%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL211-10 : 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 : n005.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 07:51:11 AM UTC 2026
% Result : Unsatisfiable 119.20s 30.32s
% Output : Refutation 108.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 10
% Syntax : Number of formulae : 202 ( 96 unt; 0 typ; 0 def)
% Number of atoms : 362 ( 361 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 2444 ( 259 ~; 160 |; 0 &;2025 @)
% ( 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 : 11 ( 9 usr; 4 con; 0-4 aty)
% Number of variables : 397 ( 0 ^; 397 !; 0 ?; 397 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_decl,type,
theorem: $i > $i ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(q_decl,type,
q: $i ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(p_decl,type,
p: $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/sandbox2/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(4,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
= true ),
file('/export/starexec/sandbox2/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(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(49,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
= true ),
inference(simp,[status(thm)],[46]) ).
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(9,axiom,
! [A: $i] :
( ( true @ ( A @ theorem @ ( true @ ( A @ axiom @ ifeq ) ) ) )
= true ),
file('/export/starexec/sandbox2/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(62,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)],[15,29]) ).
thf(64,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)],[62]) ).
thf(66,plain,
! [A: $i] :
( ( ( A @ axiom )
!= true )
| ( ( A @ theorem )
= true ) ),
inference(simp,[status(thm)],[64]) ).
thf(71,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( true != true )
| ( ( C @ theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[49,66]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( ( C @ theorem )
= true ) ),
inference(simp,[status(thm)],[71]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
= true ),
inference(pattern_uni,[status(thm)],[72:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ implies ) @ ( G @ implies ) ))]]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
= true ),
inference(simp,[status(thm)],[73]) ).
thf(125,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( C @ theorem ) )
| ( ( true @ ( true @ ( true @ ( C @ axiom @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[78,29]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( B @ ( A @ implies ) @ ( B @ implies ) @ axiom @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[125:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ implies ) @ ( G @ implies ) ))]]) ).
thf(129,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( true @ ( B @ ( A @ implies ) @ ( B @ implies ) @ axiom @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[126]) ).
thf(348,plain,
( ( true @ ( true @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[129,49]) ).
thf(1,negated_conjecture,
( ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) @ theorem )
!= true ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(11,plain,
( ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) @ theorem )
!= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(12,plain,
( ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) @ theorem )
!= true ),
inference(polarity_switch,[status(thm)],[11]) ).
thf(13,plain,
( ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) @ theorem )
!= true ),
inference(lifteq,[status(thm)],[12]) ).
thf(121,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) @ theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[78,13]) ).
thf(122,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[121]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) ) ),
inference(simp,[status(thm)],[122]) ).
thf(196,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( B
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(201,plain,
! [A: $i] :
( ( q @ not @ ( A @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) ),
inference(simp,[status(thm)],[196]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
= true ),
file('/export/starexec/sandbox2/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(68,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ( true != true )
| ( ( B @ theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[17,66]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ( ( B @ theorem )
= true ) ),
inference(simp,[status(thm)],[68]) ).
thf(70,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
= true ),
inference(pattern_uni,[status(thm)],[69:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ or ) @ implies ) ))]]) ).
thf(77,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
= true ),
inference(simp,[status(thm)],[70]) ).
thf(107,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) @ theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[77,13]) ).
thf(108,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[107]) ).
thf(113,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) ) ),
inference(simp,[status(thm)],[108]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) @ ( q @ not @ implies ) )
!= ( C @ ( C @ ( C @ or ) @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,113]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) @ ( q @ not @ implies ) )
!= ( C @ ( C @ ( C @ or ) @ implies ) ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(162,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= p )
| ( ( p @ ( q @ ( A @ implies ) @ implies ) @ ( q @ not @ implies ) )
!= ( B @ ( B @ ( B @ or ) @ implies ) ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(5,axiom,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ 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 ) @ 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(88,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(89,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom )
= true ),
inference(pattern_uni,[status(thm)],[88:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom )
= true ),
inference(simp,[status(thm)],[89]) ).
