%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUN059+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% 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 : n016.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 52.26s 10.86s
% Output : Refutation 44.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 32
% Syntax : Number of formulae : 150 ( 54 unt; 0 typ; 13 def)
% Number of atoms : 529 ( 72 equ; 0 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 1696 ( 268 ~; 170 |; 116 &;1142 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 21 ( 18 usr; 2 con; 0-3 aty)
% Number of variables : 501 ( 21 ^; 395 !; 72 ?; 501 :)
% ( 0 !>; 0 ?*; 0 @-; 13 @+)
% Comments :
%------------------------------------------------------------------------------
thf(id_decl,type,
id: $i > $i > $o ).
thf(r4_decl,type,
r4: $i > $i > $i > $o ).
thf(r3_decl,type,
r3: $i > $i > $i > $o ).
thf(r2_decl,type,
r2: $i > $i > $o ).
thf(r1_decl,type,
r1: $i > $o ).
thf(sk1_decl,type,
sk1: $i > $i > $i ).
thf(sk2_decl,type,
sk2: $i > $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk4_decl,type,
sk4: $i > $i > $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk7_decl,type,
sk7: $i > $i ).
thf(sk12_decl,type,
sk12: $i > $i ).
thf(sk13_decl,type,
sk13: $i > $i ).
thf(sk14_decl,type,
sk14: $i > $i ).
thf(sk15_decl,type,
sk15: $i > $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i > $i ).
thf(sk18_decl,type,
sk18: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( D @ ( A @ ( B @ r4 ) ) )
& ( C @ ( B @ ( D @ r3 ) ) ) )
& ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ ( B @ r4 ) ) )
& ( E @ ( A @ r2 ) ) )
& ( C @ ( D @ id ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( C @ ( D @ ( B @ r4 ) ) )
& ( D @ ( A @ r2 ) ) )
& ( B @ ( A @ sk1 ) @ ( C @ id ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( B @ ( A @ sk2 ) @ ( C @ ( B @ r4 ) ) )
& ( C @ ( A @ r2 ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ ( A @ ( B @ r4 ) ) )
& ( B @ ( A @ sk1 ) @ ( B @ ( C @ r3 ) ) ) ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] :
( ? [C: $i] :
( ( B @ ( C @ ( A @ r3 ) ) )
& ( C @ r1 ) )
& ( A @ ( B @ id ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i] :
@+[B: $i] :
( ( A @ sk6 @ ( B @ ( A @ r3 ) ) )
& ( B @ r1 ) ) ) ) ).
thf(sk12_def,definition,
( sk12
= ( ^ [A: $i] :
@+[B: $i] :
( ? [C: $i] :
( ( C @ r1 )
& ( C @ ( B @ id ) ) )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r4 ) ) )
& ( C @ r1 ) ) ) ) ) ).
thf(sk13_def,definition,
( sk13
= ( ^ [A: $i] :
@+[B: $i] :
( ( A @ sk12 @ ( B @ ( A @ r4 ) ) )
& ( B @ r1 ) ) ) ) ).
thf(sk14_def,definition,
( sk14
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ r1 )
& ( B @ ( A @ sk12 @ id ) ) ) ) ) ).
thf(sk15_def,definition,
( sk15
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( D @ ( A @ ( B @ r3 ) ) )
& ( C @ ( D @ r2 ) ) )
& ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ ( B @ r3 ) ) )
& ( E @ ( A @ r2 ) ) )
& ( C @ ( D @ id ) ) ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( C @ ( D @ ( B @ r3 ) ) )
& ( D @ ( A @ r2 ) ) )
& ( B @ ( A @ sk15 ) @ ( C @ id ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( B @ ( A @ sk16 ) @ ( C @ ( B @ r3 ) ) )
& ( C @ ( A @ r2 ) ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ ( A @ ( B @ r3 ) ) )
& ( B @ ( A @ sk15 ) @ ( C @ r2 ) ) ) ) ) ).
