%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUN056+2 : TPTP v9.3.1. Released v7.3.0.
% 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 : Sun Sep 27 08:18:36 AM UTC 2026
% Result : Theorem 9.33s 3.27s
% Output : Refutation 8.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 28
% Syntax : Number of formulae : 127 ( 50 unt; 0 typ; 16 def)
% Number of atoms : 478 ( 150 equ; 0 cnn)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 1264 ( 204 ~; 165 |; 128 &; 767 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 3 con; 0-3 aty)
% Number of variables : 384 ( 24 ^; 263 !; 81 ?; 384 :)
% ( 0 !>; 0 ?*; 0 @-; 16 @+)
% Comments :
%------------------------------------------------------------------------------
thf(r2_decl,type,
r2: $i > $i > $o ).
thf(r1_decl,type,
r1: $i > $o ).
thf(r3_decl,type,
r3: $i > $i > $i > $o ).
thf(r4_decl,type,
r4: $i > $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i > $i ).
thf(sk8_decl,type,
sk8: $i > $i > $i ).
thf(sk9_decl,type,
sk9: $i > $i > $i ).
thf(sk10_decl,type,
sk10: $i > $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
! [B: $i] :
( ( ( B = A )
& ( B @ r1 ) )
| ( ( B != A )
& ~ ( B @ r1 ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i] :
@+[B: $i] :
! [C: $i] :
( ( ( C = B )
& ( C @ ( A @ r2 ) ) )
| ( ( C != B )
& ~ ( C @ ( A @ r2 ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
! [D: $i] :
( ( ( D = C )
& ( D @ ( A @ ( B @ r3 ) ) ) )
| ( ( D != C )
& ~ ( D @ ( A @ ( B @ r3 ) ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( D @ ( A @ ( B @ r3 ) ) )
& ( C @ ( D @ r2 ) ) )
& ? [D: $i] :
( ( D = C )
& ? [E: $i] :
( ( D @ ( E @ ( B @ r3 ) ) )
& ( E @ ( A @ r2 ) ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C
= ( B @ ( A @ sk5 ) ) )
& ? [D: $i] :
( ( C @ ( D @ ( B @ r3 ) ) )
& ( D @ ( A @ r2 ) ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( B @ ( A @ sk6 ) @ ( C @ ( B @ r3 ) ) )
& ( C @ ( A @ r2 ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ ( A @ ( B @ r3 ) ) )
& ( B @ ( A @ sk5 ) @ ( C @ r2 ) ) ) ) ) ).
thf(sk9_def,definition,
( sk9
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( D @ ( A @ ( B @ r4 ) ) )
& ( C @ ( B @ ( D @ r3 ) ) ) )
& ? [D: $i] :
( ( D = C )
& ? [E: $i] :
( ( D @ ( E @ ( B @ r4 ) ) )
& ( E @ ( A @ r2 ) ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C
= ( B @ ( A @ sk9 ) ) )
& ? [D: $i] :
( ( C @ ( D @ ( B @ r4 ) ) )
& ( D @ ( A @ r2 ) ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( B @ ( A @ sk10 ) @ ( C @ ( B @ r4 ) ) )
& ( C @ ( A @ r2 ) ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ ( A @ ( B @ r4 ) ) )
& ( B @ ( A @ sk9 ) @ ( B @ ( C @ r3 ) ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] :
( ( B = A )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r3 ) ) )
& ( C @ r1 ) ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i] :
@+[B: $i] :
( ( A @ sk13 @ ( B @ ( A @ r3 ) ) )
& ( B @ r1 ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i] :
@+[B: $i] :
( ? [C: $i] :
( ( B = C )
& ( C @ r1 ) )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r4 ) ) )
& ( C @ r1 ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i] :
@+[B: $i] :
( ( A @ sk15 @ ( B @ ( A @ r4 ) ) )
& ( B @ r1 ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i] :
@+[B: $i] :
( ( ( A @ sk15 )
= B )
& ( B @ r1 ) ) ) ) ).