thf(74,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( true != true )
| ( ( C @ theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[19,66]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( ( C @ theorem )
= true ) ),
inference(simp,[status(thm)],[74]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
= true ),
inference(pattern_uni,[status(thm)],[75:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ or ) @ ( G @ implies ) ))]]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
= true ),
inference(simp,[status(thm)],[76]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( true != true )
| ( ( C @ theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[21,66]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( ( C @ theorem )
= true ) ),
inference(simp,[status(thm)],[94]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem )
= true ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( I @ ( H @ or ) @ ( H @ ( I @ or ) @ implies ) ))]]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem )
= true ),
inference(simp,[status(thm)],[96]) ).
thf(475,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) @ theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[101,13]) ).
thf(476,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[475]) ).
thf(503,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) ) ),
inference(simp,[status(thm)],[476]) ).
thf(1300,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( A @ ( B @ or ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[503]) ).
thf(1315,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( C @ ( D @ or ) )
!= ( q @ not ) ) ),
inference(paramod_ordered,[status(thm)],[27,1300]) ).
thf(1316,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( B @ not @ ( A @ or ) )
!= ( q @ not ) ) ),
inference(pattern_uni,[status(thm)],[1315:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(1320,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( B @ not @ ( A @ or ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[1316]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) )
!= C )
| ( ( C @ ( C @ or ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(161,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) @ ( p @ ( B @ ( A @ implies ) @ implies ) @ or ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[156]) ).
thf(1322,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( q @ ( p @ or ) ) )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) @ ( p @ ( B @ ( A @ implies ) @ implies ) @ or ) )
!= ( q @ not ) ) ),
inference(rewrite,[status(thm)],[161,27]) ).
thf(152,plain,
! [A: $i] :
( ( A
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( A @ ( A @ or ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(159,plain,
( ( p @ ( q @ ( p @ or ) @ implies ) @ ( p @ ( q @ ( p @ or ) @ implies ) @ or ) )
!= ( q @ not ) ),
inference(simp,[status(thm)],[152]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( p @ ( q @ ( p @ or ) @ implies ) @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( q @ not ) ) ),
inference(paramod_ordered,[status(thm)],[27,159]) ).
thf(167,plain,
! [B: $i,A: $i] :
( ( B
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( A @ not )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[164]) ).
thf(170,plain,
! [A: $i] :
( ( ( A @ not )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( p @ ( q @ ( p @ or ) @ implies ) @ ( A @ implies ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[167]) ).
thf(105,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)],[77,29]) ).
thf(106,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ ( A @ ( A @ or ) @ implies ) @ axiom @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[105:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ or ) @ implies ) ))]]) ).
thf(115,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ ( A @ ( A @ or ) @ implies ) @ axiom @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[106]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( C @ or ) ) )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,113]) ).
thf(154,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(160,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(746,plain,
! [A: $i] :
( ( ( A @ not )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( A @ not @ ( A @ implies ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[160]) ).
thf(855,plain,
! [A: $i] :
( ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= ( A @ not @ ( A @ implies ) ) )
| ( ( A @ not )
!= ( q @ not ) )
| ( ( A @ not @ ( A @ implies ) )
!= ( q @ not ) ) ),
inference(eqfactor_ordered,[status(thm)],[746]) ).
thf(857,plain,
! [A: $i] :
( ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= ( A @ not @ ( A @ implies ) ) )
| ( A != q )
| ( ( A @ not @ ( A @ implies ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[855]) ).
thf(861,plain,
( ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= ( q @ not @ ( q @ implies ) ) )
| ( ( q @ not @ ( q @ implies ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[857]) ).
thf(858,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ( ( q @ ( p @ or ) )
!= A )
| ( ( A @ not )
!= ( q @ not ) )
| ( ( A @ not @ ( A @ implies ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[855]) ).
