%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : LCL302-3 : TPTP v9.3.1. Released v2.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n006.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 07:51:28 AM UTC 2026
% Result : Unsatisfiable 165.19s 46.81s
% Output : Refutation 158.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 11
% Syntax : Number of formulae : 349 ( 185 unt; 0 typ; 0 def)
% Number of atoms : 837 ( 227 equ; 0 cnn)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 4502 ( 338 ~; 236 |; 0 &;3928 @)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 7 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 922 ( 0 ^; 922 !; 0 ?; 922 :)
% Comments :
%------------------------------------------------------------------------------
thf(theorem_decl,type,
theorem: $i > $o ).
thf(equivalent_decl,type,
equivalent: $i > $i > $i ).
thf(implies_decl,type,
implies: $i > $i > $i ).
thf(p_decl,type,
p: $i ).
thf(q_decl,type,
q: $i ).
thf(and_decl,type,
and: $i > $i > $i ).
thf(axiom_decl,type,
axiom: $i > $o ).
thf(or_decl,type,
or: $i > $i > $i ).
thf(not_decl,type,
not: $i > $i ).
thf(7,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',implies_definition) ).
thf(19,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) )
= ( B @ ( A @ not @ or ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(20,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ not @ or ) )
= ( B @ ( A @ implies ) ) ),
inference(lifteq,[status(thm)],[19]) ).
thf(5,axiom,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ axiom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_5) ).
thf(17,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(143,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( E @ ( D @ or ) @ ( C @ or ) ) )
| ( E @ ( C @ or ) @ ( D @ or ) @ ( B @ ( A @ implies ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[20,17]) ).
thf(144,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ not @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( F )),bind(B,$thf( H @ ( G @ or ) )),bind(C,$thf( F @ not )),bind(D,$thf( G )),bind(E,$thf( H ))]]) ).
thf(148,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ not @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[144]) ).
thf(545,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( A @ implies ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ implies ) @ implies ) @ axiom ),
inference(rewrite,[status(thm)],[148,20]) ).
thf(8,axiom,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_1) ).
thf(21,plain,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(22,plain,
! [A: $i] :
( ~ ( A @ axiom )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[21]) ).
thf(550,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ implies ) @ implies ) @ axiom )
!= ( D @ axiom ) )
| ~ $true
| ( D @ theorem ) ),
inference(paramod_ordered,[status(thm)],[545,22]) ).
thf(551,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ implies ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ implies ) @ implies ) @ axiom )
!= ( D @ axiom ) )
| ( D @ theorem ) ),
inference(simp,[status(thm)],[550]) ).
thf(552,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( A @ or ) @ ( C @ ( A @ or ) @ ( B @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[551:[bind(A,$thf( M )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( N @ ( M @ implies ) @ ( K @ or ) @ ( N @ ( K @ or ) @ ( M @ implies ) @ implies ) ))]]) ).
thf(555,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( A @ or ) @ ( C @ ( A @ or ) @ ( B @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[552]) ).
thf(4,axiom,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_4) ).
thf(16,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(72,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[16,22]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( B @ ( A @ or ) @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[72]) ).
thf(74,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[73:[bind(A,$thf( I )),bind(B,$thf( H )),bind(C,$thf( I @ ( H @ or ) @ ( H @ ( I @ or ) @ implies ) ))]]) ).
thf(77,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[74]) ).
thf(156,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( D @ or ) ) )
| ( D @ ( C @ or ) @ ( B @ ( A @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[20,77]) ).
thf(157,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[156:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(174,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[157]) ).
thf(2,axiom,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ axiom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_2) ).
thf(14,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[14,22]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ axiom )
!= ( B @ axiom ) )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[38]) ).
thf(40,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[39:[bind(A,$thf( D )),bind(B,$thf( D @ ( D @ ( D @ or ) @ implies ) ))]]) ).
thf(47,plain,
! [A: $i] : ( A @ ( A @ ( A @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[40]) ).
thf(9,axiom,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',rule_2) ).
thf(23,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(24,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ~ ( A @ ( B @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(cnf,[status(esa)],[23]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ~ $true
| ~ ( B @ ( C @ implies ) @ theorem )
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[47,24]) ).
thf(58,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ~ ( B @ ( C @ implies ) @ theorem )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[57]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ ( B @ or ) @ implies ) @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[58:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ or ) @ implies ) ))]]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ ( B @ ( B @ or ) @ implies ) @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[59]) ).
thf(736,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem )
!= ( C @ ( D @ ( D @ ( D @ or ) @ implies ) @ implies ) @ theorem ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[174,66]) ).
thf(737,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem )
!= ( C @ ( D @ ( D @ ( D @ or ) @ implies ) @ implies ) @ theorem ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[736]) ).
thf(738,plain,
! [A: $i] : ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[737:[bind(A,$thf( K )),bind(B,$thf( K @ ( K @ or ) )),bind(C,$thf( K @ ( K @ or ) @ not @ ( K @ or ) )),bind(D,$thf( K ))]]) ).
thf(761,plain,
! [A: $i] : ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[738]) ).
thf(1,negated_conjecture,
~ ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_this) ).
thf(12,plain,
~ ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[1]) ).
thf(13,plain,
~ ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ),
inference(polarity_switch,[status(thm)],[12]) ).
thf(10,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',and_defn) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ not @ or ) @ not ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(175,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ and ) )
= ( B @ not @ ( A @ implies ) @ not ) ),
inference(rewrite,[status(thm)],[26,20]) ).
thf(178,plain,
~ ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ),
inference(rewrite,[status(thm)],[13,175]) ).
thf(792,plain,
! [A: $i] :
( ( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[761,178]) ).
thf(793,plain,
! [A: $i] :
( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[792]) ).
thf(795,plain,
! [A: $i] :
( ( A @ ( A @ or ) @ not @ ( A @ or ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[793]) ).
