%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL050-10 : 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 : n006.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 07:50:40 AM UTC 2026
% Result : Unsatisfiable 52.39s 11.63s
% Output : Refutation 44.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 97 ( 58 unt; 0 typ; 0 def)
% Number of atoms : 165 ( 164 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 1337 ( 115 ~; 68 |; 0 &;1154 @)
% ( 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 : 10 ( 8 usr; 5 con; 0-4 aty)
% Number of variables : 187 ( 0 ^; 187 !; 0 ?; 187 :)
% 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(c_decl,type,
c: $i ).
thf(true_decl,type,
true: $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(5,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox2/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(6,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
= true ),
file('/export/starexec/sandbox2/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/sandbox2/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/sandbox2/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(85,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(101,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)],[17,85]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ not @ implies ) @ implies ) ))]]) ).
thf(110,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)],[102]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[110,11]) ).
thf(1,negated_conjecture,
( ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem )
!= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_21) ).
thf(7,plain,
( ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,plain,
( ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(lifteq,[status(thm)],[8]) ).
thf(201,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[192,9]) ).
thf(202,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[201]) ).
thf(225,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[202]) ).
thf(233,plain,
! [B: $i,A: $i] :
( ( A
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[225]) ).
thf(234,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ not )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[233]) ).
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/sandbox2/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(65,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( 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 )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( 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 ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(148,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[81]) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= b )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[148]) ).
thf(257,plain,
! [A: $i] :
( ( ( A @ ( a @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( A @ ( c @ ( b @ implies ) @ implies ) )
!= b ) ),
inference(simp,[status(thm)],[239]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( 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 )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[27]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[28]) ).
thf(96,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)],[19,85]) ).
thf(97,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[96:[bind(A,$thf( I @ not )),bind(B,$thf( G )),bind(C,$thf( G @ ( I @ not @ not @ implies ) )),bind(D,$thf( I ))]]) ).
thf(108,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[97]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( A
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(143,plain,
! [A: $i] :
( ( A @ ( c @ ( b @ implies ) @ ( a @ implies ) @ not @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(144,plain,
! [A: $i] :
( ( A
!= ( c @ ( a @ implies ) ) )
| ( ( c @ ( b @ implies ) @ ( a @ implies ) @ not )
!= b ) ),
inference(simp,[status(thm)],[143]) ).
thf(145,plain,
( ( c @ ( b @ implies ) @ ( a @ implies ) @ not )
!= b ),
inference(simp,[status(thm)],[144]) ).
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(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(405,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(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(153,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(238,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( ( C @ ( B @ implies ) )
!= b )
| ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( b @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[148]) ).
thf(248,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( b @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( b != a )
| ( ( C @ ( A @ implies ) )
!= B )
| ( ( C @ ( B @ implies ) )
!= A )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[240]) ).
thf(263,plain,
! [A: $i] :
( ( ( c @ ( b @ implies ) )
!= ( c @ ( a @ implies ) ) )
| ( b != a )
| ( ( A @ ( a @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( A @ ( c @ ( b @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[248]) ).
thf(345,plain,
! [A: $i] :
( ( c != c )
| ( b != a )
| ( b != a )
| ( ( A @ ( a @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( A @ ( c @ ( b @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[263]) ).
thf(348,plain,
! [A: $i] :
( ( b != a )
| ( ( A @ ( a @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( A @ ( c @ ( b @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[345]) ).
thf(244,plain,
! [C: $i,B: $i,A: $i] :
( ( ( c @ ( a @ implies ) @ ( b @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= B )
| ( ( C @ ( B @ implies ) )
!= A )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[240]) ).
thf(260,plain,
! [A: $i] :
( ( ( c @ ( a @ implies ) @ ( b @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) )
| ( ( A @ ( a @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( A @ ( c @ ( b @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[244]) ).
thf(346,plain,
! [A: $i] :
( ( c != c )
| ( b != a )
| ( b != a )
| ( A != c )
| ( b != a )
| ( ( A @ ( c @ ( b @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[263]) ).
thf(349,plain,
( ( b != a )
| ( ( c @ ( c @ ( b @ implies ) @ implies ) )
!= a ) ),
inference(simp,[status(thm)],[346]) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( B
!= ( c @ ( b @ implies ) ) )
| ( A != a ) ),
inference(simp,[status(thm)],[148]) ).
