TSTP Solution File: KLE158+1 by Leo-III---1.7.7
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%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : KLE158+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n010.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 11:25:12 EDT 2023
% Result : Theorem 222.93s 54.66s
% Output : Refutation 222.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 29
% Syntax : Number of formulae : 180 ( 75 unt; 10 typ; 0 def)
% Number of atoms : 311 ( 204 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 1294 ( 152 ~; 121 |; 2 &;1005 @)
% ( 1 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% Number of symbols : 13 ( 10 usr; 7 con; 0-2 aty)
% Number of variables : 212 ( 0 ^; 212 !; 0 ?; 212 :)
% Comments :
%------------------------------------------------------------------------------
thf(leq_type,type,
leq: $i > $i > $o ).
thf(multiplication_type,type,
multiplication: $i > $i > $i ).
thf(strong_iteration_type,type,
strong_iteration: $i > $i ).
thf(addition_type,type,
addition: $i > $i > $i ).
thf(zero_type,type,
zero: $i ).
thf(one_type,type,
one: $i ).
thf(star_type,type,
star: $i > $i ).
thf(sk1_type,type,
sk1: $i ).
thf(sk2_type,type,
sk2: $i ).
thf(sk3_type,type,
sk3: $i ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
=> ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction2) ).
thf(55,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)],[14]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ C @ A ) @ B ) @ C )
| ( leq @ ( multiplication @ B @ ( star @ A ) ) @ C ) ),
inference(cnf,[status(esa)],[55]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( leq @ A @ B )
<=> ( ( addition @ A @ B )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(60,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)],[16]) ).
thf(61,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)],[60]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(cnf,[status(esa)],[61]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
!= B )
| ( leq @ A @ B ) ),
inference(simp,[status(thm)],[64]) ).
thf(17,axiom,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(67,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(68,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(cnf,[status(esa)],[67]) ).
thf(69,plain,
! [A: $i] :
( ( multiplication @ A @ one )
= A ),
inference(lifteq,[status(thm)],[68]) ).
thf(1,conjecture,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( multiplication @ A @ B ) @ ( multiplication @ C @ A ) )
=> ( leq @ ( multiplication @ A @ ( strong_iteration @ B ) ) @ ( multiplication @ ( strong_iteration @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i,C: $i] :
( ( leq @ ( multiplication @ A @ B ) @ ( multiplication @ C @ A ) )
=> ( leq @ ( multiplication @ A @ ( strong_iteration @ B ) ) @ ( multiplication @ ( strong_iteration @ C ) @ A ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i,B: $i,C: $i] :
( ( leq @ ( multiplication @ A @ B ) @ ( multiplication @ C @ A ) )
=> ( leq @ ( multiplication @ A @ ( strong_iteration @ B ) ) @ ( multiplication @ ( strong_iteration @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
~ ( leq @ ( multiplication @ sk1 @ ( strong_iteration @ sk2 ) ) @ ( multiplication @ ( strong_iteration @ sk3 ) @ sk1 ) ),
inference(cnf,[status(esa)],[21]) ).
thf(124,plain,
! [A: $i] :
( ~ ( leq @ ( multiplication @ sk1 @ ( strong_iteration @ sk2 ) ) @ A )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( strong_iteration @ sk3 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[69,22]) ).
thf(133,plain,
! [A: $i] :
( ~ ( leq @ ( multiplication @ sk1 @ ( strong_iteration @ sk2 ) ) @ A )
| ( A
!= ( strong_iteration @ sk3 ) )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[124]) ).
thf(138,plain,
( ~ ( leq @ ( multiplication @ sk1 @ ( strong_iteration @ sk2 ) ) @ ( strong_iteration @ sk3 ) )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[133]) ).
thf(12,axiom,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(49,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(50,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [A: $i] :
( ( multiplication @ one @ A )
= A ),
inference(lifteq,[status(thm)],[50]) ).
thf(9,axiom,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold1) ).
thf(42,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(43,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
inference(cnf,[status(esa)],[42]) ).
thf(44,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ A @ ( star @ A ) ) )
= ( star @ A ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(199,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ A )
= ( star @ B ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ B @ ( star @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,44]) ).
