TSTP Solution File: KLE041+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE041+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n013.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 11:24:55 EDT 2023
% Result : Theorem 24.88s 5.05s
% Output : Refutation 24.88s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 25
% Syntax : Number of formulae : 119 ( 73 unt; 8 typ; 0 def)
% Number of atoms : 167 ( 107 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 638 ( 55 ~; 34 |; 2 &; 535 @)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 7 >; 0 *; 0 +; 0 <<)
% Number of symbols : 11 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 170 ( 0 ^; 170 !; 0 ?; 170 :)
% Comments :
%------------------------------------------------------------------------------
thf(leq_type,type,
leq: $i > $i > $o ).
thf(star_type,type,
star: $i > $i ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(addition_type,type,
addition: $i > $i > $i ).
thf(one_type,type,
one: $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A )
=> ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_right) ).
thf(55,plain,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A )
=> ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A )
| ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) ),
inference(cnf,[status(esa)],[55]) ).
thf(16,axiom,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_right) ).
thf(59,plain,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(60,plain,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) ),
inference(cnf,[status(esa)],[59]) ).
thf(9,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',right_annihilation) ).
thf(40,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(41,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(cnf,[status(esa)],[40]) ).
thf(42,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(lifteq,[status(thm)],[41]) ).
thf(15,axiom,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) ) @ ( star @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold_left) ).
thf(57,plain,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) ) @ ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(58,plain,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) ) @ ( star @ A ) ),
inference(cnf,[status(esa)],[57]) ).
thf(496,plain,
! [B: $i,A: $i] :
( ( leq @ ( addition @ one @ zero ) @ ( star @ B ) )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ ( star @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[42,58]) ).
thf(497,plain,
leq @ ( addition @ one @ zero ) @ ( star @ zero ),
inference(pattern_uni,[status(thm)],[496:[bind(A,$thf( star @ zero )),bind(B,$thf( zero ))]]) ).
thf(11,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(46,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(47,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(cnf,[status(esa)],[46]) ).
thf(48,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(lifteq,[status(thm)],[47]) ).
thf(526,plain,
leq @ one @ ( star @ zero ),
inference(rewrite,[status(thm)],[497,48]) ).
thf(6,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(31,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(10,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_idempotence) ).
thf(43,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(49,plain,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(lifteq,[status(thm)],[50]) ).
thf(328,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
= C )
| ( ( addition @ A @ B )
!= ( addition @ C @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[51,48]) ).
thf(329,plain,
! [A: $i] :
( ( addition @ zero @ A )
= A ),
inference(pattern_uni,[status(thm)],[328:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(63,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(64,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)],[63]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(cnf,[status(esa)],[64]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[65]) ).
thf(68,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(simp,[status(thm)],[67]) ).
thf(378,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ zero @ A )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[329,68]) ).
thf(379,plain,
! [A: $i] :
( ( A != A )
| ( leq @ zero @ A ) ),
inference(pattern_uni,[status(thm)],[378:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(400,plain,
! [A: $i] : ( leq @ zero @ A ),
inference(simp,[status(thm)],[379]) ).
thf(3,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(22,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(23,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(cnf,[status(esa)],[22]) ).
thf(24,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(lifteq,[status(thm)],[23]) ).
thf(8,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(37,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
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(25,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(13,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(52,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)],[13]) ).
thf(38,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(lifteq,[status(thm)],[38]) ).
thf(503,plain,
! [B: $i,A: $i] :
( ( leq @ ( addition @ one @ A ) @ ( star @ B ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( star @ B ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[39,58]) ).
thf(504,plain,
leq @ ( addition @ one @ ( star @ one ) ) @ ( star @ one ),
inference(pattern_uni,[status(thm)],[503:[bind(A,$thf( star @ one )),bind(B,$thf( one ))]]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( leq @ ( star @ A ) @ ( star @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( leq @ ( star @ A ) @ ( star @ B ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i,B: $i] :
( ( leq @ A @ B )
=> ( leq @ ( star @ A ) @ ( star @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
~ ( leq @ ( star @ sk1 ) @ ( star @ sk2 ) ),
inference(cnf,[status(esa)],[19]) ).
thf(44,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(cnf,[status(esa)],[43]) ).
