TSTP Solution File: KLE014+3 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE014+3 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n016.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 11:24:48 EDT 2023
% Result : Theorem 192.38s 36.05s
% Output : Refutation 192.38s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 28
% Syntax : Number of formulae : 207 ( 74 unt; 11 typ; 0 def)
% Number of atoms : 523 ( 282 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 1680 ( 273 ~; 218 |; 23 &;1140 @)
% ( 4 <=>; 22 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 222 ( 0 ^; 217 !; 5 ?; 222 :)
% Comments :
%------------------------------------------------------------------------------
thf(test_type,type,
test: $i > $o ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(c_type,type,
c: $i > $i ).
thf(addition_type,type,
addition: $i > $i > $i ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(one_type,type,
one: $i ).
thf(complement_type,type,
complement: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i > $i ).
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(52,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(53,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)],[52]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( test @ A )
| ~ ( complement @ A @ B )
| ( ( c @ A )
= B ) ),
inference(cnf,[status(esa)],[53]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ( ( c @ A )
= B )
| ~ ( test @ A )
| ~ ( complement @ A @ B ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( ( c @ A )
= B )
| ~ ( test @ A )
| ~ ( complement @ A @ B ) ),
inference(simp,[status(thm)],[58]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(49,plain,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(lifteq,[status(thm)],[50]) ).
thf(16,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(77,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(78,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(cnf,[status(esa)],[77]) ).
thf(79,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(lifteq,[status(thm)],[78]) ).
thf(425,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
= C )
| ( ( addition @ A @ B )
!= ( addition @ C @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[51,79]) ).
thf(426,plain,
! [A: $i] :
( ( addition @ zero @ A )
= A ),
inference(pattern_uni,[status(thm)],[425:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(15,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(74,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(75,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(cnf,[status(esa)],[74]) ).
thf(76,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(lifteq,[status(thm)],[75]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( test @ B )
& ( test @ A ) )
=> ( ( leq @ ( c @ ( addition @ A @ B ) ) @ ( multiplication @ ( c @ A ) @ ( c @ B ) ) )
& ( leq @ ( multiplication @ ( c @ A ) @ ( c @ B ) ) @ ( c @ ( addition @ A @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( test @ B )
& ( test @ A ) )
=> ( ( leq @ ( c @ ( addition @ A @ B ) ) @ ( multiplication @ ( c @ A ) @ ( c @ B ) ) )
& ( leq @ ( multiplication @ ( c @ A ) @ ( c @ B ) ) @ ( c @ ( addition @ A @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i] :
( ( ( test @ B )
& ( test @ A ) )
=> ( ( leq @ ( c @ ( addition @ A @ B ) ) @ ( multiplication @ ( c @ A ) @ ( c @ B ) ) )
& ( leq @ ( multiplication @ ( c @ A ) @ ( c @ B ) ) @ ( c @ ( addition @ A @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
( ~ ( leq @ ( c @ ( addition @ sk1 @ sk2 ) ) @ ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) )
| ~ ( leq @ ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) @ ( c @ ( addition @ sk1 @ sk2 ) ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(97,plain,
! [A: $i] :
( ~ ( leq @ ( c @ ( addition @ sk1 @ sk2 ) ) @ ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) )
| ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,20]) ).
thf(99,plain,
! [A: $i] :
( ~ ( leq @ ( c @ ( addition @ sk1 @ sk2 ) ) @ ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) )
| ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( A
!= ( c @ sk1 ) )
| ( ( c @ sk2 )
!= zero ) ),
inference(simp,[status(thm)],[97]) ).
thf(105,plain,
( ~ ( leq @ ( c @ ( addition @ sk1 @ sk2 ) ) @ ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) )
| ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( ( c @ sk2 )
!= zero ) ),
inference(simp,[status(thm)],[99]) ).
thf(111,plain,
! [A: $i] :
( ~ ( leq @ ( c @ ( addition @ sk1 @ sk2 ) ) @ zero )
| ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( ( c @ sk2 )
!= zero )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,105]) ).