thf(862,plain,
( ( ( q @ ( p @ or ) @ not )
!= p )
| ( ( q @ ( p @ or ) @ not )
!= ( q @ not ) )
| ( ( q @ ( p @ or ) @ not @ ( q @ ( p @ or ) @ implies ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[858]) ).
thf(1001,plain,
( ( ( q @ ( p @ or ) @ not )
!= p )
| ( ( q @ ( p @ or ) )
!= q )
| ( ( q @ ( p @ or ) @ not @ ( q @ ( p @ or ) @ implies ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[862]) ).
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/sandbox2/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(363,plain,
! [A: $i] :
( ( ( q @ not )
!= ( A @ not ) )
| ( ( p @ ( q @ ( p @ or ) @ implies ) @ ( A @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( A @ not )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) ) ),
inference(eqfactor_ordered,[status(thm)],[170]) ).
thf(366,plain,
! [A: $i] :
( ( ( q @ not )
!= ( A @ not ) )
| ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= p )
| ( A
!= ( q @ ( p @ or ) ) )
| ( ( A @ not )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) ) ),
inference(simp,[status(thm)],[363]) ).
thf(372,plain,
( ( ( q @ ( p @ or ) @ not )
!= ( q @ not ) )
| ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= p )
| ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= ( q @ ( p @ or ) @ not ) ) ),
inference(simp,[status(thm)],[366]) ).
thf(1313,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( D @ or ) ) )
| ( ( D @ ( C @ or ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( B @ ( A @ implies ) )
!= ( q @ not ) ) ),
inference(paramod_ordered,[status(thm)],[27,1300]) ).
thf(1314,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( A @ or ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( A @ ( B @ implies ) )
!= ( q @ not ) ) ),
inference(pattern_uni,[status(thm)],[1313:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(1319,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( A @ or ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( A @ ( B @ implies ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[1314]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) @ ( q @ not @ implies ) @ theorem )
!= true ) ),
inference(paramod_ordered,[status(thm)],[27,13]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) @ ( q @ not @ implies ) @ theorem )
!= true ) ),
inference(simp,[status(thm)],[42]) ).
thf(50,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ( ( p @ ( q @ ( A @ implies ) @ implies ) @ ( q @ not @ implies ) @ theorem )
!= true ) ),
inference(simp,[status(thm)],[47]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( p @ ( q @ ( C @ implies ) @ implies ) @ ( q @ not @ implies ) @ theorem ) )
| ( ( C @ not )
!= p )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[79,50]) ).
thf(139,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( p @ ( q @ ( C @ implies ) @ implies ) @ ( q @ not @ implies ) @ theorem ) )
| ( ( C @ not )
!= p ) ),
inference(simp,[status(thm)],[138]) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) )
!= ( p @ ( q @ ( C @ implies ) @ implies ) @ ( q @ not @ implies ) ) )
| ( ( C @ not )
!= p ) ),
inference(simp,[status(thm)],[139]) ).
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/sandbox2/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(411,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( D @ ( C @ implies ) @ theorem ) )
| ( ( true @ ( true @ ( D @ theorem @ ( true @ ( C @ theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[79,31]) ).
thf(412,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( A @ or ) @ theorem @ ( true @ ( B @ theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[411:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ or ) ))]]) ).
thf(462,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( A @ or ) @ theorem @ ( true @ ( B @ theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[412]) ).
thf(1215,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ or ) @ theorem @ ( true @ ( B @ theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[462,15]) ).
thf(109,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)],[27,77]) ).
thf(110,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
= true ),
inference(pattern_uni,[status(thm)],[109:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(116,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem )
= true ),
inference(simp,[status(thm)],[110]) ).
thf(134,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) @ theorem ) )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[79,13]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[134]) ).
thf(146,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(385,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( D @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,146]) ).