thf(45,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(lifteq,[status(thm)],[44]) ).
thf(276,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ A @ A )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[45,68]) ).
thf(277,plain,
! [A: $i] :
( ( A != A )
| ( leq @ A @ A ) ),
inference(pattern_uni,[status(thm)],[276:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(280,plain,
! [A: $i] : ( leq @ A @ A ),
inference(simp,[status(thm)],[277]) ).
thf(282,plain,
! [A: $i] :
( ( leq @ A @ A )
!= ( leq @ ( star @ sk1 ) @ ( star @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[280,20]) ).
thf(283,plain,
! [A: $i] :
( ( A
!= ( star @ sk1 ) )
| ( A
!= ( star @ sk2 ) ) ),
inference(simp,[status(thm)],[282]) ).
thf(284,plain,
( ( star @ sk2 )
!= ( star @ sk1 ) ),
inference(simp,[status(thm)],[283]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B )
=> ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction_left) ).
thf(61,plain,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B )
=> ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(5,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(28,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)],[5]) ).
thf(21,plain,
leq @ sk1 @ sk2,
inference(cnf,[status(esa)],[19]) ).
thf(32,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(cnf,[status(esa)],[31]) ).
thf(33,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(lifteq,[status(thm)],[32]) ).
thf(285,plain,
sk2 != sk1,
inference(simp,[status(thm)],[284]) ).
thf(7,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(34,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)],[7]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[25]) ).
thf(27,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ A @ B ) @ C )
= ( multiplication @ A @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(70,plain,
( ( leq @ ( star @ sk1 ) @ ( star @ sk2 ) )
!= ( leq @ sk1 @ sk2 ) ),
inference(paramod_ordered,[status(thm)],[21,20]) ).
thf(71,plain,
( ( ( star @ sk1 )
!= sk1 )
| ( ( star @ sk2 )
!= sk2 ) ),
inference(simp,[status(thm)],[70]) ).
thf(53,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( addition @ B @ C ) )
= ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( multiplication @ A @ B ) @ ( multiplication @ A @ C ) )
= ( multiplication @ A @ ( addition @ B @ C ) ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(404,plain,
! [A: $i] :
( ( leq @ zero @ A )
!= ( leq @ ( star @ sk1 ) @ ( star @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[400,20]) ).
thf(405,plain,
! [A: $i] :
( ( ( star @ sk1 )
!= zero )
| ( A
!= ( star @ sk2 ) ) ),
inference(simp,[status(thm)],[404]) ).
thf(406,plain,
( ( star @ sk1 )
!= zero ),
inference(simp,[status(thm)],[405]) ).
thf(80,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( ( multiplication @ one @ A )
!= ( multiplication @ zero @ B ) ) ),
inference(paramod_ordered,[status(thm)],[33,24]) ).
thf(82,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( one != zero )
| ( A != B ) ),
inference(simp,[status(thm)],[80]) ).
thf(84,plain,
! [A: $i] :
( ( A = zero )
| ( one != zero ) ),
inference(simp,[status(thm)],[82]) ).
thf(86,plain,
! [A: $i] :
( ( one != zero )
| ~ ( leq @ zero @ ( star @ sk2 ) )
| ( A
!= ( star @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[84,20]) ).
thf(87,plain,
( ( one != zero )
| ~ ( leq @ zero @ ( star @ sk2 ) ) ),
inference(pattern_uni,[status(thm)],[86:[bind(A,$thf( star @ sk1 ))]]) ).
thf(215,plain,
! [A: $i] :
( ( one != zero )
| ~ ( leq @ zero @ zero )
| ( A
!= ( star @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[84,87]) ).
thf(216,plain,
( ( one != zero )
| ~ ( leq @ zero @ zero ) ),
inference(pattern_uni,[status(thm)],[215:[bind(A,$thf( star @ sk2 ))]]) ).
thf(200,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ A @ zero )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[48,68]) ).
thf(201,plain,
! [A: $i] :
( ( A != zero )
| ( leq @ A @ zero ) ),
inference(pattern_uni,[status(thm)],[200:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( zero ))]]) ).
thf(203,plain,
leq @ zero @ zero,
inference(simp,[status(thm)],[201]) ).
