%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL203-10 : 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 : 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 07:51:09 AM UTC 2026
% Result : Unsatisfiable 13.23s 4.23s
% Output : Refutation 11.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 10
% Syntax : Number of formulae : 100 ( 67 unt; 0 typ; 0 def)
% Number of atoms : 140 ( 139 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 973 ( 78 ~; 40 |; 0 &; 855 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 177 ( 0 ^; 177 !; 0 ?; 177 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_decl,type,
theorem: $i > $i ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(p_decl,type,
p: $i ).
thf(q_decl,type,
q: $i ).
thf(true_decl,type,
true: $i ).
thf(ifeq_decl,type,
ifeq: $i > $i > $i > $i > $i ).
thf(axiom_decl,type,
axiom: $i > $i ).
thf(8,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ or ) )
= ( B @ ( A @ implies ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom )
= true ),
inference(lifteq,[status(thm)],[20]) ).
thf(75,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( ( C @ ( D @ or ) @ ( B @ ( A @ implies ) @ implies ) @ axiom )
= true ) ),
inference(paramod_ordered,[status(thm)],[27,21]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom )
= true ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom )
= true ),
inference(simp,[status(thm)],[76]) ).
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(14,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(77,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( D @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( D @ ( C @ or ) @ implies ) @ axiom )
= true ) ),
inference(paramod_ordered,[status(thm)],[27,21]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom )
= true ),
inference(pattern_uni,[status(thm)],[77:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom )
= true ),
inference(simp,[status(thm)],[78]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
= true ),
inference(lifteq,[status(thm)],[18]) ).
thf(9,axiom,
! [A: $i] :
( ( true @ ( A @ theorem @ ( true @ ( A @ axiom @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
thf(28,plain,
! [A: $i] :
( ( true @ ( A @ theorem @ ( true @ ( A @ axiom @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,plain,
! [A: $i] :
( ( true @ ( A @ theorem @ ( true @ ( A @ axiom @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[28]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( ( true @ ( C @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[19,29]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ or ) @ ( B @ implies ) @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ or ) @ ( G @ implies ) ))]]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ or ) @ ( B @ implies ) @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[40]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(lifteq,[status(thm)],[14]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
= true ),
inference(rewrite,[status(thm)],[41,15]) ).
thf(1,negated_conjecture,
( ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ or ) @ not @ implies ) @ theorem )
!= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(11,plain,
( ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ or ) @ not @ implies ) @ theorem )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
( ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ or ) @ not @ implies ) @ theorem )
!= true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( q @ not @ ( p @ not @ or ) @ ( q @ ( p @ or ) @ not @ implies ) @ theorem )
!= true ),
inference(lifteq,[status(thm)],[12]) ).
thf(42,plain,
( ( q @ not @ ( p @ implies ) @ ( q @ ( p @ or ) @ not @ implies ) @ theorem )
!= true ),
inference(rewrite,[status(thm)],[13,27]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ ( q @ ( p @ or ) @ not @ implies ) @ theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[135,42]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ ( q @ ( p @ or ) @ not @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[136]) ).
thf(152,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) )
!= ( q @ not @ ( p @ implies ) @ ( q @ ( p @ or ) @ not @ implies ) ) ),
inference(simp,[status(thm)],[137]) ).
thf(192,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( q @ not @ ( p @ implies ) ) )
| ( B
!= ( q @ ( p @ or ) @ not ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(199,plain,
! [A: $i] :
( ( q @ ( p @ or ) @ not @ ( A @ or ) )
!= ( q @ not @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[192]) ).
thf(205,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) @ not @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,199]) ).
thf(206,plain,
! [A: $i] :
( ( q @ ( p @ or ) @ not @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) ) ),
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( D )),bind(B,$thf( q @ ( p @ or ) @ not )),bind(C,$thf( D @ not ))]]) ).
thf(208,plain,
! [A: $i] :
( ( q @ ( p @ or ) @ not @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) ) ),
inference(simp,[status(thm)],[206]) ).
thf(245,plain,
! [A: $i] :
( ( ( q @ ( p @ or ) @ not )
!= ( q @ not ) )
| ( A != p ) ),
inference(simp,[status(thm)],[208]) ).
