TSTP Solution File: KLE034+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE034+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n006.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 11:24:53 EDT 2023
% Result : Theorem 31.23s 5.56s
% Output : Refutation 31.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 30
% Syntax : Number of formulae : 120 ( 56 unt; 13 typ; 0 def)
% Number of atoms : 204 ( 139 equ; 0 cnn)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 754 ( 98 ~; 54 |; 22 &; 561 @)
% ( 4 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 13 usr; 8 con; 0-2 aty)
% Number of variables : 130 ( 0 ^; 127 !; 3 ?; 130 :)
% Comments :
%------------------------------------------------------------------------------
thf(test_type,type,
test: $i > $o ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(c_type,type,
c: $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(addition_type,type,
addition: $i > $i > $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 ).
thf(sk4_type,type,
sk4: $i ).
thf(sk5_type,type,
sk5: $i ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( test @ D )
& ( test @ C )
& ( test @ E )
& ( leq @ ( multiplication @ ( multiplication @ C @ A ) @ ( c @ D ) ) @ zero )
& ( leq @ ( multiplication @ ( multiplication @ D @ B ) @ ( c @ E ) ) @ zero ) )
=> ( leq @ ( multiplication @ ( multiplication @ ( multiplication @ C @ A ) @ B ) @ ( c @ E ) ) @ zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( test @ D )
& ( test @ C )
& ( test @ E )
& ( leq @ ( multiplication @ ( multiplication @ C @ A ) @ ( c @ D ) ) @ zero )
& ( leq @ ( multiplication @ ( multiplication @ D @ B ) @ ( c @ E ) ) @ zero ) )
=> ( leq @ ( multiplication @ ( multiplication @ ( multiplication @ C @ A ) @ B ) @ ( c @ E ) ) @ zero ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( test @ D )
& ( test @ C )
& ( test @ E )
& ( leq @ ( multiplication @ ( multiplication @ C @ A ) @ ( c @ D ) ) @ zero )
& ( leq @ ( multiplication @ ( multiplication @ D @ B ) @ ( c @ E ) ) @ zero ) )
=> ( leq @ ( multiplication @ ( multiplication @ ( multiplication @ C @ A ) @ B ) @ ( c @ E ) ) @ zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
leq @ ( multiplication @ ( multiplication @ sk3 @ sk1 ) @ ( c @ sk4 ) ) @ zero,
inference(cnf,[status(esa)],[19]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(38,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)],[7]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ A @ B ) @ C )
= ( multiplication @ A @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(481,plain,
leq @ ( multiplication @ sk3 @ ( multiplication @ sk1 @ ( c @ sk4 ) ) ) @ zero,
inference(rewrite,[status(thm)],[22,40]) ).
thf(6,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(35,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(36,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(lifteq,[status(thm)],[36]) ).
thf(23,plain,
~ ( leq @ ( multiplication @ ( multiplication @ ( multiplication @ sk3 @ sk1 ) @ sk2 ) @ ( c @ sk5 ) ) @ zero ),
inference(cnf,[status(esa)],[19]) ).
thf(93,plain,
! [A: $i] :
( ~ ( leq @ zero @ zero )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ ( multiplication @ ( multiplication @ sk3 @ sk1 ) @ sk2 ) @ ( c @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[37,23]) ).
thf(96,plain,
! [A: $i] :
( ~ ( leq @ zero @ zero )
| ( ( multiplication @ ( multiplication @ sk3 @ sk1 ) @ sk2 )
!= zero )
| ( A
!= ( c @ sk5 ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(99,plain,
( ~ ( leq @ zero @ zero )
| ( ( multiplication @ ( multiplication @ sk3 @ sk1 ) @ sk2 )
!= zero ) ),
inference(simp,[status(thm)],[96]) ).
thf(102,plain,
! [A: $i] :
( ~ ( leq @ zero @ zero )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ ( multiplication @ sk3 @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[37,99]) ).
thf(104,plain,
! [A: $i] :
( ~ ( leq @ zero @ zero )
| ( ( multiplication @ sk3 @ sk1 )
!= zero )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[102]) ).
thf(106,plain,
( ~ ( leq @ zero @ zero )
| ( ( multiplication @ sk3 @ sk1 )
!= zero ) ),
inference(simp,[status(thm)],[104]) ).
thf(121,plain,
! [A: $i] :
( ~ ( leq @ zero @ zero )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[37,106]) ).
thf(123,plain,
! [A: $i] :
( ~ ( leq @ zero @ zero )
| ( sk3 != zero )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[121]) ).
thf(125,plain,
( ~ ( leq @ zero @ zero )
| ( sk3 != zero ) ),
inference(simp,[status(thm)],[123]) ).
thf(11,axiom,
! [A: $i] :
( ~ ( test @ A )
=> ( ( c @ A )
= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_4) ).
thf(58,plain,
! [A: $i] :
( ~ ( test @ A )
=> ( ( c @ A )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(59,plain,
! [A: $i] :
( ( test @ A )
| ( ( c @ A )
= zero ) ),
inference(cnf,[status(esa)],[58]) ).
