TSTP Solution File: LCL218-10 by Leo-III---1.7.15
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.15
% Problem : LCL218-10 : TPTP v8.2.0. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d THM
% Computer : n001.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Mon Jun 24 11:13:26 EDT 2024
% Result : Unsatisfiable 47.69s 10.88s
% Output : Refutation 47.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 10
% Syntax : Number of formulae : 87 ( 66 unt; 0 typ; 0 def)
% Number of atoms : 115 ( 114 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 980 ( 55 ~; 28 |; 0 &; 897 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 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 : 148 ( 0 ^ 148 !; 0 ?; 148 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_type,type,
theorem: $i > $i ).
thf(or_type,type,
or: $i > $i > $i ).
thf(not_type,type,
not: $i > $i ).
thf(p_type,type,
p: $i ).
thf(q_type,type,
q: $i ).
thf(true_type,type,
true: $i ).
thf(ifeq_type,type,
ifeq: $i > $i > $i > $i > $i ).
thf(axiom_type,type,
axiom: $i > $i ).
thf(3,axiom,
! [A: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
thf(16,plain,
! [A: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
! [A: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
= true ),
inference(lifteq,[status(thm)],[16]) ).
thf(8,axiom,
! [A: $i] :
( ( ifeq @ ( axiom @ A ) @ true @ ( theorem @ A ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
thf(26,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ A ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ A ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(lifteq,[status(thm)],[26]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ B ) @ true )
= true )
| ( ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
!= ( axiom @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17,27]) ).
thf(33,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( D )),bind(B,$thf( or @ ( not @ ( or @ D @ D ) ) @ D ))]]) ).
thf(34,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) ) @ true )
= true ),
inference(simp,[status(thm)],[33]) ).
thf(2,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom) ).
thf(14,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ A @ A @ B @ C )
= B ),
inference(lifteq,[status(thm)],[14]) ).
thf(47,plain,
! [A: $i] :
( ( theorem @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
= true ),
inference(rewrite,[status(thm)],[34,15]) ).
thf(1,negated_conjecture,
( ( theorem @ ( or @ ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) ) @ ( or @ ( not @ p ) @ q ) ) )
!= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(11,plain,
( ( theorem @ ( or @ ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) ) @ ( or @ ( not @ p ) @ q ) ) )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
( ( theorem @ ( or @ ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) ) @ ( or @ ( not @ p ) @ q ) ) )
!= true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( theorem @ ( or @ ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) ) @ ( or @ ( not @ p ) @ q ) ) )
!= true ),
inference(lifteq,[status(thm)],[12]) ).
thf(77,plain,
! [A: $i] :
( ( theorem @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
!= ( theorem @ ( or @ ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) ) @ ( or @ ( not @ p ) @ q ) ) ) ),
inference(paramod_ordered,[status(thm)],[47,13]) ).
thf(80,plain,
! [A: $i] :
( ( or @ ( not @ ( or @ A @ A ) ) @ A )
!= ( or @ ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) ) @ ( or @ ( not @ p ) @ q ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(141,plain,
! [A: $i] :
( ( ( not @ ( or @ A @ A ) )
!= ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) ) )
| ( A
!= ( or @ ( not @ p ) @ q ) ) ),
inference(simp,[status(thm)],[80]) ).
thf(142,plain,
( ( not @ ( or @ ( or @ ( not @ p ) @ q ) @ ( or @ ( not @ p ) @ q ) ) )
!= ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) )
= true ),
inference(lifteq,[status(thm)],[18]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) )
!= ( axiom @ C ) ) ),
inference(paramod_ordered,[status(thm)],[19,27]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( or @ ( not @ H ) @ ( or @ G @ H ) ))]]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[38]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) )
= true ),
inference(rewrite,[status(thm)],[39,15]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) )
!= ( theorem @ ( or @ ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) ) @ ( or @ ( not @ p ) @ q ) ) ) ),
inference(paramod_ordered,[status(thm)],[46,13]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( or @ ( not @ B ) @ ( or @ A @ B ) )
!= ( or @ ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) ) @ ( or @ ( not @ p ) @ q ) ) ),
inference(simp,[status(thm)],[70]) ).
