TSTP Solution File: KLE023+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE023+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n024.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 11:24:50 EDT 2023
% Result : Theorem 177.01s 32.76s
% Output : Refutation 177.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 31
% Syntax : Number of formulae : 781 ( 288 unt; 12 typ; 0 def)
% Number of atoms : 1632 (1153 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 6469 ( 760 ~; 583 |; 25 &;5066 @)
% ( 4 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 7 con; 0-2 aty)
% Number of variables : 843 ( 0 ^; 838 !; 5 ?; 843 :)
% Comments :
%------------------------------------------------------------------------------
thf(test_type,type,
test: $i > $o ).
thf(addition_type,type,
addition: $i > $i > $i ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(c_type,type,
c: $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(one_type,type,
one: $i ).
thf(complement_type,type,
complement: $i > $i > $o ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(sk4_type,type,
sk4: $i > $i ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( test @ B )
& ( test @ C ) )
=> ( ( ( addition @ ( multiplication @ B @ A ) @ ( multiplication @ A @ C ) )
= ( multiplication @ A @ C ) )
=> ( ( addition @ ( multiplication @ A @ ( c @ C ) ) @ ( multiplication @ ( c @ B ) @ A ) )
= ( multiplication @ ( c @ B ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( test @ B )
& ( test @ C ) )
=> ( ( ( addition @ ( multiplication @ B @ A ) @ ( multiplication @ A @ C ) )
= ( multiplication @ A @ C ) )
=> ( ( addition @ ( multiplication @ A @ ( c @ C ) ) @ ( multiplication @ ( c @ B ) @ A ) )
= ( multiplication @ ( c @ B ) @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( test @ B )
& ( test @ C ) )
=> ( ( ( addition @ ( multiplication @ B @ A ) @ ( multiplication @ A @ C ) )
= ( multiplication @ A @ C ) )
=> ( ( addition @ ( multiplication @ A @ ( c @ C ) ) @ ( multiplication @ ( c @ B ) @ A ) )
= ( multiplication @ ( c @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
test @ sk3,
inference(cnf,[status(esa)],[21]) ).
thf(9,axiom,
! [A: $i] :
( ( test @ A )
<=> ? [B: $i] : ( complement @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_1) ).
thf(46,plain,
! [A: $i] :
( ( ( test @ A )
=> ? [B: $i] : ( complement @ B @ A ) )
& ( ? [B: $i] : ( complement @ B @ A )
=> ( test @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(47,plain,
( ! [A: $i] :
( ( test @ A )
=> ? [B: $i] : ( complement @ B @ A ) )
& ! [A: $i] :
( ? [B: $i] : ( complement @ B @ A )
=> ( test @ A ) ) ),
inference(miniscope,[status(thm)],[46]) ).
thf(49,plain,
! [A: $i] :
( ~ ( test @ A )
| ( complement @ ( sk4 @ A ) @ A ) ),
inference(cnf,[status(esa)],[47]) ).
thf(660,plain,
! [A: $i] :
( ( complement @ ( sk4 @ A ) @ A )
| ( ( test @ sk3 )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[24,49]) ).
thf(661,plain,
complement @ ( sk4 @ sk3 ) @ sk3,
inference(pattern_uni,[status(thm)],[660:[bind(A,$thf( sk3 ))]]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( complement @ B @ A )
<=> ( ( ( multiplication @ A @ B )
= zero )
& ( ( multiplication @ B @ A )
= zero )
& ( ( addition @ A @ B )
= one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_2) ).
thf(65,plain,
! [A: $i,B: $i] :
( ( ( complement @ B @ A )
=> ( ( ( multiplication @ A @ B )
= zero )
& ( ( multiplication @ B @ A )
= zero )
& ( ( addition @ A @ B )
= one ) ) )
& ( ( ( ( multiplication @ A @ B )
= zero )
& ( ( multiplication @ B @ A )
= zero )
& ( ( addition @ A @ B )
= one ) )
=> ( complement @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(66,plain,
( ! [A: $i,B: $i] :
( ( complement @ B @ A )
=> ( ( ( multiplication @ A @ B )
= zero )
& ( ( multiplication @ B @ A )
= zero )
& ( ( addition @ A @ B )
= one ) ) )
& ! [A: $i,B: $i] :
( ( ( ( multiplication @ A @ B )
= zero )
& ( ( multiplication @ B @ A )
= zero )
& ( ( addition @ A @ B )
= one ) )
=> ( complement @ B @ A ) ) ),
inference(miniscope,[status(thm)],[65]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ~ ( complement @ B @ A )
| ( ( addition @ A @ B )
= one ) ),
inference(cnf,[status(esa)],[66]) ).
thf(75,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ~ ( complement @ B @ A ) ),
inference(lifteq,[status(thm)],[70]) ).
thf(2558,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( sk4 @ sk3 ) @ sk3 )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[661,75]) ).
thf(2559,plain,
( ( addition @ sk3 @ ( sk4 @ sk3 ) )
= one ),
inference(pattern_uni,[status(thm)],[2558:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 @ sk3 ))]]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(54,plain,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(cnf,[status(esa)],[54]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(3458,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ sk3 @ ( sk4 @ sk3 ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2559,56]) ).
thf(3459,plain,
( ( addition @ ( sk4 @ sk3 ) @ sk3 )
= one ),
inference(pattern_uni,[status(thm)],[3458:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 @ sk3 ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(51,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(52,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(cnf,[status(esa)],[51]) ).
thf(53,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(lifteq,[status(thm)],[52]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
thf(34,plain,
! [A: $i,B: $i,C: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ C @ B ) @ A )
= ( addition @ C @ ( addition @ B @ A ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(322,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ A @ B )
= ( addition @ D @ ( addition @ C @ B ) ) )
| ( ( addition @ A @ A )
!= ( addition @ D @ C ) ) ),
inference(paramod_ordered,[status(thm)],[53,36]) ).
thf(323,plain,
! [B: $i,A: $i] :
( ( addition @ A @ ( addition @ A @ B ) )
= ( addition @ A @ B ) ),
inference(pattern_uni,[status(thm)],[322:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( A ))]]) ).
thf(50120,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ one )
= ( addition @ A @ B ) )
| ( ( addition @ ( sk4 @ sk3 ) @ sk3 )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3459,323]) ).
thf(50121,plain,
( ( addition @ ( sk4 @ sk3 ) @ sk3 )
= ( addition @ ( sk4 @ sk3 ) @ one ) ),
inference(pattern_uni,[status(thm)],[50120:[bind(A,$thf( sk4 @ sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(54432,plain,
( ( addition @ ( sk4 @ sk3 ) @ one )
= one ),
inference(rewrite,[status(thm)],[50121,3459]) ).
thf(54446,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( sk4 @ sk3 ) @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54432,56]) ).
thf(54447,plain,
( ( addition @ one @ ( sk4 @ sk3 ) )
= one ),
inference(pattern_uni,[status(thm)],[54446:[bind(A,$thf( sk4 @ sk3 )),bind(B,$thf( one ))]]) ).
thf(18,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(88,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(89,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(cnf,[status(esa)],[88]) ).
thf(90,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(lifteq,[status(thm)],[89]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( test @ A )
=> ( ( ( c @ A )
= B )
<=> ( complement @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( test @ A )
=> ( ( ( ( c @ A )
= B )
=> ( complement @ A @ B ) )
& ( ( complement @ A @ B )
=> ( ( c @ A )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(58,plain,
! [A: $i] :
( ( test @ A )
=> ( ! [B: $i] :
( ( ( c @ A )
= B )
=> ( complement @ A @ B ) )
& ! [B: $i] :
( ( complement @ A @ B )
=> ( ( c @ A )
= B ) ) ) ),
inference(miniscope,[status(thm)],[57]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ~ ( test @ A )
| ( ( c @ A )
!= B )
| ( complement @ A @ B ) ),
inference(cnf,[status(esa)],[58]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( ( c @ A )
!= B )
| ~ ( test @ A )
| ( complement @ A @ B ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(62,plain,
! [A: $i] :
( ~ ( test @ A )
| ( complement @ A @ ( c @ A ) ) ),
inference(simp,[status(thm)],[61]) ).
thf(1037,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ sk3 )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[24,62]) ).
thf(1038,plain,
complement @ sk3 @ ( c @ sk3 ),
inference(pattern_uni,[status(thm)],[1037:[bind(A,$thf( sk3 ))]]) ).
thf(2576,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ sk3 @ ( c @ sk3 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1038,75]) ).
thf(2577,plain,
( ( addition @ ( c @ sk3 ) @ sk3 )
= one ),
inference(pattern_uni,[status(thm)],[2576:[bind(A,$thf( c @ sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(3633,plain,
! [A: $i] :
( ( A = one )
| ( ( addition @ A @ zero )
!= ( addition @ ( c @ sk3 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[90,2577]) ).
thf(3643,plain,
! [A: $i] :
( ( A = one )
| ( A
!= ( c @ sk3 ) )
| ( sk3 != zero ) ),
inference(simp,[status(thm)],[3633]) ).
thf(3657,plain,
( ( ( c @ sk3 )
= one )
| ( sk3 != zero ) ),
inference(simp,[status(thm)],[3643]) ).
thf(25,plain,
test @ sk2,
inference(cnf,[status(esa)],[21]) ).
thf(1039,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ sk2 )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25,62]) ).
thf(1040,plain,
complement @ sk2 @ ( c @ sk2 ),
inference(pattern_uni,[status(thm)],[1039:[bind(A,$thf( sk2 ))]]) ).
thf(2554,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ sk2 @ ( c @ sk2 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1040,75]) ).
thf(2555,plain,
( ( addition @ ( c @ sk2 ) @ sk2 )
= one ),
inference(pattern_uni,[status(thm)],[2554:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(3093,plain,
! [A: $i] :
( ( A = one )
| ( ( addition @ A @ zero )
!= ( addition @ ( c @ sk2 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[90,2555]) ).
thf(3095,plain,
! [A: $i] :
( ( A = one )
| ( A
!= ( c @ sk2 ) )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[3093]) ).
thf(3108,plain,
( ( ( c @ sk2 )
= one )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[3095]) ).
thf(15,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(79,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(80,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(cnf,[status(esa)],[79]) ).
thf(81,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(lifteq,[status(thm)],[80]) ).
thf(8,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(43,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(cnf,[status(esa)],[43]) ).
thf(45,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(lifteq,[status(thm)],[44]) ).
thf(22,plain,
( ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ),
inference(cnf,[status(esa)],[21]) ).
thf(26,plain,
( ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(317,plain,
! [A: $i] :
( ( A
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( addition @ A @ A )
!= ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,26]) ).
thf(329,plain,
( ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) )
| ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(simp,[status(thm)],[317]) ).
thf(334,plain,
( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ),
inference(simp,[status(thm)],[329]) ).
thf(339,plain,
! [A: $i] :
( ( A
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[45,334]) ).
thf(350,plain,
( ( ( c @ sk2 )
!= one )
| ( ( multiplication @ sk1 @ ( c @ sk3 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[339]) ).
thf(729,plain,
! [A: $i] :
( ( ( c @ sk2 )
!= one )
| ( A != sk1 )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,350]) ).
thf(737,plain,
( ( ( c @ sk2 )
!= one )
| ( sk1 != sk1 )
| ( ( c @ sk3 )
!= one ) ),
inference(simp,[status(thm)],[729]) ).
thf(743,plain,
( ( ( c @ sk2 )
!= one )
| ( ( c @ sk3 )
!= one ) ),
inference(simp,[status(thm)],[737]) ).
thf(13635,plain,
( ( sk2 != zero )
| ( ( c @ sk3 )
!= one )
| ( ( c @ sk2 )
!= ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[3108,743]) ).
thf(13636,plain,
( ( sk2 != zero )
| ( ( c @ sk3 )
!= one ) ),
inference(pattern_uni,[status(thm)],[13635:[]]) ).
thf(30965,plain,
( ( sk3 != zero )
| ( sk2 != zero )
| ( ( c @ sk3 )
!= ( c @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[3657,13636]) ).
thf(30966,plain,
( ( sk3 != zero )
| ( sk2 != zero ) ),
inference(pattern_uni,[status(thm)],[30965:[]]) ).
thf(337,plain,
( ( ( c @ sk2 )
!= sk1 )
| ( ( c @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[334]) ).
thf(363,plain,
( ( ( c @ sk2 )
!= sk1 )
| ( ( c @ sk3 )
!= ( c @ sk2 ) )
| ( sk1 != sk1 ) ),
inference(eqfactor_ordered,[status(thm)],[337]) ).
thf(365,plain,
( ( ( c @ sk2 )
!= sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[363]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ~ ( complement @ B @ A )
| ( ( multiplication @ A @ B )
= zero ) ),
inference(cnf,[status(esa)],[66]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ~ ( complement @ B @ A ) ),
inference(lifteq,[status(thm)],[68]) ).
thf(1826,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( sk4 @ sk3 ) @ sk3 )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[661,73]) ).
thf(1827,plain,
( ( multiplication @ sk3 @ ( sk4 @ sk3 ) )
= zero ),
inference(pattern_uni,[status(thm)],[1826:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 @ sk3 ))]]) ).
thf(3,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(28,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(29,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(lifteq,[status(thm)],[29]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(31,plain,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ A @ B ) @ C )
= ( multiplication @ A @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(169,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiplication @ B @ ( multiplication @ C @ D ) )
= zero )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ ( multiplication @ B @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[30,33]) ).
thf(176,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiplication @ B @ ( multiplication @ C @ D ) )
= zero )
| ( ( multiplication @ B @ C )
!= zero )
| ( A != D ) ),
inference(simp,[status(thm)],[169]) ).
thf(188,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ A @ B )
!= zero ) ),
inference(simp,[status(thm)],[176]) ).
thf(19026,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ sk3 @ ( sk4 @ sk3 ) )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1827,188]) ).
thf(19027,plain,
! [A: $i] :
( ( multiplication @ sk3 @ ( multiplication @ ( sk4 @ sk3 ) @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[19026:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 @ sk3 )),bind(C,$thf( C ))]]) ).
thf(19117,plain,
! [A: $i] :
( ( multiplication @ sk3 @ ( multiplication @ ( sk4 @ sk3 ) @ A ) )
= zero ),
inference(simp,[status(thm)],[19027]) ).
thf(23,plain,
( ( addition @ ( multiplication @ sk2 @ sk1 ) @ ( multiplication @ sk1 @ sk3 ) )
= ( multiplication @ sk1 @ sk3 ) ),
inference(cnf,[status(esa)],[21]) ).
thf(27,plain,
( ( addition @ ( multiplication @ sk2 @ sk1 ) @ ( multiplication @ sk1 @ sk3 ) )
= ( multiplication @ sk1 @ sk3 ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(94,plain,
! [A: $i,B: $i] :
( ( ( leq @ A @ B )
=> ( ( addition @ A @ B )
= B ) )
& ( ( ( addition @ A @ B )
= B )
=> ( leq @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(95,plain,
( ! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( ( addition @ A @ B )
= B ) )
& ! [A: $i,B: $i] :
( ( ( addition @ A @ B )
= B )
=> ( leq @ A @ B ) ) ),
inference(miniscope,[status(thm)],[94]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(cnf,[status(esa)],[95]) ).
thf(98,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[96]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(simp,[status(thm)],[98]) ).
thf(4712,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ sk1 @ sk3 )
!= B )
| ( leq @ A @ B )
| ( ( addition @ ( multiplication @ sk2 @ sk1 ) @ ( multiplication @ sk1 @ sk3 ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27,99]) ).
thf(4713,plain,
( ( ( multiplication @ sk1 @ sk3 )
!= ( multiplication @ sk1 @ sk3 ) )
| ( leq @ ( multiplication @ sk2 @ sk1 ) @ ( multiplication @ sk1 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[4712:[bind(A,$thf( multiplication @ sk2 @ sk1 )),bind(B,$thf( multiplication @ sk1 @ sk3 ))]]) ).
thf(4728,plain,
leq @ ( multiplication @ sk2 @ sk1 ) @ ( multiplication @ sk1 @ sk3 ),
inference(simp,[status(thm)],[4713]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ~ ( complement @ B @ A )
| ( ( multiplication @ B @ A )
= zero ) ),
inference(cnf,[status(esa)],[66]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ~ ( complement @ B @ A ) ),
inference(lifteq,[status(thm)],[69]) ).
thf(872,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
= C )
| ( ( addition @ A @ B )
!= ( addition @ C @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[56,90]) ).
thf(873,plain,
! [A: $i] :
( ( addition @ zero @ A )
= A ),
inference(pattern_uni,[status(thm)],[872:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(898,plain,
! [A: $i] :
( ( A
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( addition @ zero @ A )
!= ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[873,26]) ).
