%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE015+1 : TPTP v9.3.1. Released v4.0.0.
% 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 : n014.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 07:42:59 AM UTC 2026
% Result : Theorem 114.71s 24.68s
% Output : Refutation 111.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 20
% Syntax : Number of formulae : 562 ( 208 unt; 0 typ; 3 def)
% Number of atoms : 1368 ( 800 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 4575 ( 671 ~; 474 |; 31 &;3369 @)
% ( 4 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 676 ( 1 ^; 667 !; 5 ?; 676 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(test_decl,type,
test: $i > $o ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(c_decl,type,
c: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(one_decl,type,
one: $i ).
thf(complement_decl,type,
complement: $i > $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( A @ test )
& ( B @ test ) )
=> ( ( B @ c @ ( A @ c @ ( B @ ( A @ addition ) @ multiplication ) @ multiplication ) )
= zero ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( sk1 @ test )
& ( A @ test ) )
=> ( ( A @ c @ ( sk1 @ c @ ( A @ ( sk1 @ addition ) @ multiplication ) @ multiplication ) )
= zero ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ complement ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( A @ test )
& ( B @ test ) )
=> ( ( B @ c @ ( A @ c @ ( B @ ( A @ addition ) @ multiplication ) @ multiplication ) )
= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( A @ test )
& ( B @ test ) )
=> ( ( B @ c @ ( A @ c @ ( B @ ( A @ addition ) @ multiplication ) @ multiplication ) )
= zero ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i] :
( ( ( A @ test )
& ( B @ test ) )
=> ( ( B @ c @ ( A @ c @ ( B @ ( A @ addition ) @ multiplication ) @ multiplication ) )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
( ( ( sk2 @ c @ ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ multiplication ) )
!= zero )
& ( sk1 @ test )
& ( sk2 @ test ) ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
sk2 @ test,
inference(cnfConj,[status(thm)],[20]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ test )
<=> ? [B: $i] : ( A @ ( B @ complement ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).
thf(43,plain,
! [A: $i] :
( ( ? [B: $i] : ( A @ ( B @ complement ) )
=> ( A @ test ) )
& ( ( A @ test )
=> ? [B: $i] : ( A @ ( B @ complement ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(44,plain,
( ! [A: $i] :
( ? [B: $i] : ( A @ ( B @ complement ) )
=> ( A @ test ) )
& ! [A: $i] :
( ( A @ test )
=> ? [B: $i] : ( A @ ( B @ complement ) ) ) ),
inference(miniscope,[status(thm)],[43]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ test )
| ~ ( B @ ( C @ complement ) ) )
& ( ( A @ ( A @ sk3 @ complement ) )
| ~ ( A @ test ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [A: $i] :
( ( A @ ( A @ sk3 @ complement ) )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[45]) ).
thf(404,plain,
! [A: $i] :
( ( ( sk2 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk3 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,46]) ).
thf(405,plain,
! [A: $i] :
( ( ( sk2 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk3 @ complement ) ) ),
inference(simp,[status(thm)],[404]) ).
thf(406,plain,
sk2 @ ( sk2 @ sk3 @ complement ),
inference(pattern_uni,[status(thm)],[405:[bind(A,$thf( sk2 ))]]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ complement ) )
<=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) )
=> ( A @ ( B @ complement ) ) )
& ( ( A @ ( B @ complement ) )
=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(65,plain,
( ! [A: $i,B: $i] :
( ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) )
=> ( A @ ( B @ complement ) ) )
& ! [A: $i,B: $i] :
( ( A @ ( B @ complement ) )
=> ( ( ( B @ ( A @ addition ) )
= one )
& ( ( A @ ( B @ multiplication ) )
= zero )
& ( ( B @ ( A @ multiplication ) )
= zero ) ) ) ),
inference(miniscope,[status(thm)],[64]) ).
thf(66,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ complement ) )
| ( ( D @ ( C @ addition ) )
!= one )
| ( ( C @ ( D @ multiplication ) )
!= zero )
| ( ( D @ ( C @ multiplication ) )
!= zero ) )
& ( ( ( B @ ( A @ addition ) )
= one )
| ~ ( A @ ( B @ complement ) ) )
& ( ( ( A @ ( B @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) )
& ( ( ( B @ ( A @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ) ),
inference(cnf,[status(esa)],[65]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
= one )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[66]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(lifteq,[status(thm)],[69]) ).
thf(1877,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[406,73]) ).
thf(1878,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[1877]) ).
thf(1879,plain,
( ( sk2 @ sk3 @ ( sk2 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[1878:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 @ sk3 ))]]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( A @ c )
= B )
<=> ( B @ ( A @ complement ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( A @ test )
=> ( ( ( B @ ( A @ complement ) )
=> ( ( A @ c )
= B ) )
& ( ( ( A @ c )
= B )
=> ( B @ ( A @ complement ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(56,plain,
! [A: $i] :
( ( A @ test )
=> ( ! [B: $i] :
( ( B @ ( A @ complement ) )
=> ( ( A @ c )
= B ) )
& ! [B: $i] :
( ( ( A @ c )
= B )
=> ( B @ ( A @ complement ) ) ) ) ),
inference(miniscope,[status(thm)],[55]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( ( ( A @ c )
= C )
| ~ ( C @ ( A @ complement ) )
| ~ ( A @ test ) )
& ( ( B @ ( A @ complement ) )
| ( ( A @ c )
!= B )
| ~ ( A @ test ) ) ),
inference(cnf,[status(esa)],[56]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement ) )
| ( ( A @ c )
!= B )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
!= B ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(61,plain,
! [A: $i] :
( ( A @ c @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[60]) ).
thf(556,plain,
! [A: $i] :
( ( ( sk2 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,61]) ).
thf(557,plain,
! [A: $i] :
( ( ( sk2 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[556]) ).
thf(558,plain,
sk2 @ c @ ( sk2 @ complement ),
inference(pattern_uni,[status(thm)],[557:[bind(A,$thf( sk2 ))]]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[66]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(lifteq,[status(thm)],[67]) ).
thf(1013,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[558,71]) ).
thf(1014,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1013]) ).
thf(1015,plain,
( ( sk2 @ ( sk2 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1014:[bind(A,$thf( sk2 @ c )),bind(B,$thf( sk2 ))]]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(28,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(25,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(26,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[26]) ).
thf(151,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
!= ( D @ ( zero @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[30,27]) ).
thf(164,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C != D )
| ( ( B @ ( A @ multiplication ) )
!= zero )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[151]) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= zero )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[164]) ).
thf(7316,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ c @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( zero != zero )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1015,170]) ).
thf(7317,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ c @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[7316]) ).
thf(7318,plain,
! [A: $i] :
( ( A @ ( sk2 @ multiplication ) @ ( sk2 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[7317:[bind(A,$thf( sk2 @ c )),bind(B,$thf( sk2 )),bind(C,$thf( C ))]]) ).
thf(7427,plain,
! [A: $i] :
( ( A @ ( sk2 @ multiplication ) @ ( sk2 @ c @ multiplication ) )
= zero ),
inference(simp,[status(thm)],[7318]) ).
thf(22,plain,
sk1 @ test,
inference(cnfConj,[status(thm)],[20]) ).
thf(559,plain,
! [A: $i] :
( ( ( sk1 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,61]) ).
thf(560,plain,
! [A: $i] :
( ( ( sk1 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[559]) ).
thf(561,plain,
sk1 @ c @ ( sk1 @ complement ),
inference(pattern_uni,[status(thm)],[560:[bind(A,$thf( sk1 ))]]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( A @ test )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[45]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( A @ test )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(581,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[561,48]) ).
thf(582,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[581]) ).
thf(583,plain,
sk1 @ c @ test,
inference(pattern_uni,[status(thm)],[582:[bind(A,$thf( sk1 @ c )),bind(B,$thf( sk1 ))]]) ).
thf(586,plain,
! [A: $i] :
( ( ( sk1 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk3 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[583,46]) ).
thf(587,plain,
! [A: $i] :
( ( ( sk1 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk3 @ complement ) ) ),
inference(simp,[status(thm)],[586]) ).
thf(588,plain,
sk1 @ c @ ( sk1 @ c @ sk3 @ complement ),
inference(pattern_uni,[status(thm)],[587:[bind(A,$thf( sk1 @ c ))]]) ).
thf(1022,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[588,71]) ).
thf(1023,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1022]) ).
thf(1024,plain,
( ( sk1 @ c @ sk3 @ ( sk1 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1023:[bind(A,$thf( sk1 @ c )),bind(B,$thf( sk1 @ c @ sk3 ))]]) ).
thf(589,plain,
! [A: $i] :
( ( ( sk1 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[583,61]) ).
thf(590,plain,
! [A: $i] :
( ( ( sk1 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[589]) ).
thf(591,plain,
sk1 @ c @ c @ ( sk1 @ c @ complement ),
inference(pattern_uni,[status(thm)],[590:[bind(A,$thf( sk1 @ c ))]]) ).
thf(3444,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ ( sk1 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[591,48]) ).
thf(3445,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ ( sk1 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[3444]) ).
thf(3446,plain,
sk1 @ c @ c @ test,
inference(pattern_uni,[status(thm)],[3445:[bind(A,$thf( sk1 @ c @ c )),bind(B,$thf( sk1 @ c ))]]) ).
thf(3491,plain,
! [A: $i] :
( ( ( sk1 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3446,61]) ).
thf(3492,plain,
! [A: $i] :
( ( ( sk1 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[3491]) ).
thf(3493,plain,
sk1 @ c @ c @ c @ ( sk1 @ c @ c @ complement ),
inference(pattern_uni,[status(thm)],[3492:[bind(A,$thf( sk1 @ c @ c ))]]) ).