thf(114,plain,
! [A: $i] :
( ~ ( leq @ ( c @ ( addition @ sk1 @ sk2 ) ) @ zero )
| ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( ( c @ sk2 )
!= zero )
| ( A
!= ( c @ sk1 ) )
| ( ( c @ sk2 )
!= zero ) ),
inference(simp,[status(thm)],[111]) ).
thf(118,plain,
( ~ ( leq @ ( c @ ( addition @ sk1 @ sk2 ) ) @ zero )
| ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( ( c @ sk2 )
!= zero ) ),
inference(simp,[status(thm)],[114]) ).
thf(138,plain,
( ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( ( c @ sk2 )
!= zero )
| ( ( leq @ ( c @ ( addition @ sk1 @ sk2 ) ) @ zero )
!= ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[118]) ).
thf(140,plain,
( ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( ( c @ sk2 )
!= zero )
| ( ( c @ ( addition @ sk1 @ sk2 ) )
!= zero )
| ( ( c @ ( addition @ sk1 @ sk2 ) )
!= zero ) ),
inference(simp,[status(thm)],[138]) ).
thf(141,plain,
( ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( ( c @ sk2 )
!= zero )
| ( ( c @ ( addition @ sk1 @ sk2 ) )
!= zero ) ),
inference(simp,[status(thm)],[140]) ).
thf(142,plain,
( ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( ( c @ sk2 )
!= zero )
| ( ( c @ ( addition @ sk1 @ sk2 ) )
!= ( c @ sk2 ) )
| ( zero != zero ) ),
inference(eqfactor_ordered,[status(thm)],[141]) ).
thf(144,plain,
( ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( ( c @ sk2 )
!= zero )
| ( ( addition @ sk1 @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[142]) ).
thf(472,plain,
! [A: $i] :
( ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( ( c @ sk2 )
!= zero )
| ( A != sk2 )
| ( ( addition @ zero @ A )
!= ( addition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[426,144]) ).
thf(498,plain,
( ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( ( c @ sk2 )
!= zero )
| ( sk1 != zero )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[472]) ).
thf(512,plain,
( ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( ( c @ sk2 )
!= zero )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[498]) ).
thf(652,plain,
! [A: $i] :
( ~ ( leq @ zero @ ( c @ A ) )
| ( ( c @ sk2 )
!= zero )
| ( sk1 != zero )
| ( ( addition @ zero @ A )
!= ( addition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[426,512]) ).
thf(661,plain,
! [A: $i] :
( ~ ( leq @ zero @ ( c @ A ) )
| ( ( c @ sk2 )
!= zero )
| ( sk1 != zero )
| ( sk1 != zero )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[652]) ).
thf(666,plain,
( ~ ( leq @ zero @ ( c @ sk2 ) )
| ( ( c @ sk2 )
!= zero )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[661]) ).
thf(770,plain,
! [B: $i,A: $i] :
( ~ ( test @ A )
| ~ ( complement @ A @ B )
| ~ ( leq @ zero @ ( c @ sk2 ) )
| ( B != zero )
| ( sk1 != zero )
| ( ( c @ A )
!= ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[59,666]) ).
thf(771,plain,
! [A: $i] :
( ~ ( test @ sk2 )
| ~ ( complement @ sk2 @ A )
| ~ ( leq @ zero @ ( c @ sk2 ) )
| ( A != zero )
| ( sk1 != zero ) ),
inference(pattern_uni,[status(thm)],[770:[bind(A,$thf( sk2 ))]]) ).
thf(1106,plain,
( ~ ( test @ sk2 )
| ~ ( complement @ sk2 @ zero )
| ~ ( leq @ zero @ ( c @ sk2 ) )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[771]) ).
thf(22,plain,
test @ sk2,
inference(cnf,[status(esa)],[19]) ).
thf(1259,plain,
( ~ $true
| ~ ( complement @ sk2 @ zero )
| ~ ( leq @ zero @ ( c @ sk2 ) )
| ( sk1 != zero ) ),
inference(rewrite,[status(thm)],[1106,22]) ).
