%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL223-1 : TPTP v9.3.1. Released v1.1.0.
% 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 07:51:15 AM UTC 2026
% Result : Unsatisfiable 113.22s 28.39s
% Output : Refutation 104.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 9
% Syntax : Number of formulae : 215 ( 89 unt; 0 typ; 0 def)
% Number of atoms : 613 ( 169 equ; 0 cnn)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 2739 ( 326 ~; 198 |; 0 &;2215 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 8 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 7 usr; 5 con; 0-2 aty)
% Number of variables : 473 ( 0 ^; 473 !; 0 ?; 473 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_decl,type,
theorem: $i > $o ).
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(r_decl,type,
r: $i ).
thf(axiom_decl,type,
axiom: $i > $o ).
thf(2,axiom,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_2) ).
thf(12,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(7,axiom,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_1) ).
thf(17,plain,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(18,plain,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[17]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( B @ axiom ) )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[12,18]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( B @ axiom ) )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[111]) ).
thf(113,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[112:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ or ) @ not @ or ) ))]]) ).
thf(117,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem ),
inference(simp,[status(thm)],[113]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_4) ).
thf(14,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(8,axiom,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ not @ or ) @ axiom )
| ( A @ theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_2) ).
thf(19,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ not @ or ) @ axiom )
| ( A @ theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ not @ or ) @ axiom )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[19]) ).
thf(23,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ ( D @ not @ or ) @ axiom ) )
| ~ ( D @ theorem )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[14,20]) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ ( D @ not @ or ) @ axiom ) )
| ~ ( D @ theorem )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[23]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ or ) @ theorem )
| ( B @ ( A @ or ) @ theorem ) ),
inference(pattern_uni,[status(thm)],[24:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ or ) )),bind(D,$thf( G @ ( H @ or ) ))]]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ or ) @ theorem )
| ( B @ ( A @ or ) @ theorem ) ),
inference(simp,[status(thm)],[25]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( B @ ( C @ or ) @ theorem ) )
| ~ $true
| ( C @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[117,32]) ).
thf(211,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( B @ ( C @ or ) @ theorem ) )
| ( C @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[210]) ).
thf(212,plain,
! [A: $i] : ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[211:[bind(A,$thf( F )),bind(B,$thf( F )),bind(C,$thf( F @ ( F @ or ) @ not ))]]) ).
thf(238,plain,
! [A: $i] : ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[212]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_3) ).
thf(13,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(26,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ ( D @ not @ or ) @ axiom ) )
| ~ ( D @ theorem )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[13,20]) ).
thf(27,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ ( D @ not @ or ) @ axiom ) )
| ~ ( D @ theorem )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[26]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ( B @ ( A @ or ) @ theorem ) ),
inference(pattern_uni,[status(thm)],[27:[bind(A,$thf( F )),bind(B,$thf( E )),bind(C,$thf( F @ ( E @ or ) )),bind(D,$thf( F ))]]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ( B @ ( A @ or ) @ theorem ) ),
inference(simp,[status(thm)],[28]) ).
thf(9,axiom,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom )
| ( B @ ( A @ not @ or ) @ theorem ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',rule_3) ).
thf(21,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom )
| ( B @ ( A @ not @ or ) @ theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(22,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom )
| ( B @ ( A @ not @ or ) @ theorem ) ),
inference(cnf,[status(esa)],[21]) ).
thf(1,negated_conjecture,
~ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ theorem ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this) ).
thf(10,plain,
~ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(11,plain,
~ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ theorem ),
inference(polarity_switch,[status(thm)],[10]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[22,11]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ theorem ) )
| ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[50]) ).
thf(52,plain,
! [A: $i] :
( ~ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( A @ not @ or ) @ theorem )
| ~ ( A @ ( q @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(pattern_uni,[status(thm)],[51:[bind(A,$thf( q @ ( p @ or ) )),bind(B,$thf( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) )),bind(C,$thf( C ))]]) ).
