TSTP Solution File: KLE011+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE011+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n008.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 11:24:47 EDT 2023
% Result : Theorem 9.04s 2.79s
% Output : Refutation 9.04s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 28
% Syntax : Number of formulae : 121 ( 56 unt; 11 typ; 0 def)
% Number of atoms : 242 ( 173 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 853 ( 111 ~; 83 |; 15 &; 620 @)
% ( 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 : 13 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 146 ( 0 ^; 141 !; 5 ?; 146 :)
% Comments :
%------------------------------------------------------------------------------
thf(test_type,type,
test: $i > $o ).
thf(one_type,type,
one: $i ).
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(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 > $i ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(50,plain,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(cnf,[status(esa)],[50]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(84,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(1,conjecture,
! [A: $i,B: $i] :
( ( ( test @ B )
& ( test @ A ) )
=> ( one
= ( addition @ ( addition @ ( multiplication @ ( addition @ B @ ( c @ B ) ) @ A ) @ ( multiplication @ ( addition @ A @ ( c @ A ) ) @ B ) ) @ ( multiplication @ ( c @ A ) @ ( c @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( test @ B )
& ( test @ A ) )
=> ( one
= ( addition @ ( addition @ ( multiplication @ ( addition @ B @ ( c @ B ) ) @ A ) @ ( multiplication @ ( addition @ A @ ( c @ A ) ) @ B ) ) @ ( multiplication @ ( c @ A ) @ ( c @ B ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i] :
( ( ( test @ B )
& ( test @ A ) )
=> ( one
= ( addition @ ( addition @ ( multiplication @ ( addition @ B @ ( c @ B ) ) @ A ) @ ( multiplication @ ( addition @ A @ ( c @ A ) ) @ B ) ) @ ( multiplication @ ( c @ A ) @ ( c @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,plain,
test @ sk1,
inference(cnf,[status(esa)],[19]) ).
thf(9,axiom,
! [A: $i] :
( ( test @ A )
<=> ? [B: $i] : ( complement @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_1) ).
thf(42,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(43,plain,
( ! [A: $i] :
( ( test @ A )
=> ? [B: $i] : ( complement @ B @ A ) )
& ! [A: $i] :
( ? [B: $i] : ( complement @ B @ A )
=> ( test @ A ) ) ),
inference(miniscope,[status(thm)],[42]) ).
thf(45,plain,
! [A: $i] :
( ~ ( test @ A )
| ( complement @ ( sk3 @ A ) @ A ) ),
inference(cnf,[status(esa)],[43]) ).
thf(545,plain,
! [A: $i] :
( ( complement @ ( sk3 @ A ) @ A )
| ( ( test @ sk1 )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21,45]) ).
thf(546,plain,
complement @ ( sk3 @ sk1 ) @ sk1,
inference(pattern_uni,[status(thm)],[545:[bind(A,$thf( sk1 ))]]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( test @ A )
=> ( ( ( c @ A )
= B )
<=> ( complement @ A @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_3) ).
thf(53,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(54,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)],[53]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( test @ A )
| ( ( c @ A )
!= B )
| ( complement @ A @ B ) ),
inference(cnf,[status(esa)],[54]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( ( c @ A )
!= B )
| ~ ( test @ A )
| ( complement @ A @ B ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(58,plain,
! [A: $i] :
( ~ ( test @ A )
| ( complement @ A @ ( c @ A ) ) ),
inference(simp,[status(thm)],[57]) ).
thf(582,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ sk1 )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[21,58]) ).
thf(583,plain,
complement @ sk1 @ ( c @ sk1 ),
inference(pattern_uni,[status(thm)],[582:[bind(A,$thf( sk1 ))]]) ).
thf(8,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(39,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(40,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(cnf,[status(esa)],[39]) ).
thf(41,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(lifteq,[status(thm)],[40]) ).
thf(14,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(72,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(16,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(78,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(79,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(cnf,[status(esa)],[78]) ).
thf(80,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(lifteq,[status(thm)],[79]) ).