thf(1260,plain,
( ~ ( complement @ sk2 @ zero )
| ~ ( leq @ zero @ ( c @ sk2 ) )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[1259]) ).
thf(10,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(46,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(47,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(cnf,[status(esa)],[46]) ).
thf(48,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(lifteq,[status(thm)],[47]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ~ ( test @ A )
| ( ( c @ A )
!= B )
| ( complement @ A @ B ) ),
inference(cnf,[status(esa)],[53]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( ( c @ A )
!= B )
| ~ ( test @ A )
| ( complement @ A @ B ) ),
inference(lifteq,[status(thm)],[54]) ).
thf(57,plain,
! [A: $i] :
( ~ ( test @ A )
| ( complement @ A @ ( c @ A ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(718,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ sk2 )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[22,57]) ).
thf(719,plain,
complement @ sk2 @ ( c @ sk2 ),
inference(pattern_uni,[status(thm)],[718:[bind(A,$thf( sk2 ))]]) ).
thf(9,axiom,
! [A: $i] :
( ( test @ A )
<=> ? [B: $i] : ( complement @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_1) ).
thf(41,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(42,plain,
( ! [A: $i] :
( ( test @ A )
=> ? [B: $i] : ( complement @ B @ A ) )
& ! [A: $i] :
( ? [B: $i] : ( complement @ B @ A )
=> ( test @ A ) ) ),
inference(miniscope,[status(thm)],[41]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( complement @ B @ A )
| ( test @ A ) ),
inference(cnf,[status(esa)],[42]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ~ ( complement @ B @ A )
| ( test @ A ) ),
inference(simp,[status(thm)],[43]) ).
thf(733,plain,
! [B: $i,A: $i] :
( ( test @ A )
| ( ( complement @ sk2 @ ( c @ sk2 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[719,45]) ).
thf(734,plain,
test @ ( c @ sk2 ),
inference(pattern_uni,[status(thm)],[733:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(735,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ ( c @ sk2 ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[734,57]) ).
thf(736,plain,
complement @ ( c @ sk2 ) @ ( c @ ( c @ sk2 ) ),
inference(pattern_uni,[status(thm)],[735:[bind(A,$thf( c @ sk2 ))]]) ).
thf(1239,plain,
! [B: $i,A: $i] :
( ( test @ A )
| ( ( complement @ ( c @ sk2 ) @ ( c @ ( c @ sk2 ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[736,45]) ).
thf(1240,plain,
test @ ( c @ ( c @ sk2 ) ),
inference(pattern_uni,[status(thm)],[1239:[bind(A,$thf( c @ ( c @ sk2 ) )),bind(B,$thf( c @ sk2 ))]]) ).
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(60,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(61,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)],[60]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ~ ( complement @ B @ A )
| ( ( multiplication @ B @ A )
= zero ) ),
inference(cnf,[status(esa)],[61]) ).
thf(69,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ~ ( complement @ B @ A ) ),
inference(lifteq,[status(thm)],[64]) ).
thf(21,plain,
test @ sk1,
inference(cnf,[status(esa)],[19]) ).
thf(712,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ sk1 )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21,57]) ).
thf(713,plain,
complement @ sk1 @ ( c @ sk1 ),
inference(pattern_uni,[status(thm)],[712:[bind(A,$thf( sk1 ))]]) ).
thf(723,plain,
! [B: $i,A: $i] :
( ( test @ A )
| ( ( complement @ sk1 @ ( c @ sk1 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[713,45]) ).
thf(724,plain,
test @ ( c @ sk1 ),
inference(pattern_uni,[status(thm)],[723:[bind(A,$thf( c @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(725,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ ( c @ sk1 ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[724,57]) ).
thf(726,plain,
complement @ ( c @ sk1 ) @ ( c @ ( c @ sk1 ) ),
inference(pattern_uni,[status(thm)],[725:[bind(A,$thf( c @ sk1 ))]]) ).