thf(922,plain,
( ( ( multiplication @ sk1 @ ( c @ sk3 ) )
!= zero )
| ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(simp,[status(thm)],[898]) ).
thf(929,plain,
( ( multiplication @ sk1 @ ( c @ sk3 ) )
!= zero ),
inference(simp,[status(thm)],[922]) ).
thf(2235,plain,
! [B: $i,A: $i] :
( ~ ( complement @ B @ A )
| ( ( multiplication @ B @ A )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[74,929]) ).
thf(2236,plain,
~ ( complement @ sk1 @ ( c @ sk3 ) ),
inference(pattern_uni,[status(thm)],[2235:[bind(A,$thf( c @ sk3 )),bind(B,$thf( sk1 ))]]) ).
thf(2260,plain,
( ( complement @ sk2 @ ( c @ sk2 ) )
!= ( complement @ sk1 @ ( c @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1040,2236]) ).
thf(2280,plain,
( ( sk2 != sk1 )
| ( ( c @ sk3 )
!= ( c @ sk2 ) ) ),
inference(simp,[status(thm)],[2260]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( complement @ B @ A )
| ( test @ A ) ),
inference(cnf,[status(esa)],[47]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ~ ( complement @ B @ A )
| ( test @ A ) ),
inference(simp,[status(thm)],[48]) ).
thf(1056,plain,
! [B: $i,A: $i] :
( ( test @ A )
| ( ( complement @ sk2 @ ( c @ sk2 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1040,50]) ).
thf(1057,plain,
test @ ( c @ sk2 ),
inference(pattern_uni,[status(thm)],[1056:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(1058,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ ( c @ sk2 ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1057,62]) ).
thf(1059,plain,
complement @ ( c @ sk2 ) @ ( c @ ( c @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1058:[bind(A,$thf( c @ sk2 ))]]) ).
thf(1489,plain,
! [B: $i,A: $i] :
( ( test @ A )
| ( ( complement @ ( c @ sk2 ) @ ( c @ ( c @ sk2 ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1059,50]) ).
thf(1490,plain,
test @ ( c @ ( c @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1489:[bind(A,$thf( c @ ( c @ sk2 ) )),bind(B,$thf( c @ sk2 ))]]) ).
thf(1527,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ ( c @ ( c @ sk2 ) ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1490,62]) ).
thf(1528,plain,
complement @ ( c @ ( c @ sk2 ) ) @ ( c @ ( c @ ( c @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[1527:[bind(A,$thf( c @ ( c @ sk2 ) ))]]) ).
thf(7497,plain,
! [B: $i,A: $i] :
( ( test @ A )
| ( ( complement @ ( c @ ( c @ sk2 ) ) @ ( c @ ( c @ ( c @ sk2 ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1528,50]) ).
thf(7498,plain,
test @ ( c @ ( c @ ( c @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[7497:[bind(A,$thf( c @ ( c @ ( c @ sk2 ) ) )),bind(B,$thf( c @ ( c @ sk2 ) ))]]) ).
thf(7548,plain,
! [A: $i] :
( ( complement @ ( sk4 @ A ) @ A )
| ( ( test @ ( c @ ( c @ ( c @ sk2 ) ) ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7498,49]) ).
thf(7549,plain,
complement @ ( sk4 @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( c @ ( c @ ( c @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[7548:[bind(A,$thf( c @ ( c @ ( c @ sk2 ) ) ))]]) ).
thf(31234,plain,
( ( sk3 != zero )
| ( complement @ sk3 @ one )
| ( ( c @ sk3 )
!= ( c @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[3657,1038]) ).
thf(31235,plain,
( ( sk3 != zero )
| ( complement @ sk3 @ one ) ),
inference(pattern_uni,[status(thm)],[31234:[]]) ).
thf(662,plain,
! [A: $i] :
( ( complement @ ( sk4 @ A ) @ A )
| ( ( test @ sk2 )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[25,49]) ).
thf(663,plain,
complement @ ( sk4 @ sk2 ) @ sk2,
inference(pattern_uni,[status(thm)],[662:[bind(A,$thf( sk2 ))]]) ).
thf(1854,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( sk4 @ sk2 ) @ sk2 )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[663,73]) ).
thf(1855,plain,
( ( multiplication @ sk2 @ ( sk4 @ sk2 ) )
= zero ),
inference(pattern_uni,[status(thm)],[1854:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 @ sk2 ))]]) ).
thf(2336,plain,
! [A: $i] :
( ( zero = A )
| ( ( multiplication @ sk2 @ ( sk4 @ sk2 ) )
!= ( multiplication @ one @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1855,45]) ).
thf(2372,plain,
! [A: $i] :
( ( zero = A )
| ( sk2 != one )
| ( ( sk4 @ sk2 )
!= A ) ),
inference(simp,[status(thm)],[2336]) ).
thf(2395,plain,
( ( ( sk4 @ sk2 )
= zero )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[2372]) ).
thf(7564,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ ( c @ ( c @ ( c @ sk2 ) ) ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7498,62]) ).
thf(7565,plain,
complement @ ( c @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[7564:[bind(A,$thf( c @ ( c @ ( c @ sk2 ) ) ))]]) ).
thf(12306,plain,
! [B: $i,A: $i] :
( ( test @ A )
| ( ( complement @ ( c @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7565,50]) ).
thf(12307,plain,
test @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[12306:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk2 ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ sk2 ) ) ))]]) ).
thf(12370,plain,
! [A: $i] :
( ( complement @ ( sk4 @ A ) @ A )
| ( ( test @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12307,49]) ).
thf(12371,plain,
complement @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ),
inference(pattern_uni,[status(thm)],[12370:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ))]]) ).
thf(295,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,26]) ).
thf(305,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( addition @ C @ B )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) )
| ( A
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(simp,[status(thm)],[295]) ).
thf(308,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ ( addition @ A @ ( multiplication @ ( c @ sk2 ) @ sk1 ) ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( addition @ B @ A )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ) ),
inference(simp,[status(thm)],[305]) ).
thf(1540,plain,
! [A: $i] :
( ( complement @ ( sk4 @ A ) @ A )
| ( ( test @ ( c @ ( c @ sk2 ) ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1490,49]) ).
thf(1541,plain,
complement @ ( sk4 @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1540:[bind(A,$thf( c @ ( c @ sk2 ) ))]]) ).
thf(7632,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( sk4 @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ sk2 ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1541,75]) ).
thf(7633,plain,
( ( addition @ ( c @ ( c @ sk2 ) ) @ ( sk4 @ ( c @ ( c @ sk2 ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[7632:[bind(A,$thf( c @ ( c @ sk2 ) )),bind(B,$thf( sk4 @ ( c @ ( c @ sk2 ) ) ))]]) ).
thf(10561,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ ( c @ sk2 ) ) @ ( sk4 @ ( c @ ( c @ sk2 ) ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7633,56]) ).
thf(10562,plain,
( ( addition @ ( sk4 @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ sk2 ) ) )
= one ),
inference(pattern_uni,[status(thm)],[10561:[bind(A,$thf( c @ ( c @ sk2 ) )),bind(B,$thf( sk4 @ ( c @ ( c @ sk2 ) ) ))]]) ).
thf(1060,plain,
! [A: $i] :
( ( complement @ ( sk4 @ A ) @ A )
| ( ( test @ ( c @ sk2 ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1057,49]) ).
thf(1061,plain,
complement @ ( sk4 @ ( c @ sk2 ) ) @ ( c @ sk2 ),
inference(pattern_uni,[status(thm)],[1060:[bind(A,$thf( c @ sk2 ))]]) ).
thf(1792,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( sk4 @ ( c @ sk2 ) ) @ ( c @ sk2 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1061,73]) ).
thf(1793,plain,
( ( multiplication @ ( c @ sk2 ) @ ( sk4 @ ( c @ sk2 ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[1792:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk4 @ ( c @ sk2 ) ))]]) ).
thf(35541,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12371,73]) ).
thf(35542,plain,
( ( multiplication @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[35541:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk2 ) ) ) )),bind(B,$thf( sk4 @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ))]]) ).
thf(1046,plain,
! [B: $i,A: $i] :
( ( test @ A )
| ( ( complement @ sk3 @ ( c @ sk3 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1038,50]) ).
thf(1047,plain,
test @ ( c @ sk3 ),
inference(pattern_uni,[status(thm)],[1046:[bind(A,$thf( c @ sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(1048,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ ( c @ sk3 ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1047,62]) ).
thf(1049,plain,
complement @ ( c @ sk3 ) @ ( c @ ( c @ sk3 ) ),
inference(pattern_uni,[status(thm)],[1048:[bind(A,$thf( c @ sk3 ))]]) ).
thf(1419,plain,
! [B: $i,A: $i] :
( ( test @ A )
| ( ( complement @ ( c @ sk3 ) @ ( c @ ( c @ sk3 ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1049,50]) ).
thf(1420,plain,
test @ ( c @ ( c @ sk3 ) ),
inference(pattern_uni,[status(thm)],[1419:[bind(A,$thf( c @ ( c @ sk3 ) )),bind(B,$thf( c @ sk3 ))]]) ).
thf(1436,plain,
! [A: $i] :
( ( complement @ ( sk4 @ A ) @ A )
| ( ( test @ ( c @ ( c @ sk3 ) ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1420,49]) ).
thf(1437,plain,
complement @ ( sk4 @ ( c @ ( c @ sk3 ) ) ) @ ( c @ ( c @ sk3 ) ),
inference(pattern_uni,[status(thm)],[1436:[bind(A,$thf( c @ ( c @ sk3 ) ))]]) ).
thf(2530,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( sk4 @ ( c @ sk2 ) ) @ ( c @ sk2 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1061,75]) ).
thf(2531,plain,
( ( addition @ ( c @ sk2 ) @ ( sk4 @ ( c @ sk2 ) ) )
= one ),
inference(pattern_uni,[status(thm)],[2530:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk4 @ ( c @ sk2 ) ))]]) ).
thf(6141,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ sk2 ) @ ( sk4 @ ( c @ sk2 ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2531,56]) ).
thf(6142,plain,
( ( addition @ ( sk4 @ ( c @ sk2 ) ) @ ( c @ sk2 ) )
= one ),
inference(pattern_uni,[status(thm)],[6141:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk4 @ ( c @ sk2 ) ))]]) ).
thf(1423,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ ( c @ ( c @ sk3 ) ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1420,62]) ).
thf(1424,plain,
complement @ ( c @ ( c @ sk3 ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[1423:[bind(A,$thf( c @ ( c @ sk3 ) ))]]) ).
thf(1680,plain,
! [B: $i,A: $i] :
( ( test @ A )
| ( ( complement @ ( c @ ( c @ sk3 ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1424,50]) ).
thf(1681,plain,
test @ ( c @ ( c @ ( c @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[1680:[bind(A,$thf( c @ ( c @ ( c @ sk3 ) ) )),bind(B,$thf( c @ ( c @ sk3 ) ))]]) ).
thf(1704,plain,
! [A: $i] :
( ( complement @ ( sk4 @ A ) @ A )
| ( ( test @ ( c @ ( c @ ( c @ sk3 ) ) ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1681,49]) ).
thf(1705,plain,
complement @ ( sk4 @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[1704:[bind(A,$thf( c @ ( c @ ( c @ sk3 ) ) ))]]) ).
thf(812,plain,
( ( ( c @ sk2 )
!= one )
| ( ( c @ sk3 )
!= ( c @ sk2 ) )
| ( one != one ) ),
inference(eqfactor_ordered,[status(thm)],[743]) ).
thf(814,plain,
( ( ( c @ sk2 )
!= one )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[812]) ).
thf(2572,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( sk4 @ sk2 ) @ sk2 )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[663,75]) ).
thf(2573,plain,
( ( addition @ sk2 @ ( sk4 @ sk2 ) )
= one ),
inference(pattern_uni,[status(thm)],[2572:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 @ sk2 ))]]) ).
thf(3522,plain,
! [A: $i] :
( ( A = one )
| ( ( addition @ zero @ A )
!= ( addition @ sk2 @ ( sk4 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[873,2573]) ).
thf(3564,plain,
! [A: $i] :
( ( A = one )
| ( sk2 != zero )
| ( A
!= ( sk4 @ sk2 ) ) ),
inference(simp,[status(thm)],[3522]) ).
thf(3577,plain,
( ( ( sk4 @ sk2 )
= one )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[3564]) ).
thf(2145,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( c @ ( c @ sk3 ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1424,74]) ).
thf(2146,plain,
( ( multiplication @ ( c @ ( c @ sk3 ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[2145:[bind(A,$thf( c @ ( c @ ( c @ sk3 ) ) )),bind(B,$thf( c @ ( c @ sk3 ) ))]]) ).
thf(2187,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( sk4 @ sk3 ) @ sk3 )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[661,74]) ).
thf(2188,plain,
( ( multiplication @ ( sk4 @ sk3 ) @ sk3 )
= zero ),
inference(pattern_uni,[status(thm)],[2187:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 @ sk3 ))]]) ).
thf(18890,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ ( sk4 @ sk3 ) @ sk3 )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2188,188]) ).
thf(18891,plain,
! [A: $i] :
( ( multiplication @ ( sk4 @ sk3 ) @ ( multiplication @ sk3 @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[18890:[bind(A,$thf( sk4 @ sk3 )),bind(B,$thf( sk3 )),bind(C,$thf( C ))]]) ).
thf(19191,plain,
! [A: $i] :
( ( multiplication @ ( sk4 @ sk3 ) @ ( multiplication @ sk3 @ A ) )
= zero ),
inference(simp,[status(thm)],[18891]) ).
thf(2574,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( c @ sk3 ) @ ( c @ ( c @ sk3 ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1049,75]) ).
thf(2575,plain,
( ( addition @ ( c @ ( c @ sk3 ) ) @ ( c @ sk3 ) )
= one ),
inference(pattern_uni,[status(thm)],[2574:[bind(A,$thf( c @ ( c @ sk3 ) )),bind(B,$thf( c @ sk3 ))]]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( ( addition @ A @ B )
= B ) ),
inference(cnf,[status(esa)],[95]) ).
thf(100,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= B )
| ~ ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[97]) ).
thf(5145,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( B
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( addition @ A @ B )
!= ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[100,26]) ).
thf(5146,plain,
( ~ ( leq @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[5145:[bind(A,$thf( multiplication @ sk1 @ ( c @ sk3 ) )),bind(B,$thf( multiplication @ ( c @ sk2 ) @ sk1 ))]]) ).
thf(5163,plain,
~ ( leq @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ sk2 ) @ sk1 ) ),
inference(simp,[status(thm)],[5146]) ).
thf(2167,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( sk4 @ ( c @ ( c @ sk3 ) ) ) @ ( c @ ( c @ sk3 ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1437,74]) ).
thf(2168,plain,
( ( multiplication @ ( sk4 @ ( c @ ( c @ sk3 ) ) ) @ ( c @ ( c @ sk3 ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[2167:[bind(A,$thf( c @ ( c @ sk3 ) )),bind(B,$thf( sk4 @ ( c @ ( c @ sk3 ) ) ))]]) ).
thf(2548,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( c @ sk2 ) @ ( c @ ( c @ sk2 ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1059,75]) ).
thf(2549,plain,
( ( addition @ ( c @ ( c @ sk2 ) ) @ ( c @ sk2 ) )
= one ),
inference(pattern_uni,[status(thm)],[2548:[bind(A,$thf( c @ ( c @ sk2 ) )),bind(B,$thf( c @ sk2 ))]]) ).
thf(6250,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ ( c @ sk2 ) ) @ ( c @ sk2 ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2549,56]) ).
thf(6251,plain,
( ( addition @ ( c @ sk2 ) @ ( c @ ( c @ sk2 ) ) )
= one ),
inference(pattern_uni,[status(thm)],[6250:[bind(A,$thf( c @ ( c @ sk2 ) )),bind(B,$thf( c @ sk2 ))]]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_distributivity) ).
thf(40,plain,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(12224,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( sk4 @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( c @ ( c @ ( c @ sk2 ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7549,75]) ).
thf(12225,plain,
( ( addition @ ( c @ ( c @ ( c @ sk2 ) ) ) @ ( sk4 @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[12224:[bind(A,$thf( c @ ( c @ ( c @ sk2 ) ) )),bind(B,$thf( sk4 @ ( c @ ( c @ ( c @ sk2 ) ) ) ))]]) ).
thf(1870,plain,
! [B: $i,A: $i] :
( ~ ( complement @ B @ A )
| ( ( multiplication @ A @ B )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,929]) ).
thf(1871,plain,
~ ( complement @ ( c @ sk3 ) @ sk1 ),
inference(pattern_uni,[status(thm)],[1870:[bind(A,$thf( sk1 )),bind(B,$thf( c @ sk3 ))]]) ).
