TSTP Solution File: KLE068+1 by Leo-III---1.7.7
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- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE068+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n029.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 11:24:59 EDT 2023
% Result : Theorem 12.78s 3.29s
% Output : Refutation 12.78s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 26
% Syntax : Number of formulae : 115 ( 74 unt; 8 typ; 0 def)
% Number of atoms : 153 ( 133 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 613 ( 69 ~; 39 |; 2 &; 498 @)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 140 ( 0 ^; 140 !; 0 ?; 140 :)
% Comments :
%------------------------------------------------------------------------------
thf(domain_type,type,
domain: $i > $i ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(addition_type,type,
addition: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(leq_type,type,
leq: $i > $i > $o ).
thf(one_type,type,
one: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(4,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(26,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(27,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(cnf,[status(esa)],[26]) ).
thf(28,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(lifteq,[status(thm)],[27]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(35,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)],[7]) ).
thf(36,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)],[35]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(cnf,[status(esa)],[36]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(simp,[status(thm)],[39]) ).
thf(429,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ A @ A )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[28,40]) ).
thf(430,plain,
! [A: $i] :
( ( A != A )
| ( leq @ A @ A ) ),
inference(pattern_uni,[status(thm)],[429:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(443,plain,
! [A: $i] : ( leq @ A @ A ),
inference(simp,[status(thm)],[430]) ).
thf(19,axiom,
! [A: $i] :
( ( addition @ ( domain @ A ) @ one )
= one ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain3) ).
thf(74,plain,
! [A: $i] :
( ( addition @ ( domain @ A ) @ one )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(14,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(60,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(18,axiom,
( ( domain @ zero )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain4) ).
thf(72,plain,
( ( domain @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(73,plain,
( ( domain @ zero )
= zero ),
inference(lifteq,[status(thm)],[72]) ).
thf(15,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(63,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(64,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(cnf,[status(esa)],[63]) ).
thf(65,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(lifteq,[status(thm)],[64]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( domain @ ( multiplication @ ( domain @ A ) @ ( domain @ B ) ) )
= ( multiplication @ ( domain @ A ) @ ( domain @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( domain @ ( multiplication @ ( domain @ A ) @ ( domain @ B ) ) )
= ( multiplication @ ( domain @ A ) @ ( domain @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(20,plain,
~ ! [A: $i,B: $i] :
( ( domain @ ( multiplication @ ( domain @ A ) @ ( domain @ B ) ) )
= ( multiplication @ ( domain @ A ) @ ( domain @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(21,plain,
( ( domain @ ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) ) )
!= ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) ) ),
inference(cnf,[status(esa)],[20]) ).
thf(22,plain,
( ( domain @ ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) ) )
!= ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(84,plain,
( ( ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) )
!= zero )
| ( ( domain @ ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) ) )
!= ( domain @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[73,22]) ).
thf(88,plain,
( ( ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) )
!= zero )
| ( ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) )
!= zero ) ),
inference(simp,[status(thm)],[84]) ).
thf(93,plain,
( ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) )
!= zero ),
inference(simp,[status(thm)],[88]) ).
thf(96,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
!= ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[65,93]) ).
thf(100,plain,
! [A: $i] :
( ( A
!= ( domain @ sk1 ) )
| ( ( domain @ sk2 )
!= zero ) ),
inference(simp,[status(thm)],[96]) ).
thf(104,plain,
( ( domain @ sk2 )
!= zero ),
inference(simp,[status(thm)],[100]) ).
thf(108,plain,
( ( domain @ sk2 )
!= ( domain @ zero ) ),
inference(paramod_ordered,[status(thm)],[73,104]) ).
thf(109,plain,
sk2 != zero,
inference(simp,[status(thm)],[108]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( ( addition @ A @ B )
= B ) ),
inference(cnf,[status(esa)],[36]) ).
thf(41,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= B )
| ~ ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(12,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(54,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)],[12]) ).
thf(75,plain,
! [A: $i] :
( ( addition @ ( domain @ A ) @ one )
= one ),
inference(cnf,[status(esa)],[74]) ).
thf(76,plain,
! [A: $i] :
( ( addition @ ( domain @ A ) @ one )
= one ),
inference(lifteq,[status(thm)],[75]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( domain @ ( addition @ A @ B ) )
= ( addition @ ( domain @ A ) @ ( domain @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain5) ).