thf(229,plain,
( ( one != zero )
| ~ $true ),
inference(rewrite,[status(thm)],[216,203]) ).
thf(230,plain,
one != zero,
inference(simp,[status(thm)],[229]) ).
thf(527,plain,
( ( leq @ ( star @ sk1 ) @ ( star @ sk2 ) )
!= ( leq @ one @ ( star @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[526,20]) ).
thf(528,plain,
( ( ( star @ sk1 )
!= one )
| ( ( star @ sk2 )
!= ( star @ zero ) ) ),
inference(simp,[status(thm)],[527]) ).
thf(690,plain,
( ( ( star @ sk1 )
!= one )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[528]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ C @ B ) @ A )
= ( addition @ C @ ( addition @ B @ A ) ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(cnf,[status(esa)],[28]) ).
thf(30,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) )
= ( multiplication @ ( addition @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(241,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( addition @ ( multiplication @ B @ D ) @ zero )
= ( multiplication @ ( addition @ B @ C ) @ D ) )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ C @ D ) ) ),
inference(paramod_ordered,[status(thm)],[42,30]) ).
thf(242,plain,
! [B: $i,A: $i] :
( ( addition @ ( multiplication @ B @ zero ) @ zero )
= ( multiplication @ ( addition @ B @ A ) @ zero ) ),
inference(pattern_uni,[status(thm)],[241:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( A )),bind(D,$thf( zero ))]]) ).
thf(643,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(rewrite,[status(thm)],[242,48,42]) ).
thf(655,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( multiplication @ B @ ( multiplication @ C @ D ) )
= zero )
| ( ( multiplication @ A @ zero )
!= ( multiplication @ ( multiplication @ B @ C ) @ D ) ) ),
inference(paramod_ordered,[status(thm)],[643,27]) ).
thf(656,plain,
! [B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ zero ) )
= zero ),
inference(pattern_uni,[status(thm)],[655:[bind(A,$thf( multiplication @ E @ F )),bind(B,$thf( E )),bind(C,$thf( F )),bind(D,$thf( zero ))]]) ).
thf(685,plain,
! [B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ zero ) )
= zero ),
inference(simp,[status(thm)],[656]) ).
thf(691,plain,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
inference(rewrite,[status(thm)],[685,643]) ).
thf(10214,plain,
$false,
inference(e,[status(thm)],[56,60,526,31,43,58,400,24,37,25,52,504,20,46,284,57,280,61,28,21,33,329,285,34,45,22,59,27,71,54,49,406,230,39,48,690,63,40,55,36,30,51,19,528,68,691]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : KLE041+1 : TPTP v8.1.2. Released v4.0.0.
% 0.12/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri May 19 03:03:36 EDT 2023
% 0.15/0.36 % CPUTime :
% 0.83/0.82 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.24/0.94 % [INFO] Parsing done (113ms).
% 1.29/0.94 % [INFO] Running in sequential loop mode.
% 1.53/1.14 % [INFO] eprover registered as external prover.
% 1.53/1.14 % [INFO] cvc4 registered as external prover.
% 1.53/1.14 % [INFO] Scanning for conjecture ...
% 1.77/1.20 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 1.94/1.24 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 1.94/1.26 % [INFO] Problem is first-order (TPTP FOF).
% 1.94/1.26 % [INFO] Type checking passed.
% 1.94/1.27 % [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 ...
% 24.88/5.05 % External prover 'e' found a proof!
% 24.88/5.05 % [INFO] Killing All external provers ...
% 24.88/5.05 % Time passed: 4545ms (effective reasoning time: 4102ms)
% 24.88/5.05 % 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)>
% 24.88/5.05 % Axioms used in derivation (16): additive_identity, star_induction_right, left_annihilation, star_induction_left, right_distributivity, star_unfold_left, right_annihilation, multiplicative_left_identity, additive_idempotence, additive_associativity, multiplicative_right_identity, star_unfold_right, order, additive_commutativity, multiplicative_associativity, left_distributivity
% 24.88/5.05 % No. of inferences in proof: 111
% 24.88/5.05 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 4545 ms resp. 4102 ms w/o parsing
% 24.88/5.09 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 24.88/5.09 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------