TSTP Solution File: KLE023+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE023+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n027.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 93.42s 20.07s
% Output : Refutation 93.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 29
% Syntax : Number of formulae : 122 ( 63 unt; 12 typ; 0 def)
% Number of atoms : 195 ( 147 equ; 0 cnn)
% Maximal formula atoms : 8 ( 1 avg)
% Number of connectives : 788 ( 79 ~; 43 |; 14 &; 628 @)
% ( 4 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 12 usr; 6 con; 0-2 aty)
% Number of variables : 138 ( 0 ^; 133 !; 5 ?; 138 :)
% 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(11,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
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(29,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(14,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(74,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(75,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(cnf,[status(esa)],[74]) ).
thf(76,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(lifteq,[status(thm)],[75]) ).
thf(10,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(49,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(50,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(lifteq,[status(thm)],[50]) ).
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(19,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(20,plain,
( ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ),
inference(cnf,[status(esa)],[19]) ).
thf(24,plain,
( ( addition @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(315,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)],[51,24]) ).
thf(327,plain,
( ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) )
| ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(simp,[status(thm)],[315]) ).
thf(332,plain,
( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ),
inference(simp,[status(thm)],[327]) ).
thf(335,plain,
! [A: $i] :
( ( A
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[76,332]) ).
thf(342,plain,
( ( multiplication @ ( multiplication @ sk1 @ ( c @ sk3 ) ) @ one )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ),
inference(simp,[status(thm)],[335]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ A @ B ) @ C )
= ( multiplication @ A @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(427,plain,
( ( multiplication @ sk1 @ ( multiplication @ ( c @ sk3 ) @ one ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[342,31]) ).
thf(435,plain,
! [A: $i] :
( ( A
!= ( multiplication @ sk1 @ ( multiplication @ ( c @ sk3 ) @ one ) ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[76,427]) ).
thf(461,plain,
( ( multiplication @ ( multiplication @ sk1 @ ( multiplication @ ( c @ sk3 ) @ one ) ) @ one )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ),
inference(simp,[status(thm)],[435]) ).
thf(512,plain,
( ( multiplication @ sk1 @ ( multiplication @ ( multiplication @ ( c @ sk3 ) @ one ) @ one ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ),
inference(rewrite,[status(thm)],[461,31]) ).
thf(333,plain,
( ( ( c @ sk2 )
!= sk1 )
| ( ( c @ sk3 )
!= sk1 ) ),
inference(simp,[status(thm)],[332]) ).
thf(359,plain,
( ( ( c @ sk2 )
!= sk1 )
| ( ( c @ sk3 )
!= ( c @ sk2 ) )
| ( sk1 != sk1 ) ),
inference(eqfactor_ordered,[status(thm)],[333]) ).
thf(361,plain,
( ( ( c @ sk2 )
!= sk1 )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[359]) ).
thf(15,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(77,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(8,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(41,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(42,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(lifteq,[status(thm)],[42]) ).
thf(16,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(80,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(81,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(cnf,[status(esa)],[80]) ).
thf(82,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(lifteq,[status(thm)],[81]) ).
thf(78,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(cnf,[status(esa)],[77]) ).
thf(79,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(lifteq,[status(thm)],[78]) ).
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(38,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(39,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[39]) ).
thf(383,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)],[40,79]) ).
thf(384,plain,
! [B: $i,A: $i] :
( ( addition @ ( multiplication @ A @ zero ) @ ( multiplication @ B @ zero ) )
= zero ),
inference(pattern_uni,[status(thm)],[383:[bind(A,$thf( E )),bind(B,$thf( F )),bind(C,$thf( zero )),bind(D,$thf( addition @ E @ F ))]]) ).
thf(407,plain,
! [B: $i,A: $i] :
( ( addition @ ( multiplication @ A @ zero ) @ ( multiplication @ B @ zero ) )
= zero ),
inference(simp,[status(thm)],[384]) ).
thf(628,plain,
( ( addition @ zero @ zero )
= zero ),
inference(rewrite,[status(thm)],[407,79]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( test @ A )
=> ( ( c @ A )
= zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_4) ).
