%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE144+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n008.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 07:43:17 AM UTC 2026
% Result : Theorem 25.82s 12.33s
% Output : Refutation 22.43s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 20
% Syntax : Number of formulae : 115 ( 74 unt; 0 typ; 1 def)
% Number of atoms : 174 ( 133 equ; 0 cnn)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 694 ( 72 ~; 44 |; 3 &; 564 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 10 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 154 ( 0 ^; 153 !; 0 ?; 154 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(strong_iteration_decl,type,
strong_iteration: $i > $i ).
thf(star_decl,type,
star: $i > $i ).
thf(one_decl,type,
one: $i ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
( ( A @ star @ strong_iteration )
!= ( one @ strong_iteration ) ) ) ) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( C @ multiplication ) @ addition ) @ leq ) )
=> ( C @ ( A @ star @ ( B @ multiplication ) @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction2) ).
thf(69,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( C @ multiplication ) @ addition ) @ leq ) )
=> ( C @ ( A @ star @ ( B @ multiplication ) @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ star @ ( A @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold1) ).
thf(56,plain,
! [A: $i] :
( ( A @ star @ ( A @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(27,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(8,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',idempotence) ).
thf(39,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(40,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[39]) ).
thf(41,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[40]) ).
thf(18,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(71,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(63,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(64,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[63]) ).
thf(65,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[64]) ).
thf(19,axiom,
! [A: $i] :
( ( A @ strong_iteration )
= ( one @ ( A @ strong_iteration @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_unfold1) ).
thf(74,plain,
! [A: $i] :
( ( A @ strong_iteration )
= ( one @ ( A @ strong_iteration @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(75,plain,
! [A: $i] :
( ( A @ strong_iteration )
= ( one @ ( A @ strong_iteration @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[74]) ).
thf(76,plain,
! [A: $i] :
( ( one @ ( A @ strong_iteration @ ( A @ multiplication ) @ addition ) )
= ( A @ strong_iteration ) ),
inference(lifteq,[status(thm)],[75]) ).
thf(664,plain,
! [B: $i,A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( B @ strong_iteration @ ( B @ multiplication ) ) )
| ( ( one @ ( A @ addition ) )
= ( B @ strong_iteration ) ) ),
inference(paramod_ordered,[status(thm)],[65,76]) ).
thf(665,plain,
( ( one @ ( one @ strong_iteration @ addition ) )
= ( one @ strong_iteration ) ),
inference(pattern_uni,[status(thm)],[664:[bind(A,$thf( one @ strong_iteration )),bind(B,$thf( one ))]]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_commutativity) ).
thf(30,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(906,plain,
! [B: $i,A: $i] :
( ( ( one @ ( one @ strong_iteration @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= ( one @ strong_iteration ) ) ),
inference(paramod_ordered,[status(thm)],[665,32]) ).
thf(907,plain,
( ( one @ strong_iteration @ ( one @ addition ) )
= ( one @ strong_iteration ) ),
inference(pattern_uni,[status(thm)],[906:[bind(A,$thf( one @ strong_iteration )),bind(B,$thf( one ))]]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity1) ).
thf(45,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(47,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) )
= ( C @ ( B @ addition ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(57,plain,
! [A: $i] :
( ( A @ star @ ( A @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ),
inference(cnf,[status(esa)],[56]) ).
thf(58,plain,
! [A: $i] :
( ( A @ star @ ( A @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(215,plain,
! [B: $i,A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( B @ star @ ( B @ multiplication ) ) )
| ( ( A @ ( one @ addition ) )
= ( B @ star ) ) ),
inference(paramod_ordered,[status(thm)],[65,58]) ).
thf(216,plain,
( ( one @ star @ ( one @ addition ) )
= ( one @ star ) ),
inference(pattern_uni,[status(thm)],[215:[bind(A,$thf( one @ star )),bind(B,$thf( one ))]]) ).
