%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE143+2 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n019.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 43.52s 20.74s
% Output : Refutation 36.66s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 21
% Syntax : Number of formulae : 123 ( 64 unt; 0 typ; 2 def)
% Number of atoms : 258 ( 159 equ; 0 cnn)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 1193 ( 156 ~; 115 |; 5 &; 908 @)
% ( 1 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 12 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 150 ( 0 ^; 148 !; 0 ?; 150 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(strong_iteration_decl,type,
strong_iteration: $i > $i ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(one_decl,type,
one: $i ).
thf(star_decl,type,
star: $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( A @ strong_iteration @ ( A @ strong_iteration @ ( A @ strong_iteration @ multiplication ) @ leq ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( A @ strong_iteration @ ( A @ strong_iteration @ multiplication ) @ ( A @ strong_iteration @ leq ) ) ) ) ).
thf(17,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(68,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(69,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[68]) ).
thf(70,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[69]) ).
thf(1,conjecture,
! [A: $i] :
( ( A @ strong_iteration @ ( A @ strong_iteration @ multiplication ) @ ( A @ strong_iteration @ leq ) )
& ( A @ strong_iteration @ ( A @ strong_iteration @ ( A @ strong_iteration @ multiplication ) @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( A @ strong_iteration @ ( A @ strong_iteration @ multiplication ) @ ( A @ strong_iteration @ leq ) )
& ( A @ strong_iteration @ ( A @ strong_iteration @ ( A @ strong_iteration @ multiplication ) @ leq ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(21,plain,
~ ! [A: $i] :
( ( A @ strong_iteration @ ( A @ strong_iteration @ multiplication ) @ ( A @ strong_iteration @ leq ) )
& ( A @ strong_iteration @ ( A @ strong_iteration @ ( A @ strong_iteration @ multiplication ) @ leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(22,plain,
~ ( ! [A: $i] : ( A @ strong_iteration @ ( A @ strong_iteration @ multiplication ) @ ( A @ strong_iteration @ leq ) )
& ! [A: $i] : ( A @ strong_iteration @ ( A @ strong_iteration @ ( A @ strong_iteration @ multiplication ) @ leq ) ) ),
inference(miniscope,[status(thm)],[21]) ).
thf(23,plain,
( ~ ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ multiplication ) @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ multiplication ) @ leq ) ) ),
inference(cnf,[status(esa)],[22]) ).
thf(98,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ multiplication ) ) )
| ~ ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ multiplication ) @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[70,23]) ).
thf(103,plain,
! [A: $i] :
( ( ( sk1 @ strong_iteration )
!= one )
| ( A
!= ( sk1 @ strong_iteration ) )
| ~ ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ multiplication ) @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[98]) ).
thf(111,plain,
( ( ( sk1 @ strong_iteration )
!= one )
| ~ ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ multiplication ) @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ leq ) ) ),
inference(simp,[status(thm)],[103]) ).
thf(610,plain,
! [A: $i] :
( ( ( one @ ( A @ multiplication ) )
!= ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ multiplication ) ) )
| ( ( sk1 @ strong_iteration )
!= one )
| ~ ( A @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[70,111]) ).
thf(612,plain,
! [A: $i] :
( ( ( sk2 @ strong_iteration )
!= one )
| ( A
!= ( sk2 @ strong_iteration ) )
| ( ( sk1 @ strong_iteration )
!= one )
| ~ ( A @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ leq ) ) ),
inference(simp,[status(thm)],[610]) ).
thf(618,plain,
( ( ( sk2 @ strong_iteration )
!= one )
| ( ( sk1 @ strong_iteration )
!= one )
| ~ ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ leq ) ) ),
inference(simp,[status(thm)],[612]) ).
thf(889,plain,
( ( one != one )
| ( ( sk2 @ strong_iteration )
!= ( sk1 @ strong_iteration ) )
| ( ( sk1 @ strong_iteration )
!= one )
| ~ ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ leq ) ) ),
inference(eqfactor_ordered,[status(thm)],[618]) ).
thf(893,plain,
( ( sk2 != sk1 )
| ( ( sk1 @ strong_iteration )
!= one )
| ~ ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ leq ) ) ),
inference(simp,[status(thm)],[889]) ).
