%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE027+2 : 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 : n026.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 07:43:01 AM UTC 2026
% Result : Theorem 90.03s 24.79s
% Output : Refutation 77.79s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 23
% Syntax : Number of formulae : 298 ( 95 unt; 0 typ; 6 def)
% Number of atoms : 851 ( 432 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 3441 ( 404 ~; 334 |; 42 &;2628 @)
% ( 4 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 17 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 388 ( 1 ^; 371 !; 10 ?; 388 :)
% ( 0 !>; 0 ?*; 0 @-; 6 @+)
% Comments :
%------------------------------------------------------------------------------
thf(test_decl,type,
test: $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(multiplication_decl,type,
multiplication: $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(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i ).
thf(sk6_decl,type,
sk6: $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ leq ) )
& ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ leq ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ? [D: $i] : ( D @ test )
& ( C @ test ) )
=> ( ( B @ ( C @ c @ multiplication ) @ ( A @ ( C @ c @ multiplication ) @ ( sk1 @ ( C @ multiplication ) @ addition ) @ ( C @ multiplication ) @ addition ) @ ( B @ ( C @ c @ multiplication ) @ ( sk1 @ ( C @ multiplication ) @ addition ) @ leq ) )
& ( B @ ( C @ c @ multiplication ) @ ( sk1 @ ( C @ multiplication ) @ addition ) @ ( B @ ( C @ c @ multiplication ) @ ( A @ ( C @ c @ multiplication ) @ ( sk1 @ ( C @ multiplication ) @ addition ) @ ( C @ multiplication ) @ addition ) @ leq ) ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ? [C: $i] : ( C @ test )
& ( B @ test ) )
=> ( ( A @ ( B @ c @ multiplication ) @ ( sk2 @ ( B @ c @ multiplication ) @ ( sk1 @ ( B @ multiplication ) @ addition ) @ ( B @ multiplication ) @ addition ) @ ( A @ ( B @ c @ multiplication ) @ ( sk1 @ ( B @ multiplication ) @ addition ) @ leq ) )
& ( A @ ( B @ c @ multiplication ) @ ( sk1 @ ( B @ multiplication ) @ addition ) @ ( A @ ( B @ c @ multiplication ) @ ( sk2 @ ( B @ c @ multiplication ) @ ( sk1 @ ( B @ multiplication ) @ addition ) @ ( B @ multiplication ) @ addition ) @ leq ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ? [B: $i] : ( B @ test )
& ( A @ test ) )
=> ( ( sk3 @ ( A @ c @ multiplication ) @ ( sk2 @ ( A @ c @ multiplication ) @ ( sk1 @ ( A @ multiplication ) @ addition ) @ ( A @ multiplication ) @ addition ) @ ( sk3 @ ( A @ c @ multiplication ) @ ( sk1 @ ( A @ multiplication ) @ addition ) @ leq ) )
& ( sk3 @ ( A @ c @ multiplication ) @ ( sk1 @ ( A @ multiplication ) @ addition ) @ ( sk3 @ ( A @ c @ multiplication ) @ ( sk2 @ ( A @ c @ multiplication ) @ ( sk1 @ ( A @ multiplication ) @ addition ) @ ( A @ multiplication ) @ addition ) @ leq ) ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( @+[A: $i] : ( A @ test ) ) ) ).
thf(sk6_def,definition,
( sk6
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ complement ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ leq ) )
& ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ leq ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ leq ) )
& ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ leq ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ leq ) )
& ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ leq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ? [E: $i] : ( E @ test )
& ( D @ test ) )
=> ( ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ leq ) )
& ( C @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( C @ ( D @ c @ multiplication ) @ ( B @ ( D @ c @ multiplication ) @ ( A @ ( D @ multiplication ) @ addition ) @ ( D @ multiplication ) @ addition ) @ leq ) ) ) ),
inference(miniscope,[status(thm)],[19]) ).
thf(21,plain,
( ( ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ leq ) ) )
& ( sk5 @ test )
& ( sk4 @ test ) ),
inference(cnf,[status(esa)],[20]) ).
thf(22,plain,
sk4 @ test,
inference(cnfConj,[status(thm)],[21]) ).