thf(1903,plain,
( ( complement @ ( c @ sk3 ) @ ( c @ ( c @ sk3 ) ) )
!= ( complement @ ( c @ sk3 ) @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[1049,1871]) ).
thf(1910,plain,
( ( ( c @ sk3 )
!= ( c @ sk3 ) )
| ( ( c @ ( c @ sk3 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[1903]) ).
thf(1921,plain,
( ( c @ ( c @ sk3 ) )
!= sk1 ),
inference(simp,[status(thm)],[1910]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( test @ A )
=> ( ( c @ A )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_4) ).
thf(37,plain,
! [A: $i] :
( ~ ( test @ A )
=> ( ( c @ A )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(31219,plain,
( ( sk3 != zero )
| ( test @ ( c @ one ) )
| ( ( c @ sk3 )
!= ( c @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[3657,1420]) ).
thf(31220,plain,
( ( sk3 != zero )
| ( test @ ( c @ one ) ) ),
inference(pattern_uni,[status(thm)],[31219:[]]) ).
thf(155,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( multiplication @ sk2 @ sk1 ) @ ( multiplication @ A @ ( multiplication @ B @ C ) ) )
= ( multiplication @ sk1 @ sk3 ) )
| ( ( multiplication @ ( multiplication @ A @ B ) @ C )
!= ( multiplication @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[33,27]) ).
thf(173,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( multiplication @ sk2 @ sk1 ) @ ( multiplication @ A @ ( multiplication @ B @ C ) ) )
= ( multiplication @ sk1 @ sk3 ) )
| ( ( multiplication @ A @ B )
!= sk1 )
| ( C != sk3 ) ),
inference(simp,[status(thm)],[155]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ( ( addition @ ( multiplication @ sk2 @ sk1 ) @ ( multiplication @ A @ ( multiplication @ B @ sk3 ) ) )
= ( multiplication @ sk1 @ sk3 ) )
| ( ( multiplication @ A @ B )
!= sk1 ) ),
inference(simp,[status(thm)],[173]) ).
thf(12256,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( c @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7565,74]) ).
thf(12257,plain,
( ( multiplication @ ( c @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[12256:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk2 ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ sk2 ) ) ))]]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_distributivity) ).
thf(91,plain,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(92,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
inference(cnf,[status(esa)],[91]) ).
thf(93,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
inference(lifteq,[status(thm)],[92]) ).
thf(4409,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) )
= zero )
| ( ( multiplication @ A @ ( addition @ B @ C ) )
!= ( multiplication @ zero @ D ) ) ),
inference(paramod_ordered,[status(thm)],[93,30]) ).
thf(4410,plain,
! [B: $i,A: $i] :
( ( addition @ ( multiplication @ zero @ A ) @ ( multiplication @ zero @ B ) )
= zero ),
inference(pattern_uni,[status(thm)],[4409:[bind(A,$thf( zero )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( addition @ E @ F ))]]) ).
thf(4481,plain,
! [B: $i,A: $i] :
( ( addition @ ( multiplication @ zero @ A ) @ ( multiplication @ zero @ B ) )
= zero ),
inference(simp,[status(thm)],[4410]) ).
thf(36446,plain,
( ( addition @ zero @ zero )
= zero ),
inference(rewrite,[status(thm)],[4481,30]) ).
thf(1687,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ ( c @ ( c @ ( c @ sk3 ) ) ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1681,62]) ).
thf(1688,plain,
complement @ ( c @ ( c @ ( c @ sk3 ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[1687:[bind(A,$thf( c @ ( c @ ( c @ sk3 ) ) ))]]) ).
thf(11911,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( c @ ( c @ ( c @ sk3 ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1688,73]) ).
thf(11912,plain,
( ( multiplication @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[11911:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk3 ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ sk3 ) ) ))]]) ).
thf(2347,plain,
! [A: $i] :
( ( zero = A )
| ( ( multiplication @ sk2 @ ( sk4 @ sk2 ) )
!= ( multiplication @ A @ one ) ) ),
inference(paramod_ordered,[status(thm)],[1855,81]) ).
thf(2391,plain,
! [A: $i] :
( ( zero = A )
| ( sk2 != A )
| ( ( sk4 @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[2347]) ).
thf(2400,plain,
( ( sk2 = zero )
| ( ( sk4 @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[2391]) ).
thf(13483,plain,
( ( sk2 != zero )
| ( sk3 != sk2 )
| ( ( c @ sk2 )
!= ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[3108,814]) ).
thf(13484,plain,
( ( sk2 != zero )
| ( sk3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[13483:[]]) ).
thf(3523,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ sk2 @ ( sk4 @ sk2 ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2573,56]) ).
thf(3524,plain,
( ( addition @ ( sk4 @ sk2 ) @ sk2 )
= one ),
inference(pattern_uni,[status(thm)],[3523:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 @ sk2 ))]]) ).
thf(50092,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ one )
= ( addition @ A @ B ) )
| ( ( addition @ ( sk4 @ sk2 ) @ sk2 )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[3524,323]) ).
thf(50093,plain,
( ( addition @ ( sk4 @ sk2 ) @ sk2 )
= ( addition @ ( sk4 @ sk2 ) @ one ) ),
inference(pattern_uni,[status(thm)],[50092:[bind(A,$thf( sk4 @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(52342,plain,
( ( addition @ ( sk4 @ sk2 ) @ one )
= one ),
inference(rewrite,[status(thm)],[50093,3524]) ).
thf(1856,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( c @ sk3 ) @ ( c @ ( c @ sk3 ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1049,73]) ).
thf(1857,plain,
( ( multiplication @ ( c @ ( c @ sk3 ) ) @ ( c @ sk3 ) )
= zero ),
inference(pattern_uni,[status(thm)],[1856:[bind(A,$thf( c @ ( c @ sk3 ) )),bind(B,$thf( c @ sk3 ))]]) ).
thf(18870,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ ( c @ ( c @ sk3 ) ) @ ( c @ sk3 ) )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1857,188]) ).
thf(18871,plain,
! [A: $i] :
( ( multiplication @ ( c @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ sk3 ) @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[18870:[bind(A,$thf( c @ ( c @ sk3 ) )),bind(B,$thf( c @ sk3 )),bind(C,$thf( C ))]]) ).
thf(19184,plain,
! [A: $i] :
( ( multiplication @ ( c @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ sk3 ) @ A ) )
= zero ),
inference(simp,[status(thm)],[18871]) ).
thf(50097,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ one )
= ( addition @ A @ B ) )
| ( ( addition @ ( c @ sk2 ) @ sk2 )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2555,323]) ).
thf(50098,plain,
( ( addition @ ( c @ sk2 ) @ sk2 )
= ( addition @ ( c @ sk2 ) @ one ) ),
inference(pattern_uni,[status(thm)],[50097:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(52891,plain,
( ( addition @ ( c @ sk2 ) @ one )
= one ),
inference(rewrite,[status(thm)],[50098,2555]) ).
thf(53043,plain,
! [B: $i,A: $i] :
( ( one != B )
| ( leq @ A @ B )
| ( ( addition @ ( c @ sk2 ) @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[52891,99]) ).
thf(53044,plain,
( ( one != one )
| ( leq @ ( c @ sk2 ) @ one ) ),
inference(pattern_uni,[status(thm)],[53043:[bind(A,$thf( c @ sk2 )),bind(B,$thf( one ))]]) ).
thf(53147,plain,
leq @ ( c @ sk2 ) @ one,
inference(simp,[status(thm)],[53044]) ).
thf(813,plain,
( ( ( c @ sk2 )
!= one )
| ( ( c @ sk3 )
!= ( c @ sk2 ) ) ),
inference(simp,[status(thm)],[812]) ).
thf(31279,plain,
( ( sk3 != zero )
| ( ( c @ sk3 )
!= ( c @ sk2 ) )
| ( ( c @ sk3 )
!= ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[3657,813]) ).
thf(31431,plain,
( ( sk3 != zero )
| ( sk3 != sk2 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[31279]) ).
thf(31661,plain,
( ( sk3 != zero )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[31431]) ).
thf(852,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( multiplication @ sk1 @ sk3 ) )
| ( ( addition @ A @ B )
!= ( addition @ ( multiplication @ sk2 @ sk1 ) @ ( multiplication @ sk1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[56,27]) ).
thf(853,plain,
( ( addition @ ( multiplication @ sk1 @ sk3 ) @ ( multiplication @ sk2 @ sk1 ) )
= ( multiplication @ sk1 @ sk3 ) ),
inference(pattern_uni,[status(thm)],[852:[bind(A,$thf( multiplication @ sk2 @ sk1 )),bind(B,$thf( multiplication @ sk1 @ sk3 ))]]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ~ ( test @ A )
| ~ ( complement @ A @ B )
| ( ( c @ A )
= B ) ),
inference(cnf,[status(esa)],[58]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( c @ A )
= B )
| ~ ( test @ A )
| ~ ( complement @ A @ B ) ),
inference(lifteq,[status(thm)],[60]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( ( c @ A )
= B )
| ~ ( test @ A )
| ~ ( complement @ A @ B ) ),
inference(simp,[status(thm)],[63]) ).
thf(3588,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ sk3 ) @ sk3 )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2577,56]) ).
thf(3589,plain,
( ( addition @ sk3 @ ( c @ sk3 ) )
= one ),
inference(pattern_uni,[status(thm)],[3588:[bind(A,$thf( c @ sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(4563,plain,
! [A: $i] :
( ( A = one )
| ( ( addition @ A @ A )
!= ( addition @ sk3 @ ( c @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,3589]) ).
thf(4604,plain,
! [A: $i] :
( ( A = one )
| ( A != sk3 )
| ( A
!= ( c @ sk3 ) ) ),
inference(simp,[status(thm)],[4563]) ).
thf(4618,plain,
( ( sk3 = one )
| ( ( c @ sk3 )
!= sk3 ) ),
inference(simp,[status(thm)],[4604]) ).
thf(1858,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ sk3 @ ( c @ sk3 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1038,73]) ).
thf(1859,plain,
( ( multiplication @ ( c @ sk3 ) @ sk3 )
= zero ),
inference(pattern_uni,[status(thm)],[1858:[bind(A,$thf( c @ sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(2457,plain,
! [A: $i] :
( ( A = zero )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( c @ sk3 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[81,1859]) ).
thf(2496,plain,
! [A: $i] :
( ( A = zero )
| ( A
!= ( c @ sk3 ) )
| ( sk3 != one ) ),
inference(simp,[status(thm)],[2457]) ).
thf(2510,plain,
( ( ( c @ sk3 )
= zero )
| ( sk3 != one ) ),
inference(simp,[status(thm)],[2496]) ).
thf(16,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(82,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(83,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(cnf,[status(esa)],[82]) ).
thf(84,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(lifteq,[status(thm)],[83]) ).
thf(932,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[84,929]) ).
thf(945,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( c @ sk3 )
!= zero ) ),
inference(simp,[status(thm)],[932]) ).
thf(948,plain,
( ( c @ sk3 )
!= zero ),
inference(simp,[status(thm)],[945]) ).
thf(7449,plain,
sk3 != one,
inference(simplifyReflect,[status(thm)],[2510,948]) ).
thf(37642,plain,
( ( c @ sk3 )
!= sk3 ),
inference(simplifyReflect,[status(thm)],[4618,7449]) ).
thf(37647,plain,
! [B: $i,A: $i] :
( ~ ( test @ A )
| ~ ( complement @ A @ B )
| ( B != sk3 )
| ( ( c @ A )
!= ( c @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[64,37642]) ).
thf(37648,plain,
! [A: $i] :
( ~ ( test @ sk3 )
| ~ ( complement @ sk3 @ A )
| ( A != sk3 ) ),
inference(pattern_uni,[status(thm)],[37647:[bind(A,$thf( sk3 ))]]) ).
thf(37658,plain,
( ~ ( test @ sk3 )
| ~ ( complement @ sk3 @ sk3 ) ),
inference(simp,[status(thm)],[37648]) ).
thf(39239,plain,
( ~ $true
| ~ ( complement @ sk3 @ sk3 ) ),
inference(rewrite,[status(thm)],[37658,24]) ).
thf(39240,plain,
~ ( complement @ sk3 @ sk3 ),
inference(simp,[status(thm)],[39239]) ).
thf(39258,plain,
( ( complement @ ( sk4 @ sk2 ) @ sk2 )
!= ( complement @ sk3 @ sk3 ) ),
inference(paramod_ordered,[status(thm)],[663,39240]) ).
thf(39272,plain,
( ( ( sk4 @ sk2 )
!= sk3 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[39258]) ).
thf(1219,plain,
! [B: $i,A: $i] :
( ~ ( test @ A )
| ~ ( complement @ A @ B )
| ( B != zero )
| ( ( c @ A )
!= ( c @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[64,948]) ).
thf(1220,plain,
! [A: $i] :
( ~ ( test @ sk3 )
| ~ ( complement @ sk3 @ A )
| ( A != zero ) ),
inference(pattern_uni,[status(thm)],[1219:[bind(A,$thf( sk3 ))]]) ).
thf(1386,plain,
( ~ ( test @ sk3 )
| ~ ( complement @ sk3 @ zero ) ),
inference(simp,[status(thm)],[1220]) ).
thf(1493,plain,
( ~ $true
| ~ ( complement @ sk3 @ zero ) ),
inference(rewrite,[status(thm)],[1386,24]) ).
thf(1494,plain,
~ ( complement @ sk3 @ zero ),
inference(simp,[status(thm)],[1493]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( test @ A )
& ( test @ B ) )
=> ( ( c @ ( multiplication @ A @ B ) )
= ( addition @ ( c @ A ) @ ( c @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_deMorgan2) ).
thf(76,plain,
! [A: $i,B: $i] :
( ( ( test @ A )
& ( test @ B ) )
=> ( ( c @ ( multiplication @ A @ B ) )
= ( addition @ ( c @ A ) @ ( c @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(77,plain,
! [B: $i,A: $i] :
( ~ ( test @ A )
| ~ ( test @ B )
| ( ( c @ ( multiplication @ A @ B ) )
= ( addition @ ( c @ A ) @ ( c @ B ) ) ) ),
inference(cnf,[status(esa)],[76]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( ( c @ ( multiplication @ A @ B ) )
= ( addition @ ( c @ A ) @ ( c @ B ) ) )
| ~ ( test @ A )
| ~ ( test @ B ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(1502,plain,
! [A: $i] :
( ~ ( test @ A )
| ( ( complement @ ( sk4 @ A ) @ A )
!= ( complement @ sk3 @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[49,1494]) ).
thf(1507,plain,
! [A: $i] :
( ~ ( test @ A )
| ( ( sk4 @ A )
!= sk3 )
| ( A != zero ) ),
inference(simp,[status(thm)],[1502]) ).
thf(1515,plain,
( ~ ( test @ zero )
| ( ( sk4 @ zero )
!= sk3 ) ),
inference(simp,[status(thm)],[1507]) ).
thf(1764,plain,
( ( ( sk4 @ zero )
!= sk3 )
| ( ( test @ sk3 )
!= ( test @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[24,1515]) ).
thf(1778,plain,
( ( ( sk4 @ zero )
!= sk3 )
| ( sk3 != zero ) ),
inference(simp,[status(thm)],[1764]) ).
thf(2155,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( sk4 @ ( c @ sk2 ) ) @ ( c @ sk2 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1061,74]) ).
thf(2156,plain,
( ( multiplication @ ( sk4 @ ( c @ sk2 ) ) @ ( c @ sk2 ) )
= zero ),
inference(pattern_uni,[status(thm)],[2155:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk4 @ ( c @ sk2 ) ))]]) ).
thf(18931,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ ( sk4 @ ( c @ sk2 ) ) @ ( c @ sk2 ) )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2156,188]) ).
thf(18932,plain,
! [A: $i] :
( ( multiplication @ ( sk4 @ ( c @ sk2 ) ) @ ( multiplication @ ( c @ sk2 ) @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[18931:[bind(A,$thf( sk4 @ ( c @ sk2 ) )),bind(B,$thf( c @ sk2 )),bind(C,$thf( C ))]]) ).
thf(19197,plain,
! [A: $i] :
( ( multiplication @ ( sk4 @ ( c @ sk2 ) ) @ ( multiplication @ ( c @ sk2 ) @ A ) )
= zero ),
inference(simp,[status(thm)],[18932]) ).
thf(242,plain,
! [A: $i] :
( ( ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ A )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[81,26]) ).
thf(258,plain,
! [A: $i] :
( ( ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ A )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( A
!= ( c @ sk2 ) )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[242]) ).
thf(261,plain,
( ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ ( c @ sk2 ) ) )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[258]) ).
