%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL385-10 : TPTP v9.3.1. Released v7.5.0.
% 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 : n004.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 07:51:40 AM UTC 2026
% Result : Unsatisfiable 51.93s 21.23s
% Output : Refutation 43.35s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 96 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 175 ( 174 equ; 0 cnn)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 1271 ( 125 ~; 79 |; 0 &;1067 @)
% ( 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 : 196 ( 0 ^; 196 !; 0 ?; 196 :)
% Comments :
%------------------------------------------------------------------------------
thf(is_a_theorem_decl,type,
is_a_theorem: $i > $i ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(x_decl,type,
x: $i ).
thf(not_decl,type,
not: $i > $i ).
thf(y_decl,type,
y: $i ).
thf(true_decl,type,
true: $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $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(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(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(523,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(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(185,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(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(1,negated_conjecture,
( ( x @ not @ ( y @ implies ) @ ( y @ not @ ( x @ implies ) @ implies ) @ is_a_theorem )
!= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_cn_47) ).
thf(7,plain,
( ( x @ not @ ( y @ implies ) @ ( y @ not @ ( x @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(8,plain,
( ( x @ not @ ( y @ implies ) @ ( y @ not @ ( x @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(polarity_switch,[status(thm)],[7]) ).
thf(9,plain,
( ( x @ not @ ( y @ implies ) @ ( y @ not @ ( x @ implies ) @ implies ) @ is_a_theorem )
!= true ),
inference(lifteq,[status(thm)],[8]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) @ ( A @ implies ) @ is_a_theorem )
!= ( x @ not @ ( y @ implies ) @ ( y @ not @ ( x @ 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 )
!= ( x @ not @ ( y @ implies ) @ ( y @ not @ ( x @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[27]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ implies ) @ ( A @ implies ) )
!= ( x @ not @ ( y @ implies ) @ ( y @ not @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[28]) ).
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 )
!= ( x @ not @ ( y @ implies ) @ ( y @ not @ ( x @ 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 )
!= ( x @ not @ ( y @ implies ) @ ( y @ not @ ( x @ 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 ) )
!= ( x @ not @ ( y @ implies ) @ ( y @ not @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( x @ not @ ( y @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( y @ not @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[81]) ).
thf(144,plain,
! [C: $i,B: $i,A: $i] :
( ( ( x @ not @ ( y @ implies ) )
!= ( y @ not @ ( x @ implies ) ) )
| ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( y @ not @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[140]) ).
thf(148,plain,
! [C: $i,B: $i,A: $i] :
( ( ( x @ not @ ( y @ implies ) )
!= ( y @ not @ ( x @ implies ) ) )
| ( ( C @ ( A @ implies ) )
!= B )
| ( ( C @ ( B @ implies ) )
!= A )
| ( B
!= ( y @ not ) )
| ( A != x ) ),
inference(simp,[status(thm)],[144]) ).
thf(164,plain,
! [A: $i] :
( ( ( x @ not @ ( y @ implies ) )
!= ( y @ not @ ( x @ implies ) ) )
| ( ( A @ ( x @ implies ) )
!= ( y @ not ) )
| ( ( A @ ( y @ not @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[148]) ).
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(285,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(152,plain,
! [C: $i,B: $i,A: $i] :
( ( ( y @ not )
!= ( x @ not ) )
| ( y != x )
| ( ( C @ ( A @ implies ) )
!= B )
| ( ( C @ ( B @ implies ) )
!= A )
| ( B
!= ( y @ not ) )
| ( A != x ) ),
inference(simp,[status(thm)],[144]) ).
thf(167,plain,
! [A: $i] :
( ( ( y @ not )
!= ( x @ not ) )
| ( y != x )
| ( ( A @ ( x @ implies ) )
!= ( y @ not ) )
| ( ( A @ ( y @ not @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[152]) ).
thf(222,plain,
! [A: $i] :
( ( y != x )
| ( y != x )
| ( ( A @ ( x @ implies ) )
!= ( y @ not ) )
| ( ( A @ ( y @ not @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[167]) ).
thf(223,plain,
! [A: $i] :
( ( y != x )
| ( ( A @ ( x @ implies ) )
!= ( y @ not ) )
| ( ( A @ ( y @ not @ implies ) )
!= x ) ),
inference(simp,[status(thm)],[222]) ).