thf(1169,plain,
! [B: $i,A: $i] :
( ( test @ A )
| ( ( complement @ ( c @ sk1 ) @ ( c @ ( c @ sk1 ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[726,45]) ).
thf(1170,plain,
test @ ( c @ ( c @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1169:[bind(A,$thf( c @ ( c @ sk1 ) )),bind(B,$thf( c @ sk1 ))]]) ).
thf(1189,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ ( c @ ( c @ sk1 ) ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1170,57]) ).
thf(1190,plain,
complement @ ( c @ ( c @ sk1 ) ) @ ( c @ ( c @ ( c @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[1189:[bind(A,$thf( c @ ( c @ sk1 ) ))]]) ).
thf(44,plain,
! [A: $i] :
( ~ ( test @ A )
| ( complement @ ( sk3 @ A ) @ A ) ),
inference(cnf,[status(esa)],[42]) ).
thf(729,plain,
! [A: $i] :
( ( complement @ ( sk3 @ A ) @ A )
| ( ( test @ ( c @ sk1 ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[724,44]) ).
thf(730,plain,
complement @ ( sk3 @ ( c @ sk1 ) ) @ ( c @ sk1 ),
inference(pattern_uni,[status(thm)],[729:[bind(A,$thf( c @ sk1 ))]]) ).
thf(242,plain,
! [A: $i] :
( ~ ( leq @ zero @ ( c @ A ) )
| ( ( c @ sk2 )
!= zero )
| ( ( addition @ sk1 @ sk2 )
!= sk2 )
| ( ( addition @ A @ zero )
!= ( addition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[79,144]) ).
thf(244,plain,
! [A: $i] :
( ~ ( leq @ zero @ ( c @ A ) )
| ( ( c @ sk2 )
!= zero )
| ( ( addition @ sk1 @ sk2 )
!= sk2 )
| ( A != sk1 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[242]) ).
thf(247,plain,
( ~ ( leq @ zero @ ( c @ sk1 ) )
| ( ( c @ sk2 )
!= zero )
| ( ( addition @ sk1 @ sk2 )
!= sk2 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[244]) ).
thf(676,plain,
! [A: $i] :
( ( complement @ ( sk3 @ A ) @ A )
| ( ( test @ sk1 )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21,44]) ).
thf(677,plain,
complement @ ( sk3 @ sk1 ) @ sk1,
inference(pattern_uni,[status(thm)],[676:[bind(A,$thf( sk1 ))]]) ).
thf(1195,plain,
! [A: $i] :
( ( complement @ ( sk3 @ A ) @ A )
| ( ( test @ ( c @ ( c @ sk1 ) ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1170,44]) ).
thf(1196,plain,
complement @ ( sk3 @ ( c @ ( c @ sk1 ) ) ) @ ( c @ ( c @ sk1 ) ),
inference(pattern_uni,[status(thm)],[1195:[bind(A,$thf( c @ ( c @ sk1 ) ))]]) ).
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(35,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(36,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(3,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(23,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(24,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(lifteq,[status(thm)],[24]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ~ ( complement @ B @ A )
| ( ( multiplication @ A @ B )
= zero ) ),
inference(cnf,[status(esa)],[61]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ~ ( complement @ B @ A ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(1627,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ sk1 @ ( c @ sk1 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[713,68]) ).
thf(1628,plain,
( ( multiplication @ ( c @ sk1 ) @ sk1 )
= zero ),
inference(pattern_uni,[status(thm)],[1627:[bind(A,$thf( c @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(347,plain,
! [A: $i] :
( ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( ( c @ sk2 )
!= zero )
| ( A != sk2 )
| ( ( addition @ A @ A )
!= ( addition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[48,144]) ).
thf(364,plain,
( ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( ( c @ sk2 )
!= zero )
| ( sk2 != sk1 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[347]) ).
thf(376,plain,
( ~ ( leq @ zero @ ( c @ ( addition @ sk1 @ sk2 ) ) )
| ( ( c @ sk2 )
!= zero )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[364]) ).