thf(386,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) ) ),
inference(pattern_uni,[status(thm)],[385:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(392,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ not @ implies ) ) ),
inference(simp,[status(thm)],[386]) ).
thf(1359,plain,
! [B: $i,A: $i] :
( ( A != p )
| ( B
!= ( q @ ( p @ or ) ) )
| ( ( B @ not @ ( A @ or ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[1320]) ).
thf(1370,plain,
( ( q @ ( p @ or ) @ not @ ( p @ or ) )
!= ( q @ not ) ),
inference(simp,[status(thm)],[1359]) ).
thf(205,plain,
! [A: $i] :
( ( ( q @ not )
!= p )
| ( A
!= ( q @ ( p @ or ) ) ) ),
inference(simp,[status(thm)],[201]) ).
thf(212,plain,
( ( q @ not )
!= p ),
inference(simp,[status(thm)],[205]) ).
thf(422,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( D @ ( C @ implies ) @ theorem ) )
| ( ( true @ ( true @ ( D @ theorem @ ( true @ ( C @ theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[78,31]) ).
thf(423,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( A @ implies ) @ theorem @ ( true @ ( B @ theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[422:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(448,plain,
! [B: $i,A: $i] :
( ( true @ ( true @ ( B @ ( A @ implies ) @ theorem @ ( true @ ( B @ theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[423]) ).
thf(864,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( A @ implies ) @ theorem @ ( true @ ( B @ theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[448,15]) ).
thf(897,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ( ( true @ ( C @ ( B @ implies ) @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[77,864]) ).
thf(898,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ implies ) @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[897:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ or ) @ implies ) ))]]) ).
thf(920,plain,
! [B: $i,A: $i] :
( ( true @ ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ implies ) @ theorem @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[898]) ).
thf(1382,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ implies ) @ theorem )
= true ),
inference(rewrite,[status(thm)],[920,15]) ).
thf(367,plain,
! [A: $i] :
( ( q != A )
| ( ( p @ ( q @ ( p @ or ) @ implies ) @ ( A @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( A @ not )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) ) ),
inference(simp,[status(thm)],[363]) ).
thf(373,plain,
( ( ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[367]) ).
thf(596,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( p @ ( q @ ( p @ or ) @ implies ) @ ( q @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) )
!= ( q @ not ) ) ),
inference(paramod_ordered,[status(thm)],[27,373]) ).
thf(600,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= p )
| ( ( q @ ( p @ or ) )
!= q )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[596]) ).
thf(605,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= p )
| ( ( q @ ( p @ or ) )
!= q )
| ( ( p @ ( q @ ( A @ implies ) @ implies ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[600]) ).
thf(1132,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( p @ ( q @ ( C @ implies ) @ implies ) ) )
| ( B
!= ( q @ not ) )
| ( ( C @ not )
!= p ) ),
inference(simp,[status(thm)],[147]) ).
thf(1135,plain,
! [B: $i,A: $i] :
( ( ( q @ not @ ( A @ or ) )
!= ( p @ ( q @ ( B @ implies ) @ implies ) ) )
| ( ( B @ not )
!= p ) ),
inference(simp,[status(thm)],[1132]) ).
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/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 ) @ implies ) @ axiom )
= true ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(433,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( C @ ( B @ implies ) @ theorem ) )
| ( ( true @ ( true @ ( C @ theorem @ ( true @ ( B @ theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[77,31]) ).
thf(434,plain,
! [A: $i] :
( ( true @ ( true @ ( A @ theorem @ ( true @ ( A @ ( A @ or ) @ theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[433:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ or ) )),bind(C,$thf( E ))]]) ).
thf(452,plain,
! [A: $i] :
( ( true @ ( true @ ( A @ theorem @ ( true @ ( A @ ( A @ or ) @ theorem @ ifeq ) ) ) @ ( true @ ( true @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[434]) ).
