TSTP Solution File: KLE090+1 by Leo-III---1.7.10
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.10
% Problem : KLE090+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n026.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 : Tue May 7 07:51:31 EDT 2024
% Result : Theorem 34.65s 6.10s
% Output : Refutation 34.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 32
% Syntax : Number of formulae : 131 ( 76 unt; 11 typ; 0 def)
% Number of atoms : 174 ( 159 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 643 ( 64 ~; 44 |; 2 &; 525 @)
% ( 1 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 11 usr; 5 con; 0-2 aty)
% Number of variables : 134 ( 0 ^ 134 !; 0 ?; 134 :)
% Comments :
%------------------------------------------------------------------------------
thf(addition_type,type,
addition: $i > $i > $i ).
thf(antidomain_type,type,
antidomain: $i > $i ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(codomain_type,type,
codomain: $i > $i ).
thf(coantidomain_type,type,
coantidomain: $i > $i ).
thf(one_type,type,
one: $i ).
thf(domain_type,type,
domain: $i > $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( addition @ ( antidomain @ ( multiplication @ A @ B ) ) @ ( antidomain @ ( multiplication @ A @ ( antidomain @ ( antidomain @ B ) ) ) ) )
= ( antidomain @ ( multiplication @ A @ ( antidomain @ ( antidomain @ B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( addition @ ( antidomain @ ( multiplication @ A @ B ) ) @ ( antidomain @ ( multiplication @ A @ ( antidomain @ ( antidomain @ B ) ) ) ) )
= ( antidomain @ ( multiplication @ A @ ( antidomain @ ( antidomain @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [A: $i] :
( ( addition @ ( coantidomain @ ( coantidomain @ A ) ) @ ( coantidomain @ A ) )
= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain3) ).
thf(61,plain,
! [A: $i] :
( ( addition @ ( coantidomain @ ( coantidomain @ A ) ) @ ( coantidomain @ A ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(9,axiom,
! [A: $i] :
( ( multiplication @ A @ ( coantidomain @ A ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain1) ).
thf(46,plain,
! [A: $i] :
( ( multiplication @ A @ ( coantidomain @ A ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(47,plain,
! [A: $i] :
( ( multiplication @ A @ ( coantidomain @ A ) )
= zero ),
inference(cnf,[status(esa)],[46]) ).
thf(48,plain,
! [A: $i] :
( ( multiplication @ A @ ( coantidomain @ A ) )
= zero ),
inference(lifteq,[status(thm)],[47]) ).
thf(8,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(43,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(44,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(cnf,[status(esa)],[43]) ).
thf(45,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(lifteq,[status(thm)],[44]) ).
thf(262,plain,
! [B: $i,A: $i] :
( ( zero = B )
| ( ( multiplication @ A @ ( coantidomain @ A ) )
!= ( multiplication @ one @ B ) ) ),
inference(paramod_ordered,[status(thm)],[48,45]) ).
thf(263,plain,
( ( coantidomain @ one )
= zero ),
inference(pattern_uni,[status(thm)],[262:[bind(A,$thf( one )),bind(B,$thf( coantidomain @ one ))]]) ).
thf(6,axiom,
! [A: $i] :
( ( codomain @ A )
= ( coantidomain @ ( coantidomain @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain4) ).
thf(37,plain,
! [A: $i] :
( ( codomain @ A )
= ( coantidomain @ ( coantidomain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(38,plain,
! [A: $i] :
( ( codomain @ A )
= ( coantidomain @ ( coantidomain @ A ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
! [A: $i] :
( ( coantidomain @ ( coantidomain @ A ) )
= ( codomain @ A ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(283,plain,
! [A: $i] :
( ( ( coantidomain @ zero )
= ( codomain @ A ) )
| ( ( coantidomain @ one )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[263,39]) ).
thf(284,plain,
( ( coantidomain @ zero )
= ( codomain @ one ) ),
inference(pattern_uni,[status(thm)],[283:[bind(A,$thf( one ))]]) ).
thf(293,plain,
! [A: $i] :
( ( ( coantidomain @ ( codomain @ one ) )
= ( codomain @ A ) )
| ( ( coantidomain @ zero )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[284,39]) ).
thf(294,plain,
( ( coantidomain @ ( codomain @ one ) )
= ( codomain @ zero ) ),
inference(pattern_uni,[status(thm)],[293:[bind(A,$thf( zero ))]]) ).
thf(309,plain,
! [A: $i] :
( ( ( coantidomain @ ( codomain @ zero ) )
= ( codomain @ A ) )
| ( ( coantidomain @ ( codomain @ one ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[294,39]) ).