thf(54,plain,
! [A: $i] :
( ~ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( A @ not @ or ) @ theorem )
| ~ ( A @ ( q @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[52]) ).
thf(69,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ ( q @ ( p @ or ) @ not @ or ) @ axiom ) )
| ~ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,54]) ).
thf(70,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ ( q @ ( p @ or ) @ not @ or ) @ axiom ) )
| ~ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) ),
inference(simp,[status(thm)],[69]) ).
thf(71,plain,
! [A: $i] :
~ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( q @ ( p @ or ) @ ( A @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( q @ ( p @ or ) )),bind(B,$thf( F )),bind(C,$thf( q @ ( p @ or ) @ ( F @ or ) ))]]) ).
thf(81,plain,
! [A: $i] :
~ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( q @ ( p @ or ) @ ( A @ or ) @ not @ or ) @ theorem ),
inference(simp,[status(thm)],[71]) ).
thf(389,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( q @ ( p @ or ) @ ( C @ or ) @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,81]) ).
thf(390,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( q @ ( p @ or ) @ ( C @ or ) @ not @ or ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[389]) ).
thf(391,plain,
~ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[390:[bind(A,$thf( q @ ( p @ or ) @ ( E @ or ) @ not )),bind(B,$thf( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) )),bind(C,$thf( E ))]]) ).
thf(453,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,391]) ).
thf(454,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[453]) ).
thf(455,plain,
~ ( r @ ( p @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[454:[bind(A,$thf( r @ ( q @ not @ or ) @ ( p @ or ) @ not )),bind(B,$thf( r @ ( p @ or ) ))]]) ).
thf(479,plain,
! [A: $i] :
( ( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[238,455]) ).
thf(480,plain,
! [A: $i] :
( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ theorem ) ),
inference(simp,[status(thm)],[479]) ).
thf(498,plain,
! [A: $i] :
( ( A @ ( A @ or ) @ not @ ( A @ or ) )
!= ( r @ ( p @ or ) ) ),
inference(simp,[status(thm)],[480]) ).
thf(709,plain,
! [A: $i] :
( ( ( A @ ( A @ or ) @ not )
!= r )
| ( A != p ) ),
inference(simp,[status(thm)],[498]) ).
thf(710,plain,
( ( p @ ( p @ or ) @ not )
!= r ),
inference(simp,[status(thm)],[709]) ).
thf(105,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[13,18]) ).
thf(106,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[105]) ).
thf(107,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[106:[bind(A,$thf( H )),bind(B,$thf( G )),bind(C,$thf( H @ ( G @ or ) @ ( H @ not @ or ) ))]]) ).
thf(120,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem ),
inference(simp,[status(thm)],[107]) ).
thf(204,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( C @ ( D @ or ) @ theorem ) )
| ~ $true
| ( D @ ( C @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[120,32]) ).
thf(205,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( C @ ( D @ or ) @ theorem ) )
| ( D @ ( C @ or ) @ theorem ) ),
inference(simp,[status(thm)],[204]) ).
thf(206,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[205:[bind(A,$thf( F )),bind(B,$thf( G )),bind(C,$thf( G @ ( F @ or ) )),bind(D,$thf( G @ not ))]]) ).
thf(242,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem ),
inference(simp,[status(thm)],[206]) ).
thf(481,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,455]) ).
thf(482,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[481]) ).
thf(483,plain,
~ ( r @ theorem ),
inference(pattern_uni,[status(thm)],[482:[bind(A,$thf( p )),bind(B,$thf( r ))]]) ).
thf(521,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem )
!= ( r @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[242,483]) ).
thf(522,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem )
!= ( r @ theorem ) ),
inference(simp,[status(thm)],[521]) ).
thf(526,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( B @ ( A @ or ) @ or ) )
!= r ),
inference(simp,[status(thm)],[522]) ).
thf(509,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ theorem ) )
| ~ $true
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[32,483]) ).
thf(510,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ theorem ) )
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[509]) ).
thf(530,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= r )
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[510]) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[14,18]) ).
thf(103,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[102]) ).