thf(200,plain,
( ( addition @ one @ ( star @ one ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( star @ one )),bind(B,$thf( one ))]]) ).
thf(3,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(24,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(25,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ C @ ( addition @ B @ A ) )
= ( addition @ ( addition @ C @ B ) @ A ) ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( addition @ ( addition @ C @ B ) @ A )
= ( addition @ C @ ( addition @ B @ A ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( star @ one ) @ A )
= ( addition @ C @ ( addition @ B @ A ) ) )
| ( ( addition @ one @ ( star @ one ) )
!= ( addition @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[200,26]) ).
thf(232,plain,
! [A: $i] :
( ( addition @ one @ ( addition @ ( star @ one ) @ A ) )
= ( addition @ ( star @ one ) @ A ) ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( A )),bind(B,$thf( star @ one )),bind(C,$thf( one ))]]) ).
thf(2286,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( star @ one ) @ A )
!= C )
| ( leq @ B @ C )
| ( ( addition @ one @ ( addition @ ( star @ one ) @ A ) )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[232,65]) ).
thf(2287,plain,
! [A: $i] :
( ( ( addition @ ( star @ one ) @ A )
!= ( addition @ ( star @ one ) @ A ) )
| ( leq @ one @ ( addition @ ( star @ one ) @ A ) ) ),
inference(pattern_uni,[status(thm)],[2286:[bind(A,$thf( E )),bind(B,$thf( one )),bind(C,$thf( addition @ ( star @ one ) @ E ))]]) ).
thf(2295,plain,
! [A: $i] : ( leq @ one @ ( addition @ ( star @ one ) @ A ) ),
inference(simp,[status(thm)],[2287]) ).
thf(13,axiom,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isolation) ).
thf(52,plain,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(100,plain,
! [A: $i] :
( ~ ( leq @ A @ ( multiplication @ ( strong_iteration @ sk3 ) @ sk1 ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ sk1 @ ( strong_iteration @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[51,22]) ).
thf(106,plain,
! [A: $i] :
( ~ ( leq @ A @ ( multiplication @ ( strong_iteration @ sk3 ) @ sk1 ) )
| ( sk1 != one )
| ( A
!= ( strong_iteration @ sk2 ) ) ),
inference(simp,[status(thm)],[100]) ).
thf(110,plain,
( ~ ( leq @ ( strong_iteration @ sk2 ) @ ( multiplication @ ( strong_iteration @ sk3 ) @ sk1 ) )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[106]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
=> ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction1) ).
thf(45,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)],[10]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ ( addition @ ( multiplication @ A @ C ) @ B ) @ C )
| ( leq @ ( multiplication @ ( star @ A ) @ B ) @ C ) ),
inference(cnf,[status(esa)],[45]) ).
thf(7,axiom,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(36,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
! [A: $i] :
( ( multiplication @ zero @ A )
= zero ),
inference(lifteq,[status(thm)],[37]) ).
thf(23,plain,
leq @ ( multiplication @ sk1 @ sk2 ) @ ( multiplication @ sk3 @ sk1 ),
inference(cnf,[status(esa)],[21]) ).
thf(79,plain,
! [A: $i] :
( ( leq @ ( multiplication @ sk1 @ sk2 ) @ zero )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[38,23]) ).
thf(81,plain,
! [A: $i] :
( ( leq @ ( multiplication @ sk1 @ sk2 ) @ zero )
| ( sk3 != zero )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[79]) ).
thf(83,plain,
( ( leq @ ( multiplication @ sk1 @ sk2 ) @ zero )
| ( sk3 != zero ) ),
inference(simp,[status(thm)],[81]) ).
thf(142,plain,
! [A: $i] :
( ( leq @ A @ zero )
| ( sk3 != zero )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[69,83]) ).
thf(147,plain,
! [A: $i] :
( ( leq @ A @ zero )
| ( sk3 != zero )
| ( A != sk1 )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[142]) ).
thf(152,plain,
( ( leq @ sk1 @ zero )
| ( sk3 != zero )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[147]) ).
thf(15,axiom,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold2) ).
thf(57,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
! [A: $i] :
( ( addition @ A @ A )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence) ).
thf(27,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [A: $i] :
( ( addition @ A @ A )
= A ),
inference(lifteq,[status(thm)],[28]) ).