thf(68,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( C @ ( D @ or ) @ ( B @ ( A @ implies ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[20,16]) ).
thf(69,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[68:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(75,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[69]) ).
thf(3,axiom,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ implies ) @ axiom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_3) ).
thf(15,plain,
! [B: $i,A: $i] : ( A @ ( B @ or ) @ ( A @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(31,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( D @ or ) ) )
| ( B @ ( A @ implies ) @ ( C @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[20,15]) ).
thf(32,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[31:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(33,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom ),
inference(simp,[status(thm)],[32]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[33,22]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[41]) ).
thf(43,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[42:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ implies ) @ ( G @ implies ) ))]]) ).
thf(48,plain,
! [B: $i,A: $i] : ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem ),
inference(simp,[status(thm)],[43]) ).
thf(80,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( C @ ( D @ implies ) @ theorem ) )
| ~ ( D @ theorem )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[48,24]) ).
thf(81,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( C @ ( D @ implies ) @ theorem ) )
| ~ ( D @ theorem )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[80]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ( B @ ( A @ implies ) @ theorem ) ),
inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ implies ) )),bind(D,$thf( F ))]]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ( B @ ( A @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[82]) ).
thf(1208,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[90,178]) ).
thf(1209,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[1208]) ).
thf(1211,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[1209]) ).
thf(747,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( C @ ( D @ ( D @ ( D @ or ) @ implies ) @ implies ) @ theorem ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[48,66]) ).
thf(748,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( C @ ( D @ ( D @ ( D @ or ) @ implies ) @ implies ) @ theorem ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[747]) ).
thf(749,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[748:[bind(A,$thf( I )),bind(B,$thf( L @ ( L @ ( L @ or ) @ implies ) )),bind(C,$thf( L @ ( L @ ( L @ or ) @ implies ) @ ( I @ implies ) )),bind(D,$thf( L ))]]) ).
thf(762,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[749]) ).
thf(6,axiom,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ axiom ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',axiom_1_6) ).
thf(18,plain,
! [C: $i,B: $i,A: $i] : ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ axiom ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(212,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ axiom )
!= ( D @ axiom ) )
| ~ $true
| ( D @ theorem ) ),
inference(paramod_ordered,[status(thm)],[18,22]) ).
thf(213,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ or ) @ ( A @ ( C @ or ) @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ axiom )
!= ( D @ axiom ) )
| ( D @ theorem ) ),
inference(simp,[status(thm)],[212]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ ( B @ or ) @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[213:[bind(A,$thf( L )),bind(B,$thf( N )),bind(C,$thf( M )),bind(D,$thf( N @ ( M @ or ) @ ( L @ ( M @ or ) @ implies ) @ ( N @ ( L @ implies ) @ implies ) ))]]) ).
thf(217,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ ( B @ or ) @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[214]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[15,22]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ or ) @ ( A @ implies ) @ axiom )
!= ( C @ axiom ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[44]) ).
thf(46,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[45:[bind(A,$thf( G )),bind(B,$thf( F )),bind(C,$thf( G @ ( F @ or ) @ ( G @ implies ) ))]]) ).
thf(49,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ implies ) @ theorem ),
inference(simp,[status(thm)],[46]) ).
thf(83,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ~ ( C @ ( D @ implies ) @ theorem )
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[48,24]) ).
thf(84,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ~ ( C @ ( D @ implies ) @ theorem )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[83]) ).
thf(85,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[84:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(91,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[85]) ).
thf(1533,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) @ theorem ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[49,91]) ).
thf(1534,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) @ theorem ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[1533]) ).
thf(1535,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[1534:[bind(A,$thf( J )),bind(B,$thf( O @ ( N @ implies ) @ ( O @ implies ) )),bind(C,$thf( O @ ( N @ implies ) @ ( O @ implies ) @ ( J @ or ) )),bind(D,$thf( N )),bind(E,$thf( O ))]]) ).
thf(1612,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[1535]) ).
thf(1690,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ or ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1612,178]) ).
thf(1691,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ or ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[1690]) ).
thf(1692,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ or ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[1691]) ).
thf(1134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ( D @ ( C @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[49,90]) ).
thf(1135,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( D @ ( C @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1134]) ).
thf(1136,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[1135:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ or ) @ ( H @ implies ) ))]]) ).
thf(1230,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[1136]) ).
thf(1301,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1230,178]) ).
thf(1302,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[1301]) ).
thf(1305,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[1302]) ).
thf(1545,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) @ theorem ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[174,91]) ).
thf(1546,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem )
!= ( C @ ( E @ ( D @ implies ) @ ( E @ implies ) @ implies ) @ theorem ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[1545]) ).
thf(1547,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ ( A @ implies ) @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[1546:[bind(A,$thf( L @ ( J @ implies ) )),bind(B,$thf( L )),bind(C,$thf( L @ not @ ( L @ ( J @ implies ) @ or ) )),bind(D,$thf( J )),bind(E,$thf( L ))]]) ).
thf(1604,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ ( A @ implies ) @ or ) @ theorem ),
inference(simp,[status(thm)],[1547]) ).
thf(1616,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ implies ) @ or ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ( D @ ( C @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[1604,90]) ).
thf(1617,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ implies ) @ or ) @ theorem )
!= ( D @ theorem ) )
| ( D @ ( C @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1616]) ).
thf(1618,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( C @ ( B @ implies ) @ or ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[1617:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ not @ ( I @ ( G @ implies ) @ or ) ))]]) ).
thf(1655,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( C @ ( B @ implies ) @ or ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[1618]) ).
thf(733,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( C @ ( D @ ( D @ ( D @ or ) @ implies ) @ implies ) @ theorem ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[49,66]) ).