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(1367,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,61]) ).
thf(1368,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1367]) ).
thf(1369,plain,
sk4 @ c @ ( sk4 @ complement ),
inference(pattern_uni,[status(thm)],[1368:[bind(A,$thf( sk4 ))]]) ).
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 @ sk6 @ complement ) )
| ~ ( A @ test ) ) ),
inference(cnf,[status(esa)],[44]) ).
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(1386,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1369,48]) ).
thf(1387,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1386]) ).
thf(1388,plain,
sk4 @ c @ test,
inference(pattern_uni,[status(thm)],[1387:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(46,plain,
! [A: $i] :
( ( A @ ( A @ sk6 @ complement ) )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[45]) ).
thf(1394,plain,
! [A: $i] :
( ( ( sk4 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1388,46]) ).
thf(1395,plain,
! [A: $i] :
( ( ( sk4 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[1394]) ).
thf(1396,plain,
sk4 @ c @ ( sk4 @ c @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[1395:[bind(A,$thf( sk4 @ c ))]]) ).
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(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(3070,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1396,71]) ).
thf(3071,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[3070]) ).
thf(3072,plain,
( ( sk4 @ c @ sk6 @ ( sk4 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[3071:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 @ c @ sk6 ))]]) ).
thf(23,plain,
sk5 @ test,
inference(cnfConj,[status(thm)],[21]) ).
thf(1364,plain,
! [A: $i] :
( ( ( sk5 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,61]) ).
thf(1365,plain,
! [A: $i] :
( ( ( sk5 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1364]) ).
thf(1366,plain,
sk5 @ c @ ( sk5 @ complement ),
inference(pattern_uni,[status(thm)],[1365:[bind(A,$thf( sk5 ))]]) ).
thf(1373,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1366,48]) ).
thf(1374,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1373]) ).
thf(1375,plain,
sk5 @ c @ test,
inference(pattern_uni,[status(thm)],[1374:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 ))]]) ).
thf(1378,plain,
! [A: $i] :
( ( ( sk5 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1375,61]) ).
thf(1379,plain,
! [A: $i] :
( ( ( sk5 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1378]) ).
thf(1380,plain,
sk5 @ c @ c @ ( sk5 @ c @ complement ),
inference(pattern_uni,[status(thm)],[1379:[bind(A,$thf( sk5 @ 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(2578,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1380,72]) ).
thf(2579,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2578]) ).
thf(2580,plain,
( ( sk5 @ c @ c @ ( sk5 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2579:[bind(A,$thf( sk5 @ c @ c )),bind(B,$thf( sk5 @ c ))]]) ).
thf(1241,plain,
! [A: $i] :
( ( ( sk5 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,46]) ).
thf(1242,plain,
! [A: $i] :
( ( ( sk5 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[1241]) ).
thf(1243,plain,
sk5 @ ( sk5 @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[1242:[bind(A,$thf( sk5 ))]]) ).
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(3233,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1243,73]) ).
thf(3234,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[3233]) ).
thf(3235,plain,
( ( sk5 @ sk6 @ ( sk5 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3234:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk6 ))]]) ).
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(3394,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ sk6 @ ( sk5 @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[3235,54]) ).
thf(3395,plain,
( ( sk5 @ ( sk5 @ sk6 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3394:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk6 ))]]) ).
thf(1974,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1369,71]) ).
thf(1975,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1974]) ).
thf(1976,plain,
( ( sk4 @ ( sk4 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1975:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(2057,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1380,71]) ).
thf(2058,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2057]) ).
thf(2059,plain,
( ( sk5 @ c @ ( sk5 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2058:[bind(A,$thf( sk5 @ c @ c )),bind(B,$thf( sk5 @ c ))]]) ).
thf(2478,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1243,72]) ).
thf(2479,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2478]) ).
thf(2480,plain,
( ( sk5 @ ( sk5 @ sk6 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2479:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk6 ))]]) ).
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(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(2008,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1366,71]) ).
thf(2009,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2008]) ).
thf(2010,plain,
( ( sk5 @ ( sk5 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2009:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 ))]]) ).