thf(11,axiom,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( B = C )
& ( C @ r1 ) )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r4 ) ) )
& ( C @ r1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).
thf(88,plain,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( B = C )
& ( C @ r1 ) )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r4 ) ) )
& ( C @ r1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(3,axiom,
? [A: $i] :
! [B: $i] :
( ( ( B = A )
& ( B @ r1 ) )
| ( ( B != A )
& ~ ( B @ r1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(18,plain,
? [A: $i] :
! [B: $i] :
( ( ( B = A )
& ( B @ r1 ) )
| ( ( B != A )
& ~ ( B @ r1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(19,plain,
! [A: $i] :
( ( ( A = sk1 )
| ( A != sk1 ) )
& ( ( A @ r1 )
| ( A != sk1 ) )
& ( ( A = sk1 )
| ~ ( A @ r1 ) )
& ( ( A @ r1 )
| ~ ( A @ r1 ) ) ),
inference(cnf,[status(esa)],[18]) ).
thf(22,plain,
! [A: $i] :
( ( A @ r1 )
| ( A != sk1 ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(25,plain,
! [A: $i] :
( ( A @ r1 )
| ( A != sk1 ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(26,plain,
sk1 @ r1,
inference(simp,[status(thm)],[25]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2 ) )
| ! [C: $i] :
( ( C != B )
| ~ ( C @ r1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).
thf(104,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2 ) )
| ! [C: $i] :
( ( C != B )
| ~ ( C @ r1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ( C != B )
| ~ ( C @ r1 ) ),
inference(cnf,[status(esa)],[104]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( C @ r1 )
| ( C != B ) ),
inference(lifteq,[status(thm)],[105]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( B @ r1 ) ),
inference(simp,[status(thm)],[106]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( A @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26,107]) ).
thf(115,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( A @ r2 ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(116,plain,
! [A: $i] :
~ ( sk1 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[115:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(10,axiom,
! [A: $i] :
? [B: $i] :
( ( B = A )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r3 ) ) )
& ( C @ r1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).
thf(82,plain,
! [A: $i] :
? [B: $i] :
( ( B = A )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r3 ) ) )
& ( C @ r1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(83,plain,
! [A: $i] :
( ( ( A @ sk13 )
= A )
& ( A @ sk13 @ ( A @ sk14 @ ( A @ r3 ) ) )
& ( A @ sk14 @ r1 ) ),
inference(cnf,[status(esa)],[82]) ).
thf(84,plain,
! [A: $i] : ( A @ sk14 @ r1 ),
inference(cnfConj,[status(thm)],[83]) ).
thf(21,plain,
! [A: $i] :
( ( A = sk1 )
| ~ ( A @ r1 ) ),
inference(cnfConj,[status(thm)],[19]) ).
thf(24,plain,
! [A: $i] :
( ~ ( A @ r1 )
| ( A = sk1 ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(278,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ( B = sk1 ) ),
inference(paramod_ordered,[status(thm)],[84,24]) ).
thf(279,plain,
! [B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ( B = sk1 ) ),
inference(simp,[status(thm)],[278]) ).
thf(280,plain,
! [A: $i] :
( ( A @ sk14 )
= sk1 ),
inference(pattern_uni,[status(thm)],[279:[bind(A,$thf( C )),bind(B,$thf( C @ sk14 ))]]) ).
thf(307,plain,
! [A: $i] :
( ( A @ sk14 )
= sk1 ),
inference(simp,[status(thm)],[280]) ).
thf(8,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r4 ) ) )
& ( C @ ( A @ ( D @ r3 ) ) ) )
& ? [D: $i] :
( ( D = C )
& ? [E: $i] :
( ( D @ ( E @ ( A @ r4 ) ) )
& ( E @ ( B @ r2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).
