%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL060-10 : TPTP v9.3.1. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n007.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 07:50:42 AM UTC 2026
% Result : Unsatisfiable 59.90s 13.40s
% Output : Refutation 50.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 98 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 178 ( 177 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 1352 ( 128 ~; 80 |; 0 &;1144 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 9 ( 7 usr; 4 con; 0-4 aty)
% Number of variables : 199 ( 0 ^; 199 !; 0 ?; 199 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $i ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(a_decl,type,
a: $i ).
thf(b_decl,type,
b: $i ).
thf(not_decl,type,
not: $i > $i ).
thf(true_decl,type,
true: $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_3) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
inference(lifteq,[status(thm)],[18]) ).
thf(3,axiom,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',condensed_detachment) ).
thf(12,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(13,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[12]) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( ( true @ ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[19,13]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[47:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G )),bind(D,$thf( F @ ( G @ not @ implies ) ))]]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[48]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(10,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(11,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(lifteq,[status(thm)],[10]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[53,11]) ).
thf(96,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( D @ is_a_theorem ) )
| ( ( true @ ( C @ ( D @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[19,87]) ).
thf(97,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[96:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[97]) ).
thf(290,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[110,11]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_2) ).
thf(16,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(17,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(lifteq,[status(thm)],[16]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ ( B @ implies ) @ is_a_theorem ) )
| ( ( true @ ( true @ ( C @ is_a_theorem @ ( true @ ( B @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,13]) ).
thf(39,plain,
! [A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( A @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[38:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ not @ implies ) )),bind(C,$thf( E ))]]) ).
thf(60,plain,
! [A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( A @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[39]) ).
thf(192,plain,
! [A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( A @ not @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[60,11]) ).
thf(312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[290,192]) ).
thf(313,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[312:[bind(A,$thf( M @ ( N @ not @ implies ) @ ( N @ implies ) )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( M @ ( N @ not @ implies ) @ ( N @ implies ) ))]]) ).
thf(339,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[313]) ).
thf(347,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[339,11]) ).
thf(4,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cn_1) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
= true ),
inference(lifteq,[status(thm)],[14]) ).
thf(1,negated_conjecture,
( ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem )
!= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_cn_54) ).
thf(7,plain,
( ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,plain,
( ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(lifteq,[status(thm)],[8]) ).
thf(65,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[15,9]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[65]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[81]) ).
thf(144,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( b @ ( a @ not @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[140]) ).
thf(148,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( b @ ( a @ not @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= B )
| ( ( C @ ( B @ implies ) )
!= A )
| ( B != b )
| ( A != a ) ),
inference(simp,[status(thm)],[144]) ).
thf(164,plain,
! [A: $i] :
( ( ( b @ ( b @ ( a @ not @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( A @ ( a @ implies ) )
!= b )
| ( ( A @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[148]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( C @ is_a_theorem ) )
| ( ( true @ ( B @ ( C @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,87]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[104]) ).
thf(551,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[113,11]) ).
thf(20,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[17,9]) ).
thf(21,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[20]) ).
thf(22,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(146,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( b @ ( a @ not @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( B != b )
| ( A != a ) ),
inference(simp,[status(thm)],[144]) ).
thf(162,plain,
! [A: $i] :
( ( ( b @ ( b @ ( a @ not @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( A @ ( a @ implies ) @ ( A @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[146]) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ( b != b )
| ( ( b @ ( a @ not @ implies ) )
!= a )
| ( ( C @ ( A @ implies ) )
!= B )
| ( ( C @ ( B @ implies ) )
!= A )
| ( B != b )
| ( A != a ) ),
inference(simp,[status(thm)],[144]) ).
thf(168,plain,
! [A: $i] :
( ( ( b @ ( a @ not @ implies ) )
!= a )
| ( ( A @ ( a @ implies ) )
!= b )
| ( ( A @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[152]) ).
thf(98,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( C @ ( D @ not @ implies ) @ is_a_theorem ) )
| ( ( true @ ( true @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[19,87]) ).