thf(336,plain,
! [B: $i,A: $i] :
( ( ( one @ star @ ( one @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= ( one @ star ) ) ),
inference(paramod_ordered,[status(thm)],[216,32]) ).
thf(337,plain,
( ( one @ ( one @ star @ addition ) )
= ( one @ star ) ),
inference(pattern_uni,[status(thm)],[336:[bind(A,$thf( one )),bind(B,$thf( one @ star ))]]) ).
thf(9,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_identity) ).
thf(42,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',left_annihilation) ).
thf(24,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',order) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( ( ( B @ ( A @ addition ) )
= B )
=> ( B @ ( A @ leq ) ) )
& ( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ addition ) )
= B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(49,plain,
( ! [A: $i,B: $i] :
( ( ( B @ ( A @ addition ) )
= B )
=> ( B @ ( A @ leq ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
=> ( ( B @ ( A @ addition ) )
= B ) ) ),
inference(miniscope,[status(thm)],[48]) ).
thf(50,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ leq ) )
| ( ( D @ ( C @ addition ) )
!= D ) )
& ( ( ( B @ ( A @ addition ) )
= B )
| ~ ( B @ ( A @ leq ) ) ) ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
= B )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[50]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
= B ) ),
inference(lifteq,[status(thm)],[51]) ).
thf(43,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[42]) ).
thf(44,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[43]) ).
thf(81,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( zero @ ( C @ addition ) ) )
| ( B = C )
| ~ ( B @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[53,44]) ).
thf(82,plain,
! [A: $i] :
( ( zero = A )
| ~ ( zero @ ( A @ leq ) ) ),
inference(pattern_uni,[status(thm)],[81:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ star @ strong_iteration )
= ( one @ strong_iteration ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ star @ strong_iteration )
= ( one @ strong_iteration ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i] :
( ( A @ star @ strong_iteration )
= ( one @ strong_iteration ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
( ( sk1 @ star @ strong_iteration )
!= ( one @ strong_iteration ) ),
inference(cnf,[status(esa)],[21]) ).
thf(23,plain,
( ( sk1 @ star @ strong_iteration )
!= ( one @ strong_iteration ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(80,plain,
( ( sk1 @ star )
!= one ),
inference(simp,[status(thm)],[23]) ).
thf(95,plain,
! [A: $i] :
( ( A != sk1 )
| ( ( zero @ star )
!= one )
| ~ ( zero @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[82,80]) ).
thf(96,plain,
( ( ( zero @ star )
!= one )
| ~ ( zero @ ( sk1 @ leq ) ) ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( sk1 ))]]) ).
thf(25,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[25]) ).
thf(226,plain,
! [B: $i,A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( B @ star @ ( B @ multiplication ) ) )
| ( ( zero @ ( one @ addition ) )
= ( B @ star ) ) ),
inference(paramod_ordered,[status(thm)],[26,58]) ).
thf(227,plain,
( ( zero @ ( one @ addition ) )
= ( zero @ star ) ),
inference(pattern_uni,[status(thm)],[226:[bind(A,$thf( zero @ star )),bind(B,$thf( zero ))]]) ).
thf(251,plain,
( ( zero @ star )
= one ),
inference(rewrite,[status(thm)],[227,44]) ).
thf(252,plain,
( ( one != one )
| ~ ( zero @ ( sk1 @ leq ) ) ),
inference(rewrite,[status(thm)],[96,251]) ).
thf(253,plain,
~ ( zero @ ( sk1 @ leq ) ),
inference(simp,[status(thm)],[252]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ multiplication ) @ addition ) @ ( C @ leq ) )
=> ( B @ ( A @ strong_iteration @ multiplication ) @ ( C @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',infty_coinduction) ).
thf(61,plain,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ multiplication ) @ addition ) @ ( C @ leq ) )
=> ( B @ ( A @ strong_iteration @ multiplication ) @ ( C @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',additive_associativity) ).
thf(36,plain,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ addition ) @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',distributivity2) ).