thf(7,axiom,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( B @ ( C @ ( A @ r3 ) ) )
& ( C @ r1 ) )
& ( A @ ( B @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4a) ).
thf(46,plain,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( B @ ( C @ ( A @ r3 ) ) )
& ( C @ r1 ) )
& ( A @ ( B @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(47,plain,
! [A: $i] :
( ( A @ sk6 @ ( A @ sk7 @ ( A @ r3 ) ) )
& ( A @ sk7 @ r1 )
& ( A @ ( A @ sk6 @ id ) ) ),
inference(cnf,[status(esa)],[46]) ).
thf(49,plain,
! [A: $i] : ( A @ sk7 @ r1 ),
inference(cnfConj,[status(thm)],[47]) ).
thf(15,axiom,
! [A: $i] : ( A @ ( A @ id ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(87,plain,
! [A: $i] : ( A @ ( A @ id ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(88,plain,
! [A: $i] : ( A @ ( A @ id ) ),
inference(cnf,[status(esa)],[87]) ).
thf(9,axiom,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2 ) )
| ! [C: $i] :
( ~ ( C @ r1 )
| ~ ( B @ ( C @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7a) ).
thf(53,plain,
! [A: $i,B: $i] :
( ~ ( B @ ( A @ r2 ) )
| ! [C: $i] :
( ~ ( C @ r1 )
| ~ ( B @ ( C @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( C @ r1 )
| ~ ( B @ ( C @ id ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(116,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( C @ ( D @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( D @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,54]) ).
thf(117,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( C @ ( D @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[116]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2 ) )
| ~ ( A @ r1 ) ),
inference(pattern_uni,[status(thm)],[117:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(137,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,118]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[137]) ).
thf(139,plain,
! [B: $i,A: $i] :
~ ( B @ sk7 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[138:[bind(A,$thf( D )),bind(B,$thf( D @ sk7 ))]]) ).
thf(142,plain,
! [B: $i,A: $i] :
~ ( B @ sk7 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[139]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( ( B @ r1 )
& ( A @ r1 ) )
| ( ~ ( B @ r1 )
& ~ ( A @ r1 ) )
| ~ ( B @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_8) ).
thf(110,plain,
! [A: $i,B: $i] :
( ( ( B @ r1 )
& ( A @ r1 ) )
| ( ~ ( B @ r1 )
& ~ ( A @ r1 ) )
| ~ ( B @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(14,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r3 ) ) )
& ( C @ ( D @ r2 ) ) )
& ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ ( A @ r3 ) ) )
& ( E @ ( B @ r2 ) ) )
& ( C @ ( D @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1a) ).
thf(80,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r3 ) ) )
& ( C @ ( D @ r2 ) ) )
& ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ ( A @ r3 ) ) )
& ( E @ ( B @ r2 ) ) )
& ( C @ ( D @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk18 ) @ ( B @ ( A @ r3 ) ) )
& ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk18 ) @ r2 ) )
& ( A @ ( B @ sk16 ) @ ( A @ ( B @ sk17 ) @ ( A @ r3 ) ) )
& ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
& ( A @ ( B @ sk15 ) @ ( A @ ( B @ sk16 ) @ id ) ) ),
inference(cnf,[status(esa)],[80]) ).
thf(84,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk17 ) @ ( B @ r2 ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(1,conjecture,
? [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( D @ ( E @ ( F @ r3 ) ) )
& ( F @ ( A @ ( A @ r4 ) ) ) )
& ( E @ ( B @ ( B @ r4 ) ) ) )
& ? [E: $i] :
( ( E @ ( C @ ( C @ r4 ) ) )
& ( E @ ( D @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fermattothepoweroftwoid) ).
