TSTP Solution File: LCL203-10 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : LCL203-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n023.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 : Fri May 19 11:29:43 EDT 2023
% Result : Unsatisfiable 10.44s 3.03s
% Output : Refutation 10.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 19
% Syntax : Number of formulae : 107 ( 67 unt; 9 typ; 0 def)
% Number of atoms : 136 ( 135 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 939 ( 74 ~; 38 |; 0 &; 827 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 174 ( 0 ^; 174 !; 0 ?; 174 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_type,type,
theorem: $i > $i ).
thf(implies_type,type,
implies: $i > $i > $i ).
thf(not_type,type,
not: $i > $i ).
thf(or_type,type,
or: $i > $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(8,axiom,
! [B: $i,A: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( implies @ A @ B )
= ( or @ ( not @ A ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( or @ ( not @ A ) @ B )
= ( implies @ A @ B ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(3,axiom,
! [A: $i] :
( ( axiom @ ( implies @ ( or @ A @ A ) @ A ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
thf(16,plain,
! [A: $i] :
( ( axiom @ ( implies @ ( or @ A @ A ) @ A ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,plain,
! [A: $i] :
( ( axiom @ ( implies @ ( or @ A @ A ) @ A ) )
= true ),
inference(lifteq,[status(thm)],[16]) ).
thf(9,axiom,
! [A: $i] :
( ( ifeq @ ( axiom @ A ) @ true @ ( theorem @ A ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
thf(28,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ A ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(29,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ A ) @ true @ ( theorem @ A ) @ true )
= true ),
inference(lifteq,[status(thm)],[28]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ B ) @ true )
= true )
| ( ( axiom @ ( implies @ ( or @ A @ A ) @ A ) )
!= ( axiom @ B ) ) ),
inference(paramod_ordered,[status(thm)],[17,29]) ).
thf(33,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ ( or @ A @ A ) @ A ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[32:[bind(A,$thf( D )),bind(B,$thf( implies @ ( or @ D @ D ) @ D ))]]) ).
thf(34,plain,
! [A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ ( 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(89,plain,
! [A: $i] :
( ( theorem @ ( implies @ ( or @ A @ A ) @ A ) )
= true ),
inference(rewrite,[status(thm)],[34,15]) ).
thf(1,negated_conjecture,
( ( theorem @ ( implies @ ( not @ ( or @ p @ q ) ) @ ( or @ ( not @ p ) @ ( not @ q ) ) ) )
!= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(11,plain,
( ( theorem @ ( implies @ ( not @ ( or @ p @ q ) ) @ ( or @ ( not @ p ) @ ( not @ q ) ) ) )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
( ( theorem @ ( implies @ ( not @ ( or @ p @ q ) ) @ ( or @ ( not @ p ) @ ( not @ q ) ) ) )
!= true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( theorem @ ( implies @ ( not @ ( or @ p @ q ) ) @ ( or @ ( not @ p ) @ ( not @ q ) ) ) )
!= true ),
inference(lifteq,[status(thm)],[12]) ).
thf(40,plain,
( ( theorem @ ( implies @ ( not @ ( or @ p @ q ) ) @ ( implies @ p @ ( not @ q ) ) ) )
!= true ),
inference(rewrite,[status(thm)],[13,27]) ).
thf(93,plain,
! [A: $i] :
( ( theorem @ ( implies @ ( or @ A @ A ) @ A ) )
!= ( theorem @ ( implies @ ( not @ ( or @ p @ q ) ) @ ( implies @ p @ ( not @ q ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[89,40]) ).
thf(97,plain,
! [A: $i] :
( ( implies @ ( or @ A @ A ) @ A )
!= ( implies @ ( not @ ( or @ p @ q ) ) @ ( implies @ p @ ( not @ q ) ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(124,plain,
! [A: $i] :
( ( ( or @ A @ A )
!= ( not @ ( or @ p @ q ) ) )
| ( A
!= ( implies @ p @ ( not @ q ) ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(134,plain,
( ( or @ ( implies @ p @ ( not @ q ) ) @ ( implies @ p @ ( not @ q ) ) )
!= ( not @ ( or @ p @ q ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( not @ ( or @ p @ q ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ ( implies @ p @ ( not @ q ) ) @ ( implies @ p @ ( not @ q ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,134]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( not @ ( or @ p @ q ) ) )
| ( ( not @ A )
!= ( implies @ p @ ( not @ q ) ) )
| ( B
!= ( implies @ p @ ( not @ q ) ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
! [A: $i] :
( ( ( implies @ A @ ( implies @ p @ ( not @ q ) ) )
!= ( not @ ( or @ p @ q ) ) )
| ( ( not @ A )
!= ( implies @ p @ ( not @ q ) ) ) ),
inference(simp,[status(thm)],[137]) ).