thf(70,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r4 ) ) )
& ( C @ ( A @ ( D @ r3 ) ) ) )
& ? [D: $i] :
( ( D = C )
& ? [E: $i] :
( ( D @ ( E @ ( A @ r4 ) ) )
& ( E @ ( B @ r2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(89,plain,
! [A: $i] :
( ( ( A @ sk15 )
= ( A @ sk17 ) )
& ( A @ sk17 @ r1 )
& ( A @ sk15 @ ( A @ sk16 @ ( A @ r4 ) ) )
& ( A @ sk16 @ r1 ) ),
inference(cnf,[status(esa)],[88]) ).
thf(90,plain,
! [A: $i] : ( A @ sk16 @ r1 ),
inference(cnfConj,[status(thm)],[89]) ).
thf(301,plain,
! [B: $i,A: $i] :
( ( ( A @ sk16 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ( B = sk1 ) ),
inference(paramod_ordered,[status(thm)],[90,24]) ).
thf(302,plain,
! [B: $i,A: $i] :
( ( ( A @ sk16 @ r1 )
!= ( B @ r1 ) )
| ( B = sk1 ) ),
inference(simp,[status(thm)],[301]) ).
thf(303,plain,
! [A: $i] :
( ( A @ sk16 )
= sk1 ),
inference(pattern_uni,[status(thm)],[302:[bind(A,$thf( C )),bind(B,$thf( C @ sk16 ))]]) ).
thf(311,plain,
! [A: $i] :
( ( A @ sk16 )
= sk1 ),
inference(simp,[status(thm)],[303]) ).
thf(1,conjecture,
? [A: $i] :
( ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ( C @ ( D @ r2 ) )
& ( D @ r1 ) )
& ( B @ ( C @ r2 ) ) )
& ? [C: $i] :
( ? [D: $i] :
( ( C @ ( D @ r2 ) )
& ( D @ r1 ) )
& ( A @ ( B @ ( C @ r3 ) ) ) ) )
& ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ r2 ) )
& ( E @ r1 ) )
& ( C @ ( D @ r2 ) ) )
& ( B @ ( C @ r2 ) ) )
& ( A = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',oneplustwoeqthree) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ( C @ ( D @ r2 ) )
& ( D @ r1 ) )
& ( B @ ( C @ r2 ) ) )
& ? [C: $i] :
( ? [D: $i] :
( ( C @ ( D @ r2 ) )
& ( D @ r1 ) )
& ( A @ ( B @ ( C @ r3 ) ) ) ) )
& ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ r2 ) )
& ( E @ r1 ) )
& ( C @ ( D @ r2 ) ) )
& ( B @ ( C @ r2 ) ) )
& ( A = B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(14,plain,
~ ? [A: $i] :
( ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ( C @ ( D @ r2 ) )
& ( D @ r1 ) )
& ( B @ ( C @ r2 ) ) )
& ? [C: $i] :
( ? [D: $i] :
( ( C @ ( D @ r2 ) )
& ( D @ r1 ) )
& ( A @ ( B @ ( C @ r3 ) ) ) ) )
& ? [B: $i] :
( ? [C: $i] :
( ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ r2 ) )
& ( E @ r1 ) )
& ( C @ ( D @ r2 ) ) )
& ( B @ ( C @ r2 ) ) )
& ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( J @ r2 ) )
| ~ ( J @ r1 )
| ~ ( F @ ( I @ r2 ) )
| ~ ( G @ ( H @ r2 ) )
| ~ ( H @ r1 )
| ~ ( A @ ( F @ ( G @ r3 ) ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ( A != B ) ),
inference(cnf,[status(esa)],[14]) ).
thf(16,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( I @ ( J @ r2 ) )
| ~ ( J @ r1 )
| ~ ( F @ ( I @ r2 ) )
| ~ ( G @ ( H @ r2 ) )
| ~ ( H @ r1 )
| ~ ( A @ ( F @ ( G @ r3 ) ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( B @ ( C @ r2 ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[15]) ).
