TSTP Solution File: KLE144+2 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE144+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n025.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 11:25:09 EDT 2023
% Result : Theorem 11.91s 3.27s
% Output : Refutation 12.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 28
% Syntax : Number of formulae : 122 ( 64 unt; 9 typ; 0 def)
% Number of atoms : 210 ( 153 equ; 0 cnn)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 862 ( 113 ~; 81 |; 5 &; 654 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 128 ( 0 ^; 128 !; 0 ?; 128 :)
% Comments :
%------------------------------------------------------------------------------
thf(leq_type,type,
leq: $i > $i > $o ).
thf(strong_iteration_type,type,
strong_iteration: $i > $i ).
thf(star_type,type,
star: $i > $i ).
thf(one_type,type,
one: $i ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(addition_type,type,
addition: $i > $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(14,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(55,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(56,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(lifteq,[status(thm)],[56]) ).
thf(20,axiom,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_unfold1) ).
thf(76,plain,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(77,plain,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ),
inference(cnf,[status(esa)],[76]) ).
thf(78,plain,
! [A: $i] :
( ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one )
= ( strong_iteration @ A ) ),
inference(lifteq,[status(thm)],[77]) ).
thf(587,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ one )
= ( strong_iteration @ B ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ B @ ( strong_iteration @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[57,78]) ).
thf(588,plain,
( ( addition @ ( strong_iteration @ one ) @ one )
= ( strong_iteration @ one ) ),
inference(pattern_uni,[status(thm)],[587:[bind(A,$thf( strong_iteration @ one )),bind(B,$thf( one ))]]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(808,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( strong_iteration @ one ) )
| ( ( addition @ ( strong_iteration @ one ) @ one )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[588,32]) ).
thf(809,plain,
( ( addition @ one @ ( strong_iteration @ one ) )
= ( strong_iteration @ one ) ),
inference(pattern_uni,[status(thm)],[808:[bind(A,$thf( strong_iteration @ one )),bind(B,$thf( one ))]]) ).
thf(11,axiom,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold1) ).
thf(48,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(49,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
inference(cnf,[status(esa)],[48]) ).
thf(50,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
inference(lifteq,[status(thm)],[49]) ).
thf(157,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ A )
= ( star @ B ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ B @ ( star @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[57,50]) ).
thf(158,plain,
( ( addition @ one @ ( star @ one ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[157:[bind(A,$thf( star @ one )),bind(B,$thf( one ))]]) ).
thf(339,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( star @ one ) )
| ( ( addition @ one @ ( star @ one ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[158,32]) ).
thf(340,plain,
( ( addition @ ( star @ one ) @ one )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[339:[bind(A,$thf( one )),bind(B,$thf( star @ one ))]]) ).
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(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(161,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ zero )
= ( star @ B ) )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ B @ ( star @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,50]) ).
thf(162,plain,
( ( addition @ one @ zero )
= ( star @ zero ) ),
inference(pattern_uni,[status(thm)],[161:[bind(A,$thf( star @ zero )),bind(B,$thf( zero ))]]) ).
thf(9,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(42,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(43,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(cnf,[status(esa)],[42]) ).
thf(44,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(lifteq,[status(thm)],[43]) ).
thf(174,plain,
( ( star @ zero )
= one ),
inference(rewrite,[status(thm)],[162,44]) ).
thf(1,conjecture,
! [A: $i] :
( ( leq @ ( strong_iteration @ ( star @ A ) ) @ ( strong_iteration @ one ) )
& ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ A ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( leq @ ( strong_iteration @ ( star @ A ) ) @ ( strong_iteration @ one ) )
& ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ A ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i] :
( ( leq @ ( strong_iteration @ ( star @ A ) ) @ ( strong_iteration @ one ) )
& ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
~ ( ! [A: $i] : ( leq @ ( strong_iteration @ ( star @ A ) ) @ ( strong_iteration @ one ) )
& ! [A: $i] : ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ A ) ) ) ),
inference(miniscope,[status(thm)],[21]) ).
thf(23,plain,
( ~ ( leq @ ( strong_iteration @ ( star @ sk1 ) ) @ ( strong_iteration @ one ) )
| ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ sk2 ) ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(93,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ sk2 ) ) )
| ( ( leq @ ( strong_iteration @ ( star @ sk1 ) ) @ ( strong_iteration @ one ) )
!= ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ sk2 ) ) ) )
| ~ $true ),
inference(eqfactor_ordered,[status(thm)],[23]) ).
thf(95,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ sk2 ) ) )
| ( ( strong_iteration @ ( star @ sk1 ) )
!= ( strong_iteration @ one ) )
| ( ( strong_iteration @ ( star @ sk2 ) )
!= ( strong_iteration @ one ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(98,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ sk2 ) ) )
| ( ( star @ sk1 )
!= one )
| ( ( star @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[95]) ).
