TSTP Solution File: KLE039+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE039+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 11:24:54 EDT 2023
% Result : Theorem 18.89s 4.27s
% Output : Refutation 18.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 24
% Syntax : Number of formulae : 117 ( 71 unt; 7 typ; 0 def)
% Number of atoms : 168 ( 115 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 621 ( 60 ~; 39 |; 2 &; 511 @)
% ( 1 <=>; 8 =>; 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 : 9 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 161 ( 0 ^; 161 !; 0 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
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(leq_type,type,
leq: $i > $i > $o ).
thf(sk1_type,type,
sk1: $i ).
thf(13,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(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(11,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(46,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(55,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)],[14]) ).
thf(56,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)],[55]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( ( addition @ A @ B )
= B ) ),
inference(cnf,[status(esa)],[56]) ).
thf(61,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= B )
| ~ ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(cnf,[status(esa)],[56]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(simp,[status(thm)],[59]) ).
thf(6,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/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(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(17,axiom,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_right) ).
thf(66,plain,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(67,plain,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) ) @ ( star @ A ) ),
inference(cnf,[status(esa)],[66]) ).
thf(631,plain,
! [B: $i,A: $i] :
( ( leq @ ( addition @ one @ A ) @ ( star @ B ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ B @ ( star @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[33,67]) ).
thf(632,plain,
leq @ ( addition @ one @ ( star @ one ) ) @ ( star @ one ),
inference(pattern_uni,[status(thm)],[631:[bind(A,$thf( star @ one )),bind(B,$thf( one ))]]) ).
thf(934,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= B )
| ( ( leq @ ( addition @ one @ ( star @ one ) ) @ ( star @ one ) )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[632,61]) ).
thf(935,plain,
( ( addition @ ( addition @ one @ ( star @ one ) ) @ ( star @ one ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[934:[bind(A,$thf( addition @ one @ ( star @ one ) )),bind(B,$thf( star @ one ))]]) ).
thf(7,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(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(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(985,plain,
( ( addition @ one @ ( addition @ ( star @ one ) @ ( star @ one ) ) )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[935,36]) ).
thf(8,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/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(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(3,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/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(629,plain,
! [B: $i,A: $i] :
( ( leq @ ( addition @ one @ zero ) @ ( star @ B ) )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ B @ ( star @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[24,67]) ).
thf(630,plain,
leq @ ( addition @ one @ zero ) @ ( star @ zero ),
inference(pattern_uni,[status(thm)],[629:[bind(A,$thf( star @ zero )),bind(B,$thf( zero ))]]) ).
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(673,plain,
leq @ one @ ( star @ zero ),
inference(rewrite,[status(thm)],[630,48]) ).
thf(674,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= B )
| ( ( leq @ one @ ( star @ zero ) )
!= ( leq @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[673,61]) ).
thf(675,plain,
( ( addition @ one @ ( star @ zero ) )
= ( star @ zero ) ),
inference(pattern_uni,[status(thm)],[674:[bind(A,$thf( one )),bind(B,$thf( star @ zero ))]]) ).
thf(10,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(43,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(83,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( ( multiplication @ one @ A )
!= ( multiplication @ zero @ B ) ) ),
inference(paramod_ordered,[status(thm)],[33,24]) ).
thf(85,plain,
! [B: $i,A: $i] :
( ( A = zero )
| ( one != zero )
| ( A != B ) ),
inference(simp,[status(thm)],[83]) ).
thf(87,plain,
! [A: $i] :
( ( A = zero )
| ( one != zero ) ),
inference(simp,[status(thm)],[85]) ).
thf(1,conjecture,
! [A: $i] :
( ( star @ ( star @ A ) )
= ( star @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( star @ ( star @ A ) )
= ( star @ A ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(19,plain,
~ ! [A: $i] :
( ( star @ ( star @ A ) )
= ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(20,plain,
( ( star @ ( star @ sk1 ) )
!= ( star @ sk1 ) ),
inference(cnf,[status(esa)],[19]) ).
thf(21,plain,
( ( star @ ( star @ sk1 ) )
!= ( star @ sk1 ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(70,plain,
( ( star @ sk1 )
!= sk1 ),
inference(simp,[status(thm)],[21]) ).
thf(104,plain,
! [A: $i] :
( ( one != zero )
| ( sk1 != zero )
| ( A
!= ( star @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[87,70]) ).
thf(105,plain,
( ( one != zero )
| ( sk1 != zero ) ),
inference(pattern_uni,[status(thm)],[104:[bind(A,$thf( star @ sk1 ))]]) ).
thf(121,plain,
! [A: $i] :
( ( one != zero )
| ( A != sk1 ) ),
inference(paramod_ordered,[status(thm)],[87,105]) ).
thf(122,plain,
one != zero,
inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( sk1 ))]]) ).
thf(9,axiom,
! [A: $i] :
( ( multiplication @ A @ zero )
= zero ),
file('/export/starexec/sandbox/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(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(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(5,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(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(12,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/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(318,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(319,plain,
! [A: $i] :
( ( addition @ zero @ A )
= A ),
inference(pattern_uni,[status(thm)],[318:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(360,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ zero @ A )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[319,60]) ).
thf(361,plain,
! [A: $i] :
( ( A != A )
| ( leq @ zero @ A ) ),
inference(pattern_uni,[status(thm)],[360:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(392,plain,
! [A: $i] : ( leq @ zero @ A ),
inference(simp,[status(thm)],[361]) ).