thf(99,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[98:[bind(A,$thf( I @ not )),bind(B,$thf( G )),bind(C,$thf( G @ ( I @ not @ not @ implies ) )),bind(D,$thf( I ))]]) ).
thf(111,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[99]) ).
thf(350,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[347,9]) ).
thf(351,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[350]) ).
thf(389,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[351]) ).
thf(188,plain,
! [A: $i] :
( ( a != a )
| ( ( b @ ( a @ not @ implies ) )
!= ( A @ ( b @ implies ) ) )
| ( ( A @ ( a @ implies ) )
!= b )
| ( ( A @ ( b @ implies ) )
!= a ) ),
inference(eqfactor_ordered,[status(thm)],[168]) ).
thf(189,plain,
! [A: $i] :
( ( ( b @ ( a @ not @ implies ) )
!= ( A @ ( b @ implies ) ) )
| ( ( A @ ( a @ implies ) )
!= b )
| ( ( A @ ( b @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[188]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[19,9]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[27]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(141,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) ) )
| ( B != b )
| ( A != a ) ),
inference(simp,[status(thm)],[140]) ).
thf(160,plain,
! [A: $i] :
( ( A @ ( a @ implies ) @ ( A @ ( b @ implies ) @ implies ) )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ( ( b @ ( b @ ( a @ not @ implies ) @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[140]) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ( b != B )
| ( ( b @ ( a @ not @ implies ) )
!= A )
| ( ( C @ ( A @ implies ) )
!= b )
| ( ( C @ ( B @ implies ) )
!= a )
| ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[145]) ).
thf(173,plain,
! [A: $i] :
( ( ( A @ ( b @ ( a @ not @ implies ) @ implies ) )
!= b )
| ( ( A @ ( b @ implies ) )
!= a )
| ( ( b @ ( b @ ( a @ not @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] :
( ( b != b )
| ( ( b @ ( a @ not @ implies ) )
!= a )
| ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( B != b )
| ( A != a ) ),
inference(simp,[status(thm)],[144]) ).
thf(166,plain,
! [A: $i] :
( ( ( b @ ( a @ not @ implies ) )
!= a )
| ( ( A @ ( a @ implies ) @ ( A @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(30,plain,
! [A: $i] :
( ( A
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) ) )
| ( ( A @ ( A @ not @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(31,plain,
( ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( b @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(32,plain,
( ( ( b @ ( b @ ( a @ not @ implies ) @ implies ) )
!= b )
| ( ( b @ ( b @ ( a @ not @ implies ) @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[31]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= b )
| ( ( C @ ( B @ implies ) )
!= ( b @ ( a @ not @ implies ) ) )
| ( B != b )
| ( A != a ) ),
inference(simp,[status(thm)],[140]) ).
thf(161,plain,
! [A: $i] :
( ( ( A @ ( a @ implies ) )
!= b )
| ( ( A @ ( b @ implies ) )
!= ( b @ ( a @ not @ implies ) ) ) ),
inference(simp,[status(thm)],[143]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) ) )
| ( A
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(64,plain,
! [A: $i] :
( ( A @ ( b @ ( a @ implies ) @ not @ implies ) )
!= ( b @ ( b @ ( a @ not @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(85,plain,
! [A: $i] :
( ( A != b )
| ( ( b @ ( a @ not @ implies ) )
!= ( b @ ( a @ implies ) @ not ) ) ),
inference(simp,[status(thm)],[64]) ).
thf(86,plain,
( ( b @ ( a @ not @ implies ) )
!= ( b @ ( a @ implies ) @ not ) ),
inference(simp,[status(thm)],[85]) ).
thf(41,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
!= ( true @ ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) @ ( true @ ( E @ ( D @ implies ) @ is_a_theorem @ ifeq ) ) ) ) )
| ( B = true ) ),
inference(paramod_ordered,[status(thm)],[11,13]) ).