thf(104,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[103:[bind(A,$thf( J )),bind(B,$thf( I )),bind(C,$thf( J @ ( I @ or ) @ ( I @ ( J @ or ) @ not @ or ) ))]]) ).
thf(119,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem ),
inference(simp,[status(thm)],[104]) ).
thf(517,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( r @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[119,483]) ).
thf(518,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( r @ theorem ) ),
inference(simp,[status(thm)],[517]) ).
thf(523,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) )
!= r ),
inference(simp,[status(thm)],[518]) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( C @ ( q @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[120,54]) ).
thf(153,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ ( C @ ( q @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[152]) ).
thf(154,plain,
~ ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ axiom ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( r @ ( q @ not @ or ) @ ( p @ or ) @ not )),bind(B,$thf( r @ ( p @ or ) )),bind(C,$thf( r @ ( p @ or ) ))]]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ axiom ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13,154]) ).
thf(165,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( A @ not @ or ) @ axiom )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[164]) ).
thf(172,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ ( A @ not @ or ) )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(177,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ or ) )
!= ( r @ ( p @ or ) ) )
| ( ( A @ not )
!= ( q @ ( p @ or ) @ not ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( A != r )
| ( B != p )
| ( ( A @ not )
!= ( q @ ( p @ or ) @ not ) ) ),
inference(simp,[status(thm)],[177]) ).
thf(202,plain,
( ( q @ ( p @ or ) @ not )
!= ( r @ not ) ),
inference(simp,[status(thm)],[199]) ).
thf(488,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[120,455]) ).
thf(489,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ theorem ) ),
inference(simp,[status(thm)],[488]) ).
thf(500,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ not @ or ) )
!= ( r @ ( p @ or ) ) ),
inference(simp,[status(thm)],[489]) ).
thf(228,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( q @ ( p @ or ) @ ( C @ or ) @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[32,81]) ).
thf(229,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( q @ ( p @ or ) @ ( C @ or ) @ not @ or ) @ theorem ) )
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[228]) ).
thf(230,plain,
! [A: $i] :
~ ( q @ ( p @ or ) @ ( A @ or ) @ not @ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[229:[bind(A,$thf( q @ ( p @ or ) @ ( E @ or ) @ not )),bind(B,$thf( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) )),bind(C,$thf( E ))]]) ).
thf(239,plain,
! [A: $i] :
~ ( q @ ( p @ or ) @ ( A @ or ) @ not @ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ or ) @ theorem ),
inference(simp,[status(thm)],[230]) ).
thf(401,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( q @ ( p @ or ) @ ( C @ or ) @ not @ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,239]) ).
thf(402,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( q @ ( p @ or ) @ ( C @ or ) @ not @ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ or ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[401]) ).
thf(403,plain,
! [A: $i] :
~ ( q @ ( p @ or ) @ ( A @ or ) @ not @ theorem ),
inference(pattern_uni,[status(thm)],[402:[bind(A,$thf( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) )),bind(B,$thf( q @ ( p @ or ) @ ( O @ or ) @ not )),bind(C,$thf( O ))]]) ).
thf(417,plain,
! [A: $i] :
~ ( q @ ( p @ or ) @ ( A @ or ) @ not @ theorem ),
inference(simp,[status(thm)],[403]) ).
thf(507,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,483]) ).
thf(508,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[507]) ).
thf(527,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= r )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[508]) ).
thf(536,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( D @ theorem ) )
| ( ( D @ ( C @ or ) )
!= r )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,527]) ).
thf(537,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( D @ theorem ) )
| ( ( D @ ( C @ or ) )
!= r )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[536]) ).
thf(538,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( A @ or ) )
!= r )
| ~ ( C @ theorem ) ),
inference(pattern_uni,[status(thm)],[537:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ or ) ))]]) ).
thf(565,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( A @ or ) )
!= r )
| ~ ( C @ theorem ) ),
inference(simp,[status(thm)],[538]) ).
thf(490,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[117,455]) ).