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(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ B )
=> ( leq @ ( multiplication @ ( star @ A ) @ C ) @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction_left) ).
thf(64,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)],[16]) ).
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(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(240,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ A @ A )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[45,60]) ).
thf(241,plain,
! [A: $i] :
( ( A != A )
| ( leq @ A @ A ) ),
inference(pattern_uni,[status(thm)],[240:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( A ))]]) ).
thf(250,plain,
! [A: $i] : ( leq @ A @ A ),
inference(simp,[status(thm)],[241]) ).
thf(182,plain,
! [C: $i,B: $i,A: $i] :
( ( A = C )
| ~ ( leq @ B @ C )
| ( ( addition @ A @ zero )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[48,61]) ).
thf(183,plain,
! [A: $i] :
( ( A = zero )
| ~ ( leq @ A @ zero ) ),
inference(pattern_uni,[status(thm)],[182:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( zero ))]]) ).
thf(446,plain,
! [A: $i] :
( ~ ( leq @ A @ zero )
| ( sk1 != zero )
| ( A
!= ( star @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[183,70]) ).
thf(447,plain,
( ~ ( leq @ ( star @ sk1 ) @ zero )
| ( sk1 != zero ) ),
inference(pattern_uni,[status(thm)],[446:[bind(A,$thf( star @ sk1 ))]]) ).
thf(784,plain,
! [A: $i] :
( ( sk1 != zero )
| ( ( leq @ A @ A )
!= ( leq @ ( star @ sk1 ) @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[250,447]) ).
thf(797,plain,
! [A: $i] :
( ( sk1 != zero )
| ( A
!= ( star @ sk1 ) )
| ( A != zero ) ),
inference(simp,[status(thm)],[784]) ).
thf(799,plain,
( ( sk1 != zero )
| ( ( star @ sk1 )
!= zero ) ),
inference(simp,[status(thm)],[797]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A )
=> ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction_right) ).
thf(62,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)],[15]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ A @ B ) @ C ) @ A )
| ( leq @ ( multiplication @ C @ ( star @ B ) ) @ A ) ),
inference(cnf,[status(esa)],[62]) ).
thf(426,plain,
! [A: $i] :
( ~ ( leq @ A @ zero )
| ( A != one ) ),
inference(paramod_ordered,[status(thm)],[183,122]) ).
thf(427,plain,
~ ( leq @ one @ zero ),
inference(pattern_uni,[status(thm)],[426:[bind(A,$thf( one ))]]) ).
thf(676,plain,
( ( leq @ one @ ( star @ zero ) )
!= ( leq @ one @ zero ) ),
inference(paramod_ordered,[status(thm)],[673,427]) ).
thf(686,plain,
( ( one != one )
| ( ( star @ zero )
!= zero ) ),
inference(simp,[status(thm)],[676]) ).
thf(688,plain,
( ( star @ zero )
!= zero ),
inference(simp,[status(thm)],[686]) ).
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(739,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( star @ zero ) )
| ( ( addition @ one @ ( star @ zero ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[675,51]) ).
thf(740,plain,
( ( addition @ ( star @ zero ) @ one )
= ( star @ zero ) ),
inference(pattern_uni,[status(thm)],[739:[bind(A,$thf( one )),bind(B,$thf( star @ zero ))]]) ).
thf(18,axiom,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) ) @ ( star @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold_left) ).
thf(68,plain,
! [A: $i] : ( leq @ ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) ) @ ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(690,plain,
! [A: $i] :
( ~ ( leq @ A @ zero )
| ( A
!= ( star @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[183,688]) ).
thf(691,plain,
~ ( leq @ ( star @ zero ) @ zero ),
inference(pattern_uni,[status(thm)],[690:[bind(A,$thf( star @ zero ))]]) ).
thf(5737,plain,
$false,
inference(e,[status(thm)],[52,46,61,60,985,39,675,43,122,42,24,37,25,28,392,70,21,33,34,45,64,22,27,54,49,799,66,48,63,67,673,31,250,688,319,40,55,632,447,36,30,51,183,19,740,427,68,62,691]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : KLE039+1 : TPTP v8.1.2. Released v4.0.0.
% 0.06/0.15 % 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 03:20:59 EDT 2023
% 0.14/0.35 % CPUTime :
% 0.94/0.89 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.21/1.03 % [INFO] Parsing done (135ms).
% 1.21/1.03 % [INFO] Running in sequential loop mode.
% 1.75/1.23 % [INFO] eprover registered as external prover.
% 1.75/1.24 % [INFO] cvc4 registered as external prover.
% 1.75/1.24 % [INFO] Scanning for conjecture ...
% 1.86/1.29 % [INFO] Found a conjecture and 16 axioms. Running axiom selection ...
% 1.86/1.33 % [INFO] Axiom selection finished. Selected 16 axioms (removed 0 axioms).
% 2.06/1.35 % [INFO] Problem is first-order (TPTP FOF).
% 2.06/1.36 % [INFO] Type checking passed.
% 2.06/1.36 % [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 ...
% 18.89/4.26 % External prover 'e' found a proof!
% 18.89/4.26 % [INFO] Killing All external provers ...
% 18.89/4.26 % Time passed: 3757ms (effective reasoning time: 3227ms)
% 18.89/4.27 % 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)>
% 18.89/4.27 % 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
% 18.89/4.27 % No. of inferences in proof: 110
% 18.89/4.27 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3757 ms resp. 3227 ms w/o parsing
% 18.89/4.30 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.89/4.30 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------