a,A: a] :
( ( B != sk4 )
| ( A != sk4 )
| ( A = sk1 )
| ( A = sk2 )
| ( sk1 = B ) ),
inference(lifteq,[status(thm)],[797]) ).
thf(805,plain,
( ( sk4 = sk1 )
| ( sk4 = sk2 ) ),
inference(simp,[status(thm)],[804]) ).
thf(835,plain,
sk4 = sk1,
inference(simplifyReflect,[status(thm)],[805,451]) ).
thf(1236,plain,
! [B: a,A: a > $o] :
( ( A
= ( (=) @ a @ sk1 ) )
| ( ( A @ B )
= ( ( B = sk1 )
| ( B = sk1 ) ) )
| ( ( A @ ( sk9 @ B @ A ) )
!= ( ( ( sk9 @ B @ A )
= sk1 )
| ( ( sk9 @ B @ A )
= sk2 ) ) )
| ( sk2 = sk1 ) ),
inference(rewrite,[status(thm)],[64,835,365]) ).
thf(1237,plain,
! [B: a,A: a > $o] :
( ( A
= ( (=) @ a @ sk1 ) )
| ( ( A @ B )
= ( B = sk1 ) )
| ( ( A @ ( sk9 @ B @ A ) )
!= ( ( ( sk9 @ B @ A )
= sk1 )
| ( ( sk9 @ B @ A )
= sk2 ) ) )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[1236]) ).
thf(840,plain,
sk2 != sk1,
inference(rewrite,[status(thm)],[451,835]) ).
thf(1238,plain,
! [B: a,A: a > $o] :
( ( A
= ( (=) @ a @ sk1 ) )
| ( ( A @ B )
= ( B = sk1 ) )
| ( ( A @ ( sk9 @ B @ A ) )
!= ( ( ( sk9 @ B @ A )
= sk1 )
| ( ( sk9 @ B @ A )
= sk2 ) ) ) ),
inference(simplifyReflect,[status(thm)],[1237,840]) ).
thf(1239,plain,
! [A: a] :
( ( ( ( A = sk1 )
| ( A = sk2 ) )
= ( A = sk1 ) )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk1 ) ) ),
inference(pre_uni,[status(thm)],[1238:[bind(A,$thf( ^ [C: a] : ( ( C = sk1 ) | ( C = sk2 ) ) )),bind(B,$thf( B ))]]) ).
thf(1357,plain,
! [A: a] :
( ( ( ( A = sk1 )
| ( A = sk2 ) )
= ( A = sk1 ) )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk1 ) ) ),
inference(simp,[status(thm)],[1239]) ).
thf(1401,plain,
! [A: a] :
( ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk1 ) )
| ~ ( ( A = sk1 )
| ( A = sk2 ) )
| ( A = sk1 ) ),
inference(bool_ext,[status(thm)],[1357]) ).
thf(1412,plain,
! [A: a] :
( ( A = sk1 )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk1 ) )
| ~ ( ( A = sk1 )
| ( A = sk2 ) ) ),
inference(lifteq,[status(thm)],[1401]) ).
thf(1414,plain,
! [A: a] :
( ( ( A = sk1 )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk1 ) )
| ( A != sk1 ) )
& ( ( A = sk1 )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk1 ) )
| ( A != sk2 ) ) ),
inference(cnf,[status(esa)],[1412]) ).
thf(1416,plain,
! [A: a] :
( ( A = sk1 )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk1 ) )
| ( A != sk2 ) ),
inference(cnfConj,[status(thm)],[1414]) ).
thf(1419,plain,
! [A: a] :
( ( A != sk2 )
| ( A = sk1 )
| ( ( ^ [B: a] :
( ( B = sk1 )
| ( B = sk2 ) ) )
= ( (=) @ a @ sk1 ) ) ),
inference(lifteq,[status(thm)],[1416]) ).
thf(1420,plain,
( ( sk2 = sk1 )
| ( ( ^ [A: a] :
( ( A = sk1 )
| ( A = sk2 ) ) )
= ( (=) @ a @ sk1 ) ) ),
inference(simp,[status(thm)],[1419]) ).
thf(1424,plain,
( ( ^ [A: a] :
( ( A = sk1 )
| ( A = sk2 ) ) )
= ( (=) @ a @ sk1 ) ),
inference(simplifyReflect,[status(thm)],[1420,840]) ).
thf(1425,plain,
! [A: a] :
( ( ( A = sk1 )
| ( A = sk2 ) )
= ( sk1 = A ) ),
inference(func_ext,[status(esa)],[1424]) ).
thf(1440,plain,
! [A: a] :
( ~ ( ( A = sk1 )
| ( A = sk2 ) )
| ( sk1 = A ) ),
inference(bool_ext,[status(thm)],[1425]) ).
thf(1460,plain,
! [A: a] :
( ( sk1 = A )
| ~ ( ( A = sk1 )
| ( A = sk2 ) ) ),
inference(lifteq,[status(thm)],[1440]) ).
thf(1471,plain,
! [A: a] :
( ( ( sk1 = A )
| ( A != sk1 ) )
& ( ( sk1 = A )
| ( A != sk2 ) ) ),
inference(cnf,[status(esa)],[1460]) ).
thf(1473,plain,
! [A: a] :
( ( sk1 = A )
| ( A != sk2 ) ),
inference(cnfConj,[status(thm)],[1471]) ).
thf(1476,plain,
! [A: a] :
( ( A != sk2 )
| ( sk1 = A ) ),
inference(lifteq,[status(thm)],[1473]) ).
thf(1477,plain,
sk2 = sk1,
inference(simp,[status(thm)],[1476]) ).
thf(1489,plain,
$false,
inference(simplifyReflect,[status(thm)],[1477,840]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEV248^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % 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
% 0.06/0.12 % Computer : n012.cluster.edu
% 0.06/0.12 % Model : x86_64 x86_64
% 0.06/0.12 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.12 % Memory : 8046.5625MB
% 0.06/0.12 % OS : Linux 6.8.0-71-generic
% 0.06/0.12 % CPULimit : 300
% 0.06/0.12 % WCLimit : 300
% 0.06/0.12 % DateTime : Tue Sep 29 15:26:48 UTC 2026
% 0.06/0.12 % CPUTime :
% 0.06/0.12 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
% 0.38/0.40 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.54/0.49 % [INFO] Parsing done (89ms).
% 0.54/0.50 % [INFO] Running in sequential loop mode.
% 0.85/0.69 % [INFO] eprover registered as external prover.
% 0.85/0.69 % [INFO] Scanning for conjecture ...
% 1.00/0.73 % [INFO] Found a conjecture (or negated_conjecture) and 0 axioms. Running axiom selection ...
% 1.00/0.75 % [INFO] Axiom selection finished. Selected 0 axioms (removed 0 axioms).
% 1.00/0.75 % [INFO] Problem is higher-order (TPTP THF).
% 1.00/0.76 % [INFO] Type checking passed.
% 1.00/0.76 % [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 ...
% 13.24/3.35 % [INFO] Killing All external provers ...
% 13.24/3.36 % Time passed: 3161ms (effective reasoning time: 2853ms)
% 13.24/3.36 % 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)>
% 13.24/3.36 % Axioms used in derivation (0):
% 13.24/3.36 % No. of inferences in proof: 83
% 13.24/3.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3161 ms resp. 2853 ms w/o parsing
% 11.38/3.42 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.38/3.42 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------