thf(734,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( C @ ( D @ ( D @ ( D @ or ) @ implies ) @ implies ) @ theorem ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[733]) ).
thf(735,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[734:[bind(A,$thf( I )),bind(B,$thf( L @ ( L @ ( L @ or ) @ implies ) )),bind(C,$thf( L @ ( L @ ( L @ or ) @ implies ) @ ( I @ or ) )),bind(D,$thf( L ))]]) ).
thf(767,plain,
! [B: $i,A: $i] : ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[735]) ).
thf(914,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( D @ or ) ) )
| ( D @ ( B @ ( A @ implies ) @ implies ) @ ( C @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[20,767]) ).
thf(915,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ not @ ( B @ implies ) @ implies ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[914:[bind(A,$thf( F )),bind(B,$thf( F @ not )),bind(C,$thf( C )),bind(D,$thf( F @ not ))]]) ).
thf(945,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ not @ ( B @ implies ) @ implies ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[915]) ).
thf(100,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ~ ( C @ ( D @ implies ) @ theorem )
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[49,24]) ).
thf(101,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ~ ( C @ ( D @ implies ) @ theorem )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[100]) ).
thf(102,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ or ) @ ( C @ implies ) @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[101:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ or ) @ ( H @ implies ) ))]]) ).
thf(108,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ ( B @ or ) @ ( C @ implies ) @ implies ) @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[102]) ).
thf(3088,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ or ) @ ( C @ ( A @ or ) @ ( B @ implies ) @ implies ) @ theorem )
!= ( D @ ( F @ ( E @ or ) @ ( F @ implies ) @ implies ) @ theorem ) )
| ~ $true
| ( D @ theorem ) ),
inference(paramod_ordered,[status(thm)],[555,108]) ).
thf(3089,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ or ) @ ( C @ ( A @ or ) @ ( B @ implies ) @ implies ) @ theorem )
!= ( D @ ( F @ ( E @ or ) @ ( F @ implies ) @ implies ) @ theorem ) )
| ( D @ theorem ) ),
inference(simp,[status(thm)],[3088]) ).
thf(3090,plain,
! [B: $i,A: $i] : ( B @ ( B @ implies ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[3089:[bind(A,$thf( G )),bind(B,$thf( J )),bind(C,$thf( J )),bind(D,$thf( J @ ( J @ implies ) @ ( G @ or ) )),bind(E,$thf( G )),bind(F,$thf( J ))]]) ).
thf(3207,plain,
! [B: $i,A: $i] : ( B @ ( B @ implies ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[3090]) ).
thf(3234,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( D @ implies ) @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[20,3207]) ).
thf(3235,plain,
! [B: $i,A: $i] : ( B @ ( B @ implies ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[3234:[bind(A,$thf( E )),bind(B,$thf( G @ ( G @ implies ) )),bind(C,$thf( E @ not )),bind(D,$thf( G ))]]) ).
thf(3281,plain,
! [B: $i,A: $i] : ( B @ ( B @ implies ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[3235]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ~ $true
| ( ( A @ ( B @ implies ) @ theorem )
!= ( B @ theorem ) )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(eqfactor_ordered,[status(thm)],[24]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= B )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[35]) ).
thf(11,axiom,
! [B: $i,A: $i] :
( ( B @ ( A @ equivalent ) )
= ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',equivalent_defn) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ equivalent ) )
= ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ ( A @ implies ) @ and ) )
= ( B @ ( A @ equivalent ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(266,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ not @ ( B @ ( A @ implies ) @ implies ) @ not )
= ( B @ ( A @ equivalent ) ) ),
inference(rewrite,[status(thm)],[28,175]) ).
thf(154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ ( C @ ( D @ or ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[20,77]) ).
thf(155,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[154:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(173,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[155]) ).
thf(225,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ not @ ( C @ or ) ) )
| ( C @ ( D @ implies ) @ ( B @ ( A @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[20,173]) ).
thf(226,plain,
! [B: $i,A: $i] : ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[225:[bind(A,$thf( E )),bind(B,$thf( F @ not )),bind(C,$thf( E @ not )),bind(D,$thf( F ))]]) ).
thf(239,plain,
! [B: $i,A: $i] : ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[226]) ).
thf(750,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( C @ ( D @ ( D @ ( D @ or ) @ implies ) @ implies ) @ theorem ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[239,66]) ).
thf(751,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( C @ ( D @ ( D @ ( D @ or ) @ implies ) @ implies ) @ theorem ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[750]) ).
thf(752,plain,
! [A: $i] : ( A @ not @ ( A @ not @ or ) @ not @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[751:[bind(A,$thf( N @ not @ ( N @ not @ or ) )),bind(B,$thf( N )),bind(C,$thf( N @ not @ ( N @ not @ or ) @ not @ ( N @ implies ) )),bind(D,$thf( N @ not ))]]) ).
thf(763,plain,
! [A: $i] : ( A @ not @ ( A @ not @ or ) @ not @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[752]) ).
thf(806,plain,
! [A: $i] : ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ theorem ),
inference(rewrite,[status(thm)],[763,20]) ).
thf(809,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ not @ ( B @ ( A @ implies ) @ implies ) @ not )
!= ( C @ not @ ( C @ implies ) @ not ) )
| ( B @ ( A @ equivalent ) @ ( C @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[266,806]) ).
thf(810,plain,
! [A: $i] : ( A @ ( A @ equivalent ) @ ( A @ ( A @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[809:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(841,plain,
! [A: $i] : ( A @ ( A @ equivalent ) @ ( A @ ( A @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[810]) ).
thf(1196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ( D @ ( C @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[48,90]) ).
thf(1197,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( D @ ( C @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1196]) ).
thf(1198,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[1197:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(1229,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[1198]) ).
thf(1262,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1229,178]) ).
thf(1263,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[1262]) ).