thf(4,axiom,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ A @ ( or @ B @ A ) ) )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
thf(18,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ A @ ( or @ B @ A ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ 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 @ ( implies @ A @ ( or @ B @ A ) ) )
!= ( axiom @ C ) ) ),
inference(paramod_ordered,[status(thm)],[19,29]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ B @ ( or @ A @ B ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[37:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( implies @ G @ ( or @ F @ G ) ))]]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ B @ ( or @ A @ B ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[38]) ).
thf(109,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( or @ A @ B ) ) )
= true ),
inference(rewrite,[status(thm)],[39,15]) ).
thf(117,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( or @ A @ B ) ) )
!= ( theorem @ ( implies @ ( not @ ( or @ p @ q ) ) @ ( implies @ p @ ( not @ q ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[109,40]) ).
thf(120,plain,
! [B: $i,A: $i] :
( ( implies @ B @ ( or @ A @ B ) )
!= ( implies @ ( not @ ( or @ p @ q ) ) @ ( implies @ p @ ( not @ q ) ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(152,plain,
! [B: $i,A: $i] :
( ( B
!= ( not @ ( or @ p @ q ) ) )
| ( ( or @ A @ B )
!= ( implies @ p @ ( not @ q ) ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(159,plain,
! [A: $i] :
( ( or @ A @ ( not @ ( or @ p @ q ) ) )
!= ( implies @ p @ ( not @ q ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(165,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ A @ B )
!= ( implies @ p @ ( not @ q ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ ( not @ ( or @ p @ q ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,159]) ).
thf(166,plain,
! [A: $i] :
( ( implies @ A @ ( not @ ( or @ p @ q ) ) )
!= ( implies @ p @ ( not @ q ) ) ),
inference(pattern_uni,[status(thm)],[165:[bind(A,$thf( D )),bind(B,$thf( not @ ( or @ p @ q ) )),bind(C,$thf( not @ D ))]]) ).
thf(168,plain,
! [A: $i] :
( ( implies @ A @ ( not @ ( or @ p @ q ) ) )
!= ( implies @ p @ ( not @ q ) ) ),
inference(simp,[status(thm)],[166]) ).
thf(195,plain,
! [A: $i] :
( ( A != p )
| ( ( not @ ( or @ p @ q ) )
!= ( not @ q ) ) ),
inference(simp,[status(thm)],[168]) ).
thf(200,plain,
( ( not @ ( or @ p @ q ) )
!= ( not @ q ) ),
inference(simp,[status(thm)],[195]) ).
thf(205,plain,
! [B: $i,A: $i] :
( ( ( not @ ( implies @ A @ B ) )
!= ( not @ q ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ p @ q ) ) ),
inference(paramod_ordered,[status(thm)],[27,200]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
!= q )
| ( ( not @ A )
!= p )
| ( B != q ) ),
inference(simp,[status(thm)],[205]) ).
thf(209,plain,
! [A: $i] :
( ( ( implies @ A @ q )
!= q )
| ( ( not @ A )
!= p ) ),
inference(simp,[status(thm)],[208]) ).
thf(7,axiom,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( 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 @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ B ) @ ( implies @ ( or @ C @ A ) @ ( or @ C @ B ) ) ) )
= true ),
inference(lifteq,[status(thm)],[24]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ ( 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 @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(43,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( axiom @ ( implies @ C @ ( implies @ A @ B ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27,19]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ A @ ( implies @ B @ A ) ) )
= true ),
inference(pattern_uni,[status(thm)],[43:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( not @ E ))]]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ A @ ( implies @ B @ A ) ) )
= true ),
inference(simp,[status(thm)],[44]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ ( not @ ( implies @ A @ B ) ) @ ( implies @ p @ ( not @ q ) ) )
!= ( implies @ ( or @ C @ C ) @ C ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ p @ q ) ) ),
inference(paramod_ordered,[status(thm)],[27,97]) ).
thf(130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( not @ ( implies @ A @ B ) )
!= ( or @ C @ C ) )
| ( ( implies @ p @ ( not @ q ) )
!= C )
| ( ( not @ A )
!= p )
| ( B != q ) ),
inference(simp,[status(thm)],[127]) ).
thf(133,plain,
! [A: $i] :
( ( ( not @ ( implies @ A @ q ) )
!= ( or @ ( implies @ p @ ( not @ q ) ) @ ( implies @ p @ ( not @ q ) ) ) )
| ( ( not @ A )
!= p ) ),
inference(simp,[status(thm)],[130]) ).