thf(1052,plain,
! [A: $i] :
( ( true @ ( A @ theorem @ ( true @ ( A @ ( A @ or ) @ theorem @ ifeq ) ) ) )
= true ),
inference(rewrite,[status(thm)],[452,15]) ).
thf(1080,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( C @ or ) ) )
| ( ( true @ ( C @ theorem @ ( true @ ( B @ ( A @ implies ) @ theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[27,1052]) ).
thf(1081,plain,
! [A: $i] :
( ( true @ ( A @ not @ theorem @ ( true @ ( A @ not @ ( A @ implies ) @ theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[1080:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(1125,plain,
! [A: $i] :
( ( true @ ( A @ not @ theorem @ ( true @ ( A @ not @ ( A @ implies ) @ theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[1081]) ).
thf(197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) @ ( q @ not @ implies ) )
!= ( D @ ( C @ implies ) @ ( D @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,128]) ).
thf(200,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) )
!= ( D @ ( C @ implies ) ) )
| ( ( q @ not )
!= D ) ),
inference(simp,[status(thm)],[197]) ).
thf(204,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= p )
| ( ( p @ ( q @ ( A @ implies ) @ implies ) )
!= ( q @ not @ ( B @ implies ) ) ) ),
inference(simp,[status(thm)],[200]) ).
thf(384,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( B
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[146]) ).
thf(391,plain,
! [A: $i] :
( ( q @ not @ ( A @ or ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) ),
inference(simp,[status(thm)],[384]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) @ ( p @ ( q @ ( p @ or ) @ implies ) @ or ) )
!= ( q @ not ) ) ),
inference(paramod_ordered,[status(thm)],[27,159]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) @ ( p @ ( q @ ( p @ or ) @ implies ) @ or ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[166]) ).
thf(172,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ( ( p @ ( q @ ( A @ implies ) @ implies ) @ ( p @ ( q @ ( p @ or ) @ implies ) @ or ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(491,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( D @ or ) ) )
| ( ( D @ ( C @ or ) @ ( B @ ( A @ implies ) @ implies ) @ theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[27,101]) ).
thf(492,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem )
= true ),
inference(pattern_uni,[status(thm)],[491:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(509,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem )
= true ),
inference(simp,[status(thm)],[492]) ).
thf(86,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(87,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom )
= true ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom )
= true ),
inference(simp,[status(thm)],[87]) ).
thf(123,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( p @ ( q @ ( C @ implies ) @ implies ) @ ( q @ not @ implies ) @ theorem ) )
| ( ( C @ not )
!= p )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[78,50]) ).
thf(124,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( p @ ( q @ ( C @ implies ) @ implies ) @ ( q @ not @ implies ) @ theorem ) )
| ( ( C @ not )
!= p ) ),
inference(simp,[status(thm)],[123]) ).
thf(127,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( p @ ( q @ ( C @ implies ) @ implies ) @ ( q @ not @ implies ) ) )
| ( ( C @ not )
!= p ) ),
inference(simp,[status(thm)],[124]) ).
thf(1028,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( p @ ( q @ ( C @ implies ) @ implies ) ) )
| ( B
!= ( q @ not ) )
| ( ( C @ not )
!= p ) ),
inference(simp,[status(thm)],[127]) ).
thf(1029,plain,
! [B: $i,A: $i] :
( ( ( q @ not @ ( A @ implies ) )
!= ( p @ ( q @ ( B @ implies ) @ implies ) ) )
| ( ( B @ not )
!= p ) ),
inference(simp,[status(thm)],[1028]) ).
thf(899,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( C @ ( B @ implies ) @ theorem ) )
| ( ( true @ ( true @ ( true @ ( C @ theorem @ ifeq ) ) ) )
= true ) ),
inference(paramod_ordered,[status(thm)],[77,864]) ).
thf(900,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ theorem @ ifeq ) ) ) )
= true ),
inference(pattern_uni,[status(thm)],[899:[bind(A,$thf( E )),bind(B,$thf( E @ ( E @ or ) )),bind(C,$thf( E ))]]) ).