thf(250,plain,
( ( q @ ( p @ or ) @ not )
!= ( q @ not ) ),
inference(simp,[status(thm)],[245]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( B @ ( A @ implies ) @ not )
!= ( q @ not ) ) ),
inference(paramod_ordered,[status(thm)],[27,250]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= q ) ),
inference(simp,[status(thm)],[255]) ).
thf(380,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( q @ ( p @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= q ) ),
inference(rewrite,[status(thm)],[256,27]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
thf(16,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
= true ),
inference(lifteq,[status(thm)],[16]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ( ( true @ ( B @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,29]) ).
thf(33,plain,
! [A: $i] :
( ( true @ ( A @ ( A @ ( A @ or ) @ implies ) @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ or ) @ implies ) ))]]) ).
thf(34,plain,
! [A: $i] :
( ( true @ ( A @ ( A @ ( A @ or ) @ implies ) @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[33]) ).
thf(109,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
= true ),
inference(rewrite,[status(thm)],[34,15]) ).
thf(254,plain,
( ( q @ ( p @ or ) )
!= q ),
inference(simp,[status(thm)],[250]) ).
thf(110,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ ( q @ ( p @ or ) @ not @ implies ) @ theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[109,42]) ).
thf(111,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ ( q @ ( p @ or ) @ not @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[110]) ).
thf(118,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) )
!= ( q @ not @ ( p @ implies ) @ ( q @ ( p @ or ) @ not @ implies ) ) ),
inference(simp,[status(thm)],[111]) ).
thf(156,plain,
! [A: $i] :
( ( A
!= ( q @ not @ ( p @ implies ) ) )
| ( ( A @ ( A @ or ) )
!= ( q @ ( p @ or ) @ not ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(166,plain,
( ( q @ not @ ( p @ implies ) @ ( q @ not @ ( p @ implies ) @ or ) )
!= ( q @ ( p @ or ) @ not ) ),
inference(simp,[status(thm)],[156]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ not @ ( p @ implies ) @ ( q @ not @ ( p @ implies ) @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( q @ ( p @ or ) @ not ) ) ),
inference(paramod_ordered,[status(thm)],[27,166]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( B
!= ( q @ not @ ( p @ implies ) ) )
| ( ( A @ not )
!= ( q @ not @ ( p @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( q @ ( p @ or ) @ not ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(170,plain,
! [A: $i] :
( ( ( A @ not )
!= ( q @ not @ ( p @ implies ) ) )
| ( ( q @ not @ ( p @ implies ) @ ( A @ implies ) )
!= ( q @ ( p @ or ) @ not ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( B @ theorem ) )
| ( ( true @ ( true @ ( true @ ( B @ axiom @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[109,29]) ).
thf(113,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ ( A @ ( A @ or ) @ implies ) @ axiom @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[112:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ or ) @ implies ) ))]]) ).
thf(120,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ ( A @ ( A @ or ) @ implies ) @ axiom @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[113]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ axiom )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ axiom )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ axiom )
= true ),
inference(lifteq,[status(thm)],[24]) ).
thf(246,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( B @ ( A @ implies ) @ not @ ( C @ implies ) )
!= ( q @ not @ ( p @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,208]) ).
thf(249,plain,
! [C: $i,B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( B @ ( A @ implies ) @ not )
!= ( q @ not ) )
| ( C != p ) ),
inference(simp,[status(thm)],[246]) ).
thf(253,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ( ( q @ ( A @ implies ) @ not )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[249]) ).
thf(114,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( C @ or ) ) )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) @ theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[27,109]) ).
thf(115,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
= true ),
inference(pattern_uni,[status(thm)],[114:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(121,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
= true ),
inference(simp,[status(thm)],[115]) ).
thf(258,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( B @ ( A @ implies ) )
!= q ) ),
inference(simp,[status(thm)],[255]) ).