thf(2282,plain,
! [B: $i,A: $i] :
( ( ( star @ one )
!= B )
| ( leq @ A @ B )
| ( ( addition @ one @ ( star @ one ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[200,65]) ).
thf(2283,plain,
( ( ( star @ one )
!= ( star @ one ) )
| ( leq @ one @ ( star @ one ) ) ),
inference(pattern_uni,[status(thm)],[2282:[bind(A,$thf( one )),bind(B,$thf( star @ one ))]]) ).
thf(2291,plain,
leq @ one @ ( star @ one ),
inference(simp,[status(thm)],[2283]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( addition @ A @ B )
= ( addition @ B @ A ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(352,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( star @ one ) )
| ( ( addition @ one @ ( star @ one ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[200,35]) ).
thf(353,plain,
( ( addition @ ( star @ one ) @ one )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[352:[bind(A,$thf( one )),bind(B,$thf( star @ one ))]]) ).
thf(876,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ one @ ( addition @ A @ B ) )
= ( addition @ ( star @ one ) @ C ) )
| ( ( addition @ B @ A )
!= ( addition @ ( star @ one ) @ C ) ) ),
inference(paramod_ordered,[status(thm)],[35,232]) ).
thf(877,plain,
! [A: $i] :
( ( addition @ one @ ( addition @ A @ ( star @ one ) ) )
= ( addition @ ( star @ one ) @ A ) ),
inference(pattern_uni,[status(thm)],[876:[bind(A,$thf( A )),bind(B,$thf( star @ one )),bind(C,$thf( A ))]]) ).
thf(87,plain,
! [A: $i] :
( ( leq @ ( multiplication @ sk1 @ sk2 ) @ A )
| ( ( multiplication @ one @ A )
!= ( multiplication @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[51,23]) ).
thf(91,plain,
! [A: $i] :
( ( leq @ ( multiplication @ sk1 @ sk2 ) @ A )
| ( sk3 != one )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[87]) ).
thf(95,plain,
( ( leq @ ( multiplication @ sk1 @ sk2 ) @ sk1 )
| ( sk3 != one ) ),
inference(simp,[status(thm)],[91]) ).
thf(301,plain,
! [A: $i] :
( ( leq @ A @ sk1 )
| ( sk3 != one )
| ( ( multiplication @ one @ A )
!= ( multiplication @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[51,95]) ).
thf(305,plain,
! [A: $i] :
( ( leq @ A @ sk1 )
| ( sk3 != one )
| ( sk1 != one )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[301]) ).
thf(312,plain,
( ( leq @ sk2 @ sk1 )
| ( sk3 != one )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[305]) ).
thf(195,plain,
! [B: $i,A: $i] :
( ( ( addition @ one @ zero )
= ( star @ B ) )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ B @ ( star @ B ) ) ) ),
inference(paramod_ordered,[status(thm)],[38,44]) ).
thf(196,plain,
( ( addition @ one @ zero )
= ( star @ zero ) ),
inference(pattern_uni,[status(thm)],[195:[bind(A,$thf( star @ zero )),bind(B,$thf( zero ))]]) ).
thf(5,axiom,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(30,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [A: $i] :
( ( addition @ A @ zero )
= A ),
inference(lifteq,[status(thm)],[31]) ).
thf(220,plain,
( ( star @ zero )
= one ),
inference(rewrite,[status(thm)],[196,32]) ).
thf(53,plain,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [A: $i] :
( ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) )
= ( strong_iteration @ A ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(1424,plain,
! [A: $i] :
( ( ( addition @ one @ ( multiplication @ ( strong_iteration @ A ) @ zero ) )
= ( strong_iteration @ A ) )
| ( ( star @ zero )
!= ( star @ A ) ) ),
inference(paramod_ordered,[status(thm)],[220,54]) ).
thf(1425,plain,
( ( addition @ one @ ( multiplication @ ( strong_iteration @ zero ) @ zero ) )
= ( strong_iteration @ zero ) ),
inference(pattern_uni,[status(thm)],[1424:[bind(A,$thf( zero ))]]) ).