thf(1264,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[1263]) ).
thf(52,plain,
! [A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,13]) ).
thf(53,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[52]) ).
thf(63,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[53]) ).
thf(116,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( C @ or ) ) )
| ( ( C @ ( B @ ( A @ implies ) @ implies ) )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,63]) ).
thf(117,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(pattern_uni,[status(thm)],[116:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(118,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(196,plain,
! [A: $i] :
( ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(rewrite,[status(thm)],[118,175]) ).
thf(1202,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ or ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ( D @ ( C @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[767,90]) ).
thf(1203,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ or ) @ theorem )
!= ( D @ theorem ) )
| ( D @ ( C @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1202]) ).
thf(1204,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( C @ or ) @ implies ) @ ( B @ or ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[1203:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( H @ ( H @ or ) @ implies ) @ ( E @ or ) ))]]) ).
thf(1232,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( C @ or ) @ implies ) @ ( B @ or ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[1204]) ).
thf(97,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( C @ ( D @ implies ) @ theorem ) )
| ~ ( D @ theorem )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[49,24]) ).
thf(98,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( C @ ( D @ implies ) @ theorem ) )
| ~ ( D @ theorem )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[97]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ( B @ ( A @ or ) @ theorem ) ),
inference(pattern_uni,[status(thm)],[98:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( F @ ( E @ or ) )),bind(D,$thf( F ))]]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ~ ( B @ theorem )
| ( B @ ( A @ or ) @ theorem ) ),
inference(simp,[status(thm)],[99]) ).
thf(2321,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[107,178]) ).
thf(2322,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[2321]) ).
thf(2324,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[2322]) ).
thf(95,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49,13]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[95]) ).
thf(106,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(134,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( D @ implies ) )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,106]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(179,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(rewrite,[status(thm)],[136,175]) ).
thf(236,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[173,178]) ).
thf(237,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[236]) ).
thf(238,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(2232,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ implies ) @ or ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ( D @ ( C @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[1604,107]) ).
thf(2233,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ implies ) @ or ) @ theorem )
!= ( D @ theorem ) )
| ( D @ ( C @ or ) @ theorem ) ),
inference(simp,[status(thm)],[2232]) ).
thf(2234,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( C @ ( B @ implies ) @ or ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[2233:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ not @ ( I @ ( G @ implies ) @ or ) ))]]) ).
thf(2367,plain,
! [C: $i,B: $i,A: $i] : ( C @ not @ ( C @ ( B @ implies ) @ or ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[2234]) ).
thf(833,plain,
! [A: $i] :
( ( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[806,178]) ).
thf(834,plain,
! [A: $i] :
( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[833]) ).
thf(837,plain,
! [A: $i] :
( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[834]) ).
thf(856,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ not @ ( B @ ( A @ implies ) @ implies ) @ not )
!= ( C @ not @ ( C @ implies ) @ not ) )
| ( ( B @ ( A @ equivalent ) @ ( C @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ) ),
inference(paramod_ordered,[status(thm)],[266,837]) ).
thf(857,plain,
! [A: $i] :
( ( A @ ( A @ equivalent ) @ ( A @ ( A @ implies ) @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(pattern_uni,[status(thm)],[856:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(866,plain,
! [A: $i] :
( ( A @ ( A @ equivalent ) @ ( A @ ( A @ implies ) @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[857]) ).
thf(1517,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( E @ ( D @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( E @ implies ) @ ( C @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,1305]) ).
thf(1518,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ implies ) @ ( B @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(pattern_uni,[status(thm)],[1517:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ not )),bind(E,$thf( B ))]]) ).
thf(1526,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( C @ implies ) @ ( A @ implies ) @ ( B @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[1518]) ).
thf(254,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[174,178]) ).
thf(255,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[254]) ).
thf(256,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ or ) @ ( A @ ( B @ implies ) @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[255]) ).
thf(594,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ not @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) @ ( C @ ( D @ implies ) @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ) ),
inference(paramod_ordered,[status(thm)],[20,256]) ).
thf(595,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(pattern_uni,[status(thm)],[594:[bind(A,$thf( E )),bind(B,$thf( F @ not )),bind(C,$thf( E @ not )),bind(D,$thf( F ))]]) ).
thf(598,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[595]) ).
thf(86,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( ( C @ ( D @ implies ) )
!= D )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[48,37]) ).
thf(87,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( ( C @ ( D @ implies ) )
!= D )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[86]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) )
!= ( C @ ( B @ implies ) @ ( C @ implies ) ) )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[87:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ implies ) @ ( H @ implies ) ))]]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ ( B @ implies ) @ ( C @ implies ) @ implies ) )
!= ( C @ ( B @ implies ) @ ( C @ implies ) ) )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[88]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( B @ ( C @ implies ) @ theorem ) )
| ~ ( C @ theorem )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[47,24]) ).
thf(55,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( B @ ( C @ implies ) @ theorem ) )
| ~ ( C @ theorem )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[54]) ).
thf(56,plain,
! [A: $i] :
( ~ ( A @ ( A @ or ) @ theorem )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[55:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ or ) ))]]) ).
thf(65,plain,
! [A: $i] :
( ~ ( A @ ( A @ or ) @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[56]) ).
thf(1619,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ implies ) @ or ) @ theorem )
!= ( D @ theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1604,1211]) ).
thf(1620,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ implies ) @ or ) @ theorem )
!= ( D @ theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ) ),
inference(simp,[status(thm)],[1619]) ).
thf(1621,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ not @ ( C @ ( B @ implies ) @ or ) @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(pattern_uni,[status(thm)],[1620:[bind(A,$thf( G )),bind(B,$thf( I )),bind(C,$thf( C )),bind(D,$thf( I @ not @ ( I @ ( G @ implies ) @ or ) ))]]) ).