thf(260,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ( ( q @ ( A @ implies ) )
!= q ) ),
inference(simp,[status(thm)],[258]) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( q @ not @ ( p @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) )
!= ( C @ ( C @ ( C @ or ) @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,118]) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( q @ not @ ( p @ implies ) )
!= C )
| ( ( B @ ( A @ implies ) @ not )
!= ( C @ ( C @ or ) ) ) ),
inference(simp,[status(thm)],[159]) ).
thf(165,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ( ( q @ ( A @ implies ) @ not )
!= ( q @ not @ ( p @ implies ) @ ( q @ not @ ( p @ implies ) @ or ) ) ) ),
inference(simp,[status(thm)],[162]) ).
thf(45,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( D @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( C @ implies ) @ axiom )
= true ) ),
inference(paramod_ordered,[status(thm)],[27,19]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
= true ),
inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
= true ),
inference(simp,[status(thm)],[46]) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( ( true @ ( C @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[48,29]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[52:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ implies ) @ ( G @ implies ) ))]]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[53]) ).
thf(264,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
= true ),
inference(rewrite,[status(thm)],[62,15]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ axiom )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ axiom )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ theorem @ ( true @ ( A @ theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ implies ) @ theorem @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ theorem @ ( true @ ( A @ theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ implies ) @ theorem @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ theorem @ ( true @ ( A @ theorem @ ifeq ) ) ) @ ( true @ ( B @ ( A @ implies ) @ theorem @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[30]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( C @ theorem ) )
| ( ( true @ ( true @ ( true @ ( C @ axiom @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[135,29]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( B @ ( A @ or ) @ ( B @ implies ) @ axiom @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[138:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ or ) @ ( G @ implies ) ))]]) ).
thf(155,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( B @ ( A @ or ) @ ( B @ implies ) @ axiom @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[139]) ).
thf(351,plain,
( ( true @ ( true @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[155,19]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ axiom )
= true ),
inference(lifteq,[status(thm)],[22]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( q @ not @ ( p @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[27,42]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( q @ not @ ( p @ implies ) @ ( B @ ( A @ implies ) @ not @ implies ) @ theorem )
!= true ) ),
inference(simp,[status(thm)],[49]) ).
thf(51,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ( ( q @ not @ ( p @ implies ) @ ( q @ ( A @ implies ) @ not @ implies ) @ theorem )
!= true ) ),
inference(simp,[status(thm)],[50]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( C @ or ) ) )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) @ axiom )
= true ) ),
inference(paramod_ordered,[status(thm)],[27,17]) ).
thf(44,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom )
= true ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(47,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom )
= true ),
inference(simp,[status(thm)],[44]) ).
thf(898,plain,
$false,
inference(e,[status(thm)],[88,14,89,380,109,208,135,11,250,254,170,120,42,24,25,20,152,29,253,121,260,28,21,165,166,264,17,22,118,27,48,18,199,16,31,26,351,23,30,51,19,47,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : LCL203-10 : 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
% 0.14/0.40 % 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 21:59:56 UTC 2026
% 0.14/0.40 % CPUTime :
% 0.14/0.40 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
% 0.91/0.91 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.12/1.10 % [INFO] Parsing done (186ms).
% 1.12/1.11 % [INFO] Running in sequential loop mode.
% 1.80/1.52 % [INFO] eprover registered as external prover.
% 1.80/1.53 % [INFO] Scanning for conjecture ...
% 1.98/1.61 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 1.98/1.64 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.98/1.66 % [INFO] Problem is propositional (TPTP CNF).
% 1.98/1.67 % [INFO] Type checking passed.
% 1.98/1.68 % [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 ...
% 13.23/4.22 % External prover 'e' found a proof!
% 13.23/4.22 % [INFO] Killing All external provers ...
% 13.23/4.23 % Time passed: 3731ms (effective reasoning time: 3107ms)
% 13.23/4.23 % Axioms used in derivation (9): axiom_1_5, ifeq_axiom, axiom_1_4, rule_1, axiom_1_3, implies_definition, axiom_1_2, rule_2, axiom_1_6
% 13.23/4.23 % No. of inferences in proof: 100
% 13.23/4.23 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 3731 ms resp. 3107 ms w/o parsing
% 11.69/4.30 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 11.69/4.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------