thf(7,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(36,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(37,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[36]) ).
thf(38,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[37]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ star @ ( A @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold1) ).
thf(42,plain,
! [A: $i] :
( ( A @ star @ ( A @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(43,plain,
! [A: $i] :
( ( A @ star @ ( A @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ),
inference(cnf,[status(esa)],[42]) ).
thf(44,plain,
! [A: $i] :
( ( A @ star @ ( A @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ),
inference(lifteq,[status(thm)],[43]) ).
thf(166,plain,
! [B: $i,A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( B @ star @ ( B @ multiplication ) ) )
| ( ( zero @ ( one @ addition ) )
= ( B @ star ) ) ),
inference(paramod_ordered,[status(thm)],[38,44]) ).
thf(167,plain,
( ( zero @ ( one @ addition ) )
= ( zero @ star ) ),
inference(pattern_uni,[status(thm)],[166:[bind(A,$thf( zero @ star )),bind(B,$thf( zero ))]]) ).
thf(5,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(30,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(31,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[30]) ).
thf(32,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[31]) ).
thf(188,plain,
( ( zero @ star )
= one ),
inference(rewrite,[status(thm)],[167,32]) ).
thf(189,plain,
! [A: $i] :
( ( ( zero @ star )
!= ( A @ star ) )
| ( ( one @ ( A @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ) ),
inference(paramod_ordered,[status(thm)],[188,44]) ).
thf(190,plain,
( ( one @ ( zero @ multiplication ) @ ( one @ addition ) )
= ( zero @ star ) ),
inference(pattern_uni,[status(thm)],[189:[bind(A,$thf( zero ))]]) ).
thf(219,plain,
( ( zero @ ( one @ addition ) )
= one ),
inference(rewrite,[status(thm)],[190,70,188]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_associativity) ).
thf(24,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)],[3]) ).
thf(25,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(cnf,[status(esa)],[24]) ).
thf(26,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ addition ) @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ( ( zero @ ( one @ addition ) )
!= ( B @ ( C @ addition ) ) )
| ( ( A @ ( one @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[219,26]) ).
thf(232,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) @ ( one @ addition ) )
= ( A @ ( one @ addition ) ) ),
inference(pattern_uni,[status(thm)],[231:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( one ))]]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(33,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(cnf,[status(esa)],[33]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(357,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( zero @ addition ) @ ( one @ addition ) )
!= ( C @ ( B @ addition ) ) )
| ( ( A @ ( one @ addition ) )
= ( B @ ( C @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[232,35]) ).
thf(358,plain,
! [A: $i] :
( ( one @ ( A @ ( zero @ addition ) @ addition ) )
= ( A @ ( one @ addition ) ) ),
inference(pattern_uni,[status(thm)],[357:[bind(A,$thf( E )),bind(B,$thf( one )),bind(C,$thf( E @ ( zero @ addition ) ))]]) ).
thf(384,plain,
! [A: $i] :
( ( one @ ( A @ ( zero @ addition ) @ addition ) )
= ( A @ ( one @ addition ) ) ),
inference(simp,[status(thm)],[358]) ).
thf(683,plain,
! [A: $i] :
( ( one @ ( A @ addition ) @ ( zero @ addition ) )
= ( A @ ( one @ addition ) ) ),
inference(rewrite,[status(thm)],[384,26]) ).
thf(687,plain,
! [B: $i,A: $i] :
( ( ( A @ ( one @ addition ) )
!= ( zero @ ( B @ addition ) ) )
| ( ( one @ ( A @ addition ) @ ( zero @ addition ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[683,32]) ).
thf(688,plain,
( ( one @ ( zero @ addition ) @ ( zero @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[687:[bind(A,$thf( zero )),bind(B,$thf( one ))]]) ).
thf(329,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( zero @ ( C @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[35,32]) ).
thf(330,plain,
! [A: $i] :
( ( A @ ( zero @ addition ) )
= A ),
inference(pattern_uni,[status(thm)],[329:[bind(A,$thf( A )),bind(B,$thf( zero )),bind(C,$thf( A ))]]) ).
thf(821,plain,
( ( one @ ( zero @ addition ) )
= one ),
inference(rewrite,[status(thm)],[688,330]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ addition ) @ ( A @ multiplication ) )
= ( C @ ( A @ multiplication ) @ ( B @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity1) ).
