TSTP Solution File: KLE025+2 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE025+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n032.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 11:24:51 EDT 2023
% Result : Theorem 11.85s 3.13s
% Output : Refutation 11.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 30
% Syntax : Number of formulae : 126 ( 63 unt; 11 typ; 0 def)
% Number of atoms : 207 ( 156 equ; 0 cnn)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 681 ( 82 ~; 46 |; 18 &; 507 @)
% ( 4 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 154 ( 0 ^; 151 !; 3 ?; 154 :)
% Comments :
%------------------------------------------------------------------------------
thf(test_type,type,
test: $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(leq_type,type,
leq: $i > $i > $o ).
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(11,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(56,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)],[11]) ).
thf(9,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(50,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)],[9]) ).
thf(51,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(cnf,[status(esa)],[50]) ).
thf(52,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) )
= ( multiplication @ ( addition @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(17,axiom,
! [A: $i,B: $i] :
( ( ( test @ A )
& ( test @ B ) )
=> ( ( c @ ( addition @ A @ B ) )
= ( multiplication @ ( c @ A ) @ ( c @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_deMorgan1) ).
thf(84,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(5,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(18,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(87,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(88,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(cnf,[status(esa)],[87]) ).
thf(89,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(lifteq,[status(thm)],[88]) ).
thf(247,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
= C )
| ( ( addition @ A @ B )
!= ( addition @ C @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[36,89]) ).
thf(248,plain,
! [A: $i] :
( ( addition @ zero @ A )
= A ),
inference(pattern_uni,[status(thm)],[247:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(53,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( ( test @ B )
& ( test @ C ) )
=> ( ( ( multiplication @ ( multiplication @ B @ A ) @ ( c @ C ) )
= zero )
=> ( ( multiplication @ B @ A )
= ( multiplication @ ( multiplication @ B @ A ) @ C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( ( test @ B )
& ( test @ C ) )
=> ( ( ( multiplication @ ( multiplication @ B @ A ) @ ( c @ C ) )
= zero )
=> ( ( multiplication @ B @ A )
= ( multiplication @ ( multiplication @ B @ A ) @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( ( test @ B )
& ( test @ C ) )
=> ( ( ( multiplication @ ( multiplication @ B @ A ) @ ( c @ C ) )
= zero )
=> ( ( multiplication @ B @ A )
= ( multiplication @ ( multiplication @ B @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(23,plain,
( ( multiplication @ ( multiplication @ sk2 @ sk1 ) @ ( c @ sk3 ) )
= zero ),
inference(cnf,[status(esa)],[21]) ).
thf(27,plain,
( ( multiplication @ ( multiplication @ sk2 @ sk1 ) @ ( c @ sk3 ) )
= zero ),
inference(lifteq,[status(thm)],[23]) ).
thf(8,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(47,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)],[8]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ A @ B ) @ C )
= ( multiplication @ A @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(409,plain,
( ( multiplication @ sk2 @ ( multiplication @ sk1 @ ( c @ sk3 ) ) )
= zero ),
inference(rewrite,[status(thm)],[27,49]) ).
thf(7,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(44,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(45,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(lifteq,[status(thm)],[45]) ).
thf(22,plain,
( ( multiplication @ sk2 @ sk1 )
!= ( multiplication @ ( multiplication @ sk2 @ sk1 ) @ sk3 ) ),
inference(cnf,[status(esa)],[21]) ).
thf(26,plain,
( ( multiplication @ ( multiplication @ sk2 @ sk1 ) @ sk3 )
!= ( multiplication @ sk2 @ sk1 ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(107,plain,
! [A: $i] :
( ( ( multiplication @ sk2 @ sk1 )
!= zero )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ ( multiplication @ sk2 @ sk1 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[46,26]) ).
thf(117,plain,
! [A: $i] :
( ( ( multiplication @ sk2 @ sk1 )
!= zero )
| ( ( multiplication @ sk2 @ sk1 )
!= zero )
| ( A != sk3 ) ),
inference(simp,[status(thm)],[107]) ).
thf(122,plain,
( ( multiplication @ sk2 @ sk1 )
!= zero ),
inference(simp,[status(thm)],[117]) ).