thf(2221,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( c @ sk3 ) @ ( c @ ( c @ sk3 ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1049,74]) ).
thf(2222,plain,
( ( multiplication @ ( c @ sk3 ) @ ( c @ ( c @ sk3 ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[2221:[bind(A,$thf( c @ ( c @ sk3 ) )),bind(B,$thf( c @ sk3 ))]]) ).
thf(35611,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12371,75]) ).
thf(35612,plain,
( ( addition @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[35611:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk2 ) ) ) )),bind(B,$thf( sk4 @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ))]]) ).
thf(40310,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35612,56]) ).
thf(40311,plain,
( ( addition @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[40310:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk2 ) ) ) )),bind(B,$thf( sk4 @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ))]]) ).
thf(2274,plain,
( ( complement @ sk3 @ ( c @ sk3 ) )
!= ( complement @ sk1 @ ( c @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1038,2236]) ).
thf(2284,plain,
( ( sk3 != sk1 )
| ( ( c @ sk3 )
!= ( c @ sk3 ) ) ),
inference(simp,[status(thm)],[2274]) ).
thf(2291,plain,
sk3 != sk1,
inference(simp,[status(thm)],[2284]) ).
thf(341,plain,
! [A: $i] :
( ( A
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[81,334]) ).
thf(353,plain,
( ( ( multiplication @ sk1 @ ( c @ sk3 ) )
!= ( c @ sk2 ) )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[341]) ).
thf(1050,plain,
! [A: $i] :
( ( complement @ ( sk4 @ A ) @ A )
| ( ( test @ ( c @ sk3 ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1047,49]) ).
thf(1051,plain,
complement @ ( sk4 @ ( c @ sk3 ) ) @ ( c @ sk3 ),
inference(pattern_uni,[status(thm)],[1050:[bind(A,$thf( c @ sk3 ))]]) ).
thf(292,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( multiplication @ sk1 @ sk3 ) @ A )
= ( addition @ C @ ( addition @ B @ A ) ) )
| ( ( addition @ ( multiplication @ sk2 @ sk1 ) @ ( multiplication @ sk1 @ sk3 ) )
!= ( addition @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27,36]) ).
thf(293,plain,
! [A: $i] :
( ( addition @ ( multiplication @ sk2 @ sk1 ) @ ( addition @ ( multiplication @ sk1 @ sk3 ) @ A ) )
= ( addition @ ( multiplication @ sk1 @ sk3 ) @ A ) ),
inference(pattern_uni,[status(thm)],[292:[bind(A,$thf( A )),bind(B,$thf( multiplication @ sk1 @ sk3 )),bind(C,$thf( multiplication @ sk2 @ sk1 ))]]) ).
thf(41392,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( multiplication @ sk1 @ sk3 ) @ A )
!= C )
| ( leq @ B @ C )
| ( ( addition @ ( multiplication @ sk2 @ sk1 ) @ ( addition @ ( multiplication @ sk1 @ sk3 ) @ A ) )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[293,99]) ).
thf(41393,plain,
! [A: $i] :
( ( ( addition @ ( multiplication @ sk1 @ sk3 ) @ A )
!= ( addition @ ( multiplication @ sk1 @ sk3 ) @ A ) )
| ( leq @ ( multiplication @ sk2 @ sk1 ) @ ( addition @ ( multiplication @ sk1 @ sk3 ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[41392:[bind(A,$thf( G )),bind(B,$thf( multiplication @ sk2 @ sk1 )),bind(C,$thf( addition @ ( multiplication @ sk1 @ sk3 ) @ G ))]]) ).
thf(41840,plain,
! [A: $i] : ( leq @ ( multiplication @ sk2 @ sk1 ) @ ( addition @ ( multiplication @ sk1 @ sk3 ) @ A ) ),
inference(simp,[status(thm)],[41393]) ).
thf(41864,plain,
! [C: $i,B: $i,A: $i] :
( ( leq @ ( multiplication @ sk2 @ sk1 ) @ ( addition @ A @ B ) )
| ( ( addition @ B @ A )
!= ( addition @ ( multiplication @ sk1 @ sk3 ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[56,41840]) ).
thf(41865,plain,
! [A: $i] : ( leq @ ( multiplication @ sk2 @ sk1 ) @ ( addition @ A @ ( multiplication @ sk1 @ sk3 ) ) ),
inference(pattern_uni,[status(thm)],[41864:[bind(A,$thf( A )),bind(B,$thf( multiplication @ sk1 @ sk3 )),bind(C,$thf( A ))]]) ).
thf(274,plain,
! [A: $i] :
( ( ( multiplication @ sk1 @ sk3 )
= A )
| ( ( addition @ ( multiplication @ sk2 @ sk1 ) @ ( multiplication @ sk1 @ sk3 ) )
!= ( addition @ A @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[27,90]) ).
thf(278,plain,
! [A: $i] :
( ( ( multiplication @ sk1 @ sk3 )
= A )
| ( ( multiplication @ sk2 @ sk1 )
!= A )
| ( ( multiplication @ sk1 @ sk3 )
!= zero ) ),
inference(simp,[status(thm)],[274]) ).
thf(280,plain,
( ( ( multiplication @ sk2 @ sk1 )
= ( multiplication @ sk1 @ sk3 ) )
| ( ( multiplication @ sk1 @ sk3 )
!= zero ) ),
inference(simp,[status(thm)],[278]) ).
thf(197,plain,
! [A: $i] :
( ( ( addition @ A @ ( multiplication @ sk1 @ sk3 ) )
= ( multiplication @ sk1 @ sk3 ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[45,27]) ).
thf(209,plain,
! [A: $i] :
( ( ( addition @ A @ ( multiplication @ sk1 @ sk3 ) )
= ( multiplication @ sk1 @ sk3 ) )
| ( sk2 != one )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[197]) ).
thf(221,plain,
( ( ( addition @ sk1 @ ( multiplication @ sk1 @ sk3 ) )
= ( multiplication @ sk1 @ sk3 ) )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[209]) ).
thf(1818,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ sk2 @ ( c @ sk2 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1040,73]) ).
thf(1819,plain,
( ( multiplication @ ( c @ sk2 ) @ sk2 )
= zero ),
inference(pattern_uni,[status(thm)],[1818:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(1976,plain,
! [A: $i] :
( ( A = zero )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( c @ sk2 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[81,1819]) ).
thf(1999,plain,
! [A: $i] :
( ( A = zero )
| ( A
!= ( c @ sk2 ) )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[1976]) ).
thf(2026,plain,
( ( ( c @ sk2 )
= zero )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[1999]) ).
thf(3807,plain,
( ( sk2 != one )
| ( test @ zero )
| ( ( c @ sk2 )
!= ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2026,1057]) ).
thf(3808,plain,
( ( sk2 != one )
| ( test @ zero ) ),
inference(pattern_uni,[status(thm)],[3807:[]]) ).
thf(50184,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ one )
= ( addition @ A @ B ) )
| ( ( addition @ sk2 @ ( sk4 @ sk2 ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2573,323]) ).
thf(50185,plain,
( ( addition @ sk2 @ ( sk4 @ sk2 ) )
= ( addition @ sk2 @ one ) ),
inference(pattern_uni,[status(thm)],[50184:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 @ sk2 ))]]) ).
thf(51047,plain,
( ( addition @ sk2 @ one )
= one ),
inference(rewrite,[status(thm)],[50185,2573]) ).
thf(51060,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ sk2 @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[51047,56]) ).
thf(51061,plain,
( ( addition @ one @ sk2 )
= one ),
inference(pattern_uni,[status(thm)],[51060:[bind(A,$thf( sk2 )),bind(B,$thf( one ))]]) ).
thf(51462,plain,
! [B: $i,A: $i] :
( ( one = B )
| ~ ( leq @ A @ B )
| ( ( addition @ one @ sk2 )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[51061,100]) ).
thf(51463,plain,
( ( sk2 = one )
| ~ ( leq @ one @ sk2 ) ),
inference(pattern_uni,[status(thm)],[51462:[bind(A,$thf( one )),bind(B,$thf( sk2 ))]]) ).
thf(7459,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( c @ ( c @ sk2 ) ) @ ( c @ ( c @ ( c @ sk2 ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1528,74]) ).
thf(7460,plain,
( ( multiplication @ ( c @ ( c @ sk2 ) ) @ ( c @ ( c @ ( c @ sk2 ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[7459:[bind(A,$thf( c @ ( c @ ( c @ sk2 ) ) )),bind(B,$thf( c @ ( c @ sk2 ) ))]]) ).
thf(35537,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12371,74]) ).
thf(35538,plain,
( ( multiplication @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[35537:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk2 ) ) ) )),bind(B,$thf( sk4 @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ))]]) ).
thf(18712,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ ( c @ ( c @ sk3 ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ) )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2146,188]) ).
thf(18713,plain,
! [A: $i] :
( ( multiplication @ ( c @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ ( c @ ( c @ sk3 ) ) ) @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[18712:[bind(A,$thf( c @ ( c @ sk3 ) )),bind(B,$thf( c @ ( c @ ( c @ sk3 ) ) )),bind(C,$thf( C ))]]) ).
thf(19095,plain,
! [A: $i] :
( ( multiplication @ ( c @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ ( c @ ( c @ sk3 ) ) ) @ A ) )
= zero ),
inference(simp,[status(thm)],[18713]) ).
thf(2277,plain,
! [A: $i] :
( ~ ( test @ A )
| ( ( complement @ A @ ( c @ A ) )
!= ( complement @ sk1 @ ( c @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[62,2236]) ).
thf(2285,plain,
! [A: $i] :
( ~ ( test @ A )
| ( A != sk1 )
| ( ( c @ A )
!= ( c @ sk3 ) ) ),
inference(simp,[status(thm)],[2277]) ).
thf(2292,plain,
( ~ ( test @ sk1 )
| ( ( c @ sk3 )
!= ( c @ sk1 ) ) ),
inference(simp,[status(thm)],[2285]) ).
thf(6910,plain,
( ( ( c @ sk3 )
!= ( c @ sk1 ) )
| ( ( test @ sk2 )
!= ( test @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[25,2292]) ).
thf(6947,plain,
( ( ( c @ sk3 )
!= ( c @ sk1 ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[6910]) ).
thf(30986,plain,
( ( sk3 != zero )
| ~ ( complement @ sk1 @ one )
| ( ( c @ sk3 )
!= ( c @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[3657,2236]) ).
thf(30987,plain,
( ( sk3 != zero )
| ~ ( complement @ sk1 @ one ) ),
inference(pattern_uni,[status(thm)],[30986:[]]) ).
thf(291,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
= ( multiplication @ sk1 @ sk3 ) )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ ( multiplication @ sk2 @ sk1 ) @ ( multiplication @ sk1 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[36,27]) ).
thf(304,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ C @ ( addition @ B @ A ) )
= ( multiplication @ sk1 @ sk3 ) )
| ( ( addition @ C @ B )
!= ( multiplication @ sk2 @ sk1 ) )
| ( A
!= ( multiplication @ sk1 @ sk3 ) ) ),
inference(simp,[status(thm)],[291]) ).
thf(307,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ ( addition @ A @ ( multiplication @ sk1 @ sk3 ) ) )
= ( multiplication @ sk1 @ sk3 ) )
| ( ( addition @ B @ A )
!= ( multiplication @ sk2 @ sk1 ) ) ),
inference(simp,[status(thm)],[304]) ).
thf(13563,plain,
( ( sk2 != zero )
| ( test @ one )
| ( ( c @ sk2 )
!= ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[3108,1057]) ).
thf(13564,plain,
( ( sk2 != zero )
| ( test @ one ) ),
inference(pattern_uni,[status(thm)],[13563:[]]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( test @ A )
& ( test @ B ) )
=> ( ( c @ ( addition @ A @ B ) )
= ( multiplication @ ( c @ A ) @ ( c @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_deMorgan1) ).
thf(85,plain,
! [A: $i,B: $i] :
( ( ( test @ A )
& ( test @ B ) )
=> ( ( c @ ( addition @ A @ B ) )
= ( multiplication @ ( c @ A ) @ ( c @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(1890,plain,
( ( complement @ ( c @ sk3 ) @ sk1 )
!= ( complement @ sk2 @ ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[1040,1871]) ).
thf(1915,plain,
( ( ( c @ sk3 )
!= sk2 )
| ( ( c @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[1890]) ).
thf(1782,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( c @ ( c @ sk3 ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1424,73]) ).
thf(1783,plain,
( ( multiplication @ ( c @ ( c @ ( c @ sk3 ) ) ) @ ( c @ ( c @ sk3 ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[1782:[bind(A,$thf( c @ ( c @ ( c @ sk3 ) ) )),bind(B,$thf( c @ ( c @ sk3 ) ))]]) ).
thf(52357,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( sk4 @ sk2 ) @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[52342,56]) ).
thf(52358,plain,
( ( addition @ one @ ( sk4 @ sk2 ) )
= one ),
inference(pattern_uni,[status(thm)],[52357:[bind(A,$thf( sk4 @ sk2 )),bind(B,$thf( one ))]]) ).
thf(12168,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( sk4 @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( c @ ( c @ ( c @ sk2 ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7549,74]) ).
thf(12169,plain,
( ( multiplication @ ( sk4 @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( c @ ( c @ ( c @ sk2 ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[12168:[bind(A,$thf( c @ ( c @ ( c @ sk2 ) ) )),bind(B,$thf( sk4 @ ( c @ ( c @ ( c @ sk2 ) ) ) ))]]) ).
thf(21383,plain,
( ( sk2 != zero )
| ( complement @ one @ sk2 )
| ( ( sk4 @ sk2 )
!= ( sk4 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[3577,663]) ).
thf(21384,plain,
( ( sk2 != zero )
| ( complement @ one @ sk2 ) ),
inference(pattern_uni,[status(thm)],[21383:[]]) ).
thf(12082,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( sk4 @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1705,73]) ).
thf(12083,plain,
( ( multiplication @ ( c @ ( c @ ( c @ sk3 ) ) ) @ ( sk4 @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[12082:[bind(A,$thf( c @ ( c @ ( c @ sk3 ) ) )),bind(B,$thf( sk4 @ ( c @ ( c @ ( c @ sk3 ) ) ) ))]]) ).
thf(393,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiplication @ ( addition @ C @ ( addition @ B @ A ) ) @ F )
= ( addition @ ( multiplication @ D @ F ) @ ( multiplication @ E @ F ) ) )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[36,42]) ).
thf(394,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ C @ ( addition @ D @ A ) ) @ B )
= ( addition @ ( multiplication @ ( addition @ C @ D ) @ B ) @ ( multiplication @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[393:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( addition @ G @ H )),bind(E,$thf( A ))]]) ).
thf(413,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ C @ ( addition @ D @ A ) ) @ B )
= ( addition @ ( multiplication @ ( addition @ C @ D ) @ B ) @ ( multiplication @ A @ B ) ) ),
inference(simp,[status(thm)],[394]) ).
thf(60238,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( addition @ ( multiplication @ C @ B ) @ ( multiplication @ ( addition @ D @ A ) @ B ) )
= ( addition @ ( addition @ ( multiplication @ C @ B ) @ ( multiplication @ D @ B ) ) @ ( multiplication @ A @ B ) ) ),
inference(rewrite,[status(thm)],[413,42]) ).
thf(3473,plain,
! [A: $i] :
( ( A = one )
| ( ( addition @ A @ A )
!= ( addition @ sk3 @ ( sk4 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,2559]) ).
thf(3497,plain,
! [A: $i] :
( ( A = one )
| ( A != sk3 )
| ( A
!= ( sk4 @ sk3 ) ) ),
inference(simp,[status(thm)],[3473]) ).
thf(3511,plain,
( ( sk3 = one )
| ( ( sk4 @ sk3 )
!= sk3 ) ),
inference(simp,[status(thm)],[3497]) ).
thf(17755,plain,
( ( sk4 @ sk3 )
!= sk3 ),
inference(simplifyReflect,[status(thm)],[3511,7449]) ).
thf(1899,plain,
! [A: $i] :
( ~ ( test @ A )
| ( ( complement @ ( sk4 @ A ) @ A )
!= ( complement @ ( c @ sk3 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[49,1871]) ).
thf(1907,plain,
! [A: $i] :
( ~ ( test @ A )
| ( ( sk4 @ A )
!= ( c @ sk3 ) )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[1899]) ).
thf(1920,plain,
( ~ ( test @ sk1 )
| ( ( sk4 @ sk1 )
!= ( c @ sk3 ) ) ),
inference(simp,[status(thm)],[1907]) ).
thf(7590,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( sk4 @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ sk2 ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1541,74]) ).