thf(7920,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ c @ ( sk1 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[3493,71]) ).
thf(7921,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ c @ ( sk1 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[7920]) ).
thf(7922,plain,
( ( sk1 @ c @ c @ ( sk1 @ c @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[7921:[bind(A,$thf( sk1 @ c @ c @ c )),bind(B,$thf( sk1 @ c @ c ))]]) ).
thf(568,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[558,48]) ).
thf(569,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[568]) ).
thf(570,plain,
sk2 @ c @ test,
inference(pattern_uni,[status(thm)],[569:[bind(A,$thf( sk2 @ c )),bind(B,$thf( sk2 ))]]) ).
thf(576,plain,
! [A: $i] :
( ( ( sk2 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[570,61]) ).
thf(577,plain,
! [A: $i] :
( ( ( sk2 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[576]) ).
thf(578,plain,
sk2 @ c @ c @ ( sk2 @ c @ complement ),
inference(pattern_uni,[status(thm)],[577:[bind(A,$thf( sk2 @ c ))]]) ).
thf(857,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ ( sk2 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[578,48]) ).
thf(858,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ ( sk2 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[857]) ).
thf(859,plain,
sk2 @ c @ c @ test,
inference(pattern_uni,[status(thm)],[858:[bind(A,$thf( sk2 @ c @ c )),bind(B,$thf( sk2 @ c ))]]) ).
thf(885,plain,
! [A: $i] :
( ( ( sk2 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk3 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[859,46]) ).
thf(886,plain,
! [A: $i] :
( ( ( sk2 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk3 @ complement ) ) ),
inference(simp,[status(thm)],[885]) ).
thf(887,plain,
sk2 @ c @ c @ ( sk2 @ c @ c @ sk3 @ complement ),
inference(pattern_uni,[status(thm)],[886:[bind(A,$thf( sk2 @ c @ c ))]]) ).
thf(7658,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ ( sk2 @ c @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[887,71]) ).
thf(7659,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ ( sk2 @ c @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[7658]) ).
thf(7660,plain,
( ( sk2 @ c @ c @ sk3 @ ( sk2 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[7659:[bind(A,$thf( sk2 @ c @ c )),bind(B,$thf( sk2 @ c @ c @ sk3 ))]]) ).
thf(1848,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[561,73]) ).
thf(1849,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[1848]) ).
thf(1850,plain,
( ( sk1 @ ( sk1 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[1849:[bind(A,$thf( sk1 @ c )),bind(B,$thf( sk1 ))]]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ addition ) )
= B )
=> ( B @ ( A @ leq ) ) )
& ( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ addition ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(3486,plain,
! [A: $i] :
( ( ( sk1 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk3 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3446,46]) ).
thf(3487,plain,
! [A: $i] :
( ( ( sk1 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk3 @ complement ) ) ),
inference(simp,[status(thm)],[3486]) ).
thf(3488,plain,
sk1 @ c @ c @ ( sk1 @ c @ c @ sk3 @ complement ),
inference(pattern_uni,[status(thm)],[3487:[bind(A,$thf( sk1 @ c @ c ))]]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[66]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(lifteq,[status(thm)],[68]) ).
thf(7884,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ ( sk1 @ c @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[3488,72]) ).
thf(7885,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ ( sk1 @ c @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[7884]) ).
thf(7886,plain,
( ( sk1 @ c @ c @ ( sk1 @ c @ c @ sk3 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[7885:[bind(A,$thf( sk1 @ c @ c )),bind(B,$thf( sk1 @ c @ c @ sk3 ))]]) ).
thf(23,plain,
( ( sk2 @ c @ ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ multiplication ) )
!= zero ),
inference(cnfConj,[status(thm)],[20]) ).
thf(24,plain,
( ( sk2 @ c @ ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ multiplication ) )
!= zero ),
inference(lifteq,[status(thm)],[23]) ).
thf(106,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[27,24]) ).
thf(107,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ multiplication ) ) ),
inference(simp,[status(thm)],[106]) ).
thf(111,plain,
! [A: $i] :
( ( A
!= ( sk2 @ c ) )
| ( ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[107]) ).
thf(115,plain,
( ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= zero ),
inference(simp,[status(thm)],[111]) ).
thf(573,plain,
! [A: $i] :
( ( ( sk2 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk3 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[570,46]) ).
thf(574,plain,
! [A: $i] :
( ( ( sk2 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk3 @ complement ) ) ),
inference(simp,[status(thm)],[573]) ).
thf(575,plain,
sk2 @ c @ ( sk2 @ c @ sk3 @ complement ),
inference(pattern_uni,[status(thm)],[574:[bind(A,$thf( sk2 @ c ))]]) ).
thf(1833,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[575,73]) ).
thf(1834,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[1833]) ).
thf(1835,plain,
( ( sk2 @ c @ sk3 @ ( sk2 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[1834:[bind(A,$thf( sk2 @ c )),bind(B,$thf( sk2 @ c @ sk3 ))]]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(5695,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ sk3 @ ( sk2 @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1835,54]) ).
thf(5696,plain,
( ( sk2 @ c @ ( sk2 @ c @ sk3 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[5695:[bind(A,$thf( sk2 @ c )),bind(B,$thf( sk2 @ c @ sk3 ))]]) ).
thf(407,plain,
! [A: $i] :
( ( ( sk1 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk3 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,46]) ).
thf(408,plain,
! [A: $i] :
( ( ( sk1 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk3 @ complement ) ) ),
inference(simp,[status(thm)],[407]) ).
thf(409,plain,
sk1 @ ( sk1 @ sk3 @ complement ),
inference(pattern_uni,[status(thm)],[408:[bind(A,$thf( sk1 ))]]) ).
thf(1071,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[409,71]) ).
thf(1072,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1071]) ).
thf(1073,plain,
( ( sk1 @ sk3 @ ( sk1 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1072:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk3 ))]]) ).
thf(143,plain,
( ( sk2 @ c @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= zero ),
inference(rewrite,[status(thm)],[24,30]) ).
thf(1076,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ( zero != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[71,143]) ).
thf(1077,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[1076]) ).
thf(1078,plain,
~ ( sk2 @ ( sk1 @ addition ) @ ( sk2 @ c @ ( sk1 @ c @ multiplication ) @ complement ) ),
inference(pattern_uni,[status(thm)],[1077:[bind(A,$thf( sk2 @ ( sk1 @ addition ) )),bind(B,$thf( sk2 @ c @ ( sk1 @ c @ multiplication ) ))]]) ).
thf(7693,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ ( sk2 @ c @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[887,72]) ).
thf(7694,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ ( sk2 @ c @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[7693]) ).
thf(7695,plain,
( ( sk2 @ c @ c @ ( sk2 @ c @ c @ sk3 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[7694:[bind(A,$thf( sk2 @ c @ c )),bind(B,$thf( sk2 @ c @ c @ sk3 ))]]) ).
thf(15,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(79,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(80,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[79]) ).
thf(81,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[80]) ).
thf(135,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[81,115]) ).
thf(136,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) ),
inference(simp,[status(thm)],[135]) ).
thf(140,plain,
! [A: $i] :
( ( ( sk1 @ c )
!= zero )
| ( A
!= ( sk2 @ ( sk1 @ addition ) ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(142,plain,
( ( sk1 @ c )
!= zero ),
inference(simp,[status(thm)],[140]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(49,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(50,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[50]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
thf(31,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ addition ) @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(237,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ addition ) @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( ( sk1 @ c @ ( A @ ( B @ addition ) @ ( C @ addition ) @ multiplication ) )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[33,115]) ).
thf(247,plain,
! [C: $i,B: $i,A: $i] :
( ( A != sk2 )
| ( ( B @ ( C @ addition ) )
!= sk1 )
| ( ( sk1 @ c @ ( A @ ( B @ addition ) @ ( C @ addition ) @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[237]) ).
thf(251,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ addition ) )
!= sk1 )
| ( ( sk1 @ c @ ( sk2 @ ( A @ addition ) @ ( B @ addition ) @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[247]) ).
thf(15093,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( B @ ( C @ addition ) ) )
| ( A != sk1 )
| ( ( sk1 @ c @ ( sk2 @ ( B @ addition ) @ ( C @ addition ) @ multiplication ) )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[51,251]) ).
thf(15094,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( sk1 @ c @ ( sk2 @ ( A @ addition ) @ ( A @ addition ) @ multiplication ) )
!= zero ) ),
inference(pattern_uni,[status(thm)],[15093:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(15307,plain,
( ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) @ multiplication ) )
!= zero ),
inference(simp,[status(thm)],[15094]) ).
thf(15392,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[27,15307]) ).
thf(15393,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) @ multiplication ) ) ),
inference(simp,[status(thm)],[15392]) ).
thf(15570,plain,
! [A: $i] :
( ( A
!= ( sk1 @ c ) )
| ( ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) )
!= zero ) ),
inference(simp,[status(thm)],[15393]) ).
thf(15600,plain,
( ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) )
!= zero ),
inference(simp,[status(thm)],[15570]) ).
thf(266,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[81,143]) ).
thf(267,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) ),
inference(simp,[status(thm)],[266]) ).
thf(283,plain,
! [A: $i] :
( ( ( sk2 @ c @ ( sk1 @ c @ multiplication ) )
!= zero )
| ( A
!= ( sk2 @ ( sk1 @ addition ) ) ) ),
inference(simp,[status(thm)],[267]) ).
thf(293,plain,
( ( sk2 @ c @ ( sk1 @ c @ multiplication ) )
!= zero ),
inference(simp,[status(thm)],[283]) ).