thf(1690,plain,
! [B: $i,A: $i] :
( ( ( addition @ B @ A )
= ( strong_iteration @ zero ) )
| ( ( addition @ one @ ( multiplication @ ( strong_iteration @ zero ) @ zero ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[1425,35]) ).
thf(1691,plain,
( ( addition @ ( multiplication @ ( strong_iteration @ zero ) @ zero ) @ one )
= ( strong_iteration @ zero ) ),
inference(pattern_uni,[status(thm)],[1690:[bind(A,$thf( one )),bind(B,$thf( multiplication @ ( strong_iteration @ zero ) @ zero ))]]) ).
thf(18,axiom,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_unfold1) ).
thf(70,plain,
! [A: $i] :
( ( strong_iteration @ A )
= ( addition @ ( multiplication @ A @ ( strong_iteration @ A ) ) @ one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(126,plain,
! [A: $i] :
( ( leq @ ( multiplication @ sk1 @ sk2 ) @ A )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[69,23]) ).
thf(136,plain,
! [A: $i] :
( ( leq @ ( multiplication @ sk1 @ sk2 ) @ A )
| ( A != sk3 )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[126]) ).
thf(141,plain,
( ( leq @ ( multiplication @ sk1 @ sk2 ) @ sk3 )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[136]) ).
thf(98,plain,
! [A: $i] :
( ~ ( leq @ ( multiplication @ sk1 @ ( strong_iteration @ sk2 ) ) @ zero )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ ( strong_iteration @ sk3 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[38,22]) ).
thf(104,plain,
! [A: $i] :
( ~ ( leq @ ( multiplication @ sk1 @ ( strong_iteration @ sk2 ) ) @ zero )
| ( ( strong_iteration @ sk3 )
!= zero )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[98]) ).
thf(109,plain,
( ~ ( leq @ ( multiplication @ sk1 @ ( strong_iteration @ sk2 ) ) @ zero )
| ( ( strong_iteration @ sk3 )
!= zero ) ),
inference(simp,[status(thm)],[104]) ).
thf(1209,plain,
! [B: $i,A: $i] :
( ( A
= ( addition @ one @ ( addition @ B @ ( star @ one ) ) ) )
| ( ( addition @ A @ A )
!= ( addition @ ( star @ one ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[29,877]) ).
thf(1210,plain,
( ( addition @ one @ ( addition @ ( star @ one ) @ ( star @ one ) ) )
= ( star @ one ) ),
inference(pattern_uni,[status(thm)],[1209:[bind(A,$thf( star @ one )),bind(B,$thf( star @ one ))]]) ).
thf(2080,plain,
( ( addition @ ( star @ one ) @ ( star @ one ) )
= ( star @ one ) ),
inference(rewrite,[status(thm)],[1210,232]) ).
thf(88,plain,
! [A: $i] :
( ( leq @ A @ ( multiplication @ sk3 @ sk1 ) )
| ( ( multiplication @ one @ A )
!= ( multiplication @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[51,23]) ).
thf(92,plain,
! [A: $i] :
( ( leq @ A @ ( multiplication @ sk3 @ sk1 ) )
| ( sk1 != one )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[88]) ).
thf(96,plain,
( ( leq @ sk2 @ ( multiplication @ sk3 @ sk1 ) )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[92]) ).
thf(696,plain,
! [A: $i] :
( ~ ( leq @ ( strong_iteration @ sk2 ) @ A )
| ( sk1 != one )
| ( ( multiplication @ A @ one )
!= ( multiplication @ ( strong_iteration @ sk3 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[69,110]) ).
thf(717,plain,
! [A: $i] :
( ~ ( leq @ ( strong_iteration @ sk2 ) @ A )
| ( sk1 != one )
| ( A
!= ( strong_iteration @ sk3 ) )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[696]) ).
thf(721,plain,
( ~ ( leq @ ( strong_iteration @ sk2 ) @ ( strong_iteration @ sk3 ) )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[717]) ).
thf(8,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(39,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)],[8]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ A @ ( multiplication @ B @ C ) )
= ( multiplication @ ( multiplication @ A @ B ) @ C ) ),
inference(cnf,[status(esa)],[39]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( multiplication @ ( multiplication @ A @ B ) @ C )
= ( multiplication @ A @ ( multiplication @ B @ C ) ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(19,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',distributivity1) ).