thf(35,plain,
! [A: $i] :
( ~ ( test @ A )
=> ( ( c @ A )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(36,plain,
! [A: $i] :
( ( test @ A )
| ( ( c @ A )
= zero ) ),
inference(cnf,[status(esa)],[35]) ).
thf(37,plain,
! [A: $i] :
( ( ( c @ A )
= zero )
| ( test @ A ) ),
inference(lifteq,[status(thm)],[36]) ).
thf(21,plain,
( ( addition @ ( multiplication @ sk2 @ sk1 ) @ ( multiplication @ sk1 @ sk3 ) )
= ( multiplication @ sk1 @ sk3 ) ),
inference(cnf,[status(esa)],[19]) ).
thf(25,plain,
( ( addition @ ( multiplication @ sk2 @ sk1 ) @ ( multiplication @ sk1 @ sk3 ) )
= ( multiplication @ sk1 @ sk3 ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(23,plain,
test @ sk2,
inference(cnf,[status(esa)],[19]) ).
thf(9,axiom,
! [A: $i] :
( ( test @ A )
<=> ? [B: $i] : ( complement @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_1) ).
thf(44,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(45,plain,
( ! [A: $i] :
( ( test @ A )
=> ? [B: $i] : ( complement @ B @ A ) )
& ! [A: $i] :
( ? [B: $i] : ( complement @ B @ A )
=> ( test @ A ) ) ),
inference(miniscope,[status(thm)],[44]) ).
thf(47,plain,
! [A: $i] :
( ~ ( test @ A )
| ( complement @ ( sk4 @ A ) @ A ) ),
inference(cnf,[status(esa)],[45]) ).
thf(659,plain,
! [A: $i] :
( ( complement @ ( sk4 @ A ) @ A )
| ( ( test @ sk2 )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[23,47]) ).
thf(660,plain,
complement @ ( sk4 @ sk2 ) @ sk2,
inference(pattern_uni,[status(thm)],[659:[bind(A,$thf( sk2 ))]]) ).
thf(3,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(26,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(lifteq,[status(thm)],[27]) ).
thf(343,plain,
( ( ( multiplication @ sk1 @ ( c @ sk3 ) )
!= ( c @ sk2 ) )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[335]) ).
thf(360,plain,
( ( ( c @ sk2 )
!= sk1 )
| ( ( c @ sk3 )
!= ( c @ sk2 ) ) ),
inference(simp,[status(thm)],[359]) ).
thf(432,plain,
! [A: $i] :
( ( A
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk1 @ ( multiplication @ ( c @ sk3 ) @ one ) ) ) ),
inference(paramod_ordered,[status(thm)],[76,427]) ).
thf(468,plain,
( ( multiplication @ ( multiplication @ ( c @ sk2 ) @ sk1 ) @ one )
!= ( multiplication @ sk1 @ ( multiplication @ ( c @ sk3 ) @ one ) ) ),
inference(simp,[status(thm)],[432]) ).
thf(662,plain,
( ( multiplication @ ( c @ sk2 ) @ ( multiplication @ sk1 @ one ) )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ),
inference(rewrite,[status(thm)],[468,76,31]) ).
thf(97,plain,
! [A: $i] :
( ( ( addition @ zero @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[28,24]) ).
thf(101,plain,
! [A: $i] :
( ( ( addition @ zero @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( sk1 != zero )
| ( A
!= ( c @ sk3 ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(105,plain,
( ( ( addition @ zero @ ( multiplication @ ( c @ sk2 ) @ sk1 ) )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[101]) ).
thf(110,plain,
! [A: $i] :
( ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( addition @ zero @ zero ) )
| ( sk1 != zero )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79,105]) ).
thf(112,plain,
! [A: $i] :
( ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( addition @ zero @ zero ) )
| ( sk1 != zero )
| ( A
!= ( c @ sk2 ) )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[110]) ).
thf(113,plain,
( ( ( multiplication @ ( c @ sk2 ) @ sk1 )
!= ( addition @ zero @ zero ) )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[112]) ).
thf(138,plain,
! [A: $i] :
( ( ( addition @ zero @ zero )
!= zero )
| ( sk1 != zero )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ ( c @ sk2 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[79,113]) ).
thf(140,plain,
! [A: $i] :
( ( ( addition @ zero @ zero )
!= zero )
| ( sk1 != zero )
| ( A
!= ( c @ sk2 ) )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[138]) ).
thf(142,plain,
( ( ( addition @ zero @ zero )
!= zero )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[140]) ).
thf(263,plain,
( ( zero != zero )
| ( sk1 != zero ) ),
inference(rewrite,[status(thm)],[142,82]) ).
thf(264,plain,
sk1 != zero,
inference(simp,[status(thm)],[263]) ).
