%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL218-10 : 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 : n012.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 07:51:14 AM UTC 2026
% Result : Unsatisfiable 45.99s 16.19s
% Output : Refutation 37.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 91 ( 66 unt; 0 typ; 0 def)
% Number of atoms : 124 ( 123 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 1059 ( 63 ~; 33 |; 0 &; 963 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-4 aty)
% Number of variables : 156 ( 0 ^; 156 !; 0 ?; 156 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_decl,type,
theorem: $i > $i ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(not_decl,type,
not: $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(5,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
= true ),
inference(lifteq,[status(thm)],[20]) ).
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(14,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
= B ),
inference(lifteq,[status(thm)],[14]) ).
thf(8,axiom,
! [A: $i] :
( ( true @ ( A @ theorem @ ( true @ ( A @ axiom @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
thf(26,plain,
! [A: $i] :
( ( true @ ( A @ theorem @ ( true @ ( A @ axiom @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,plain,
! [A: $i] :
( ( true @ ( A @ theorem @ ( true @ ( A @ axiom @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[26]) ).
thf(56,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ ( A @ ifeq ) ) ) )
!= ( true @ ( D @ theorem @ ( true @ ( D @ axiom @ ifeq ) ) ) ) )
| ( B = true ) ),
inference(paramod_ordered,[status(thm)],[15,27]) ).
thf(58,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C != true )
| ( B
!= ( D @ theorem ) )
| ( A != true )
| ( A
!= ( D @ axiom ) )
| ( B = true ) ),
inference(simp,[status(thm)],[56]) ).
thf(60,plain,
! [A: $i] :
( ( ( A @ axiom )
!= true )
| ( ( A @ theorem )
= true ) ),
inference(simp,[status(thm)],[58]) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ axiom ) )
| ( true != true )
| ( ( C @ theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[21,60]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ axiom ) )
| ( ( C @ theorem )
= true ) ),
inference(simp,[status(thm)],[70]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
= true ),
inference(pattern_uni,[status(thm)],[71:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( J @ ( I @ or ) @ ( I @ ( J @ or ) @ not @ or ) ))]]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
= true ),
inference(simp,[status(thm)],[72]) ).
thf(1,negated_conjecture,
( ( q @ ( p @ not @ or ) @ ( q @ ( q @ ( p @ or ) @ not @ or ) @ not @ or ) @ theorem )
!= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(11,plain,
( ( q @ ( p @ not @ or ) @ ( q @ ( q @ ( p @ or ) @ not @ or ) @ not @ or ) @ theorem )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
( ( q @ ( p @ not @ or ) @ ( q @ ( q @ ( p @ or ) @ not @ or ) @ not @ or ) @ theorem )
!= true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( q @ ( p @ not @ or ) @ ( q @ ( q @ ( p @ or ) @ not @ or ) @ not @ or ) @ theorem )
!= true ),
inference(lifteq,[status(thm)],[12]) ).
thf(163,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( q @ ( p @ not @ or ) @ ( q @ ( q @ ( p @ or ) @ not @ or ) @ not @ or ) @ theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[83,13]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( q @ ( p @ not @ or ) @ ( q @ ( q @ ( p @ or ) @ not @ or ) @ not @ or ) @ theorem ) ),
inference(simp,[status(thm)],[163]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) )
!= ( q @ ( p @ not @ or ) @ ( q @ ( q @ ( p @ or ) @ not @ or ) @ not @ or ) ) ),
inference(simp,[status(thm)],[164]) ).
thf(357,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( q @ ( p @ not @ or ) ) )
| ( ( A @ ( B @ or ) @ not )
!= ( q @ ( q @ ( p @ or ) @ not @ or ) @ not ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(360,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( A
!= ( p @ not ) )
| ( ( A @ ( B @ or ) )
!= ( q @ ( q @ ( p @ or ) @ not @ or ) ) ) ),
inference(simp,[status(thm)],[357]) ).
thf(362,plain,
( ( q @ ( q @ ( p @ or ) @ not @ or ) )
!= ( p @ not @ ( q @ or ) ) ),
inference(simp,[status(thm)],[360]) ).
thf(365,plain,
( ( ( p @ not )
!= q )
| ( ( q @ ( p @ or ) @ not )
!= q ) ),
inference(simp,[status(thm)],[362]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
= true ),
inference(lifteq,[status(thm)],[18]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ theorem @ ( true @ ( B @ ( A @ not @ or ) @ axiom @ ifeq ) ) ) @ ( true @ ( A @ theorem @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ theorem @ ( true @ ( B @ ( A @ not @ or ) @ axiom @ ifeq ) ) ) @ ( true @ ( A @ theorem @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ theorem @ ( true @ ( B @ ( A @ not @ or ) @ axiom @ ifeq ) ) ) @ ( true @ ( A @ theorem @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[28]) ).
thf(229,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( D @ ( C @ not @ or ) @ axiom ) )
| ( ( true @ ( true @ ( D @ theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( C @ theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[19,29]) ).