thf(73,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)],[19]) ).
thf(342,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ B @ A )
= C )
| ( ( addition @ A @ B )
!= ( addition @ C @ zero ) ) ),
inference(paramod_ordered,[status(thm)],[35,32]) ).
thf(343,plain,
! [A: $i] :
( ( addition @ zero @ A )
= A ),
inference(pattern_uni,[status(thm)],[342:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(58,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
inference(cnf,[status(esa)],[57]) ).
thf(59,plain,
! [A: $i] :
( ( addition @ one @ ( multiplication @ ( star @ A ) @ A ) )
= ( star @ A ) ),
inference(lifteq,[status(thm)],[58]) ).
thf(2441,plain,
! [B: $i,A: $i] :
( ( leq @ one @ ( strong_iteration @ A ) )
| ( ( addition @ ( star @ A ) @ ( multiplication @ ( strong_iteration @ A ) @ zero ) )
!= ( addition @ ( star @ one ) @ B ) ) ),
inference(paramod_ordered,[status(thm)],[54,2295]) ).
thf(2442,plain,
leq @ one @ ( strong_iteration @ one ),
inference(pattern_uni,[status(thm)],[2441:[bind(A,$thf( one )),bind(B,$thf( multiplication @ ( strong_iteration @ one ) @ zero ))]]) ).
thf(20,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',distributivity2) ).
thf(76,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)],[20]) ).
thf(127,plain,
! [A: $i] :
( ( leq @ A @ ( multiplication @ sk3 @ sk1 ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[69,23]) ).
thf(135,plain,
! [A: $i] :
( ( leq @ A @ ( multiplication @ sk3 @ sk1 ) )
| ( A != sk1 )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[127]) ).
thf(140,plain,
( ( leq @ sk1 @ ( multiplication @ sk3 @ sk1 ) )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[135]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ~ ( leq @ A @ B )
| ( ( addition @ A @ B )
= B ) ),
inference(cnf,[status(esa)],[61]) ).
thf(66,plain,
! [B: $i,A: $i] :
( ( ( addition @ A @ B )
= B )
| ~ ( leq @ A @ B ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(221,plain,
! [A: $i] :
( ( ( addition @ one @ ( multiplication @ A @ one ) )
= ( star @ A ) )
| ( ( star @ zero )
!= ( star @ A ) ) ),
inference(paramod_ordered,[status(thm)],[220,44]) ).
thf(222,plain,
( ( addition @ one @ ( multiplication @ zero @ one ) )
= ( star @ zero ) ),
inference(pattern_uni,[status(thm)],[221:[bind(A,$thf( zero ))]]) ).
thf(267,plain,
( ( addition @ one @ zero )
= one ),
inference(rewrite,[status(thm)],[222,69,220]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( leq @ C @ ( addition @ ( multiplication @ A @ C ) @ B ) )
=> ( leq @ C @ ( multiplication @ ( strong_iteration @ A ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_coinduction) ).
thf(47,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)],[11]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( leq @ C @ ( addition @ ( multiplication @ A @ C ) @ B ) )
| ( leq @ C @ ( multiplication @ ( strong_iteration @ A ) @ B ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(2250,plain,
! [C: $i,B: $i,A: $i] :
( ( A != C )
| ( leq @ B @ C )
| ( ( addition @ zero @ A )
!= ( addition @ B @ C ) ) ),
inference(paramod_ordered,[status(thm)],[343,65]) ).
thf(2251,plain,
! [A: $i] :
( ( A != A )
| ( leq @ zero @ A ) ),
inference(pattern_uni,[status(thm)],[2250:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(2290,plain,
! [A: $i] : ( leq @ zero @ A ),
inference(simp,[status(thm)],[2251]) ).
thf(2413,plain,
! [A: $i] :
( ( leq @ zero @ A )
!= ( leq @ ( multiplication @ sk1 @ ( strong_iteration @ sk2 ) ) @ ( multiplication @ ( strong_iteration @ sk3 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[2290,22]) ).
thf(2419,plain,
! [A: $i] :
( ( ( multiplication @ sk1 @ ( strong_iteration @ sk2 ) )
!= zero )
| ( A
!= ( multiplication @ ( strong_iteration @ sk3 ) @ sk1 ) ) ),
inference(simp,[status(thm)],[2413]) ).