thf(7591,plain,
( ( multiplication @ ( sk4 @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ sk2 ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[7590:[bind(A,$thf( c @ ( c @ sk2 ) )),bind(B,$thf( sk4 @ ( c @ ( c @ sk2 ) ) ))]]) ).
thf(16718,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ ( c @ ( c @ sk2 ) ) ) @ ( sk4 @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12225,56]) ).
thf(16719,plain,
( ( addition @ ( sk4 @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( c @ ( c @ ( c @ sk2 ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[16718:[bind(A,$thf( c @ ( c @ ( c @ sk2 ) ) )),bind(B,$thf( sk4 @ ( c @ ( c @ ( c @ sk2 ) ) ) ))]]) ).
thf(194,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( multiplication @ B @ ( multiplication @ C @ D ) ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( multiplication @ B @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[45,33]) ).
thf(214,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( multiplication @ B @ ( multiplication @ C @ D ) ) )
| ( ( multiplication @ B @ C )
!= one )
| ( A != D ) ),
inference(simp,[status(thm)],[194]) ).
thf(224,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= C )
| ( ( multiplication @ A @ B )
!= one ) ),
inference(simp,[status(thm)],[214]) ).
thf(123,plain,
! [A: $i] :
( ( ( addition @ ( multiplication @ sk2 @ sk1 ) @ zero )
= ( multiplication @ sk1 @ sk3 ) )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[84,27]) ).
thf(132,plain,
! [A: $i] :
( ( ( addition @ ( multiplication @ sk2 @ sk1 ) @ zero )
= ( multiplication @ sk1 @ sk3 ) )
| ( A != sk1 )
| ( sk3 != zero ) ),
inference(simp,[status(thm)],[123]) ).
thf(137,plain,
( ( ( addition @ ( multiplication @ sk2 @ sk1 ) @ zero )
= ( multiplication @ sk1 @ sk3 ) )
| ( sk3 != zero ) ),
inference(simp,[status(thm)],[132]) ).
thf(9095,plain,
( ( ( multiplication @ sk2 @ sk1 )
= ( multiplication @ sk1 @ sk3 ) )
| ( sk3 != zero ) ),
inference(rewrite,[status(thm)],[137,90]) ).
thf(2443,plain,
! [A: $i] :
( ( zero = A )
| ( ( multiplication @ ( c @ sk3 ) @ sk3 )
!= ( multiplication @ one @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1859,45]) ).
thf(2504,plain,
! [A: $i] :
( ( zero = A )
| ( ( c @ sk3 )
!= one )
| ( sk3 != A ) ),
inference(simp,[status(thm)],[2443]) ).
thf(2515,plain,
( ( sk3 = zero )
| ( ( c @ sk3 )
!= one ) ),
inference(simp,[status(thm)],[2504]) ).
thf(153,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiplication @ ( multiplication @ A @ ( multiplication @ B @ C ) ) @ F )
= ( multiplication @ D @ ( multiplication @ E @ F ) ) )
| ( ( multiplication @ ( multiplication @ A @ B ) @ C )
!= ( multiplication @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[33,33]) ).
thf(154,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ C @ ( multiplication @ D @ A ) ) @ B )
= ( multiplication @ ( multiplication @ C @ D ) @ ( multiplication @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( multiplication @ G @ H )),bind(E,$thf( C ))]]) ).
thf(190,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ C @ ( multiplication @ D @ A ) ) @ B )
= ( multiplication @ ( multiplication @ C @ D ) @ ( multiplication @ A @ B ) ) ),
inference(simp,[status(thm)],[154]) ).
thf(20148,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiplication @ C @ ( multiplication @ ( multiplication @ D @ A ) @ B ) )
= ( multiplication @ C @ ( multiplication @ D @ ( multiplication @ A @ B ) ) ) ),
inference(rewrite,[status(thm)],[190,33]) ).
thf(12317,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( c @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7565,75]) ).
thf(12318,plain,
( ( addition @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( c @ ( c @ ( c @ sk2 ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[12317:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk2 ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ sk2 ) ) ))]]) ).
thf(17549,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( c @ ( c @ ( c @ sk2 ) ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12318,56]) ).
thf(17550,plain,
( ( addition @ ( c @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[17549:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk2 ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ sk2 ) ) ))]]) ).
thf(7592,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( sk4 @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ sk2 ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1541,73]) ).
thf(7593,plain,
( ( multiplication @ ( c @ ( c @ sk2 ) ) @ ( sk4 @ ( c @ ( c @ sk2 ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[7592:[bind(A,$thf( c @ ( c @ sk2 ) )),bind(B,$thf( sk4 @ ( c @ ( c @ sk2 ) ) ))]]) ).
thf(340,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) )
| ( ( multiplication @ ( multiplication @ A @ B ) @ C )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[33,334]) ).
thf(347,plain,
! [C: $i,B: $i,A: $i] :
( ( A != sk1 )
| ( ( multiplication @ B @ C )
!= ( c @ sk3 ) )
| ( ( multiplication @ A @ B )
!= ( c @ sk2 ) )
| ( C != sk1 ) ),
inference(simp,[status(thm)],[340]) ).
thf(356,plain,
! [A: $i] :
( ( ( multiplication @ A @ sk1 )
!= ( c @ sk3 ) )
| ( ( multiplication @ sk1 @ A )
!= ( c @ sk2 ) ) ),
inference(simp,[status(thm)],[347]) ).
thf(2536,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( sk4 @ ( c @ ( c @ sk3 ) ) ) @ ( c @ ( c @ sk3 ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1437,75]) ).
thf(2537,plain,
( ( addition @ ( c @ ( c @ sk3 ) ) @ ( sk4 @ ( c @ ( c @ sk3 ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[2536:[bind(A,$thf( c @ ( c @ sk3 ) )),bind(B,$thf( sk4 @ ( c @ ( c @ sk3 ) ) ))]]) ).
thf(1073,plain,
! [B: $i,A: $i] :
( ~ ( test @ A )
| ~ ( complement @ A @ B )
| ( B != sk1 )
| ( sk3 != sk2 )
| ( ( c @ A )
!= ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[64,365]) ).
thf(1074,plain,
! [A: $i] :
( ~ ( test @ sk2 )
| ~ ( complement @ sk2 @ A )
| ( A != sk1 )
| ( sk3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[1073:[bind(A,$thf( sk2 ))]]) ).
thf(1359,plain,
( ~ ( test @ sk2 )
| ~ ( complement @ sk2 @ sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[1074]) ).
thf(13393,plain,
( ~ $true
| ~ ( complement @ sk2 @ sk1 )
| ( sk3 != sk2 ) ),
inference(rewrite,[status(thm)],[1359,25]) ).
thf(13394,plain,
( ~ ( complement @ sk2 @ sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[13393]) ).
thf(199,plain,
! [A: $i] :
( ( ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ A )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[45,26]) ).
thf(215,plain,
! [A: $i] :
( ( ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ A )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( c @ sk2 )
!= one )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[199]) ).
thf(225,plain,
( ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ sk1 ) )
| ( ( c @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[215]) ).
thf(2185,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( sk4 @ ( c @ sk3 ) ) @ ( c @ sk3 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1051,74]) ).
thf(2186,plain,
( ( multiplication @ ( sk4 @ ( c @ sk3 ) ) @ ( c @ sk3 ) )
= zero ),
inference(pattern_uni,[status(thm)],[2185:[bind(A,$thf( c @ sk3 )),bind(B,$thf( sk4 @ ( c @ sk3 ) ))]]) ).
thf(19017,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ ( sk4 @ ( c @ sk3 ) ) @ ( c @ sk3 ) )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2186,188]) ).
thf(19018,plain,
! [A: $i] :
( ( multiplication @ ( sk4 @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ sk3 ) @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[19017:[bind(A,$thf( sk4 @ ( c @ sk3 ) )),bind(B,$thf( c @ sk3 )),bind(C,$thf( C ))]]) ).
thf(19114,plain,
! [A: $i] :
( ( multiplication @ ( sk4 @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ sk3 ) @ A ) )
= zero ),
inference(simp,[status(thm)],[19018]) ).
thf(50015,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ one )
= ( addition @ A @ B ) )
| ( ( addition @ sk3 @ ( sk4 @ sk3 ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2559,323]) ).
thf(50016,plain,
( ( addition @ sk3 @ ( sk4 @ sk3 ) )
= ( addition @ sk3 @ one ) ),
inference(pattern_uni,[status(thm)],[50015:[bind(A,$thf( sk3 )),bind(B,$thf( sk4 @ sk3 ))]]) ).
thf(50557,plain,
( ( addition @ sk3 @ one )
= one ),
inference(rewrite,[status(thm)],[50016,2559]) ).
thf(1824,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( sk4 @ ( c @ sk3 ) ) @ ( c @ sk3 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1051,73]) ).
thf(1825,plain,
( ( multiplication @ ( c @ sk3 ) @ ( sk4 @ ( c @ sk3 ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[1824:[bind(A,$thf( c @ sk3 )),bind(B,$thf( sk4 @ ( c @ sk3 ) ))]]) ).
thf(13804,plain,
( ( sk2 != zero )
| ( test @ ( c @ one ) )
| ( ( c @ sk2 )
!= ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[3108,1490]) ).
thf(13805,plain,
( ( sk2 != zero )
| ( test @ ( c @ one ) ) ),
inference(pattern_uni,[status(thm)],[13804:[]]) ).
thf(12389,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12307,62]) ).
thf(12390,plain,
complement @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[12389:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ))]]) ).
thf(35771,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12390,75]) ).
thf(35772,plain,
( ( addition @ ( c @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[35771:[bind(A,$thf( c @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ))]]) ).
thf(43398,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35772,56]) ).
thf(43399,plain,
( ( addition @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[43398:[bind(A,$thf( c @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ))]]) ).
thf(50128,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ one )
= ( addition @ A @ B ) )
| ( ( addition @ ( c @ sk3 ) @ sk3 )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2577,323]) ).
thf(50129,plain,
( ( addition @ ( c @ sk3 ) @ sk3 )
= ( addition @ ( c @ sk3 ) @ one ) ),
inference(pattern_uni,[status(thm)],[50128:[bind(A,$thf( c @ sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(56130,plain,
( ( addition @ ( c @ sk3 ) @ one )
= one ),
inference(rewrite,[status(thm)],[50129,2577]) ).
thf(5044,plain,
( ( ( sk4 @ sk1 )
!= ( c @ sk3 ) )
| ( ( test @ sk2 )
!= ( test @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[25,1920]) ).
thf(5058,plain,
( ( ( sk4 @ sk1 )
!= ( c @ sk3 ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[5044]) ).
thf(35697,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12390,73]) ).
thf(35698,plain,
( ( multiplication @ ( c @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[35697:[bind(A,$thf( c @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ))]]) ).
thf(13414,plain,
( ( sk3 != sk2 )
| ( ( complement @ sk3 @ ( c @ sk3 ) )
!= ( complement @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[1038,13394]) ).
thf(13418,plain,
( ( sk3 != sk2 )
| ( sk3 != sk2 )
| ( ( c @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[13414]) ).
thf(13436,plain,
( ( sk3 != sk2 )
| ( ( c @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[13418]) ).
thf(1765,plain,
( ( ( sk4 @ zero )
!= sk3 )
| ( ( test @ sk2 )
!= ( test @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[25,1515]) ).
thf(1779,plain,
( ( ( sk4 @ zero )
!= sk3 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[1765]) ).
thf(2223,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ sk3 @ ( c @ sk3 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1038,74]) ).
thf(2224,plain,
( ( multiplication @ sk3 @ ( c @ sk3 ) )
= zero ),
inference(pattern_uni,[status(thm)],[2223:[bind(A,$thf( c @ sk3 )),bind(B,$thf( sk3 ))]]) ).
thf(18941,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ sk3 @ ( c @ sk3 ) )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2224,188]) ).
thf(18942,plain,
! [A: $i] :
( ( multiplication @ sk3 @ ( multiplication @ ( c @ sk3 ) @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[18941:[bind(A,$thf( sk3 )),bind(B,$thf( c @ sk3 )),bind(C,$thf( C ))]]) ).
thf(19198,plain,
! [A: $i] :
( ( multiplication @ sk3 @ ( multiplication @ ( c @ sk3 ) @ A ) )
= zero ),
inference(simp,[status(thm)],[18942]) ).
thf(18700,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ ( c @ sk2 ) @ ( sk4 @ ( c @ sk2 ) ) )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1793,188]) ).
thf(18701,plain,
! [A: $i] :
( ( multiplication @ ( c @ sk2 ) @ ( multiplication @ ( sk4 @ ( c @ sk2 ) ) @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[18700:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk4 @ ( c @ sk2 ) )),bind(C,$thf( C ))]]) ).
thf(19090,plain,
! [A: $i] :
( ( multiplication @ ( c @ sk2 ) @ ( multiplication @ ( sk4 @ ( c @ sk2 ) ) @ A ) )
= zero ),
inference(simp,[status(thm)],[18701]) ).
thf(13740,plain,
( ( sk2 != zero )
| ( ( c @ sk3 )
!= ( c @ sk2 ) )
| ( ( c @ sk2 )
!= ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[3108,813]) ).
thf(13741,plain,
( ( sk2 != zero )
| ( ( c @ sk3 )
!= ( c @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[13740:[]]) ).
thf(2528,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( c @ ( c @ sk3 ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1424,75]) ).
thf(2529,plain,
( ( addition @ ( c @ ( c @ ( c @ sk3 ) ) ) @ ( c @ ( c @ sk3 ) ) )
= one ),
inference(pattern_uni,[status(thm)],[2528:[bind(A,$thf( c @ ( c @ ( c @ sk3 ) ) )),bind(B,$thf( c @ ( c @ sk3 ) ))]]) ).
thf(8795,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ ( c @ ( c @ sk3 ) ) ) @ ( c @ ( c @ sk3 ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2529,56]) ).
thf(8796,plain,
( ( addition @ ( c @ ( c @ sk3 ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[8795:[bind(A,$thf( c @ ( c @ ( c @ sk3 ) ) )),bind(B,$thf( c @ ( c @ sk3 ) ))]]) ).
thf(1767,plain,
( ( ( sk4 @ zero )
!= sk3 )
| ( ( test @ ( c @ sk2 ) )
!= ( test @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[1057,1515]) ).
thf(1775,plain,
( ( ( sk4 @ zero )
!= sk3 )
| ( ( c @ sk2 )
!= zero ) ),
inference(simp,[status(thm)],[1767]) ).
thf(3838,plain,
( ( sk2 != one )
| ( ( sk4 @ zero )
!= sk3 )
| ( ( c @ sk2 )
!= ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2026,1775]) ).
thf(3839,plain,
( ( sk2 != one )
| ( ( sk4 @ zero )
!= sk3 ) ),
inference(pattern_uni,[status(thm)],[3838:[]]) ).
thf(3493,plain,
! [A: $i] :
( ( one = A )
| ( ( addition @ sk3 @ ( sk4 @ sk3 ) )
!= ( addition @ A @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[2559,90]) ).
thf(3503,plain,
! [A: $i] :
( ( one = A )
| ( sk3 != A )
| ( ( sk4 @ sk3 )
!= zero ) ),
inference(simp,[status(thm)],[3493]) ).
thf(3515,plain,
( ( sk3 = one )
| ( ( sk4 @ sk3 )
!= zero ) ),
inference(simp,[status(thm)],[3503]) ).
thf(18682,plain,
( ( sk4 @ sk3 )
!= zero ),
inference(simplifyReflect,[status(thm)],[3515,7449]) ).
thf(11959,plain,
! [B: $i,A: $i] :
( ( test @ A )
| ( ( complement @ ( c @ ( c @ ( c @ sk3 ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1688,50]) ).
thf(11960,plain,
test @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[11959:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk3 ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ sk3 ) ) ))]]) ).
thf(12041,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11960,62]) ).
thf(12042,plain,
complement @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[12041:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ))]]) ).
thf(35355,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12042,75]) ).
thf(35356,plain,
( ( addition @ ( c @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[35355:[bind(A,$thf( c @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ))]]) ).
thf(38954,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35356,56]) ).
thf(38955,plain,
( ( addition @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[38954:[bind(A,$thf( c @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ))]]) ).
thf(35283,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12042,73]) ).
thf(35284,plain,
( ( multiplication @ ( c @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[35283:[bind(A,$thf( c @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ))]]) ).
thf(12258,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( c @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7565,73]) ).
thf(12259,plain,
( ( multiplication @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( c @ ( c @ ( c @ sk2 ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[12258:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk2 ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ sk2 ) ) ))]]) ).
thf(52486,plain,
! [B: $i,A: $i] :
( ( one != B )
| ( leq @ A @ B )
| ( ( addition @ ( sk4 @ sk2 ) @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[52342,99]) ).
