%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUN068+1 : 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 : n009.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 08:18:38 AM UTC 2026
% Result : Theorem 39.87s 10.50s
% Output : Refutation 40.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 35
% Syntax : Number of formulae : 153 ( 51 unt; 0 typ; 16 def)
% Number of atoms : 543 ( 67 equ; 0 cnn)
% Maximal formula atoms : 20 ( 3 avg)
% Number of connectives : 1625 ( 273 ~; 183 |; 111 &;1058 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 25 ( 22 usr; 2 con; 0-3 aty)
% Number of variables : 450 ( 24 ^; 356 !; 54 ?; 450 :)
% ( 0 !>; 0 ?*; 0 @-; 16 @+)
% Comments :
%------------------------------------------------------------------------------
thf(r1_decl,type,
r1: $i > $o ).
thf(r2_decl,type,
r2: $i > $i > $o ).
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(sk1_decl,type,
sk1: $i > $o ).
thf(sk2_decl,type,
sk2: $i > $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk4_decl,type,
sk4: $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(sk10_decl,type,
sk10: $i > $i ).
thf(sk11_decl,type,
sk11: $i > $i ).
thf(sk16_decl,type,
sk16: $i > $i ).
thf(sk17_decl,type,
sk17: $i > $i ).
thf(sk18_decl,type,
sk18: $i > $i ).
thf(sk19_decl,type,
sk19: $i > $i > $i ).
thf(sk20_decl,type,
sk20: $i > $i > $i ).
thf(sk21_decl,type,
sk21: $i > $i > $i ).
thf(sk22_decl,type,
sk22: $i > $i > $i ).
thf(sk2_def,definition,
( sk2
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ~ ( B @ ( A @ id ) )
| ! [C: $i] :
( ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ~ ( A @ sk2 @ ( B @ r2 ) )
| ~ ( B @ r1 ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [A: $i] :
@+[B: $i] :
~ ( ~ ( B @ r1 )
| ~ ( B @ ( A @ id ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [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(sk6_def,definition,
( sk6
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( C @ ( D @ ( B @ r4 ) ) )
& ( D @ ( A @ r2 ) ) )
& ( B @ ( A @ sk5 ) @ ( C @ id ) ) ) ) ) ).
thf(sk7_def,definition,
( sk7
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( B @ ( A @ sk6 ) @ ( C @ ( B @ r4 ) ) )
& ( C @ ( A @ r2 ) ) ) ) ) ).
thf(sk8_def,definition,
( sk8
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ ( A @ ( B @ r4 ) ) )
& ( B @ ( A @ sk5 ) @ ( B @ ( C @ r3 ) ) ) ) ) ) ).
thf(sk10_def,definition,
( sk10
= ( ^ [A: $i] :
@+[B: $i] :
( ? [C: $i] :
( ( B @ ( C @ ( A @ r3 ) ) )
& ( C @ r1 ) )
& ( A @ ( B @ id ) ) ) ) ) ).
thf(sk11_def,definition,
( sk11
= ( ^ [A: $i] :
@+[B: $i] :
( ( A @ sk10 @ ( B @ ( A @ r3 ) ) )
& ( B @ r1 ) ) ) ) ).
thf(sk16_def,definition,
( sk16
= ( ^ [A: $i] :
@+[B: $i] :
( ? [C: $i] :
( ( C @ r1 )
& ( C @ ( B @ id ) ) )
& ? [C: $i] :
( ( B @ ( C @ ( A @ r4 ) ) )
& ( C @ r1 ) ) ) ) ) ).
thf(sk17_def,definition,
( sk17
= ( ^ [A: $i] :
@+[B: $i] :
( ( A @ sk16 @ ( B @ ( A @ r4 ) ) )
& ( B @ r1 ) ) ) ) ).
thf(sk18_def,definition,
( sk18
= ( ^ [A: $i] :
@+[B: $i] :
( ( B @ r1 )
& ( B @ ( A @ sk16 @ id ) ) ) ) ) ).
thf(sk19_def,definition,
( sk19
= ( ^ [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(sk20_def,definition,
( sk20
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ? [D: $i] :
( ( C @ ( D @ ( B @ r3 ) ) )
& ( D @ ( A @ r2 ) ) )
& ( B @ ( A @ sk19 ) @ ( C @ id ) ) ) ) ) ).
thf(sk21_def,definition,
( sk21
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( B @ ( A @ sk20 ) @ ( C @ ( B @ r3 ) ) )
& ( C @ ( A @ r2 ) ) ) ) ) ).
