%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE035+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 : n002.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 07:43:03 AM UTC 2026
% Result : Theorem 90.99s 19.28s
% Output : Refutation 91.98s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 24
% Syntax : Number of formulae : 709 ( 226 unt; 0 typ; 5 def)
% Number of atoms : 1832 (1007 equ; 0 cnn)
% Maximal formula atoms : 10 ( 2 avg)
% Number of connectives : 6206 ( 886 ~; 661 |; 53 &;4570 @)
% ( 4 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 725 ( 1 ^; 714 !; 5 ?; 725 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(test_decl,type,
test: $i > $o ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(c_decl,type,
c: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(addition_decl,type,
addition: $i > $i > $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 > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i,C: $i,D: $i] :
( ( ( zero @ ( D @ c @ ( B @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( D @ c @ ( A @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( C @ test )
& ( D @ test ) )
=> ( zero @ ( D @ c @ ( B @ ( A @ addition ) @ ( C @ multiplication ) @ multiplication ) @ leq ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ! [B: $i,C: $i] :
( ( ( zero @ ( C @ c @ ( A @ ( B @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( C @ c @ ( sk1 @ ( B @ multiplication ) @ multiplication ) @ leq ) )
& ( B @ test )
& ( C @ test ) )
=> ( zero @ ( C @ c @ ( A @ ( sk1 @ addition ) @ ( B @ multiplication ) @ multiplication ) @ leq ) ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( zero @ ( B @ c @ ( sk2 @ ( A @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( B @ c @ ( sk1 @ ( A @ multiplication ) @ multiplication ) @ leq ) )
& ( A @ test )
& ( B @ test ) )
=> ( zero @ ( B @ c @ ( sk2 @ ( sk1 @ addition ) @ ( A @ multiplication ) @ multiplication ) @ leq ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ( zero @ ( A @ c @ ( sk2 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( A @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
& ( sk3 @ test )
& ( A @ test ) )
=> ( zero @ ( A @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i] :
@+[B: $i] : ( A @ ( B @ complement ) ) ) ) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( zero @ ( D @ c @ ( B @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( D @ c @ ( A @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( C @ test )
& ( D @ test ) )
=> ( zero @ ( D @ c @ ( B @ ( A @ addition ) @ ( C @ multiplication ) @ multiplication ) @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( zero @ ( D @ c @ ( B @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( D @ c @ ( A @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( C @ test )
& ( D @ test ) )
=> ( zero @ ( D @ c @ ( B @ ( A @ addition ) @ ( C @ multiplication ) @ multiplication ) @ leq ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i,B: $i,C: $i,D: $i] :
( ( ( zero @ ( D @ c @ ( B @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( D @ c @ ( A @ ( C @ multiplication ) @ multiplication ) @ leq ) )
& ( C @ test )
& ( D @ test ) )
=> ( zero @ ( D @ c @ ( B @ ( A @ addition ) @ ( C @ multiplication ) @ multiplication ) @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
( ~ ( zero @ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( sk4 @ c @ ( sk2 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
& ( zero @ ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
& ( sk3 @ test )
& ( sk4 @ test ) ),
inference(cnf,[status(esa)],[21]) ).
thf(26,plain,
zero @ ( sk4 @ c @ ( sk2 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ),
inference(cnfConj,[status(thm)],[22]) ).
thf(24,plain,
~ ( zero @ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) ),
inference(cnfConj,[status(thm)],[22]) ).
thf(154,plain,
( ( ( zero @ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
!= ( zero @ ( sk4 @ c @ ( sk2 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26,24]) ).
thf(155,plain,
( ( zero @ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
!= ( zero @ ( sk4 @ c @ ( sk2 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(158,plain,
( ( zero != zero )
| ( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk3 @ multiplication ) @ multiplication ) ) ) ),
inference(simp,[status(thm)],[155]) ).
thf(164,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk3 @ multiplication ) @ multiplication ) ) ),
inference(simp,[status(thm)],[158]) ).
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(31,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(32,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(810,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ multiplication ) @ ( sk3 @ multiplication ) ) ),
inference(rewrite,[status(thm)],[164,33]) ).
thf(811,plain,
( ( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ multiplication ) ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[810]) ).
thf(892,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ multiplication ) ) ),
inference(simp,[status(thm)],[811]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(29,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[29]) ).
thf(114,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[30,24]) ).
thf(118,plain,
! [A: $i] :
( ( A
!= ( sk4 @ c ) )
| ( ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) )
!= zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[114]) ).
thf(122,plain,
( ( ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) )
!= zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[118]) ).
thf(321,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
!= zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[33,122]) ).
thf(324,plain,
! [C: $i,B: $i,A: $i] :
( ( C
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( ( B @ ( A @ multiplication ) )
!= sk3 )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
!= zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[321]) ).
thf(330,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= sk3 )
| ( ( sk2 @ ( sk1 @ addition ) @ ( B @ multiplication ) @ ( A @ multiplication ) )
!= zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[324]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(52,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(53,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[53]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(97,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)],[20]) ).
thf(98,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)],[97]) ).
thf(99,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)],[98]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(103,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(lifteq,[status(thm)],[101]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(simp,[status(thm)],[103]) ).
thf(6530,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( C @ ( B @ addition ) ) )
| ( C @ ( B @ leq ) )
| ( A != C ) ),
inference(paramod_ordered,[status(thm)],[54,104]) ).
thf(6531,plain,
! [A: $i] :
( ( A @ ( A @ leq ) )
| ( A != A ) ),
inference(pattern_uni,[status(thm)],[6530:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(6552,plain,
! [A: $i] : ( A @ ( A @ leq ) ),
inference(simp,[status(thm)],[6531]) ).
thf(26455,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= sk3 )
| ( ( sk2 @ ( sk1 @ addition ) @ ( B @ multiplication ) @ ( A @ multiplication ) )
!= zero )
| ~ $true ),
inference(rewrite,[status(thm)],[330,6552]) ).
thf(26456,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= sk3 )
| ( ( sk2 @ ( sk1 @ addition ) @ ( B @ multiplication ) @ ( A @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[26455]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(lifteq,[status(thm)],[56]) ).
thf(18,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(91,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(92,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[91]) ).
thf(93,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[92]) ).
thf(940,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( zero @ ( C @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[57,93]) ).
thf(941,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) )
= A ),
inference(pattern_uni,[status(thm)],[940:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(43,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[43]) ).
thf(45,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[44]) ).
thf(170,plain,
! [B: $i,A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( B @ ( zero @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[45,30]) ).
thf(178,plain,
! [B: $i,A: $i] :
( ( A != B )
| ( one != zero )
| ( A = zero ) ),
inference(simp,[status(thm)],[170]) ).
thf(186,plain,
! [A: $i] :
( ( one != zero )
| ( A = zero ) ),
inference(simp,[status(thm)],[178]) ).
thf(15,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(82,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(83,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[82]) ).
thf(84,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[83]) ).
thf(27,plain,
sk3 @ test,
inference(cnfConj,[status(thm)],[22]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ test )
<=> ? [B: $i] : ( A @ ( B @ complement ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).
thf(46,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(47,plain,
( ! [A: $i] :
( ? [B: $i] : ( A @ ( B @ complement ) )
=> ( A @ test ) )
& ! [A: $i] :
( ( A @ test )
=> ? [B: $i] : ( A @ ( B @ complement ) ) ) ),
inference(miniscope,[status(thm)],[46]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ test )
| ~ ( B @ ( C @ complement ) ) )
& ( ( A @ ( A @ sk5 @ complement ) )
| ~ ( A @ test ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
! [A: $i] :
( ( A @ ( A @ sk5 @ complement ) )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[48]) ).
thf(772,plain,
! [A: $i] :
( ( ( sk3 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27,49]) ).
thf(773,plain,
! [A: $i] :
( ( ( sk3 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) ) ),
inference(simp,[status(thm)],[772]) ).
thf(774,plain,
sk3 @ ( sk3 @ sk5 @ complement ),
inference(pattern_uni,[status(thm)],[773:[bind(A,$thf( sk3 ))]]) ).
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(67,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(68,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)],[67]) ).
thf(69,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)],[68]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(lifteq,[status(thm)],[70]) ).
thf(1595,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[774,74]) ).
thf(1596,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1595]) ).
thf(1597,plain,
( ( sk3 @ sk5 @ ( sk3 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1596:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 @ sk5 ))]]) ).
thf(1779,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk3 @ sk5 @ ( sk3 @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[84,1597]) ).
thf(1838,plain,
! [A: $i] :
( ( ( sk3 @ sk5 )
!= one )
| ( A != sk3 )
| ( A = zero ) ),
inference(simp,[status(thm)],[1779]) ).
thf(1863,plain,
( ( ( sk3 @ sk5 )
!= one )
| ( sk3 = zero ) ),
inference(simp,[status(thm)],[1838]) ).
thf(25,plain,
zero @ ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ),
inference(cnfConj,[status(thm)],[22]) ).
thf(128,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[30,25]) ).
thf(133,plain,
! [A: $i] :
( ( A
!= ( sk4 @ c ) )
| ( ( sk1 @ ( sk3 @ multiplication ) )
!= zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[128]) ).
thf(139,plain,
( ( ( sk1 @ ( sk3 @ multiplication ) )
!= zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[133]) ).
thf(286,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( zero != zero )
| ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[30,139]) ).
thf(287,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[286]) ).
thf(293,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk3 != zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[287]) ).
thf(295,plain,
( ( sk3 != zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[293]) ).
thf(113,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) ) )
| ~ ( zero @ ( sk4 @ c @ ( zero @ multiplication ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[30,24]) ).
thf(117,plain,
! [A: $i] :
( ( A
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( sk3 != zero )
| ~ ( zero @ ( sk4 @ c @ ( zero @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(121,plain,
( ( sk3 != zero )
| ~ ( zero @ ( sk4 @ c @ ( zero @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(236,plain,
( ( sk3 != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(rewrite,[status(thm)],[121,30]) ).
thf(680,plain,
( ( ( zero @ ( zero @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( sk3 != zero )
| ~ $true
| ( sk3 != zero ) ),
inference(paramod_ordered,[status(thm)],[295,236]) ).
thf(681,plain,
( ( ( zero @ ( zero @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( sk3 != zero ) ),
inference(simp,[status(thm)],[680]) ).
thf(682,plain,
sk3 != zero,
inference(pattern_uni,[status(thm)],[681:[]]) ).
thf(4143,plain,
( ( sk3 @ sk5 )
!= one ),
inference(simplifyReflect,[status(thm)],[1863,682]) ).
thf(8644,plain,
! [A: $i] :
( ( A
!= ( sk3 @ sk5 ) )
| ( one != zero )
| ( one != zero ) ),
inference(paramod_ordered,[status(thm)],[186,4143]) ).
thf(8645,plain,
! [A: $i] :
( ( A
!= ( sk3 @ sk5 ) )
| ( one != zero ) ),
inference(simp,[status(thm)],[8644]) ).
thf(8646,plain,
one != zero,
inference(pattern_uni,[status(thm)],[8645:[bind(A,$thf( sk3 @ sk5 ))]]) ).
thf(23,plain,
sk4 @ test,
inference(cnfConj,[status(thm)],[22]) ).
thf(775,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,49]) ).
thf(776,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) ) ),
inference(simp,[status(thm)],[775]) ).