thf(1656,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ not @ ( C @ ( B @ implies ) @ or ) @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[1621]) ).
thf(2195,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( D @ theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[107,1211]) ).
thf(2196,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ theorem )
!= ( D @ theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[2195]) ).
thf(2197,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) )
| ~ ( C @ theorem ) ),
inference(pattern_uni,[status(thm)],[2196:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ or ) ))]]) ).
thf(2344,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) )
| ~ ( C @ theorem ) ),
inference(simp,[status(thm)],[2197]) ).
thf(1129,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( C @ theorem ) )
| ~ $true
| ( C @ ( B @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[761,90]) ).
thf(1130,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( C @ theorem ) )
| ( C @ ( B @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1129]) ).
thf(1131,plain,
! [B: $i,A: $i] : ( B @ ( B @ or ) @ not @ ( B @ or ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[1130:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( H @ ( H @ or ) @ not @ ( H @ or ) ))]]) ).
thf(1227,plain,
! [B: $i,A: $i] : ( B @ ( B @ or ) @ not @ ( B @ or ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[1131]) ).
thf(1345,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ or ) @ not @ ( B @ or ) @ ( A @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1227,178]) ).
thf(1346,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ or ) @ not @ ( B @ or ) @ ( A @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[1345]) ).
thf(1350,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ or ) @ not @ ( B @ or ) @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[1346]) ).
thf(354,plain,
! [B: $i,A: $i] :
( ( ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[239,178]) ).
thf(355,plain,
! [B: $i,A: $i] :
( ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[354]) ).
thf(356,plain,
! [B: $i,A: $i] :
( ( A @ not @ ( B @ implies ) @ ( B @ not @ ( A @ implies ) @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[355]) ).
thf(2568,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( C @ or ) ) )
| ( ( B @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) )
| ~ ( D @ theorem ) ),
inference(paramod_ordered,[status(thm)],[20,2324]) ).
thf(2569,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) )
| ~ ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[2568:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ not )),bind(D,$thf( B ))]]) ).
thf(2666,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) )
| ~ ( A @ theorem ) ),
inference(simp,[status(thm)],[2569]) ).
thf(936,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ or ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[767,178]) ).
thf(937,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ or ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[936]) ).
thf(938,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ or ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[937]) ).
thf(726,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( A @ ( B @ or ) @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ theorem )
!= ( D @ ( E @ ( E @ ( E @ or ) @ implies ) @ implies ) @ theorem ) )
| ~ $true
| ( D @ theorem ) ),
inference(paramod_ordered,[status(thm)],[217,66]) ).
thf(727,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( A @ ( B @ or ) @ implies ) @ ( C @ ( A @ implies ) @ implies ) @ theorem )
!= ( D @ ( E @ ( E @ ( E @ or ) @ implies ) @ implies ) @ theorem ) )
| ( D @ theorem ) ),
inference(simp,[status(thm)],[726]) ).
thf(728,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ ( B @ or ) @ ( A @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[727:[bind(A,$thf( O @ ( O @ or ) )),bind(B,$thf( N )),bind(C,$thf( O )),bind(D,$thf( O @ ( N @ or ) @ ( O @ ( O @ or ) @ ( N @ or ) @ implies ) )),bind(E,$thf( O ))]]) ).
thf(765,plain,
! [B: $i,A: $i] : ( B @ ( A @ or ) @ ( B @ ( B @ or ) @ ( A @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[728]) ).
thf(1173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ( D @ ( C @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[77,90]) ).
thf(1174,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( D @ ( C @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1173]) ).
thf(1175,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( B @ ( C @ or ) @ implies ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[1174:[bind(A,$thf( I )),bind(B,$thf( J )),bind(C,$thf( C )),bind(D,$thf( J @ ( I @ or ) @ ( I @ ( J @ or ) @ implies ) ))]]) ).
thf(1219,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( B @ ( C @ or ) @ implies ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[1175]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( C @ or ) ) )
| ( C @ ( B @ ( A @ implies ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[20,14]) ).
thf(30,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[29:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(34,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[30]) ).
thf(50,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( C @ or ) ) )
| ( C @ ( B @ ( A @ implies ) @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[20,47]) ).
thf(51,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[50:[bind(A,$thf( E )),bind(B,$thf( E @ not )),bind(C,$thf( E @ not ))]]) ).
thf(64,plain,
! [A: $i] : ( A @ not @ ( A @ not @ ( A @ implies ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[51]) ).
thf(180,plain,
! [A: $i] :
( ( A @ ( A @ ( A @ or ) @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(rewrite,[status(thm)],[63,175]) ).
thf(145,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ axiom )
!= ( D @ axiom ) )
| ~ $true
| ( D @ theorem ) ),
inference(paramod_ordered,[status(thm)],[17,22]) ).
thf(146,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ or ) @ ( B @ or ) @ ( C @ ( B @ or ) @ ( A @ or ) @ implies ) @ axiom )
!= ( D @ axiom ) )
| ( D @ theorem ) ),
inference(simp,[status(thm)],[145]) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ or ) @ ( C @ ( A @ or ) @ ( B @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[146:[bind(A,$thf( M )),bind(B,$thf( K )),bind(C,$thf( N )),bind(D,$thf( N @ ( M @ or ) @ ( K @ or ) @ ( N @ ( K @ or ) @ ( M @ or ) @ implies ) ))]]) ).
thf(149,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ or ) @ ( C @ ( A @ or ) @ ( B @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[147]) ).
thf(176,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( B @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(rewrite,[status(thm)],[106,175]) ).
thf(141,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( E @ ( D @ or ) ) )
| ( E @ ( C @ or ) @ ( D @ or ) @ ( B @ ( A @ implies ) @ ( C @ or ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[20,17]) ).