thf(84,plain,
! [B: $i,A: $i] :
( ( ( not @ B )
!= ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) ) )
| ( ( or @ A @ B )
!= ( or @ ( not @ p ) @ q ) ) ),
inference(simp,[status(thm)],[73]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ( ( not @ B )
!= ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) ) )
| ( A
!= ( not @ p ) )
| ( B != q ) ),
inference(simp,[status(thm)],[84]) ).
thf(89,plain,
( ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) )
!= ( not @ q ) ),
inference(simp,[status(thm)],[86]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ A ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ A ) @ B ) ) @ true @ ( theorem @ B ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ A ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ A ) @ B ) ) @ true @ ( theorem @ B ) @ true ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ A ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ A ) @ B ) ) @ true @ ( theorem @ B ) @ true ) @ true )
= true ),
inference(lifteq,[status(thm)],[28]) ).
thf(168,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ B ) @ true @ ( ifeq @ true @ true @ ( theorem @ C ) @ true ) @ true )
= true )
| ( ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
!= ( axiom @ ( or @ ( not @ B ) @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[17,29]) ).
thf(169,plain,
! [A: $i] :
( ( ifeq @ ( theorem @ ( or @ A @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[168:[bind(A,$thf( E )),bind(B,$thf( or @ E @ E )),bind(C,$thf( E ))]]) ).
thf(212,plain,
! [A: $i] :
( ( ifeq @ ( theorem @ ( or @ A @ A ) ) @ true @ ( ifeq @ true @ true @ ( theorem @ A ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[169]) ).
thf(224,plain,
! [A: $i] :
( ( ifeq @ ( theorem @ ( or @ A @ A ) ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(rewrite,[status(thm)],[212,15]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ B ) @ true @ true @ true )
= true )
| ( ( theorem @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[47,27]) ).
thf(79,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[78:[bind(A,$thf( D )),bind(B,$thf( or @ ( not @ ( or @ D @ D ) ) @ D ))]]) ).
thf(81,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[79]) ).
thf(143,plain,
( ( or @ ( or @ ( not @ p ) @ q ) @ ( or @ ( not @ p ) @ q ) )
!= ( or @ ( not @ ( or @ p @ q ) ) @ q ) ),
inference(simp,[status(thm)],[142]) ).
thf(145,plain,
( ( ( or @ ( not @ p ) @ q )
!= ( not @ ( or @ p @ q ) ) )
| ( ( or @ ( not @ p ) @ q )
!= q ) ),
inference(simp,[status(thm)],[143]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) )
= true ),
inference(lifteq,[status(thm)],[20]) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = true )
| ( ( ifeq @ A @ A @ B @ C )
!= ( ifeq @ ( axiom @ D ) @ true @ ( theorem @ D ) @ true ) ) ),
inference(paramod_ordered,[status(thm)],[15,27]) ).
thf(50,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B = true )
| ( A
!= ( axiom @ D ) )
| ( A != true )
| ( B
!= ( theorem @ D ) )
| ( C != true ) ),
inference(simp,[status(thm)],[48]) ).
thf(52,plain,
! [A: $i] :
( ( ( theorem @ A )
= true )
| ( ( axiom @ A )
!= true ) ),
inference(simp,[status(thm)],[50]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ C )
= true )
| ( ( axiom @ ( or @ ( not @ ( or @ A @ B ) ) @ ( or @ B @ A ) ) )
!= ( axiom @ C ) ) ),
inference(paramod_ordered,[status(thm)],[21,52]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( not @ ( or @ B @ A ) ) @ ( or @ A @ B ) ) )
= true ),
inference(pattern_uni,[status(thm)],[60:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( or @ ( not @ ( or @ J @ I ) ) @ ( or @ I @ J ) ))]]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( not @ ( or @ B @ A ) ) @ ( or @ A @ B ) ) )
= true ),
inference(simp,[status(thm)],[61]) ).