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(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(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(2090,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk4 @ ( sk4 @ c @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[78,1976]) ).
thf(2130,plain,
! [A: $i] :
( ( sk4 != one )
| ( A
!= ( sk4 @ c ) )
| ( A = zero ) ),
inference(simp,[status(thm)],[2090]) ).
thf(2157,plain,
( ( sk4 != one )
| ( ( sk4 @ c )
= zero ) ),
inference(simp,[status(thm)],[2130]) ).
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(24,plain,
( ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ leq ) ) ),
inference(cnfConj,[status(thm)],[21]) ).
thf(119,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[27,24]) ).
thf(133,plain,
! [A: $i] :
( ( A
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[119]) ).
thf(158,plain,
( ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(195,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[27,158]) ).
thf(210,plain,
! [A: $i] :
( ( A
!= ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) ) )
| ( sk4 != zero )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[195]) ).
thf(230,plain,
( ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[210]) ).
thf(317,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[27,230]) ).
thf(332,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk4 != zero )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[317]) ).
thf(352,plain,
( ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[332]) ).
thf(371,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[27,352]) ).
thf(372,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[371]) ).
thf(385,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk4 != zero )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[372]) ).
thf(402,plain,
( ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[385]) ).
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(947,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(948,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) )
= A ),
inference(pattern_uni,[status(thm)],[947:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(1033,plain,
( ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ leq ) ) ),
inference(rewrite,[status(thm)],[402,948]) ).
thf(1254,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( sk4 != zero )
| ~ ( zero @ ( sk3 @ ( sk4 @ c @ multiplication ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[27,1033]) ).
thf(1265,plain,
! [A: $i] :
( ( A != sk3 )
| ( ( sk4 @ c )
!= zero )
| ( sk4 != zero )
| ~ ( zero @ ( sk3 @ ( sk4 @ c @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[1254]) ).
thf(1277,plain,
( ( ( sk4 @ c )
!= zero )
| ( sk4 != zero )
| ~ ( zero @ ( sk3 @ ( sk4 @ c @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[1265]) ).
thf(1334,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( ( sk4 @ c )
!= zero )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[27,1277]) ).
thf(1344,plain,
! [A: $i] :
( ( A != sk3 )
| ( ( sk4 @ c )
!= zero )
| ( ( sk4 @ c )
!= zero )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[1334]) ).
thf(1349,plain,
( ( ( sk4 @ c )
!= zero )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[1344]) ).
thf(3151,plain,
( ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( zero != zero )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) )
| ( sk4 != one ) ),
inference(paramod_ordered,[status(thm)],[2157,1349]) ).
thf(3152,plain,
( ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) )
| ( sk4 != one ) ),
inference(simp,[status(thm)],[3151]) ).
thf(3153,plain,
( ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) )
| ( sk4 != one ) ),
inference(pattern_uni,[status(thm)],[3152:[]]) ).
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(5026,plain,
! [C: $i,B: $i,A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( C @ ( B @ addition ) ) )
| ( C @ ( B @ leq ) )
| ( A != C ) ),
inference(paramod_ordered,[status(thm)],[84,95]) ).
thf(5027,plain,
! [A: $i] :
( ( zero @ ( A @ leq ) )
| ( A != zero ) ),
inference(pattern_uni,[status(thm)],[5026:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( zero ))]]) ).
thf(5056,plain,
zero @ ( zero @ leq ),
inference(simp,[status(thm)],[5027]) ).
thf(5063,plain,
( ( sk4 != zero )
| ~ $true
| ( sk4 != one ) ),
inference(rewrite,[status(thm)],[3153,5056]) ).
thf(5064,plain,
( ( sk4 != zero )
| ( sk4 != one ) ),
inference(simp,[status(thm)],[5063]) ).
thf(1391,plain,
! [A: $i] :
( ( ( sk4 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1388,61]) ).
thf(1392,plain,
! [A: $i] :
( ( ( sk4 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1391]) ).
thf(1393,plain,
sk4 @ c @ c @ ( sk4 @ c @ complement ),
inference(pattern_uni,[status(thm)],[1392:[bind(A,$thf( sk4 @ c ))]]) ).
thf(1858,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1393,48]) ).
thf(1859,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1858]) ).
thf(1860,plain,
sk4 @ c @ c @ test,
inference(pattern_uni,[status(thm)],[1859:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c ))]]) ).
thf(3248,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1366,73]) ).
thf(3249,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[3248]) ).
thf(3250,plain,
( ( sk5 @ ( sk5 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3249:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 ))]]) ).
thf(3462,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[3250,54]) ).
thf(3463,plain,
( ( sk5 @ c @ ( sk5 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3462:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 ))]]) ).