thf(sk22_def,definition,
( sk22
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ ( A @ ( B @ r3 ) ) )
& ( B @ ( A @ sk19 ) @ ( C @ r2 ) ) ) ) ) ).
thf(1,conjecture,
? [A: $i] :
( ! [B: $i] :
( ~ ( B @ r1 )
| ~ ( B @ ( A @ id ) ) )
& ! [B: $i] :
( ~ ( B @ ( A @ id ) )
| ! [C: $i] :
( ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',nonzerosnononesexistid) ).
thf(2,negated_conjecture,
~ ? [A: $i] :
( ! [B: $i] :
( ~ ( B @ r1 )
| ~ ( B @ ( A @ id ) ) )
& ! [B: $i] :
( ~ ( B @ ( A @ id ) )
| ! [C: $i] :
( ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ? [A: $i] :
( ! [B: $i] :
( ~ ( B @ r1 )
| ~ ( B @ ( A @ id ) ) )
& ! [B: $i] :
( ~ ( B @ ( A @ id ) )
| ! [C: $i] :
( ~ ( B @ ( C @ r2 ) )
| ~ ( C @ r1 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
! [A: $i] :
( ( ( A @ sk4 @ r1 )
| ( A @ sk1 ) )
& ( ( A @ sk4 @ ( A @ id ) )
| ( A @ sk1 ) )
& ( ~ ( A @ sk1 )
| ( A @ sk2 @ ( A @ id ) ) )
& ( ~ ( A @ sk1 )
| ( A @ sk2 @ ( A @ sk3 @ r2 ) ) )
& ( ~ ( A @ sk1 )
| ( A @ sk3 @ r1 ) ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
! [A: $i] :
( ~ ( A @ sk1 )
| ( A @ sk2 @ ( A @ sk3 @ r2 ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
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(51,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(52,plain,
! [A: $i] :
( ( A @ sk10 @ ( A @ sk11 @ ( A @ r3 ) ) )
& ( A @ sk11 @ r1 )
& ( A @ ( A @ sk10 @ id ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(53,plain,
! [A: $i] : ( A @ ( A @ sk10 @ id ) ),
inference(cnfConj,[status(thm)],[52]) ).
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(58,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(59,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( C @ r1 )
| ~ ( B @ ( C @ id ) ) ),
inference(cnf,[status(esa)],[58]) ).
thf(148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk10 @ id ) )
!= ( C @ ( D @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( D @ r1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[53,59]) ).
thf(149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ sk10 @ id ) )
!= ( C @ ( D @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[148]) ).
thf(150,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( B @ sk10 @ r1 ) ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E )),bind(D,$thf( E @ sk10 ))]]) ).
thf(151,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ r2 ) )
| ~ ( B @ sk10 @ r1 ) ),
inference(simp,[status(thm)],[150]) ).
thf(226,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk2 @ ( A @ sk3 @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ $true
| ~ ( C @ sk10 @ r1 )
| ~ ( A @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[23,151]) ).
thf(227,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk2 @ ( A @ sk3 @ r2 ) )
!= ( C @ ( B @ r2 ) ) )
| ~ ( C @ sk10 @ r1 )
| ~ ( A @ sk1 ) ),
inference(simp,[status(thm)],[226]) ).
thf(228,plain,
! [A: $i] :
( ~ ( A @ sk2 @ sk10 @ r1 )
| ~ ( A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[227:[bind(A,$thf( E )),bind(B,$thf( E @ sk3 )),bind(C,$thf( E @ sk2 ))]]) ).
thf(234,plain,
! [A: $i] :
( ~ ( A @ sk2 @ sk10 @ r1 )
| ~ ( A @ sk1 ) ),
inference(simp,[status(thm)],[228]) ).
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(115,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(15,axiom,
! [A: $i] : ( A @ ( A @ id ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_5) ).
thf(92,plain,
! [A: $i] : ( A @ ( A @ id ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(93,plain,
! [A: $i] : ( A @ ( A @ id ) ),
inference(cnf,[status(esa)],[92]) ).