thf(451,plain,
! [A: $i] :
( ~ ( leq @ zero @ ( c @ A ) )
| ( ( c @ sk2 )
!= zero )
| ( sk2 != sk1 )
| ( ( addition @ A @ A )
!= ( addition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[48,376]) ).
thf(457,plain,
! [A: $i] :
( ~ ( leq @ zero @ ( c @ A ) )
| ( ( c @ sk2 )
!= zero )
| ( sk2 != sk1 )
| ( A != sk1 )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[451]) ).
thf(460,plain,
( ~ ( leq @ zero @ ( c @ sk1 ) )
| ( ( c @ sk2 )
!= zero )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[457]) ).
thf(678,plain,
! [A: $i] :
( ( complement @ ( sk3 @ A ) @ A )
| ( ( test @ sk2 )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[22,44]) ).
thf(679,plain,
complement @ ( sk3 @ sk2 ) @ sk2,
inference(pattern_uni,[status(thm)],[678:[bind(A,$thf( sk2 ))]]) ).
thf(1962,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( sk3 @ sk2 ) @ sk2 )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[679,69]) ).
thf(1963,plain,
( ( multiplication @ ( sk3 @ sk2 ) @ sk2 )
= zero ),
inference(pattern_uni,[status(thm)],[1962:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 @ sk2 ))]]) ).
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(29,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(1278,plain,
( ~ ( leq @ zero @ ( c @ sk2 ) )
| ( sk1 != zero )
| ( ( complement @ sk2 @ zero )
!= ( complement @ sk1 @ ( c @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[713,1260]) ).
thf(1283,plain,
( ~ ( leq @ zero @ ( c @ sk2 ) )
| ( sk1 != zero )
| ( sk2 != sk1 )
| ( ( c @ sk1 )
!= zero ) ),
inference(simp,[status(thm)],[1278]) ).
thf(14,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(71,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(72,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(cnf,[status(esa)],[71]) ).
thf(73,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(lifteq,[status(thm)],[72]) ).
thf(1589,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( sk3 @ sk1 ) @ sk1 )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[677,68]) ).
thf(1590,plain,
( ( multiplication @ sk1 @ ( sk3 @ sk1 ) )
= zero ),
inference(pattern_uni,[status(thm)],[1589:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ sk1 ))]]) ).
thf(1665,plain,
! [A: $i] :
( ( A = zero )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk1 @ ( sk3 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[73,1590]) ).
thf(1685,plain,
! [A: $i] :
( ( A = zero )
| ( A != sk1 )
| ( ( sk3 @ sk1 )
!= one ) ),
inference(simp,[status(thm)],[1665]) ).
thf(1696,plain,
( ( sk1 = zero )
| ( ( sk3 @ sk1 )
!= one ) ),
inference(simp,[status(thm)],[1685]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( complement @ B @ A )
| ( ( addition @ A @ B )
= one ) ),
inference(cnf,[status(esa)],[61]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ~ ( complement @ B @ A ) ),
inference(lifteq,[status(thm)],[65]) ).
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(26,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(27,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ A @ B ) @ C )
= ( multiplication @ A @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(8,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(38,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(1601,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ sk2 @ ( c @ sk2 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[719,68]) ).
thf(1602,plain,
( ( multiplication @ ( c @ sk2 ) @ sk2 )
= zero ),
inference(pattern_uni,[status(thm)],[1601:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(657,plain,
! [A: $i] :
( ~ ( leq @ zero @ ( c @ A ) )
| ( ( c @ sk2 )
!= zero )
| ( sk1 != zero )
| ( ( addition @ A @ zero )
!= ( addition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[79,512]) ).
thf(660,plain,
! [A: $i] :
( ~ ( leq @ zero @ ( c @ A ) )
| ( ( c @ sk2 )
!= zero )
| ( sk1 != zero )
| ( A != sk1 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[657]) ).