thf(17,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( H @ ( I @ r2 ) )
| ~ ( I @ r1 )
| ~ ( E @ ( H @ r2 ) )
| ~ ( F @ ( G @ r2 ) )
| ~ ( G @ r1 )
| ~ ( A @ ( E @ ( F @ r3 ) ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[16]) ).
thf(164,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( F @ ( G @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ ( H @ ( I @ r2 ) )
| ~ ( I @ r1 )
| ~ ( E @ ( H @ r2 ) )
| ~ ( G @ r1 )
| ~ ( A @ ( E @ ( F @ r3 ) ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( D @ r1 )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(eqfactor_ordered,[status(thm)],[17]) ).
thf(175,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( G @ r2 ) )
| ~ ( G @ r1 )
| ~ ( C @ ( F @ r2 ) )
| ~ ( E @ r1 )
| ~ ( A @ ( C @ ( D @ r3 ) ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( B @ ( D @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( F )),bind(D,$thf( G ))]]) ).
thf(200,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( F @ ( G @ r2 ) )
| ~ ( G @ r1 )
| ~ ( C @ ( F @ r2 ) )
| ~ ( A @ ( C @ ( D @ r3 ) ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( B @ ( D @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(247,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( F @ ( G @ r2 ) )
!= ( D @ ( E @ r2 ) ) )
| ~ ( G @ r1 )
| ~ ( C @ ( F @ r2 ) )
| ~ ( A @ ( C @ ( D @ r3 ) ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( B @ ( D @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(eqfactor_ordered,[status(thm)],[200]) ).
thf(253,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( E @ r1 )
| ~ ( C @ ( D @ r2 ) )
| ~ ( A @ ( C @ ( D @ r3 ) ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( B @ ( D @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[247:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F )),bind(E,$thf( G ))]]) ).
thf(272,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ r2 ) )
| ~ ( A @ ( C @ ( D @ r3 ) ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( B @ ( D @ r2 ) )
| ~ ( A @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[253]) ).
thf(409,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( B @ ( D @ r2 ) )
!= ( A @ ( B @ r2 ) ) )
| ~ ( C @ ( D @ r2 ) )
| ~ ( A @ ( C @ ( D @ r3 ) ) )
| ~ ( D @ ( E @ r2 ) )
| ~ ( E @ r1 )
| ~ ( A @ ( B @ r2 ) ) ),
inference(eqfactor_ordered,[status(thm)],[272]) ).
thf(418,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ r2 ) )
| ~ ( B @ ( A @ ( B @ r3 ) ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 )
| ~ ( B @ ( B @ r2 ) ) ),
inference(pattern_uni,[status(thm)],[409:[bind(A,$thf( D )),bind(B,$thf( D ))]]) ).
thf(423,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( B @ r2 ) )
| ~ ( B @ ( A @ ( B @ r3 ) ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 )
| ~ ( B @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[418]) ).
thf(85,plain,
! [A: $i] : ( A @ sk13 @ ( A @ sk14 @ ( A @ r3 ) ) ),
inference(cnfConj,[status(thm)],[83]) ).
thf(86,plain,
! [A: $i] :
( ( A @ sk13 )
= A ),
inference(cnfConj,[status(thm)],[83]) ).
thf(87,plain,
! [A: $i] :
( ( A @ sk13 )
= A ),
inference(lifteq,[status(thm)],[86]) ).
thf(845,plain,
! [A: $i] : ( A @ ( sk1 @ ( A @ r3 ) ) ),
inference(rewrite,[status(thm)],[85,307,87]) ).