thf(1416,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ multiplication ) ) )
| ( zero != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[72,293]) ).
thf(1417,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ multiplication ) ) )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[1416]) ).
thf(1418,plain,
~ ( sk2 @ c @ ( sk1 @ c @ complement ) ),
inference(pattern_uni,[status(thm)],[1417:[bind(A,$thf( sk2 @ c )),bind(B,$thf( sk1 @ c ))]]) ).
thf(3434,plain,
( ( ( sk1 @ c @ c @ ( sk1 @ c @ complement ) )
!= ( sk2 @ c @ ( sk1 @ c @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[591,1418]) ).
thf(3435,plain,
( ( sk1 @ c @ c @ ( sk1 @ c @ complement ) )
!= ( sk2 @ c @ ( sk1 @ c @ complement ) ) ),
inference(simp,[status(thm)],[3434]) ).
thf(3478,plain,
( ( ( sk1 @ c @ c )
!= ( sk2 @ c ) )
| ( ( sk1 @ c )
!= ( sk1 @ c ) ) ),
inference(simp,[status(thm)],[3435]) ).
thf(3481,plain,
( ( sk1 @ c @ c )
!= ( sk2 @ c ) ),
inference(simp,[status(thm)],[3478]) ).
thf(16,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(82,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(83,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[82]) ).
thf(84,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[83]) ).
thf(444,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( zero @ ( C @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[54,84]) ).
thf(445,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) )
= A ),
inference(pattern_uni,[status(thm)],[444:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(1886,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[409,73]) ).
thf(1887,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[1886]) ).
thf(1888,plain,
( ( sk1 @ sk3 @ ( sk1 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[1887:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk3 ))]]) ).
thf(2548,plain,
! [A: $i] :
( ( ( A @ ( zero @ addition ) )
!= ( sk1 @ sk3 @ ( sk1 @ addition ) ) )
| ( A = one ) ),
inference(paramod_ordered,[status(thm)],[445,1888]) ).
thf(2566,plain,
! [A: $i] :
( ( A
!= ( sk1 @ sk3 ) )
| ( sk1 != zero )
| ( A = one ) ),
inference(simp,[status(thm)],[2548]) ).
thf(2580,plain,
( ( sk1 != zero )
| ( ( sk1 @ sk3 )
= one ) ),
inference(simp,[status(thm)],[2566]) ).
thf(7917,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ c @ ( sk1 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[3493,73]) ).
thf(7918,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ c @ ( sk1 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[7917]) ).
thf(7919,plain,
( ( sk1 @ c @ c @ ( sk1 @ c @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[7918:[bind(A,$thf( sk1 @ c @ c @ c )),bind(B,$thf( sk1 @ c @ c ))]]) ).
thf(10858,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ ( sk1 @ c @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[7919,54]) ).
thf(10859,plain,
( ( sk1 @ c @ c @ c @ ( sk1 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[10858:[bind(A,$thf( sk1 @ c @ c @ c )),bind(B,$thf( sk1 @ c @ c ))]]) ).
thf(89,plain,
( ! [A: $i,B: $i] :
( ( ( B @ ( A @ addition ) )
= B )
=> ( B @ ( A @ leq ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ addition ) )
= B ) ) ),
inference(miniscope,[status(thm)],[88]) ).
thf(90,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ leq ) )
| ( ( D @ ( C @ addition ) )
!= D ) )
& ( ( ( B @ ( A @ addition ) )
= B )
| ~ ( B @ ( A @ leq ) ) ) ),
inference(cnf,[status(esa)],[89]) ).
thf(92,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(cnfConj,[status(thm)],[90]) ).
thf(94,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(lifteq,[status(thm)],[92]) ).
thf(95,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(simp,[status(thm)],[94]) ).
thf(3345,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( zero @ addition ) )
!= ( C @ ( B @ addition ) ) )
| ( C @ ( B @ leq ) )
| ( A != C ) ),
inference(paramod_ordered,[status(thm)],[445,95]) ).
thf(3346,plain,
! [A: $i] :
( ( A @ ( zero @ leq ) )
| ( A != A ) ),
inference(pattern_uni,[status(thm)],[3345:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(3370,plain,
! [A: $i] : ( A @ ( zero @ leq ) ),
inference(simp,[status(thm)],[3346]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
= B )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[57]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
= B ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
= B ) ),
inference(simp,[status(thm)],[62]) ).
thf(103,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[81,24]) ).
thf(104,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ multiplication ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(109,plain,
! [A: $i] :
( ( ( sk2 @ c )
!= zero )
| ( A
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(113,plain,
( ( sk2 @ c )
!= zero ),
inference(simp,[status(thm)],[109]) ).
thf(755,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
!= ( sk2 @ c ) )
| ( B != zero )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[63,113]) ).
thf(756,plain,
! [A: $i] :
( ( A != zero )
| ~ ( A @ ( sk2 @ complement ) )
| ~ ( sk2 @ test ) ),
inference(pattern_uni,[status(thm)],[755:[bind(A,$thf( sk2 ))]]) ).
thf(827,plain,
( ~ ( zero @ ( sk2 @ complement ) )
| ~ ( sk2 @ test ) ),
inference(simp,[status(thm)],[756]) ).
thf(968,plain,
( ~ ( zero @ ( sk2 @ complement ) )
| ~ $true ),
inference(rewrite,[status(thm)],[827,21]) ).
thf(969,plain,
~ ( zero @ ( sk2 @ complement ) ),
inference(simp,[status(thm)],[968]) ).
thf(976,plain,
! [A: $i] :
( ( ( A @ ( A @ sk3 @ complement ) )
!= ( zero @ ( sk2 @ complement ) ) )
| ~ $true
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[46,969]) ).
thf(977,plain,
! [A: $i] :
( ( ( A @ ( A @ sk3 @ complement ) )
!= ( zero @ ( sk2 @ complement ) ) )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[976]) ).
thf(990,plain,
! [A: $i] :
( ( A != zero )
| ( ( A @ sk3 )
!= sk2 )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[977]) ).
thf(1001,plain,
( ( ( zero @ sk3 )
!= sk2 )
| ~ ( zero @ test ) ),
inference(simp,[status(thm)],[990]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(40,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(41,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[40]) ).
thf(42,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[41]) ).
thf(1044,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ ( sk2 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[578,71]) ).
thf(1045,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ ( sk2 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1044]) ).
thf(1046,plain,
( ( sk2 @ c @ ( sk2 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1045:[bind(A,$thf( sk2 @ c @ c )),bind(B,$thf( sk2 @ c ))]]) ).
thf(261,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ addition ) @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( ( sk2 @ c @ ( sk1 @ c @ multiplication ) @ ( A @ ( B @ addition ) @ ( C @ addition ) @ multiplication ) )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[33,143]) ).
thf(276,plain,
! [C: $i,B: $i,A: $i] :
( ( A != sk2 )
| ( ( B @ ( C @ addition ) )
!= sk1 )
| ( ( sk2 @ c @ ( sk1 @ c @ multiplication ) @ ( A @ ( B @ addition ) @ ( C @ addition ) @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[261]) ).
thf(288,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ addition ) )
!= sk1 )
| ( ( sk2 @ c @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( A @ addition ) @ ( B @ addition ) @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[276]) ).
thf(1384,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ( zero != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[72,115]) ).
thf(1385,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[1384]) ).
thf(1386,plain,
~ ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ complement ) ),
inference(pattern_uni,[status(thm)],[1385:[bind(A,$thf( sk1 @ c )),bind(B,$thf( sk2 @ ( sk1 @ addition ) ))]]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
thf(37,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( B @ ( one @ multiplication ) ) )
| ( zero = B ) ),
inference(paramod_ordered,[status(thm)],[27,42]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( one != zero )
| ( zero = B ) ),
inference(simp,[status(thm)],[119]) ).
thf(129,plain,
! [A: $i] :
( ( one != zero )
| ( zero = A ) ),
inference(simp,[status(thm)],[128]) ).
thf(3889,plain,
! [A: $i] :
( ( A
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ( zero != zero )
| ( one != zero ) ),
inference(paramod_ordered,[status(thm)],[129,115]) ).
thf(3890,plain,
! [A: $i] :
( ( A
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ( one != zero ) ),
inference(simp,[status(thm)],[3889]) ).
thf(3891,plain,
one != zero,
inference(pattern_uni,[status(thm)],[3890:[bind(A,$thf( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ))]]) ).
thf(2163,plain,
! [A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( sk1 @ ( sk1 @ c @ addition ) ) )
| ( A = one ) ),
inference(paramod_ordered,[status(thm)],[84,1850]) ).
thf(2209,plain,
! [A: $i] :
( ( sk1 != zero )
| ( A
!= ( sk1 @ c ) )
| ( A = one ) ),
inference(simp,[status(thm)],[2163]) ).
thf(2215,plain,
( ( sk1 != zero )
| ( ( sk1 @ c )
= one ) ),
inference(simp,[status(thm)],[2209]) ).
thf(12416,plain,
( ( ( sk1 @ c )
!= ( sk1 @ c ) )
| ( one @ test )
| ( sk1 != zero ) ),
inference(paramod_ordered,[status(thm)],[2215,583]) ).
thf(12417,plain,
( ( one @ test )
| ( sk1 != zero ) ),
inference(pattern_uni,[status(thm)],[12416:[]]) ).
thf(1830,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[588,73]) ).
thf(1831,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[1830]) ).
thf(1832,plain,
( ( sk1 @ c @ sk3 @ ( sk1 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[1831:[bind(A,$thf( sk1 @ c )),bind(B,$thf( sk1 @ c @ sk3 ))]]) ).