thf(230,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( A @ or ) @ theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( B @ theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[229:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ or ) ))]]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( A @ or ) @ theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( B @ theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[230]) ).
thf(276,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ or ) @ theorem @ ( true @ ( B @ theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[262,15]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
thf(16,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
= true ),
inference(lifteq,[status(thm)],[16]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( B @ axiom ) )
| ( ( true @ ( B @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,27]) ).
thf(33,plain,
! [A: $i] :
( ( true @ ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ or ) @ not @ or ) ))]]) ).
thf(34,plain,
! [A: $i] :
( ( true @ ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[33]) ).
thf(55,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
= true ),
inference(rewrite,[status(thm)],[34,15]) ).
thf(91,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( q @ ( p @ not @ or ) @ ( q @ ( q @ ( p @ or ) @ not @ or ) @ not @ or ) @ theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[55,13]) ).
thf(92,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( q @ ( p @ not @ or ) @ ( q @ ( q @ ( p @ or ) @ not @ or ) @ not @ or ) @ theorem ) ),
inference(simp,[status(thm)],[91]) ).
thf(99,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) )
!= ( q @ ( p @ not @ or ) @ ( q @ ( q @ ( p @ or ) @ not @ or ) @ not @ or ) ) ),
inference(simp,[status(thm)],[92]) ).
thf(178,plain,
! [A: $i] :
( ( A
!= ( q @ ( p @ not @ or ) ) )
| ( ( A @ ( A @ or ) @ not )
!= ( q @ ( q @ ( p @ or ) @ not @ or ) @ not ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(179,plain,
( ( q @ ( p @ not @ or ) @ ( q @ ( p @ not @ or ) @ or ) @ not )
!= ( q @ ( q @ ( p @ or ) @ not @ or ) @ not ) ),
inference(simp,[status(thm)],[178]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ axiom ) )
| ( ( true @ ( C @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[19,27]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ or ) @ ( H @ not @ or ) ))]]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[40]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
= true ),
inference(rewrite,[status(thm)],[41,15]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( q @ ( p @ not @ or ) @ ( q @ ( q @ ( p @ or ) @ not @ or ) @ not @ or ) @ theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[54,13]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( q @ ( p @ not @ or ) @ ( q @ ( q @ ( p @ or ) @ not @ or ) @ not @ or ) @ theorem ) ),
inference(simp,[status(thm)],[85]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ not @ or ) )
!= ( q @ ( p @ not @ or ) @ ( q @ ( q @ ( p @ or ) @ not @ or ) @ not @ or ) ) ),
inference(simp,[status(thm)],[86]) ).
thf(359,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( A
!= ( p @ not ) )
| ( ( A @ ( B @ or ) @ not )
!= ( q @ ( q @ ( p @ or ) @ not @ or ) @ not ) ) ),
inference(simp,[status(thm)],[357]) ).
thf(361,plain,
( ( q @ ( q @ ( p @ or ) @ not @ or ) @ not )
!= ( p @ not @ ( q @ or ) @ not ) ),
inference(simp,[status(thm)],[359]) ).
thf(298,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( C @ ( B @ or ) @ theorem ) )
| ( ( true @ ( true @ ( true @ ( C @ theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[55,276]) ).
thf(299,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[298:[bind(A,$thf( F )),bind(B,$thf( F @ ( F @ or ) @ not )),bind(C,$thf( F ))]]) ).
thf(317,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[299]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( q @ ( p @ not @ or ) ) )
| ( ( B @ not )
!= ( q @ ( q @ ( p @ or ) @ not @ or ) @ not ) ) ),
inference(simp,[status(thm)],[89]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( A
!= ( p @ not ) )
| ( B
!= ( q @ ( q @ ( p @ or ) @ not @ or ) ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(109,plain,
( ( q @ ( q @ ( p @ or ) @ not @ or ) )
!= q ),
inference(simp,[status(thm)],[106]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( q @ ( p @ not @ or ) ) )
| ( B
!= ( q @ ( q @ ( p @ or ) @ not @ or ) ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(107,plain,
! [A: $i] :
( ( q @ ( q @ ( p @ or ) @ not @ or ) @ ( A @ or ) )
!= ( q @ ( p @ not @ or ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ not @ or ) @ ( B @ ( A @ not @ or ) @ not @ or ) @ axiom )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ not @ or ) @ ( B @ ( A @ not @ or ) @ not @ or ) @ 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 ) @ not @ or ) @ ( B @ ( A @ not @ or ) @ not @ or ) @ axiom )
= true ),
inference(lifteq,[status(thm)],[24]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( C @ theorem ) )
| ( ( true @ ( true @ ( true @ ( C @ axiom @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[54,27]) ).
thf(88,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( B @ ( A @ or ) @ ( B @ not @ or ) @ axiom @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( H @ ( G @ or ) @ ( H @ not @ or ) ))]]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( B @ ( A @ or ) @ ( B @ not @ or ) @ axiom @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[88]) ).