thf(922,plain,
! [A: $i] :
( ( true @ ( true @ ( true @ ( A @ theorem @ ifeq ) ) ) )
= true ),
inference(simp,[status(thm)],[900]) ).
thf(645,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ not @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( C @ ( D @ implies ) @ implies ) @ theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[27,509]) ).
thf(646,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) @ theorem )
= true ),
inference(pattern_uni,[status(thm)],[645:[bind(A,$thf( E )),bind(B,$thf( F @ not )),bind(C,$thf( E @ not )),bind(D,$thf( F ))]]) ).
thf(658,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) @ theorem )
= true ),
inference(simp,[status(thm)],[646]) ).
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(48,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom )
= true ),
inference(simp,[status(thm)],[44]) ).
thf(595,plain,
( ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= p )
| ( ( q @ ( p @ or ) )
!= q )
| ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[373]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( p @ ( q @ ( B @ implies ) @ implies ) @ ( q @ not @ implies ) @ theorem ) )
| ( ( B @ not )
!= p )
| ( true != true ) ),
inference(paramod_ordered,[status(thm)],[77,50]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( p @ ( q @ ( B @ implies ) @ implies ) @ ( q @ not @ implies ) @ theorem ) )
| ( ( B @ not )
!= p ) ),
inference(simp,[status(thm)],[111]) ).
thf(114,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) )
!= ( p @ ( q @ ( B @ implies ) @ implies ) @ ( q @ not @ implies ) ) )
| ( ( B @ not )
!= p ) ),
inference(simp,[status(thm)],[112]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( p @ ( q @ ( p @ or ) @ implies ) @ ( p @ ( B @ ( A @ implies ) @ implies ) @ or ) )
!= ( q @ not ) ) ),
inference(paramod_ordered,[status(thm)],[27,159]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( p @ ( q @ ( p @ or ) @ implies ) @ ( p @ ( B @ ( A @ implies ) @ implies ) @ or ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(171,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ( ( p @ ( q @ ( p @ or ) @ implies ) @ ( p @ ( q @ ( A @ implies ) @ implies ) @ or ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[168]) ).
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(493,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( C @ ( D @ or ) @ implies ) @ theorem )
= true ) ),
inference(paramod_ordered,[status(thm)],[27,101]) ).
thf(494,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ theorem )
= true ),
inference(pattern_uni,[status(thm)],[493:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(510,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ theorem )
= true ),
inference(simp,[status(thm)],[494]) ).
thf(534,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ not @ ( C @ or ) ) )
| ( ( C @ ( D @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ axiom )
= true ) ),
inference(paramod_ordered,[status(thm)],[27,103]) ).
thf(535,plain,
! [B: $i,A: $i] :
( ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) @ axiom )
= true ),
inference(pattern_uni,[status(thm)],[534:[bind(A,$thf( E )),bind(B,$thf( F @ not )),bind(C,$thf( E @ not )),bind(D,$thf( F ))]]) ).
thf(549,plain,
! [B: $i,A: $i] :
( ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) @ axiom )
= true ),
inference(simp,[status(thm)],[535]) ).
thf(387,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) @ ( q @ not @ implies ) )
!= ( D @ ( C @ or ) @ ( D @ implies ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,146]) ).
thf(390,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) )
!= ( D @ ( C @ or ) ) )
| ( ( q @ not )
!= D ) ),
inference(simp,[status(thm)],[387]) ).
thf(395,plain,
! [B: $i,A: $i] :
( ( ( A @ not )
!= p )
| ( ( p @ ( q @ ( A @ implies ) @ implies ) )
!= ( q @ not @ ( B @ or ) ) ) ),
inference(simp,[status(thm)],[390]) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) )
!= C )
| ( ( C @ ( C @ or ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(163,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ( ( p @ ( q @ ( A @ implies ) @ implies ) @ ( p @ ( q @ ( A @ implies ) @ implies ) @ or ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(368,plain,
! [A: $i] :
( ( q != A )
| ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= p )
| ( A
!= ( q @ ( p @ or ) ) )
| ( ( A @ not )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) ) ),
inference(simp,[status(thm)],[363]) ).