thf(310,plain,
( ( coantidomain @ ( codomain @ zero ) )
= ( codomain @ ( codomain @ one ) ) ),
inference(pattern_uni,[status(thm)],[309:[bind(A,$thf( codomain @ one ))]]) ).
thf(377,plain,
! [A: $i] :
( ( ( coantidomain @ ( codomain @ ( codomain @ one ) ) )
= ( codomain @ A ) )
| ( ( coantidomain @ ( codomain @ zero ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[310,39]) ).
thf(378,plain,
( ( coantidomain @ ( codomain @ ( codomain @ one ) ) )
= ( codomain @ ( codomain @ zero ) ) ),
inference(pattern_uni,[status(thm)],[377:[bind(A,$thf( codomain @ zero ))]]) ).
thf(498,plain,
! [A: $i] :
( ( ( multiplication @ A @ ( codomain @ ( codomain @ zero ) ) )
= zero )
| ( ( coantidomain @ ( codomain @ ( codomain @ one ) ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[378,48]) ).
thf(499,plain,
( ( multiplication @ ( codomain @ ( codomain @ one ) ) @ ( codomain @ ( codomain @ zero ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[498:[bind(A,$thf( codomain @ ( codomain @ one ) ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( multiplication @ ( antidomain @ A ) @ A )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
thf(49,plain,
! [A: $i] :
( ( multiplication @ ( antidomain @ A ) @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(50,plain,
! [A: $i] :
( ( multiplication @ ( antidomain @ A ) @ A )
= zero ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [A: $i] :
( ( multiplication @ ( antidomain @ A ) @ A )
= zero ),
inference(lifteq,[status(thm)],[50]) ).
thf(7,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(40,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(41,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(cnf,[status(esa)],[40]) ).
thf(42,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(lifteq,[status(thm)],[41]) ).
thf(322,plain,
! [B: $i,A: $i] :
( ( zero = B )
| ( ( multiplication @ ( antidomain @ A ) @ A )
!= ( multiplication @ B @ one ) ) ),
inference(paramod_ordered,[status(thm)],[51,42]) ).
thf(323,plain,
( ( antidomain @ one )
= zero ),
inference(pattern_uni,[status(thm)],[322:[bind(A,$thf( one )),bind(B,$thf( antidomain @ one ))]]) ).
thf(19,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(76,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(77,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(cnf,[status(esa)],[76]) ).
thf(78,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(lifteq,[status(thm)],[77]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( addition @ A @ B )
= B )
=> ( ( addition @ ( antidomain @ B ) @ ( antidomain @ A ) )
= ( antidomain @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( addition @ A @ B )
= B )
=> ( ( addition @ ( antidomain @ B ) @ ( antidomain @ A ) )
= ( antidomain @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(23,plain,
~ ! [A: $i,B: $i] :
( ( ( addition @ A @ B )
= B )
=> ( ( addition @ ( antidomain @ B ) @ ( antidomain @ A ) )
= ( antidomain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(24,plain,
( ( addition @ ( antidomain @ sk2 ) @ ( antidomain @ sk1 ) )
!= ( antidomain @ sk1 ) ),
inference(cnf,[status(esa)],[23]) ).
thf(26,plain,
( ( addition @ ( antidomain @ sk2 ) @ ( antidomain @ sk1 ) )
!= ( antidomain @ sk1 ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(228,plain,
! [A: $i] :
( ( A
!= ( antidomain @ sk1 ) )
| ( ( addition @ A @ zero )
!= ( addition @ ( antidomain @ sk2 ) @ ( antidomain @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[78,26]) ).
thf(232,plain,
( ( ( antidomain @ sk2 )
!= ( antidomain @ sk1 ) )
| ( ( antidomain @ sk1 )
!= zero ) ),
inference(simp,[status(thm)],[228]) ).
thf(367,plain,
( ( ( antidomain @ sk2 )
!= ( antidomain @ sk1 ) )
| ( ( antidomain @ sk1 )
!= ( antidomain @ one ) ) ),
inference(paramod_ordered,[status(thm)],[323,232]) ).
thf(371,plain,
( ( sk2 != sk1 )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[367]) ).
thf(18,axiom,
! [A: $i] :
( ( addition @ ( antidomain @ ( antidomain @ A ) ) @ ( antidomain @ A ) )
= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
thf(73,plain,
! [A: $i] :
( ( addition @ ( antidomain @ ( antidomain @ A ) ) @ ( antidomain @ A ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(25,plain,
( ( addition @ sk1 @ sk2 )
= sk2 ),
inference(cnf,[status(esa)],[23]) ).
thf(27,plain,
( ( addition @ sk1 @ sk2 )
= sk2 ),
inference(lifteq,[status(thm)],[25]) ).