thf(142,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ or ) @ ( C @ not @ or ) @ ( A @ ( C @ implies ) @ ( B @ or ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[141:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( F @ not )),bind(E,$thf( B ))]]) ).
thf(152,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ or ) @ ( C @ not @ or ) @ ( A @ ( C @ implies ) @ ( B @ or ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[142]) ).
thf(694,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( B @ or ) @ ( C @ implies ) @ ( A @ ( C @ implies ) @ ( B @ or ) @ implies ) @ axiom ),
inference(rewrite,[status(thm)],[152,20]) ).
thf(1242,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ theorem )
!= ( E @ theorem ) )
| ~ $true
| ( E @ ( D @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[1229,90]) ).
thf(1243,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( C @ implies ) @ ( A @ implies ) @ theorem )
!= ( E @ theorem ) )
| ( E @ ( D @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1242]) ).
thf(1244,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[1243:[bind(A,$thf( F )),bind(B,$thf( J )),bind(C,$thf( K )),bind(D,$thf( D )),bind(E,$thf( K @ ( J @ implies ) @ ( K @ implies ) @ ( F @ implies ) ))]]) ).
thf(1271,plain,
! [D: $i,C: $i,B: $i,A: $i] : ( D @ ( C @ implies ) @ ( D @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[1244]) ).
thf(869,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( D @ or ) ) )
| ( D @ ( B @ ( A @ implies ) @ implies ) @ ( C @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[20,762]) ).
thf(870,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ not @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[869:[bind(A,$thf( F )),bind(B,$thf( F @ not )),bind(C,$thf( C )),bind(D,$thf( F @ not ))]]) ).
thf(900,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ not @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[870]) ).
thf(2268,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ( D @ ( C @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[49,107]) ).
thf(2269,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( B @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( D @ ( C @ or ) @ theorem ) ),
inference(simp,[status(thm)],[2268]) ).
thf(2270,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[2269:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ or ) @ ( H @ implies ) ))]]) ).
thf(2351,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[2270]) ).
thf(2405,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ or ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2351,178]) ).
thf(2406,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ or ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[2405]) ).
thf(2415,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ or ) @ ( C @ implies ) @ ( A @ or ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[2406]) ).
thf(70,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( C @ ( D @ or ) ) )
| ( B @ ( A @ implies ) @ ( D @ ( C @ or ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[20,16]) ).
thf(71,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[70:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( B )),bind(D,$thf( E @ not ))]]) ).
thf(76,plain,
! [B: $i,A: $i] : ( A @ ( B @ implies ) @ ( B @ not @ ( A @ or ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[71]) ).
thf(2229,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ theorem )
!= ( C @ theorem ) )
| ~ $true
| ( C @ ( B @ or ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[806,107]) ).
thf(2230,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ theorem )
!= ( C @ theorem ) )
| ( C @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[2229]) ).
thf(2231,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ implies ) @ not @ ( B @ implies ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[2230:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( I @ not @ ( I @ implies ) @ not @ ( I @ implies ) ))]]) ).
thf(2365,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ implies ) @ not @ ( B @ implies ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[2231]) ).
thf(137,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( E @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ ( D @ or ) @ ( E @ ( D @ or ) @ ( C @ or ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[20,17]) ).
thf(138,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ implies ) @ ( B @ or ) @ ( A @ ( B @ or ) @ ( C @ not @ or ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( F @ not )),bind(D,$thf( D )),bind(E,$thf( B ))]]) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ implies ) @ ( B @ or ) @ ( A @ ( B @ or ) @ ( C @ not @ or ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[138]) ).
thf(636,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ implies ) @ ( B @ or ) @ ( A @ ( B @ or ) @ ( C @ implies ) @ implies ) @ axiom ),
inference(rewrite,[status(thm)],[150,20]) ).
thf(2235,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)],[761,107]) ).
thf(2236,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ or ) @ not @ ( A @ or ) @ theorem )
!= ( C @ theorem ) )
| ( C @ ( B @ or ) @ theorem ) ),
inference(simp,[status(thm)],[2235]) ).
thf(2237,plain,
! [B: $i,A: $i] : ( B @ ( B @ or ) @ not @ ( B @ or ) @ ( A @ or ) @ theorem ),
inference(pattern_uni,[status(thm)],[2236:[bind(A,$thf( H )),bind(B,$thf( B )),bind(C,$thf( H @ ( H @ or ) @ not @ ( H @ or ) ))]]) ).
thf(2369,plain,
! [B: $i,A: $i] : ( B @ ( B @ or ) @ not @ ( B @ or ) @ ( A @ or ) @ theorem ),
inference(simp,[status(thm)],[2237]) ).
thf(305,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ equivalent ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) )
| ~ ( A @ ( B @ implies ) @ not @ ( B @ ( A @ implies ) @ implies ) @ not @ theorem ) ),
inference(paramod_ordered,[status(thm)],[266,178]) ).
thf(306,plain,
~ ( q @ ( p @ implies ) @ ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ implies ) @ not @ ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ implies ) @ implies ) @ not @ theorem ),
inference(pattern_uni,[status(thm)],[305:[bind(A,$thf( q @ ( p @ implies ) )),bind(B,$thf( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) ))]]) ).
thf(139,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( E @ ( C @ or ) @ ( D @ or ) ) )
| ( B @ ( A @ implies ) @ ( E @ ( D @ or ) @ ( C @ or ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[20,17]) ).
thf(140,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ not @ or ) @ ( B @ or ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[139:[bind(A,$thf( F )),bind(B,$thf( H @ ( G @ or ) )),bind(C,$thf( G )),bind(D,$thf( F @ not )),bind(E,$thf( H ))]]) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ not @ or ) @ ( B @ or ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[140]) ).
thf(648,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ implies ) @ ( B @ or ) @ implies ) @ axiom ),
inference(rewrite,[status(thm)],[151,20]) ).