thf(357,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
= C )
| ( ( addition @ A @ B )
!= ( addition @ C @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[52,80]) ).
thf(358,plain,
! [A: $i] :
( ( addition @ zero @ A )
= A ),
inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(47,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(75,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(76,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(cnf,[status(esa)],[75]) ).
thf(77,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(lifteq,[status(thm)],[76]) ).
thf(7,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(36,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(37,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(447,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ ( multiplication @ B @ D ) @ ( multiplication @ C @ D ) )
= zero )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ ( addition @ B @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[77,38]) ).
thf(448,plain,
! [B: $i,A: $i] :
( ( addition @ ( multiplication @ A @ zero ) @ ( multiplication @ B @ zero ) )
= zero ),
inference(pattern_uni,[status(thm)],[447:[bind(A,$thf( addition @ E @ F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( zero ))]]) ).
thf(475,plain,
! [B: $i,A: $i] :
( ( addition @ ( multiplication @ A @ zero ) @ ( multiplication @ B @ zero ) )
= zero ),
inference(simp,[status(thm)],[448]) ).
thf(500,plain,
( ( addition @ zero @ zero )
= zero ),
inference(rewrite,[status(thm)],[475,77]) ).
thf(20,plain,
( one
!= ( addition @ ( addition @ ( multiplication @ ( addition @ sk2 @ ( c @ sk2 ) ) @ sk1 ) @ ( multiplication @ ( addition @ sk1 @ ( c @ sk1 ) ) @ sk2 ) ) @ ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) ) ),
inference(cnf,[status(esa)],[19]) ).
thf(23,plain,
( ( addition @ ( addition @ ( multiplication @ ( addition @ sk2 @ ( c @ sk2 ) ) @ sk1 ) @ ( multiplication @ ( addition @ sk1 @ ( c @ sk1 ) ) @ sk2 ) ) @ ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) )
!= one ),
inference(lifteq,[status(thm)],[20]) ).
thf(96,plain,
! [A: $i] :
( ( ( addition @ ( addition @ ( multiplication @ ( addition @ sk2 @ ( c @ sk2 ) ) @ sk1 ) @ zero ) @ ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) )
!= one )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ ( addition @ sk1 @ ( c @ sk1 ) ) @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[77,23]) ).
thf(102,plain,
! [A: $i] :
( ( ( addition @ ( addition @ ( multiplication @ ( addition @ sk2 @ ( c @ sk2 ) ) @ sk1 ) @ zero ) @ ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) )
!= one )
| ( A
!= ( addition @ sk1 @ ( c @ sk1 ) ) )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[96]) ).
thf(108,plain,
( ( ( addition @ ( addition @ ( multiplication @ ( addition @ sk2 @ ( c @ sk2 ) ) @ sk1 ) @ zero ) @ ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) )
!= one )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[102]) ).
thf(113,plain,
! [A: $i] :
( ( ( addition @ ( addition @ zero @ zero ) @ ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) )
!= one )
| ( sk2 != zero )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ ( addition @ sk2 @ ( c @ sk2 ) ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[77,108]) ).
thf(117,plain,
! [A: $i] :
( ( ( addition @ ( addition @ zero @ zero ) @ ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) )
!= one )
| ( sk2 != zero )
| ( A
!= ( addition @ sk2 @ ( c @ sk2 ) ) )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[113]) ).
thf(121,plain,
( ( ( addition @ ( addition @ zero @ zero ) @ ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) )
!= one )
| ( sk2 != zero )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[117]) ).
thf(248,plain,
( ( ( addition @ zero @ ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) )
!= one )
| ( sk2 != zero )
| ( sk1 != zero ) ),
inference(rewrite,[status(thm)],[121,80]) ).
thf(391,plain,
( ( ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) )
!= one )
| ( sk2 != zero )
| ( sk1 != zero ) ),
inference(rewrite,[status(thm)],[248,358]) ).