thf(777,plain,
sk4 @ ( sk4 @ sk5 @ complement ),
inference(pattern_uni,[status(thm)],[776:[bind(A,$thf( sk4 ))]]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ addition ) @ c )
= ( B @ c @ ( A @ c @ multiplication ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_deMorgan1) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ addition ) @ c )
= ( B @ c @ ( A @ c @ multiplication ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
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(58,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(59,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)],[58]) ).
thf(60,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)],[59]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement ) )
| ( ( A @ c )
!= B )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[60]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
!= B ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(64,plain,
! [A: $i] :
( ( A @ c @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[63]) ).
thf(1067,plain,
! [A: $i] :
( ( ( sk3 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27,64]) ).
thf(1068,plain,
! [A: $i] :
( ( ( sk3 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1067]) ).
thf(1069,plain,
sk3 @ c @ ( sk3 @ complement ),
inference(pattern_uni,[status(thm)],[1068:[bind(A,$thf( sk3 ))]]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( A @ test )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[48]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( A @ test )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[50]) ).
thf(1081,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1069,51]) ).
thf(1082,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1081]) ).
thf(1083,plain,
sk3 @ c @ test,
inference(pattern_uni,[status(thm)],[1082:[bind(A,$thf( sk3 @ c )),bind(B,$thf( sk3 ))]]) ).
thf(1086,plain,
! [A: $i] :
( ( ( sk3 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1083,64]) ).
thf(1087,plain,
! [A: $i] :
( ( ( sk3 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1086]) ).
thf(1088,plain,
sk3 @ c @ c @ ( sk3 @ c @ complement ),
inference(pattern_uni,[status(thm)],[1087:[bind(A,$thf( sk3 @ c ))]]) ).
thf(1426,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ ( sk3 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1088,51]) ).
thf(1427,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ ( sk3 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1426]) ).
thf(1428,plain,
sk3 @ c @ c @ test,
inference(pattern_uni,[status(thm)],[1427:[bind(A,$thf( sk3 @ c @ c )),bind(B,$thf( sk3 @ c ))]]) ).
thf(1447,plain,
! [A: $i] :
( ( ( sk3 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1428,64]) ).
thf(1448,plain,
! [A: $i] :
( ( ( sk3 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1447]) ).
thf(1449,plain,
sk3 @ c @ c @ c @ ( sk3 @ c @ c @ complement ),
inference(pattern_uni,[status(thm)],[1448:[bind(A,$thf( sk3 @ c @ c ))]]) ).
thf(9795,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1449,51]) ).
thf(9796,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[9795]) ).
thf(9797,plain,
sk3 @ c @ c @ c @ test,
inference(pattern_uni,[status(thm)],[9796:[bind(A,$thf( sk3 @ c @ c @ c )),bind(B,$thf( sk3 @ c @ c ))]]) ).
thf(9829,plain,
! [A: $i] :
( ( ( sk3 @ c @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9797,49]) ).
thf(9830,plain,
! [A: $i] :
( ( ( sk3 @ c @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) ) ),
inference(simp,[status(thm)],[9829]) ).
thf(9831,plain,
sk3 @ c @ c @ c @ ( sk3 @ c @ c @ c @ sk5 @ complement ),
inference(pattern_uni,[status(thm)],[9830:[bind(A,$thf( sk3 @ c @ c @ c ))]]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
= one )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(18813,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[9831,76]) ).
thf(18814,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[18813]) ).
thf(18815,plain,
( ( sk3 @ c @ c @ c @ sk5 @ ( sk3 @ c @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[18814:[bind(A,$thf( sk3 @ c @ c @ c )),bind(B,$thf( sk3 @ c @ c @ c @ sk5 ))]]) ).
thf(20682,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ sk5 @ ( sk3 @ c @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[18815,57]) ).
thf(20683,plain,
( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ c @ sk5 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[20682:[bind(A,$thf( sk3 @ c @ c @ c )),bind(B,$thf( sk3 @ c @ c @ c @ sk5 ))]]) ).
thf(6514,plain,
! [C: $i,B: $i,A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( C @ ( B @ addition ) ) )
| ( C @ ( B @ leq ) )
| ( A != C ) ),
inference(paramod_ordered,[status(thm)],[93,104]) ).
thf(6515,plain,
! [A: $i] :
( ( zero @ ( A @ leq ) )
| ( A != zero ) ),
inference(pattern_uni,[status(thm)],[6514:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( zero ))]]) ).
thf(6559,plain,
zero @ ( zero @ leq ),
inference(simp,[status(thm)],[6515]) ).
thf(296,plain,
~ ( zero @ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) @ leq ) ),
inference(rewrite,[status(thm)],[24,33]) ).
thf(6570,plain,
( ( ( zero @ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6559,296]) ).
thf(6571,plain,
( ( zero @ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) @ leq ) )
!= ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[6570]) ).
thf(6575,plain,
( ( zero != zero )
| ( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[6571]) ).
thf(6576,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) )
!= zero ),
inference(simp,[status(thm)],[6575]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
= zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( B @ complement ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(2115,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[774,75]) ).
thf(2116,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2115]) ).
thf(2117,plain,
( ( sk3 @ ( sk3 @ sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2116:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 @ sk5 ))]]) ).
thf(1072,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,64]) ).
thf(1073,plain,
! [A: $i] :
( ( ( sk4 @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1072]) ).
thf(1074,plain,
sk4 @ c @ ( sk4 @ complement ),
inference(pattern_uni,[status(thm)],[1073:[bind(A,$thf( sk4 ))]]) ).
thf(1094,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1074,51]) ).
thf(1095,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1094]) ).
thf(1096,plain,
sk4 @ c @ test,
inference(pattern_uni,[status(thm)],[1095:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(1099,plain,
! [A: $i] :
( ( ( sk4 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1096,64]) ).
thf(1100,plain,
! [A: $i] :
( ( ( sk4 @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1099]) ).
thf(1101,plain,
sk4 @ c @ c @ ( sk4 @ c @ complement ),
inference(pattern_uni,[status(thm)],[1100:[bind(A,$thf( sk4 @ c ))]]) ).
thf(1503,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1101,51]) ).
thf(1504,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[1503]) ).
thf(1505,plain,
sk4 @ c @ c @ test,
inference(pattern_uni,[status(thm)],[1504:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c ))]]) ).
thf(1568,plain,
! [A: $i] :
( ( ( sk4 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1505,64]) ).
thf(1569,plain,
! [A: $i] :
( ( ( sk4 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[1568]) ).
thf(1570,plain,
sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ),
inference(pattern_uni,[status(thm)],[1569:[bind(A,$thf( sk4 @ c @ c ))]]) ).
thf(9973,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1570,76]) ).
thf(9974,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[9973]) ).
thf(9975,plain,
( ( sk4 @ c @ c @ ( sk4 @ c @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[9974:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c ))]]) ).
thf(15189,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[9975,57]) ).
thf(15190,plain,
( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[15189:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c ))]]) ).
thf(1102,plain,
! [A: $i] :
( ( ( sk4 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1096,49]) ).
thf(1103,plain,
! [A: $i] :
( ( ( sk4 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) ) ),
inference(simp,[status(thm)],[1102]) ).
thf(1104,plain,
sk4 @ c @ ( sk4 @ c @ sk5 @ complement ),
inference(pattern_uni,[status(thm)],[1103:[bind(A,$thf( sk4 @ c ))]]) ).
thf(4491,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1104,75]) ).
thf(4492,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[4491]) ).
thf(4493,plain,
( ( sk4 @ c @ ( sk4 @ c @ sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[4492:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 @ c @ sk5 ))]]) ).
thf(16,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(85,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(86,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[85]) ).
thf(87,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[86]) ).
thf(11292,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[87,6576]) ).
thf(11293,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) ) ),
inference(simp,[status(thm)],[11292]) ).
thf(11343,plain,
! [A: $i] :
( ( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= zero )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[11293]) ).
thf(11405,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= zero ),
inference(simp,[status(thm)],[11343]) ).
thf(11444,plain,
( ( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk4 @ c @ ( sk4 @ c @ sk5 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[4493,11405]) ).
thf(11445,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk4 @ c @ ( sk4 @ c @ sk5 @ multiplication ) ) ),
inference(simp,[status(thm)],[11444]) ).
thf(11515,plain,
( ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( ( sk2 @ ( sk1 @ addition ) )
!= ( sk4 @ c @ sk5 ) ) ),
inference(simp,[status(thm)],[11445]) ).
thf(11571,plain,
( ( sk2 @ ( sk1 @ addition ) )
!= ( sk4 @ c @ sk5 ) ),
inference(simp,[status(thm)],[11515]) ).
thf(2852,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1101,76]) ).
thf(2853,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[2852]) ).
thf(2854,plain,
( ( sk4 @ c @ ( sk4 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[2853:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c ))]]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
= B )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[99]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
= B ) ),
inference(lifteq,[status(thm)],[100]) ).
thf(5938,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( ( sk4 @ c @ ( B @ multiplication ) @ ( sk3 @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ multiplication ) @ ( sk3 @ multiplication ) ) )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[102,810]) ).
thf(5939,plain,
( ( ( sk4 @ c @ ( sk2 @ multiplication ) @ ( sk3 @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ multiplication ) @ ( sk3 @ multiplication ) ) )
| ~ ( sk2 @ ( sk1 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[5938:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(6017,plain,
~ ( sk2 @ ( sk1 @ leq ) ),
inference(simp,[status(thm)],[5939]) ).
thf(2112,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[777,75]) ).
thf(2113,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2112]) ).
thf(2114,plain,
( ( sk4 @ ( sk4 @ sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2113:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ sk5 ))]]) ).
thf(10020,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1570,51]) ).
thf(10021,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[10020]) ).
thf(10022,plain,
sk4 @ c @ c @ c @ test,
inference(pattern_uni,[status(thm)],[10021:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c ))]]) ).
thf(10055,plain,
! [A: $i] :
( ( ( sk4 @ c @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10022,49]) ).
thf(10056,plain,
! [A: $i] :
( ( ( sk4 @ c @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) ) ),
inference(simp,[status(thm)],[10055]) ).
thf(10057,plain,
sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk5 @ complement ),
inference(pattern_uni,[status(thm)],[10056:[bind(A,$thf( sk4 @ c @ c @ c ))]]) ).
thf(19172,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[10057,76]) ).
thf(19173,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[19172]) ).
thf(19174,plain,
( ( sk4 @ c @ c @ c @ sk5 @ ( sk4 @ c @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[19173:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c @ c @ sk5 ))]]) ).
thf(22665,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ sk5 @ ( sk4 @ c @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[19174,57]) ).
thf(22666,plain,
( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk5 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[22665:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c @ c @ sk5 ))]]) ).
thf(1669,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ ( sk3 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1088,74]) ).
thf(1670,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ ( sk3 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1669]) ).
thf(1671,plain,
( ( sk3 @ c @ ( sk3 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1670:[bind(A,$thf( sk3 @ c @ c )),bind(B,$thf( sk3 @ c ))]]) ).
thf(2222,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1069,75]) ).
thf(2223,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2222]) ).
thf(2224,plain,
( ( sk3 @ c @ ( sk3 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2223:[bind(A,$thf( sk3 @ c )),bind(B,$thf( sk3 ))]]) ).
thf(6563,plain,
( ( ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) )
!= zero )
| ~ $true ),
inference(rewrite,[status(thm)],[122,6559]) ).
thf(6564,plain,
( ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) )
!= zero ),
inference(simp,[status(thm)],[6563]) ).
thf(6699,plain,
( ( ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) )
!= ( sk3 @ c @ ( sk3 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[2224,6564]) ).