thf(33,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(693,plain,
! [B: $i,A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( B @ strong_iteration @ ( B @ multiplication ) ) )
| ( ( one @ ( zero @ addition ) )
= ( B @ strong_iteration ) ) ),
inference(paramod_ordered,[status(thm)],[26,76]) ).
thf(694,plain,
( ( one @ ( zero @ addition ) )
= ( zero @ strong_iteration ) ),
inference(pattern_uni,[status(thm)],[693:[bind(A,$thf( zero @ strong_iteration )),bind(B,$thf( zero ))]]) ).
thf(326,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( zero @ ( C @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[32,44]) ).
thf(327,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) )
= A ),
inference(pattern_uni,[status(thm)],[326:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(883,plain,
( ( zero @ strong_iteration )
= one ),
inference(rewrite,[status(thm)],[694,327]) ).
thf(889,plain,
( ( ( sk1 @ star @ strong_iteration )
!= ( zero @ strong_iteration ) )
| ( ( one @ strong_iteration )
!= one ) ),
inference(paramod_ordered,[status(thm)],[883,23]) ).
thf(897,plain,
( ( ( sk1 @ star )
!= zero )
| ( ( one @ strong_iteration )
!= one ) ),
inference(simp,[status(thm)],[889]) ).
thf(1055,plain,
( ( ( zero @ strong_iteration )
!= ( one @ strong_iteration ) )
| ( ( sk1 @ star )
!= zero )
| ( one != one ) ),
inference(paramod_ordered,[status(thm)],[883,897]) ).
thf(1056,plain,
( ( ( zero @ strong_iteration )
!= ( one @ strong_iteration ) )
| ( ( sk1 @ star )
!= zero ) ),
inference(simp,[status(thm)],[1055]) ).
thf(1066,plain,
( ( zero != one )
| ( ( sk1 @ star )
!= zero ) ),
inference(simp,[status(thm)],[1056]) ).
thf(1069,plain,
! [A: $i] :
( ( zero != zero )
| ( A != one )
| ( ( sk1 @ star )
!= zero )
| ~ ( zero @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[82,1066]) ).
thf(1070,plain,
! [A: $i] :
( ( A != one )
| ( ( sk1 @ star )
!= zero )
| ~ ( zero @ ( A @ leq ) ) ),
inference(pattern_uni,[status(thm)],[1069:[]]) ).
thf(1079,plain,
( ( ( sk1 @ star )
!= zero )
| ~ ( zero @ ( one @ leq ) ) ),
inference(simp,[status(thm)],[1070]) ).
thf(93,plain,
! [A: $i] :
( ( A
!= ( sk1 @ star ) )
| ( zero != one )
| ~ ( zero @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[82,80]) ).
thf(94,plain,
( ( zero != one )
| ~ ( zero @ ( sk1 @ star @ leq ) ) ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( sk1 @ star ))]]) ).
thf(131,plain,
! [A: $i] :
( ( zero != zero )
| ( A != one )
| ~ ( zero @ ( sk1 @ star @ leq ) )
| ~ ( zero @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[82,94]) ).
thf(132,plain,
! [A: $i] :
( ( A != one )
| ~ ( zero @ ( sk1 @ star @ leq ) )
| ~ ( zero @ ( A @ leq ) ) ),
inference(pattern_uni,[status(thm)],[131:[]]) ).
thf(141,plain,
( ~ ( zero @ ( sk1 @ star @ leq ) )
| ~ ( zero @ ( one @ leq ) ) ),
inference(simp,[status(thm)],[132]) ).
thf(108,plain,
! [A: $i] :
( ( A
!= ( sk1 @ star @ strong_iteration ) )
| ( ( one @ strong_iteration )
!= zero )
| ~ ( zero @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[82,23]) ).
thf(109,plain,
( ( ( one @ strong_iteration )
!= zero )
| ~ ( zero @ ( sk1 @ star @ strong_iteration @ leq ) ) ),
inference(pattern_uni,[status(thm)],[108:[bind(A,$thf( sk1 @ star @ strong_iteration ))]]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ( A @ star @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_unfold2) ).