thf(888,plain,
! [A: $i] :
( ( ( sk2 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[859,61]) ).
thf(889,plain,
! [A: $i] :
( ( ( sk2 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[888]) ).
thf(890,plain,
sk2 @ c @ c @ c @ ( sk2 @ c @ c @ complement ),
inference(pattern_uni,[status(thm)],[889:[bind(A,$thf( sk2 @ c @ c ))]]) ).
thf(7741,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ c @ ( sk2 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[890,48]) ).
thf(7742,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ c @ ( sk2 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[7741]) ).
thf(7743,plain,
sk2 @ c @ c @ c @ test,
inference(pattern_uni,[status(thm)],[7742:[bind(A,$thf( sk2 @ c @ c @ c )),bind(B,$thf( sk2 @ c @ c ))]]) ).
thf(1053,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[406,71]) ).
thf(1054,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1053]) ).
thf(1055,plain,
( ( sk2 @ sk3 @ ( sk2 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1054:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 @ sk3 ))]]) ).
thf(1095,plain,
! [A: $i] :
( ( ( sk2 @ ( sk2 @ c @ multiplication ) )
!= ( A @ ( one @ multiplication ) ) )
| ( zero = A ) ),
inference(paramod_ordered,[status(thm)],[1015,42]) ).
thf(1142,plain,
! [A: $i] :
( ( sk2 != A )
| ( ( sk2 @ c )
!= one )
| ( zero = A ) ),
inference(simp,[status(thm)],[1095]) ).
thf(1159,plain,
( ( ( sk2 @ c )
!= one )
| ( sk2 = zero ) ),
inference(simp,[status(thm)],[1142]) ).
thf(203,plain,
! [A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( ( sk1 @ c @ ( A @ multiplication ) )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[84,115]) ).
thf(205,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A != sk1 )
| ( ( sk1 @ c @ ( A @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[203]) ).
thf(208,plain,
( ( sk2 != zero )
| ( ( sk1 @ c @ ( sk1 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[205]) ).
thf(1419,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[561,72]) ).
thf(1420,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1419]) ).
thf(1421,plain,
( ( sk1 @ c @ ( sk1 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1420:[bind(A,$thf( sk1 @ c )),bind(B,$thf( sk1 ))]]) ).
thf(1731,plain,
( ( sk2 != zero )
| ( zero != zero ) ),
inference(rewrite,[status(thm)],[208,1421]) ).
thf(1732,plain,
sk2 != zero,
inference(simp,[status(thm)],[1731]) ).
thf(3029,plain,
( ( sk2 @ c )
!= one ),
inference(simplifyReflect,[status(thm)],[1159,1732]) ).
thf(14,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(76,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(77,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[76]) ).
thf(78,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[77]) ).
thf(2564,plain,
! [A: $i] :
( ( ( sk1 @ sk3 @ ( sk1 @ addition ) )
!= ( A @ ( A @ addition ) ) )
| ( one = A ) ),
inference(paramod_ordered,[status(thm)],[1888,51]) ).
thf(2570,plain,
! [A: $i] :
( ( ( sk1 @ sk3 )
!= A )
| ( sk1 != A )
| ( one = A ) ),
inference(simp,[status(thm)],[2564]) ).
thf(2583,plain,
( ( ( sk1 @ sk3 )
!= sk1 )
| ( sk1 = one ) ),
inference(simp,[status(thm)],[2570]) ).
thf(1041,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[561,71]) ).
thf(1042,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1041]) ).
thf(1043,plain,
( ( sk1 @ ( sk1 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1042:[bind(A,$thf( sk1 @ c )),bind(B,$thf( sk1 ))]]) ).
thf(1227,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk1 @ ( sk1 @ c @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[78,1043]) ).
thf(1282,plain,
! [A: $i] :
( ( sk1 != one )
| ( A
!= ( sk1 @ c ) )
| ( A = zero ) ),
inference(simp,[status(thm)],[1227]) ).
thf(1288,plain,
( ( sk1 != one )
| ( ( sk1 @ c )
= zero ) ),
inference(simp,[status(thm)],[1282]) ).
thf(3729,plain,
sk1 != one,
inference(simplifyReflect,[status(thm)],[1288,142]) ).
thf(17107,plain,
( ( sk1 @ sk3 )
!= sk1 ),
inference(simplifyReflect,[status(thm)],[2583,3729]) ).
thf(91,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
= B )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[90]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
= B ) ),
inference(lifteq,[status(thm)],[91]) ).
thf(1505,plain,
! [A: $i] :
( ( ( sk1 @ sk3 @ ( sk1 @ multiplication ) )
!= ( one @ ( A @ multiplication ) ) )
| ( zero = A ) ),
inference(paramod_ordered,[status(thm)],[1073,78]) ).
thf(1570,plain,
! [A: $i] :
( ( ( sk1 @ sk3 )
!= one )
| ( sk1 != A )
| ( zero = A ) ),
inference(simp,[status(thm)],[1505]) ).
thf(1572,plain,
( ( ( sk1 @ sk3 )
!= one )
| ( sk1 = zero ) ),
inference(simp,[status(thm)],[1570]) ).
thf(148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( D @ ( C @ ( B @ multiplication ) @ multiplication ) ) )
| ( A
= ( D @ ( C @ multiplication ) @ ( B @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[42,30]) ).
thf(161,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != D )
| ( ( C @ ( B @ multiplication ) )
!= one )
| ( A
= ( D @ ( C @ multiplication ) @ ( B @ multiplication ) ) ) ),
inference(simp,[status(thm)],[148]) ).
thf(167,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= one )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= C ) ),
inference(simp,[status(thm)],[161]) ).
thf(7307,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ c @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( zero != zero )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1043,170]) ).
thf(7308,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ c @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[7307]) ).
thf(7309,plain,
! [A: $i] :
( ( A @ ( sk1 @ multiplication ) @ ( sk1 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[7308:[bind(A,$thf( sk1 @ c )),bind(B,$thf( sk1 )),bind(C,$thf( C ))]]) ).
thf(7423,plain,
! [A: $i] :
( ( A @ ( sk1 @ multiplication ) @ ( sk1 @ c @ multiplication ) )
= zero ),
inference(simp,[status(thm)],[7309]) ).
thf(13140,plain,
! [A: $i] :
( ( ( A @ ( sk1 @ multiplication ) @ ( sk1 @ c @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[7423,293]) ).
thf(13141,plain,
! [A: $i] :
( ( A @ ( sk1 @ multiplication ) @ ( sk1 @ c @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ multiplication ) ) ),
inference(simp,[status(thm)],[13140]) ).
thf(13323,plain,
! [A: $i] :
( ( ( A @ ( sk1 @ multiplication ) )
!= ( sk2 @ c ) )
| ( ( sk1 @ c )
!= ( sk1 @ c ) ) ),
inference(simp,[status(thm)],[13141]) ).
thf(13365,plain,
! [A: $i] :
( ( A @ ( sk1 @ multiplication ) )
!= ( sk2 @ c ) ),
inference(simp,[status(thm)],[13323]) ).
thf(13461,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
!= ( D @ ( sk1 @ multiplication ) ) )
| ( C
!= ( sk2 @ c ) )
| ( ( B @ ( A @ multiplication ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[167,13365]) ).
thf(13462,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ c ) )
| ( ( A @ ( sk1 @ multiplication ) )
!= one ) ),
inference(pattern_uni,[status(thm)],[13461:[bind(A,$thf( sk1 )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( F @ ( E @ multiplication ) ))]]) ).
thf(13506,plain,
! [A: $i] :
( ( A @ ( sk1 @ multiplication ) )
!= one ),
inference(simp,[status(thm)],[13462]) ).
thf(1038,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ multiplication ) ) )
| ( zero != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[71,293]) ).
thf(1039,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ multiplication ) ) )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[1038]) ).
thf(1040,plain,
~ ( sk1 @ c @ ( sk2 @ c @ complement ) ),
inference(pattern_uni,[status(thm)],[1039:[bind(A,$thf( sk1 @ c )),bind(B,$thf( sk2 @ c ))]]) ).
thf(7773,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ c @ ( sk2 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[890,72]) ).
thf(7774,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ c @ ( sk2 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[7773]) ).
thf(7775,plain,
( ( sk2 @ c @ c @ c @ ( sk2 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[7774:[bind(A,$thf( sk2 @ c @ c @ c )),bind(B,$thf( sk2 @ c @ c ))]]) ).
thf(610,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
!= ( sk1 @ c ) )
| ( B != zero )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[63,142]) ).
thf(611,plain,
! [A: $i] :
( ( A != zero )
| ~ ( A @ ( sk1 @ complement ) )
| ~ ( sk1 @ test ) ),
inference(pattern_uni,[status(thm)],[610:[bind(A,$thf( sk1 ))]]) ).
thf(818,plain,
( ~ ( zero @ ( sk1 @ complement ) )
| ~ ( sk1 @ test ) ),
inference(simp,[status(thm)],[611]) ).
thf(934,plain,
( ~ ( zero @ ( sk1 @ complement ) )
| ~ $true ),
inference(rewrite,[status(thm)],[818,22]) ).
thf(935,plain,
~ ( zero @ ( sk1 @ complement ) ),
inference(simp,[status(thm)],[934]) ).
thf(942,plain,
! [A: $i] :
( ( ( A @ ( A @ sk3 @ complement ) )
!= ( zero @ ( sk1 @ complement ) ) )
| ~ $true
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[46,935]) ).