thf(6700,plain,
( ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) )
!= ( sk3 @ c @ ( sk3 @ multiplication ) ) ),
inference(simp,[status(thm)],[6699]) ).
thf(6738,plain,
( ( ( sk2 @ ( sk1 @ addition ) )
!= ( sk3 @ c ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[6700]) ).
thf(6764,plain,
( ( sk2 @ ( sk1 @ addition ) )
!= ( sk3 @ c ) ),
inference(simp,[status(thm)],[6738]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
= B )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(cnfConj,[status(thm)],[60]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
= B ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ complement ) )
| ~ ( A @ test )
| ( ( A @ c )
= B ) ),
inference(simp,[status(thm)],[65]) ).
thf(1672,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1069,74]) ).
thf(1673,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1672]) ).
thf(1674,plain,
( ( sk3 @ ( sk3 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1673:[bind(A,$thf( sk3 @ c )),bind(B,$thf( sk3 ))]]) ).
thf(2024,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk3 @ ( sk3 @ c @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[45,1674]) ).
thf(2054,plain,
! [A: $i] :
( ( A != sk3 )
| ( ( sk3 @ c )
!= one )
| ( A = zero ) ),
inference(simp,[status(thm)],[2024]) ).
thf(2079,plain,
( ( ( sk3 @ c )
!= one )
| ( sk3 = zero ) ),
inference(simp,[status(thm)],[2054]) ).
thf(6995,plain,
( ( sk3 @ c )
!= one ),
inference(simplifyReflect,[status(thm)],[2079,682]) ).
thf(6998,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
!= ( sk3 @ c ) )
| ( B != one )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[66,6995]) ).
thf(6999,plain,
! [A: $i] :
( ( A != one )
| ~ ( A @ ( sk3 @ complement ) )
| ~ ( sk3 @ test ) ),
inference(pattern_uni,[status(thm)],[6998:[bind(A,$thf( sk3 ))]]) ).
thf(7005,plain,
( ~ ( one @ ( sk3 @ complement ) )
| ~ ( sk3 @ test ) ),
inference(simp,[status(thm)],[6999]) ).
thf(8602,plain,
( ~ ( one @ ( sk3 @ complement ) )
| ~ $true ),
inference(rewrite,[status(thm)],[7005,27]) ).
thf(8603,plain,
~ ( one @ ( sk3 @ complement ) ),
inference(simp,[status(thm)],[8602]) ).
thf(8613,plain,
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( one @ ( sk3 @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1074,8603]) ).
thf(8614,plain,
( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( one @ ( sk3 @ complement ) ) ),
inference(simp,[status(thm)],[8613]) ).
thf(8635,plain,
( ( ( sk4 @ c )
!= one )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[8614]) ).
thf(11315,plain,
( ( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) )
!= ( sk3 @ sk5 @ ( sk3 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[1597,6576]) ).
thf(11316,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) )
!= ( sk3 @ sk5 @ ( sk3 @ multiplication ) ) ),
inference(simp,[status(thm)],[11315]) ).
thf(11325,plain,
( ( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk3 @ sk5 ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[11316]) ).
thf(11399,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk3 @ sk5 ) ),
inference(simp,[status(thm)],[11325]) ).
thf(11301,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) ) )
| ( zero != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[75,6576]) ).
thf(11302,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) ) )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[11301]) ).
thf(11303,plain,
~ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ complement ) ),
inference(pattern_uni,[status(thm)],[11302:[bind(A,$thf( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )),bind(B,$thf( sk3 ))]]) ).
thf(6508,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( zero @ addition ) )
!= ( C @ ( B @ addition ) ) )
| ( C @ ( B @ leq ) )
| ( A != C ) ),
inference(paramod_ordered,[status(thm)],[941,104]) ).
thf(6509,plain,
! [A: $i] :
( ( A @ ( zero @ leq ) )
| ( A != A ) ),
inference(pattern_uni,[status(thm)],[6508:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(6556,plain,
! [A: $i] : ( A @ ( zero @ leq ) ),
inference(simp,[status(thm)],[6509]) ).
thf(6630,plain,
! [A: $i] :
( ( ( A @ ( zero @ leq ) )
!= ( sk2 @ ( sk1 @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[6556,6017]) ).
thf(6631,plain,
! [A: $i] :
( ( A @ ( zero @ leq ) )
!= ( sk2 @ ( sk1 @ leq ) ) ),
inference(simp,[status(thm)],[6630]) ).
thf(6638,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[6631]) ).
thf(6640,plain,
sk1 != zero,
inference(simp,[status(thm)],[6638]) ).
thf(4494,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1104,74]) ).
thf(4495,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[4494]) ).
thf(4496,plain,
( ( sk4 @ c @ sk5 @ ( sk4 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[4495:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 @ c @ sk5 ))]]) ).
thf(2130,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1074,75]) ).
thf(2131,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2130]) ).
thf(2132,plain,
( ( sk4 @ c @ ( sk4 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2131:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(11446,plain,
( ( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk4 @ c @ ( sk4 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[2132,11405]) ).
thf(11447,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk4 @ c @ ( sk4 @ multiplication ) ) ),
inference(simp,[status(thm)],[11446]) ).
thf(11554,plain,
( ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( ( sk2 @ ( sk1 @ addition ) )
!= sk4 ) ),
inference(simp,[status(thm)],[11447]) ).
thf(11568,plain,
( ( sk2 @ ( sk1 @ addition ) )
!= sk4 ),
inference(simp,[status(thm)],[11554]) ).
thf(1987,plain,
! [A: $i] :
( ( ( sk3 @ ( sk3 @ c @ multiplication ) )
!= ( one @ ( A @ multiplication ) ) )
| ( zero = A ) ),
inference(paramod_ordered,[status(thm)],[1674,84]) ).
thf(2059,plain,
! [A: $i] :
( ( sk3 != one )
| ( ( sk3 @ c )
!= A )
| ( zero = A ) ),
inference(simp,[status(thm)],[1987]) ).
thf(2082,plain,
( ( sk3 != one )
| ( ( sk3 @ c )
= zero ) ),
inference(simp,[status(thm)],[2059]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_4) ).
thf(37,plain,
! [A: $i] :
( ~ ( A @ test )
=> ( ( A @ c )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(320,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( D @ ( C @ ( B @ multiplication ) @ multiplication ) ) )
| ( ( D @ ( C @ multiplication ) @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[30,33]) ).
thf(323,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A != D )
| ( ( C @ ( B @ multiplication ) )
!= zero )
| ( ( D @ ( C @ multiplication ) @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[320]) ).
thf(329,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= zero )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[323]) ).
thf(25439,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk5 @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( zero != zero )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[2114,329]) ).
thf(25440,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk5 @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[25439]) ).
thf(25441,plain,
! [A: $i] :
( ( A @ ( sk4 @ multiplication ) @ ( sk4 @ sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[25440:[bind(A,$thf( sk4 @ sk5 )),bind(B,$thf( sk4 )),bind(C,$thf( C ))]]) ).
thf(25938,plain,
! [A: $i] :
( ( A @ ( sk4 @ multiplication ) @ ( sk4 @ sk5 @ multiplication ) )
= zero ),
inference(simp,[status(thm)],[25441]) ).
thf(9826,plain,
! [A: $i] :
( ( ( sk3 @ c @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9797,64]) ).
thf(9827,plain,
! [A: $i] :
( ( ( sk3 @ c @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[9826]) ).
thf(9828,plain,
sk3 @ c @ c @ c @ c @ ( sk3 @ c @ c @ c @ complement ),
inference(pattern_uni,[status(thm)],[9827:[bind(A,$thf( sk3 @ c @ c @ c ))]]) ).
thf(18583,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ c @ ( sk3 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[9828,74]) ).
thf(18584,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ c @ ( sk3 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[18583]) ).
thf(18585,plain,
( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[18584:[bind(A,$thf( sk3 @ c @ c @ c @ c )),bind(B,$thf( sk3 @ c @ c @ c ))]]) ).
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(40,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(41,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) )
= ( C @ ( B @ ( A @ addition ) @ multiplication ) ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(2822,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1074,76]) ).
thf(2823,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[2822]) ).
thf(2824,plain,
( ( sk4 @ ( sk4 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[2823:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(3050,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[2824,57]) ).
thf(3051,plain,
( ( sk4 @ c @ ( sk4 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3050:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(3703,plain,
! [A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( sk4 @ c @ ( sk4 @ addition ) ) )
| ( A = one ) ),
inference(paramod_ordered,[status(thm)],[54,3051]) ).
thf(3744,plain,
! [A: $i] :
( ( A
!= ( sk4 @ c ) )
| ( A != sk4 )
| ( A = one ) ),
inference(simp,[status(thm)],[3703]) ).
thf(3769,plain,
( ( ( sk4 @ c )
!= sk4 )
| ( sk4 = one ) ),
inference(simp,[status(thm)],[3744]) ).
thf(1598,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1074,74]) ).
thf(1599,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1598]) ).
thf(1600,plain,
( ( sk4 @ ( sk4 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1599:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 ))]]) ).
thf(1883,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ c @ multiplication ) )
!= ( one @ ( A @ multiplication ) ) )
| ( zero = A ) ),
inference(paramod_ordered,[status(thm)],[1600,84]) ).
thf(1946,plain,
! [A: $i] :
( ( sk4 != one )
| ( ( sk4 @ c )
!= A )
| ( zero = A ) ),
inference(simp,[status(thm)],[1883]) ).
thf(1972,plain,
( ( sk4 != one )
| ( ( sk4 @ c )
= zero ) ),
inference(simp,[status(thm)],[1946]) ).
thf(126,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[87,25]) ).
thf(136,plain,
! [A: $i] :
( ( ( sk4 @ c )
!= zero )
| ( A
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[126]) ).
thf(142,plain,
( ( ( sk4 @ c )
!= zero )
| ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[136]) ).
thf(112,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[87,24]) ).
thf(116,plain,
! [A: $i] :
( ( ( sk4 @ c )
!= zero )
| ( A
!= ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) ) )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[112]) ).
thf(120,plain,
( ( ( sk4 @ c )
!= zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(143,plain,
( ( ( zero @ ( zero @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( ( sk4 @ c )
!= zero )
| ~ $true
| ( ( sk4 @ c )
!= zero ) ),
inference(paramod_ordered,[status(thm)],[142,120]) ).
thf(144,plain,
( ( ( zero @ ( zero @ leq ) )
!= ( zero @ ( zero @ leq ) ) )
| ( ( sk4 @ c )
!= zero ) ),
inference(simp,[status(thm)],[143]) ).
thf(145,plain,
( ( sk4 @ c )
!= zero ),
inference(pattern_uni,[status(thm)],[144:[]]) ).
thf(5903,plain,
sk4 != one,
inference(simplifyReflect,[status(thm)],[1972,145]) ).
thf(22618,plain,
( ( sk4 @ c )
!= sk4 ),
inference(simplifyReflect,[status(thm)],[3769,5903]) ).
thf(22624,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
!= ( sk4 @ c ) )
| ( B != sk4 )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[66,22618]) ).
thf(22625,plain,
! [A: $i] :
( ( A != sk4 )
| ~ ( A @ ( sk4 @ complement ) )
| ~ ( sk4 @ test ) ),
inference(pattern_uni,[status(thm)],[22624:[bind(A,$thf( sk4 ))]]) ).