thf(110,plain,
( ( true @ ( true @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[90,19]) ).
thf(180,plain,
( ( q @ ( p @ not @ or ) @ ( q @ ( p @ not @ or ) @ or ) )
!= ( q @ ( q @ ( p @ or ) @ not @ or ) ) ),
inference(simp,[status(thm)],[179]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ not @ or ) @ axiom )
= true ),
file('/export/starexec/sandbox2/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 ) @ not @ or ) @ axiom )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( A
!= ( p @ not ) )
| ( ( B @ not )
!= ( q @ ( q @ ( p @ or ) @ not @ or ) @ not ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(108,plain,
( ( q @ ( q @ ( p @ or ) @ not @ or ) @ not )
!= ( q @ not ) ),
inference(simp,[status(thm)],[105]) ).
thf(234,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ ( B @ not @ or ) @ axiom ) )
| ( ( true @ ( true @ ( C @ theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( B @ theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,29]) ).
thf(235,plain,
! [A: $i] :
( ( true @ ( true @ ( A @ theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( A @ or ) @ theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[234:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ or ) )),bind(C,$thf( E ))]]) ).
thf(263,plain,
! [A: $i] :
( ( true @ ( true @ ( A @ theorem @ ( true @ ( true @ ifeq ) ) ) @ ( true @ ( A @ ( A @ or ) @ theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[235]) ).
thf(462,plain,
! [A: $i] :
( ( true @ ( A @ theorem @ ( true @ ( A @ ( A @ or ) @ theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[263,15]) ).
thf(182,plain,
( ( ( q @ ( p @ not @ or ) )
!= q )
| ( ( q @ ( p @ not @ or ) )
!= ( q @ ( p @ or ) @ not ) ) ),
inference(simp,[status(thm)],[180]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( C @ not @ or ) @ theorem @ ( true @ ( A @ ( C @ not @ or ) @ axiom @ ifeq ) ) ) @ ( true @ ( B @ ( A @ not @ or ) @ theorem @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_3) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( C @ not @ or ) @ theorem @ ( true @ ( A @ ( C @ not @ or ) @ axiom @ ifeq ) ) ) @ ( true @ ( B @ ( A @ not @ or ) @ theorem @ ifeq ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( C @ not @ or ) @ theorem @ ( true @ ( A @ ( C @ not @ or ) @ axiom @ ifeq ) ) ) @ ( true @ ( B @ ( A @ not @ or ) @ theorem @ ifeq ) ) ) )
= true ),
inference(lifteq,[status(thm)],[30]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ not @ or ) @ axiom )
= true ),
inference(lifteq,[status(thm)],[22]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( B @ theorem ) )
| ( ( true @ ( true @ ( true @ ( B @ axiom @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[55,27]) ).
thf(94,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ or ) @ not @ or ) ))]]) ).
thf(100,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[94]) ).
thf(9642,plain,
$false,
inference(e,[status(thm)],[365,276,179,89,60,361,317,109,13,54,362,18,99,107,15,24,25,14,110,357,20,29,28,21,180,17,22,27,103,108,462,182,16,31,11,175,26,55,23,30,19,83,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : LCL218-10 : TPTP v9.3.1. Released v7.3.0.
% 0.00/0.06 % 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
% 0.11/5.59 % Computer : n012.cluster.edu
% 0.11/5.59 % Model : x86_64 x86_64
% 0.11/5.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/5.59 % Memory : 8046.5625MB
% 0.11/5.59 % OS : Linux 6.8.0-71-generic
% 0.11/5.59 % CPULimit : 300
% 0.11/5.59 % WCLimit : 300
% 0.11/5.59 % DateTime : Fri Sep 25 22:01:58 UTC 2026
% 0.11/5.59 % CPUTime :
% 0.11/5.59 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
% 0.76/6.05 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.08/6.20 % [INFO] Parsing done (141ms).
% 1.08/6.21 % [INFO] Running in sequential loop mode.
% 1.51/6.53 % [INFO] eprover registered as external prover.
% 1.51/6.53 % [INFO] Scanning for conjecture ...
% 1.71/6.60 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 1.71/6.63 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.71/6.65 % [INFO] Problem is propositional (TPTP CNF).
% 1.71/6.65 % [INFO] Type checking passed.
% 1.71/6.66 % [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 ...
% 45.99/16.19 % External prover 'e' found a proof!
% 45.99/16.19 % [INFO] Killing All external provers ...
% 45.99/16.19 % Time passed: 10481ms (effective reasoning time: 9980ms)
% 45.99/16.19 % Axioms used in derivation (9): axiom_1_5, ifeq_axiom, axiom_1_4, rule_1, axiom_1_3, rule_3, axiom_1_2, rule_2, axiom_1_6
% 45.99/16.19 % No. of inferences in proof: 91
% 45.99/16.19 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 10481 ms resp. 9980 ms w/o parsing
% 37.16/16.25 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 37.16/16.25 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------