thf(133,plain,
! [B: $i,A: $i] :
( ( theorem @ ( or @ ( not @ ( or @ B @ A ) ) @ ( or @ A @ B ) ) )
!= ( theorem @ ( or @ ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) ) @ ( or @ ( not @ p ) @ q ) ) ) ),
inference(paramod_ordered,[status(thm)],[69,13]) ).
thf(138,plain,
! [B: $i,A: $i] :
( ( or @ ( not @ ( or @ B @ A ) ) @ ( or @ A @ B ) )
!= ( or @ ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) ) @ ( or @ ( not @ p ) @ q ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(322,plain,
! [B: $i,A: $i] :
( ( ( not @ ( or @ B @ A ) )
!= ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) ) )
| ( ( or @ A @ B )
!= ( or @ ( not @ p ) @ q ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(324,plain,
! [B: $i,A: $i] :
( ( ( not @ ( or @ B @ A ) )
!= ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) ) )
| ( A
!= ( not @ p ) )
| ( B != q ) ),
inference(simp,[status(thm)],[322]) ).
thf(326,plain,
( ( not @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) )
!= ( not @ ( or @ q @ ( not @ p ) ) ) ),
inference(simp,[status(thm)],[324]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( B
!= ( or @ ( not @ ( or @ p @ q ) ) @ q ) )
| ( ( or @ A @ B )
!= ( or @ ( not @ p ) @ q ) ) ),
inference(simp,[status(thm)],[84]) ).
thf(88,plain,
! [A: $i] :
( ( or @ A @ ( or @ ( not @ ( or @ p @ q ) ) @ q ) )
!= ( or @ ( not @ p ) @ q ) ),
inference(simp,[status(thm)],[85]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( or @ ( not @ ( or @ C @ A ) ) @ ( or @ C @ B ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).
thf(24,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( or @ ( not @ ( or @ C @ A ) ) @ ( or @ C @ B ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(181,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ C ) @ true @ ( ifeq @ true @ true @ ( theorem @ D ) @ true ) @ true )
= true )
| ( ( axiom @ ( or @ ( not @ A ) @ ( or @ B @ A ) ) )
!= ( axiom @ ( or @ ( not @ C ) @ D ) ) ) ),
inference(paramod_ordered,[status(thm)],[19,29]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ B ) @ true @ ( ifeq @ true @ true @ ( theorem @ ( or @ A @ B ) ) @ true ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[181:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( or @ E @ F ))]]) ).
thf(219,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ B ) @ true @ ( ifeq @ true @ true @ ( theorem @ ( or @ A @ B ) ) @ true ) @ true )
= true ),
inference(simp,[status(thm)],[182]) ).
thf(257,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ B ) @ true @ ( theorem @ ( or @ A @ B ) ) @ true )
= true ),
inference(rewrite,[status(thm)],[219,15]) ).
thf(279,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( theorem @ C ) @ true @ true @ true )
= true )
| ( ( theorem @ ( or @ ( not @ ( or @ A @ A ) ) @ A ) )
!= ( theorem @ ( or @ B @ C ) ) ) ),
inference(paramod_ordered,[status(thm)],[47,257]) ).
thf(280,plain,
! [A: $i] :
( ( ifeq @ ( theorem @ A ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[279:[bind(A,$thf( F )),bind(B,$thf( not @ ( or @ F @ F ) )),bind(C,$thf( F ))]]) ).