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(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(142,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= ( x @ not ) )
| ( ( C @ ( B @ implies ) )
!= y )
| ( ( B @ ( A @ implies ) )
!= ( y @ not @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[140]) ).
thf(286,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)],[285,185]) ).
thf(287,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[286:[bind(A,$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(335,plain,
! [B: $i,A: $i] :
( ( true @ ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[287]) ).
thf(340,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
= true ),
inference(rewrite,[status(thm)],[335,11]) ).
thf(306,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)],[285,55]) ).
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 @ ( E @ is_a_theorem @ ( true @ ( D @ is_a_theorem @ ifeq ) ) ) )
= true ) ),
inference(simp,[status(thm)],[306]) ).
thf(308,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( A @ is_a_theorem @ ( true @ ( B @ ( C @ not @ implies ) @ ( C @ implies ) @ not @ is_a_theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[307:[bind(A,$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(334,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)],[308]) ).
thf(141,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( x @ not @ ( y @ implies ) ) )
| ( B
!= ( y @ not ) )
| ( A != x ) ),
inference(simp,[status(thm)],[140]) ).
thf(160,plain,
! [A: $i] :
( ( A @ ( x @ implies ) @ ( A @ ( y @ not @ implies ) @ implies ) )
!= ( x @ not @ ( y @ implies ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ( ( x @ not @ ( y @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( y @ not @ ( x @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( y @ not @ ( x @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[140]) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ( ( x @ not )
!= B )
| ( y != A )
| ( ( C @ ( A @ implies ) )
!= ( y @ not ) )
| ( ( C @ ( B @ implies ) )
!= x )
| ( ( B @ ( A @ implies ) )
!= ( y @ not @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[145]) ).
thf(172,plain,
! [A: $i] :
( ( ( A @ ( y @ implies ) )
!= ( y @ not ) )
| ( ( A @ ( x @ not @ implies ) )
!= x )
| ( ( x @ not @ ( y @ implies ) )
!= ( y @ not @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(520,plain,
! [A: $i] :
( ( ( A @ ( y @ implies ) )
!= ( y @ not ) )
| ( ( A @ ( x @ not @ implies ) )
!= x )
| ( ( y @ not )
!= ( x @ not ) )
| ( y != x ) ),
inference(simp,[status(thm)],[172]) ).
thf(592,plain,
! [A: $i] :
( ( ( A @ ( y @ implies ) )
!= ( y @ not ) )
| ( ( A @ ( x @ not @ implies ) )
!= x )
| ( y != x )
| ( y != x ) ),
inference(simp,[status(thm)],[520]) ).
thf(593,plain,
! [A: $i] :
( ( ( A @ ( y @ implies ) )
!= ( y @ not ) )
| ( ( A @ ( x @ not @ implies ) )
!= x )
| ( y != x ) ),
inference(simp,[status(thm)],[592]) ).
thf(20,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ not @ implies ) @ implies ) @ is_a_theorem )
!= ( x @ not @ ( y @ implies ) @ ( y @ not @ ( x @ 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 )
!= ( x @ not @ ( y @ implies ) @ ( y @ not @ ( x @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[20]) ).
thf(22,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ not @ implies ) @ implies ) )
!= ( x @ not @ ( y @ implies ) @ ( y @ not @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[21]) ).
thf(30,plain,
! [A: $i] :
( ( A
!= ( x @ not @ ( y @ implies ) ) )
| ( ( A @ ( A @ not @ implies ) )
!= ( y @ not @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[22]) ).
thf(31,plain,
( ( x @ not @ ( y @ implies ) @ ( x @ not @ ( y @ implies ) @ not @ implies ) )
!= ( y @ not @ ( x @ implies ) ) ),
inference(simp,[status(thm)],[30]) ).
thf(32,plain,
( ( ( x @ not @ ( y @ implies ) )
!= ( y @ not ) )
| ( ( x @ not @ ( y @ implies ) @ not )
!= x ) ),
inference(simp,[status(thm)],[31]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) )
!= ( x @ not ) )
| ( ( C @ ( B @ implies ) )
!= y )
| ( B
!= ( y @ not ) )
| ( A != x ) ),
inference(simp,[status(thm)],[140]) ).
thf(161,plain,
! [A: $i] :
( ( ( A @ ( x @ implies ) )
!= ( x @ not ) )
| ( ( A @ ( y @ not @ implies ) )
!= y ) ),
inference(simp,[status(thm)],[143]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ implies ) )
!= ( x @ not @ ( y @ implies ) ) )
| ( A
!= ( y @ not @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(64,plain,
! [A: $i] :
( ( A @ ( y @ not @ ( x @ implies ) @ not @ implies ) )
!= ( x @ not @ ( y @ implies ) ) ),
inference(simp,[status(thm)],[63]) ).