thf(119,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ sk2 ) ) )
| ( ( star @ sk1 )
!= one )
| ( ( star @ sk2 )
!= ( star @ sk1 ) )
| ( one != one ) ),
inference(eqfactor_ordered,[status(thm)],[98]) ).
thf(121,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ sk2 ) ) )
| ( ( star @ sk1 )
!= one )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[119]) ).
thf(176,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ sk2 ) ) )
| ( sk2 != sk1 )
| ( ( star @ sk1 )
!= ( star @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[174,121]) ).
thf(196,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ sk2 ) ) )
| ( sk2 != sk1 )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[176]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
=> ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction2) ).
thf(61,plain,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
=> ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(595,plain,
! [B: $i,A: $i] :
( ( ( addition @ zero @ one )
= ( strong_iteration @ B ) )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ B @ ( strong_iteration @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[26,78]) ).
thf(596,plain,
( ( addition @ zero @ one )
= ( strong_iteration @ zero ) ),
inference(pattern_uni,[status(thm)],[595:[bind(A,$thf( strong_iteration @ zero )),bind(B,$thf( zero ))]]) ).
thf(317,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
= C )
| ( ( addition @ A @ B )
!= ( addition @ C @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[32,44]) ).
thf(318,plain,
! [A: $i] :
( ( addition @ zero @ A )
= A ),
inference(pattern_uni,[status(thm)],[317:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(735,plain,
( ( strong_iteration @ zero )
= one ),
inference(rewrite,[status(thm)],[596,318]) ).
thf(179,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ sk2 ) ) )
| ( ( star @ sk1 )
!= one )
| ( ( star @ sk2 )
!= ( star @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[174,98]) ).
thf(188,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ sk2 ) ) )
| ( ( star @ sk1 )
!= one )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[179]) ).
thf(253,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ sk2 ) ) )
| ( sk2 != zero )
| ( ( star @ sk1 )
!= ( star @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[174,188]) ).
thf(255,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ sk2 ) ) )
| ( sk2 != zero )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[253]) ).
thf(300,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ one ) )
| ( sk2 != zero )
| ( sk1 != zero )
| ( ( star @ sk2 )
!= ( star @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[174,255]) ).
thf(301,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ one ) )
| ( sk2 != zero )
| ( sk1 != zero )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[300]) ).
thf(302,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ one ) )
| ( sk2 != zero )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[301]) ).
thf(752,plain,
( ~ ( leq @ one @ ( strong_iteration @ one ) )
| ( sk2 != zero )
| ( sk1 != zero )
| ( ( strong_iteration @ zero )
!= ( strong_iteration @ one ) ) ),
inference(paramod_ordered,[status(thm)],[735,302]) ).
thf(793,plain,
( ~ ( leq @ one @ ( strong_iteration @ one ) )
| ( sk2 != zero )
| ( sk1 != zero )
| ( zero != one ) ),
inference(simp,[status(thm)],[752]) ).
thf(17,axiom,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold2) ).
thf(63,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(64,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
inference(cnf,[status(esa)],[63]) ).
thf(65,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
inference(lifteq,[status(thm)],[64]) ).
thf(252,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ one ) )
| ( ( star @ sk1 )
!= one )
| ( sk2 != zero )
| ( ( star @ sk2 )
!= ( star @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[174,188]) ).
thf(254,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ one ) )
| ( ( star @ sk1 )
!= one )
| ( sk2 != zero )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[252]) ).
thf(256,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ one ) )
| ( ( star @ sk1 )
!= one )
| ( sk2 != zero ) ),
inference(simp,[status(thm)],[254]) ).
thf(8,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence) ).
thf(39,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(40,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(cnf,[status(esa)],[39]) ).
thf(41,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(lifteq,[status(thm)],[40]) ).
thf(19,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(73,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(66,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(6,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',distributivity2) ).
thf(33,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)],[6]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( addition @ A @ B ) @ C )
= ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( multiplication @ A @ C ) @ ( multiplication @ B @ C ) )
= ( multiplication @ ( addition @ A @ B ) @ C ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(183,plain,
! [A: $i] :
( ( ( addition @ one @ ( multiplication @ A @ one ) )
= ( star @ A ) )
| ( ( star @ zero )
!= ( star @ A ) ) ),
inference(paramod_ordered,[status(thm)],[174,50]) ).
thf(184,plain,
( ( addition @ one @ ( multiplication @ zero @ one ) )
= ( star @ zero ) ),
inference(pattern_uni,[status(thm)],[183:[bind(A,$thf( zero ))]]) ).
thf(74,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(cnf,[status(esa)],[73]) ).
thf(75,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(lifteq,[status(thm)],[74]) ).
thf(227,plain,
( ( addition @ one @ zero )
= one ),
inference(rewrite,[status(thm)],[184,75,174]) ).
thf(753,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ one )
| ( sk2 != zero )
| ( sk1 != zero )
| ( ( strong_iteration @ zero )
!= ( strong_iteration @ one ) ) ),
inference(paramod_ordered,[status(thm)],[735,302]) ).
thf(782,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ one )
| ( sk2 != zero )
| ( sk1 != zero )
| ( zero != one ) ),
inference(simp,[status(thm)],[753]) ).