thf(665,plain,
( ~ ( leq @ zero @ ( c @ sk1 ) )
| ( ( c @ sk2 )
!= zero )
| ( sk1 != zero )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[660]) ).
thf(1263,plain,
( ~ ( leq @ zero @ ( c @ sk2 ) )
| ( sk1 != zero )
| ( ( complement @ ( sk3 @ sk1 ) @ sk1 )
!= ( complement @ sk2 @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[677,1260]) ).
thf(1282,plain,
( ~ ( leq @ zero @ ( c @ sk2 ) )
| ( sk1 != zero )
| ( ( sk3 @ sk1 )
!= sk2 )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[1263]) ).
thf(1291,plain,
( ~ ( leq @ zero @ ( c @ sk2 ) )
| ( sk1 != zero )
| ( ( sk3 @ sk1 )
!= sk2 ) ),
inference(simp,[status(thm)],[1282]) ).
thf(917,plain,
! [B: $i,A: $i] :
( ~ ( test @ A )
| ~ ( complement @ A @ B )
| ~ ( leq @ zero @ ( c @ sk1 ) )
| ( B != zero )
| ( sk2 != sk1 )
| ( ( c @ A )
!= ( c @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[59,460]) ).
thf(918,plain,
! [A: $i] :
( ~ ( test @ sk2 )
| ~ ( complement @ sk2 @ A )
| ~ ( leq @ zero @ ( c @ sk1 ) )
| ( A != zero )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[917:[bind(A,$thf( sk2 ))]]) ).
thf(1143,plain,
( ~ ( test @ sk2 )
| ~ ( complement @ sk2 @ zero )
| ~ ( leq @ zero @ ( c @ sk1 ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[918]) ).
thf(1534,plain,
( ~ $true
| ~ ( complement @ sk2 @ zero )
| ~ ( leq @ zero @ ( c @ sk1 ) )
| ( sk2 != sk1 ) ),
inference(rewrite,[status(thm)],[1143,22]) ).
thf(1535,plain,
( ~ ( complement @ sk2 @ zero )
| ~ ( leq @ zero @ ( c @ sk1 ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[1534]) ).
thf(1556,plain,
( ~ ( leq @ zero @ ( c @ sk1 ) )
| ( sk2 != sk1 )
| ( ( complement @ sk2 @ zero )
!= ( complement @ sk1 @ ( c @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[713,1535]) ).
thf(1570,plain,
( ~ ( leq @ zero @ ( c @ sk1 ) )
| ( sk2 != sk1 )
| ( sk2 != sk1 )
| ( ( c @ sk1 )
!= zero ) ),
inference(simp,[status(thm)],[1556]) ).
thf(1573,plain,
( ~ ( leq @ zero @ ( c @ sk1 ) )
| ( sk2 != sk1 )
| ( ( c @ sk1 )
!= zero ) ),
inference(simp,[status(thm)],[1570]) ).
thf(529,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) )
= zero )
| ( ( multiplication @ ( addition @ A @ B ) @ C )
!= ( multiplication @ D @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[37,76]) ).
thf(530,plain,
! [B: $i,A: $i] :
( ( addition @ ( multiplication @ A @ zero ) @ ( multiplication @ B @ zero ) )
= zero ),
inference(pattern_uni,[status(thm)],[529:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( zero )),bind(D,$thf( addition @ E @ F ))]]) ).
thf(576,plain,
! [B: $i,A: $i] :
( ( addition @ ( multiplication @ A @ zero ) @ ( multiplication @ B @ zero ) )
= zero ),
inference(simp,[status(thm)],[530]) ).
thf(593,plain,
( ( addition @ zero @ zero )
= zero ),
inference(rewrite,[status(thm)],[576,76]) ).
thf(1423,plain,
! [B: $i,A: $i] :
( ( test @ A )
| ( ( complement @ ( c @ ( c @ sk1 ) ) @ ( c @ ( c @ ( c @ sk1 ) ) ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[1190,45]) ).