thf(22632,plain,
( ~ ( sk4 @ ( sk4 @ complement ) )
| ~ ( sk4 @ test ) ),
inference(simp,[status(thm)],[22625]) ).
thf(23628,plain,
( ~ ( sk4 @ ( sk4 @ complement ) )
| ~ $true ),
inference(rewrite,[status(thm)],[22632,23]) ).
thf(23629,plain,
~ ( sk4 @ ( sk4 @ complement ) ),
inference(simp,[status(thm)],[23628]) ).
thf(23637,plain,
( ( ( sk3 @ ( sk3 @ sk5 @ complement ) )
!= ( sk4 @ ( sk4 @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[774,23629]) ).
thf(23638,plain,
( ( sk3 @ ( sk3 @ sk5 @ complement ) )
!= ( sk4 @ ( sk4 @ complement ) ) ),
inference(simp,[status(thm)],[23637]) ).
thf(23675,plain,
( ( sk4 != sk3 )
| ( ( sk3 @ sk5 )
!= sk4 ) ),
inference(simp,[status(thm)],[23638]) ).
thf(18799,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[9831,74]) ).
thf(18800,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[18799]) ).
thf(18801,plain,
( ( sk3 @ c @ c @ c @ sk5 @ ( sk3 @ c @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[18800:[bind(A,$thf( sk3 @ c @ c @ c )),bind(B,$thf( sk3 @ c @ c @ c @ sk5 ))]]) ).
thf(1450,plain,
! [A: $i] :
( ( ( sk3 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1428,49]) ).
thf(1451,plain,
! [A: $i] :
( ( ( sk3 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) ) ),
inference(simp,[status(thm)],[1450]) ).
thf(1452,plain,
sk3 @ c @ c @ ( sk3 @ c @ c @ sk5 @ complement ),
inference(pattern_uni,[status(thm)],[1451:[bind(A,$thf( sk3 @ c @ c ))]]) ).
thf(9895,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ ( sk3 @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1452,76]) ).
thf(9896,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ ( sk3 @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[9895]) ).
thf(9897,plain,
( ( sk3 @ c @ c @ sk5 @ ( sk3 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[9896:[bind(A,$thf( sk3 @ c @ c )),bind(B,$thf( sk3 @ c @ c @ sk5 ))]]) ).
thf(14439,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ sk5 @ ( sk3 @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[9897,57]) ).
thf(14440,plain,
( ( sk3 @ c @ c @ ( sk3 @ c @ c @ sk5 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[14439:[bind(A,$thf( sk3 @ c @ c )),bind(B,$thf( sk3 @ c @ c @ sk5 ))]]) ).
thf(176,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk2 @ ( sk3 @ multiplication ) ) )
| ( zero @ ( sk4 @ c @ ( A @ multiplication ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[45,26]) ).
thf(181,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk3 != one )
| ( zero @ ( sk4 @ c @ ( A @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[176]) ).
thf(189,plain,
( ( sk3 != one )
| ( zero @ ( sk4 @ c @ ( sk2 @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[181]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
!= one )
| ( ( A @ ( B @ multiplication ) )
!= zero )
| ( ( B @ ( A @ multiplication ) )
!= zero ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
!= one )
| ( ( A @ ( B @ multiplication ) )
!= zero )
| ( ( B @ ( A @ multiplication ) )
!= zero ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ complement ) )
| ( ( B @ ( A @ addition ) )
!= one )
| ( ( A @ ( B @ multiplication ) )
!= zero )
| ( ( B @ ( A @ multiplication ) )
!= zero ) ),
inference(simp,[status(thm)],[77]) ).
thf(11288,plain,
( ( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) )
!= ( sk3 @ c @ ( sk3 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[2224,6576]) ).
thf(11289,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) )
!= ( sk3 @ c @ ( sk3 @ multiplication ) ) ),
inference(simp,[status(thm)],[11288]) ).
thf(11338,plain,
( ( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk3 @ c ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[11289]) ).
thf(11404,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk3 @ c ) ),
inference(simp,[status(thm)],[11338]) ).
thf(1089,plain,
! [A: $i] :
( ( ( sk3 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1083,49]) ).
thf(1090,plain,
! [A: $i] :
( ( ( sk3 @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) ) ),
inference(simp,[status(thm)],[1089]) ).
thf(1091,plain,
sk3 @ c @ ( sk3 @ c @ sk5 @ complement ),
inference(pattern_uni,[status(thm)],[1090:[bind(A,$thf( sk3 @ c ))]]) ).
thf(2827,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1091,76]) ).
thf(2828,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[2827]) ).
thf(2829,plain,
( ( sk3 @ c @ sk5 @ ( sk3 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[2828:[bind(A,$thf( sk3 @ c )),bind(B,$thf( sk3 @ c @ sk5 ))]]) ).
thf(2868,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1069,76]) ).
thf(2869,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[2868]) ).
thf(2870,plain,
( ( sk3 @ ( sk3 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[2869:[bind(A,$thf( sk3 @ c )),bind(B,$thf( sk3 ))]]) ).
thf(3143,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[2870,57]) ).
thf(3144,plain,
( ( sk3 @ c @ ( sk3 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[3143:[bind(A,$thf( sk3 @ c )),bind(B,$thf( sk3 ))]]) ).
thf(4001,plain,
! [A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( sk3 @ c @ ( sk3 @ addition ) ) )
| ( A = one ) ),
inference(paramod_ordered,[status(thm)],[54,3144]) ).
thf(4046,plain,
! [A: $i] :
( ( A
!= ( sk3 @ c ) )
| ( A != sk3 )
| ( A = one ) ),
inference(simp,[status(thm)],[4001]) ).
thf(4072,plain,
( ( ( sk3 @ c )
!= sk3 )
| ( sk3 = one ) ),
inference(simp,[status(thm)],[4046]) ).
thf(2804,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[777,76]) ).
thf(2805,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[2804]) ).
thf(2806,plain,
( ( sk4 @ sk5 @ ( sk4 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[2805:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ sk5 ))]]) ).
thf(2892,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ sk5 @ ( sk4 @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[2806,57]) ).
thf(2893,plain,
( ( sk4 @ ( sk4 @ sk5 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[2892:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ sk5 ))]]) ).
thf(248,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) ) )
| ( zero != zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[87,122]) ).
thf(249,plain,
! [A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) ) )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[248]) ).
thf(257,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ addition ) )
!= zero )
| ( A != sk3 )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[249]) ).
thf(267,plain,
( ( ( sk2 @ ( sk1 @ addition ) )
!= zero )
| ~ ( zero @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[257]) ).
thf(6561,plain,
( ( ( sk2 @ ( sk1 @ addition ) )
!= zero )
| ~ $true ),
inference(rewrite,[status(thm)],[267,6559]) ).
thf(6562,plain,
( ( sk2 @ ( sk1 @ addition ) )
!= zero ),
inference(simp,[status(thm)],[6561]) ).
thf(9968,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1570,74]) ).
thf(9969,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[9968]) ).
thf(9970,plain,
( ( sk4 @ c @ c @ ( sk4 @ c @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[9969:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c ))]]) ).
thf(208,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk2 @ ( sk3 @ multiplication ) ) )
| ( zero @ ( sk4 @ c @ ( A @ multiplication ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[84,26]) ).
thf(213,plain,
! [A: $i] :
( ( sk2 != one )
| ( A != sk3 )
| ( zero @ ( sk4 @ c @ ( A @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[208]) ).
thf(221,plain,
( ( sk2 != one )
| ( zero @ ( sk4 @ c @ ( sk3 @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[213]) ).
thf(7212,plain,
( ( ( sk3 @ c )
!= ( sk3 @ c ) )
| ( zero @ ( sk3 @ complement ) )
| ( sk3 != one ) ),
inference(paramod_ordered,[status(thm)],[2082,1069]) ).
thf(7213,plain,
( ( zero @ ( sk3 @ complement ) )
| ( sk3 != one ) ),
inference(pattern_uni,[status(thm)],[7212:[]]) ).
thf(4499,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1104,76]) ).
thf(4500,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[4499]) ).
thf(4501,plain,
( ( sk4 @ c @ sk5 @ ( sk4 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[4500:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 @ c @ sk5 ))]]) ).
thf(7687,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ sk5 @ ( sk4 @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[4501,57]) ).
thf(7688,plain,
( ( sk4 @ c @ ( sk4 @ c @ sk5 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[7687:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk4 @ c @ sk5 ))]]) ).
thf(10052,plain,
! [A: $i] :
( ( ( sk4 @ c @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10022,64]) ).
thf(10053,plain,
! [A: $i] :
( ( ( sk4 @ c @ c @ c @ test )
!= ( A @ test ) )
| ( A @ c @ ( A @ complement ) ) ),
inference(simp,[status(thm)],[10052]) ).
thf(10054,plain,
sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ),
inference(pattern_uni,[status(thm)],[10053:[bind(A,$thf( sk4 @ c @ c @ c ))]]) ).
thf(18926,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[10054,74]) ).
thf(18927,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[18926]) ).
thf(18928,plain,
( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[18927:[bind(A,$thf( sk4 @ c @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c @ c ))]]) ).
thf(298,plain,
zero @ ( sk4 @ c @ ( sk2 @ multiplication ) @ ( sk3 @ multiplication ) @ leq ),
inference(rewrite,[status(thm)],[26,33]) ).
thf(5949,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( sk4 @ c @ ( sk2 @ multiplication ) @ ( sk3 @ multiplication ) @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[298,102]) ).
thf(5950,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( sk4 @ c @ ( sk2 @ multiplication ) @ ( sk3 @ multiplication ) @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( ( B @ ( A @ addition ) )
= B ) ),
inference(simp,[status(thm)],[5949]) ).
thf(5951,plain,
( ( zero @ ( sk4 @ c @ ( sk2 @ multiplication ) @ ( sk3 @ multiplication ) @ addition ) )
= zero ),
inference(pattern_uni,[status(thm)],[5950:[bind(A,$thf( sk4 @ c @ ( sk2 @ multiplication ) @ ( sk3 @ multiplication ) )),bind(B,$thf( zero ))]]) ).
thf(10811,plain,
( ( sk4 @ c @ ( sk2 @ multiplication ) @ ( sk3 @ multiplication ) )
= zero ),
inference(rewrite,[status(thm)],[5951,93]) ).
thf(204,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) ) )
| ~ ( zero @ ( sk4 @ c @ ( A @ multiplication ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[84,24]) ).
thf(212,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ addition ) )
!= one )
| ( A != sk3 )
| ~ ( zero @ ( sk4 @ c @ ( A @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[204]) ).
thf(220,plain,
( ( ( sk2 @ ( sk1 @ addition ) )
!= one )
| ~ ( zero @ ( sk4 @ c @ ( sk3 @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[212]) ).
thf(8609,plain,
( ( ( sk3 @ ( sk3 @ sk5 @ complement ) )
!= ( one @ ( sk3 @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[774,8603]) ).
thf(8610,plain,
( ( sk3 @ ( sk3 @ sk5 @ complement ) )
!= ( one @ ( sk3 @ complement ) ) ),
inference(simp,[status(thm)],[8609]) ).
thf(8630,plain,
( ( sk3 != one )
| ( ( sk3 @ sk5 )
!= sk3 ) ),
inference(simp,[status(thm)],[8610]) ).
thf(3049,plain,
! [A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( sk4 @ ( sk4 @ c @ addition ) ) )
| ( A = one ) ),
inference(paramod_ordered,[status(thm)],[93,2824]) ).