thf(60,plain,
! [A: $i] :
( ( ( c @ A )
= zero )
| ( test @ A ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(13,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(64,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(65,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(cnf,[status(esa)],[64]) ).
thf(66,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(lifteq,[status(thm)],[65]) ).
thf(21,plain,
leq @ ( multiplication @ ( multiplication @ sk4 @ sk2 ) @ ( c @ sk5 ) ) @ zero,
inference(cnf,[status(esa)],[19]) ).
thf(109,plain,
( ( leq @ ( multiplication @ ( multiplication @ ( multiplication @ sk3 @ sk1 ) @ sk2 ) @ ( c @ sk5 ) ) @ zero )
!= ( leq @ ( multiplication @ ( multiplication @ sk4 @ sk2 ) @ ( c @ sk5 ) ) @ zero ) ),
inference(paramod_ordered,[status(thm)],[21,23]) ).
thf(113,plain,
( ( ( multiplication @ ( multiplication @ ( multiplication @ sk3 @ sk1 ) @ sk2 ) @ ( c @ sk5 ) )
!= ( multiplication @ ( multiplication @ sk4 @ sk2 ) @ ( c @ sk5 ) ) )
| ( zero != zero ) ),
inference(simp,[status(thm)],[109]) ).
thf(117,plain,
( ( multiplication @ ( multiplication @ ( multiplication @ sk3 @ sk1 ) @ sk2 ) @ ( c @ sk5 ) )
!= ( multiplication @ ( multiplication @ sk4 @ sk2 ) @ ( c @ sk5 ) ) ),
inference(simp,[status(thm)],[113]) ).
thf(317,plain,
! [A: $i] :
( ( ( multiplication @ ( multiplication @ sk4 @ sk2 ) @ ( c @ sk5 ) )
!= ( multiplication @ zero @ ( c @ sk5 ) ) )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ ( multiplication @ sk3 @ sk1 ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[66,117]) ).
thf(338,plain,
! [A: $i] :
( ( ( multiplication @ sk4 @ sk2 )
!= zero )
| ( ( c @ sk5 )
!= ( c @ sk5 ) )
| ( A
!= ( multiplication @ sk3 @ sk1 ) )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[317]) ).
thf(368,plain,
( ( ( multiplication @ sk4 @ sk2 )
!= zero )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[338]) ).
thf(671,plain,
! [A: $i] :
( ( sk2 != zero )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ sk4 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[66,368]) ).
thf(682,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A != sk4 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[671]) ).
thf(686,plain,
sk2 != zero,
inference(simp,[status(thm)],[682]) ).
thf(9,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(44,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(86,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(15,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(72,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(315,plain,
( ( ( multiplication @ ( multiplication @ sk3 @ sk1 ) @ sk2 )
!= ( multiplication @ sk4 @ sk2 ) )
| ( ( c @ sk5 )
!= ( c @ sk5 ) ) ),
inference(simp,[status(thm)],[117]) ).
thf(386,plain,
( ( multiplication @ ( multiplication @ sk3 @ sk1 ) @ sk2 )
!= ( multiplication @ sk4 @ sk2 ) ),
inference(simp,[status(thm)],[315]) ).
thf(482,plain,
( ( multiplication @ sk4 @ sk2 )
!= ( multiplication @ sk3 @ ( multiplication @ sk1 @ sk2 ) ) ),
inference(rewrite,[status(thm)],[386,40]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( complement @ B @ A )
<=> ( ( ( multiplication @ A @ B )
= zero )
& ( ( multiplication @ B @ A )
= zero )
& ( ( addition @ A @ B )
= one ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_2) ).
thf(47,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)],[10]) ).
thf(25,plain,
test @ sk5,
inference(cnf,[status(esa)],[19]) ).
thf(389,plain,
! [A: $i] :
( ( ( multiplication @ sk4 @ sk2 )
!= ( multiplication @ zero @ sk2 ) )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[66,386]) ).
thf(398,plain,
! [A: $i] :
( ( sk4 != zero )
| ( sk2 != sk2 )
| ( A != sk3 )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[389]) ).
thf(417,plain,
( ( sk4 != zero )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[398]) ).
thf(24,plain,
test @ sk3,
inference(cnf,[status(esa)],[19]) ).
thf(20,plain,
test @ sk4,
inference(cnf,[status(esa)],[19]) ).
thf(45,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(lifteq,[status(thm)],[45]) ).
thf(4,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(29,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(73,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(cnf,[status(esa)],[72]) ).
thf(74,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(lifteq,[status(thm)],[73]) ).
thf(442,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
= C )
| ( ( addition @ A @ B )
!= ( addition @ C @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[34,74]) ).
thf(443,plain,
! [A: $i] :
( ( addition @ zero @ A )
= A ),
inference(pattern_uni,[status(thm)],[442:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(12,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(61,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(395,plain,
! [A: $i] :
( ( ( multiplication @ A @ sk2 )
!= ( multiplication @ sk4 @ sk2 ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[46,386]) ).
thf(413,plain,
! [A: $i] :
( ( A != sk4 )
| ( sk2 != sk2 )
| ( sk3 != one )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[395]) ).