thf(420,plain,
! [A: $i] :
( ( A != one )
| ( sk2 != zero )
| ( sk1 != zero )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[41,391]) ).
thf(429,plain,
( ( sk2 != zero )
| ( sk1 != zero )
| ( ( c @ sk1 )
!= one )
| ( ( c @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[420]) ).
thf(536,plain,
( ( sk2 != zero )
| ( sk1 != zero )
| ( ( c @ sk1 )
!= one )
| ( ( c @ sk2 )
!= ( c @ sk1 ) )
| ( one != one ) ),
inference(eqfactor_ordered,[status(thm)],[429]) ).
thf(538,plain,
( ( sk2 != zero )
| ( sk1 != zero )
| ( ( c @ sk1 )
!= one )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[536]) ).
thf(3,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(24,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(44,plain,
! [B: $i,A: $i] :
( ~ ( complement @ B @ A )
| ( test @ A ) ),
inference(cnf,[status(esa)],[43]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( complement @ B @ A )
| ( test @ A ) ),
inference(simp,[status(thm)],[44]) ).
thf(4,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(27,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(28,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ A @ B ) @ C )
= ( multiplication @ A @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[28]) ).
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/sandbox2/benchmark/theBenchmark.p',test_2) ).
thf(61,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(150,plain,
! [A: $i] :
( ( ( addition @ ( addition @ zero @ zero ) @ zero )
!= one )
| ( sk2 != zero )
| ( sk1 != zero )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[77,121]) ).
thf(153,plain,
! [A: $i] :
( ( ( addition @ ( addition @ zero @ zero ) @ zero )
!= one )
| ( sk2 != zero )
| ( sk1 != zero )
| ( A
!= ( c @ sk1 ) )
| ( ( c @ sk2 )
!= zero ) ),
inference(simp,[status(thm)],[150]) ).
thf(156,plain,
( ( ( addition @ ( addition @ zero @ zero ) @ zero )
!= one )
| ( sk2 != zero )
| ( sk1 != zero )
| ( ( c @ sk2 )
!= zero ) ),
inference(simp,[status(thm)],[153]) ).
thf(249,plain,
( ( ( addition @ zero @ zero )
!= one )
| ( sk2 != zero )
| ( sk1 != zero )
| ( ( c @ sk2 )
!= zero ) ),
inference(rewrite,[status(thm)],[156,80]) ).
thf(265,plain,
( ( zero != one )
| ( sk2 != zero )
| ( sk1 != zero )
| ( ( c @ sk2 )
!= zero ) ),
inference(rewrite,[status(thm)],[249,80]) ).
thf(73,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(cnf,[status(esa)],[72]) ).
thf(74,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(lifteq,[status(thm)],[73]) ).
thf(6,axiom,
! [A: $i] :
( ~ ( test @ A )
=> ( ( c @ A )
= zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',test_4) ).
thf(33,plain,
! [A: $i] :
( ~ ( test @ A )
=> ( ( c @ A )
= zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(537,plain,
( ( sk2 != zero )
| ( sk1 != zero )
| ( ( c @ sk1 )
!= one )
| ( ( c @ sk2 )
!= ( c @ sk1 ) ) ),
inference(simp,[status(thm)],[536]) ).
thf(5,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(30,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(31,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ C @ B ) @ A )
= ( addition @ C @ ( addition @ B @ A ) ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(22,plain,
test @ sk2,
inference(cnf,[status(esa)],[19]) ).
thf(578,plain,
! [A: $i] :
( ( complement @ A @ ( c @ A ) )
| ( ( test @ sk2 )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[22,58]) ).
thf(579,plain,
complement @ sk2 @ ( c @ sk2 ),
inference(pattern_uni,[status(thm)],[578:[bind(A,$thf( sk2 ))]]) ).
thf(48,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(lifteq,[status(thm)],[48]) ).