thf(5,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ( D = C )
& ( D @ ( B @ ( A @ r3 ) ) ) )
| ( ( D != C )
& ~ ( D @ ( B @ ( A @ r3 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(40,plain,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ( D = C )
& ( D @ ( B @ ( A @ r3 ) ) ) )
| ( ( D != C )
& ~ ( D @ ( B @ ( A @ r3 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C
= ( A @ ( B @ sk3 ) ) )
| ( C
!= ( A @ ( B @ sk3 ) ) ) )
& ( ( C @ ( B @ ( A @ r3 ) ) )
| ( C
!= ( A @ ( B @ sk3 ) ) ) )
& ( ( C
= ( A @ ( B @ sk3 ) ) )
| ~ ( C @ ( B @ ( A @ r3 ) ) ) )
& ( ( C @ ( B @ ( A @ r3 ) ) )
| ~ ( C @ ( B @ ( A @ r3 ) ) ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C
= ( A @ ( B @ sk3 ) ) )
| ~ ( C @ ( B @ ( A @ r3 ) ) ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( C @ ( B @ ( A @ r3 ) ) )
| ( C
= ( A @ ( B @ sk3 ) ) ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(846,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ ( A @ r3 ) ) )
!= ( D @ ( C @ ( B @ r3 ) ) ) )
| ~ $true
| ( D
= ( B @ ( C @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[845,46]) ).
thf(847,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ ( A @ r3 ) ) )
!= ( D @ ( C @ ( B @ r3 ) ) ) )
| ( D
= ( B @ ( C @ sk3 ) ) ) ),
inference(simp,[status(thm)],[846]) ).
thf(848,plain,
! [A: $i] :
( ( A @ ( sk1 @ sk3 ) )
= A ),
inference(pattern_uni,[status(thm)],[847:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( sk1 )),bind(D,$thf( A ))]]) ).
thf(4,axiom,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ( C = B )
& ( C @ ( A @ r2 ) ) )
| ( ( C != B )
& ~ ( C @ ( A @ r2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(29,plain,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ( C = B )
& ( C @ ( A @ r2 ) ) )
| ( ( C != B )
& ~ ( C @ ( A @ r2 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( ( B
= ( A @ sk2 ) )
| ( B
!= ( A @ sk2 ) ) )
& ( ( B @ ( A @ r2 ) )
| ( B
!= ( A @ sk2 ) ) )
& ( ( B
= ( A @ sk2 ) )
| ~ ( B @ ( A @ r2 ) ) )
& ( ( B @ ( A @ r2 ) )
| ~ ( B @ ( A @ r2 ) ) ) ),
inference(cnf,[status(esa)],[29]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B
= ( A @ sk2 ) )
| ~ ( B @ ( A @ r2 ) ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ( B
= ( A @ sk2 ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(7,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r3 ) ) )
& ( C @ ( D @ r2 ) ) )
& ? [D: $i] :
( ( D = C )
& ? [E: $i] :
( ( D @ ( E @ ( A @ r3 ) ) )
& ( E @ ( B @ r2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
thf(62,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r3 ) ) )
& ( C @ ( D @ r2 ) ) )
& ? [D: $i] :
( ( D = C )
& ? [E: $i] :
( ( D @ ( E @ ( A @ r3 ) ) )
& ( E @ ( B @ r2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk8 ) @ ( B @ ( A @ r3 ) ) )
& ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk8 ) @ r2 ) )
& ( ( A @ ( B @ sk6 ) )
= ( A @ ( B @ sk5 ) ) )
& ( A @ ( B @ sk6 ) @ ( A @ ( B @ sk7 ) @ ( A @ r3 ) ) )
& ( A @ ( B @ sk7 ) @ ( B @ r2 ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(65,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk7 ) @ ( B @ r2 ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(498,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk7 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ( D
= ( C @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[65,35]) ).
thf(499,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk7 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ( D
= ( C @ sk2 ) ) ),
inference(simp,[status(thm)],[498]) ).
thf(500,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk7 ) )
= ( A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[499:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk7 ) ))]]) ).
thf(548,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk7 ) )
= ( A @ sk2 ) ),
inference(simp,[status(thm)],[500]) ).
thf(6,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ( D = C )
& ( D @ ( B @ ( A @ r4 ) ) ) )
| ( ( D != C )
& ~ ( D @ ( B @ ( A @ r4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(51,plain,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ( D = C )
& ( D @ ( B @ ( A @ r4 ) ) ) )
| ( ( D != C )
& ~ ( D @ ( B @ ( A @ r4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r2 ) )
| ( B
!= ( A @ sk2 ) ) ),
inference(cnfConj,[status(thm)],[30]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ r2 ) )
| ( B
!= ( A @ sk2 ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(37,plain,
! [A: $i] : ( A @ sk2 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[36]) ).