thf(3094,plain,
! [A: $i] :
( ( sk4 != zero )
| ( A
!= ( sk4 @ c ) )
| ( A = one ) ),
inference(simp,[status(thm)],[3049]) ).
thf(3119,plain,
( ( sk4 != zero )
| ( ( sk4 @ c )
= one ) ),
inference(simp,[status(thm)],[3094]) ).
thf(16996,plain,
( ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( one @ test )
| ( sk4 != zero ) ),
inference(paramod_ordered,[status(thm)],[3119,1096]) ).
thf(16997,plain,
( ( one @ test )
| ( sk4 != zero ) ),
inference(pattern_uni,[status(thm)],[16996:[]]) ).
thf(8619,plain,
! [A: $i] :
( ( ( A @ ( A @ sk5 @ complement ) )
!= ( one @ ( sk3 @ complement ) ) )
| ~ $true
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[49,8603]) ).
thf(8620,plain,
! [A: $i] :
( ( ( A @ ( A @ sk5 @ complement ) )
!= ( one @ ( sk3 @ complement ) ) )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[8619]) ).
thf(8637,plain,
! [A: $i] :
( ( A != one )
| ( ( A @ sk5 )
!= sk3 )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[8620]) ).
thf(8641,plain,
( ( ( one @ sk5 )
!= sk3 )
| ~ ( one @ test ) ),
inference(simp,[status(thm)],[8637]) ).
thf(17829,plain,
( ( ( one @ test )
!= ( one @ test ) )
| ( ( one @ sk5 )
!= sk3 )
| ~ $true
| ( sk4 != zero ) ),
inference(paramod_ordered,[status(thm)],[16997,8641]) ).
thf(17830,plain,
( ( ( one @ test )
!= ( one @ test ) )
| ( ( one @ sk5 )
!= sk3 )
| ( sk4 != zero ) ),
inference(simp,[status(thm)],[17829]) ).
thf(17831,plain,
( ( ( one @ sk5 )
!= sk3 )
| ( sk4 != zero ) ),
inference(pattern_uni,[status(thm)],[17830:[]]) ).
thf(19156,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[10057,74]) ).
thf(19157,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[19156]) ).
thf(19158,plain,
( ( sk4 @ c @ c @ c @ sk5 @ ( sk4 @ c @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[19157:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c @ c @ sk5 ))]]) ).
thf(23667,plain,
( ( ( sk4 @ ( sk4 @ complement ) )
!= ( sk3 @ c @ ( sk3 @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1069,23629]) ).
thf(23668,plain,
( ( sk4 @ ( sk4 @ complement ) )
!= ( sk3 @ c @ ( sk3 @ complement ) ) ),
inference(simp,[status(thm)],[23667]) ).
thf(23671,plain,
( ( ( sk3 @ c )
!= sk4 )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[23668]) ).
thf(11437,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ( zero != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[74,11405]) ).
thf(11438,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[11437]) ).
thf(11439,plain,
~ ( sk2 @ ( sk1 @ addition ) @ ( sk4 @ c @ complement ) ),
inference(pattern_uni,[status(thm)],[11438:[bind(A,$thf( sk2 @ ( sk1 @ addition ) )),bind(B,$thf( sk4 @ c ))]]) ).
thf(175,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ( zero @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[45,25]) ).
thf(184,plain,
! [A: $i] :
( ( A
!= ( sk4 @ c ) )
| ( ( sk1 @ ( sk3 @ multiplication ) )
!= one )
| ( zero @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[175]) ).
thf(192,plain,
( ( ( sk1 @ ( sk3 @ multiplication ) )
!= one )
| ( zero @ ( sk4 @ c @ leq ) ) ),
inference(simp,[status(thm)],[184]) ).
thf(9743,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1449,74]) ).
thf(9744,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[9743]) ).
thf(9745,plain,
( ( sk3 @ c @ c @ ( sk3 @ c @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[9744:[bind(A,$thf( sk3 @ c @ c @ c )),bind(B,$thf( sk3 @ c @ c ))]]) ).
thf(2198,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1101,75]) ).
thf(2199,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2198]) ).
thf(2200,plain,
( ( sk4 @ c @ c @ ( sk4 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2199:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c ))]]) ).
thf(1654,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1101,74]) ).
thf(1655,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1654]) ).
thf(1656,plain,
( ( sk4 @ c @ ( sk4 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1655:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c ))]]) ).
thf(6664,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) ) )
| ( zero != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[74,6564]) ).
thf(6665,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) ) )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[6664]) ).
thf(6666,plain,
~ ( sk3 @ ( sk2 @ ( sk1 @ addition ) @ complement ) ),
inference(pattern_uni,[status(thm)],[6665:[bind(A,$thf( sk3 )),bind(B,$thf( sk2 @ ( sk1 @ addition ) ))]]) ).
thf(2819,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[774,76]) ).
thf(2820,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[2819]) ).
thf(2821,plain,
( ( sk3 @ sk5 @ ( sk3 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[2820:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 @ sk5 ))]]) ).
thf(2984,plain,
! [A: $i] :
( ( ( sk3 @ sk5 @ ( sk3 @ addition ) )
!= ( A @ ( A @ addition ) ) )
| ( one = A ) ),
inference(paramod_ordered,[status(thm)],[2821,54]) ).
thf(3023,plain,
! [A: $i] :
( ( ( sk3 @ sk5 )
!= A )
| ( sk3 != A )
| ( one = A ) ),
inference(simp,[status(thm)],[2984]) ).
thf(3033,plain,
( ( ( sk3 @ sk5 )
!= sk3 )
| ( sk3 = one ) ),
inference(simp,[status(thm)],[3023]) ).
thf(1571,plain,
! [A: $i] :
( ( ( sk4 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1505,49]) ).
thf(1572,plain,
! [A: $i] :
( ( ( sk4 @ c @ c @ test )
!= ( A @ test ) )
| ( A @ ( A @ sk5 @ complement ) ) ),
inference(simp,[status(thm)],[1571]) ).
thf(1573,plain,
sk4 @ c @ c @ ( sk4 @ c @ c @ sk5 @ complement ),
inference(pattern_uni,[status(thm)],[1572:[bind(A,$thf( sk4 @ c @ c ))]]) ).
thf(1915,plain,
! [A: $i] :
( ( ( sk4 @ ( sk4 @ c @ multiplication ) )
!= ( A @ ( one @ multiplication ) ) )
| ( zero = A ) ),
inference(paramod_ordered,[status(thm)],[1600,45]) ).
thf(1945,plain,
! [A: $i] :
( ( sk4 != A )
| ( ( sk4 @ c )
!= one )
| ( zero = A ) ),
inference(simp,[status(thm)],[1915]) ).
thf(1970,plain,
( ( ( sk4 @ c )
!= one )
| ( sk4 = zero ) ),
inference(simp,[status(thm)],[1945]) ).
thf(1310,plain,
! [B: $i,A: $i] :
( ( ( A @ c )
!= ( sk4 @ c ) )
| ( B != zero )
| ~ ( B @ ( A @ complement ) )
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[66,145]) ).
thf(1311,plain,
! [A: $i] :
( ( A != zero )
| ~ ( A @ ( sk4 @ complement ) )
| ~ ( sk4 @ test ) ),
inference(pattern_uni,[status(thm)],[1310:[bind(A,$thf( sk4 ))]]) ).
thf(1379,plain,
( ~ ( zero @ ( sk4 @ complement ) )
| ~ ( sk4 @ test ) ),
inference(simp,[status(thm)],[1311]) ).
thf(1508,plain,
( ~ ( zero @ ( sk4 @ complement ) )
| ~ $true ),
inference(rewrite,[status(thm)],[1379,23]) ).
thf(1509,plain,
~ ( zero @ ( sk4 @ complement ) ),
inference(simp,[status(thm)],[1508]) ).
thf(1522,plain,
! [A: $i] :
( ( ( A @ ( A @ sk5 @ complement ) )
!= ( zero @ ( sk4 @ complement ) ) )
| ~ $true
| ~ ( A @ test ) ),
inference(paramod_ordered,[status(thm)],[49,1509]) ).
thf(1523,plain,
! [A: $i] :
( ( ( A @ ( A @ sk5 @ complement ) )
!= ( zero @ ( sk4 @ complement ) ) )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[1522]) ).
thf(1537,plain,
! [A: $i] :
( ( A != zero )
| ( ( A @ sk5 )
!= sk4 )
| ~ ( A @ test ) ),
inference(simp,[status(thm)],[1523]) ).
thf(1540,plain,
( ( ( zero @ sk5 )
!= sk4 )
| ~ ( zero @ test ) ),
inference(simp,[status(thm)],[1537]) ).
thf(12128,plain,
( ( ( sk3 @ test )
!= ( one @ test ) )
| ( ( one @ sk5 )
!= sk3 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[27,8641]) ).
thf(12129,plain,
( ( ( sk3 @ test )
!= ( one @ test ) )
| ( ( one @ sk5 )
!= sk3 ) ),
inference(simp,[status(thm)],[12128]) ).
thf(12142,plain,
( ( sk3 != one )
| ( ( one @ sk5 )
!= sk3 ) ),
inference(simp,[status(thm)],[12129]) ).
thf(297,plain,
zero @ ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) @ leq ),
inference(rewrite,[status(thm)],[25,33]) ).
thf(5940,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[297,102]) ).
thf(5941,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) @ leq ) )
!= ( B @ ( A @ leq ) ) )
| ( ( B @ ( A @ addition ) )
= B ) ),
inference(simp,[status(thm)],[5940]) ).
thf(5942,plain,
( ( zero @ ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) @ addition ) )
= zero ),
inference(pattern_uni,[status(thm)],[5941:[bind(A,$thf( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) )),bind(B,$thf( zero ))]]) ).
thf(10440,plain,
( ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) )
= zero ),
inference(rewrite,[status(thm)],[5942,93]) ).
thf(10560,plain,
( ( ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[10440,6564]) ).
thf(10561,plain,
( ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) ) ),
inference(simp,[status(thm)],[10560]) ).
thf(10621,plain,
( ( ( sk2 @ ( sk1 @ addition ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[10561]) ).
thf(10676,plain,
( ( sk2 @ ( sk1 @ addition ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) ) ),
inference(simp,[status(thm)],[10621]) ).
thf(173,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ~ ( zero @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[45,24]) ).
thf(180,plain,
! [A: $i] :
( ( A
!= ( sk4 @ c ) )
| ( ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) )
!= one )
| ~ ( zero @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[173]) ).
thf(188,plain,
( ( ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) )
!= one )
| ~ ( zero @ ( sk4 @ c @ leq ) ) ),
inference(simp,[status(thm)],[180]) ).
thf(207,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ( zero @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[84,25]) ).
thf(217,plain,
! [A: $i] :
( ( ( sk4 @ c )
!= one )
| ( A
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( zero @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[207]) ).
thf(225,plain,
( ( ( sk4 @ c )
!= one )
| ( zero @ ( sk1 @ ( sk3 @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[217]) ).
thf(6716,plain,
( ( ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) )
!= ( sk3 @ sk5 @ ( sk3 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[1597,6564]) ).
thf(6717,plain,
( ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) )
!= ( sk3 @ sk5 @ ( sk3 @ multiplication ) ) ),
inference(simp,[status(thm)],[6716]) ).
thf(6737,plain,
( ( ( sk2 @ ( sk1 @ addition ) )
!= ( sk3 @ sk5 ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[6717]) ).