thf(428,plain,
( ( sk3 != one )
| ( sk4 != sk1 ) ),
inference(simp,[status(thm)],[413]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
thf(26,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)],[3]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ C @ B ) @ A )
= ( addition @ C @ ( addition @ B @ A ) ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(147,plain,
! [A: $i] :
( ~ ( leq @ zero @ zero )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[66,106]) ).
thf(163,plain,
! [A: $i] :
( ~ ( leq @ zero @ zero )
| ( A != sk3 )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[147]) ).
thf(173,plain,
( ~ ( leq @ zero @ zero )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[163]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_distributivity) ).
thf(41,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)],[8]) ).
thf(62,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(cnf,[status(esa)],[61]) ).
thf(63,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(lifteq,[status(thm)],[62]) ).
thf(391,plain,
! [A: $i] :
( ( ( multiplication @ A @ sk2 )
!= ( multiplication @ sk4 @ sk2 ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[63,386]) ).
thf(406,plain,
! [A: $i] :
( ( A != sk4 )
| ( sk2 != sk2 )
| ( A != sk3 )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[391]) ).
thf(425,plain,
( ( sk4 != sk3 )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[406]) ).
thf(387,plain,
( ( ( multiplication @ sk3 @ sk1 )
!= sk4 )
| ( sk2 != sk2 ) ),
inference(simp,[status(thm)],[386]) ).
thf(414,plain,
( ( multiplication @ sk3 @ sk1 )
!= sk4 ),
inference(simp,[status(thm)],[387]) ).
thf(14,axiom,
! [A: $i] :
( ( test @ A )
<=> ? [B: $i] : ( complement @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).
thf(67,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)],[14]) ).
thf(154,plain,
! [A: $i] :
( ~ ( leq @ zero @ zero )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ ( multiplication @ ( multiplication @ sk3 @ sk1 ) @ sk2 ) @ ( c @ sk5 ) ) ) ),
inference(paramod_ordered,[status(thm)],[66,23]) ).
thf(167,plain,
! [A: $i] :
( ~ ( leq @ zero @ zero )
| ( A
!= ( multiplication @ ( multiplication @ sk3 @ sk1 ) @ sk2 ) )
| ( ( c @ sk5 )
!= zero ) ),
inference(simp,[status(thm)],[154]) ).
thf(177,plain,
( ~ ( leq @ zero @ zero )
| ( ( c @ sk5 )
!= zero ) ),
inference(simp,[status(thm)],[167]) ).
thf(30,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(lifteq,[status(thm)],[30]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( test @ A )
=> ( ( ( c @ A )
= B )
<=> ( complement @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
thf(75,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)],[16]) ).
thf(393,plain,
! [A: $i] :
( ( ( multiplication @ sk4 @ sk2 )
!= ( multiplication @ zero @ sk2 ) )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[37,386]) ).
thf(403,plain,
! [A: $i] :
( ( sk4 != zero )
| ( sk2 != sk2 )
| ( sk3 != zero )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[393]) ).
thf(422,plain,
( ( sk4 != zero )
| ( sk3 != zero ) ),
inference(simp,[status(thm)],[403]) ).
thf(486,plain,
leq @ ( multiplication @ sk4 @ ( multiplication @ sk2 @ ( c @ sk5 ) ) ) @ zero,
inference(rewrite,[status(thm)],[21,40]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_distributivity) ).
thf(83,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(10517,plain,
$false,
inference(e,[status(thm)],[481,125,60,686,44,86,66,35,72,482,47,37,25,417,24,20,46,29,443,106,61,428,74,28,38,173,41,425,64,32,34,63,414,67,177,31,40,26,75,58,19,422,486,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : KLE034+1 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n006.cluster.edu
% 0.15/0.35 % Model : x86_64 x86_64
% 0.15/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35 % Memory : 8042.1875MB
% 0.15/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35 % CPULimit : 300
% 0.15/0.35 % WCLimit : 300
% 0.15/0.35 % DateTime : Fri May 19 03:00:07 EDT 2023
% 0.15/0.36 % CPUTime :
% 1.01/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.15/1.02 % [INFO] Parsing done (139ms).
% 1.43/1.03 % [INFO] Running in sequential loop mode.
% 1.84/1.23 % [INFO] eprover registered as external prover.
% 1.84/1.23 % [INFO] cvc4 registered as external prover.
% 1.87/1.23 % [INFO] Scanning for conjecture ...
% 1.87/1.29 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 2.08/1.34 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.08/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 2.08/1.36 % [INFO] Type checking passed.
% 2.08/1.36 % [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 ...
% 31.23/5.56 % External prover 'e' found a proof!
% 31.23/5.56 % [INFO] Killing All external provers ...
% 31.23/5.56 % Time passed: 5049ms (effective reasoning time: 4522ms)
% 31.23/5.56 % 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)>
% 31.23/5.56 % 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
% 31.23/5.56 % No. of inferences in proof: 107
% 31.23/5.56 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5049 ms resp. 4522 ms w/o parsing
% 31.23/5.60 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 31.23/5.60 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------