thf(491,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ theorem ) ),
inference(simp,[status(thm)],[490]) ).
thf(504,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) )
!= ( r @ ( p @ or ) ) ),
inference(simp,[status(thm)],[491]) ).
thf(168,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ axiom ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12,154]) ).
thf(169,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[168]) ).
thf(173,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) )
!= ( r @ ( p @ or ) @ ( q @ ( p @ or ) @ not @ or ) ) ),
inference(simp,[status(thm)],[169]) ).
thf(356,plain,
! [A: $i] :
( ( A
!= ( r @ ( p @ or ) ) )
| ( ( A @ ( A @ or ) @ not )
!= ( q @ ( p @ or ) @ not ) ) ),
inference(simp,[status(thm)],[173]) ).
thf(357,plain,
( ( r @ ( p @ or ) @ ( r @ ( p @ or ) @ or ) @ not )
!= ( q @ ( p @ or ) @ not ) ),
inference(simp,[status(thm)],[356]) ).
thf(44,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) @ theorem )
!= ( E @ ( F @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( F @ ( D @ not @ or ) @ axiom )
| ( E @ ( D @ not @ or ) @ theorem )
| ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[22,22]) ).
thf(45,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) @ theorem )
!= ( E @ ( F @ not @ or ) @ theorem ) )
| ~ ( F @ ( D @ not @ or ) @ axiom )
| ( E @ ( D @ not @ or ) @ theorem )
| ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[44]) ).
thf(46,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ not @ or ) @ axiom )
| ( B @ ( D @ not @ or ) @ theorem )
| ~ ( B @ ( C @ not @ or ) @ theorem )
| ~ ( C @ ( A @ not @ or ) @ axiom ) ),
inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( D )),bind(E,$thf( B )),bind(F,$thf( A ))]]) ).
thf(456,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[32,391]) ).
thf(457,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ theorem ) )
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[456]) ).
thf(458,plain,
~ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ ( r @ ( p @ or ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[457:[bind(A,$thf( r @ ( q @ not @ or ) @ ( p @ or ) @ not )),bind(B,$thf( r @ ( p @ or ) ))]]) ).
thf(600,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ ( r @ ( p @ or ) @ or ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,458]) ).
thf(601,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ ( r @ ( p @ or ) @ or ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[600]) ).
thf(602,plain,
~ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ theorem ),
inference(pattern_uni,[status(thm)],[601:[bind(A,$thf( r @ ( p @ or ) )),bind(B,$thf( r @ ( q @ not @ or ) @ ( p @ or ) @ not ))]]) ).
thf(940,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( C @ ( D @ or ) @ theorem ) )
| ( ( D @ ( C @ or ) )
!= r )
| ~ $true
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[32,530]) ).
thf(941,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( C @ ( D @ or ) @ theorem ) )
| ( ( D @ ( C @ or ) )
!= r )
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[940]) ).
thf(942,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ or ) )
!= r )
| ~ ( A @ ( B @ or ) @ theorem ) ),
inference(pattern_uni,[status(thm)],[941:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(515,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( r @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[117,483]) ).
thf(516,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( r @ theorem ) ),
inference(simp,[status(thm)],[515]) ).
thf(529,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ not @ or ) )
!= r ),
inference(simp,[status(thm)],[516]) ).
thf(198,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ or ) )
!= ( r @ ( p @ or ) ) )
| ( A
!= ( q @ ( p @ or ) ) ) ),
inference(simp,[status(thm)],[177]) ).
thf(201,plain,
! [A: $i] :
( ( q @ ( p @ or ) @ ( A @ or ) )
!= ( r @ ( p @ or ) ) ),
inference(simp,[status(thm)],[198]) ).
thf(545,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( D @ theorem ) )
| ( ( D @ ( C @ or ) )
!= r )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[120,527]) ).
thf(546,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( D @ theorem ) )
| ( ( D @ ( C @ or ) )
!= r ) ),
inference(simp,[status(thm)],[545]) ).