thf(74,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)],[19]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(60,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)],[16]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_associativity) ).
thf(39,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)],[8]) ).
thf(40,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[39]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[40]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(49,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(50,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[50]) ).
thf(95,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ multiplication ) ) )
| ~ ( A @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ multiplication ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[51,23]) ).
thf(104,plain,
! [A: $i] :
( ( A
!= ( sk2 @ strong_iteration ) )
| ( ( sk2 @ strong_iteration )
!= one )
| ~ ( A @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[95]) ).
thf(112,plain,
( ( ( sk2 @ strong_iteration )
!= one )
| ~ ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[104]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( B @ ( C @ ( A @ multiplication ) @ addition ) @ ( C @ leq ) )
=> ( B @ ( A @ strong_iteration @ multiplication ) @ ( C @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_coinduction) ).
thf(47,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)],[11]) ).
thf(48,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ strong_iteration @ multiplication ) @ ( C @ leq ) )
| ~ ( B @ ( C @ ( A @ multiplication ) @ addition ) @ ( C @ leq ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(895,plain,
( ~ $true
| ( ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ leq ) )
!= ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ leq ) ) )
| ( sk2 != sk1 )
| ( ( sk1 @ strong_iteration )
!= one )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ leq ) ) ),
inference(eqfactor_ordered,[status(thm)],[893]) ).
thf(897,plain,
( ( ( sk2 @ strong_iteration )
!= ( sk1 @ strong_iteration ) )
| ( ( sk2 @ strong_iteration )
!= ( sk1 @ strong_iteration ) )
| ( sk2 != sk1 )
| ( ( sk1 @ strong_iteration )
!= one )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ leq ) ) ),
inference(simp,[status(thm)],[895]) ).
thf(898,plain,
( ( ( sk2 @ strong_iteration )
!= ( sk1 @ strong_iteration ) )
| ( sk2 != sk1 )
| ( ( sk1 @ strong_iteration )
!= one )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ leq ) ) ),
inference(simp,[status(thm)],[897]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ strong_iteration )
= ( zero @ ( A @ strong_iteration @ multiplication ) @ ( A @ star @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',isolation) ).
thf(52,plain,
! [A: $i] :
( ( A @ strong_iteration )
= ( zero @ ( A @ strong_iteration @ multiplication ) @ ( A @ star @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(96,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ multiplication ) ) )
| ~ ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ multiplication ) @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[38,23]) ).
thf(102,plain,
! [A: $i] :
( ( A
!= ( sk1 @ strong_iteration ) )
| ( ( sk1 @ strong_iteration )
!= zero )
| ~ ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ multiplication ) @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(110,plain,
( ( ( sk1 @ strong_iteration )
!= zero )
| ~ ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ multiplication ) @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[102]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( C @ ( A @ multiplication ) @ addition ) @ leq ) )
=> ( C @ ( B @ ( A @ star @ multiplication ) @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction1) ).
thf(45,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)],[10]) ).
thf(46,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ star @ multiplication ) @ leq ) )
| ~ ( C @ ( B @ ( C @ ( A @ multiplication ) @ addition ) @ leq ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ ( A @ star @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_unfold2) ).
thf(57,plain,
! [A: $i] :
( ( A @ ( A @ star @ multiplication ) @ ( one @ addition ) )
= ( A @ star ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(4,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',idempotence) ).
thf(27,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[27]) ).
thf(29,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[28]) ).
thf(725,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ addition ) )
!= ( B @ ( one @ addition ) ) )
| ( A
= ( one @ ( B @ addition ) @ ( zero @ addition ) ) ) ),
inference(paramod_ordered,[status(thm)],[29,683]) ).
thf(726,plain,
( ( one @ ( one @ addition ) @ ( zero @ addition ) )
= one ),
inference(pattern_uni,[status(thm)],[725:[bind(A,$thf( one )),bind(B,$thf( one ))]]) ).
thf(952,plain,
( ( one @ ( one @ addition ) )
= one ),
inference(rewrite,[status(thm)],[726,330]) ).