thf(50,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != true )
| ( B
!= ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) ) )
| ( A != true )
| ( A
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( B = true ) ),
inference(simp,[status(thm)],[41]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ is_a_theorem )
!= true )
| ( ( true @ ( B @ is_a_theorem @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[50]) ).
thf(307,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[290,55]) ).
thf(308,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( E @ ( D @ implies ) @ is_a_theorem ) )
| ( ( true @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[307]) ).
thf(309,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[308:[bind(A,$thf( A )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( J @ ( K @ not @ implies ) @ ( K @ implies ) @ not )),bind(E,$thf( A ))]]) ).
thf(338,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[309]) ).
thf(543,plain,
! [A: $i] :
( ( ( A @ ( b @ ( a @ not @ implies ) @ implies ) )
!= b )
| ( ( A @ ( b @ implies ) )
!= a )
| ( b != b )
| ( ( b @ ( a @ not @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[173]) ).
thf(544,plain,
! [A: $i] :
( ( ( A @ ( b @ ( a @ not @ implies ) @ implies ) )
!= b )
| ( ( A @ ( b @ implies ) )
!= a )
| ( ( b @ ( a @ not @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[543]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( B @ is_a_theorem ) )
| ( ( true @ ( true @ ( C @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( C @ ( B @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,13]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[34:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) )),bind(C,$thf( C ))]]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( A @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[35]) ).
thf(401,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ implies ) @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[56,11]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( b != B )
| ( ( b @ ( a @ not @ implies ) )
!= A )
| ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[145]) ).
thf(171,plain,
! [A: $i] :
( ( ( A @ ( b @ ( a @ not @ implies ) @ implies ) @ ( A @ ( b @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) )
| ( ( b @ ( b @ ( a @ not @ implies ) @ implies ) )
!= ( b @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(177,plain,
! [A: $i] :
( ( ( A @ ( a @ implies ) )
!= b )
| ( A != b )
| ( ( a @ not )
!= b ) ),
inference(simp,[status(thm)],[161]) ).
thf(178,plain,
( ( ( b @ ( a @ implies ) )
!= b )
| ( ( a @ not )
!= b ) ),
inference(simp,[status(thm)],[177]) ).
thf(6102,plain,
$false,
inference(e,[status(thm)],[347,10,164,551,9,22,140,162,18,11,87,290,168,111,389,14,189,29,160,192,173,13,166,32,161,64,17,12,86,81,7,16,338,544,31,55,401,171,15,178]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL060-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/0.38 % Computer : n007.cluster.edu
% 0.14/0.38 % Model : x86_64 x86_64
% 0.14/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.38 % Memory : 8046.5625MB
% 0.14/0.38 % OS : Linux 6.8.0-71-generic
% 0.14/0.38 % CPULimit : 300
% 0.14/0.38 % WCLimit : 300
% 0.14/0.38 % DateTime : Fri Sep 25 21:44:54 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.34/1.21 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.71/1.49 % [INFO] Parsing done (279ms).
% 1.91/1.51 % [INFO] Running in sequential loop mode.
% 2.83/2.16 % [INFO] eprover registered as external prover.
% 2.83/2.17 % [INFO] Scanning for conjecture ...
% 3.07/2.31 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 3.07/2.36 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 3.07/2.38 % [INFO] Problem is propositional (TPTP CNF).
% 3.07/2.39 % [INFO] Type checking passed.
% 3.23/2.40 % [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 ...
% 59.90/13.39 % External prover 'e' found a proof!
% 59.90/13.39 % [INFO] Killing All external provers ...
% 59.90/13.39 % Time passed: 12872ms (effective reasoning time: 11872ms)
% 59.90/13.40 % Axioms used in derivation (5): cn_2, ifeq_axiom, condensed_detachment, cn_1, cn_3
% 59.90/13.40 % No. of inferences in proof: 98
% 59.90/13.40 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 12872 ms resp. 11872 ms w/o parsing
% 50.15/13.48 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 50.15/13.48 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------