thf(6763,plain,
( ( sk2 @ ( sk1 @ addition ) )
!= ( sk3 @ sk5 ) ),
inference(simp,[status(thm)],[6737]) ).
thf(10929,plain,
( ( ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ multiplication ) @ ( sk3 @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[10811,6564]) ).
thf(10930,plain,
( ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ multiplication ) @ ( sk3 @ multiplication ) ) ),
inference(simp,[status(thm)],[10929]) ).
thf(11013,plain,
( ( ( sk2 @ ( sk1 @ addition ) )
!= ( sk4 @ c @ ( sk2 @ multiplication ) ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[10930]) ).
thf(11026,plain,
( ( sk2 @ ( sk1 @ addition ) )
!= ( sk4 @ c @ ( sk2 @ multiplication ) ) ),
inference(simp,[status(thm)],[11013]) ).
thf(19,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(94,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)],[19]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[94]) ).
thf(96,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) )
= ( C @ ( B @ addition ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[95]) ).
thf(1528,plain,
( ( ( zero @ ( sk4 @ complement ) )
!= ( sk3 @ c @ ( sk3 @ complement ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1069,1509]) ).
thf(1529,plain,
( ( zero @ ( sk4 @ complement ) )
!= ( sk3 @ c @ ( sk3 @ complement ) ) ),
inference(simp,[status(thm)],[1528]) ).
thf(1530,plain,
( ( ( sk3 @ c )
!= zero )
| ( sk4 != sk3 ) ),
inference(simp,[status(thm)],[1529]) ).
thf(129,plain,
( ( ( zero @ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
!= ( zero @ ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[25,24]) ).
thf(130,plain,
( ( zero @ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) )
!= ( zero @ ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(134,plain,
( ( zero != zero )
| ( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) ) ),
inference(simp,[status(thm)],[130]) ).
thf(140,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ ( sk3 @ multiplication ) @ multiplication ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(539,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk3 @ multiplication ) ) ),
inference(rewrite,[status(thm)],[140,33]) ).
thf(540,plain,
( ( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) ) )
| ( sk3 != sk3 ) ),
inference(simp,[status(thm)],[539]) ).
thf(601,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) ) ),
inference(simp,[status(thm)],[540]) ).
thf(619,plain,
( ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( ( sk2 @ ( sk1 @ addition ) )
!= sk1 ) ),
inference(simp,[status(thm)],[601]) ).
thf(654,plain,
( ( sk2 @ ( sk1 @ addition ) )
!= sk1 ),
inference(simp,[status(thm)],[619]) ).
thf(1807,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk3 @ sk5 @ ( sk3 @ multiplication ) ) )
| ( A = zero ) ),
inference(paramod_ordered,[status(thm)],[45,1597]) ).
thf(1856,plain,
! [A: $i] :
( ( A
!= ( sk3 @ sk5 ) )
| ( sk3 != one )
| ( A = zero ) ),
inference(simp,[status(thm)],[1807]) ).
thf(1857,plain,
( ( sk3 != one )
| ( ( sk3 @ sk5 )
= zero ) ),
inference(simp,[status(thm)],[1856]) ).
thf(19225,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[10057,75]) ).
thf(19226,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[19225]) ).
thf(19227,plain,
( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[19226:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c @ c @ sk5 ))]]) ).
thf(9748,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1449,76]) ).
thf(9749,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[9748]) ).
thf(9750,plain,
( ( sk3 @ c @ c @ ( sk3 @ c @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[9749:[bind(A,$thf( sk3 @ c @ c @ c )),bind(B,$thf( sk3 @ c @ c ))]]) ).
thf(2219,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ ( sk3 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1088,75]) ).
thf(2220,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ ( sk3 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2219]) ).
thf(2221,plain,
( ( sk3 @ c @ c @ ( sk3 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2220:[bind(A,$thf( sk3 @ c @ c )),bind(B,$thf( sk3 @ c ))]]) ).
thf(7101,plain,
( ( ( sk3 @ c )
!= ( sk3 @ c ) )
| ( zero @ test )
| ( sk3 != one ) ),
inference(paramod_ordered,[status(thm)],[2082,1083]) ).
thf(7102,plain,
( ( zero @ test )
| ( sk3 != one ) ),
inference(pattern_uni,[status(thm)],[7101:[]]) ).
thf(7644,plain,
( ( ( zero @ test )
!= ( zero @ test ) )
| ( ( zero @ sk5 )
!= sk4 )
| ~ $true
| ( sk3 != one ) ),
inference(paramod_ordered,[status(thm)],[7102,1540]) ).
thf(7645,plain,
( ( ( zero @ test )
!= ( zero @ test ) )
| ( ( zero @ sk5 )
!= sk4 )
| ( sk3 != one ) ),
inference(simp,[status(thm)],[7644]) ).
thf(7646,plain,
( ( ( zero @ sk5 )
!= sk4 )
| ( sk3 != one ) ),
inference(pattern_uni,[status(thm)],[7645:[]]) ).
thf(10208,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1573,76]) ).
thf(10209,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[10208]) ).
thf(10210,plain,
( ( sk4 @ c @ c @ sk5 @ ( sk4 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[10209:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c @ c @ sk5 ))]]) ).
thf(15975,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ sk5 @ ( sk4 @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[10210,57]) ).
thf(15976,plain,
( ( sk4 @ c @ c @ ( sk4 @ c @ c @ sk5 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[15975:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c @ c @ sk5 ))]]) ).
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(34,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(177,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ( zero @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[45,26]) ).
thf(183,plain,
! [A: $i] :
( ( A
!= ( sk4 @ c ) )
| ( ( sk2 @ ( sk3 @ multiplication ) )
!= one )
| ( zero @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[177]) ).
thf(191,plain,
( ( ( sk2 @ ( sk3 @ multiplication ) )
!= one )
| ( zero @ ( sk4 @ c @ leq ) ) ),
inference(simp,[status(thm)],[183]) ).
thf(18942,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[10054,76]) ).
thf(18943,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[18942]) ).
thf(18944,plain,
( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[18943:[bind(A,$thf( sk4 @ c @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c @ c ))]]) ).
thf(18998,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[10054,75]) ).
thf(18999,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[18998]) ).
thf(19000,plain,
( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[18999:[bind(A,$thf( sk4 @ c @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c @ c ))]]) ).
thf(1592,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[777,74]) ).
thf(1593,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ ( sk4 @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1592]) ).
thf(1594,plain,
( ( sk4 @ sk5 @ ( sk4 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1593:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ sk5 ))]]) ).
thf(1687,plain,
! [A: $i] :
( ( ( sk4 @ sk5 @ ( sk4 @ multiplication ) )
!= ( one @ ( A @ multiplication ) ) )
| ( zero = A ) ),
inference(paramod_ordered,[status(thm)],[1594,84]) ).
thf(1744,plain,
! [A: $i] :
( ( ( sk4 @ sk5 )
!= one )
| ( sk4 != A )
| ( zero = A ) ),
inference(simp,[status(thm)],[1687]) ).
thf(1765,plain,
( ( ( sk4 @ sk5 )
!= one )
| ( sk4 = zero ) ),
inference(simp,[status(thm)],[1744]) ).
thf(3139,plain,
! [A: $i] :
( ( ( sk3 @ ( sk3 @ c @ addition ) )
!= ( A @ ( zero @ addition ) ) )
| ( one = A ) ),
inference(paramod_ordered,[status(thm)],[2870,941]) ).
thf(3213,plain,
! [A: $i] :
( ( sk3 != A )
| ( ( sk3 @ c )
!= zero )
| ( one = A ) ),
inference(simp,[status(thm)],[3139]) ).
thf(3223,plain,
( ( ( sk3 @ c )
!= zero )
| ( sk3 = one ) ),
inference(simp,[status(thm)],[3213]) ).
thf(174,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( zero @ ( sk4 @ c @ ( A @ multiplication ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[45,25]) ).
thf(179,plain,
! [A: $i] :
( ( A != sk1 )
| ( sk3 != one )
| ( zero @ ( sk4 @ c @ ( A @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[174]) ).
thf(187,plain,
( ( sk3 != one )
| ( zero @ ( sk4 @ c @ ( sk1 @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[179]) ).
thf(205,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ~ ( zero @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[84,24]) ).
thf(211,plain,
! [A: $i] :
( ( ( sk4 @ c )
!= one )
| ( A
!= ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) ) )
| ~ ( zero @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[205]) ).
thf(219,plain,
( ( ( sk4 @ c )
!= one )
| ~ ( zero @ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[211]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ multiplication ) @ c )
= ( B @ c @ ( A @ c @ addition ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_deMorgan2) ).
thf(79,plain,
! [A: $i,B: $i] :
( ( ( B @ test )
& ( A @ test ) )
=> ( ( B @ ( A @ multiplication ) @ c )
= ( B @ c @ ( A @ c @ addition ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) @ c )
= ( B @ c @ ( A @ c @ addition ) ) )
| ~ ( B @ test )
| ~ ( A @ test ) ),
inference(cnf,[status(esa)],[79]) ).
thf(81,plain,
! [B: $i,A: $i] :
( ~ ( B @ test )
| ~ ( A @ test )
| ( ( B @ c @ ( A @ c @ addition ) )
= ( B @ ( A @ multiplication ) @ c ) ) ),
inference(lifteq,[status(thm)],[80]) ).
thf(38,plain,
! [A: $i] :
( ( ( A @ c )
= zero )
| ( A @ test ) ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
! [A: $i] :
( ( A @ test )
| ( ( A @ c )
= zero ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(10017,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1570,75]) ).
thf(10018,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[10017]) ).
thf(10019,plain,
( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[10018:[bind(A,$thf( sk4 @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c ))]]) ).
thf(2969,plain,
! [A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( sk3 @ sk5 @ ( sk3 @ addition ) ) )
| ( A = one ) ),
inference(paramod_ordered,[status(thm)],[93,2821]) ).
thf(3005,plain,
! [A: $i] :
( ( ( sk3 @ sk5 )
!= zero )
| ( A != sk3 )
| ( A = one ) ),
inference(simp,[status(thm)],[2969]) ).
thf(3038,plain,
( ( ( sk3 @ sk5 )
!= zero )
| ( sk3 = one ) ),
inference(simp,[status(thm)],[3005]) ).
thf(10202,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1573,74]) ).
thf(10203,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[10202]) ).
thf(10204,plain,
( ( sk4 @ c @ c @ sk5 @ ( sk4 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[10203:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c @ c @ sk5 ))]]) ).
thf(19005,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10054,51]) ).
thf(19006,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[19005]) ).
thf(19007,plain,
sk4 @ c @ c @ c @ c @ test,
inference(pattern_uni,[status(thm)],[19006:[bind(A,$thf( sk4 @ c @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c @ c ))]]) ).
thf(11586,plain,
! [A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( A != sk4 ) ),
inference(paramod_ordered,[status(thm)],[54,11568]) ).
thf(11623,plain,
( ( sk4 != sk2 )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[11586]) ).
thf(18147,plain,
( ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( ( sk2 @ ( sk1 @ addition ) )
!= sk2 ) ),
inference(simp,[status(thm)],[892]) ).
thf(18448,plain,
( ( sk2 @ ( sk1 @ addition ) )
!= sk2 ),
inference(simp,[status(thm)],[18147]) ).
thf(6043,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ sk5 @ ( sk3 @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[2829,57]) ).