thf(21,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ A @ B ) @ ( or @ B @ A ) ) )
= true ),
inference(lifteq,[status(thm)],[20]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( ( axiom @ ( implies @ ( implies @ A @ B ) @ C ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27,17]) ).
thf(42,plain,
! [A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) )
= true ),
inference(pattern_uni,[status(thm)],[41:[bind(A,$thf( E )),bind(B,$thf( not @ E )),bind(C,$thf( not @ E ))]]) ).
thf(45,plain,
! [A: $i] :
( ( axiom @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) )
= true ),
inference(simp,[status(thm)],[42]) ).
thf(118,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ C ) @ true @ true @ true )
= true )
| ( ( theorem @ ( implies @ B @ ( or @ A @ B ) ) )
!= ( theorem @ C ) ) ),
inference(paramod_ordered,[status(thm)],[109,29]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( implies @ B @ ( or @ A @ B ) ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( implies @ G @ ( or @ F @ G ) ))]]) ).
thf(123,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( axiom @ ( implies @ B @ ( or @ A @ B ) ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[119]) ).
thf(279,plain,
( ( ifeq @ true @ true @ true @ true )
= true ),
inference(rewrite,[status(thm)],[123,19]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( 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 @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(204,plain,
( ( or @ p @ q )
!= q ),
inference(simp,[status(thm)],[200]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( ( theorem @ ( implies @ ( not @ ( implies @ A @ B ) ) @ ( implies @ p @ ( not @ q ) ) ) )
!= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ p @ q ) ) ),
inference(paramod_ordered,[status(thm)],[27,40]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( ( theorem @ ( implies @ ( not @ ( implies @ A @ B ) ) @ ( implies @ p @ ( not @ q ) ) ) )
!= true )
| ( ( not @ A )
!= p )
| ( B != q ) ),
inference(simp,[status(thm)],[47]) ).
thf(49,plain,
! [A: $i] :
( ( ( theorem @ ( implies @ ( not @ ( implies @ A @ q ) ) @ ( implies @ p @ ( not @ q ) ) ) )
!= true )
| ( ( not @ A )
!= p ) ),
inference(simp,[status(thm)],[48]) ).
thf(67,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( axiom @ ( implies @ ( or @ C @ D ) @ ( implies @ A @ B ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27,21]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) )
= true ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( not @ E ))]]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ A @ ( not @ B ) ) @ ( implies @ B @ A ) ) )
= true ),
inference(simp,[status(thm)],[68]) ).
thf(90,plain,
! [C: $i,B: $i,A: $i] :
( ( ( theorem @ ( implies @ ( implies @ A @ B ) @ C ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ C ) ) ),
inference(paramod_ordered,[status(thm)],[27,89]) ).
thf(91,plain,
! [A: $i] :
( ( theorem @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) )
= true ),
inference(pattern_uni,[status(thm)],[90:[bind(A,$thf( E )),bind(B,$thf( not @ E )),bind(C,$thf( not @ E ))]]) ).
thf(98,plain,
! [A: $i] :
( ( theorem @ ( implies @ ( implies @ A @ ( not @ A ) ) @ ( not @ A ) ) )
= true ),
inference(simp,[status(thm)],[91]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ A @ B ) ) @ true @ ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ B ) @ true ) @ true )
= true ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ A @ B ) ) @ true @ ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ B ) @ true ) @ true )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( ifeq @ ( theorem @ ( implies @ A @ B ) ) @ true @ ( ifeq @ ( theorem @ A ) @ true @ ( theorem @ B ) @ true ) @ true )
= true ),
inference(lifteq,[status(thm)],[30]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( ( ifeq @ ( axiom @ B ) @ true @ true @ true )
= true )
| ( ( theorem @ ( implies @ ( or @ A @ A ) @ A ) )
!= ( theorem @ B ) ) ),
inference(paramod_ordered,[status(thm)],[89,29]) ).
thf(95,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( implies @ ( or @ A @ A ) @ A ) ) @ true @ true @ true )
= true ),
inference(pattern_uni,[status(thm)],[94:[bind(A,$thf( D )),bind(B,$thf( implies @ ( or @ D @ D ) @ D ))]]) ).
thf(99,plain,
! [A: $i] :
( ( ifeq @ ( axiom @ ( implies @ ( or @ A @ A ) @ A ) ) @ true @ true @ true )
= true ),
inference(simp,[status(thm)],[95]) ).