thf(93,plain,
! [A: $i] :
( ( A @ sk15 )
= ( A @ sk17 ) ),
inference(cnfConj,[status(thm)],[89]) ).
thf(94,plain,
! [A: $i] :
( ( A @ sk17 )
= ( A @ sk15 ) ),
inference(lifteq,[status(thm)],[93]) ).
thf(92,plain,
! [A: $i] : ( A @ sk17 @ r1 ),
inference(cnfConj,[status(thm)],[89]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( ( A @ sk17 @ r1 )
!= ( B @ r1 ) )
| ~ $true
| ( B = sk1 ) ),
inference(paramod_ordered,[status(thm)],[92,24]) ).
thf(288,plain,
! [B: $i,A: $i] :
( ( ( A @ sk17 @ r1 )
!= ( B @ r1 ) )
| ( B = sk1 ) ),
inference(simp,[status(thm)],[287]) ).
thf(289,plain,
! [A: $i] :
( ( A @ sk17 )
= sk1 ),
inference(pattern_uni,[status(thm)],[288:[bind(A,$thf( C )),bind(B,$thf( C @ sk17 ))]]) ).
thf(304,plain,
! [A: $i] :
( ( A @ sk17 )
= sk1 ),
inference(simp,[status(thm)],[289]) ).
thf(389,plain,
! [A: $i] :
( ( A @ sk15 )
= sk1 ),
inference(rewrite,[status(thm)],[94,304]) ).
thf(324,plain,
! [B: $i,A: $i] :
( ( ( A @ sk2 @ ( A @ r2 ) )
!= ( sk1 @ ( B @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[37,116]) ).
thf(325,plain,
! [B: $i,A: $i] :
( ( A @ sk2 @ ( A @ r2 ) )
!= ( sk1 @ ( B @ r2 ) ) ),
inference(simp,[status(thm)],[324]) ).
thf(364,plain,
! [B: $i,A: $i] :
( ( ( A @ sk2 )
!= sk1 )
| ( A != B ) ),
inference(simp,[status(thm)],[325]) ).
thf(372,plain,
! [A: $i] :
( ( A @ sk2 )
!= sk1 ),
inference(simp,[status(thm)],[364]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ( A = B )
| ! [C: $i] :
( ~ ( C @ ( B @ r2 ) )
| ! [D: $i] :
( ( D != C )
| ~ ( D @ ( A @ r2 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3a) ).
thf(78,plain,
! [A: $i,B: $i] :
( ( A = B )
| ! [C: $i] :
( ~ ( C @ ( B @ r2 ) )
| ! [D: $i] :
( ( D != C )
| ~ ( D @ ( A @ r2 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(91,plain,
! [A: $i] : ( A @ sk15 @ ( A @ sk16 @ ( A @ r4 ) ) ),
inference(cnfConj,[status(thm)],[89]) ).
thf(900,plain,
! [A: $i] : ( sk1 @ ( sk1 @ ( A @ r4 ) ) ),
inference(rewrite,[status(thm)],[91,389,311]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk12 ) @ ( B @ ( A @ r4 ) ) )
& ( A @ ( B @ sk9 ) @ ( A @ ( A @ ( B @ sk12 ) @ r3 ) ) )
& ( ( A @ ( B @ sk10 ) )
= ( A @ ( B @ sk9 ) ) )
& ( A @ ( B @ sk10 ) @ ( A @ ( B @ sk11 ) @ ( A @ r4 ) ) )
& ( A @ ( B @ sk11 ) @ ( B @ r2 ) ) ),
inference(cnf,[status(esa)],[70]) ).