thf(943,plain,
! [A: $i] :
( ( ( A @ ( A @ sk3 @ complement ) )
!= ( zero @ ( sk1 @ complement ) ) )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[942]) ).
thf(961,plain,
! [A: $i] :
( ( A != zero )
| ( ( A @ sk3 )
!= sk1 )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[943]) ).
thf(966,plain,
( ( ( zero @ sk3 )
!= sk1 )
| ~ ( zero @ test ) ),
inference(simp,[status(thm)],[961]) ).
thf(3436,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ ( sk1 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[591,73]) ).
thf(3437,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ ( sk1 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[3436]) ).
thf(3438,plain,
( ( sk1 @ c @ ( sk1 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3437:[bind(A,$thf( sk1 @ c @ c )),bind(B,$thf( sk1 @ c ))]]) ).
thf(1862,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[558,73]) ).
thf(1863,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[1862]) ).
thf(1864,plain,
( ( sk2 @ ( sk2 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[1863:[bind(A,$thf( sk2 @ c )),bind(B,$thf( sk2 ))]]) ).
thf(1391,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[558,72]) ).
thf(1392,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1391]) ).
thf(1393,plain,
( ( sk2 @ c @ ( sk2 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1392:[bind(A,$thf( sk2 @ c )),bind(B,$thf( sk2 ))]]) ).
thf(1623,plain,
( ( ( sk2 @ c @ ( sk1 @ c @ multiplication ) )
!= ( sk2 @ c @ ( sk2 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[1393,293]) ).
thf(1624,plain,
( ( sk2 @ c @ ( sk1 @ c @ multiplication ) )
!= ( sk2 @ c @ ( sk2 @ multiplication ) ) ),
inference(simp,[status(thm)],[1623]) ).
thf(1688,plain,
( ( ( sk2 @ c )
!= ( sk2 @ c ) )
| ( ( sk1 @ c )
!= sk2 ) ),
inference(simp,[status(thm)],[1624]) ).
thf(1702,plain,
( ( sk1 @ c )
!= sk2 ),
inference(simp,[status(thm)],[1688]) ).
thf(1704,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
!= ( sk1 @ c ) )
| ( B != sk2 )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[63,1702]) ).
thf(1705,plain,
! [A: $i] :
( ( A != sk2 )
| ~ ( A @ ( sk1 @ complement ) )
| ~ ( sk1 @ test ) ),
inference(pattern_uni,[status(thm)],[1704:[bind(A,$thf( sk1 ))]]) ).
thf(1711,plain,
( ~ ( sk2 @ ( sk1 @ complement ) )
| ~ ( sk1 @ test ) ),
inference(simp,[status(thm)],[1705]) ).
thf(3387,plain,
( ~ ( sk2 @ ( sk1 @ complement ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1711,22]) ).
thf(3388,plain,
~ ( sk2 @ ( sk1 @ complement ) ),
inference(simp,[status(thm)],[3387]) ).
thf(3406,plain,
( ( ( sk2 @ ( sk2 @ sk3 @ complement ) )
!= ( sk2 @ ( sk1 @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[406,3388]) ).
thf(3407,plain,
( ( sk2 @ ( sk2 @ sk3 @ complement ) )
!= ( sk2 @ ( sk1 @ complement ) ) ),
inference(simp,[status(thm)],[3406]) ).
thf(3413,plain,
( ( sk2 != sk2 )
| ( ( sk2 @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[3407]) ).
thf(3421,plain,
( ( sk2 @ sk3 )
!= sk1 ),
inference(simp,[status(thm)],[3413]) ).
thf(3624,plain,
( ( ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ complement ) )
!= ( sk1 @ c @ ( sk1 @ c @ sk3 @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[588,1386]) ).
thf(3625,plain,
( ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ complement ) )
!= ( sk1 @ c @ ( sk1 @ c @ sk3 @ complement ) ) ),
inference(simp,[status(thm)],[3624]) ).
thf(3699,plain,
( ( ( sk1 @ c )
!= ( sk1 @ c ) )
| ( ( sk2 @ ( sk1 @ addition ) )
!= ( sk1 @ c @ sk3 ) ) ),
inference(simp,[status(thm)],[3625]) ).
thf(3712,plain,
( ( sk2 @ ( sk1 @ addition ) )
!= ( sk1 @ c @ sk3 ) ),
inference(simp,[status(thm)],[3699]) ).
thf(1174,plain,
( ( ( sk1 @ c @ ( sk2 @ c @ complement ) )
!= ( sk1 @ c @ ( sk1 @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[561,1040]) ).
thf(1175,plain,
( ( sk1 @ c @ ( sk2 @ c @ complement ) )
!= ( sk1 @ c @ ( sk1 @ complement ) ) ),
inference(simp,[status(thm)],[1174]) ).
thf(1200,plain,
( ( ( sk1 @ c )
!= ( sk1 @ c ) )
| ( ( sk2 @ c )
!= sk1 ) ),
inference(simp,[status(thm)],[1175]) ).
thf(1206,plain,
( ( sk2 @ c )
!= sk1 ),
inference(simp,[status(thm)],[1200]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
thf(85,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(7733,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ c @ ( sk2 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[890,73]) ).
thf(7734,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ c @ ( sk2 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[7733]) ).
thf(7735,plain,
( ( sk2 @ c @ c @ ( sk2 @ c @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[7734:[bind(A,$thf( sk2 @ c @ c @ c )),bind(B,$thf( sk2 @ c @ c ))]]) ).
thf(7655,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ ( sk2 @ c @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[887,73]) ).
thf(7656,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ ( sk2 @ c @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[7655]) ).
thf(7657,plain,
( ( sk2 @ c @ c @ sk3 @ ( sk2 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[7656:[bind(A,$thf( sk2 @ c @ c )),bind(B,$thf( sk2 @ c @ c @ sk3 ))]]) ).
thf(9555,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ ( sk2 @ c @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[7735,54]) ).
thf(9556,plain,
( ( sk2 @ c @ c @ c @ ( sk2 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[9555:[bind(A,$thf( sk2 @ c @ c @ c )),bind(B,$thf( sk2 @ c @ c ))]]) ).
thf(1747,plain,
( ( ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk1 @ c @ ( sk1 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[1421,115]) ).
thf(1748,plain,
( ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk1 @ c @ ( sk1 @ multiplication ) ) ),
inference(simp,[status(thm)],[1747]) ).
thf(1812,plain,
( ( ( sk1 @ c )
!= ( sk1 @ c ) )
| ( ( sk2 @ ( sk1 @ addition ) )
!= sk1 ) ),
inference(simp,[status(thm)],[1748]) ).
thf(1824,plain,
( ( sk2 @ ( sk1 @ addition ) )
!= sk1 ),
inference(simp,[status(thm)],[1812]) ).
thf(133,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[27,115]) ).
thf(134,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(139,plain,
! [A: $i] :
( ( A
!= ( sk1 @ c ) )
| ( ( sk2 @ ( sk1 @ addition ) )
!= zero ) ),
inference(simp,[status(thm)],[134]) ).
thf(141,plain,
( ( sk2 @ ( sk1 @ addition ) )
!= zero ),
inference(simp,[status(thm)],[139]) ).
thf(244,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ addition ) @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( ( A @ ( B @ addition ) @ ( C @ addition ) )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[33,141]) ).
thf(248,plain,
! [C: $i,B: $i,A: $i] :
( ( A != sk2 )
| ( ( B @ ( C @ addition ) )
!= sk1 )
| ( ( A @ ( B @ addition ) @ ( C @ addition ) )
!= zero ) ),
inference(simp,[status(thm)],[244]) ).
thf(252,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ addition ) )
!= sk1 )
| ( ( sk2 @ ( A @ addition ) @ ( B @ addition ) )
!= zero ) ),
inference(simp,[status(thm)],[248]) ).
thf(149,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
!= ( E @ ( D @ multiplication ) ) )
| ( ( F @ ( C @ ( B @ multiplication ) @ ( A @ multiplication ) @ multiplication ) )
= ( F @ ( E @ multiplication ) @ ( D @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,30]) ).
thf(150,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ multiplication ) @ ( C @ multiplication ) @ multiplication ) )
= ( B @ ( A @ multiplication ) @ ( D @ ( C @ multiplication ) @ multiplication ) ) ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( H @ ( G @ multiplication ) )),bind(E,$thf( C ))]]) ).
thf(173,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ multiplication ) @ ( C @ multiplication ) @ multiplication ) )
= ( B @ ( A @ multiplication ) @ ( D @ ( C @ multiplication ) @ multiplication ) ) ),
inference(simp,[status(thm)],[150]) ).
thf(8026,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ multiplication ) @ multiplication ) @ ( C @ multiplication ) )
= ( B @ ( A @ multiplication ) @ ( D @ multiplication ) @ ( C @ multiplication ) ) ),
inference(rewrite,[status(thm)],[173,30]) ).
thf(2178,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1850,54]) ).
thf(2179,plain,
( ( sk1 @ c @ ( sk1 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[2178:[bind(A,$thf( sk1 @ c )),bind(B,$thf( sk1 ))]]) ).
thf(1025,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[575,71]) ).
thf(1026,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1025]) ).
thf(1027,plain,
( ( sk2 @ c @ sk3 @ ( sk2 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1026:[bind(A,$thf( sk2 @ c )),bind(B,$thf( sk2 @ c @ sk3 ))]]) ).
thf(1930,plain,
( ( ( sk2 @ c @ ( sk2 @ c @ sk3 @ complement ) )
!= ( sk2 @ c @ ( sk1 @ c @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[575,1418]) ).