thf(2,negated_conjecture,
~ ? [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( D @ ( E @ ( F @ r3 ) ) )
& ( F @ ( A @ ( A @ r4 ) ) ) )
& ( E @ ( B @ ( B @ r4 ) ) ) )
& ? [E: $i] :
( ( E @ ( C @ ( C @ r4 ) ) )
& ( E @ ( D @ id ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ? [A: $i,B: $i,C: $i,D: $i] :
( ? [E: $i] :
( ? [F: $i] :
( ( D @ ( E @ ( F @ r3 ) ) )
& ( F @ ( A @ ( A @ r4 ) ) ) )
& ( E @ ( B @ ( B @ r4 ) ) ) )
& ? [E: $i] :
( ( E @ ( C @ ( C @ r4 ) ) )
& ( E @ ( D @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( D @ ( F @ ( G @ r3 ) ) )
| ~ ( G @ ( A @ ( A @ r4 ) ) )
| ~ ( F @ ( B @ ( B @ r4 ) ) )
| ~ ( E @ ( C @ ( C @ r4 ) ) )
| ~ ( E @ ( D @ id ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(153,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( F @ ( B @ ( B @ r4 ) ) )
!= ( E @ ( C @ ( C @ r4 ) ) ) )
| ~ ( D @ ( F @ ( G @ r3 ) ) )
| ~ ( G @ ( A @ ( A @ r4 ) ) )
| ~ ( E @ ( C @ ( C @ r4 ) ) )
| ~ ( E @ ( D @ id ) ) ),
inference(eqfactor_ordered,[status(thm)],[22]) ).
thf(156,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ r3 ) ) )
| ~ ( E @ ( A @ ( A @ r4 ) ) )
| ~ ( D @ ( B @ ( B @ r4 ) ) )
| ~ ( D @ ( C @ id ) ) ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( D )),bind(E,$thf( F ))]]) ).
thf(161,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ ( C @ ( D @ ( E @ r3 ) ) )
| ~ ( E @ ( A @ ( A @ r4 ) ) )
| ~ ( D @ ( B @ ( B @ r4 ) ) )
| ~ ( D @ ( C @ id ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(170,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ~ $true
| ( ( E @ ( A @ ( A @ r4 ) ) )
!= ( D @ ( B @ ( B @ r4 ) ) ) )
| ~ ( C @ ( D @ ( E @ r3 ) ) )
| ~ ( D @ ( B @ ( B @ r4 ) ) )
| ~ ( D @ ( C @ id ) ) ),
inference(eqfactor_ordered,[status(thm)],[161]) ).
thf(171,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( C @ r3 ) ) )
| ~ ( C @ ( A @ ( A @ r4 ) ) )
| ~ ( C @ ( B @ id ) ) ),
inference(pattern_uni,[status(thm)],[170:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( C )),bind(D,$thf( E ))]]) ).
thf(174,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ ( C @ r3 ) ) )
| ~ ( C @ ( A @ ( A @ r4 ) ) )
| ~ ( C @ ( B @ id ) ) ),
inference(simp,[status(thm)],[171]) ).
thf(290,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( D @ ( C @ id ) ) )
| ~ ( C @ ( D @ ( D @ r3 ) ) )
| ~ ( D @ ( B @ ( B @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[88,174]) ).
thf(291,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( D @ ( C @ id ) ) )
| ~ ( C @ ( D @ ( D @ r3 ) ) )
| ~ ( D @ ( B @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[290]) ).
thf(292,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( A @ ( A @ r3 ) ) )
| ~ ( A @ ( B @ ( B @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[291:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(13,axiom,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( C @ r1 )
& ( C @ ( B @ id ) ) )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r4 ) ) )
& ( C @ r1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5a) ).
thf(74,plain,
! [A: $i] :
? [B: $i] :
( ? [C: $i] :
( ( C @ r1 )
& ( C @ ( B @ id ) ) )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r4 ) ) )
& ( C @ r1 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(75,plain,
! [A: $i] :
( ( A @ sk14 @ r1 )
& ( A @ sk14 @ ( A @ sk12 @ id ) )
& ( A @ sk12 @ ( A @ sk13 @ ( A @ r4 ) ) )
& ( A @ sk13 @ r1 ) ),
inference(cnf,[status(esa)],[74]) ).
thf(76,plain,
! [A: $i] : ( A @ sk13 @ r1 ),
inference(cnfConj,[status(thm)],[75]) ).