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(1381,plain,
! [A: $i] :
( ( ( sk5 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1375,46]) ).
thf(1382,plain,
! [A: $i] :
( ( ( sk5 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[1381]) ).
thf(1383,plain,
sk5 @ c @ ( sk5 @ c @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[1382:[bind(A,$thf( sk5 @ c ))]]) ).
thf(2276,plain,
! [A: $i] :
( ( ( sk5 @ ( sk5 @ c @ multiplication ) )
!= ( one @ ( A @ multiplication ) ) )
| ( zero = A ) ),
inference(paramod_ordered,[status(thm)],[2010,78]) ).
thf(2325,plain,
! [A: $i] :
( ( sk5 != one )
| ( ( sk5 @ c )
!= A )
| ( zero = A ) ),
inference(simp,[status(thm)],[2276]) ).
thf(2349,plain,
( ( sk5 != one )
| ( ( sk5 @ c )
= zero ) ),
inference(simp,[status(thm)],[2325]) ).
thf(4934,plain,
( ( ( sk5 @ c )
!= ( sk5 @ c ) )
| ( zero @ test )
| ( sk5 != one ) ),
inference(paramod_ordered,[status(thm)],[2349,1375]) ).
thf(4935,plain,
( ( zero @ test )
| ( sk5 != one ) ),
inference(pattern_uni,[status(thm)],[4934:[]]) ).
thf(126,plain,
( ~ $true
| ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) ) ),
inference(eqfactor_ordered,[status(thm)],[24]) ).
thf(149,plain,
( ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[126]) ).
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(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 @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(5328,plain,
( ( ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk4 @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ ( sk4 @ multiplication ) @ addition ) @ addition ) @ leq ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk4 @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ ( sk4 @ multiplication ) @ addition ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk4 @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ ( sk4 @ multiplication ) @ addition ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) ) ),
inference(rewrite,[status(thm)],[149,87]) ).
thf(1781,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1380,48]) ).
thf(1782,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ c @ ( sk5 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1781]) ).
thf(1783,plain,
sk5 @ c @ c @ test,
inference(pattern_uni,[status(thm)],[1782:[bind(A,$thf( sk5 @ c @ c )),bind(B,$thf( sk5 @ c ))]]) ).
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(3067,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1396,72]) ).
thf(3068,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[3067]) ).
thf(3069,plain,
( ( sk4 @ c @ ( sk4 @ c @ sk6 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[3068:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 @ c @ sk6 ))]]) ).
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(2475,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1369,72]) ).
thf(2476,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2475]) ).
thf(2477,plain,
( ( sk4 @ c @ ( sk4 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2476:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(1244,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22,46]) ).
thf(1245,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk6 @ complement ) ) ),
inference(simp,[status(thm)],[1244]) ).
thf(1246,plain,
sk4 @ ( sk4 @ sk6 @ complement ),
inference(pattern_uni,[status(thm)],[1245:[bind(A,$thf( sk4 ))]]) ).
thf(3265,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1246,73]) ).
thf(3266,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[3265]) ).
thf(3267,plain,
( ( sk4 @ sk6 @ ( sk4 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3266:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ sk6 ))]]) ).
thf(3545,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ sk6 @ ( sk4 @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[3267,54]) ).
thf(3546,plain,
( ( sk4 @ ( sk4 @ sk6 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3545:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ sk6 ))]]) ).