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(32,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(33,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ C @ B ) @ A )
= ( addition @ C @ ( addition @ B @ A ) ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(22,plain,
test @ sk3,
inference(cnf,[status(esa)],[19]) ).
thf(640,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ zero @ A )
= ( addition @ C @ ( addition @ B @ A ) ) )
| ( ( addition @ zero @ zero )
!= ( addition @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[628,34]) ).
thf(641,plain,
! [A: $i] :
( ( addition @ zero @ ( addition @ zero @ A ) )
= ( addition @ zero @ A ) ),
inference(pattern_uni,[status(thm)],[640:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( zero ))]]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox/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(657,plain,
! [A: $i] :
( ( complement @ ( sk4 @ A ) @ A )
| ( ( test @ sk3 )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[22,47]) ).
thf(658,plain,
complement @ ( sk4 @ sk3 ) @ sk3,
inference(pattern_uni,[status(thm)],[657:[bind(A,$thf( sk3 ))]]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( complement @ B @ A )
| ( test @ A ) ),
inference(cnf,[status(esa)],[45]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ~ ( complement @ B @ A )
| ( test @ A ) ),
inference(simp,[status(thm)],[46]) ).
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(63,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(12,axiom,
! [A: $i,B: $i] :
( ( test @ A )
=> ( ( ( c @ A )
= B )
<=> ( complement @ A @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',test_3) ).
thf(55,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(725,plain,
! [A: $i] :
( ( A
!= ( c @ sk2 ) )
| ( sk1 != one )
| ( ( multiplication @ one @ A )
!= ( multiplication @ sk1 @ ( c @ sk3 ) ) ) ),
inference(paramod_ordered,[status(thm)],[43,343]) ).
thf(733,plain,
( ( sk1 != one )
| ( sk1 != one )
| ( ( c @ sk3 )
!= ( c @ sk2 ) ) ),
inference(simp,[status(thm)],[725]) ).
thf(740,plain,
( ( sk1 != one )
| ( ( c @ sk3 )
!= ( c @ sk2 ) ) ),
inference(simp,[status(thm)],[733]) ).
thf(803,plain,
( ( sk1 != one )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[740]) ).
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(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(69889,plain,
$false,
inference(cvc4,[status(thm)],[52,29,512,361,77,41,76,31,43,82,79,333,628,24,37,25,660,74,28,38,343,360,662,264,32,34,22,44,641,54,49,86,80,35,658,48,63,40,26,55,23,51,19,740,332,427,47,803,83]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : KLE023+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.15 % Command : run_Leo-III %s %d
% 0.15/0.35 % Computer : n027.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 03:21:37 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.93/0.88 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.01 % [INFO] Parsing done (132ms).
% 1.27/1.02 % [INFO] Running in sequential loop mode.
% 1.62/1.22 % [INFO] eprover registered as external prover.
% 1.62/1.22 % [INFO] cvc4 registered as external prover.
% 1.62/1.23 % [INFO] Scanning for conjecture ...
% 1.93/1.29 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 1.93/1.32 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 1.93/1.34 % [INFO] Problem is first-order (TPTP FOF).
% 2.16/1.35 % [INFO] Type checking passed.
% 2.16/1.35 % [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 ...
% 93.42/20.06 % External prover 'cvc4' found a proof!
% 93.42/20.06 % [INFO] Killing All external provers ...
% 93.42/20.06 % Time passed: 19544ms (effective reasoning time: 19039ms)
% 93.42/20.06 % 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)>
% 93.42/20.07 % 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
% 93.42/20.07 % No. of inferences in proof: 110
% 93.42/20.07 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 19544 ms resp. 19039 ms w/o parsing
% 93.42/20.10 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 93.42/20.11 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------