thf(164,plain,
! [B: $i,A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( B @ star @ ( B @ multiplication ) ) )
| ( ( A @ ( one @ addition ) )
= ( B @ star ) ) ),
inference(paramod_ordered,[status(thm)],[51,44]) ).
thf(165,plain,
( ( one @ star @ ( one @ addition ) )
= ( one @ star ) ),
inference(pattern_uni,[status(thm)],[164:[bind(A,$thf( one @ star )),bind(B,$thf( one ))]]) ).
thf(97,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ multiplication ) ) )
| ~ ( zero @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ multiplication ) @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[38,23]) ).
thf(101,plain,
! [A: $i] :
( ( A
!= ( sk2 @ strong_iteration ) )
| ( ( sk2 @ strong_iteration )
!= zero )
| ~ ( zero @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[97]) ).
thf(109,plain,
( ( ( sk2 @ strong_iteration )
!= zero )
| ~ ( zero @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ multiplication ) @ leq ) ) ),
inference(simp,[status(thm)],[101]) ).
thf(116,plain,
! [A: $i] :
( ( ( A @ ( zero @ multiplication ) )
!= ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ multiplication ) ) )
| ( ( sk2 @ strong_iteration )
!= zero )
| ~ ( zero @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[38,109]) ).
thf(120,plain,
! [A: $i] :
( ( A
!= ( sk1 @ strong_iteration ) )
| ( ( sk1 @ strong_iteration )
!= zero )
| ( ( sk2 @ strong_iteration )
!= zero )
| ~ ( zero @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[116]) ).
thf(125,plain,
( ( ( sk1 @ strong_iteration )
!= zero )
| ( ( sk2 @ strong_iteration )
!= zero )
| ~ ( zero @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[120]) ).
thf(131,plain,
( ~ $true
| ( ( zero @ ( sk2 @ strong_iteration @ leq ) )
!= ( sk1 @ strong_iteration @ ( zero @ leq ) ) )
| ( ( sk1 @ strong_iteration )
!= zero )
| ( ( sk2 @ strong_iteration )
!= zero )
| ~ ( sk1 @ strong_iteration @ ( zero @ leq ) ) ),
inference(eqfactor_ordered,[status(thm)],[125]) ).
thf(134,plain,
( ( ( sk1 @ strong_iteration )
!= zero )
| ( ( sk2 @ strong_iteration )
!= zero )
| ( ( sk1 @ strong_iteration )
!= zero )
| ( ( sk2 @ strong_iteration )
!= zero )
| ~ ( sk1 @ strong_iteration @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(137,plain,
( ( ( sk1 @ strong_iteration )
!= zero )
| ( ( sk2 @ strong_iteration )
!= zero )
| ~ ( sk1 @ strong_iteration @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[134]) ).
thf(115,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ multiplication ) ) )
| ( ( sk2 @ strong_iteration )
!= zero )
| ~ ( zero @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( A @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[51,109]) ).
thf(119,plain,
! [A: $i] :
( ( A
!= ( sk1 @ strong_iteration ) )
| ( ( sk1 @ strong_iteration )
!= one )
| ( ( sk2 @ strong_iteration )
!= zero )
| ~ ( zero @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( A @ leq ) ) ),
inference(simp,[status(thm)],[115]) ).
thf(124,plain,
( ( ( sk1 @ strong_iteration )
!= one )
| ( ( sk2 @ strong_iteration )
!= zero )
| ~ ( zero @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( sk1 @ strong_iteration @ leq ) ) ),
inference(simp,[status(thm)],[119]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',distributivity2) ).
thf(77,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)],[20]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ strong_iteration )
= ( one @ ( A @ strong_iteration @ ( A @ multiplication ) @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',infty_unfold1) ).
thf(71,plain,
! [A: $i] :
( ( A @ strong_iteration )
= ( one @ ( A @ strong_iteration @ ( A @ multiplication ) @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(309,plain,
! [A: $i] :
( ( ( A @ ( one @ multiplication ) )
!= ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ multiplication ) ) )
| ( ( sk1 @ strong_iteration )
!= zero )
| ~ ( A @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( zero @ leq ) ) ),
inference(paramod_ordered,[status(thm)],[51,110]) ).