thf(196,plain,
! [C: $i,B: $i,A: $i] :
( ( ( implies @ C @ ( not @ ( implies @ A @ B ) ) )
!= ( implies @ p @ ( not @ q ) ) )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ p @ q ) ) ),
inference(paramod_ordered,[status(thm)],[27,168]) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] :
( ( C != p )
| ( ( not @ ( implies @ A @ B ) )
!= ( not @ q ) )
| ( ( not @ A )
!= p )
| ( B != q ) ),
inference(simp,[status(thm)],[196]) ).
thf(203,plain,
! [A: $i] :
( ( ( not @ ( implies @ A @ q ) )
!= ( not @ q ) )
| ( ( not @ A )
!= p ) ),
inference(simp,[status(thm)],[199]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
!= q )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ p @ q ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(304,plain,
! [B: $i,A: $i] :
( ( ( implies @ A @ B )
!= q )
| ( ( implies @ A @ B )
!= ( or @ p @ q ) ) ),
inference(rewrite,[status(thm)],[206,27]) ).
thf(23,plain,
! [C: $i,B: $i,A: $i] :
( ( axiom @ ( implies @ ( or @ A @ ( or @ B @ C ) ) @ ( or @ B @ ( or @ A @ C ) ) ) )
= true ),
inference(lifteq,[status(thm)],[22]) ).
thf(65,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( axiom @ ( implies @ ( implies @ A @ B ) @ ( or @ D @ C ) ) )
= true )
| ( ( or @ ( not @ A ) @ B )
!= ( or @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[27,21]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[65:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( not @ E )),bind(D,$thf( B ))]]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( axiom @ ( implies @ ( implies @ B @ A ) @ ( or @ A @ ( not @ B ) ) ) )
= true ),
inference(simp,[status(thm)],[66]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ifeq @ true @ true @ ( theorem @ C ) @ true )
= true )
| ( ( axiom @ ( implies @ A @ ( implies @ B @ A ) ) )
!= ( axiom @ C ) ) ),
inference(paramod_ordered,[status(thm)],[46,29]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ B @ ( implies @ A @ B ) ) ) @ true )
= true ),
inference(pattern_uni,[status(thm)],[54:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( implies @ G @ ( implies @ F @ G ) ))]]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( ifeq @ true @ true @ ( theorem @ ( implies @ B @ ( implies @ A @ B ) ) ) @ true )
= true ),
inference(simp,[status(thm)],[55]) ).
thf(214,plain,
! [B: $i,A: $i] :
( ( theorem @ ( implies @ B @ ( implies @ A @ B ) ) )
= true ),
inference(rewrite,[status(thm)],[56,15]) ).
thf(668,plain,
$false,
inference(e,[status(thm)],[138,120,14,97,109,134,209,18,11,24,25,20,46,29,89,133,28,21,45,279,17,22,204,27,49,159,76,98,16,31,99,203,40,304,26,23,75,214,168,30,19,15,200]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : LCL203-10 : TPTP v8.1.2. Released v7.3.0.
% 0.14/0.16 % Command : run_Leo-III %s %d
% 0.15/0.37 % Computer : n023.cluster.edu
% 0.15/0.37 % Model : x86_64 x86_64
% 0.15/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.37 % Memory : 8042.1875MB
% 0.15/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.37 % CPULimit : 300
% 0.15/0.37 % WCLimit : 300
% 0.15/0.37 % DateTime : Thu May 18 16:27:45 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.96/0.86 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.22/0.98 % [INFO] Parsing done (115ms).
% 1.22/0.99 % [INFO] Running in sequential loop mode.
% 1.67/1.23 % [INFO] eprover registered as external prover.
% 1.67/1.23 % [INFO] cvc4 registered as external prover.
% 1.67/1.24 % [INFO] Scanning for conjecture ...
% 1.73/1.29 % [INFO] Found a conjecture and 9 axioms. Running axiom selection ...
% 1.73/1.31 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 1.88/1.33 % [INFO] Problem is propositional (TPTP CNF).
% 1.88/1.33 % [INFO] Type checking passed.
% 1.88/1.34 % [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 ...
% 10.44/3.02 % External prover 'e' found a proof!
% 10.44/3.02 % [INFO] Killing All external provers ...
% 10.44/3.02 % Time passed: 2491ms (effective reasoning time: 2030ms)
% 10.44/3.02 % Solved by 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)>
% 10.44/3.02 % 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
% 10.44/3.02 % No. of inferences in proof: 98
% 10.44/3.03 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 2491 ms resp. 2030 ms w/o parsing
% 10.44/3.07 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 10.44/3.07 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------