thf(365,plain,
( ( sk2 != sk1 )
| ( ( antidomain @ sk1 )
!= zero ) ),
inference(simp,[status(thm)],[232]) ).
thf(22,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(85,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)],[22]) ).
thf(86,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)],[85]) ).
thf(87,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(cnf,[status(esa)],[86]) ).
thf(89,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[87]) ).
thf(90,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(simp,[status(thm)],[89]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( sk2 != B )
| ( leq @ A @ B )
| ( ( addition @ sk1 @ sk2 )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[27,90]) ).
thf(100,plain,
( ( sk2 != sk2 )
| ( leq @ sk1 @ sk2 ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(101,plain,
leq @ sk1 @ sk2,
inference(simp,[status(thm)],[100]) ).
thf(5,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(34,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(35,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(lifteq,[status(thm)],[35]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( ( multiplication @ A @ one )
!= ( multiplication @ B @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[42,36]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( A != B )
| ( one != zero ) ),
inference(simp,[status(thm)],[102]) ).
thf(110,plain,
! [A: $i] :
( ( A = zero )
| ( one != zero ) ),
inference(simp,[status(thm)],[108]) ).
thf(136,plain,
! [A: $i] :
( ( one != zero )
| ( ( antidomain @ sk1 )
!= zero )
| ( A
!= ( addition @ ( antidomain @ sk2 ) @ ( antidomain @ sk1 ) ) ) ),
inference(paramod_ordered,[status(thm)],[110,26]) ).
thf(137,plain,
( ( one != zero )
| ( ( antidomain @ sk1 )
!= zero ) ),
inference(pattern_uni,[status(thm)],[136:[bind(A,$thf( addition @ ( antidomain @ sk2 ) @ ( antidomain @ sk1 ) ))]]) ).
thf(247,plain,
! [A: $i] :
( ( one != zero )
| ( A
!= ( antidomain @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[110,137]) ).
thf(248,plain,
one != zero,
inference(pattern_uni,[status(thm)],[247:[bind(A,$thf( antidomain @ sk1 ))]]) ).
thf(380,plain,
! [A: $i] :
( ( ( multiplication @ A @ ( codomain @ ( codomain @ one ) ) )
= zero )
| ( ( coantidomain @ ( codomain @ zero ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[310,48]) ).
thf(381,plain,
( ( multiplication @ ( codomain @ zero ) @ ( codomain @ ( codomain @ one ) ) )
= zero ),
inference(pattern_uni,[status(thm)],[380:[bind(A,$thf( codomain @ zero ))]]) ).
thf(3,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(28,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(17,axiom,
! [A: $i] :
( ( domain @ A )
= ( antidomain @ ( antidomain @ A ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
thf(70,plain,
! [A: $i] :
( ( domain @ A )
= ( antidomain @ ( antidomain @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
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(31,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(32,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ A @ B ) @ C )
= ( multiplication @ A @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(15,axiom,
! [A: $i,B: $i] :
( ( addition @ ( coantidomain @ ( multiplication @ A @ B ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ A ) ) @ B ) ) )
= ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ A ) ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',codomain2) ).
thf(64,plain,
! [A: $i,B: $i] :
( ( addition @ ( coantidomain @ ( multiplication @ A @ B ) ) @ ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ A ) ) @ B ) ) )
= ( coantidomain @ ( multiplication @ ( coantidomain @ ( coantidomain @ A ) ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( addition @ ( antidomain @ ( multiplication @ A @ B ) ) @ ( antidomain @ ( multiplication @ A @ ( antidomain @ ( antidomain @ B ) ) ) ) )
= ( antidomain @ ( multiplication @ A @ ( antidomain @ ( antidomain @ B ) ) ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( addition @ ( antidomain @ ( multiplication @ A @ B ) ) @ ( antidomain @ ( multiplication @ A @ ( antidomain @ ( antidomain @ B ) ) ) ) )
= ( antidomain @ ( multiplication @ A @ ( antidomain @ ( antidomain @ B ) ) ) ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(312,plain,
! [A: $i] :
( ( ( multiplication @ A @ ( codomain @ zero ) )
= zero )
| ( ( coantidomain @ ( codomain @ one ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[294,48]) ).
thf(313,plain,
( ( multiplication @ ( codomain @ one ) @ ( codomain @ zero ) )
= zero ),
inference(pattern_uni,[status(thm)],[312:[bind(A,$thf( codomain @ one ))]]) ).
thf(226,plain,
! [A: $i] :
( ( A = sk2 )
| ( ( addition @ A @ zero )
!= ( addition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[78,27]) ).
thf(233,plain,
! [A: $i] :
( ( A = sk2 )
| ( A != sk1 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[226]) ).
thf(236,plain,
( ( sk2 = sk1 )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[233]) ).