thf(256,plain,
! [A: $i] :
( ( A @ ( a @ implies ) @ ( A @ ( c @ ( b @ implies ) @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(94,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)],[19,85]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[94:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( I @ not @ implies ) @ ( I @ implies ) ))]]) ).
thf(114,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)],[95]) ).
thf(476,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[114,11]) ).
thf(20,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( 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 )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[20]) ).
thf(22,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(30,plain,
! [A: $i] :
( ( A
!= ( c @ ( a @ implies ) @ ( b @ implies ) ) )
| ( ( A @ ( A @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(31,plain,
( ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( a @ implies ) @ ( b @ implies ) @ not @ implies ) )
!= ( c @ ( b @ implies ) @ ( a @ implies ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(32,plain,
( ( ( c @ ( a @ implies ) @ ( b @ implies ) )
!= ( c @ ( b @ implies ) ) )
| ( ( c @ ( a @ implies ) @ ( b @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[31]) ).
thf(63,plain,
( ( ( c @ ( a @ implies ) )
!= c )
| ( b != b )
| ( ( c @ ( a @ implies ) @ ( b @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[32]) ).
thf(64,plain,
( ( ( c @ ( a @ implies ) )
!= c )
| ( ( c @ ( a @ implies ) @ ( b @ implies ) @ not )
!= a ) ),
inference(simp,[status(thm)],[63]) ).
thf(477,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)],[476,153]) ).
thf(478,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[477:[bind(A,$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(540,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[478]) ).
thf(545,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[540,11]) ).
thf(555,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[545,9]) ).
thf(556,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[555]) ).
thf(601,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) )
!= ( c @ ( a @ implies ) @ ( b @ implies ) @ ( c @ ( b @ implies ) @ ( a @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[556]) ).
thf(270,plain,
! [A: $i] :
( ( A != c )
| ( a != a )
| ( ( A @ ( c @ ( b @ implies ) @ implies ) )
!= b ) ),
inference(simp,[status(thm)],[257]) ).
thf(271,plain,
( ( c @ ( c @ ( b @ implies ) @ implies ) )
!= b ),
inference(simp,[status(thm)],[270]) ).
thf(288,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( true != true )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[192,55]) ).
thf(289,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ implies ) @ is_a_theorem )
!= ( D @ ( C @ implies ) @ is_a_theorem ) )
| ( ( true @ ( D @ is_a_theorem @ ( true @ ( C @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[288]) ).
thf(290,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[289:[bind(A,$thf( A )),bind(B,$thf( G )),bind(C,$thf( G @ ( G @ ( G @ not @ implies ) @ implies ) @ not )),bind(D,$thf( A ))]]) ).
thf(327,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( B @ ( B @ ( B @ not @ implies ) @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[290]) ).
thf(4529,plain,
$false,
inference(e,[status(thm)],[234,257,14,29,85,9,13,12,108,145,55,405,15,10,153,238,348,192,260,349,256,225,476,32,148,64,17,601,22,545,81,7,271,18,327,16,31,11,143]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL050-10 : 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
% 0.14/0.40 % Computer : n006.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 : Fri Sep 25 21:46:10 UTC 2026
% 0.18/0.41 % CPUTime :
% 0.18/0.41 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
% 1.17/1.13 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.60/1.39 % [INFO] Parsing done (261ms).
% 1.78/1.41 % [INFO] Running in sequential loop mode.
% 2.44/2.01 % [INFO] eprover registered as external prover.
% 2.44/2.03 % [INFO] Scanning for conjecture ...
% 2.86/2.16 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.94/2.20 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.94/2.22 % [INFO] Problem is propositional (TPTP CNF).
% 2.94/2.23 % [INFO] Type checking passed.
% 2.94/2.24 % [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 ...
% 52.39/11.62 % External prover 'e' found a proof!
% 52.39/11.62 % [INFO] Killing All external provers ...
% 52.39/11.62 % Time passed: 11063ms (effective reasoning time: 10200ms)
% 52.39/11.63 % Axioms used in derivation (5): cn_2, ifeq_axiom, condensed_detachment, cn_1, cn_3
% 52.39/11.63 % No. of inferences in proof: 97
% 52.39/11.63 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 11063 ms resp. 10200 ms w/o parsing
% 44.02/11.74 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 44.02/11.74 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------