thf(72,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk11 ) @ ( B @ r2 ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(722,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk11 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ( D
= ( C @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[72,35]) ).
thf(723,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk11 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ( D
= ( C @ sk2 ) ) ),
inference(simp,[status(thm)],[722]) ).
thf(724,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk11 ) )
= ( A @ sk2 ) ),
inference(pattern_uni,[status(thm)],[723:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk11 ) ))]]) ).
thf(736,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ sk11 ) )
= ( A @ sk2 ) ),
inference(simp,[status(thm)],[724]) ).
thf(344,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk2 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ r1 ) ),
inference(paramod_ordered,[status(thm)],[37,107]) ).
thf(345,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk2 @ ( A @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[344]) ).
thf(346,plain,
! [A: $i] :
~ ( A @ sk2 @ r1 ),
inference(pattern_uni,[status(thm)],[345:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( D @ sk2 ))]]) ).
thf(377,plain,
! [A: $i] :
~ ( A @ sk2 @ r1 ),
inference(simp,[status(thm)],[346]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r3 ) ) )
| ( C
!= ( A @ ( B @ sk3 ) ) ) ),
inference(cnfConj,[status(thm)],[41]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r3 ) ) )
| ( C
!= ( A @ ( B @ sk3 ) ) ) ),
inference(lifteq,[status(thm)],[44]) ).
thf(48,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk3 ) @ ( B @ ( A @ r3 ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(12,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( ( A = C )
& ( C @ ( B @ r2 ) ) )
| ? [B: $i] :
( ( A = B )
& ( B @ r1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6a) ).
thf(95,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( ( A = C )
& ( C @ ( B @ r2 ) ) )
| ? [B: $i] :
( ( A = B )
& ( B @ r1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1030,plain,
$false,
inference(e,[status(thm)],[88,116,307,70,311,17,423,848,35,548,51,107,24,37,389,14,372,46,78,29,900,736,377,48,18,95,845,87,104,40,304,26,272,82,200,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : NUN056+2 : TPTP v9.3.1. Released v7.3.0.
% 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
% 0.05/0.31 % Computer : n012.cluster.edu
% 0.05/0.31 % Model : x86_64 x86_64
% 0.05/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.31 % Memory : 8046.5625MB
% 0.05/0.31 % OS : Linux 6.8.0-71-generic
% 0.05/0.31 % CPULimit : 300
% 0.05/0.31 % WCLimit : 300
% 0.05/0.31 % DateTime : Sat Sep 26 04:27:35 UTC 2026
% 0.05/0.32 % CPUTime :
% 0.05/0.32 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
% 0.61/0.77 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 0.96/0.93 % [INFO] Parsing done (159ms).
% 0.96/0.94 % [INFO] Running in sequential loop mode.
% 1.53/1.26 % [INFO] eprover registered as external prover.
% 1.53/1.26 % [INFO] Scanning for conjecture ...
% 1.74/1.34 % [INFO] Found a conjecture (or negated_conjecture) and 11 axioms. Running axiom selection ...
% 1.74/1.37 % [INFO] Axiom selection finished. Selected 11 axioms (removed 0 axioms).
% 1.94/1.40 % [INFO] Problem is first-order (TPTP FOF).
% 1.94/1.41 % [INFO] Type checking passed.
% 1.94/1.41 % [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 ...
% 9.33/3.26 % External prover 'e' found a proof!
% 9.33/3.26 % [INFO] Killing All external provers ...
% 9.33/3.26 % Time passed: 2831ms (effective reasoning time: 2317ms)
% 9.33/3.26 % 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)>
% 9.33/3.27 % Axioms used in derivation (11): axiom_1a, axiom_4a, axiom_2, axiom_3, axiom_7a, axiom_6a, axiom_3a, axiom_4, axiom_1, axiom_2a, axiom_5a
% 9.33/3.27 % No. of inferences in proof: 111
% 9.33/3.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2831 ms resp. 2317 ms w/o parsing
% 8.65/3.36 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 8.65/3.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------