thf(1931,plain,
( ( sk2 @ c @ ( sk2 @ c @ sk3 @ complement ) )
!= ( sk2 @ c @ ( sk1 @ c @ complement ) ) ),
inference(simp,[status(thm)],[1930]) ).
thf(1962,plain,
( ( ( sk2 @ c )
!= ( sk2 @ c ) )
| ( ( sk2 @ c @ sk3 )
!= ( sk1 @ c ) ) ),
inference(simp,[status(thm)],[1931]) ).
thf(1970,plain,
( ( sk2 @ c @ sk3 )
!= ( sk1 @ c ) ),
inference(simp,[status(thm)],[1962]) ).
thf(1470,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[409,72]) ).
thf(1471,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1470]) ).
thf(1472,plain,
( ( sk1 @ ( sk1 @ sk3 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1471:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk3 ))]]) ).
thf(7339,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk3 @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( zero != zero )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1472,170]) ).
thf(7340,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( sk1 @ sk3 @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[7339]) ).
thf(7341,plain,
! [A: $i] :
( ( A @ ( sk1 @ multiplication ) @ ( sk1 @ sk3 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[7340:[bind(A,$thf( sk1 @ sk3 )),bind(B,$thf( sk1 )),bind(C,$thf( C ))]]) ).
thf(7435,plain,
! [A: $i] :
( ( A @ ( sk1 @ multiplication ) @ ( sk1 @ sk3 @ multiplication ) )
= zero ),
inference(simp,[status(thm)],[7341]) ).
thf(8937,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ sk3 @ ( sk2 @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[7657,54]) ).
thf(8938,plain,
( ( sk2 @ c @ c @ ( sk2 @ c @ c @ sk3 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[8937:[bind(A,$thf( sk2 @ c @ c )),bind(B,$thf( sk2 @ c @ c @ sk3 ))]]) ).
thf(1006,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ( zero != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[71,115]) ).
thf(1007,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[1006]) ).
thf(1008,plain,
~ ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ c @ complement ) ),
inference(pattern_uni,[status(thm)],[1007:[bind(A,$thf( sk2 @ ( sk1 @ addition ) )),bind(B,$thf( sk1 @ c ))]]) ).
thf(3547,plain,
( ( ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ c @ complement ) )
!= ( sk1 @ c @ c @ ( sk1 @ c @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[591,1008]) ).
thf(3548,plain,
( ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ c @ complement ) )
!= ( sk1 @ c @ c @ ( sk1 @ c @ complement ) ) ),
inference(simp,[status(thm)],[3547]) ).
thf(3610,plain,
( ( ( sk2 @ ( sk1 @ addition ) )
!= ( sk1 @ c @ c ) )
| ( ( sk1 @ c )
!= ( sk1 @ c ) ) ),
inference(simp,[status(thm)],[3548]) ).
thf(3622,plain,
( ( sk2 @ ( sk1 @ addition ) )
!= ( sk1 @ c @ c ) ),
inference(simp,[status(thm)],[3610]) ).
thf(1422,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ ( sk2 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[578,72]) ).
thf(1423,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ ( sk2 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1422]) ).
thf(1424,plain,
( ( sk2 @ c @ c @ ( sk2 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1423:[bind(A,$thf( sk2 @ c @ c )),bind(B,$thf( sk2 @ c ))]]) ).
thf(3439,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ ( sk1 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[591,71]) ).
thf(3440,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ ( sk1 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[3439]) ).
thf(3441,plain,
( ( sk1 @ c @ ( sk1 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[3440:[bind(A,$thf( sk1 @ c @ c )),bind(B,$thf( sk1 @ c ))]]) ).
thf(1437,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[406,72]) ).
thf(1438,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1437]) ).
thf(1439,plain,
( ( sk2 @ ( sk2 @ sk3 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1438:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 @ sk3 ))]]) ).
thf(7294,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ sk3 @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( zero != zero )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1439,170]) ).
thf(7295,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ sk3 @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[7294]) ).
thf(7296,plain,
! [A: $i] :
( ( A @ ( sk2 @ multiplication ) @ ( sk2 @ sk3 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[7295:[bind(A,$thf( sk2 @ sk3 )),bind(B,$thf( sk2 )),bind(C,$thf( C ))]]) ).
thf(7417,plain,
! [A: $i] :
( ( A @ ( sk2 @ multiplication ) @ ( sk2 @ sk3 @ multiplication ) )
= zero ),
inference(simp,[status(thm)],[7296]) ).
thf(1176,plain,
( ( ( sk2 @ c @ c @ ( sk2 @ c @ complement ) )
!= ( sk1 @ c @ ( sk2 @ c @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[578,1040]) ).
thf(1177,plain,
( ( sk2 @ c @ c @ ( sk2 @ c @ complement ) )
!= ( sk1 @ c @ ( sk2 @ c @ complement ) ) ),
inference(simp,[status(thm)],[1176]) ).
thf(1201,plain,
( ( ( sk2 @ c @ c )
!= ( sk1 @ c ) )
| ( ( sk2 @ c )
!= ( sk2 @ c ) ) ),
inference(simp,[status(thm)],[1177]) ).
thf(1207,plain,
( ( sk2 @ c @ c )
!= ( sk1 @ c ) ),
inference(simp,[status(thm)],[1201]) ).
thf(7925,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ c @ ( sk1 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3493,48]) ).
thf(7926,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ c @ ( sk1 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[7925]) ).
thf(7927,plain,
sk1 @ c @ c @ c @ test,
inference(pattern_uni,[status(thm)],[7926:[bind(A,$thf( sk1 @ c @ c @ c )),bind(B,$thf( sk1 @ c @ c ))]]) ).
thf(15380,plain,
( ( ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk1 @ c @ ( sk1 @ c @ c @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[3441,15307]) ).
thf(15381,plain,
( ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk1 @ c @ ( sk1 @ c @ c @ multiplication ) ) ),
inference(simp,[status(thm)],[15380]) ).
thf(15576,plain,
( ( ( sk1 @ c )
!= ( sk1 @ c ) )
| ( ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) )
!= ( sk1 @ c @ c ) ) ),
inference(simp,[status(thm)],[15381]) ).
thf(15602,plain,
( ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) )
!= ( sk1 @ c @ c ) ),
inference(simp,[status(thm)],[15576]) ).
thf(7736,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ c @ ( sk2 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[890,71]) ).
thf(7737,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ c @ ( sk2 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[7736]) ).
thf(7738,plain,
( ( sk2 @ c @ c @ ( sk2 @ c @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[7737:[bind(A,$thf( sk2 @ c @ c @ c )),bind(B,$thf( sk2 @ c @ c ))]]) ).
thf(1478,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[588,72]) ).
thf(1479,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1478]) ).
thf(1480,plain,
( ( sk1 @ c @ ( sk1 @ c @ sk3 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1479:[bind(A,$thf( sk1 @ c )),bind(B,$thf( sk1 @ c @ sk3 ))]]) ).
thf(15462,plain,
( ( ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk1 @ c @ ( sk1 @ c @ sk3 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[1480,15307]) ).
thf(15463,plain,
( ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk1 @ c @ ( sk1 @ c @ sk3 @ multiplication ) ) ),
inference(simp,[status(thm)],[15462]) ).
thf(15522,plain,
( ( ( sk1 @ c )
!= ( sk1 @ c ) )
| ( ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) )
!= ( sk1 @ c @ sk3 ) ) ),
inference(simp,[status(thm)],[15463]) ).
thf(15587,plain,
( ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) )
!= ( sk1 @ c @ sk3 ) ),
inference(simp,[status(thm)],[15522]) ).
thf(1223,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk1 @ ( sk1 @ c @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[42,1043]) ).
thf(1280,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( sk1 @ c )
!= one )
| ( A = zero ) ),
inference(simp,[status(thm)],[1223]) ).
thf(1286,plain,
( ( ( sk1 @ c )
!= one )
| ( sk1 = zero ) ),
inference(simp,[status(thm)],[1280]) ).
thf(1100,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk2 @ ( sk2 @ c @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[78,1015]) ).
thf(1143,plain,
! [A: $i] :
( ( sk2 != one )
| ( A
!= ( sk2 @ c ) )
| ( A = zero ) ),
inference(simp,[status(thm)],[1100]) ).
thf(1160,plain,
( ( sk2 != one )
| ( ( sk2 @ c )
= zero ) ),
inference(simp,[status(thm)],[1143]) ).
thf(3321,plain,
sk2 != one,
inference(simplifyReflect,[status(thm)],[1160,113]) ).
thf(5968,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ ( sk1 @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[3438,54]) ).
thf(5969,plain,
( ( sk1 @ c @ c @ ( sk1 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[5968:[bind(A,$thf( sk1 @ c @ c )),bind(B,$thf( sk1 @ c ))]]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_4) ).
thf(34,plain,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(1212,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
!= ( sk2 @ c ) )
| ( B != sk1 )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[63,1206]) ).
thf(1213,plain,
! [A: $i] :
( ( A != sk1 )
| ~ ( A @ ( sk2 @ complement ) )
| ~ ( sk2 @ test ) ),
inference(pattern_uni,[status(thm)],[1212:[bind(A,$thf( sk2 ))]]) ).
thf(1219,plain,
( ~ ( sk1 @ ( sk2 @ complement ) )
| ~ ( sk2 @ test ) ),
inference(simp,[status(thm)],[1213]) ).
thf(2986,plain,
( ~ ( sk1 @ ( sk2 @ complement ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1219,21]) ).
thf(2987,plain,
~ ( sk1 @ ( sk2 @ complement ) ),
inference(simp,[status(thm)],[2986]) ).