thf(52487,plain,
( ( one != one )
| ( leq @ ( sk4 @ sk2 ) @ one ) ),
inference(pattern_uni,[status(thm)],[52486:[bind(A,$thf( sk4 @ sk2 )),bind(B,$thf( one ))]]) ).
thf(52577,plain,
leq @ ( sk4 @ sk2 ) @ one,
inference(simp,[status(thm)],[52487]) ).
thf(18823,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ ( c @ sk2 ) @ sk2 )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1819,188]) ).
thf(18824,plain,
! [A: $i] :
( ( multiplication @ ( c @ sk2 ) @ ( multiplication @ sk2 @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[18823:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk2 )),bind(C,$thf( C ))]]) ).
thf(19170,plain,
! [A: $i] :
( ( multiplication @ ( c @ sk2 ) @ ( multiplication @ sk2 @ A ) )
= zero ),
inference(simp,[status(thm)],[18824]) ).
thf(11968,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( c @ ( c @ ( c @ sk3 ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1688,75]) ).
thf(11969,plain,
( ( addition @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[11968:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk3 ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ sk3 ) ) ))]]) ).
thf(12950,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[11969,56]) ).
thf(12951,plain,
( ( addition @ ( c @ ( c @ ( c @ sk3 ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[12950:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk3 ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ sk3 ) ) ))]]) ).
thf(1812,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( c @ sk2 ) @ ( c @ ( c @ sk2 ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1059,73]) ).
thf(1813,plain,
( ( multiplication @ ( c @ ( c @ sk2 ) ) @ ( c @ sk2 ) )
= zero ),
inference(pattern_uni,[status(thm)],[1812:[bind(A,$thf( c @ ( c @ sk2 ) )),bind(B,$thf( c @ sk2 ))]]) ).
thf(18947,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ ( c @ ( c @ sk2 ) ) @ ( c @ sk2 ) )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1813,188]) ).
thf(18948,plain,
! [A: $i] :
( ( multiplication @ ( c @ ( c @ sk2 ) ) @ ( multiplication @ ( c @ sk2 ) @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[18947:[bind(A,$thf( c @ ( c @ sk2 ) )),bind(B,$thf( c @ sk2 )),bind(C,$thf( C ))]]) ).
thf(19086,plain,
! [A: $i] :
( ( multiplication @ ( c @ ( c @ sk2 ) ) @ ( multiplication @ ( c @ sk2 ) @ A ) )
= zero ),
inference(simp,[status(thm)],[18948]) ).
thf(2261,plain,
( ( complement @ ( sk4 @ ( c @ sk3 ) ) @ ( c @ sk3 ) )
!= ( complement @ sk1 @ ( c @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[1051,2236]) ).
thf(2286,plain,
( ( ( sk4 @ ( c @ sk3 ) )
!= sk1 )
| ( ( c @ sk3 )
!= ( c @ sk3 ) ) ),
inference(simp,[status(thm)],[2261]) ).
thf(2293,plain,
( ( sk4 @ ( c @ sk3 ) )
!= sk1 ),
inference(simp,[status(thm)],[2286]) ).
thf(3055,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ sk2 ) @ sk2 )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2555,56]) ).
thf(3056,plain,
( ( addition @ sk2 @ ( c @ sk2 ) )
= one ),
inference(pattern_uni,[status(thm)],[3055:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(3682,plain,
! [A: $i] :
( ( A = one )
| ( ( addition @ A @ A )
!= ( addition @ sk2 @ ( c @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,3056]) ).
thf(3713,plain,
! [A: $i] :
( ( A = one )
| ( A != sk2 )
| ( A
!= ( c @ sk2 ) ) ),
inference(simp,[status(thm)],[3682]) ).
thf(3726,plain,
( ( sk2 = one )
| ( ( c @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[3713]) ).
thf(12023,plain,
! [A: $i] :
( ( complement @ ( sk4 @ A ) @ A )
| ( ( test @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[11960,49]) ).
thf(12024,plain,
complement @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ),
inference(pattern_uni,[status(thm)],[12023:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ))]]) ).
thf(35198,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12024,75]) ).
thf(35199,plain,
( ( addition @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[35198:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk3 ) ) ) )),bind(B,$thf( sk4 @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ))]]) ).
thf(37677,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[35199,56]) ).
thf(37678,plain,
( ( addition @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[37677:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk3 ) ) ) )),bind(B,$thf( sk4 @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ))]]) ).
thf(3558,plain,
! [A: $i] :
( ( one = A )
| ( ( addition @ sk2 @ ( sk4 @ sk2 ) )
!= ( addition @ A @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[2573,90]) ).
thf(3566,plain,
! [A: $i] :
( ( one = A )
| ( sk2 != A )
| ( ( sk4 @ sk2 )
!= zero ) ),
inference(simp,[status(thm)],[3558]) ).
thf(3579,plain,
( ( sk2 = one )
| ( ( sk4 @ sk2 )
!= zero ) ),
inference(simp,[status(thm)],[3566]) ).
thf(2556,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( sk4 @ ( c @ sk3 ) ) @ ( c @ sk3 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1051,75]) ).
thf(2557,plain,
( ( addition @ ( c @ sk3 ) @ ( sk4 @ ( c @ sk3 ) ) )
= one ),
inference(pattern_uni,[status(thm)],[2556:[bind(A,$thf( c @ sk3 )),bind(B,$thf( sk4 @ ( c @ sk3 ) ))]]) ).
thf(30943,plain,
( ( sk3 != zero )
| ( ( c @ one )
!= sk1 )
| ( ( c @ sk3 )
!= ( c @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[3657,1921]) ).
thf(30944,plain,
( ( sk3 != zero )
| ( ( c @ one )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[30943:[]]) ).
thf(2219,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( sk4 @ sk2 ) @ sk2 )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[663,74]) ).
thf(2220,plain,
( ( multiplication @ ( sk4 @ sk2 ) @ sk2 )
= zero ),
inference(pattern_uni,[status(thm)],[2219:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 @ sk2 ))]]) ).
thf(156,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( multiplication @ A @ ( multiplication @ B @ C ) ) @ ( multiplication @ sk1 @ sk3 ) )
= ( multiplication @ sk1 @ sk3 ) )
| ( ( multiplication @ ( multiplication @ A @ B ) @ C )
!= ( multiplication @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[33,27]) ).
thf(175,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( multiplication @ A @ ( multiplication @ B @ C ) ) @ ( multiplication @ sk1 @ sk3 ) )
= ( multiplication @ sk1 @ sk3 ) )
| ( ( multiplication @ A @ B )
!= sk2 )
| ( C != sk1 ) ),
inference(simp,[status(thm)],[156]) ).
thf(187,plain,
! [B: $i,A: $i] :
( ( ( addition @ ( multiplication @ A @ ( multiplication @ B @ sk1 ) ) @ ( multiplication @ sk1 @ sk3 ) )
= ( multiplication @ sk1 @ sk3 ) )
| ( ( multiplication @ A @ B )
!= sk2 ) ),
inference(simp,[status(thm)],[175]) ).
thf(196,plain,
! [A: $i] :
( ( ( addition @ ( multiplication @ sk2 @ sk1 ) @ A )
= ( multiplication @ sk1 @ sk3 ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ sk1 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[45,27]) ).
thf(207,plain,
! [A: $i] :
( ( ( addition @ ( multiplication @ sk2 @ sk1 ) @ A )
= ( multiplication @ sk1 @ sk3 ) )
| ( sk1 != one )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[196]) ).
thf(219,plain,
( ( ( addition @ ( multiplication @ sk2 @ sk1 ) @ sk3 )
= ( multiplication @ sk1 @ sk3 ) )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[207]) ).
thf(7129,plain,
( ( sk2 != one )
| ( complement @ zero @ sk2 )
| ( ( sk4 @ sk2 )
!= ( sk4 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2395,663]) ).
thf(7130,plain,
( ( sk2 != one )
| ( complement @ zero @ sk2 ) ),
inference(pattern_uni,[status(thm)],[7129:[]]) ).
thf(35279,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12042,74]) ).
thf(35280,plain,
( ( multiplication @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[35279:[bind(A,$thf( c @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ))]]) ).
thf(38,plain,
! [A: $i] :
( ( test @ A )
| ( ( c @ A )
= zero ) ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
! [A: $i] :
( ( ( c @ A )
= zero )
| ( test @ A ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(2179,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ sk2 @ ( c @ sk2 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1040,74]) ).
thf(2180,plain,
( ( multiplication @ sk2 @ ( c @ sk2 ) )
= zero ),
inference(pattern_uni,[status(thm)],[2179:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(50570,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ sk3 @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[50557,56]) ).
thf(50571,plain,
( ( addition @ one @ sk3 )
= one ),
inference(pattern_uni,[status(thm)],[50570:[bind(A,$thf( sk3 )),bind(B,$thf( one ))]]) ).
thf(324,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( A
= ( addition @ D @ ( addition @ C @ B ) ) )
| ( ( addition @ A @ A )
!= ( addition @ ( addition @ D @ C ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[53,36]) ).
thf(325,plain,
! [B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ ( addition @ A @ B ) ) )
= ( addition @ A @ B ) ),
inference(pattern_uni,[status(thm)],[324:[bind(A,$thf( addition @ G @ H )),bind(B,$thf( addition @ G @ H )),bind(C,$thf( H )),bind(D,$thf( G ))]]) ).
thf(332,plain,
! [B: $i,A: $i] :
( ( addition @ A @ ( addition @ B @ ( addition @ A @ B ) ) )
= ( addition @ A @ B ) ),
inference(simp,[status(thm)],[325]) ).
thf(51784,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ ( addition @ B @ one ) )
= ( addition @ A @ B ) )
| ( ( addition @ one @ sk3 )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[50571,332]) ).
thf(51785,plain,
( ( addition @ one @ ( addition @ sk3 @ one ) )
= ( addition @ one @ sk3 ) ),
inference(pattern_uni,[status(thm)],[51784:[bind(A,$thf( one )),bind(B,$thf( sk3 ))]]) ).
thf(57200,plain,
( ( addition @ one @ one )
= one ),
inference(rewrite,[status(thm)],[51785,50571,50557]) ).
thf(52906,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ sk2 ) @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[52891,56]) ).
thf(52907,plain,
( ( addition @ one @ ( c @ sk2 ) )
= one ),
inference(pattern_uni,[status(thm)],[52906:[bind(A,$thf( c @ sk2 )),bind(B,$thf( one ))]]) ).
thf(4708,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ A @ A )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[53,99]) ).
thf(4709,plain,
! [A: $i] :
( ( A != A )
| ( leq @ A @ A ) ),
inference(pattern_uni,[status(thm)],[4708:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(4726,plain,
! [A: $i] : ( leq @ A @ A ),
inference(simp,[status(thm)],[4709]) ).
thf(31157,plain,
( ( sk3 != zero )
| ( ( sk4 @ one )
!= sk1 )
| ( ( c @ sk3 )
!= ( c @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[3657,2293]) ).
thf(31158,plain,
( ( sk3 != zero )
| ( ( sk4 @ one )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[31157:[]]) ).
thf(35693,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12390,74]) ).
thf(35694,plain,
( ( multiplication @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[35693:[bind(A,$thf( c @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ))]]) ).
thf(31135,plain,
( ( sk3 != zero )
| ( ( c @ sk2 )
!= one )
| ( ( c @ sk3 )
!= ( c @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[3657,743]) ).
thf(31136,plain,
( ( sk3 != zero )
| ( ( c @ sk2 )
!= one ) ),
inference(pattern_uni,[status(thm)],[31135:[]]) ).
thf(31016,plain,
( ( sk3 != zero )
| ( test @ one )
| ( ( c @ sk3 )
!= ( c @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[3657,1047]) ).
thf(31017,plain,
( ( sk3 != zero )
| ( test @ one ) ),
inference(pattern_uni,[status(thm)],[31016:[]]) ).
thf(18706,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ sk2 @ ( sk4 @ sk2 ) )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1855,188]) ).
thf(18707,plain,
! [A: $i] :
( ( multiplication @ sk2 @ ( multiplication @ ( sk4 @ sk2 ) @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[18706:[bind(A,$thf( sk2 )),bind(B,$thf( sk4 @ sk2 )),bind(C,$thf( C ))]]) ).
thf(19093,plain,
! [A: $i] :
( ( multiplication @ sk2 @ ( multiplication @ ( sk4 @ sk2 ) @ A ) )
= zero ),
inference(simp,[status(thm)],[18707]) ).
thf(198,plain,
! [A: $i] :
( ( ( addition @ A @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[45,26]) ).
thf(213,plain,
! [A: $i] :
( ( ( addition @ A @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( sk1 != one )
| ( A
!= ( c @ sk3 ) ) ),
inference(simp,[status(thm)],[198]) ).
thf(223,plain,
( ( ( addition @ ( c @ sk3 ) @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[213]) ).
thf(125,plain,
( ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( multiplication @ sk1 @ sk3 ) )
| ( ( addition @ ( multiplication @ sk2 @ sk1 ) @ ( multiplication @ sk1 @ sk3 ) )
!= ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[27,26]) ).
thf(129,plain,
( ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( multiplication @ sk1 @ sk3 ) )
| ( ( multiplication @ sk2 @ sk1 )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) )
| ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( multiplication @ sk1 @ sk3 ) ) ),
inference(simp,[status(thm)],[125]) ).
thf(135,plain,
( ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( multiplication @ sk1 @ sk3 ) )
| ( ( multiplication @ sk2 @ sk1 )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(1963,plain,
! [A: $i] :
( ( A = zero )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( c @ sk2 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[45,1819]) ).
thf(1990,plain,
! [A: $i] :
( ( A = zero )
| ( ( c @ sk2 )
!= one )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[1963]) ).
thf(2022,plain,
( ( sk2 = zero )
| ( ( c @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[1990]) ).
thf(240,plain,
! [A: $i] :
( ( ( addition @ A @ ( multiplication @ sk1 @ sk3 ) )
= ( multiplication @ sk1 @ sk3 ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[81,27]) ).
thf(254,plain,
! [A: $i] :
( ( ( addition @ A @ ( multiplication @ sk1 @ sk3 ) )
= ( multiplication @ sk1 @ sk3 ) )
| ( A != sk2 )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[240]) ).
thf(267,plain,
( ( ( addition @ sk2 @ ( multiplication @ sk1 @ sk3 ) )
= ( multiplication @ sk1 @ sk3 ) )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[254]) ).
thf(352,plain,
( ( multiplication @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ one )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ),
inference(simp,[status(thm)],[341]) ).
thf(431,plain,
( ( multiplication @ sk1 @ ( multiplication @ ( c @ sk3 ) @ one ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[352,33]) ).
thf(7506,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( c @ ( c @ sk2 ) ) @ ( c @ ( c @ ( c @ sk2 ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1528,75]) ).
thf(7507,plain,
( ( addition @ ( c @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ sk2 ) ) )
= one ),
inference(pattern_uni,[status(thm)],[7506:[bind(A,$thf( c @ ( c @ ( c @ sk2 ) ) )),bind(B,$thf( c @ ( c @ sk2 ) ))]]) ).
thf(35126,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12024,74]) ).
thf(35127,plain,
( ( multiplication @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[35126:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk3 ) ) ) )),bind(B,$thf( sk4 @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ))]]) ).
thf(12134,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( sk4 @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1705,75]) ).
thf(12135,plain,
( ( addition @ ( c @ ( c @ ( c @ sk3 ) ) ) @ ( sk4 @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[12134:[bind(A,$thf( c @ ( c @ ( c @ sk3 ) ) )),bind(B,$thf( sk4 @ ( c @ ( c @ ( c @ sk3 ) ) ) ))]]) ).
thf(9957,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ sk2 ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7507,56]) ).
thf(9958,plain,
( ( addition @ ( c @ ( c @ sk2 ) ) @ ( c @ ( c @ ( c @ sk2 ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[9957:[bind(A,$thf( c @ ( c @ ( c @ sk2 ) ) )),bind(B,$thf( c @ ( c @ sk2 ) ))]]) ).
thf(13539,plain,
( ( sk2 != zero )
| ( complement @ sk2 @ one )
| ( ( c @ sk2 )
!= ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[3108,1040]) ).
thf(13540,plain,
( ( sk2 != zero )
| ( complement @ sk2 @ one ) ),
inference(pattern_uni,[status(thm)],[13539:[]]) ).
thf(1503,plain,
( ( complement @ ( sk4 @ sk2 ) @ sk2 )
!= ( complement @ sk3 @ zero ) ),
inference(paramod_ordered,[status(thm)],[663,1494]) ).
thf(1509,plain,
( ( ( sk4 @ sk2 )
!= sk3 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[1503]) ).
thf(35343,plain,
! [B: $i,A: $i] :
( ( test @ A )
| ( ( complement @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12042,50]) ).