thf(547,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ or ) @ ( C @ not @ or ) @ ( A @ or ) )
!= r ),
inference(pattern_uni,[status(thm)],[546:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ ( H @ or ) @ ( I @ not @ or ) ))]]) ).
thf(561,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ or ) @ ( C @ not @ or ) @ ( A @ or ) )
!= r ),
inference(simp,[status(thm)],[547]) ).
thf(47,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( D @ ( B @ not @ or ) @ axiom ) )
| ~ ( C @ ( D @ not @ or ) @ theorem )
| ~ $true
| ( C @ ( B @ not @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[12,22]) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( D @ ( B @ not @ or ) @ axiom ) )
| ~ ( C @ ( D @ not @ or ) @ theorem )
| ( C @ ( B @ not @ or ) @ theorem ) ),
inference(simp,[status(thm)],[47]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ not @ or ) @ theorem )
| ( A @ ( B @ ( B @ or ) @ not @ or ) @ theorem ) ),
inference(pattern_uni,[status(thm)],[48:[bind(A,$thf( F )),bind(B,$thf( F @ ( F @ or ) )),bind(C,$thf( C )),bind(D,$thf( F ))]]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ not @ or ) @ theorem )
| ( A @ ( B @ ( B @ or ) @ not @ or ) @ theorem ) ),
inference(simp,[status(thm)],[49]) ).
thf(857,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= r )
| ( ( B @ not )
!= p ) ),
inference(simp,[status(thm)],[500]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( B @ ( C @ not @ or ) @ axiom ) )
| ~ ( C @ theorem )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[12,20]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ axiom )
!= ( B @ ( C @ not @ or ) @ axiom ) )
| ~ ( C @ theorem )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[29]) ).
thf(31,plain,
! [A: $i] :
( ~ ( A @ ( A @ or ) @ theorem )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[30:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ or ) ))]]) ).
thf(34,plain,
! [A: $i] :
( ~ ( A @ ( A @ or ) @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[31]) ).
thf(548,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( C @ theorem ) )
| ( ( C @ ( B @ or ) )
!= r )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[117,527]) ).
thf(549,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( C @ theorem ) )
| ( ( C @ ( B @ or ) )
!= r ) ),
inference(simp,[status(thm)],[548]) ).
thf(550,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ or ) @ not @ or ) @ ( A @ or ) )
!= r ),
inference(pattern_uni,[status(thm)],[549:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ or ) @ not @ or ) ))]]) ).
thf(562,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ or ) @ not @ or ) @ ( A @ or ) )
!= r ),
inference(simp,[status(thm)],[550]) ).
thf(362,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( C @ theorem ) )
| ~ $true
| ( C @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[238,33]) ).
thf(363,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( C @ theorem ) )
| ( C @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[362]) ).
thf(364,plain,
! [B: $i,A: $i] : ( B @ ( B @ or ) @ not @ ( B @ or ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[363:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( H @ ( H @ or ) @ not @ ( H @ or ) ))]]) ).
thf(413,plain,
! [B: $i,A: $i] : ( B @ ( B @ or ) @ not @ ( B @ or ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[364]) ).
thf(383,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( C @ theorem ) )
| ~ $true
| ( C @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[117,33]) ).
thf(384,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ not @ or ) @ theorem )
!= ( C @ theorem ) )
| ( C @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[383]) ).
thf(385,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ or ) @ not @ or ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[384:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ or ) @ not @ or ) ))]]) ).
thf(410,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ or ) @ not @ or ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[385]) ).
thf(674,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ or ) @ not @ or ) @ ( A @ or ) @ theorem )
!= ( C @ ( D @ or ) @ theorem ) )
| ~ $true
| ( D @ ( C @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[410,32]) ).
thf(675,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ or ) @ not @ or ) @ ( A @ or ) @ theorem )
!= ( C @ ( D @ or ) @ theorem ) )
| ( D @ ( C @ or ) @ theorem ) ),
inference(simp,[status(thm)],[674]) ).