thf(2429,plain,
( ( multiplication @ sk1 @ ( strong_iteration @ sk2 ) )
!= zero ),
inference(simp,[status(thm)],[2419]) ).
thf(146,plain,
! [A: $i] :
( ( leq @ A @ zero )
| ( sk3 != zero )
| ( ( multiplication @ one @ A )
!= ( multiplication @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[51,83]) ).
thf(151,plain,
! [A: $i] :
( ( leq @ A @ zero )
| ( sk3 != zero )
| ( sk1 != one )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[146]) ).
thf(154,plain,
( ( leq @ sk2 @ zero )
| ( sk3 != zero )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[151]) ).
thf(298,plain,
! [A: $i] :
( ( leq @ A @ sk1 )
| ( sk3 != one )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk1 @ sk2 ) ) ),
inference(paramod_ordered,[status(thm)],[69,95]) ).
thf(307,plain,
! [A: $i] :
( ( leq @ A @ sk1 )
| ( sk3 != one )
| ( A != sk1 )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[298]) ).
thf(314,plain,
( ( leq @ sk1 @ sk1 )
| ( sk3 != one )
| ( sk2 != one ) ),
inference(simp,[status(thm)],[307]) ).
thf(317,plain,
! [A: $i] :
( ( leq @ sk2 @ A )
| ( sk1 != one )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk3 @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[69,96]) ).
thf(326,plain,
! [A: $i] :
( ( leq @ sk2 @ A )
| ( sk1 != one )
| ( A != sk3 )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[317]) ).
thf(332,plain,
( ( leq @ sk2 @ sk3 )
| ( sk1 != one ) ),
inference(simp,[status(thm)],[326]) ).
thf(942,plain,
( ( sk1 != one )
| ( ( leq @ ( strong_iteration @ sk2 ) @ ( strong_iteration @ sk3 ) )
!= ( leq @ sk2 @ sk3 ) ) ),
inference(paramod_ordered,[status(thm)],[332,721]) ).
thf(946,plain,
( ( sk1 != one )
| ( ( strong_iteration @ sk2 )
!= sk2 )
| ( ( strong_iteration @ sk3 )
!= sk3 ) ),
inference(simp,[status(thm)],[942]) ).
thf(123,plain,
! [A: $i] :
( ~ ( leq @ A @ ( multiplication @ ( strong_iteration @ sk3 ) @ sk1 ) )
| ( ( multiplication @ A @ one )
!= ( multiplication @ sk1 @ ( strong_iteration @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[69,22]) ).
thf(134,plain,
! [A: $i] :
( ~ ( leq @ A @ ( multiplication @ ( strong_iteration @ sk3 ) @ sk1 ) )
| ( A != sk1 )
| ( ( strong_iteration @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[123]) ).
thf(139,plain,
( ~ ( leq @ sk1 @ ( multiplication @ ( strong_iteration @ sk3 ) @ sk1 ) )
| ( ( strong_iteration @ sk2 )
!= one ) ),
inference(simp,[status(thm)],[134]) ).
thf(101,plain,
! [A: $i] :
( ~ ( leq @ ( multiplication @ sk1 @ ( strong_iteration @ sk2 ) ) @ A )
| ( ( multiplication @ one @ A )
!= ( multiplication @ ( strong_iteration @ sk3 ) @ sk1 ) ) ),
inference(paramod_ordered,[status(thm)],[51,22]) ).
thf(102,plain,
! [A: $i] :
( ~ ( leq @ ( multiplication @ sk1 @ ( strong_iteration @ sk2 ) ) @ A )
| ( ( strong_iteration @ sk3 )
!= one )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[101]) ).
thf(107,plain,
( ~ ( leq @ ( multiplication @ sk1 @ ( strong_iteration @ sk2 ) ) @ sk1 )
| ( ( strong_iteration @ sk3 )
!= one ) ),
inference(simp,[status(thm)],[102]) ).
thf(97,plain,
! [A: $i] :
( ~ ( leq @ zero @ ( multiplication @ ( strong_iteration @ sk3 ) @ sk1 ) )
| ( ( multiplication @ zero @ A )
!= ( multiplication @ sk1 @ ( strong_iteration @ sk2 ) ) ) ),
inference(paramod_ordered,[status(thm)],[38,22]) ).