thf(35344,plain,
test @ ( c @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[35343:[bind(A,$thf( c @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ))]]) ).
thf(18851,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ ( c @ sk3 ) @ ( sk4 @ ( c @ sk3 ) ) )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1825,188]) ).
thf(18852,plain,
! [A: $i] :
( ( multiplication @ ( c @ sk3 ) @ ( multiplication @ ( sk4 @ ( c @ sk3 ) ) @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[18851:[bind(A,$thf( c @ sk3 )),bind(B,$thf( sk4 @ ( c @ sk3 ) )),bind(C,$thf( C ))]]) ).
thf(19182,plain,
! [A: $i] :
( ( multiplication @ ( c @ sk3 ) @ ( multiplication @ ( sk4 @ ( c @ sk3 ) ) @ A ) )
= zero ),
inference(simp,[status(thm)],[18852]) ).
thf(346,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) )
| ( ( multiplication @ A @ B )
!= ( c @ sk2 ) )
| ( C != sk1 ) ),
inference(simp,[status(thm)],[340]) ).
thf(355,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ sk1 ) )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) )
| ( ( multiplication @ A @ B )
!= ( c @ sk2 ) ) ),
inference(simp,[status(thm)],[346]) ).
thf(7461,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( c @ ( c @ sk2 ) ) @ ( c @ ( c @ ( c @ sk2 ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1528,73]) ).
thf(7462,plain,
( ( multiplication @ ( c @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ sk2 ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[7461:[bind(A,$thf( c @ ( c @ ( c @ sk2 ) ) )),bind(B,$thf( c @ ( c @ sk2 ) ))]]) ).
thf(385,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( multiplication @ ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) @ F )
= ( multiplication @ D @ ( multiplication @ E @ F ) ) )
| ( ( multiplication @ ( addition @ A @ B ) @ C )
!= ( multiplication @ D @ E ) ) ),
inference(paramod_ordered,[status(thm)],[42,33]) ).
thf(386,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ ( multiplication @ C @ A ) @ ( multiplication @ D @ A ) ) @ B )
= ( multiplication @ ( addition @ C @ D ) @ ( multiplication @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[385:[bind(A,$thf( G )),bind(B,$thf( H )),bind(C,$thf( C )),bind(D,$thf( addition @ G @ H )),bind(E,$thf( C ))]]) ).
thf(410,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ ( multiplication @ C @ A ) @ ( multiplication @ D @ A ) ) @ B )
= ( multiplication @ ( addition @ C @ D ) @ ( multiplication @ A @ B ) ) ),
inference(simp,[status(thm)],[386]) ).
thf(57476,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( addition @ ( multiplication @ ( multiplication @ C @ A ) @ B ) @ ( multiplication @ ( multiplication @ D @ A ) @ B ) )
= ( addition @ ( multiplication @ C @ ( multiplication @ A @ B ) ) @ ( multiplication @ D @ ( multiplication @ A @ B ) ) ) ),
inference(rewrite,[status(thm)],[410,42]) ).
thf(30963,plain,
( ( sk3 != zero )
| ~ ( complement @ one @ sk1 )
| ( ( c @ sk3 )
!= ( c @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[3657,1871]) ).
thf(30964,plain,
( ( sk3 != zero )
| ~ ( complement @ one @ sk1 ) ),
inference(pattern_uni,[status(thm)],[30963:[]]) ).
thf(157,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( multiplication @ A @ ( multiplication @ B @ C ) ) @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( multiplication @ ( multiplication @ A @ B ) @ C )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,26]) ).
thf(170,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( multiplication @ A @ ( multiplication @ B @ C ) ) @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( multiplication @ A @ B )
!= sk1 )
| ( C
!= ( c @ sk3 ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(182,plain,
! [B: $i,A: $i] :
( ( ( addition @ ( multiplication @ A @ ( multiplication @ B @ ( c @ sk3 ) ) ) @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( multiplication @ A @ B )
!= sk1 ) ),
inference(simp,[status(thm)],[170]) ).
thf(50962,plain,
! [B: $i,A: $i] :
( ( one = B )
| ~ ( leq @ A @ B )
| ( ( addition @ one @ sk3 )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[50571,100]) ).
thf(50963,plain,
( ( sk3 = one )
| ~ ( leq @ one @ sk3 ) ),
inference(pattern_uni,[status(thm)],[50962:[bind(A,$thf( one )),bind(B,$thf( sk3 ))]]) ).
thf(60207,plain,
~ ( leq @ one @ sk3 ),
inference(simplifyReflect,[status(thm)],[50963,7449]) ).
thf(1497,plain,
( ( complement @ sk3 @ zero )
!= ( complement @ sk2 @ ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[1040,1494]) ).
thf(1506,plain,
( ( sk3 != sk2 )
| ( ( c @ sk2 )
!= zero ) ),
inference(simp,[status(thm)],[1497]) ).
thf(3852,plain,
( ( sk2 != one )
| ( sk3 != sk2 )
| ( ( c @ sk2 )
!= ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2026,1506]) ).
thf(3853,plain,
( ( sk2 != one )
| ( sk3 != sk2 ) ),
inference(pattern_uni,[status(thm)],[3852:[]]) ).
thf(15183,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ ( c @ ( c @ sk3 ) ) ) @ ( sk4 @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[12135,56]) ).
thf(15184,plain,
( ( addition @ ( sk4 @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ) )
= one ),
inference(pattern_uni,[status(thm)],[15183:[bind(A,$thf( c @ ( c @ ( c @ sk3 ) ) )),bind(B,$thf( sk4 @ ( c @ ( c @ ( c @ sk3 ) ) ) ))]]) ).
thf(3053,plain,
! [A: $i] :
( ( one = A )
| ( ( addition @ ( c @ sk2 ) @ sk2 )
!= ( addition @ zero @ A ) ) ),
inference(paramod_ordered,[status(thm)],[2555,873]) ).
thf(3094,plain,
! [A: $i] :
( ( one = A )
| ( ( c @ sk2 )
!= zero )
| ( sk2 != A ) ),
inference(simp,[status(thm)],[3053]) ).
thf(3107,plain,
( ( sk2 = one )
| ( ( c @ sk2 )
!= zero ) ),
inference(simp,[status(thm)],[3094]) ).
thf(2272,plain,
( ( complement @ ( sk4 @ sk2 ) @ sk2 )
!= ( complement @ sk1 @ ( c @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[663,2236]) ).
thf(2279,plain,
( ( ( sk4 @ sk2 )
!= sk1 )
| ( ( c @ sk3 )
!= sk2 ) ),
inference(simp,[status(thm)],[2272]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
!= zero )
| ( ( multiplication @ B @ A )
!= zero )
| ( ( addition @ A @ B )
!= one )
| ( complement @ B @ A ) ),
inference(cnf,[status(esa)],[66]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
!= zero )
| ( ( multiplication @ B @ A )
!= zero )
| ( ( addition @ A @ B )
!= one )
| ( complement @ B @ A ) ),
inference(lifteq,[status(thm)],[67]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
!= zero )
| ( ( multiplication @ B @ A )
!= zero )
| ( ( addition @ A @ B )
!= one )
| ( complement @ B @ A ) ),
inference(simp,[status(thm)],[71]) ).
thf(51181,plain,
! [B: $i,A: $i] :
( ( one != B )
| ( leq @ A @ B )
| ( ( addition @ sk2 @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[51047,99]) ).
thf(51182,plain,
( ( one != one )
| ( leq @ sk2 @ one ) ),
inference(pattern_uni,[status(thm)],[51181:[bind(A,$thf( sk2 )),bind(B,$thf( one ))]]) ).
thf(51290,plain,
leq @ sk2 @ one,
inference(simp,[status(thm)],[51182]) ).
thf(56290,plain,
! [B: $i,A: $i] :
( ( one != B )
| ( leq @ A @ B )
| ( ( addition @ ( c @ sk3 ) @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[56130,99]) ).
thf(56291,plain,
( ( one != one )
| ( leq @ ( c @ sk3 ) @ one ) ),
inference(pattern_uni,[status(thm)],[56290:[bind(A,$thf( c @ sk3 )),bind(B,$thf( one ))]]) ).
thf(56413,plain,
leq @ ( c @ sk3 ) @ one,
inference(simp,[status(thm)],[56291]) ).
thf(39246,plain,
( ( complement @ sk3 @ sk3 )
!= ( complement @ sk2 @ ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[1040,39240]) ).
thf(39277,plain,
( ( sk3 != sk2 )
| ( ( c @ sk2 )
!= sk3 ) ),
inference(simp,[status(thm)],[39246]) ).
thf(51431,plain,
! [B: $i,A: $i] :
( ( one != B )
| ( leq @ A @ B )
| ( ( addition @ one @ sk2 )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[51061,99]) ).
thf(51432,plain,
( ( sk2 != one )
| ( leq @ one @ sk2 ) ),
inference(pattern_uni,[status(thm)],[51431:[bind(A,$thf( one )),bind(B,$thf( sk2 ))]]) ).
thf(50687,plain,
! [B: $i,A: $i] :
( ( one != B )
| ( leq @ A @ B )
| ( ( addition @ sk3 @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[50557,99]) ).
thf(50688,plain,
( ( one != one )
| ( leq @ sk3 @ one ) ),
inference(pattern_uni,[status(thm)],[50687:[bind(A,$thf( sk3 )),bind(B,$thf( one ))]]) ).
thf(50768,plain,
leq @ sk3 @ one,
inference(simp,[status(thm)],[50688]) ).
thf(6407,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ sk3 ) @ ( sk4 @ ( c @ sk3 ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2557,56]) ).
thf(6408,plain,
( ( addition @ ( sk4 @ ( c @ sk3 ) ) @ ( c @ sk3 ) )
= one ),
inference(pattern_uni,[status(thm)],[6407:[bind(A,$thf( c @ sk3 )),bind(B,$thf( sk4 @ ( c @ sk3 ) ))]]) ).
thf(86,plain,
! [B: $i,A: $i] :
( ~ ( test @ A )
| ~ ( test @ B )
| ( ( c @ ( addition @ A @ B ) )
= ( multiplication @ ( c @ A ) @ ( c @ B ) ) ) ),
inference(cnf,[status(esa)],[85]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ ( c @ A ) @ ( c @ B ) )
= ( c @ ( addition @ A @ B ) ) )
| ~ ( test @ A )
| ~ ( test @ B ) ),
inference(lifteq,[status(thm)],[86]) ).
thf(3873,plain,
( ( sk2 != one )
| ( test @ ( c @ zero ) )
| ( ( c @ sk2 )
!= ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2026,1490]) ).
thf(3874,plain,
( ( sk2 != one )
| ( test @ ( c @ zero ) ) ),
inference(pattern_uni,[status(thm)],[3873:[]]) ).
thf(397,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ D )
= ( addition @ ( multiplication @ B @ D ) @ ( multiplication @ C @ D ) ) )
| ( ( addition @ A @ zero )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[90,42]) ).
thf(398,plain,
! [B: $i,A: $i] :
( ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ zero @ B ) )
= ( multiplication @ A @ B ) ),
inference(pattern_uni,[status(thm)],[397:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( zero ))]]) ).
thf(414,plain,
! [B: $i,A: $i] :
( ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ zero @ B ) )
= ( multiplication @ A @ B ) ),
inference(simp,[status(thm)],[398]) ).
thf(62626,plain,
! [B: $i,A: $i] :
( ( addition @ ( multiplication @ A @ B ) @ zero )
= ( multiplication @ A @ B ) ),
inference(rewrite,[status(thm)],[414,30]) ).
thf(19011,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ ( c @ sk3 ) @ sk3 )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1859,188]) ).
thf(19012,plain,
! [A: $i] :
( ( multiplication @ ( c @ sk3 ) @ ( multiplication @ sk3 @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[19011:[bind(A,$thf( c @ sk3 )),bind(B,$thf( sk3 )),bind(C,$thf( C ))]]) ).
thf(19111,plain,
! [A: $i] :
( ( multiplication @ ( c @ sk3 ) @ ( multiplication @ sk3 @ A ) )
= zero ),
inference(simp,[status(thm)],[19012]) ).
thf(1806,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( sk4 @ ( c @ ( c @ sk3 ) ) ) @ ( c @ ( c @ sk3 ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1437,73]) ).
thf(1807,plain,
( ( multiplication @ ( c @ ( c @ sk3 ) ) @ ( sk4 @ ( c @ ( c @ sk3 ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[1806:[bind(A,$thf( c @ ( c @ sk3 ) )),bind(B,$thf( sk4 @ ( c @ ( c @ sk3 ) ) ))]]) ).
thf(4690,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ zero @ A )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[873,99]) ).
thf(4691,plain,
! [A: $i] :
( ( A != A )
| ( leq @ zero @ A ) ),
inference(pattern_uni,[status(thm)],[4690:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(4730,plain,
! [A: $i] : ( leq @ zero @ A ),
inference(simp,[status(thm)],[4691]) ).
thf(3796,plain,
( ( sk2 != one )
| ( complement @ sk2 @ zero )
| ( ( c @ sk2 )
!= ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[2026,1040]) ).
thf(3797,plain,
( ( sk2 != one )
| ( complement @ sk2 @ zero ) ),
inference(pattern_uni,[status(thm)],[3796:[]]) ).
thf(2173,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( c @ sk2 ) @ ( c @ ( c @ sk2 ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1059,74]) ).
thf(2174,plain,
( ( multiplication @ ( c @ sk2 ) @ ( c @ ( c @ sk2 ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[2173:[bind(A,$thf( c @ ( c @ sk2 ) )),bind(B,$thf( c @ sk2 ))]]) ).
thf(18975,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ ( c @ sk2 ) @ ( c @ ( c @ sk2 ) ) )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2174,188]) ).
thf(18976,plain,
! [A: $i] :
( ( multiplication @ ( c @ sk2 ) @ ( multiplication @ ( c @ ( c @ sk2 ) ) @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[18975:[bind(A,$thf( c @ sk2 )),bind(B,$thf( c @ ( c @ sk2 ) )),bind(C,$thf( C ))]]) ).
thf(19097,plain,
! [A: $i] :
( ( multiplication @ ( c @ sk2 ) @ ( multiplication @ ( c @ ( c @ sk2 ) ) @ A ) )
= zero ),
inference(simp,[status(thm)],[18976]) ).
thf(18692,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ ( c @ ( c @ ( c @ sk2 ) ) ) @ ( c @ ( c @ sk2 ) ) )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[7462,188]) ).
thf(18693,plain,
! [A: $i] :
( ( multiplication @ ( c @ ( c @ ( c @ sk2 ) ) ) @ ( multiplication @ ( c @ ( c @ sk2 ) ) @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[18692:[bind(A,$thf( c @ ( c @ ( c @ sk2 ) ) )),bind(B,$thf( c @ ( c @ sk2 ) )),bind(C,$thf( C ))]]) ).
thf(19087,plain,
! [A: $i] :
( ( multiplication @ ( c @ ( c @ ( c @ sk2 ) ) ) @ ( multiplication @ ( c @ ( c @ sk2 ) ) @ A ) )
= zero ),
inference(simp,[status(thm)],[18693]) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ ( multiplication @ A @ ( multiplication @ B @ C ) ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( multiplication @ ( multiplication @ A @ B ) @ C )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[33,26]) ).
thf(174,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ ( multiplication @ A @ ( multiplication @ B @ C ) ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( multiplication @ A @ B )
!= ( c @ sk2 ) )
| ( C != sk1 ) ),
inference(simp,[status(thm)],[158]) ).
thf(186,plain,
! [B: $i,A: $i] :
( ( ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ ( multiplication @ A @ ( multiplication @ B @ sk1 ) ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( multiplication @ A @ B )
!= ( c @ sk2 ) ) ),
inference(simp,[status(thm)],[174]) ).
thf(3457,plain,
! [A: $i] :
( ( A = one )
| ( ( addition @ zero @ A )
!= ( addition @ sk3 @ ( sk4 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[873,2559]) ).
thf(3504,plain,
! [A: $i] :
( ( A = one )
| ( sk3 != zero )
| ( A
!= ( sk4 @ sk3 ) ) ),
inference(simp,[status(thm)],[3457]) ).
thf(3516,plain,
( ( ( sk4 @ sk3 )
= one )
| ( sk3 != zero ) ),
inference(simp,[status(thm)],[3504]) ).
thf(302,plain,
! [F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ ( addition @ C @ ( addition @ B @ A ) ) @ D )
= ( addition @ F @ ( addition @ E @ D ) ) )
| ( ( addition @ ( addition @ C @ B ) @ A )
!= ( addition @ F @ E ) ) ),
inference(paramod_ordered,[status(thm)],[36,36]) ).