thf(66,plain,
! [A: $i,B: $i] :
( ( domain @ ( addition @ A @ B ) )
= ( addition @ ( domain @ A ) @ ( domain @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(11,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(51,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(17,axiom,
! [A: $i] :
( ( addition @ A @ ( multiplication @ ( domain @ A ) @ A ) )
= ( multiplication @ ( domain @ A ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain1) ).
thf(69,plain,
! [A: $i] :
( ( addition @ A @ ( multiplication @ ( domain @ A ) @ A ) )
= ( multiplication @ ( domain @ A ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(32,plain,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(cnf,[status(esa)],[32]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(lifteq,[status(thm)],[33]) ).
thf(5,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(29,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(30,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(cnf,[status(esa)],[29]) ).
thf(31,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(lifteq,[status(thm)],[30]) ).
thf(319,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
= C )
| ( ( addition @ A @ B )
!= ( addition @ C @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[34,31]) ).
thf(320,plain,
! [A: $i] :
( ( addition @ zero @ A )
= A ),
inference(pattern_uni,[status(thm)],[319:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(657,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ zero @ A )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[320,40]) ).
thf(658,plain,
! [A: $i] :
( ( A != A )
| ( leq @ zero @ A ) ),
inference(pattern_uni,[status(thm)],[657:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(666,plain,
! [A: $i] : ( leq @ zero @ A ),
inference(simp,[status(thm)],[658]) ).
thf(8,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(42,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
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(23,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(24,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ C @ B ) @ A )
= ( addition @ C @ ( addition @ B @ A ) ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( domain @ ( multiplication @ A @ B ) )
= ( domain @ ( multiplication @ A @ ( domain @ B ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',domain2) ).
thf(57,plain,
! [A: $i,B: $i] :
( ( domain @ ( multiplication @ A @ B ) )
= ( domain @ ( multiplication @ A @ ( domain @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(52,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(cnf,[status(esa)],[51]) ).
thf(53,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(lifteq,[status(thm)],[52]) ).
thf(157,plain,
! [A: $i] :
( ( ( domain @ A )
!= ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,22]) ).
thf(160,plain,
! [A: $i] :
( ( ( domain @ A )
!= ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) ) )
| ( ( domain @ sk1 )
!= one )
| ( A
!= ( domain @ sk2 ) ) ),
inference(simp,[status(thm)],[157]) ).
thf(165,plain,
( ( ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) )
!= ( domain @ ( domain @ sk2 ) ) )
| ( ( domain @ sk1 )
!= one ) ),
inference(simp,[status(thm)],[160]) ).
thf(268,plain,
! [A: $i] :
( ( A
!= ( domain @ ( domain @ sk2 ) ) )
| ( ( domain @ sk1 )
!= one )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[53,165]) ).
thf(282,plain,
( ( ( domain @ sk1 )
!= one )
| ( ( domain @ sk1 )
!= one )
| ( ( domain @ ( domain @ sk2 ) )
!= ( domain @ sk2 ) ) ),
inference(simp,[status(thm)],[268]) ).
thf(285,plain,
( ( ( domain @ sk1 )
!= one )
| ( ( domain @ ( domain @ sk2 ) )
!= ( domain @ sk2 ) ) ),
inference(simp,[status(thm)],[282]) ).
thf(61,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(cnf,[status(esa)],[60]) ).
thf(62,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(lifteq,[status(thm)],[61]) ).
thf(177,plain,
! [A: $i] :
( ( ( domain @ A )
!= ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[62,22]) ).
thf(185,plain,
! [A: $i] :
( ( ( domain @ A )
!= ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) ) )
| ( A
!= ( domain @ sk1 ) )
| ( ( domain @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[177]) ).
thf(188,plain,
( ( ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) )
!= ( domain @ ( domain @ sk1 ) ) )
| ( ( domain @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[185]) ).
thf(43,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(cnf,[status(esa)],[42]) ).
thf(44,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(lifteq,[status(thm)],[43]) ).
thf(99,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
!= ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[44,93]) ).
thf(103,plain,
! [A: $i] :
( ( ( domain @ sk1 )
!= zero )
| ( A
!= ( domain @ sk2 ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(105,plain,
( ( domain @ sk1 )
!= zero ),
inference(simp,[status(thm)],[103]) ).