thf(4,axiom,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r4 ) ) )
& ( C @ ( A @ ( D @ r3 ) ) ) )
& ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ ( A @ r4 ) ) )
& ( E @ ( B @ r2 ) ) )
& ( C @ ( D @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2a) ).
thf(30,plain,
! [A: $i,B: $i] :
? [C: $i] :
( ? [D: $i] :
( ( D @ ( B @ ( A @ r4 ) ) )
& ( C @ ( A @ ( D @ r3 ) ) ) )
& ? [D: $i] :
( ? [E: $i] :
( ( D @ ( E @ ( A @ r4 ) ) )
& ( E @ ( B @ r2 ) ) )
& ( C @ ( D @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( B @ ( A @ r4 ) ) )
& ( A @ ( B @ sk1 ) @ ( A @ ( A @ ( B @ sk4 ) @ r3 ) ) )
& ( A @ ( B @ sk2 ) @ ( A @ ( B @ sk3 ) @ ( A @ r4 ) ) )
& ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
& ( A @ ( B @ sk1 ) @ ( A @ ( B @ sk2 ) @ id ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(34,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk3 ) @ ( B @ r2 ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(275,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ $true
| ~ ( C @ r1 ) ),
inference(paramod_ordered,[status(thm)],[34,118]) ).
thf(276,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[275]) ).
thf(277,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk3 ) @ r1 ),
inference(pattern_uni,[status(thm)],[276:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ sk3 ) )),bind(D,$thf( E ))]]) ).
thf(285,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk3 ) @ r1 ),
inference(simp,[status(thm)],[277]) ).
thf(392,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,285]) ).
thf(393,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) ),
inference(simp,[status(thm)],[392]) ).
thf(398,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk13 )
!= ( C @ ( B @ sk3 ) ) ),
inference(simp,[status(thm)],[393]) ).
thf(48,plain,
! [A: $i] : ( A @ ( A @ sk6 @ id ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(50,plain,
! [A: $i] : ( A @ sk6 @ ( A @ sk7 @ ( A @ r3 ) ) ),
inference(cnfConj,[status(thm)],[47]) ).
thf(79,plain,
! [A: $i] : ( A @ sk14 @ r1 ),
inference(cnfConj,[status(thm)],[75]) ).
thf(134,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,118]) ).
thf(135,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(136,plain,
! [B: $i,A: $i] :
~ ( B @ sk14 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[135:[bind(A,$thf( D )),bind(B,$thf( D @ sk14 ))]]) ).
thf(141,plain,
! [B: $i,A: $i] :
~ ( B @ sk14 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[136]) ).
thf(268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk14 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,141]) ).
thf(269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk14 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[268]) ).
thf(281,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk14 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[269]) ).
thf(287,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk14 ) ),
inference(simp,[status(thm)],[281]) ).
thf(296,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( D @ ( C @ id ) ) )
| ~ ( C @ ( D @ ( D @ r3 ) ) )
| ~ ( D @ ( B @ ( B @ r4 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,174]) ).
thf(297,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( D @ ( C @ id ) ) )
| ~ ( C @ ( D @ ( D @ r3 ) ) )
| ~ ( D @ ( B @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[296]) ).
thf(298,plain,
! [B: $i,A: $i] :
( ~ ( B @ sk6 @ ( B @ ( B @ r3 ) ) )
| ~ ( B @ ( A @ ( A @ r4 ) ) ) ),
inference(pattern_uni,[status(thm)],[297:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ sk6 )),bind(D,$thf( E ))]]) ).
thf(303,plain,
! [B: $i,A: $i] :
( ~ ( B @ sk6 @ ( B @ ( B @ r3 ) ) )
| ~ ( B @ ( A @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[298]) ).
thf(468,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ sk7 @ ( A @ r3 ) ) )
!= ( C @ sk6 @ ( C @ ( C @ r3 ) ) ) )
| ~ $true
| ~ ( C @ ( B @ ( B @ r4 ) ) ) ),
inference(paramod_ordered,[status(thm)],[50,303]) ).