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(79,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(80,plain,
! [A: $i] :
( ( A @ sk18 @ r1 )
& ( A @ sk18 @ ( A @ sk16 @ id ) )
& ( A @ sk16 @ ( A @ sk17 @ ( A @ r4 ) ) )
& ( A @ sk17 @ r1 ) ),
inference(cnf,[status(esa)],[79]) ).
thf(84,plain,
! [A: $i] : ( A @ sk18 @ r1 ),
inference(cnfConj,[status(thm)],[80]) ).
thf(54,plain,
! [A: $i] : ( A @ sk11 @ r1 ),
inference(cnfConj,[status(thm)],[52]) ).
thf(121,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)],[93,59]) ).
thf(122,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ id ) )
!= ( C @ ( D @ id ) ) )
| ~ ( C @ ( B @ r2 ) )
| ~ ( D @ r1 ) ),
inference(simp,[status(thm)],[121]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ r2 ) )
| ~ ( A @ r1 ) ),
inference(pattern_uni,[status(thm)],[122:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(139,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk11 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54,123]) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk11 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[139]) ).
thf(141,plain,
! [B: $i,A: $i] :
~ ( B @ sk11 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[140:[bind(A,$thf( D )),bind(B,$thf( D @ sk11 ))]]) ).
thf(147,plain,
! [B: $i,A: $i] :
~ ( B @ sk11 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[141]) ).
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(73,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(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(108,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(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(35,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(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(56,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(36,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk8 ) @ ( B @ ( A @ r4 ) ) )
& ( A @ ( B @ sk5 ) @ ( A @ ( A @ ( B @ sk8 ) @ r3 ) ) )
& ( A @ ( B @ sk6 ) @ ( A @ ( B @ sk7 ) @ ( A @ r4 ) ) )
& ( A @ ( B @ sk7 ) @ ( B @ r2 ) )
& ( A @ ( B @ sk5 ) @ ( A @ ( B @ sk6 ) @ id ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk7 ) @ ( B @ r2 ) ),
inference(cnfConj,[status(thm)],[36]) ).
thf(318,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk7 ) @ ( B @ r2 ) )
!= ( D @ sk11 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[37,147]) ).
thf(319,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk7 ) @ ( B @ r2 ) )
!= ( D @ sk11 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[318]) ).
thf(334,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk7 ) )
!= ( D @ sk11 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[319]) ).
thf(340,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk7 ) )
!= ( C @ sk11 ) ),
inference(simp,[status(thm)],[334]) ).
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(42,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(24,plain,
! [A: $i] :
( ~ ( A @ sk1 )
| ( A @ sk2 @ ( A @ id ) ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(25,plain,
! [A: $i] :
( ( A @ sk4 @ ( A @ id ) )
| ( A @ sk1 ) ),
inference(cnfConj,[status(thm)],[22]) ).
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(60,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(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(85,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(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(102,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(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(28,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(26,plain,
! [A: $i] :
( ( A @ sk4 @ r1 )
| ( A @ sk1 ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(27,plain,
! [A: $i] :
( ~ ( A @ sk1 )
| ( A @ sk3 @ r1 ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( ( A @ sk1 )
!= ( B @ sk1 ) )
| ~ $true
| ( B @ sk3 @ r1 )
| ( A @ sk4 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[26,27]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( ( A @ sk1 )
!= ( B @ sk1 ) )
| ( B @ sk3 @ r1 )
| ( A @ sk4 @ r1 ) ),
inference(simp,[status(thm)],[163]) ).
thf(165,plain,
! [A: $i] :
( ( A @ sk3 @ r1 )
| ( A @ sk4 @ r1 ) ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk3 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ $true
| ~ ( A @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[27,123]) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk3 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ ( A @ sk1 ) ),
inference(simp,[status(thm)],[160]) ).
thf(162,plain,
! [B: $i,A: $i] :
( ~ ( B @ sk3 @ ( A @ r2 ) )
| ~ ( B @ sk1 ) ),
inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( D )),bind(B,$thf( D @ sk3 ))]]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ~ ( B @ sk3 @ ( A @ r2 ) )
| ~ ( B @ sk1 ) ),
inference(simp,[status(thm)],[162]) ).
thf(81,plain,
! [A: $i] : ( A @ sk17 @ r1 ),
inference(cnfConj,[status(thm)],[80]) ).
thf(142,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk17 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[81,123]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk17 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(144,plain,
! [B: $i,A: $i] :
~ ( B @ sk17 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( D )),bind(B,$thf( D @ sk17 ))]]) ).
thf(145,plain,
! [B: $i,A: $i] :
~ ( B @ sk17 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[144]) ).
thf(326,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk7 ) @ ( B @ r2 ) )
!= ( D @ sk17 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[37,145]) ).
thf(327,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk7 ) @ ( B @ r2 ) )
!= ( D @ sk17 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[326]) ).
thf(333,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk7 ) )
!= ( D @ sk17 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[327]) ).
thf(339,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk7 ) )
!= ( C @ sk17 ) ),
inference(simp,[status(thm)],[333]) ).