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(402,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(352,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( x @ not @ ( y @ implies ) @ ( y @ not @ ( x @ implies ) @ implies ) @ is_a_theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[340,9]) ).
thf(353,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) @ is_a_theorem )
!= ( x @ not @ ( y @ implies ) @ ( y @ not @ ( x @ implies ) @ implies ) @ is_a_theorem ) ),
inference(simp,[status(thm)],[352]) ).
thf(382,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ not @ implies ) @ ( B @ implies ) )
!= ( x @ not @ ( y @ implies ) @ ( y @ not @ ( x @ implies ) @ implies ) ) ),
inference(simp,[status(thm)],[353]) ).
thf(85,plain,
! [A: $i] :
( ( A
!= ( x @ not ) )
| ( ( y @ not @ ( x @ implies ) @ not )
!= y ) ),
inference(simp,[status(thm)],[64]) ).
thf(86,plain,
( ( y @ not @ ( x @ implies ) @ not )
!= y ),
inference(simp,[status(thm)],[85]) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] :
( ( ( y @ not )
!= ( x @ not ) )
| ( y != x )
| ( ( C @ ( A @ implies ) @ ( C @ ( B @ implies ) @ implies ) )
!= ( B @ ( A @ implies ) ) )
| ( B
!= ( y @ not ) )
| ( A != x ) ),
inference(simp,[status(thm)],[144]) ).
thf(165,plain,
! [A: $i] :
( ( ( y @ not )
!= ( x @ not ) )
| ( y != x )
| ( ( A @ ( x @ implies ) @ ( A @ ( y @ not @ implies ) @ implies ) )
!= ( y @ not @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(393,plain,
! [A: $i] :
( ( y != x )
| ( y != x )
| ( ( A @ ( x @ implies ) @ ( A @ ( y @ not @ implies ) @ implies ) )
!= ( y @ not @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(395,plain,
! [A: $i] :
( ( y != x )
| ( ( A @ ( x @ implies ) @ ( A @ ( y @ not @ implies ) @ implies ) )
!= ( y @ not @ ( x @ implies ) ) ) ),
inference(simp,[status(thm)],[393]) ).
thf(7316,plain,
$false,
inference(e,[status(thm)],[523,185,14,29,164,285,13,140,223,18,11,87,55,111,10,142,340,334,160,9,593,32,161,64,17,402,22,12,382,86,172,81,7,16,31,395,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL385-10 : TPTP v9.3.1. Released v7.5.0.
% 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
% 0.14/10.43 % Computer : n004.cluster.edu
% 0.14/10.43 % Model : x86_64 x86_64
% 0.14/10.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/10.43 % Memory : 8046.5625MB
% 0.14/10.43 % OS : Linux 6.8.0-71-generic
% 0.14/10.43 % CPULimit : 300
% 0.14/10.43 % WCLimit : 300
% 0.14/10.43 % DateTime : Fri Sep 25 22:24:03 UTC 2026
% 0.14/10.43 % CPUTime :
% 0.14/10.43 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
% 0.18/11.02 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.35/11.20 % [INFO] Parsing done (181ms).
% 1.35/11.22 % [INFO] Running in sequential loop mode.
% 1.94/11.63 % [INFO] eprover registered as external prover.
% 1.94/11.64 % [INFO] Scanning for conjecture ...
% 2.14/11.73 % [INFO] Found a conjecture (or negated_conjecture) and 5 axioms. Running axiom selection ...
% 2.14/11.76 % [INFO] Axiom selection finished. Selected 5 axioms (removed 0 axioms).
% 2.14/11.77 % [INFO] Problem is propositional (TPTP CNF).
% 2.14/11.78 % [INFO] Type checking passed.
% 2.14/11.78 % [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 ...
% 51.93/21.22 % External prover 'e' found a proof!
% 51.93/21.22 % [INFO] Killing All external provers ...
% 51.93/21.22 % Time passed: 10651ms (effective reasoning time: 9999ms)
% 51.93/21.23 % Axioms used in derivation (5): cn_2, ifeq_axiom, condensed_detachment, cn_1, cn_3
% 51.93/21.23 % No. of inferences in proof: 96
% 51.93/21.23 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10651 ms resp. 9999 ms w/o parsing
% 43.35/21.30 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 43.35/21.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------