thf(303,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ C @ ( addition @ D @ A ) ) @ B )
= ( addition @ ( addition @ C @ D ) @ ( addition @ A @ B ) ) ),
inference(pattern_uni,[status(thm)],[302:[bind(A,$thf( A )),bind(B,$thf( H )),bind(C,$thf( G )),bind(D,$thf( D )),bind(E,$thf( A )),bind(F,$thf( addition @ G @ H ))]]) ).
thf(312,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ C @ ( addition @ D @ A ) ) @ B )
= ( addition @ ( addition @ C @ D ) @ ( addition @ A @ B ) ) ),
inference(simp,[status(thm)],[303]) ).
thf(48519,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( addition @ C @ ( addition @ ( addition @ D @ A ) @ B ) )
= ( addition @ C @ ( addition @ D @ ( addition @ A @ B ) ) ) ),
inference(rewrite,[status(thm)],[312,36]) ).
thf(18923,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ sk2 @ ( c @ sk2 ) )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2180,188]) ).
thf(18924,plain,
! [A: $i] :
( ( multiplication @ sk2 @ ( multiplication @ ( c @ sk2 ) @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[18923:[bind(A,$thf( sk2 )),bind(B,$thf( c @ sk2 )),bind(C,$thf( C ))]]) ).
thf(19196,plain,
! [A: $i] :
( ( multiplication @ sk2 @ ( multiplication @ ( c @ sk2 ) @ A ) )
= zero ),
inference(simp,[status(thm)],[18924]) ).
thf(6520,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ ( c @ sk3 ) ) @ ( c @ sk3 ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2575,56]) ).
thf(6521,plain,
( ( addition @ ( c @ sk3 ) @ ( c @ ( c @ sk3 ) ) )
= one ),
inference(pattern_uni,[status(thm)],[6520:[bind(A,$thf( c @ ( c @ sk3 ) )),bind(B,$thf( c @ sk3 ))]]) ).
thf(106,plain,
! [A: $i] :
( ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ zero ) )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[84,26]) ).
thf(110,plain,
! [A: $i] :
( ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ zero ) )
| ( A
!= ( c @ sk2 ) )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[106]) ).
thf(115,plain,
( ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ zero ) )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[110]) ).
thf(117,plain,
! [A: $i] :
( ( ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ zero )
!= zero )
| ( sk1 != zero )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[84,115]) ).
thf(119,plain,
! [A: $i] :
( ( ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ zero )
!= zero )
| ( sk1 != zero )
| ( A
!= ( c @ sk2 ) )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[117]) ).
thf(121,plain,
( ( ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ zero )
!= zero )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[119]) ).
thf(141,plain,
! [A: $i] :
( ( ( addition @ zero @ zero )
!= zero )
| ( sk1 != zero )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[30,121]) ).
thf(144,plain,
! [A: $i] :
( ( ( addition @ zero @ zero )
!= zero )
| ( sk1 != zero )
| ( sk1 != zero )
| ( A
!= ( c @ sk3 ) ) ),
inference(simp,[status(thm)],[141]) ).
thf(146,plain,
( ( ( addition @ zero @ zero )
!= zero )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[144]) ).
thf(271,plain,
( ( zero != zero )
| ( sk1 != zero ) ),
inference(rewrite,[status(thm)],[146,90]) ).
thf(272,plain,
sk1 != zero,
inference(simp,[status(thm)],[271]) ).
thf(8952,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ ( c @ sk3 ) ) @ ( sk4 @ ( c @ ( c @ sk3 ) ) ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2537,56]) ).
thf(8953,plain,
( ( addition @ ( sk4 @ ( c @ ( c @ sk3 ) ) ) @ ( c @ ( c @ sk3 ) ) )
= one ),
inference(pattern_uni,[status(thm)],[8952:[bind(A,$thf( c @ ( c @ sk3 ) )),bind(B,$thf( sk4 @ ( c @ ( c @ sk3 ) ) ))]]) ).
thf(12170,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( sk4 @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( c @ ( c @ ( c @ sk2 ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[7549,73]) ).
thf(12171,plain,
( ( multiplication @ ( c @ ( c @ ( c @ sk2 ) ) ) @ ( sk4 @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[12170:[bind(A,$thf( c @ ( c @ ( c @ sk2 ) ) )),bind(B,$thf( sk4 @ ( c @ ( c @ ( c @ sk2 ) ) ) ))]]) ).
thf(12080,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( sk4 @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1705,74]) ).
thf(12081,plain,
( ( multiplication @ ( sk4 @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( c @ ( c @ ( c @ sk3 ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[12080:[bind(A,$thf( c @ ( c @ ( c @ sk3 ) ) )),bind(B,$thf( sk4 @ ( c @ ( c @ ( c @ sk3 ) ) ) ))]]) ).
thf(35757,plain,
! [B: $i,A: $i] :
( ( test @ A )
| ( ( complement @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12390,50]) ).
thf(35758,plain,
test @ ( c @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) ),
inference(pattern_uni,[status(thm)],[35757:[bind(A,$thf( c @ ( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ ( c @ sk2 ) ) ) ))]]) ).
thf(345,plain,
! [C: $i,B: $i,A: $i] :
( ( A != sk1 )
| ( ( multiplication @ B @ C )
!= ( c @ sk3 ) )
| ( ( multiplication @ ( multiplication @ A @ B ) @ C )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(simp,[status(thm)],[340]) ).
thf(354,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
!= ( c @ sk3 ) )
| ( ( multiplication @ ( multiplication @ sk1 @ A ) @ B )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(simp,[status(thm)],[345]) ).
thf(53661,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
!= ( c @ sk3 ) )
| ( ( multiplication @ sk1 @ ( multiplication @ A @ B ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(rewrite,[status(thm)],[354,33]) ).
thf(241,plain,
! [A: $i] :
( ( ( addition @ A @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,26]) ).
thf(255,plain,
! [A: $i] :
( ( ( addition @ A @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( A != sk1 )
| ( ( c @ sk3 )
!= one ) ),
inference(simp,[status(thm)],[241]) ).
thf(268,plain,
( ( ( addition @ sk1 @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( c @ sk3 )
!= one ) ),
inference(simp,[status(thm)],[255]) ).
thf(445,plain,
! [A: $i] :
( ( A
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk1 @ ( multiplication @ ( c @ sk3 ) @ one ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,431]) ).
thf(471,plain,
( ( multiplication @ ( multiplication @ ( c @ sk2 ) @ sk1 ) @ one )
!= ( multiplication @ sk1 @ ( multiplication @ ( c @ sk3 ) @ one ) ) ),
inference(simp,[status(thm)],[445]) ).
thf(664,plain,
( ( multiplication @ ( c @ sk2 ) @ ( multiplication @ sk1 @ one ) )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ),
inference(rewrite,[status(thm)],[471,33,81]) ).
thf(19624,plain,
( ( sk3 != zero )
| ( complement @ one @ sk3 )
| ( ( sk4 @ sk3 )
!= ( sk4 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[3516,661]) ).
thf(19625,plain,
( ( sk3 != zero )
| ( complement @ one @ sk3 ) ),
inference(pattern_uni,[status(thm)],[19624:[]]) ).
thf(18969,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ ( c @ ( c @ sk3 ) ) @ ( sk4 @ ( c @ ( c @ sk3 ) ) ) )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1807,188]) ).
thf(18970,plain,
! [A: $i] :
( ( multiplication @ ( c @ ( c @ sk3 ) ) @ ( multiplication @ ( sk4 @ ( c @ ( c @ sk3 ) ) ) @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[18969:[bind(A,$thf( c @ ( c @ sk3 ) )),bind(B,$thf( sk4 @ ( c @ ( c @ sk3 ) ) )),bind(C,$thf( C ))]]) ).
thf(19096,plain,
! [A: $i] :
( ( multiplication @ ( c @ ( c @ sk3 ) ) @ ( multiplication @ ( sk4 @ ( c @ ( c @ sk3 ) ) ) @ A ) )
= zero ),
inference(simp,[status(thm)],[18970]) ).
thf(54582,plain,
! [B: $i,A: $i] :
( ( one != B )
| ( leq @ A @ B )
| ( ( addition @ ( sk4 @ sk3 ) @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54432,99]) ).
thf(54583,plain,
( ( one != one )
| ( leq @ ( sk4 @ sk3 ) @ one ) ),
inference(pattern_uni,[status(thm)],[54582:[bind(A,$thf( sk4 @ sk3 )),bind(B,$thf( one ))]]) ).
thf(54687,plain,
leq @ ( sk4 @ sk3 ) @ one,
inference(simp,[status(thm)],[54583]) ).
thf(2076,plain,
! [A: $i] :
( ( A = zero )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk3 @ ( sk4 @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[81,1827]) ).
thf(2109,plain,
! [A: $i] :
( ( A = zero )
| ( A != sk3 )
| ( ( sk4 @ sk3 )
!= one ) ),
inference(simp,[status(thm)],[2076]) ).
thf(2127,plain,
( ( sk3 = zero )
| ( ( sk4 @ sk3 )
!= one ) ),
inference(simp,[status(thm)],[2109]) ).
thf(6383,plain,
( ( sk2 != sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[2280]) ).
thf(206,plain,
! [B: $i,A: $i] :
( ( zero = B )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ one @ B ) ) ),
inference(paramod_ordered,[status(thm)],[30,45]) ).
thf(208,plain,
! [B: $i,A: $i] :
( ( zero = B )
| ( one != zero )
| ( A != B ) ),
inference(simp,[status(thm)],[206]) ).
thf(220,plain,
! [A: $i] :
( ( zero = A )
| ( one != zero ) ),
inference(simp,[status(thm)],[208]) ).
thf(24644,plain,
! [A: $i] :
( ( one != zero )
| ( A != sk3 ) ),
inference(paramod_ordered,[status(thm)],[220,7449]) ).
thf(24645,plain,
one != zero,
inference(pattern_uni,[status(thm)],[24644:[bind(A,$thf( sk3 ))]]) ).
thf(11909,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( c @ ( c @ ( c @ sk3 ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1688,74]) ).
thf(11910,plain,
( ( multiplication @ ( c @ ( c @ ( c @ sk3 ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[11909:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk3 ) ) ) )),bind(B,$thf( c @ ( c @ ( c @ sk3 ) ) ))]]) ).
thf(35130,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[12024,73]) ).
thf(35131,plain,
( ( multiplication @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) @ ( sk4 @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[35130:[bind(A,$thf( c @ ( c @ ( c @ ( c @ sk3 ) ) ) )),bind(B,$thf( sk4 @ ( c @ ( c @ ( c @ ( c @ sk3 ) ) ) ) ))]]) ).
thf(3538,plain,
! [A: $i] :
( ( A = one )
| ( ( addition @ A @ A )
!= ( addition @ sk2 @ ( sk4 @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,2573]) ).
thf(3567,plain,
! [A: $i] :
( ( A = one )
| ( A != sk2 )
| ( A
!= ( sk4 @ sk2 ) ) ),
inference(simp,[status(thm)],[3538]) ).
thf(3580,plain,
( ( sk2 = one )
| ( ( sk4 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[3567]) ).
thf(18768,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ ( c @ sk3 ) @ ( c @ ( c @ sk3 ) ) )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2222,188]) ).
thf(18769,plain,
! [A: $i] :
( ( multiplication @ ( c @ sk3 ) @ ( multiplication @ ( c @ ( c @ sk3 ) ) @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[18768:[bind(A,$thf( c @ sk3 )),bind(B,$thf( c @ ( c @ sk3 ) )),bind(C,$thf( C ))]]) ).
thf(19116,plain,
! [A: $i] :
( ( multiplication @ ( c @ sk3 ) @ ( multiplication @ ( c @ ( c @ sk3 ) ) @ A ) )
= zero ),
inference(simp,[status(thm)],[18769]) ).
thf(18904,plain,
! [C: $i,B: $i,A: $i] :
( ( ( multiplication @ A @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ ( sk4 @ sk2 ) @ sk2 )
!= ( multiplication @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2220,188]) ).
thf(18905,plain,
! [A: $i] :
( ( multiplication @ ( sk4 @ sk2 ) @ ( multiplication @ sk2 @ A ) )
= zero ),
inference(pattern_uni,[status(thm)],[18904:[bind(A,$thf( sk4 @ sk2 )),bind(B,$thf( sk2 )),bind(C,$thf( C ))]]) ).
thf(19193,plain,
! [A: $i] :
( ( multiplication @ ( sk4 @ sk2 ) @ ( multiplication @ sk2 @ A ) )
= zero ),
inference(simp,[status(thm)],[18905]) ).
thf(1902,plain,
( ( complement @ ( sk4 @ sk2 ) @ sk2 )
!= ( complement @ ( c @ sk3 ) @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[663,1871]) ).
thf(1917,plain,
( ( ( sk4 @ sk2 )
!= ( c @ sk3 ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[1902]) ).
thf(364,plain,
( ( ( c @ sk2 )
!= sk1 )
| ( ( c @ sk3 )
!= ( c @ sk2 ) ) ),
inference(simp,[status(thm)],[363]) ).
thf(56146,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ ( c @ sk3 ) @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[56130,56]) ).
thf(56147,plain,
( ( addition @ one @ ( c @ sk3 ) )
= one ),
inference(pattern_uni,[status(thm)],[56146:[bind(A,$thf( c @ sk3 )),bind(B,$thf( one ))]]) ).
thf(114244,plain,
$false,
inference(e,[status(thm)],[54447,30966,365,2559,19117,4728,88,2280,7549,31235,2395,12371,308,10562,3108,873,1793,35542,1437,1855,6142,1705,56,814,3577,2146,19191,2575,5163,2168,6251,42,12225,24,1921,37,2531,25,31220,185,12257,36446,11912,2400,54432,13484,1871,52342,13636,19184,1059,53147,31661,853,46,93,3657,39272,1494,57,78,7633,1778,19197,261,2222,40311,3524,1040,2291,353,1051,41865,2236,2555,84,280,221,293,3808,51463,7460,35538,19095,6947,74,30987,307,13564,3459,661,85,1915,1783,52358,12169,52891,1047,1057,334,21384,39240,28,12083,21,60238,33,7565,17755,65,1920,7449,1819,7591,16719,224,9095,1541,2515,948,2577,20148,188,53,17550,7593,356,2537,13394,225,19114,1424,50557,1825,13805,43399,56130,5058,35698,13436,1779,19198,19090,1515,13741,8796,73,1857,2529,12318,2292,34,45,64,3839,18682,38955,35284,2188,743,12259,52577,19170,27,12951,19086,2293,3726,37678,49,3579,2557,30944,2573,350,54,2220,187,219,7130,81,37642,35280,76,39,2180,57200,323,52907,51047,4726,1061,1688,91,31158,35694,31136,50571,31017,19093,223,135,1775,2022,267,2156,431,7507,35127,1528,12135,9958,35772,663,1420,13540,1509,35344,1049,19182,355,12390,7462,57476,30964,2224,1813,182,1038,60207,11969,3853,15184,31,35199,50,3107,2279,1506,72,51061,7498,43,51290,56413,39277,51432,50768,6408,87,3874,62626,3056,19111,1807,4730,3797,3589,99,813,2174,40,26,19097,19087,186,2026,3516,75,48519,19196,929,6521,272,8953,35356,12171,82,11960,41840,36,30,51,12081,35758,1859,53661,2186,268,664,12024,94,2549,79,12307,19625,19096,54687,2127,332,1827,12042,6383,24645,35612,62,11910,35131,90,3580,337,19116,1490,19193,1917,364,100,1681,56147]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE023+2 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.14/0.36 % Computer : n024.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Fri May 19 02:54:23 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.84/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/0.95 % [INFO] Parsing done (126ms).
% 1.27/0.96 % [INFO] Running in sequential loop mode.
% 1.61/1.16 % [INFO] eprover registered as external prover.
% 1.61/1.16 % [INFO] cvc4 registered as external prover.
% 1.61/1.16 % [INFO] Scanning for conjecture ...
% 1.88/1.22 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 1.97/1.26 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 1.97/1.29 % [INFO] Problem is first-order (TPTP FOF).
% 1.97/1.29 % [INFO] Type checking passed.
% 1.97/1.29 % [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 ...
% 177.01/32.76 % External prover 'e' found a proof!
% 177.01/32.76 % [INFO] Killing All external provers ...
% 177.01/32.76 % Time passed: 32246ms (effective reasoning time: 31797ms)
% 177.01/32.76 % 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)>
% 177.01/32.76 % 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
% 177.01/32.76 % No. of inferences in proof: 769
% 177.01/32.76 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 32246 ms resp. 31797 ms w/o parsing
% 177.57/32.92 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 177.57/32.92 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------