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(732,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[81,402]) ).
thf(738,plain,
! [A: $i] :
( ( sk3 != zero )
| ( A
!= ( sk4 @ c ) )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[732]) ).
thf(747,plain,
( ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[738]) ).
thf(757,plain,
( ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ leq ) ) ),
inference(rewrite,[status(thm)],[747,84]) ).
thf(763,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ ( zero @ addition ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[81,757]) ).
thf(769,plain,
! [A: $i] :
( ( sk3 != zero )
| ( A
!= ( sk4 @ c ) )
| ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[763]) ).
thf(771,plain,
( ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ ( zero @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[769]) ).
thf(812,plain,
( ( sk3 != zero )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(rewrite,[status(thm)],[771,84]) ).
thf(5079,plain,
( ( sk3 != zero )
| ( sk4 != zero )
| ~ $true ),
inference(rewrite,[status(thm)],[812,5056]) ).
thf(5080,plain,
( ( sk3 != zero )
| ( sk4 != zero ) ),
inference(simp,[status(thm)],[5079]) ).
thf(1251,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[78,1033]) ).
thf(1268,plain,
! [A: $i] :
( ( sk3 != one )
| ( A
!= ( sk4 @ c ) )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[1251]) ).
thf(1280,plain,
( ( sk3 != one )
| ( sk4 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk4 @ c @ leq ) ) ),
inference(simp,[status(thm)],[1268]) ).
thf(1400,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk3 @ ( sk4 @ c @ multiplication ) ) )
| ( sk3 != one )
| ( sk4 != zero )
| ~ ( A @ ( sk4 @ c @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[78,1280]) ).
thf(1413,plain,
! [A: $i] :
( ( sk3 != one )
| ( A
!= ( sk4 @ c ) )
| ( sk3 != one )
| ( sk4 != zero )
| ~ ( A @ ( sk4 @ c @ leq ) ) ),
inference(simp,[status(thm)],[1400]) ).
thf(1419,plain,
( ( sk3 != one )
| ( sk4 != zero )
| ~ ( sk4 @ c @ ( sk4 @ c @ leq ) ) ),
inference(simp,[status(thm)],[1413]) ).
thf(5034,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( zero @ addition ) )
!= ( C @ ( B @ addition ) ) )
| ( C @ ( B @ leq ) )
| ( A != C ) ),
inference(paramod_ordered,[status(thm)],[948,95]) ).
thf(5035,plain,
! [A: $i] :
( ( A @ ( zero @ leq ) )
| ( A != A ) ),
inference(pattern_uni,[status(thm)],[5034:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(5058,plain,
! [A: $i] : ( A @ ( zero @ leq ) ),
inference(simp,[status(thm)],[5035]) ).
thf(1977,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1243,71]) ).
thf(1978,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ ( sk5 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1977]) ).
thf(1979,plain,
( ( sk5 @ sk6 @ ( sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1978:[bind(A,$thf( sk5 )),bind(B,$thf( sk5 @ sk6 ))]]) ).
thf(2527,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1383,72]) ).
thf(2528,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2527]) ).
thf(2529,plain,
( ( sk5 @ c @ ( sk5 @ c @ sk6 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2528:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 @ c @ sk6 ))]]) ).
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(2026,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1393,71]) ).
thf(2027,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2026]) ).
thf(2028,plain,
( ( sk4 @ c @ ( sk4 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2027:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c ))]]) ).
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(2175,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk5 @ sk6 @ ( sk5 @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[42,1979]) ).
thf(2233,plain,
! [A: $i] :
( ( A
!= ( sk5 @ sk6 ) )
| ( sk5 != one )
| ( A = zero ) ),
inference(simp,[status(thm)],[2175]) ).
thf(2257,plain,
( ( sk5 != one )
| ( ( sk5 @ sk6 )
= zero ) ),
inference(simp,[status(thm)],[2233]) ).