thf(653,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ implies ) @ ( B @ or ) @ implies ) @ axiom )
!= ( D @ axiom ) )
| ~ $true
| ( D @ theorem ) ),
inference(paramod_ordered,[status(thm)],[648,22]) ).
thf(654,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ implies ) @ ( B @ or ) @ implies ) @ axiom )
!= ( D @ axiom ) )
| ( D @ theorem ) ),
inference(simp,[status(thm)],[653]) ).
thf(655,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ implies ) @ ( B @ or ) @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[654:[bind(A,$thf( K )),bind(B,$thf( M )),bind(C,$thf( N )),bind(D,$thf( N @ ( M @ or ) @ ( K @ implies ) @ ( N @ ( K @ implies ) @ ( M @ or ) @ implies ) ))]]) ).
thf(658,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( B @ or ) @ ( A @ implies ) @ ( C @ ( A @ implies ) @ ( B @ or ) @ implies ) @ theorem ),
inference(simp,[status(thm)],[655]) ).
thf(208,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ ( E @ or ) ) )
| ( B @ ( A @ implies ) @ ( C @ ( E @ or ) @ implies ) @ ( D @ ( C @ implies ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[20,18]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ implies ) @ ( B @ ( C @ not @ or ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[208:[bind(A,$thf( F )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( B )),bind(E,$thf( F @ not ))]]) ).
thf(215,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ implies ) @ ( B @ ( C @ not @ or ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[209]) ).
thf(712,plain,
! [C: $i,B: $i,A: $i] : ( A @ ( C @ implies ) @ ( B @ ( C @ implies ) @ implies ) @ ( A @ ( B @ implies ) @ implies ) @ axiom ),
inference(rewrite,[status(thm)],[215,20]) ).
thf(1643,plain,
! [B: $i,A: $i] :
( ( ( B @ not @ ( B @ ( A @ implies ) @ or ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1604,178]) ).
thf(1644,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( B @ ( A @ implies ) @ or ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[1643]) ).
thf(1647,plain,
! [B: $i,A: $i] :
( ( B @ not @ ( B @ ( A @ implies ) @ or ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[1644]) ).
thf(60,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ( ( B @ ( C @ implies ) )
!= C )
| ~ $true
| ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[47,37]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ ( A @ or ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ( ( B @ ( C @ implies ) )
!= C )
| ( B @ theorem ) ),
inference(simp,[status(thm)],[60]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ or ) @ implies ) @ implies ) )
!= ( B @ ( B @ ( B @ or ) @ implies ) ) )
| ( A @ theorem ) ),
inference(pattern_uni,[status(thm)],[61:[bind(A,$thf( E )),bind(B,$thf( B )),bind(C,$thf( E @ ( E @ ( E @ or ) @ implies ) ))]]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ ( B @ ( B @ or ) @ implies ) @ implies ) )
!= ( B @ ( B @ ( B @ or ) @ implies ) ) )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[62]) ).
thf(1372,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) )
| ~ $true
| ~ ( B @ theorem ) ),
inference(paramod_ordered,[status(thm)],[90,1211]) ).
thf(1373,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( ( D @ ( C @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) )
| ~ ( B @ theorem ) ),
inference(simp,[status(thm)],[1372]) ).
thf(1374,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) )
| ~ ( C @ theorem ) ),
inference(pattern_uni,[status(thm)],[1373:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( C )),bind(D,$thf( F @ ( E @ implies ) ))]]) ).
thf(1452,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ implies ) @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) )
| ~ ( C @ theorem ) ),
inference(simp,[status(thm)],[1374]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48,13]) ).
thf(79,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) @ theorem )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[78]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[79]) ).
thf(177,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ implies ) @ ( B @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(rewrite,[status(thm)],[89,175]) ).
thf(3239,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ or ) @ theorem )
!= ( C @ ( C @ or ) @ theorem ) )
| ~ $true
| ( C @ theorem ) ),
inference(paramod_ordered,[status(thm)],[3207,65]) ).
thf(3240,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ implies ) @ ( A @ or ) @ theorem )
!= ( C @ ( C @ or ) @ theorem ) )
| ( C @ theorem ) ),
inference(simp,[status(thm)],[3239]) ).
thf(3241,plain,
! [A: $i] : ( A @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[3240:[bind(A,$thf( E @ ( E @ implies ) )),bind(B,$thf( E )),bind(C,$thf( E @ ( E @ implies ) ))]]) ).
thf(3284,plain,
! [A: $i] : ( A @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[3241]) ).
thf(3337,plain,
! [A: $i] :
( ( ( A @ ( A @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3284,178]) ).
thf(3338,plain,
! [A: $i] :
( ( A @ ( A @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[3337]) ).
thf(3344,plain,
! [A: $i] :
( ( A @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[3338]) ).
thf(1170,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ theorem )
!= ( C @ theorem ) )
| ~ $true
| ( C @ ( B @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[806,90]) ).
thf(1171,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ not @ ( A @ implies ) @ not @ ( A @ implies ) @ theorem )
!= ( C @ theorem ) )
| ( C @ ( B @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1170]) ).
thf(1172,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ implies ) @ not @ ( B @ implies ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[1171:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( I @ not @ ( I @ implies ) @ not @ ( I @ implies ) ))]]) ).
thf(1218,plain,
! [B: $i,A: $i] : ( B @ not @ ( B @ implies ) @ not @ ( B @ implies ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[1172]) ).
thf(198,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ not @ or ) )
!= ( D @ not @ ( C @ or ) ) )
| ( B @ ( A @ implies ) @ ( C @ ( D @ implies ) @ implies ) @ axiom ) ),
inference(paramod_ordered,[status(thm)],[20,75]) ).