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(96,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(29,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)],[28]) ).
thf(30,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)],[29]) ).
thf(32,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)],[30]) ).
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(45,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(171,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk2 @ ( A @ sk3 @ r2 ) )
!= ( B @ ( C @ r2 ) ) )
| ~ $true
| ~ ( B @ r1 )
| ~ ( A @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[23,123]) ).
thf(172,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk2 @ ( A @ sk3 @ r2 ) )
!= ( B @ ( C @ r2 ) ) )
| ~ ( B @ r1 )
| ~ ( A @ sk1 ) ),
inference(simp,[status(thm)],[171]) ).
thf(173,plain,
! [A: $i] :
( ~ ( A @ sk2 @ r1 )
| ~ ( A @ sk1 ) ),
inference(pattern_uni,[status(thm)],[172:[bind(A,$thf( E )),bind(B,$thf( E @ sk2 )),bind(C,$thf( E @ sk3 ))]]) ).
thf(181,plain,
! [A: $i] :
( ~ ( A @ sk2 @ r1 )
| ~ ( A @ sk1 ) ),
inference(simp,[status(thm)],[173]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk4 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ $true
| ( A @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[26,123]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk4 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) )
| ( A @ sk1 ) ),
inference(simp,[status(thm)],[155]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ~ ( B @ sk4 @ ( A @ r2 ) )
| ( B @ sk1 ) ),
inference(pattern_uni,[status(thm)],[156:[bind(A,$thf( D )),bind(B,$thf( D @ sk4 ))]]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ~ ( B @ sk4 @ ( A @ r2 ) )
| ( B @ sk1 ) ),
inference(simp,[status(thm)],[157]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk22 ) @ ( B @ ( A @ r3 ) ) )
& ( A @ ( B @ sk19 ) @ ( A @ ( B @ sk22 ) @ r2 ) )
& ( A @ ( B @ sk20 ) @ ( A @ ( B @ sk21 ) @ ( A @ r3 ) ) )
& ( A @ ( B @ sk21 ) @ ( B @ r2 ) )
& ( A @ ( B @ sk19 ) @ ( A @ ( B @ sk20 ) @ id ) ) ),
inference(cnf,[status(esa)],[85]) ).
thf(90,plain,
! [B: $i,A: $i] : ( A @ ( B @ sk21 ) @ ( B @ r2 ) ),
inference(cnfConj,[status(thm)],[86]) ).
thf(394,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk21 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ sk10 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[90,151]) ).
thf(395,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk21 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ sk10 @ r1 ) ),
inference(simp,[status(thm)],[394]) ).
thf(396,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk21 ) @ sk10 @ r1 ),
inference(pattern_uni,[status(thm)],[395:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk21 ) ))]]) ).
thf(406,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk21 ) @ sk10 @ r1 ),
inference(simp,[status(thm)],[396]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( ( A @ sk1 )
!= ( B @ sk1 ) )
| ~ ( B @ sk2 @ r1 )
| ~ $true
| ( A @ sk4 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[26,181]) ).
thf(207,plain,
! [B: $i,A: $i] :
( ( ( A @ sk1 )
!= ( B @ sk1 ) )
| ~ ( B @ sk2 @ r1 )
| ( A @ sk4 @ r1 ) ),
inference(simp,[status(thm)],[206]) ).
thf(208,plain,
! [A: $i] :
( ~ ( A @ sk2 @ r1 )
| ( A @ sk4 @ r1 ) ),
inference(pattern_uni,[status(thm)],[207:[bind(A,$thf( A )),bind(B,$thf( A ))]]) ).
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(67,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(328,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk7 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ $true
| ~ ( D @ sk10 @ r1 ) ),
inference(paramod_ordered,[status(thm)],[37,151]) ).
thf(329,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk7 ) @ ( B @ r2 ) )
!= ( D @ ( C @ r2 ) ) )
| ~ ( D @ sk10 @ r1 ) ),
inference(simp,[status(thm)],[328]) ).
thf(330,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk7 ) @ sk10 @ r1 ),
inference(pattern_uni,[status(thm)],[329:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( E )),bind(D,$thf( F @ ( E @ sk7 ) ))]]) ).
thf(338,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk7 ) @ sk10 @ r1 ),
inference(simp,[status(thm)],[330]) ).
thf(323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk7 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ $true
| ~ ( C @ r1 ) ),
inference(paramod_ordered,[status(thm)],[37,123]) ).
thf(324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk7 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[323]) ).
thf(325,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk7 ) @ r1 ),
inference(pattern_uni,[status(thm)],[324:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ sk7 ) )),bind(D,$thf( E ))]]) ).