thf(313,plain,
! [A: $i] :
( ( A
!= ( sk2 @ strong_iteration ) )
| ( ( sk2 @ strong_iteration )
!= one )
| ( ( sk1 @ strong_iteration )
!= zero )
| ~ ( A @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[309]) ).
thf(318,plain,
( ( ( sk2 @ strong_iteration )
!= one )
| ( ( sk1 @ strong_iteration )
!= zero )
| ~ ( sk2 @ strong_iteration @ ( sk2 @ strong_iteration @ leq ) )
| ~ ( sk1 @ strong_iteration @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[313]) ).
thf(138,plain,
( ( zero != zero )
| ( ( sk2 @ strong_iteration )
!= ( sk1 @ strong_iteration ) )
| ( ( sk1 @ strong_iteration )
!= zero )
| ~ ( sk1 @ strong_iteration @ ( zero @ leq ) ) ),
inference(eqfactor_ordered,[status(thm)],[137]) ).
thf(140,plain,
( ( sk2 != sk1 )
| ( ( sk1 @ strong_iteration )
!= zero )
| ~ ( sk1 @ strong_iteration @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( C @ multiplication ) @ addition ) @ leq ) )
=> ( C @ ( A @ star @ ( B @ multiplication ) @ leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',star_induction2) ).
thf(55,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)],[14]) ).
thf(139,plain,
( ( ( sk2 @ strong_iteration )
!= ( sk1 @ strong_iteration ) )
| ( ( sk1 @ strong_iteration )
!= zero )
| ~ ( sk1 @ strong_iteration @ ( zero @ leq ) ) ),
inference(simp,[status(thm)],[138]) ).
thf(363,plain,
! [B: $i,A: $i] :
( ( ( one @ star @ ( one @ addition ) )
!= ( B @ ( A @ addition ) ) )
| ( ( A @ ( B @ addition ) )
= ( one @ star ) ) ),
inference(paramod_ordered,[status(thm)],[165,35]) ).
thf(364,plain,
( ( one @ ( one @ star @ addition ) )
= ( one @ star ) ),
inference(pattern_uni,[status(thm)],[363:[bind(A,$thf( one )),bind(B,$thf( one @ star ))]]) ).
thf(14741,plain,
$false,
inference(e,[status(thm)],[893,683,821,74,60,188,41,35,112,48,898,42,24,52,110,46,57,29,952,38,70,165,33,21,137,109,124,77,618,32,45,44,27,71,49,219,318,39,140,330,26,55,139,23,36,30,51,47,68,111,364]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE143+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.14/5.44 % Computer : n019.cluster.edu
% 0.14/5.44 % Model : x86_64 x86_64
% 0.14/5.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/5.44 % Memory : 8046.5625MB
% 0.14/5.44 % OS : Linux 6.8.0-71-generic
% 0.14/5.44 % CPULimit : 300
% 0.14/5.44 % WCLimit : 300
% 0.14/5.44 % DateTime : Fri Sep 25 19:26:39 UTC 2026
% 0.14/5.44 % CPUTime :
% 0.14/5.44 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.93/6.25 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.36/6.52 % [INFO] Parsing done (263ms).
% 1.36/6.54 % [INFO] Running in sequential loop mode.
% 1.91/7.08 % [INFO] eprover registered as external prover.
% 1.91/7.09 % [INFO] Scanning for conjecture ...
% 2.29/7.22 % [INFO] Found a conjecture (or negated_conjecture) and 18 axioms. Running axiom selection ...
% 2.41/7.31 % [INFO] Axiom selection finished. Selected 18 axioms (removed 0 axioms).
% 2.41/7.37 % [INFO] Problem is first-order (TPTP FOF).
% 2.41/7.37 % [INFO] Type checking passed.
% 2.41/7.38 % [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 ...
% 43.52/20.73 % External prover 'e' found a proof!
% 43.52/20.73 % [INFO] Killing All external provers ...
% 43.52/20.73 % Time passed: 15070ms (effective reasoning time: 14190ms)
% 43.52/20.73 % 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)>
% 43.52/20.74 % 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
% 43.52/20.74 % No. of inferences in proof: 121
% 43.52/20.74 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 15070 ms resp. 14190 ms w/o parsing
% 36.66/20.89 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 36.66/20.89 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------