thf(77,plain,
! [A: $i] :
( ( A @ ( A @ star @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(72,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[71]) ).
thf(73,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[72]) ).
thf(259,plain,
! [A: $i] :
( ( ( zero @ star )
!= ( A @ star ) )
| ( ( one @ ( A @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ) ),
inference(paramod_ordered,[status(thm)],[251,58]) ).
thf(260,plain,
( ( one @ ( zero @ multiplication ) @ ( one @ addition ) )
= ( zero @ star ) ),
inference(pattern_uni,[status(thm)],[259:[bind(A,$thf( zero ))]]) ).
thf(398,plain,
( ( zero @ ( one @ addition ) )
= one ),
inference(rewrite,[status(thm)],[260,26,251]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( C @ ( A @ multiplication ) @ addition ) @ leq ) )
=> ( C @ ( B @ ( A @ star @ multiplication ) @ leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',star_induction1) ).
thf(59,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( C @ ( A @ multiplication ) @ addition ) @ leq ) )
=> ( C @ ( B @ ( A @ star @ multiplication ) @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ strong_iteration )
= ( zero @ ( A @ strong_iteration @ multiplication ) @ ( A @ star @ addition ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',isolation) ).
thf(66,plain,
! [A: $i] :
( ( A @ strong_iteration )
= ( zero @ ( A @ strong_iteration @ multiplication ) @ ( A @ star @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(34,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) )
= ( C @ ( B @ ( A @ addition ) @ multiplication ) ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(254,plain,
( ( ( sk1 @ star )
!= ( zero @ star ) )
| ( one != one ) ),
inference(paramod_ordered,[status(thm)],[251,80]) ).
thf(255,plain,
( ( sk1 @ star )
!= ( zero @ star ) ),
inference(simp,[status(thm)],[254]) ).
thf(268,plain,
sk1 != zero,
inference(simp,[status(thm)],[255]) ).
thf(3037,plain,
$false,
inference(e,[status(thm)],[69,56,29,41,71,907,47,337,42,24,216,253,61,74,38,21,33,65,665,1079,53,141,109,77,73,398,32,45,44,59,27,76,39,66,251,1066,883,80,35,48,63,327,26,23,58,82,36,30,268,897,94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : KLE144+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.12 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.22/5.50 % Computer : n008.cluster.edu
% 0.22/5.50 % Model : x86_64 x86_64
% 0.22/5.50 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.22/5.50 % Memory : 8046.5625MB
% 0.22/5.50 % OS : Linux 6.8.0-71-generic
% 0.22/5.50 % CPULimit : 300
% 0.22/5.50 % WCLimit : 300
% 0.22/5.50 % DateTime : Fri Sep 25 19:27:29 UTC 2026
% 0.22/5.50 % CPUTime :
% 0.22/5.50 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 1.38/6.36 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.85/6.65 % [INFO] Parsing done (289ms).
% 1.85/6.67 % [INFO] Running in sequential loop mode.
% 2.84/7.26 % [INFO] eprover registered as external prover.
% 2.84/7.28 % [INFO] Scanning for conjecture ...
% 3.19/7.40 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 3.19/7.47 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 3.39/7.51 % [INFO] Problem is first-order (TPTP FOF).
% 3.39/7.52 % [INFO] Type checking passed.
% 3.39/7.52 % [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 ...
% 25.82/12.32 % External prover 'e' found a proof!
% 25.82/12.32 % [INFO] Killing All external provers ...
% 25.82/12.33 % Time passed: 6615ms (effective reasoning time: 5644ms)
% 25.82/12.33 % 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)>
% 25.82/12.33 % 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
% 25.82/12.33 % No. of inferences in proof: 114
% 25.82/12.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 6615 ms resp. 5644 ms w/o parsing
% 22.43/12.44 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 22.43/12.45 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------