thf(1424,plain,
test @ ( c @ ( c @ ( c @ sk1 ) ) ),
inference(pattern_uni,[status(thm)],[1423:[bind(A,$thf( c @ ( c @ ( c @ sk1 ) ) )),bind(B,$thf( c @ ( c @ sk1 ) ))]]) ).
thf(39,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(lifteq,[status(thm)],[39]) ).
thf(1680,plain,
! [A: $i] :
( ( A = zero )
| ( ( multiplication @ one @ A )
!= ( multiplication @ sk1 @ ( sk3 @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[40,1590]) ).
thf(1690,plain,
! [A: $i] :
( ( A = zero )
| ( sk1 != one )
| ( A
!= ( sk3 @ sk1 ) ) ),
inference(simp,[status(thm)],[1680]) ).
thf(1700,plain,
( ( ( sk3 @ sk1 )
= zero )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[1690]) ).
thf(1978,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ sk1 @ ( c @ sk1 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[713,69]) ).
thf(1979,plain,
( ( multiplication @ sk1 @ ( c @ sk1 ) )
= zero ),
inference(pattern_uni,[status(thm)],[1978:[bind(A,$thf( c @ sk1 )),bind(B,$thf( sk1 ))]]) ).
thf(1615,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
= zero )
| ( ( complement @ ( sk3 @ sk2 ) @ sk2 )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[679,68]) ).
thf(1616,plain,
( ( multiplication @ sk2 @ ( sk3 @ sk2 ) )
= zero ),
inference(pattern_uni,[status(thm)],[1615:[bind(A,$thf( sk2 )),bind(B,$thf( sk3 @ sk2 ))]]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( test @ A )
=> ( ( c @ A )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_4) ).
thf(32,plain,
! [A: $i] :
( ~ ( test @ A )
=> ( ( c @ A )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(33,plain,
! [A: $i] :
( ( test @ A )
| ( ( c @ A )
= zero ) ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [A: $i] :
( ( ( c @ A )
= zero )
| ( test @ A ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(1928,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ ( sk3 @ sk1 ) @ sk1 )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[677,69]) ).
thf(1929,plain,
( ( multiplication @ ( sk3 @ sk1 ) @ sk1 )
= zero ),
inference(pattern_uni,[status(thm)],[1928:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ sk1 ))]]) ).
thf(658,plain,
( ~ ( leq @ zero @ ( c @ zero ) )
| ( ( c @ sk2 )
!= zero )
| ( sk1 != zero )
| ( ( addition @ sk1 @ sk2 )
!= ( addition @ zero @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[593,512]) ).
thf(663,plain,
( ~ ( leq @ zero @ ( c @ zero ) )
| ( ( c @ sk2 )
!= zero )
| ( sk1 != zero )
| ( sk1 != zero )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[658]) ).
thf(668,plain,
( ~ ( leq @ zero @ ( c @ zero ) )
| ( ( c @ sk2 )
!= zero )
| ( sk1 != zero )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[663]) ).
thf(17,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(80,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)],[17]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
!= zero )
| ( ( multiplication @ B @ A )
!= zero )
| ( ( addition @ A @ B )
!= one )
| ( complement @ B @ A ) ),
inference(cnf,[status(esa)],[61]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
!= zero )
| ( ( multiplication @ B @ A )
!= zero )
| ( ( addition @ A @ B )
!= one )
| ( complement @ B @ A ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ A @ B )
!= zero )
| ( ( multiplication @ B @ A )
!= zero )
| ( ( addition @ A @ B )
!= one )
| ( complement @ B @ A ) ),
inference(simp,[status(thm)],[66]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ C @ B ) @ A )
= ( addition @ C @ ( addition @ B @ A ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(2365,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ ( sk3 @ sk1 ) @ sk1 )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[677,70]) ).
thf(2366,plain,
( ( addition @ sk1 @ ( sk3 @ sk1 ) )
= one ),
inference(pattern_uni,[status(thm)],[2365:[bind(A,$thf( sk1 )),bind(B,$thf( sk3 @ sk1 ))]]) ).