thf(369,plain,
( ( ( q @ ( p @ or ) )
!= q )
| ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= p )
| ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= ( q @ ( p @ or ) @ not ) ) ),
inference(simp,[status(thm)],[368]) ).
thf(597,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( q @ ( p @ or ) ) )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) @ ( q @ implies ) )
!= ( p @ ( q @ ( p @ or ) @ implies ) ) )
| ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= ( q @ not ) ) ),
inference(paramod_ordered,[status(thm)],[27,373]) ).
thf(603,plain,
! [B: $i,A: $i] :
( ( B != q )
| ( ( A @ not )
!= p )
| ( ( p @ ( B @ ( A @ implies ) @ implies ) )
!= p )
| ( ( q @ ( p @ or ) )
!= q )
| ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[597]) ).
thf(607,plain,
! [A: $i] :
( ( ( A @ not )
!= p )
| ( ( p @ ( q @ ( A @ implies ) @ implies ) )
!= p )
| ( ( q @ ( p @ or ) )
!= q )
| ( ( p @ ( q @ ( p @ or ) @ implies ) )
!= ( q @ not ) ) ),
inference(simp,[status(thm)],[603]) ).
thf(18282,plain,
$false,
inference(e,[status(thm)],[348,201,128,162,104,79,1320,1322,101,170,115,861,1001,24,25,14,372,20,1319,78,29,147,1215,116,746,862,28,160,392,21,1370,77,212,1382,13,503,605,1135,17,22,1125,204,27,391,49,159,172,113,509,103,66,1029,922,658,48,18,50,1300,16,127,31,1052,864,11,595,26,114,171,23,510,549,146,30,19,373,395,15,163,369,607]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL211-10 : TPTP v9.3.1. Released v7.5.0.
% 0.00/0.12 % 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
% 0.21/0.48 % Computer : n005.cluster.edu
% 0.21/0.48 % Model : x86_64 x86_64
% 0.21/0.48 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.21/0.48 % Memory : 8046.5625MB
% 0.21/0.48 % OS : Linux 6.8.0-71-generic
% 0.21/0.48 % CPULimit : 300
% 0.21/0.48 % WCLimit : 300
% 0.21/0.48 % DateTime : Fri Sep 25 22:00:47 UTC 2026
% 0.21/0.48 % CPUTime :
% 0.21/0.48 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
% 1.43/1.37 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.94/1.65 % [INFO] Parsing done (277ms).
% 1.94/1.68 % [INFO] Running in sequential loop mode.
% 3.04/2.32 % [INFO] eprover registered as external prover.
% 3.04/2.33 % [INFO] Scanning for conjecture ...
% 3.22/2.47 % [INFO] Found a conjecture (or negated_conjecture) and 9 axioms. Running axiom selection ...
% 3.38/2.52 % [INFO] Axiom selection finished. Selected 9 axioms (removed 0 axioms).
% 3.38/2.55 % [INFO] Problem is propositional (TPTP CNF).
% 3.38/2.56 % [INFO] Type checking passed.
% 3.38/2.57 % [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 ...
% 119.20/30.31 % External prover 'e' found a proof!
% 119.20/30.31 % [INFO] Killing All external provers ...
% 119.20/30.31 % Time passed: 29611ms (effective reasoning time: 28626ms)
% 119.20/30.31 % 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
% 119.20/30.31 % No. of inferences in proof: 202
% 119.20/30.32 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 29611 ms resp. 28626 ms w/o parsing
% 108.11/30.47 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 108.11/30.47 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------