thf(3009,plain,
( ( ( sk1 @ ( sk1 @ sk3 @ complement ) )
!= ( sk1 @ ( sk2 @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[409,2987]) ).
thf(3010,plain,
( ( sk1 @ ( sk1 @ sk3 @ complement ) )
!= ( sk1 @ ( sk2 @ complement ) ) ),
inference(simp,[status(thm)],[3009]) ).
thf(3019,plain,
( ( sk1 != sk1 )
| ( ( sk1 @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[3010]) ).
thf(3023,plain,
( ( sk1 @ sk3 )
!= sk2 ),
inference(simp,[status(thm)],[3019]) ).
thf(1166,plain,
( ( ( sk1 @ c @ ( sk1 @ c @ sk3 @ complement ) )
!= ( sk1 @ c @ ( sk2 @ c @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[588,1040]) ).
thf(1167,plain,
( ( sk1 @ c @ ( sk1 @ c @ sk3 @ complement ) )
!= ( sk1 @ c @ ( sk2 @ c @ complement ) ) ),
inference(simp,[status(thm)],[1166]) ).
thf(1204,plain,
( ( ( sk1 @ c )
!= ( sk1 @ c ) )
| ( ( sk1 @ c @ sk3 )
!= ( sk2 @ c ) ) ),
inference(simp,[status(thm)],[1167]) ).
thf(1209,plain,
( ( sk1 @ c @ sk3 )
!= ( sk2 @ c ) ),
inference(simp,[status(thm)],[1204]) ).
thf(1857,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ ( sk2 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[578,73]) ).
thf(1858,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ c @ ( sk2 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[1857]) ).
thf(1859,plain,
( ( sk2 @ c @ ( sk2 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[1858:[bind(A,$thf( sk2 @ c @ c )),bind(B,$thf( sk2 @ c ))]]) ).
thf(5826,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1859,54]) ).
thf(5827,plain,
( ( sk2 @ c @ c @ ( sk2 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[5826:[bind(A,$thf( sk2 @ c @ c )),bind(B,$thf( sk2 @ c ))]]) ).
thf(3466,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ ( sk1 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[591,72]) ).
thf(3467,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ ( sk1 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[3466]) ).
thf(3468,plain,
( ( sk1 @ c @ c @ ( sk1 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[3467:[bind(A,$thf( sk1 @ c @ c )),bind(B,$thf( sk1 @ c ))]]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) )
= ( C @ ( B @ ( A @ addition ) @ multiplication ) ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(2698,plain,
( ( ( sk1 @ test )
!= ( zero @ test ) )
| ( ( zero @ sk3 )
!= sk2 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,1001]) ).
thf(2699,plain,
( ( ( sk1 @ test )
!= ( zero @ test ) )
| ( ( zero @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[2698]) ).
thf(2710,plain,
( ( sk1 != zero )
| ( ( zero @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[2699]) ).
thf(2400,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk2 @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1864,54]) ).
thf(2401,plain,
( ( sk2 @ c @ ( sk2 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[2400:[bind(A,$thf( sk2 @ c )),bind(B,$thf( sk2 ))]]) ).
thf(7846,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ ( sk1 @ c @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[3488,73]) ).
thf(7847,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ ( sk1 @ c @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[7846]) ).
thf(7848,plain,
( ( sk1 @ c @ c @ sk3 @ ( sk1 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[7847:[bind(A,$thf( sk1 @ c @ c )),bind(B,$thf( sk1 @ c @ c @ sk3 ))]]) ).
thf(10207,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ sk3 @ ( sk1 @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[7848,54]) ).
thf(10208,plain,
( ( sk1 @ c @ c @ ( sk1 @ c @ c @ sk3 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[10207:[bind(A,$thf( sk1 @ c @ c )),bind(B,$thf( sk1 @ c @ c @ sk3 ))]]) ).
thf(7210,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( zero != zero )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1055,170]) ).
thf(7211,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[7210]) ).
thf(7212,plain,
! [A: $i] :
( ( A @ ( sk2 @ sk3 @ multiplication ) @ ( sk2 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[7211:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 @ sk3 )),bind(C,$thf( C ))]]) ).
thf(7434,plain,
! [A: $i] :
( ( A @ ( sk2 @ sk3 @ multiplication ) @ ( sk2 @ multiplication ) )
= zero ),
inference(simp,[status(thm)],[7212]) ).
thf(1475,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ( zero != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[72,143]) ).
thf(1476,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk2 @ c @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[1475]) ).
thf(1477,plain,
~ ( sk2 @ c @ ( sk1 @ c @ multiplication ) @ ( sk2 @ ( sk1 @ addition ) @ complement ) ),
inference(pattern_uni,[status(thm)],[1476:[bind(A,$thf( sk2 @ c @ ( sk1 @ c @ multiplication ) )),bind(B,$thf( sk2 @ ( sk1 @ addition ) ))]]) ).
thf(1718,plain,
( ( ( sk1 @ test )
!= ( zero @ test ) )
| ( ( zero @ sk3 )
!= sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,966]) ).
thf(1719,plain,
( ( ( sk1 @ test )
!= ( zero @ test ) )
| ( ( zero @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[1718]) ).
thf(1726,plain,
( ( sk1 != zero )
| ( ( zero @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[1719]) ).
thf(2549,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ sk3 @ ( sk1 @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1888,54]) ).
thf(2550,plain,
( ( sk1 @ ( sk1 @ sk3 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[2549:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk3 ))]]) ).
thf(15445,plain,
( ( ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk1 @ c @ ( sk1 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[1421,15307]) ).
thf(15446,plain,
( ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk1 @ c @ ( sk1 @ multiplication ) ) ),
inference(simp,[status(thm)],[15445]) ).
thf(15527,plain,
( ( ( sk1 @ c )
!= ( sk1 @ c ) )
| ( ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) )
!= sk1 ) ),
inference(simp,[status(thm)],[15446]) ).
thf(15588,plain,
( ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) )
!= sk1 ),
inference(simp,[status(thm)],[15527]) ).
thf(494,plain,
! [A: $i] :
( ( ( A @ ( zero @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( ( sk1 @ c @ ( A @ multiplication ) )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[445,115]) ).
thf(525,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk1 != zero )
| ( ( sk1 @ c @ ( A @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[494]) ).
thf(531,plain,
( ( sk1 != zero )
| ( ( sk1 @ c @ ( sk2 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[525]) ).
thf(2534,plain,
! [A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( sk1 @ sk3 @ ( sk1 @ addition ) ) )
| ( A = one ) ),
inference(paramod_ordered,[status(thm)],[84,1888]) ).
thf(2571,plain,
! [A: $i] :
( ( ( sk1 @ sk3 )
!= zero )
| ( A != sk1 )
| ( A = one ) ),
inference(simp,[status(thm)],[2534]) ).
thf(2584,plain,
( ( ( sk1 @ sk3 )
!= zero )
| ( sk1 = one ) ),
inference(simp,[status(thm)],[2571]) ).
thf(17504,plain,
( ( sk1 @ sk3 )
!= zero ),
inference(simplifyReflect,[status(thm)],[2584,3729]) ).
thf(1310,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk2 @ sk3 @ ( sk2 @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[78,1055]) ).
thf(1363,plain,
! [A: $i] :
( ( ( sk2 @ sk3 )
!= one )
| ( A != sk2 )
| ( A = zero ) ),
inference(simp,[status(thm)],[1310]) ).
thf(1374,plain,
( ( ( sk2 @ sk3 )
!= one )
| ( sk2 = zero ) ),
inference(simp,[status(thm)],[1363]) ).
thf(7635,plain,
( ( sk2 @ sk3 )
!= one ),
inference(simplifyReflect,[status(thm)],[1374,1732]) ).
thf(15394,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) @ multiplication ) ) )
| ( zero != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[71,15307]) ).
thf(15395,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) @ multiplication ) ) )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[15394]) ).
thf(15396,plain,
~ ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) @ ( sk1 @ c @ complement ) ),
inference(pattern_uni,[status(thm)],[15395:[bind(A,$thf( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) )),bind(B,$thf( sk1 @ c ))]]) ).
thf(3030,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
!= ( sk2 @ c ) )
| ( B != one )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[63,3029]) ).
thf(3031,plain,
! [A: $i] :
( ( A != one )
| ~ ( A @ ( sk2 @ complement ) )
| ~ ( sk2 @ test ) ),
inference(pattern_uni,[status(thm)],[3030:[bind(A,$thf( sk2 ))]]) ).
thf(3037,plain,
( ~ ( one @ ( sk2 @ complement ) )
| ~ ( sk2 @ test ) ),
inference(simp,[status(thm)],[3031]) ).
thf(8807,plain,
( ~ ( one @ ( sk2 @ complement ) )
| ~ $true ),
inference(rewrite,[status(thm)],[3037,21]) ).
thf(8808,plain,
~ ( one @ ( sk2 @ complement ) ),
inference(simp,[status(thm)],[8807]) ).
thf(3363,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( C @ ( B @ addition ) ) )
| ( C @ ( B @ leq ) )
| ( A != C ) ),
inference(paramod_ordered,[status(thm)],[51,95]) ).
thf(3364,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ( A != A ) ),
inference(pattern_uni,[status(thm)],[3363:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(3366,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[3364]) ).
thf(2478,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1879,54]) ).
thf(2479,plain,
( ( sk2 @ ( sk2 @ sk3 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[2478:[bind(A,$thf( sk2 )),bind(B,$thf( sk2 @ sk3 ))]]) ).
thf(86,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[85]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) )
= ( C @ ( B @ addition ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(245,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( B @ ( C @ addition ) @ addition ) )
!= ( E @ ( F @ addition ) ) )
| ( ( D @ ( A @ ( B @ addition ) @ ( C @ addition ) @ addition ) )
= ( D @ ( E @ addition ) @ ( F @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,33]) ).