thf(469,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 @ ( A @ sk7 @ ( A @ r3 ) ) )
!= ( C @ sk6 @ ( C @ ( C @ r3 ) ) ) )
| ~ ( C @ ( B @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[468]) ).
thf(476,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk6 )
!= ( C @ sk6 ) )
| ( ( A @ sk7 )
!= C )
| ( A != C )
| ~ ( C @ ( B @ ( B @ r4 ) ) ) ),
inference(simp,[status(thm)],[469]) ).
thf(479,plain,
! [B: $i,A: $i] :
( ( ( B @ sk7 )
!= B )
| ~ ( B @ ( A @ ( A @ r4 ) ) ) ),
inference(simp,[status(thm)],[476]) ).
thf(266,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,142]) ).
thf(267,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(282,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk7 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[267]) ).
thf(288,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk7 ) ),
inference(simp,[status(thm)],[282]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ id ) )
| ( C @ ( A @ id ) )
| ~ ( B @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_7) ).
thf(37,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( C @ ( B @ id ) )
| ( C @ ( A @ id ) )
| ~ ( B @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(143,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( C @ ( D @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( D @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,54]) ).
thf(144,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk6 @ id ) )
!= ( C @ ( D @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[143]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( B @ sk6 @ r1 ) ),
inference(pattern_uni,[status(thm)],[144:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( E @ sk6 ))]]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( B @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[145]) ).
thf(272,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ sk6 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[34,146]) ).
thf(273,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[272]) ).
thf(274,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk3 ) @ sk6 @ r1 ),
inference(pattern_uni,[status(thm)],[273:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk3 ) ))]]) ).
thf(284,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk3 ) @ sk6 @ r1 ),
inference(simp,[status(thm)],[274]) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[76,118]) ).
thf(132,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk13 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(133,plain,
! [B: $i,A: $i] :
~ ( B @ sk13 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( D )),bind(B,$thf( D @ sk13 ))]]) ).
thf(140,plain,
! [B: $i,A: $i] :
~ ( B @ sk13 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[133]) ).
thf(270,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk13 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[34,140]) ).
thf(271,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( B @ r2 ) )
!= ( D @ sk13 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[270]) ).
thf(283,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) )
!= ( D @ sk13 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[271]) ).
thf(289,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk3 ) )
!= ( C @ sk13 ) ),
inference(simp,[status(thm)],[283]) ).
thf(78,plain,
! [A: $i] : ( A @ sk14 @ ( A @ sk12 @ id ) ),
inference(cnfConj,[status(thm)],[75]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ id ) )
| ~ ( B @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(89,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ id ) )
| ~ ( B @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(416,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ sk6 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[84,146]) ).
thf(417,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ sk6 @ r1 ) ),
inference(simp,[status(thm)],[416]) ).
thf(418,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk17 ) @ sk6 @ r1 ),
inference(pattern_uni,[status(thm)],[417:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk17 ) ))]]) ).
thf(428,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk17 ) @ sk6 @ r1 ),
inference(simp,[status(thm)],[418]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ r4 ) ) )
& ( C @ ( B @ ( A @ r4 ) ) ) )
| ( ~ ( F @ ( E @ ( D @ r4 ) ) )
& ~ ( C @ ( B @ ( A @ r4 ) ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_11) ).
thf(23,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ r4 ) ) )
& ( C @ ( B @ ( A @ r4 ) ) ) )
| ( ~ ( F @ ( E @ ( D @ r4 ) ) )
& ~ ( C @ ( B @ ( A @ r4 ) ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ! [E: $i] :
( ! [F: $i] :
( ( ( F @ ( E @ ( D @ r4 ) ) )
& ( C @ ( B @ ( A @ r4 ) ) ) )
| ( ~ ( F @ ( E @ ( D @ r4 ) ) )
& ~ ( C @ ( B @ ( A @ r4 ) ) ) )
| ~ ( F @ ( C @ id ) ) )
| ~ ( E @ ( B @ id ) ) )
| ~ ( D @ ( A @ id ) ) ),
inference(miniscope,[status(thm)],[23]) ).