thf(337,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk7 ) @ r1 ),
inference(simp,[status(thm)],[325]) ).
thf(342,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk18 @ r1 )
!= ( C @ ( B @ sk7 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[84,337]) ).
thf(343,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk18 @ r1 )
!= ( C @ ( B @ sk7 ) @ r1 ) ),
inference(simp,[status(thm)],[342]) ).
thf(359,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk18 )
!= ( C @ ( B @ sk7 ) ) ),
inference(simp,[status(thm)],[343]) ).
thf(136,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk18 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[84,123]) ).
thf(137,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk18 @ r1 )
!= ( B @ r1 ) )
| ~ ( B @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
! [B: $i,A: $i] :
~ ( B @ sk18 @ ( A @ r2 ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( D )),bind(B,$thf( D @ sk18 ))]]) ).
thf(146,plain,
! [B: $i,A: $i] :
~ ( B @ sk18 @ ( A @ r2 ) ),
inference(simp,[status(thm)],[138]) ).
thf(389,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk21 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ $true
| ~ ( C @ r1 ) ),
inference(paramod_ordered,[status(thm)],[90,123]) ).
thf(390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk21 ) @ ( B @ r2 ) )
!= ( C @ ( D @ r2 ) ) )
| ~ ( C @ r1 ) ),
inference(simp,[status(thm)],[389]) ).
thf(391,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk21 ) @ r1 ),
inference(pattern_uni,[status(thm)],[390:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ sk21 ) )),bind(D,$thf( E ))]]) ).
thf(405,plain,
! [B: $i,A: $i] :
~ ( B @ ( A @ sk21 ) @ r1 ),
inference(simp,[status(thm)],[391]) ).
thf(331,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk7 ) @ ( B @ r2 ) )
!= ( D @ sk18 @ ( C @ r2 ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[37,146]) ).
thf(332,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk7 ) @ ( B @ r2 ) )
!= ( D @ sk18 @ ( C @ r2 ) ) ),
inference(simp,[status(thm)],[331]) ).
thf(335,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ sk7 ) )
!= ( D @ sk18 ) )
| ( B != C ) ),
inference(simp,[status(thm)],[332]) ).
thf(341,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ sk7 ) )
!= ( C @ sk18 ) ),
inference(simp,[status(thm)],[335]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ id ) )
| ~ ( B @ ( A @ id ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_6) ).
thf(94,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ id ) )
| ~ ( B @ ( A @ id ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(348,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ sk11 @ r1 )
!= ( C @ ( B @ sk7 ) @ r1 ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54,337]) ).
thf(349,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk11 @ r1 )
!= ( C @ ( B @ sk7 ) @ r1 ) ),
inference(simp,[status(thm)],[348]) ).
thf(358,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ sk11 )
!= ( C @ ( B @ sk7 ) ) ),
inference(simp,[status(thm)],[349]) ).
thf(83,plain,
! [A: $i] : ( A @ sk18 @ ( A @ sk16 @ id ) ),
inference(cnfConj,[status(thm)],[80]) ).
thf(13908,plain,
$false,
inference(e,[status(thm)],[234,115,93,84,147,92,73,108,35,58,56,340,42,24,37,25,60,85,102,28,21,165,53,169,339,96,32,45,59,27,54,181,159,406,81,208,123,145,67,338,359,26,23,151,146,51,405,341,94,358,79,90,337,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUN068+1 : TPTP v9.3.1. Released v7.3.0.
% 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
% 0.14/0.41 % Computer : n009.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Sat Sep 26 04:30:00 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
% 0.83/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.38/1.20 % [INFO] Parsing done (209ms).
% 1.38/1.21 % [INFO] Running in sequential loop mode.
% 2.02/1.61 % [INFO] eprover registered as external prover.
% 2.02/1.61 % [INFO] Scanning for conjecture ...
% 2.19/1.71 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.19/1.77 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.37/1.83 % [INFO] Problem is first-order (TPTP FOF).
% 2.37/1.84 % [INFO] Type checking passed.
% 2.37/1.85 % [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 ...
% 47.37/10.49 % External prover 'e' found a proof!
% 47.37/10.49 % [INFO] Killing All external provers ...
% 47.37/10.50 % Time passed: 9944ms (effective reasoning time: 9276ms)
% 47.37/10.50 % 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)>
% 39.87/10.50 % 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
% 39.87/10.50 % No. of inferences in proof: 137
% 39.87/10.50 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 9944 ms resp. 9276 ms w/o parsing
% 40.22/10.62 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 40.22/10.62 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------