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 @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(2023,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1246,71]) ).
thf(2024,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2023]) ).
thf(2025,plain,
( ( sk4 @ sk6 @ ( sk4 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2024:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ sk6 ))]]) ).
thf(2190,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk5 @ sk6 @ ( sk5 @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[78,1979]) ).
thf(2242,plain,
! [A: $i] :
( ( ( sk5 @ sk6 )
!= one )
| ( A != sk5 )
| ( A = zero ) ),
inference(simp,[status(thm)],[2190]) ).
thf(2252,plain,
( ( ( sk5 @ sk6 )
!= one )
| ( sk5 = zero ) ),
inference(simp,[status(thm)],[2242]) ).
thf(3149,plain,
( ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( zero @ test )
| ( sk4 != one ) ),
inference(paramod_ordered,[status(thm)],[2157,1388]) ).
thf(3150,plain,
( ( zero @ test )
| ( sk4 != one ) ),
inference(pattern_uni,[status(thm)],[3149:[]]) ).
thf(2020,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1383,71]) ).
thf(2021,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ c @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2020]) ).
thf(2022,plain,
( ( sk5 @ c @ sk6 @ ( sk5 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2021:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 @ c @ sk6 ))]]) ).
thf(3230,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1369,73]) ).
thf(3231,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[3230]) ).
thf(3232,plain,
( ( sk4 @ ( sk4 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3231:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(3324,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[3232,54]) ).
thf(3325,plain,
( ( sk4 @ c @ ( sk4 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3324:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
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(5073,plain,
( ( ( sk4 @ c )
!= zero )
| ( sk4 != zero )
| ~ $true ),
inference(rewrite,[status(thm)],[1349,5056]) ).
thf(5074,plain,
( ( ( sk4 @ c )
!= zero )
| ( sk4 != zero ) ),
inference(simp,[status(thm)],[5073]) ).
thf(2075,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk4 @ ( sk4 @ c @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[42,1976]) ).
thf(2141,plain,
! [A: $i] :
( ( A != sk4 )
| ( ( sk4 @ c )
!= one )
| ( A = zero ) ),
inference(simp,[status(thm)],[2075]) ).
thf(2165,plain,
( ( ( sk4 @ c )
!= one )
| ( sk4 = zero ) ),
inference(simp,[status(thm)],[2141]) ).
thf(2541,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1393,72]) ).
thf(2542,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2541]) ).
thf(2543,plain,
( ( sk4 @ c @ c @ ( sk4 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2542:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c ))]]) ).
thf(1649,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
!= ( sk4 @ c ) )
| ( B != zero )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[63,1349]) ).
thf(1650,plain,
! [A: $i] :
( ( A != zero )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) )
| ~ ( A @ ( sk4 @ complement ) )
| ~ ( sk4 @ test ) ),
inference(pattern_uni,[status(thm)],[1649:[bind(A,$thf( sk4 ))]]) ).
thf(1748,plain,
( ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) )
| ~ ( zero @ ( sk4 @ complement ) )
| ~ ( sk4 @ test ) ),
inference(simp,[status(thm)],[1650]) ).
thf(1904,plain,
( ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) )
| ~ ( zero @ ( sk4 @ complement ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1748,22]) ).
thf(1905,plain,
( ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) )
| ~ ( zero @ ( sk4 @ complement ) ) ),
inference(simp,[status(thm)],[1904]) ).
thf(1918,plain,
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( zero @ ( sk4 @ complement ) ) )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1246,1905]) ).
thf(1919,plain,
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( zero @ ( sk4 @ complement ) ) )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[1918]) ).
thf(1929,plain,
( ( sk4 != zero )
| ( ( sk4 @ sk6 )
!= sk4 )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[1919]) ).
thf(1938,plain,
( ( ( sk4 @ sk6 )
!= sk4 )
| ( sk4 != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[1929]) ).
thf(5067,plain,
( ( ( sk4 @ sk6 )
!= sk4 )
| ( sk4 != zero )
| ~ $true ),
inference(rewrite,[status(thm)],[1938,5056]) ).
thf(5068,plain,
( ( ( sk4 @ sk6 )
!= sk4 )
| ( sk4 != zero ) ),
inference(simp,[status(thm)],[5067]) ).
thf(105,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk1 @ ( sk4 @ multiplication ) ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[81,24]) ).
thf(128,plain,
! [A: $i] :
( ( sk1 != zero )
| ( A != sk4 )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(153,plain,
( ( sk1 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( zero @ addition ) @ ( sk4 @ multiplication ) @ addition ) @ leq ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(8469,plain,
( ( sk1 != zero )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk4 @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ ( sk4 @ multiplication ) @ addition ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ leq ) )
| ~ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk1 @ ( sk4 @ multiplication ) @ addition ) @ ( sk3 @ ( sk4 @ c @ multiplication ) @ ( sk2 @ ( sk4 @ c @ multiplication ) @ ( sk4 @ multiplication ) @ ( zero @ ( sk4 @ multiplication ) @ addition ) @ addition ) @ leq ) ) ),
inference(rewrite,[status(thm)],[153,87]) ).