thf(481,plain,
( ( multiplication @ sk2 @ ( multiplication @ sk1 @ ( c @ sk3 ) ) )
!= ( multiplication @ sk2 @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[409,122]) ).
thf(489,plain,
( ( sk2 != sk2 )
| ( ( multiplication @ sk1 @ ( c @ sk3 ) )
!= sk1 ) ),
inference(simp,[status(thm)],[481]) ).
thf(503,plain,
( ( multiplication @ sk1 @ ( c @ sk3 ) )
!= sk1 ),
inference(simp,[status(thm)],[489]) ).
thf(54,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(cnf,[status(esa)],[53]) ).
thf(55,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(lifteq,[status(thm)],[54]) ).
thf(14,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(73,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(74,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(cnf,[status(esa)],[73]) ).
thf(75,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(lifteq,[status(thm)],[74]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(37,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)],[6]) ).
thf(38,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)],[37]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(cnf,[status(esa)],[38]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(simp,[status(thm)],[41]) ).
thf(24,plain,
test @ sk3,
inference(cnf,[status(esa)],[21]) ).
thf(25,plain,
test @ sk2,
inference(cnf,[status(esa)],[21]) ).
thf(15,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(76,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(77,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(cnf,[status(esa)],[76]) ).
thf(78,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(lifteq,[status(thm)],[77]) ).
thf(145,plain,
( ( multiplication @ ( multiplication @ sk2 @ sk1 ) @ ( c @ sk3 ) )
!= ( multiplication @ sk2 @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[27,122]) ).
thf(148,plain,
( ( ( multiplication @ sk2 @ sk1 )
!= sk2 )
| ( ( c @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[145]) ).
thf(390,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( c @ sk3 )
!= sk1 )
| ( ( multiplication @ one @ A )
!= ( multiplication @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[55,148]) ).
thf(397,plain,
( ( ( c @ sk3 )
!= sk1 )
| ( sk2 != one )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[390]) ).
thf(323,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ zero @ A )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[248,42]) ).
thf(324,plain,
! [A: $i] :
( ( A != A )
| ( leq @ zero @ A ) ),
inference(pattern_uni,[status(thm)],[323:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(334,plain,
! [A: $i] : ( leq @ zero @ A ),
inference(simp,[status(thm)],[324]) ).
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(28,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(13,axiom,
! [A: $i] :
( ~ ( test @ A )
=> ( ( c @ A )
= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_4) ).
thf(70,plain,
! [A: $i] :
( ~ ( test @ A )
=> ( ( c @ A )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(4,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(31,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(32,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(lifteq,[status(thm)],[32]) ).
thf(105,plain,
( ( ( multiplication @ sk2 @ sk1 )
!= sk2 )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[26]) ).
thf(513,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[75,503]) ).
thf(525,plain,
( ( sk1 != sk1 )
| ( ( c @ sk3 )
!= one ) ),
inference(simp,[status(thm)],[513]) ).
thf(530,plain,
( ( c @ sk3 )
!= one ),
inference(simp,[status(thm)],[525]) ).
thf(164,plain,
! [A: $i] :
( ( ( multiplication @ A @ sk3 )
!= ( multiplication @ sk2 @ sk1 ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[55,26]) ).
thf(170,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk3 != sk1 )
| ( sk2 != one )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[164]) ).
thf(180,plain,
( ( sk3 != sk1 )
| ( sk2 != one )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[170]) ).
thf(143,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
!= ( multiplication @ sk2 @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[46,122]) ).
thf(146,plain,
! [A: $i] :
( ( sk2 != zero )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[143]) ).
thf(149,plain,
sk2 != zero,
inference(simp,[status(thm)],[146]) ).
thf(325,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ A @ A )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[33,42]) ).
thf(326,plain,
! [A: $i] :
( ( A != A )
| ( leq @ A @ A ) ),
inference(pattern_uni,[status(thm)],[325:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(335,plain,
! [A: $i] : ( leq @ A @ A ),
inference(simp,[status(thm)],[326]) ).
thf(197,plain,
! [A: $i] :
( ( ( multiplication @ A @ sk3 )
!= ( multiplication @ sk2 @ sk1 ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[75,26]) ).
thf(207,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk3 != sk1 )
| ( A != sk2 )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[197]) ).