thf(676,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ or ) @ not @ or ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[675:[bind(A,$thf( A )),bind(B,$thf( F )),bind(C,$thf( F @ ( F @ ( F @ or ) @ not @ or ) )),bind(D,$thf( A ))]]) ).
thf(704,plain,
! [B: $i,A: $i] : ( A @ ( B @ ( B @ ( B @ or ) @ not @ or ) @ or ) @ theorem ),
inference(simp,[status(thm)],[676]) ).
thf(404,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ( D @ ( C @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[242,33]) ).
thf(405,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem )
!= ( D @ theorem ) )
| ( D @ ( C @ or ) @ theorem ) ),
inference(simp,[status(thm)],[404]) ).
thf(406,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( C @ ( B @ or ) @ or ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[405:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ not @ ( I @ ( G @ or ) @ or ) ))]]) ).
thf(419,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( C @ ( B @ or ) @ or ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[406]) ).
thf(496,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem )
!= ( r @ ( p @ or ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[242,455]) ).
thf(497,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem )
!= ( r @ ( p @ or ) @ theorem ) ),
inference(simp,[status(thm)],[496]) ).
thf(502,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( B @ ( A @ or ) @ or ) )
!= ( r @ ( p @ or ) ) ),
inference(simp,[status(thm)],[497]) ).
thf(858,plain,
! [B: $i,A: $i] :
( ( ( B @ not )
!= r )
| ( ( B @ ( A @ or ) )
!= p ) ),
inference(simp,[status(thm)],[502]) ).
thf(533,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( C @ theorem ) )
| ( ( C @ ( B @ or ) )
!= r )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[238,527]) ).
thf(534,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( C @ theorem ) )
| ( ( C @ ( B @ or ) )
!= r ) ),
inference(simp,[status(thm)],[533]) ).
thf(535,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ or ) @ not @ ( B @ or ) @ ( A @ or ) )
!= r ),
inference(pattern_uni,[status(thm)],[534:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( H @ ( H @ or ) @ not @ ( H @ or ) ))]]) ).
thf(563,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ or ) @ not @ ( B @ or ) @ ( A @ or ) )
!= r ),
inference(simp,[status(thm)],[535]) ).
thf(505,plain,
! [A: $i] :
( ( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( r @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[238,483]) ).
thf(506,plain,
! [A: $i] :
( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( r @ theorem ) ),
inference(simp,[status(thm)],[505]) ).
thf(531,plain,
! [A: $i] :
( ( A @ ( A @ or ) @ not @ ( A @ or ) )
!= r ),
inference(simp,[status(thm)],[506]) ).
thf(925,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( C @ ( D @ or ) @ theorem ) )
| ( ( D @ ( C @ or ) )
!= r )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,530]) ).
thf(926,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( C @ ( D @ or ) @ theorem ) )
| ( ( D @ ( C @ or ) )
!= r )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[925]) ).
thf(927,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ or ) )
!= r )
| ~ ( B @ theorem ) ),
inference(pattern_uni,[status(thm)],[926:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( A ))]]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ not @ or ) @ ( B @ ( A @ not @ or ) @ not @ or ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_6) ).
thf(16,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ not @ or ) @ ( B @ ( A @ not @ or ) @ not @ or ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(358,plain,
( ( r @ ( p @ or ) @ ( r @ ( p @ or ) @ or ) )
!= ( q @ ( p @ or ) ) ),
inference(simp,[status(thm)],[357]) ).
thf(450,plain,
( ( ( r @ ( p @ or ) )
!= q )
| ( ( r @ ( p @ or ) )
!= p ) ),
inference(simp,[status(thm)],[358]) ).
thf(200,plain,
! [B: $i,A: $i] :
( ( A != r )
| ( B != p )
| ( A
!= ( q @ ( p @ or ) ) ) ),
inference(simp,[status(thm)],[177]) ).
thf(203,plain,
( ( q @ ( p @ or ) )
!= r ),
inference(simp,[status(thm)],[200]) ).