thf(199,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) @ axiom ),
inference(pattern_uni,[status(thm)],[198:[bind(A,$thf( E )),bind(B,$thf( F @ not )),bind(C,$thf( E @ not )),bind(D,$thf( F ))]]) ).
thf(203,plain,
! [B: $i,A: $i] : ( B @ not @ ( A @ implies ) @ ( A @ not @ ( B @ implies ) @ implies ) @ axiom ),
inference(simp,[status(thm)],[199]) ).
thf(1161,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ equivalent ) @ ( A @ ( A @ implies ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ~ $true
| ( C @ ( B @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[841,90]) ).
thf(1162,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ equivalent ) @ ( A @ ( A @ implies ) @ implies ) @ theorem )
!= ( C @ theorem ) )
| ( C @ ( B @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1161]) ).
thf(1163,plain,
! [B: $i,A: $i] : ( B @ ( B @ equivalent ) @ ( B @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[1162:[bind(A,$thf( I )),bind(B,$thf( B )),bind(C,$thf( I @ ( I @ equivalent ) @ ( I @ ( I @ implies ) @ implies ) ))]]) ).
thf(1216,plain,
! [B: $i,A: $i] : ( B @ ( B @ equivalent ) @ ( B @ ( B @ implies ) @ implies ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[1163]) ).
thf(893,plain,
! [B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[762,178]) ).
thf(894,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ implies ) @ theorem )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[893]) ).
thf(896,plain,
! [B: $i,A: $i] :
( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[894]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ implies ) @ theorem )
!= ( B @ theorem ) )
| ~ ( B @ theorem )
| ( A @ theorem ) ),
inference(simp,[status(thm)],[35]) ).
thf(158,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[77,13]) ).
thf(159,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) @ theorem )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) @ theorem ) ),
inference(simp,[status(thm)],[158]) ).
thf(169,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) )
!= ( q @ ( p @ and ) @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(simp,[status(thm)],[159]) ).
thf(400,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ or ) @ ( A @ ( B @ or ) @ implies ) )
!= ( q @ not @ ( p @ implies ) @ not @ ( p @ implies ) @ ( q @ ( p @ implies ) @ equivalent ) ) ),
inference(rewrite,[status(thm)],[169,175]) ).
thf(1149,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ implies ) @ theorem )
!= ( D @ theorem ) )
| ~ $true
| ( D @ ( C @ implies ) @ theorem ) ),
inference(paramod_ordered,[status(thm)],[762,90]) ).
thf(1150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( B @ ( B @ or ) @ implies ) @ ( A @ implies ) @ theorem )
!= ( D @ theorem ) )
| ( D @ ( C @ implies ) @ theorem ) ),
inference(simp,[status(thm)],[1149]) ).
thf(1151,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( C @ or ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ theorem ),
inference(pattern_uni,[status(thm)],[1150:[bind(A,$thf( E )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( H @ ( H @ or ) @ implies ) @ ( E @ implies ) ))]]) ).
thf(1236,plain,
! [C: $i,B: $i,A: $i] : ( C @ ( C @ ( C @ or ) @ implies ) @ ( B @ implies ) @ ( A @ implies ) @ theorem ),
inference(simp,[status(thm)],[1151]) ).
thf(42058,plain,
$false,
inference(e,[status(thm)],[555,795,175,75,1211,762,217,1692,1305,1655,945,174,3281,37,25,841,24,14,1264,196,20,1232,2324,179,238,806,2367,866,1526,1604,761,598,21,3207,33,92,65,1656,2344,1350,1227,356,256,77,2666,1612,837,173,938,266,765,1219,34,64,180,17,149,176,694,22,27,12,1271,49,900,2415,76,91,66,108,2365,636,2369,306,658,48,712,18,1647,1230,67,1452,177,16,3344,1218,3284,203,1216,896,23,36,1229,19,107,239,767,400,1236,47,15,178,90,2351]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : LCL302-3 : TPTP v9.3.1. Released v2.3.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.25/5.51 % Computer : n006.cluster.edu
% 0.25/5.51 % Model : x86_64 x86_64
% 0.25/5.51 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.25/5.51 % Memory : 8046.5625MB
% 0.25/5.51 % OS : Linux 6.8.0-71-generic
% 0.25/5.51 % CPULimit : 300
% 0.25/5.51 % WCLimit : 300
% 0.25/5.51 % DateTime : Fri Sep 25 22:13:02 UTC 2026
% 0.25/5.51 % CPUTime :
% 0.25/5.51 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 1.40/6.36 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.92/6.65 % [INFO] Parsing done (292ms).
% 1.92/6.68 % [INFO] Running in sequential loop mode.
% 2.94/7.27 % [INFO] eprover registered as external prover.
% 2.94/7.28 % [INFO] Scanning for conjecture ...
% 3.32/7.41 % [INFO] Found a conjecture (or negated_conjecture) and 10 axioms. Running axiom selection ...
% 3.32/7.45 % [INFO] Axiom selection finished. Selected 10 axioms (removed 0 axioms).
% 3.32/7.48 % [INFO] Problem is propositional (TPTP CNF).
% 3.32/7.49 % [INFO] Type checking passed.
% 3.50/7.50 % [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 ...
% 165.19/46.80 % External prover 'e' found a proof!
% 165.19/46.80 % [INFO] Killing All external provers ...
% 165.19/46.80 % Time passed: 41083ms (effective reasoning time: 40117ms)
% 165.19/46.81 % Axioms used in derivation (10): axiom_1_5, equivalent_defn, and_defn, axiom_1_4, rule_1, axiom_1_3, implies_definition, axiom_1_2, rule_2, axiom_1_6
% 165.19/46.81 % No. of inferences in proof: 349
% 165.19/46.81 % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p : 41083 ms resp. 40117 ms w/o parsing
% 158.57/46.96 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 158.57/46.97 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------