thf(219,plain,
( ( sk3 != sk1 )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[207]) ).
thf(20,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(98,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)],[20]) ).
thf(144,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
!= ( multiplication @ sk2 @ sk1 ) ),
inference(paramod_ordered,[status(thm)],[78,122]) ).
thf(147,plain,
! [A: $i] :
( ( A != sk2 )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[144]) ).
thf(150,plain,
sk1 != zero,
inference(simp,[status(thm)],[147]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( ( test @ A )
& ( test @ B ) )
=> ( ( c @ ( multiplication @ A @ B ) )
= ( addition @ ( c @ A ) @ ( c @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_deMorgan2) ).
thf(67,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)],[12]) ).
thf(71,plain,
! [A: $i] :
( ( test @ A )
| ( ( c @ A )
= zero ) ),
inference(cnf,[status(esa)],[70]) ).
thf(72,plain,
! [A: $i] :
( ( ( c @ A )
= zero )
| ( test @ A ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( ( addition @ A @ B )
= B ) ),
inference(cnf,[status(esa)],[38]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= B )
| ~ ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ C @ B ) @ A )
= ( addition @ C @ ( addition @ B @ A ) ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(16,axiom,
! [A: $i] :
( ( test @ A )
<=> ? [B: $i] : ( complement @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).
thf(79,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)],[16]) ).
thf(387,plain,
! [A: $i] :
( ( A != sk2 )
| ( ( c @ sk3 )
!= sk1 )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk2 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[75,148]) ).
thf(394,plain,
( ( ( c @ sk3 )
!= sk1 )
| ( sk2 != sk2 )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[387]) ).
thf(400,plain,
( ( ( c @ sk3 )
!= sk1 )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[394]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( test @ A )
=> ( ( ( c @ A )
= B )
<=> ( complement @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
thf(90,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)],[19]) ).
thf(198,plain,
! [A: $i] :
( ( A
!= ( multiplication @ sk2 @ sk1 ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( multiplication @ sk2 @ sk1 ) @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[75,26]) ).
thf(211,plain,
( ( ( multiplication @ sk2 @ sk1 )
!= ( multiplication @ sk2 @ sk1 ) )
| ( sk3 != one ) ),
inference(simp,[status(thm)],[198]) ).
thf(222,plain,
sk3 != one,
inference(simp,[status(thm)],[211]) ).
thf(1419,plain,
$false,
inference(e,[status(thm)],[56,52,84,248,53,503,44,87,55,75,47,42,24,37,25,46,78,397,89,334,28,70,21,33,73,105,530,34,148,180,149,49,335,219,76,98,150,409,50,67,31,72,43,36,30,79,400,90,122,222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.08 % Problem : KLE025+2 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.10 % Command : run_Leo-III %s %d
% 0.10/0.28 % Computer : n032.cluster.edu
% 0.10/0.28 % Model : x86_64 x86_64
% 0.10/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.28 % Memory : 8042.1875MB
% 0.10/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.28 % CPULimit : 300
% 0.10/0.28 % WCLimit : 300
% 0.10/0.28 % DateTime : Fri May 19 03:00:51 EDT 2023
% 0.10/0.28 % CPUTime :
% 0.76/0.73 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.03/0.87 % [INFO] Parsing done (137ms).
% 1.03/0.88 % [INFO] Running in sequential loop mode.
% 1.54/1.09 % [INFO] eprover registered as external prover.
% 1.54/1.09 % [INFO] cvc4 registered as external prover.
% 1.54/1.09 % [INFO] Scanning for conjecture ...
% 1.54/1.15 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 1.76/1.19 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 1.88/1.22 % [INFO] Problem is first-order (TPTP FOF).
% 1.88/1.22 % [INFO] Type checking passed.
% 1.88/1.22 % [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 ...
% 11.85/3.12 % External prover 'e' found a proof!
% 11.85/3.12 % [INFO] Killing All external provers ...
% 11.85/3.13 % Time passed: 2726ms (effective reasoning time: 2245ms)
% 11.85/3.13 % 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)>
% 11.85/3.13 % 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
% 11.85/3.13 % No. of inferences in proof: 115
% 11.85/3.13 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2726 ms resp. 2245 ms w/o parsing
% 11.85/3.18 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.85/3.18 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------