thf(513,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( r @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[120,483]) ).
thf(514,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( r @ theorem ) ),
inference(simp,[status(thm)],[513]) ).
thf(524,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ not @ or ) )
!= r ),
inference(simp,[status(thm)],[514]) ).
thf(184,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ $true
| ~ ( C @ ( q @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[119,54]) ).
thf(185,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) )
| ~ ( C @ ( q @ ( p @ or ) @ not @ or ) @ axiom ) ),
inference(simp,[status(thm)],[184]) ).
thf(186,plain,
~ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ ( r @ ( p @ or ) @ or ) @ ( q @ ( p @ or ) @ not @ or ) @ axiom ),
inference(pattern_uni,[status(thm)],[185:[bind(A,$thf( r @ ( q @ not @ or ) @ ( p @ or ) @ not )),bind(B,$thf( r @ ( p @ or ) )),bind(C,$thf( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ ( r @ ( p @ or ) @ or ) ))]]) ).
thf(35,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( E @ ( C @ not @ or ) @ axiom ) )
| ~ ( D @ ( E @ not @ or ) @ theorem )
| ~ $true
| ( D @ ( C @ not @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[14,22]) ).
thf(36,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( E @ ( C @ not @ or ) @ axiom ) )
| ~ ( D @ ( E @ not @ or ) @ theorem )
| ( D @ ( C @ not @ or ) @ theorem ) ),
inference(simp,[status(thm)],[35]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ or ) @ not @ or ) @ theorem )
| ( A @ ( B @ ( C @ or ) @ not @ or ) @ theorem ) ),
inference(pattern_uni,[status(thm)],[36:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( H @ ( I @ or ) )),bind(D,$thf( D )),bind(E,$thf( I @ ( H @ or ) ))]]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ or ) @ not @ or ) @ theorem )
| ( A @ ( B @ ( C @ or ) @ not @ or ) @ theorem ) ),
inference(simp,[status(thm)],[37]) ).
thf(557,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem )
!= ( D @ theorem ) )
| ( ( D @ ( C @ or ) )
!= r )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[242,527]) ).
thf(558,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ or ) @ or ) @ theorem )
!= ( D @ theorem ) )
| ( ( D @ ( C @ or ) )
!= r ) ),
inference(simp,[status(thm)],[557]) ).
thf(559,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ not @ ( C @ ( B @ or ) @ or ) @ ( A @ or ) )
!= r ),
inference(pattern_uni,[status(thm)],[558:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ not @ ( I @ ( G @ or ) @ or ) ))]]) ).
thf(568,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ not @ ( C @ ( B @ or ) @ or ) @ ( A @ or ) )
!= r ),
inference(simp,[status(thm)],[559]) ).
thf(222,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( C @ ( D @ or ) @ theorem ) )
| ~ $true
| ( D @ ( C @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[119,32]) ).
thf(223,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ not @ or ) @ theorem )
!= ( C @ ( D @ or ) @ theorem ) )
| ( D @ ( C @ or ) @ theorem ) ),
inference(simp,[status(thm)],[222]) ).
thf(224,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ not @ ( B @ ( A @ or ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[223:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( I @ ( H @ or ) )),bind(D,$thf( H @ ( I @ or ) @ not ))]]) ).
thf(235,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ not @ ( B @ ( A @ or ) @ or ) @ theorem ),
inference(simp,[status(thm)],[224]) ).
thf(380,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ( D @ ( C @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[120,33]) ).
thf(381,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ not @ or ) @ theorem )
!= ( D @ theorem ) )
| ( D @ ( C @ or ) @ theorem ) ),
inference(simp,[status(thm)],[380]) ).
thf(382,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( C @ not @ or ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[381:[bind(A,$thf( H )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ ( H @ or ) @ ( I @ not @ or ) ))]]) ).
thf(422,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( C @ not @ or ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[382]) ).
thf(859,plain,
! [A: $i] :
( ( A != r )
| ( ( A @ ( A @ or ) @ not )
!= p ) ),
inference(simp,[status(thm)],[504]) ).