thf(6044,plain,
( ( sk3 @ c @ ( sk3 @ c @ sk5 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[6043:[bind(A,$thf( sk3 @ c )),bind(B,$thf( sk3 @ c @ sk5 ))]]) ).
thf(6801,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ~ ( sk3 @ ( one @ complement ) )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[76,6666]) ).
thf(6802,plain,
( ~ ( sk3 @ ( one @ complement ) )
| ~ ( sk1 @ ( sk2 @ complement ) ) ),
inference(pattern_uni,[status(thm)],[6801:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(18597,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ c @ ( sk3 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[9828,76]) ).
thf(18598,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ c @ ( sk3 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[18597]) ).
thf(18599,plain,
( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[18598:[bind(A,$thf( sk3 @ c @ c @ c @ c )),bind(B,$thf( sk3 @ c @ c @ c ))]]) ).
thf(2903,plain,
! [A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( sk4 @ sk5 @ ( sk4 @ addition ) ) )
| ( A = one ) ),
inference(paramod_ordered,[status(thm)],[54,2806]) ).
thf(2928,plain,
! [A: $i] :
( ( A
!= ( sk4 @ sk5 ) )
| ( A != sk4 )
| ( A = one ) ),
inference(simp,[status(thm)],[2903]) ).
thf(2949,plain,
( ( ( sk4 @ sk5 )
!= sk4 )
| ( sk4 = one ) ),
inference(simp,[status(thm)],[2928]) ).
thf(15420,plain,
( ( sk4 @ sk5 )
!= sk4 ),
inference(simplifyReflect,[status(thm)],[2949,5903]) ).
thf(6708,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) ) )
| ( zero != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[75,6564]) ).
thf(6709,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) ) )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[6708]) ).
thf(6710,plain,
~ ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ complement ) ),
inference(pattern_uni,[status(thm)],[6709:[bind(A,$thf( sk2 @ ( sk1 @ addition ) )),bind(B,$thf( sk3 ))]]) ).
thf(2863,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ ( sk3 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[1088,76]) ).
thf(2864,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ ( sk3 @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ addition ) )
= one ) ),
inference(simp,[status(thm)],[2863]) ).
thf(2865,plain,
( ( sk3 @ c @ ( sk3 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[2864:[bind(A,$thf( sk3 @ c @ c )),bind(B,$thf( sk3 @ c ))]]) ).
thf(6352,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[2865,57]) ).
thf(6353,plain,
( ( sk3 @ c @ c @ ( sk3 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[6352:[bind(A,$thf( sk3 @ c @ c )),bind(B,$thf( sk3 @ c ))]]) ).
thf(2137,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1091,75]) ).
thf(2138,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[2137]) ).
thf(2139,plain,
( ( sk3 @ c @ ( sk3 @ c @ sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[2138:[bind(A,$thf( sk3 @ c )),bind(B,$thf( sk3 @ c @ sk5 ))]]) ).
thf(209,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk3 @ multiplication ) @ multiplication ) ) )
| ( zero @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[84,26]) ).
thf(215,plain,
! [A: $i] :
( ( ( sk4 @ c )
!= one )
| ( A
!= ( sk2 @ ( sk3 @ multiplication ) ) )
| ( zero @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[209]) ).
thf(223,plain,
( ( ( sk4 @ c )
!= one )
| ( zero @ ( sk2 @ ( sk3 @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[215]) ).
thf(2739,plain,
( ( ( sk3 @ c @ test )
!= ( zero @ test ) )
| ( ( zero @ sk5 )
!= sk4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1083,1540]) ).
thf(2740,plain,
( ( ( sk3 @ c @ test )
!= ( zero @ test ) )
| ( ( zero @ sk5 )
!= sk4 ) ),
inference(simp,[status(thm)],[2739]) ).
thf(2752,plain,
( ( ( sk3 @ c )
!= zero )
| ( ( zero @ sk5 )
!= sk4 ) ),
inference(simp,[status(thm)],[2740]) ).
thf(25430,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk5 @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( zero != zero )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[2117,329]) ).
thf(25431,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk3 @ ( sk3 @ sk5 @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[25430]) ).
thf(25432,plain,
! [A: $i] :
( ( A @ ( sk3 @ multiplication ) @ ( sk3 @ sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[25431:[bind(A,$thf( sk3 @ sk5 )),bind(B,$thf( sk3 )),bind(C,$thf( C ))]]) ).
thf(25935,plain,
! [A: $i] :
( ( A @ ( sk3 @ multiplication ) @ ( sk3 @ sk5 @ multiplication ) )
= zero ),
inference(simp,[status(thm)],[25432]) ).
thf(626,plain,
! [A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( ( sk4 @ c @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[54,601]) ).
thf(647,plain,
! [A: $i] :
( ( A != sk2 )
| ( A != sk1 )
| ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[626]) ).
thf(653,plain,
sk2 != sk1,
inference(simp,[status(thm)],[647]) ).
thf(620,plain,
! [A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( ( sk4 @ c @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk1 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[93,601]) ).
thf(635,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A != sk1 )
| ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[620]) ).
thf(658,plain,
sk2 != zero,
inference(simp,[status(thm)],[635]) ).
thf(6190,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ ( sk4 @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[2854,57]) ).
thf(6191,plain,
( ( sk4 @ c @ c @ ( sk4 @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[6190:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c ))]]) ).
thf(4112,plain,
( ( ( sk3 @ sk5 )
!= ( sk3 @ sk5 ) )
| ( sk3 @ ( zero @ complement ) )
| ( sk3 != one ) ),
inference(paramod_ordered,[status(thm)],[1857,774]) ).
thf(4113,plain,
( ( sk3 @ ( zero @ complement ) )
| ( sk3 != one ) ),
inference(pattern_uni,[status(thm)],[4112:[]]) ).
thf(9792,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1449,75]) ).
thf(9793,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[9792]) ).
thf(9794,plain,
( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[9793:[bind(A,$thf( sk3 @ c @ c @ c )),bind(B,$thf( sk3 @ c @ c ))]]) ).
thf(11062,plain,
! [A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( A
!= ( sk4 @ c @ ( sk2 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[54,11026]) ).
thf(11105,plain,
( ( sk4 @ c @ ( sk2 @ multiplication ) @ ( sk4 @ c @ ( sk2 @ multiplication ) @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) ),
inference(simp,[status(thm)],[11062]) ).
thf(25097,plain,
( ( sk4 @ c @ ( sk4 @ c @ addition ) @ ( sk2 @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) ) ),
inference(rewrite,[status(thm)],[11105,96]) ).
thf(18472,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( sk2 != one )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[76,18448]) ).
thf(18473,plain,
( ( sk2 != one )
| ~ ( sk1 @ ( sk2 @ complement ) ) ),
inference(pattern_uni,[status(thm)],[18472:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(2830,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( sk1 != one )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[76,654]) ).
thf(2831,plain,
( ( sk1 != one )
| ~ ( sk1 @ ( sk2 @ complement ) ) ),
inference(pattern_uni,[status(thm)],[2830:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(18866,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[9831,75]) ).
thf(18867,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[18866]) ).
thf(18868,plain,
( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ c @ sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[18867:[bind(A,$thf( sk3 @ c @ c @ c )),bind(B,$thf( sk3 @ c @ c @ c @ sk5 ))]]) ).
thf(2890,plain,
! [A: $i] :
( ( ( sk4 @ sk5 @ ( sk4 @ addition ) )
!= ( zero @ ( A @ addition ) ) )
| ( one = A ) ),
inference(paramod_ordered,[status(thm)],[2806,93]) ).
thf(2922,plain,
! [A: $i] :
( ( ( sk4 @ sk5 )
!= zero )
| ( sk4 != A )
| ( one = A ) ),
inference(simp,[status(thm)],[2890]) ).
thf(2946,plain,
( ( ( sk4 @ sk5 )
!= zero )
| ( sk4 = one ) ),
inference(simp,[status(thm)],[2922]) ).
thf(13320,plain,
( ( sk4 @ sk5 )
!= zero ),
inference(simplifyReflect,[status(thm)],[2946,5903]) ).
thf(2889,plain,
! [A: $i] :
( ( ( A @ ( zero @ addition ) )
!= ( sk4 @ sk5 @ ( sk4 @ addition ) ) )
| ( A = one ) ),
inference(paramod_ordered,[status(thm)],[941,2806]) ).
thf(2919,plain,
! [A: $i] :
( ( A
!= ( sk4 @ sk5 ) )
| ( sk4 != zero )
| ( A = one ) ),
inference(simp,[status(thm)],[2889]) ).
thf(2944,plain,
( ( sk4 != zero )
| ( ( sk4 @ sk5 )
= one ) ),
inference(simp,[status(thm)],[2919]) ).
thf(13133,plain,
( ( ( sk4 @ sk5 )
!= ( sk3 @ sk5 ) )
| ( one != one )
| ( sk4 != zero ) ),
inference(paramod_ordered,[status(thm)],[2944,4143]) ).
thf(13134,plain,
( ( ( sk4 @ sk5 )
!= ( sk3 @ sk5 ) )
| ( sk4 != zero ) ),
inference(simp,[status(thm)],[13133]) ).
thf(13185,plain,
( ( sk4 != sk3 )
| ( sk4 != zero ) ),
inference(simp,[status(thm)],[13134]) ).
thf(307,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
!= ( D @ ( one @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= D ) ),
inference(paramod_ordered,[status(thm)],[33,45]) ).
thf(325,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( C != D )
| ( ( B @ ( A @ multiplication ) )
!= one )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= D ) ),
inference(simp,[status(thm)],[307]) ).
thf(331,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= one )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= C ) ),
inference(simp,[status(thm)],[325]) ).
thf(19723,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[18599,57]) ).
thf(19724,plain,
( ( sk3 @ c @ c @ c @ c @ ( sk3 @ c @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[19723:[bind(A,$thf( sk3 @ c @ c @ c @ c )),bind(B,$thf( sk3 @ c @ c @ c ))]]) ).
thf(9889,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ ( sk3 @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1452,74]) ).
thf(9890,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ ( sk3 @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[9889]) ).
thf(9891,plain,
( ( sk3 @ c @ c @ sk5 @ ( sk3 @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[9890:[bind(A,$thf( sk3 @ c @ c )),bind(B,$thf( sk3 @ c @ c @ sk5 ))]]) ).
thf(13594,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ ( sk3 @ c @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[9750,57]) ).
thf(13595,plain,
( ( sk3 @ c @ c @ c @ ( sk3 @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[13594:[bind(A,$thf( sk3 @ c @ c @ c )),bind(B,$thf( sk3 @ c @ c ))]]) ).
thf(18660,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ c @ ( sk3 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9828,51]) ).
thf(18661,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ c @ ( sk3 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( A @ test ) ),
inference(simp,[status(thm)],[18660]) ).
thf(18662,plain,
sk3 @ c @ c @ c @ c @ test,
inference(pattern_uni,[status(thm)],[18661:[bind(A,$thf( sk3 @ c @ c @ c @ c )),bind(B,$thf( sk3 @ c @ c @ c ))]]) ).
thf(206,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk1 @ ( sk3 @ multiplication ) ) )
| ( zero @ ( sk4 @ c @ ( A @ multiplication ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[84,25]) ).
thf(210,plain,
! [A: $i] :
( ( sk1 != one )
| ( A != sk3 )
| ( zero @ ( sk4 @ c @ ( A @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[206]) ).
thf(218,plain,
( ( sk1 != one )
| ( zero @ ( sk4 @ c @ ( sk3 @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[210]) ).