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(2515,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1366,72]) ).
thf(2516,plain,
! [B: $i,A: $i] :
( ( ( sk5 @ c @ ( sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2515]) ).
thf(2517,plain,
( ( sk5 @ c @ ( sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2516:[bind(A,$thf( sk5 @ c )),bind(B,$thf( sk5 ))]]) ).
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(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(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(2532,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1246,72]) ).
thf(2533,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk6 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2532]) ).
thf(2534,plain,
( ( sk4 @ ( sk4 @ sk6 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2533:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ sk6 ))]]) ).
thf(1109,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
!= ( zero @ ( D @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[39,81]) ).
thf(1110,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( zero @ ( A @ multiplication ) @ addition ) )
= zero ),
inference(pattern_uni,[status(thm)],[1109:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( zero )),bind(D,$thf( F @ ( E @ addition ) ))]]) ).
thf(1140,plain,
! [B: $i,A: $i] :
( ( zero @ ( B @ multiplication ) @ ( zero @ ( A @ multiplication ) @ addition ) )
= zero ),
inference(simp,[status(thm)],[1110]) ).
thf(1172,plain,
( ( zero @ ( zero @ addition ) )
= zero ),
inference(rewrite,[status(thm)],[1140,81]) ).
thf(15835,plain,
$false,
inference(e,[status(thm)],[3072,2580,3395,1976,2059,1369,2480,88,1243,42,2010,1366,37,25,52,5064,1860,3463,46,93,78,1383,84,4935,61,5328,85,1783,28,3069,3250,33,2477,3546,2157,948,1375,5080,2349,1419,5058,1246,1979,1393,73,2529,34,64,2028,22,1388,27,71,54,49,81,2257,76,39,2025,2252,3150,1396,2022,3325,48,63,95,5074,2165,31,2543,72,43,87,5068,8469,40,55,3235,23,75,3267,82,2517,1280,36,30,51,1380,19,2534,3232,79,1172,1033]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : KLE027+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % 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
% 0.15/5.63 % Computer : n026.cluster.edu
% 0.15/5.63 % Model : x86_64 x86_64
% 0.15/5.63 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/5.63 % Memory : 8046.5625MB
% 0.15/5.63 % OS : Linux 6.8.0-71-generic
% 0.15/5.63 % CPULimit : 300
% 0.15/5.63 % WCLimit : 300
% 0.15/5.63 % DateTime : Fri Sep 25 19:17:46 UTC 2026
% 0.15/5.64 % CPUTime :
% 0.15/5.64 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
% 1.22/6.33 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.62/6.53 % [INFO] Parsing done (197ms).
% 1.62/6.54 % [INFO] Running in sequential loop mode.
% 2.73/6.90 % [INFO] eprover registered as external prover.
% 2.73/6.90 % [INFO] Scanning for conjecture ...
% 2.73/7.00 % [INFO] Found a conjecture (or negated_conjecture) and 16 axioms. Running axiom selection ...
% 3.09/7.06 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 3.09/7.09 % [INFO] Problem is first-order (TPTP FOF).
% 3.09/7.09 % [INFO] Type checking passed.
% 3.09/7.10 % [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 ...
% 90.03/24.79 % External prover 'e' found a proof!
% 90.03/24.79 % [INFO] Killing All external provers ...
% 90.03/24.79 % Time passed: 19006ms (effective reasoning time: 18242ms)
% 90.03/24.79 % 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)>
% 90.03/24.79 % 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
% 90.03/24.79 % No. of inferences in proof: 292
% 90.03/24.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 19006 ms resp. 18242 ms w/o parsing
% 77.79/24.94 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 77.79/24.94 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------