thf(311,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
= one )
| ( ( addition @ A @ B )
!= ( addition @ ( domain @ C ) @ one ) ) ),
inference(paramod_ordered,[status(thm)],[34,76]) ).
thf(312,plain,
! [A: $i] :
( ( addition @ one @ ( domain @ A ) )
= one ),
inference(pattern_uni,[status(thm)],[311:[bind(A,$thf( domain @ D )),bind(B,$thf( one )),bind(C,$thf( D ))]]) ).
thf(360,plain,
! [A: $i] :
( ( addition @ one @ ( domain @ A ) )
= one ),
inference(simp,[status(thm)],[312]) ).
thf(9,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(45,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)],[9]) ).
thf(286,plain,
( ( ( domain @ sk1 )
!= one )
| ( ( domain @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[285]) ).
thf(10,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(48,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)],[10]) ).
thf(425,plain,
! [C: $i,B: $i,A: $i] :
( ( one != C )
| ( leq @ B @ C )
| ( ( addition @ ( domain @ A ) @ one )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[76,40]) ).
thf(426,plain,
! [A: $i] :
( ( one != one )
| ( leq @ ( domain @ A ) @ one ) ),
inference(pattern_uni,[status(thm)],[425:[bind(A,$thf( D )),bind(B,$thf( domain @ D )),bind(C,$thf( one ))]]) ).
thf(441,plain,
! [A: $i] : ( leq @ ( domain @ A ) @ one ),
inference(simp,[status(thm)],[426]) ).
thf(688,plain,
! [A: $i] :
( ( A
!= ( domain @ ( domain @ sk1 ) ) )
| ( ( domain @ sk2 )
!= one )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( domain @ sk1 ) @ ( domain @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[62,188]) ).
thf(698,plain,
( ( ( domain @ sk2 )
!= one )
| ( ( domain @ ( domain @ sk1 ) )
!= ( domain @ sk1 ) )
| ( ( domain @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[688]) ).
thf(703,plain,
( ( ( domain @ sk2 )
!= one )
| ( ( domain @ ( domain @ sk1 ) )
!= ( domain @ sk1 ) ) ),
inference(simp,[status(thm)],[698]) ).
thf(130,plain,
( ( domain @ sk1 )
!= ( domain @ zero ) ),
inference(paramod_ordered,[status(thm)],[73,105]) ).
thf(131,plain,
sk1 != zero,
inference(simp,[status(thm)],[130]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[45]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ A @ B ) @ C )
= ( multiplication @ A @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(2457,plain,
$false,
inference(e,[status(thm)],[443,74,60,109,41,54,76,66,35,104,51,69,666,42,320,25,20,93,57,29,28,165,65,285,188,53,73,105,360,45,32,34,22,44,286,48,63,441,31,703,72,40,26,23,62,131,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : KLE068+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.14 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n029.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 03:16:59 EDT 2023
% 0.14/0.35 % CPUTime :
% 1.00/0.88 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/1.02 % [INFO] Parsing done (139ms).
% 1.40/1.03 % [INFO] Running in sequential loop mode.
% 1.81/1.23 % [INFO] eprover registered as external prover.
% 1.81/1.23 % [INFO] cvc4 registered as external prover.
% 1.81/1.23 % [INFO] Scanning for conjecture ...
% 1.81/1.29 % [INFO] Found a conjecture and 17 axioms. Running axiom selection ...
% 2.10/1.32 % [INFO] Axiom selection finished. Selected 17 axioms (removed 0 axioms).
% 2.10/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 2.10/1.35 % [INFO] Type checking passed.
% 2.10/1.35 % [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 ...
% 12.78/3.28 % External prover 'e' found a proof!
% 12.78/3.28 % [INFO] Killing All external provers ...
% 12.78/3.29 % Time passed: 2765ms (effective reasoning time: 2256ms)
% 12.78/3.29 % 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)>
% 12.78/3.29 % Axioms used in derivation (17): additive_identity, domain4, domain5, domain3, left_annihilation, multiplicative_right_identity, right_annihilation, multiplicative_left_identity, domain1, additive_idempotence, additive_associativity, right_distributivity, domain2, order, additive_commutativity, multiplicative_associativity, left_distributivity
% 12.78/3.29 % No. of inferences in proof: 107
% 12.78/3.29 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2765 ms resp. 2256 ms w/o parsing
% 12.78/3.33 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.78/3.33 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------