thf(25,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( F @ ( E @ ( D @ r4 ) ) )
| ~ ( F @ ( E @ ( D @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) )
& ( ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( E @ ( D @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) )
& ( ( F @ ( E @ ( D @ r4 ) ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) )
& ( ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(28,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( E @ ( D @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[25]) ).
thf(419,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ $true
| ~ ( C @ r1 ) ),
inference(paramod_ordered,[status(thm)],[84,118]) ).
thf(420,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[419]) ).
thf(421,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk17 ) @ r1 ),
inference(pattern_uni,[status(thm)],[420:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ sk17 ) )),bind(D,$thf( E ))]]) ).
thf(429,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk17 ) @ r1 ),
inference(simp,[status(thm)],[421]) ).
thf(18,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ~ ( C @ ( D @ id ) )
& ~ ( D @ ( B @ ( A @ r3 ) ) ) )
| ( ( D @ ( B @ ( A @ r3 ) ) )
& ( C @ ( D @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3) ).
thf(97,plain,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ~ ( C @ ( D @ id ) )
& ~ ( D @ ( B @ ( A @ r3 ) ) ) )
| ( ( D @ ( B @ ( A @ r3 ) ) )
& ( C @ ( D @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(32,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk1 ) @ ( A @ ( A @ ( B @ sk4 ) @ r3 ) ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(27,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( F @ ( E @ ( D @ r4 ) ) )
| ~ ( C @ ( B @ ( A @ r4 ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[25]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r2 ) )
& ( B @ ( A @ r2 ) ) )
| ( ~ ( D @ ( C @ r2 ) )
& ~ ( B @ ( A @ r2 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_9) ).
thf(103,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ r2 ) )
& ( B @ ( A @ r2 ) ) )
| ( ~ ( D @ ( C @ r2 ) )
& ~ ( B @ ( A @ r2 ) ) )
| ~ ( D @ ( B @ id ) )
| ~ ( C @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(17,axiom,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ~ ( C @ ( D @ id ) )
& ~ ( D @ ( B @ ( A @ r4 ) ) ) )
| ( ( D @ ( B @ ( A @ r4 ) ) )
& ( C @ ( D @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_4) ).
thf(91,plain,
! [A: $i,B: $i] :
? [C: $i] :
! [D: $i] :
( ( ~ ( C @ ( D @ id ) )
& ~ ( D @ ( B @ ( A @ r4 ) ) ) )
| ( ( D @ ( B @ ( A @ r4 ) ) )
& ( C @ ( D @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(394,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[79,285]) ).
thf(395,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) ),
inference(simp,[status(thm)],[394]) ).
thf(399,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk14 )
!= ( C @ ( B @ sk3 ) ) ),
inference(simp,[status(thm)],[395]) ).
thf(410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[84,142]) ).
thf(411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) @ ( B @ r2 ) )
!= ( D @ sk7 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[410]) ).
thf(425,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk17 ) )
!= ( D @ sk7 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[411]) ).
thf(431,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk17 ) )
!= ( C @ sk7 ) ),
inference(simp,[status(thm)],[425]) ).
thf(6,axiom,
? [A: $i] :
! [B: $i] :
( ( ~ ( A @ ( B @ id ) )
& ~ ( B @ r1 ) )
| ( ( B @ r1 )
& ( A @ ( B @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1) ).
thf(40,plain,
? [A: $i] :
! [B: $i] :
( ( ~ ( A @ ( B @ id ) )
& ~ ( B @ r1 ) )
| ( ( B @ r1 )
& ( A @ ( B @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ r3 ) ) )
& ( C @ ( B @ ( A @ r3 ) ) ) )
| ( ~ ( F @ ( E @ ( D @ r3 ) ) )
& ~ ( C @ ( B @ ( A @ r3 ) ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_10) ).