thf(288,plain,
! [A: $i] :
( ( ifeq @ ( theorem @ A ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[280]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( or @ ( not @ ( or @ ( not @ A ) @ B ) ) @ ( or @ ( not @ ( or @ C @ A ) ) @ ( or @ C @ B ) ) ) )
= true ),
inference(lifteq,[status(thm)],[24]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ C ) @ true @ true @ true )
= true )
| ( ( theorem @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[46,27]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[71:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( or @ ( not @ H ) @ ( or @ G @ H ) ))]]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( or @ ( not @ B ) @ ( or @ A @ B ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[72]) ).
thf(91,plain,
( ( ifeq @ true @ true @ true @ true )
= true ),
inference(rewrite,[status(thm)],[74,19]) ).
thf(325,plain,
! [B: $i,A: $i] :
( ( ( or @ B @ A )
!= ( or @ ( not @ ( or @ p @ q ) ) @ q ) )
| ( A
!= ( not @ p ) )
| ( B != q ) ),
inference(simp,[status(thm)],[322]) ).
thf(327,plain,
( ( or @ ( not @ ( or @ p @ q ) ) @ q )
!= ( or @ q @ ( not @ p ) ) ),
inference(simp,[status(thm)],[325]) ).
thf(330,plain,
( ( ( not @ ( or @ p @ q ) )
!= q )
| ( ( not @ p )
!= q ) ),
inference(simp,[status(thm)],[327]) ).
thf(10,axiom,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( or @ ( not @ A ) @ B ) ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ C ) @ A ) ) @ true @ ( theorem @ ( or @ ( not @ C ) @ B ) ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_3) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( or @ ( not @ A ) @ B ) ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ C ) @ A ) ) @ true @ ( theorem @ ( or @ ( not @ C ) @ B ) ) @ true ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( or @ ( not @ A ) @ B ) ) @ true @ ( ifeq @ ( axiom @ ( or @ ( not @ C ) @ A ) ) @ true @ ( theorem @ ( or @ ( not @ C ) @ B ) ) @ true ) @ true )
= true ),
inference(lifteq,[status(thm)],[30]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( or @ ( not @ ( or @ A @ ( or @ B @ C ) ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
= true ),
inference(lifteq,[status(thm)],[22]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( B
!= ( or @ ( not @ ( or @ p @ q ) ) @ q ) )
| ( A
!= ( not @ p ) )
| ( B != q ) ),
inference(simp,[status(thm)],[84]) ).
thf(90,plain,
( ( or @ ( not @ ( or @ p @ q ) ) @ q )
!= q ),
inference(simp,[status(thm)],[87]) ).
thf(6802,plain,
$false,
inference(e,[status(thm)],[142,84,89,224,13,73,17,81,80,145,326,69,138,88,24,288,25,257,52,14,20,46,29,28,21,22,27,91,330,18,327,16,31,11,143,26,23,30,19,47,15,90,322]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : LCL218-10 : TPTP v8.2.0. Released v7.3.0.
% 0.00/0.11 % Command : run_Leo-III %s %d THM
% 0.11/0.33 % Computer : n001.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Sat Jun 22 17:56:40 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.87/0.84 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.25/0.95 % [INFO] Parsing done (106ms).
% 1.25/0.96 % [INFO] Running in sequential loop mode.
% 1.68/1.18 % [INFO] eprover registered as external prover.
% 1.68/1.18 % [INFO] Scanning for conjecture ...
% 1.81/1.24 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 1.87/1.26 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.87/1.28 % [INFO] Problem is propositional (TPTP CNF).
% 1.87/1.29 % [INFO] Type checking passed.
% 1.87/1.29 % [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 ...
% 47.69/10.88 % External prover 'e' found a proof!
% 47.69/10.88 % [INFO] Killing All external provers ...
% 47.69/10.88 % Time passed: 10367ms (effective reasoning time: 9920ms)
% 47.69/10.88 % 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
% 47.69/10.88 % No. of inferences in proof: 87
% 47.69/10.88 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 10367 ms resp. 9920 ms w/o parsing
% 47.69/10.93 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 47.69/10.93 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------