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(81,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(25,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(lifteq,[status(thm)],[25]) ).
thf(271,plain,
! [A: $i] :
( ( ( addition @ zero @ zero )
!= one )
| ( sk2 != zero )
| ( sk1 != zero )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,248]) ).
thf(276,plain,
! [A: $i] :
( ( ( addition @ zero @ zero )
!= one )
| ( sk2 != zero )
| ( sk1 != zero )
| ( ( c @ sk1 )
!= zero )
| ( A
!= ( c @ sk2 ) ) ),
inference(simp,[status(thm)],[271]) ).
thf(281,plain,
( ( ( addition @ zero @ zero )
!= one )
| ( sk2 != zero )
| ( sk1 != zero )
| ( ( c @ sk1 )
!= zero ) ),
inference(simp,[status(thm)],[276]) ).
thf(299,plain,
( ( zero != one )
| ( sk2 != zero )
| ( sk1 != zero )
| ( ( c @ sk1 )
!= zero ) ),
inference(rewrite,[status(thm)],[281,80]) ).
thf(34,plain,
! [A: $i] :
( ( test @ A )
| ( ( c @ A )
= zero ) ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [A: $i] :
( ( ( c @ A )
= zero )
| ( test @ A ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(543,plain,
! [A: $i] :
( ( complement @ ( sk3 @ A ) @ A )
| ( ( test @ sk2 )
!= ( test @ A ) ) ),
inference(paramod_ordered,[status(thm)],[22,45]) ).
thf(544,plain,
complement @ ( sk3 @ sk2 ) @ sk2,
inference(pattern_uni,[status(thm)],[543:[bind(A,$thf( sk2 ))]]) ).
thf(587,plain,
! [B: $i,A: $i] :
( ( test @ A )
| ( ( complement @ sk2 @ ( c @ sk2 ) )
!= ( complement @ B @ A ) ) ),
inference(paramod_ordered,[status(thm)],[579,46]) ).
thf(588,plain,
test @ ( c @ sk2 ),
inference(pattern_uni,[status(thm)],[587:[bind(A,$thf( c @ sk2 )),bind(B,$thf( sk2 ))]]) ).
thf(269,plain,
! [A: $i] :
( ( A != one )
| ( sk2 != zero )
| ( sk1 != zero )
| ( ( addition @ A @ zero )
!= ( addition @ zero @ ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[80,248]) ).
thf(273,plain,
( ( sk2 != zero )
| ( sk1 != zero )
| ( zero != one )
| ( ( multiplication @ ( c @ sk1 ) @ ( c @ sk2 ) )
!= zero ) ),
inference(simp,[status(thm)],[269]) ).
thf(1307,plain,
$false,
inference(cvc4,[status(thm)],[52,84,546,583,53,41,72,358,47,500,538,42,24,46,78,29,61,265,74,38,429,21,33,77,537,32,45,22,579,27,391,49,81,39,299,80,35,50,544,588,26,75,58,36,30,19,273]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : KLE011+1 : TPTP v8.1.2. Released v4.0.0.
% 0.11/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri May 19 03:02:55 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.90/0.83 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.20/0.97 % [INFO] Parsing done (133ms).
% 1.20/0.98 % [INFO] Running in sequential loop mode.
% 1.59/1.17 % [INFO] eprover registered as external prover.
% 1.59/1.17 % [INFO] cvc4 registered as external prover.
% 1.59/1.17 % [INFO] Scanning for conjecture ...
% 1.93/1.23 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 1.93/1.27 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 1.93/1.29 % [INFO] Problem is first-order (TPTP FOF).
% 1.93/1.30 % [INFO] Type checking passed.
% 1.93/1.30 % [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 ...
% 9.04/2.79 % External prover 'cvc4' found a proof!
% 9.04/2.79 % [INFO] Killing All external provers ...
% 9.04/2.79 % Time passed: 2272ms (effective reasoning time: 1808ms)
% 9.04/2.79 % 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)>
% 9.04/2.79 % 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
% 9.04/2.79 % No. of inferences in proof: 110
% 9.04/2.79 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2272 ms resp. 1808 ms w/o parsing
% 9.04/2.84 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 9.04/2.84 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------