thf(1261,plain,
( ~ ( leq @ zero @ ( c @ sk2 ) )
| ( sk1 != zero )
| ( ( complement @ ( sk3 @ sk2 ) @ sk2 )
!= ( complement @ sk2 @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[679,1260]) ).
thf(1288,plain,
( ~ ( leq @ zero @ ( c @ sk2 ) )
| ( sk1 != zero )
| ( ( sk3 @ sk2 )
!= sk2 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[1261]) ).
thf(739,plain,
! [A: $i] :
( ( complement @ ( sk3 @ A ) @ A )
| ( ( test @ ( c @ sk2 ) )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[734,44]) ).
thf(740,plain,
complement @ ( sk3 @ ( c @ sk2 ) ) @ ( c @ sk2 ),
inference(pattern_uni,[status(thm)],[739:[bind(A,$thf( c @ sk2 ))]]) ).
thf(2371,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= one )
| ( ( complement @ sk2 @ ( c @ sk2 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[719,70]) ).
thf(2372,plain,
( ( addition @ ( c @ sk2 ) @ sk2 )
= one ),
inference(pattern_uni,[status(thm)],[2371:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(83,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)],[18]) ).
thf(1944,plain,
! [B: $i,A: $i] :
( ( ( multiplication @ B @ A )
= zero )
| ( ( complement @ sk2 @ ( c @ sk2 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[719,69]) ).
thf(1945,plain,
( ( multiplication @ sk2 @ ( c @ sk2 ) )
= zero ),
inference(pattern_uni,[status(thm)],[1944:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(123745,plain,
$false,
inference(cvc4,[status(thm)],[1260,426,48,1240,69,1190,666,730,247,677,1196,37,25,1628,719,460,52,724,20,46,57,1963,29,376,1283,734,74,1696,60,512,70,21,28,38,1602,665,1291,1573,593,141,77,1424,1700,679,1979,41,73,105,1170,1616,45,32,34,22,44,1929,1535,59,118,71,144,713,49,736,76,726,668,80,35,67,31,1590,40,26,23,51,19,79,2366,1288,740,68,2372,83,1945]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE014+3 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.15/0.34 % Computer : n016.cluster.edu
% 0.15/0.34 % Model : x86_64 x86_64
% 0.15/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.34 % Memory : 8042.1875MB
% 0.15/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.34 % CPULimit : 300
% 0.15/0.34 % WCLimit : 300
% 0.15/0.34 % DateTime : Fri May 19 03:34:28 EDT 2023
% 0.15/0.34 % CPUTime :
% 0.85/0.82 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/0.94 % [INFO] Parsing done (115ms).
% 1.30/0.95 % [INFO] Running in sequential loop mode.
% 1.54/1.13 % [INFO] eprover registered as external prover.
% 1.54/1.13 % [INFO] cvc4 registered as external prover.
% 1.54/1.14 % [INFO] Scanning for conjecture ...
% 1.78/1.19 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 1.86/1.23 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 1.96/1.25 % [INFO] Problem is first-order (TPTP FOF).
% 1.96/1.25 % [INFO] Type checking passed.
% 1.96/1.25 % [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 ...
% 192.38/36.05 % External prover 'cvc4' found a proof!
% 192.38/36.05 % [INFO] Killing All external provers ...
% 192.38/36.05 % Time passed: 35549ms (effective reasoning time: 35099ms)
% 192.38/36.05 % 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)>
% 192.38/36.05 % Axioms used in derivation (16): additive_identity, test_3, test_4, left_annihilation, right_distributivity, multiplicative_right_identity, test_1, right_annihilation, additive_idempotence, additive_associativity, order, additive_commutativity, test_2, multiplicative_left_identity, multiplicative_associativity, left_distributivity
% 192.38/36.05 % No. of inferences in proof: 196
% 192.38/36.05 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 35549 ms resp. 35099 ms w/o parsing
% 192.38/36.10 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 192.38/36.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------