thf(25698,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ sk5 @ ( sk4 @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( zero != zero )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1594,329]) ).
thf(25699,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk4 @ sk5 @ ( sk4 @ multiplication ) )
!= ( B @ ( A @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[25698]) ).
thf(25700,plain,
! [A: $i] :
( ( A @ ( sk4 @ sk5 @ multiplication ) @ ( sk4 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[25699:[bind(A,$thf( sk4 )),bind(B,$thf( sk4 @ sk5 )),bind(C,$thf( C ))]]) ).
thf(25939,plain,
! [A: $i] :
( ( A @ ( sk4 @ sk5 @ multiplication ) @ ( sk4 @ multiplication ) )
= zero ),
inference(simp,[status(thm)],[25700]) ).
thf(2970,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ sk5 @ ( sk3 @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[2821,57]) ).
thf(2971,plain,
( ( sk3 @ ( sk3 @ sk5 @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[2970:[bind(A,$thf( sk3 )),bind(B,$thf( sk3 @ sk5 ))]]) ).
thf(11225,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) ) )
| ( zero != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[74,6576]) ).
thf(11226,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ ( sk3 @ multiplication ) ) )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[11225]) ).
thf(11227,plain,
~ ( sk3 @ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ complement ) ),
inference(pattern_uni,[status(thm)],[11226:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ))]]) ).
thf(1605,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1091,74]) ).
thf(1606,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ ( sk3 @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( B @ ( A @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[1605]) ).
thf(1607,plain,
( ( sk3 @ c @ sk5 @ ( sk3 @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1606:[bind(A,$thf( sk3 @ c )),bind(B,$thf( sk3 @ c @ sk5 ))]]) ).
thf(11495,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ( zero != zero )
| ~ ( A @ ( B @ complement ) ) ),
inference(paramod_ordered,[status(thm)],[75,11405]) ).
thf(11496,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ multiplication ) )
!= ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) ) )
| ~ ( A @ ( B @ complement ) ) ),
inference(simp,[status(thm)],[11495]) ).
thf(11497,plain,
~ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ complement ) ),
inference(pattern_uni,[status(thm)],[11496:[bind(A,$thf( sk4 @ c )),bind(B,$thf( sk2 @ ( sk1 @ addition ) ))]]) ).
thf(7138,plain,
( ( ( sk3 @ c )
!= ( sk3 @ c ) )
| ( zero != zero )
| ( sk4 != sk3 )
| ( sk3 != one ) ),
inference(paramod_ordered,[status(thm)],[2082,1530]) ).
thf(7139,plain,
( ( ( sk3 @ c )
!= ( sk3 @ c ) )
| ( sk4 != sk3 )
| ( sk3 != one ) ),
inference(simp,[status(thm)],[7138]) ).
thf(7140,plain,
( ( sk4 != sk3 )
| ( sk3 != one ) ),
inference(pattern_uni,[status(thm)],[7139:[]]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ addition ) @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(7152,plain,
( ( ( sk3 @ c )
!= ( sk3 @ c ) )
| ( zero @ c @ test )
| ( sk3 != one ) ),
inference(paramod_ordered,[status(thm)],[2082,1428]) ).
thf(7153,plain,
( ( zero @ c @ test )
| ( sk3 != one ) ),
inference(pattern_uni,[status(thm)],[7152:[]]) ).
thf(172,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) @ ( sk3 @ multiplication ) ) )
| ~ ( zero @ ( sk4 @ c @ ( A @ multiplication ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[45,24]) ).
thf(182,plain,
! [A: $i] :
( ( A
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( sk3 != one )
| ~ ( zero @ ( sk4 @ c @ ( A @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[172]) ).
thf(190,plain,
( ( sk3 != one )
| ~ ( zero @ ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[182]) ).
thf(11452,plain,
( ( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk4 @ c @ ( sk4 @ c @ c @ multiplication ) ) )
| ( zero != zero ) ),
inference(paramod_ordered,[status(thm)],[1656,11405]) ).
thf(11453,plain,
( ( sk4 @ c @ ( sk2 @ ( sk1 @ addition ) @ multiplication ) )
!= ( sk4 @ c @ ( sk4 @ c @ c @ multiplication ) ) ),
inference(simp,[status(thm)],[11452]) ).
thf(11526,plain,
( ( ( sk4 @ c )
!= ( sk4 @ c ) )
| ( ( sk2 @ ( sk1 @ addition ) )
!= ( sk4 @ c @ c ) ) ),
inference(simp,[status(thm)],[11453]) ).
thf(11563,plain,
( ( sk2 @ ( sk1 @ addition ) )
!= ( sk4 @ c @ c ) ),
inference(simp,[status(thm)],[11526]) ).
thf(10248,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1573,75]) ).
thf(10249,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ ( sk4 @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[10248]) ).
thf(10250,plain,
( ( sk4 @ c @ c @ ( sk4 @ c @ c @ sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[10249:[bind(A,$thf( sk4 @ c @ c )),bind(B,$thf( sk4 @ c @ c @ sk5 ))]]) ).
thf(9935,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ ( sk3 @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[1452,75]) ).
thf(9936,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ ( sk3 @ c @ c @ sk5 @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[9935]) ).
thf(9937,plain,
( ( sk3 @ c @ c @ ( sk3 @ c @ c @ sk5 @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[9936:[bind(A,$thf( sk3 @ c @ c )),bind(B,$thf( sk3 @ c @ c @ sk5 ))]]) ).
thf(21652,plain,
! [B: $i,A: $i] :
( ( ( sk4 @ c @ c @ c @ ( sk4 @ c @ c @ c @ c @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= one ) ),
inference(paramod_ordered,[status(thm)],[18944,57]) ).
thf(21653,plain,
( ( sk4 @ c @ c @ c @ c @ ( sk4 @ c @ c @ c @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[21652:[bind(A,$thf( sk4 @ c @ c @ c @ c )),bind(B,$thf( sk4 @ c @ c @ c ))]]) ).
thf(10757,plain,
! [A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) )
| ( A
!= ( sk4 @ c @ ( sk1 @ multiplication ) ) ) ),
inference(paramod_ordered,[status(thm)],[54,10676]) ).
thf(10790,plain,
( ( sk4 @ c @ ( sk1 @ multiplication ) @ ( sk4 @ c @ ( sk1 @ multiplication ) @ addition ) )
!= ( sk2 @ ( sk1 @ addition ) ) ),
inference(simp,[status(thm)],[10757]) ).
thf(24778,plain,
( ( sk4 @ c @ ( sk4 @ c @ addition ) @ ( sk1 @ multiplication ) )
!= ( sk2 @ ( sk1 @ addition ) ) ),
inference(rewrite,[status(thm)],[10790,96]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) @ c )
= ( B @ c @ ( A @ c @ multiplication ) ) )
| ~ ( B @ test )
| ~ ( A @ test ) ),
inference(cnf,[status(esa)],[88]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ~ ( B @ test )
| ~ ( A @ test )
| ( ( B @ ( A @ addition ) @ c )
= ( B @ c @ ( A @ c @ multiplication ) ) ) ),
inference(lifteq,[status(thm)],[89]) ).
thf(2747,plain,
( ( ( sk4 @ test )
!= ( zero @ test ) )
| ( ( zero @ sk5 )
!= sk4 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,1540]) ).
thf(2748,plain,
( ( ( sk4 @ test )
!= ( zero @ test ) )
| ( ( zero @ sk5 )
!= sk4 ) ),
inference(simp,[status(thm)],[2747]) ).
thf(2754,plain,
( ( sk4 != zero )
| ( ( zero @ sk5 )
!= sk4 ) ),
inference(simp,[status(thm)],[2748]) ).
thf(18653,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ c @ ( sk3 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ~ $true
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[9828,75]) ).
thf(18654,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ c @ c @ c @ c @ ( sk3 @ c @ c @ c @ complement ) )
!= ( A @ ( B @ complement ) ) )
| ( ( A @ ( B @ multiplication ) )
= zero ) ),
inference(simp,[status(thm)],[18653]) ).
thf(18655,plain,
( ( sk3 @ c @ c @ c @ c @ ( sk3 @ c @ c @ c @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[18654:[bind(A,$thf( sk3 @ c @ c @ c @ c )),bind(B,$thf( sk3 @ c @ c @ c ))]]) ).
thf(36121,plain,
$false,
inference(e,[status(thm)],[892,26456,941,8646,777,88,20683,1083,6576,2117,15190,11571,2854,6017,2114,22666,1671,19174,6764,8635,11399,11303,6640,4496,11568,2082,37,25938,18585,8603,10022,42,23675,5903,52,6552,18801,9828,14440,189,46,93,57,78,11404,2829,4072,2893,84,6562,9897,9970,221,774,10057,7213,1600,1104,7688,74,18928,1074,10811,85,9797,220,8630,102,17831,19158,1091,23671,11439,192,4493,2132,33,1570,28,21,9745,2200,3144,1656,682,6666,3033,1573,97,6556,329,6995,1970,1540,3119,12142,10676,1096,188,225,6763,11026,22618,96,1530,654,1857,19227,16997,9750,23629,2221,7646,8641,15976,34,45,64,296,601,191,2806,18944,19000,27,54,3051,49,1765,1428,3223,187,219,81,76,39,10019,3038,10204,2824,19007,11623,91,66,18448,6044,6802,18599,15420,6710,6353,18815,1594,9975,2139,223,2752,25935,653,658,6191,1509,7102,145,6564,4113,9794,25097,18473,2821,2831,18868,67,2224,1452,13320,13185,31,331,19724,9891,4143,43,13595,2865,87,2870,18662,218,104,1674,40,25939,1101,55,2971,23,2944,75,58,11405,11227,1607,82,11497,10210,7140,36,7153,51,190,10054,11563,10250,30,9937,21653,79,94,10440,1597,24778,4501,1505,90,2754,18655,1088,1449,1069,9831]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE035+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.14/0.41 % Computer : n002.cluster.edu
% 0.14/0.41 % Model : x86_64 x86_64
% 0.14/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.41 % Memory : 8046.5625MB
% 0.14/0.41 % OS : Linux 6.8.0-71-generic
% 0.14/0.41 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 19:18:34 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.85/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/1.19 % [INFO] Parsing done (207ms).
% 1.45/1.21 % [INFO] Running in sequential loop mode.
% 2.23/1.61 % [INFO] eprover registered as external prover.
% 2.23/1.62 % [INFO] Scanning for conjecture ...
% 2.44/1.72 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.44/1.79 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.62/1.83 % [INFO] Problem is first-order (TPTP FOF).
% 2.62/1.83 % [INFO] Type checking passed.
% 2.62/1.84 % [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 ...
% 90.99/19.28 % External prover 'e' found a proof!
% 90.99/19.28 % [INFO] Killing All external provers ...
% 90.99/19.28 % Time passed: 18727ms (effective reasoning time: 18065ms)
% 90.99/19.28 % 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)>
% 90.99/19.28 % Axioms used in derivation (18): test_3, test_4, left_annihilation, right_distributivity, multiplicative_right_identity, test_1, test_deMorgan2, additive_identity, additive_idempotence, additive_associativity, order, additive_commutativity, right_annihilation, test_deMorgan1, test_2, multiplicative_left_identity, multiplicative_associativity, left_distributivity
% 90.99/19.28 % No. of inferences in proof: 704
% 90.99/19.28 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 18727 ms resp. 18065 ms w/o parsing
% 91.98/19.53 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 91.98/19.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------