thf(860,plain,
( ( r @ ( r @ or ) @ not )
!= p ),
inference(simp,[status(thm)],[859]) ).
thf(519,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ not @ ( B @ ( A @ or ) @ or ) @ theorem )
!= ( r @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[235,483]) ).
thf(520,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ not @ ( B @ ( A @ or ) @ or ) @ theorem )
!= ( r @ theorem ) ),
inference(simp,[status(thm)],[519]) ).
thf(528,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ or ) @ not @ ( B @ ( A @ or ) @ or ) )
!= r ),
inference(simp,[status(thm)],[520]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ not @ or ) @ axiom ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',axiom_1_5) ).
thf(15,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ not @ or ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ ( q @ ( p @ or ) @ not @ or ) @ axiom ) )
| ~ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14,54]) ).
thf(67,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ not @ or ) @ axiom )
!= ( C @ ( q @ ( p @ or ) @ not @ or ) @ axiom ) )
| ~ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( C @ not @ or ) @ theorem ) ),
inference(simp,[status(thm)],[66]) ).
thf(68,plain,
~ ( r @ ( p @ or ) @ ( r @ ( q @ not @ or ) @ ( p @ or ) @ not @ or ) @ ( p @ ( q @ or ) @ not @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[67:[bind(A,$thf( p )),bind(B,$thf( q )),bind(C,$thf( p @ ( q @ or ) ))]]) ).
thf(16328,plain,
$false,
inference(e,[status(thm)],[238,710,526,530,18,523,120,202,10,500,417,565,14,504,357,20,46,602,527,117,942,529,201,561,21,33,53,857,173,13,17,32,34,562,22,413,391,12,54,498,704,172,419,81,858,483,455,563,531,927,458,177,16,502,154,11,450,203,524,186,55,568,119,235,410,19,422,358,239,242,860,528,15,68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL223-1 : TPTP v9.3.1. Released v1.1.0.
% 0.00/0.13 % 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
% 0.26/0.51 % Computer : n005.cluster.edu
% 0.26/0.51 % Model : x86_64 x86_64
% 0.26/0.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.26/0.51 % Memory : 8046.5625MB
% 0.26/0.51 % OS : Linux 6.8.0-71-generic
% 0.26/0.51 % CPULimit : 300
% 0.26/0.51 % WCLimit : 300
% 0.26/0.51 % DateTime : Fri Sep 25 22:03:03 UTC 2026
% 0.26/0.52 % CPUTime :
% 0.26/0.52 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
% 1.42/1.38 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.95/1.67 % [INFO] Parsing done (285ms).
% 1.95/1.69 % [INFO] Running in sequential loop mode.
% 3.18/2.32 % [INFO] eprover registered as external prover.
% 3.18/2.34 % [INFO] Scanning for conjecture ...
% 3.37/2.48 % [INFO] Found a conjecture (or negated_conjecture) and 8 axioms. Running axiom selection ...
% 3.54/2.53 % [INFO] Axiom selection finished. Selected 8 axioms (removed 0 axioms).
% 3.54/2.56 % [INFO] Problem is propositional (TPTP CNF).
% 3.54/2.57 % [INFO] Type checking passed.
% 3.54/2.58 % [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 ...
% 113.22/28.38 % External prover 'e' found a proof!
% 113.22/28.38 % [INFO] Killing All external provers ...
% 113.22/28.38 % Time passed: 27656ms (effective reasoning time: 26680ms)
% 113.22/28.39 % Axioms used in derivation (8): axiom_1_5, axiom_1_4, rule_1, axiom_1_3, rule_3, axiom_1_2, rule_2, axiom_1_6
% 113.22/28.39 % No. of inferences in proof: 215
% 113.22/28.39 % SZS status Unsatisfiable for /export/starexec/sandbox2/benchmark/theBenchmark.p : 27656 ms resp. 26680 ms w/o parsing
% 104.62/28.59 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 104.62/28.59 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------