thf(103,plain,
! [A: $i] :
( ~ ( leq @ zero @ ( multiplication @ ( strong_iteration @ sk3 ) @ sk1 ) )
| ( sk1 != zero )
| ( A
!= ( strong_iteration @ sk2 ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(108,plain,
( ~ ( leq @ zero @ ( multiplication @ ( strong_iteration @ sk3 ) @ sk1 ) )
| ( sk1 != zero ) ),
inference(simp,[status(thm)],[103]) ).
thf(2403,plain,
( ~ $true
| ( sk1 != zero ) ),
inference(rewrite,[status(thm)],[108,2290]) ).
thf(2404,plain,
sk1 != zero,
inference(simp,[status(thm)],[2403]) ).
thf(485,plain,
! [C: $i,B: $i,A: $i] :
( ( ( addition @ ( star @ one ) @ A )
= ( addition @ C @ ( addition @ B @ A ) ) )
| ( ( addition @ ( star @ one ) @ one )
!= ( addition @ C @ B ) ) ),
inference(paramod_ordered,[status(thm)],[353,26]) ).
thf(486,plain,
! [A: $i] :
( ( addition @ ( star @ one ) @ ( addition @ one @ A ) )
= ( addition @ ( star @ one ) @ A ) ),
inference(pattern_uni,[status(thm)],[485:[bind(A,$thf( A )),bind(B,$thf( one )),bind(C,$thf( star @ one ))]]) ).
thf(2266,plain,
! [B: $i,A: $i] :
( ( ( star @ one )
!= B )
| ( leq @ A @ B )
| ( ( addition @ ( star @ one ) @ ( star @ one ) )
!= ( addition @ A @ B ) ) ),
inference(paramod_ordered,[status(thm)],[2080,65]) ).
thf(2267,plain,
( ( ( star @ one )
!= ( star @ one ) )
| ( leq @ ( star @ one ) @ ( star @ one ) ) ),
inference(pattern_uni,[status(thm)],[2266:[bind(A,$thf( star @ one )),bind(B,$thf( star @ one ))]]) ).
thf(2297,plain,
leq @ ( star @ one ) @ ( star @ one ),
inference(simp,[status(thm)],[2267]) ).
thf(245222,plain,
$false,
inference(cvc4,[status(thm)],[56,65,69,138,2295,42,24,52,110,46,152,57,29,2291,353,877,312,60,1691,220,38,70,21,33,1425,141,109,2080,96,721,41,73,343,32,45,22,44,59,27,54,49,2442,76,39,140,66,267,35,48,95,67,2429,154,314,2290,26,946,55,139,23,36,30,51,107,2404,332,47,200,486,83,2297,232]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE158+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.15 % Command : run_Leo-III %s %d
% 0.14/0.35 % Computer : n010.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 02:57:58 EDT 2023
% 0.14/0.36 % CPUTime :
% 0.95/0.87 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.24/1.00 % [INFO] Parsing done (131ms).
% 1.24/1.01 % [INFO] Running in sequential loop mode.
% 1.63/1.20 % [INFO] eprover registered as external prover.
% 1.63/1.21 % [INFO] cvc4 registered as external prover.
% 1.63/1.21 % [INFO] Scanning for conjecture ...
% 1.88/1.27 % [INFO] Found a conjecture and 18 axioms. Running axiom selection ...
% 1.88/1.30 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 1.88/1.33 % [INFO] Problem is first-order (TPTP FOF).
% 2.15/1.33 % [INFO] Type checking passed.
% 2.15/1.34 % [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 ...
% 222.93/54.65 % External prover 'cvc4' found a proof!
% 222.93/54.65 % [INFO] Killing All external provers ...
% 222.93/54.66 % Time passed: 54147ms (effective reasoning time: 53643ms)
% 222.93/54.66 % 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)>
% 222.93/54.66 % 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
% 222.93/54.66 % No. of inferences in proof: 170
% 222.93/54.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 54147 ms resp. 53643 ms w/o parsing
% 222.93/54.75 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 222.93/54.75 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------