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(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(36,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(37,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ C @ B ) @ A )
= ( addition @ C @ ( addition @ B @ A ) ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ C @ ( addition @ ( multiplication @ A @ C ) @ B ) )
=> ( leq @ C @ ( multiplication @ ( strong_iteration @ A ) @ B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_coinduction) ).
thf(53,plain,
! [A: $i,B: $i,C: $i] :
( ( leq @ C @ ( addition @ ( multiplication @ A @ C ) @ B ) )
=> ( leq @ C @ ( multiplication @ ( strong_iteration @ A ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10,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',distributivity1) ).
thf(45,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)],[10]) ).
thf(181,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ sk2 ) ) )
| ( ( strong_iteration @ ( star @ sk2 ) )
!= ( strong_iteration @ one ) )
| ( ( star @ sk1 )
!= ( star @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[174,95]) ).
thf(199,plain,
( ~ ( leq @ ( strong_iteration @ one ) @ ( strong_iteration @ ( star @ sk2 ) ) )
| ( ( star @ sk2 )
!= one )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[181]) ).
thf(944,plain,
( ~ ( leq @ one @ one )
| ( sk2 != zero )
| ( sk1 != zero )
| ( zero != one )
| ( ( strong_iteration @ zero )
!= ( strong_iteration @ one ) ) ),
inference(paramod_ordered,[status(thm)],[735,782]) ).
thf(945,plain,
( ~ ( leq @ one @ one )
| ( sk2 != zero )
| ( sk1 != zero )
| ( zero != one )
| ( zero != one ) ),
inference(simp,[status(thm)],[944]) ).
thf(946,plain,
( ~ ( leq @ one @ one )
| ( sk2 != zero )
| ( sk1 != zero )
| ( zero != one ) ),
inference(simp,[status(thm)],[945]) ).
thf(742,plain,
( ~ ( leq @ one @ ( strong_iteration @ one ) )
| ( ( star @ sk1 )
!= one )
| ( sk2 != zero )
| ( ( strong_iteration @ zero )
!= ( strong_iteration @ one ) ) ),
inference(paramod_ordered,[status(thm)],[735,256]) ).
thf(781,plain,
( ~ ( leq @ one @ ( strong_iteration @ one ) )
| ( ( star @ sk1 )
!= one )
| ( sk2 != zero )
| ( zero != one ) ),
inference(simp,[status(thm)],[742]) ).
thf(15,axiom,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isolation) ).
thf(58,plain,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
=> ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction1) ).
thf(51,plain,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
=> ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(1758,plain,
$false,
inference(e,[status(thm)],[809,340,196,121,61,793,65,256,41,73,66,35,255,227,174,42,782,24,57,78,29,302,38,21,33,188,53,32,45,44,27,76,318,39,98,48,63,95,50,199,588,26,946,158,55,781,23,75,58,36,30,51,735]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE144+2 : TPTP v8.1.2. Released v4.0.0.
% 0.14/0.15 % Command : run_Leo-III %s %d
% 0.15/0.36 % Computer : n025.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
% 0.15/0.37 % DateTime : Fri May 19 03:07:04 EDT 2023
% 0.15/0.37 % CPUTime :
% 0.78/0.81 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.21/0.94 % [INFO] Parsing done (129ms).
% 1.21/0.95 % [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 ...
% 1.70/1.23 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 1.81/1.28 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.02/1.31 % [INFO] Problem is first-order (TPTP FOF).
% 2.02/1.31 % [INFO] Type checking passed.
% 2.02/1.31 % [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 ...
% 11.91/3.26 % External prover 'e' found a proof!
% 11.91/3.26 % [INFO] Killing All external provers ...
% 11.91/3.26 % Time passed: 2755ms (effective reasoning time: 2312ms)
% 11.91/3.26 % 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)>
% 11.91/3.27 % Axioms used in derivation (18): additive_identity, isolation, additive_associativity, multiplicative_right_identity, star_unfold2, multiplicative_left_identity, idempotence, multiplicative_associativity, infty_unfold1, star_induction2, distributivity2, star_induction1, star_unfold1, left_annihilation, infty_coinduction, order, additive_commutativity, distributivity1
% 11.91/3.27 % No. of inferences in proof: 113
% 11.91/3.27 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 2755 ms resp. 2312 ms w/o parsing
% 12.13/3.35 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.13/3.36 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------