thf(246,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ addition ) @ ( C @ addition ) @ addition ) )
= ( B @ ( A @ addition ) @ ( D @ ( C @ addition ) @ addition ) ) ),
inference(pattern_uni,[status(thm)],[245:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( H @ ( G @ addition ) ))]]) ).
thf(250,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ addition ) @ ( C @ addition ) @ addition ) )
= ( B @ ( A @ addition ) @ ( D @ ( C @ addition ) @ addition ) ) ),
inference(simp,[status(thm)],[246]) ).
thf(14015,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( B @ ( A @ ( D @ addition ) @ addition ) @ ( C @ addition ) )
= ( B @ ( A @ addition ) @ ( D @ addition ) @ ( C @ addition ) ) ),
inference(rewrite,[status(thm)],[250,33]) ).
thf(370,plain,
! [A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( ( sk1 @ c @ ( A @ multiplication ) )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[51,115]) ).
thf(390,plain,
! [A: $i] :
( ( A != sk2 )
| ( A != sk1 )
| ( ( sk1 @ c @ ( A @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[370]) ).
thf(394,plain,
( ( sk2 != sk1 )
| ( ( sk1 @ c @ ( sk1 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[390]) ).
thf(1733,plain,
( ( sk2 != sk1 )
| ( zero != zero ) ),
inference(rewrite,[status(thm)],[394,1421]) ).
thf(1734,plain,
sk2 != sk1,
inference(simp,[status(thm)],[1733]) ).
thf(7957,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ c @ ( sk1 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[3493,72]) ).
thf(7958,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ c @ ( sk1 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[7957]) ).
thf(7959,plain,
( ( sk1 @ c @ c @ c @ ( sk1 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[7958:[bind(A,$thf( sk1 @ c @ c @ c )),bind(B,$thf( sk1 @ c @ c ))]]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
!= one )
| ( ( A @ ( B @ multiplication ) )
!= zero )
| ( ( B @ ( A @ multiplication ) )
!= zero ) ),
inference(cnfConj,[status(thm)],[66]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
!= one )
| ( ( A @ ( B @ multiplication ) )
!= zero )
| ( ( B @ ( A @ multiplication ) )
!= zero ) ),
inference(lifteq,[status(thm)],[70]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
!= one )
| ( ( A @ ( B @ multiplication ) )
!= zero )
| ( ( B @ ( A @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[74]) ).
thf(144,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[30,115]) ).
thf(162,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( sk1 @ c ) )
| ( ( B @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[144]) ).
thf(168,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( ( sk1 @ c @ ( B @ multiplication ) @ ( A @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[162]) ).
thf(2463,plain,
! [A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( sk2 @ sk3 @ ( sk2 @ addition ) ) )
| ( A = one ) ),
inference(paramod_ordered,[status(thm)],[84,1879]) ).
thf(2500,plain,
! [A: $i] :
( ( ( sk2 @ sk3 )
!= zero )
| ( A != sk2 )
| ( A = one ) ),
inference(simp,[status(thm)],[2463]) ).
thf(2510,plain,
( ( ( sk2 @ sk3 )
!= zero )
| ( sk2 = one ) ),
inference(simp,[status(thm)],[2500]) ).
thf(15604,plain,
( ( sk2 @ sk3 )
!= zero ),
inference(simplifyReflect,[status(thm)],[2510,3321]) ).
thf(35,plain,
! [A: $i] :
( ( ( A @ c )
= zero )
| ( A @ test ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [A: $i] :
( ( A @ test )
| ( ( A @ c )
= zero ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(7849,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ ( sk1 @ c @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[3488,71]) ).
thf(7850,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ c @ ( sk1 @ c @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[7849]) ).
thf(7851,plain,
( ( sk1 @ c @ c @ sk3 @ ( sk1 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[7850:[bind(A,$thf( sk1 @ c @ c )),bind(B,$thf( sk1 @ c @ c @ sk3 ))]]) ).
thf(15442,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) @ multiplication ) ) )
| ( zero != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[72,15307]) ).
thf(15443,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) @ multiplication ) ) )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[15442]) ).
thf(15444,plain,
~ ( sk1 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) @ complement ) ),
inference(pattern_uni,[status(thm)],[15443:[bind(A,$thf( sk1 @ c )),bind(B,$thf( sk2 @ ( sk1 @ addition ) @ ( sk1 @ addition ) ))]]) ).
thf(1397,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[575,72]) ).
thf(1398,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ c @ ( sk2 @ c @ sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1397]) ).
thf(1399,plain,
( ( sk2 @ c @ ( sk2 @ c @ sk3 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1398:[bind(A,$thf( sk2 @ c )),bind(B,$thf( sk2 @ c @ sk3 ))]]) ).
thf(2493,plain,
! [A: $i] :
( ( ( sk2 @ sk3 @ ( sk2 @ addition ) )
!= ( A @ ( A @ addition ) ) )
| ( one = A ) ),
inference(paramod_ordered,[status(thm)],[1879,51]) ).
thf(2498,plain,
! [A: $i] :
( ( ( sk2 @ sk3 )
!= A )
| ( sk2 != A )
| ( one = A ) ),
inference(simp,[status(thm)],[2493]) ).
thf(2509,plain,
( ( ( sk2 @ sk3 )
!= sk2 )
| ( sk2 = one ) ),
inference(simp,[status(thm)],[2498]) ).
thf(14863,plain,
( ( sk2 @ sk3 )
!= sk2 ),
inference(simplifyReflect,[status(thm)],[2509,3321]) ).
thf(5568,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ c @ sk3 @ ( sk1 @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1832,54]) ).
thf(5569,plain,
( ( sk1 @ c @ ( sk1 @ c @ sk3 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[5568:[bind(A,$thf( sk1 @ c )),bind(B,$thf( sk1 @ c @ sk3 ))]]) ).
thf(7184,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ sk3 @ ( sk1 @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( zero != zero )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1073,170]) ).
thf(7185,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ sk3 @ ( sk1 @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[7184]) ).
thf(7186,plain,
! [A: $i] :
( ( A @ ( sk1 @ sk3 @ multiplication ) @ ( sk1 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[7185:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ sk3 )),bind(C,$thf( C ))]]) ).
thf(7424,plain,
! [A: $i] :
( ( A @ ( sk1 @ sk3 @ multiplication ) @ ( sk1 @ multiplication ) )
= zero ),
inference(simp,[status(thm)],[7186]) ).
thf(39655,plain,
$false,
inference(e,[status(thm)],[1879,7427,1024,7922,7660,1850,88,170,7886,115,5696,1073,1078,7695,142,15600,3446,3481,2580,10859,3370,1835,1001,42,1046,288,1386,37,25,3891,12417,1832,7743,52,1055,3029,570,46,78,17107,969,93,1572,13506,13365,1040,1418,7775,84,966,7423,591,3438,1864,61,3421,3712,293,1206,85,7735,7657,9556,28,561,33,1824,21,252,8026,1888,583,2179,1027,578,1970,141,7435,8938,3622,1424,3441,7417,1207,7927,15602,7738,15587,1393,73,15307,558,1732,1286,3321,5969,34,64,22,27,71,3023,445,54,49,1209,406,113,2987,81,5827,3468,76,1439,39,1043,890,251,2710,2401,10208,1015,7434,1477,1726,167,2550,15588,531,17504,1472,48,63,7635,887,95,409,15396,8808,31,3488,3493,1008,3366,859,7919,1702,3388,72,143,43,1421,2479,87,2215,14015,1734,3729,588,40,55,7959,75,82,168,30,51,19,1480,15604,36,1859,7851,79,575,15444,1399,14863,5569,7424,935,7848]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE015+1 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.24/0.49 % Computer : n014.cluster.edu
% 0.24/0.49 % Model : x86_64 x86_64
% 0.24/0.49 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.24/0.49 % Memory : 8046.5625MB
% 0.24/0.49 % OS : Linux 6.8.0-71-generic
% 0.24/0.49 % CPULimit : 300
% 0.24/0.49 % WCLimit : 300
% 0.24/0.49 % DateTime : Fri Sep 25 19:13:02 UTC 2026
% 0.24/0.50 % CPUTime :
% 0.24/0.50 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
% 1.30/1.29 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.12/1.60 % [INFO] Parsing done (303ms).
% 2.12/1.62 % [INFO] Running in sequential loop mode.
% 3.12/2.25 % [INFO] eprover registered as external prover.
% 3.12/2.27 % [INFO] Scanning for conjecture ...
% 3.50/2.42 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 3.68/2.51 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 3.68/2.56 % [INFO] Problem is first-order (TPTP FOF).
% 3.68/2.57 % [INFO] Type checking passed.
% 3.68/2.58 % [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 ...
% 114.71/24.67 % External prover 'e' found a proof!
% 114.71/24.67 % [INFO] Killing All external provers ...
% 114.71/24.67 % Time passed: 24009ms (effective reasoning time: 23044ms)
% 114.71/24.67 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 114.71/24.67 % Axioms used in derivation (16): additive_identity, test_3, test_4, left_annihilation, right_distributivity, multiplicative_right_identity, test_1, right_annihilation, additive_idempotence, additive_associativity, order, additive_commutativity, test_2, multiplicative_left_identity, multiplicative_associativity, left_distributivity
% 114.71/24.68 % No. of inferences in proof: 559
% 114.71/24.68 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 24009 ms resp. 23044 ms w/o parsing
% 111.74/24.86 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 111.74/24.86 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------