thf(96,plain,
( ( ( antidomain @ sk1 )
!= sk2 )
| ( ( addition @ ( antidomain @ sk2 ) @ ( antidomain @ sk1 ) )
!= ( addition @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[27,26]) ).
thf(97,plain,
( ( ( antidomain @ sk1 )
!= sk2 )
| ( ( antidomain @ sk2 )
!= sk1 )
| ( ( antidomain @ sk1 )
!= sk2 ) ),
inference(simp,[status(thm)],[96]) ).
thf(98,plain,
( ( ( antidomain @ sk1 )
!= sk2 )
| ( ( antidomain @ sk2 )
!= sk1 ) ),
inference(simp,[status(thm)],[97]) ).
thf(16,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(67,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(366,plain,
( ( ( antidomain @ sk1 )
!= zero )
| ( ( antidomain @ sk2 )
!= ( antidomain @ one ) ) ),
inference(paramod_ordered,[status(thm)],[323,232]) ).
thf(368,plain,
( ( ( antidomain @ sk1 )
!= zero )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[366]) ).
thf(580,plain,
( ( sk2 != one )
| ( ( antidomain @ sk1 )
!= ( antidomain @ one ) ) ),
inference(paramod_ordered,[status(thm)],[323,368]) ).
thf(581,plain,
( ( sk2 != one )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[580]) ).
thf(12,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(55,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)],[12]) ).
thf(229,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ A @ zero )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[78,90]) ).
thf(230,plain,
! [A: $i] :
( ( A != zero )
| ( leq @ A @ zero ) ),
inference(pattern_uni,[status(thm)],[229:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( zero ))]]) ).
thf(235,plain,
leq @ zero @ zero,
inference(simp,[status(thm)],[230]) ).
thf(21,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(82,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)],[21]) ).
thf(13,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(58,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)],[13]) ).
thf(29,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(lifteq,[status(thm)],[29]) ).
thf(20,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(79,plain,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(495,plain,
! [A: $i] :
( ( ( coantidomain @ ( codomain @ ( codomain @ zero ) ) )
= ( codomain @ A ) )
| ( ( coantidomain @ ( codomain @ ( codomain @ one ) ) )
!= ( coantidomain @ A ) ) ),
inference(paramod_ordered,[status(thm)],[378,39]) ).
thf(496,plain,
( ( coantidomain @ ( codomain @ ( codomain @ zero ) ) )
= ( codomain @ ( codomain @ ( codomain @ one ) ) ) ),
inference(pattern_uni,[status(thm)],[495:[bind(A,$thf( codomain @ ( codomain @ one ) ))]]) ).
thf(9142,plain,
$false,
inference(e,[status(thm)],[52,61,499,371,73,27,323,43,365,101,42,37,46,284,78,248,85,381,28,70,33,34,45,64,54,313,49,236,76,39,98,48,263,310,67,31,581,368,40,26,55,23,235,82,58,378,36,30,51,294,79,90,496,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE090+1 : TPTP v8.1.2. Released v4.0.0.
% 0.13/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n026.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Mon May 6 16:44:54 EDT 2024
% 0.16/0.37 % CPUTime :
% 1.08/0.94 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.27/1.08 % [INFO] Parsing done (137ms).
% 1.46/1.09 % [INFO] Running in sequential loop mode.
% 1.86/1.30 % [INFO] eprover registered as external prover.
% 1.86/1.31 % [INFO] cvc4 registered as external prover.
% 1.86/1.31 % [INFO] Scanning for conjecture ...
% 2.10/1.37 % [INFO] Found a conjecture and 20 axioms. Running axiom selection ...
% 2.25/1.41 % [INFO] Axiom selection finished. Selected 20 axioms (removed 0 axioms).
% 2.25/1.44 % [INFO] Problem is first-order (TPTP FOF).
% 2.25/1.44 % [INFO] Type checking passed.
% 2.25/1.44 % [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 ...
% 34.65/6.09 % External prover 'e' found a proof!
% 34.65/6.09 % [INFO] Killing All external provers ...
% 34.65/6.10 % Time passed: 5543ms (effective reasoning time: 5003ms)
% 34.65/6.10 % 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)>
% 34.65/6.10 % Axioms used in derivation (20): additive_identity, domain4, codomain4, domain3, multiplicative_right_identity, codomain2, right_annihilation, domain1, left_annihilation, codomain1, additive_idempotence, additive_associativity, right_distributivity, domain2, order, additive_commutativity, multiplicative_left_identity, codomain3, multiplicative_associativity, left_distributivity
% 34.65/6.10 % No. of inferences in proof: 120
% 34.65/6.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 5543 ms resp. 5003 ms w/o parsing
% 34.65/6.13 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 34.65/6.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------