thf(55,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( F @ ( E @ ( D @ r3 ) ) )
& ( C @ ( B @ ( A @ r3 ) ) ) )
| ( ~ ( F @ ( E @ ( D @ r3 ) ) )
& ~ ( C @ ( B @ ( A @ r3 ) ) ) )
| ~ ( F @ ( C @ id ) )
| ~ ( E @ ( B @ id ) )
| ~ ( D @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ id ) )
| ! [C: $i] :
( ~ ( C @ ( B @ r2 ) )
| ! [D: $i] :
( ~ ( D @ ( A @ r2 ) )
| ~ ( C @ ( D @ id ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_3a) ).
thf(51,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ id ) )
| ! [C: $i] :
( ~ ( C @ ( B @ r2 ) )
| ! [D: $i] :
( ~ ( D @ ( A @ r2 ) )
| ~ ( C @ ( D @ id ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(396,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,285]) ).
thf(397,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 @ r1 )
!= ( C @ ( B @ sk3 ) @ r1 ) ),
inference(simp,[status(thm)],[396]) ).
thf(400,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk7 )
!= ( C @ ( B @ sk3 ) ) ),
inference(simp,[status(thm)],[397]) ).
thf(12,axiom,
! [A: $i] :
( ? [B: $i,C: $i] :
( ( C @ ( B @ r2 ) )
& ( C @ ( A @ id ) ) )
| ? [B: $i] :
( ( B @ r1 )
& ( B @ ( A @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6a) ).
thf(68,plain,
! [A: $i] :
( ? [B: $i,C: $i] :
( ( C @ ( B @ r2 ) )
& ( C @ ( A @ id ) ) )
| ? [B: $i] :
( ( B @ r1 )
& ( B @ ( A @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(11,axiom,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ~ ( B @ ( C @ id ) )
& ~ ( C @ ( A @ r2 ) ) )
| ( ( C @ ( A @ r2 ) )
& ( B @ ( C @ id ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_2) ).
thf(62,plain,
! [A: $i] :
? [B: $i] :
! [C: $i] :
( ( ~ ( B @ ( C @ id ) )
& ~ ( C @ ( A @ r2 ) ) )
| ( ( C @ ( A @ r2 ) )
& ( B @ ( C @ id ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14892,plain,
$false,
inference(e,[status(thm)],[142,110,84,292,398,48,50,87,287,479,88,174,288,37,46,284,289,78,89,428,74,28,429,21,97,285,53,141,161,32,34,22,118,27,54,49,76,303,103,140,91,399,431,80,40,55,23,146,30,51,79,400,68,62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN059+1 : TPTP v9.3.1. Bugfixed v7.4.0.
% 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
% 0.14/0.40 % Computer : n016.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 04:33:17 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.87/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.42/1.21 % [INFO] Parsing done (211ms).
% 1.42/1.22 % [INFO] Running in sequential loop mode.
% 2.12/1.63 % [INFO] eprover registered as external prover.
% 2.12/1.64 % [INFO] Scanning for conjecture ...
% 2.31/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.50/1.81 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.50/1.87 % [INFO] Problem is first-order (TPTP FOF).
% 2.50/1.88 % [INFO] Type checking passed.
% 2.50/1.88 % [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 ...
% 52.26/10.86 % External prover 'e' found a proof!
% 52.26/10.86 % [INFO] Killing All external provers ...
% 52.26/10.86 % Time passed: 10311ms (effective reasoning time: 9630ms)
% 52.26/10.86 % 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)>
% 52.26/10.86 % Axioms used in derivation (18): axiom_7, axiom_10, axiom_1a, axiom_4a, axiom_2, axiom_6, axiom_3, axiom_7a, axiom_8, axiom_6a, axiom_5, axiom_3a, axiom_11, axiom_9, axiom_4, axiom_1, axiom_2a, axiom_5a
% 52.26/10.86 % No. of inferences in proof: 137
% 52.26/10.86 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10311 ms resp. 9630 ms w/o parsing
% 44.61/10.98 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 44.61/10.98 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------