%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : KLE135+1 : 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 : n003.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 07:43:15 AM UTC 2026
% Result : Theorem 24.89s 10.15s
% Output : Refutation 25.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 30
% Syntax : Number of formulae : 141 ( 99 unt; 0 typ; 1 def)
% Number of atoms : 212 ( 196 equ; 0 cnn)
% Maximal formula atoms : 7 ( 1 avg)
% Number of connectives : 1051 ( 66 ~; 55 |; 4 &; 915 @)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 18 usr; 4 con; 0-2 aty)
% Number of variables : 233 ( 0 ^; 232 !; 0 ?; 233 :)
% ( 0 !>; 0 ?*; 0 @-; 1 @+)
% Comments :
%------------------------------------------------------------------------------
thf(divergence_decl,type,
divergence: $i > $i ).
thf(zero_decl,type,
zero: $i ).
thf(forward_diamond_decl,type,
forward_diamond: $i > $i > $i ).
thf(star_decl,type,
star: $i > $i ).
thf(antidomain_decl,type,
antidomain: $i > $i ).
thf(one_decl,type,
one: $i ).
thf(multiplication_decl,type,
multiplication: $i > $i > $i ).
thf(addition_decl,type,
addition: $i > $i > $i ).
thf(codomain_decl,type,
codomain: $i > $i ).
thf(coantidomain_decl,type,
coantidomain: $i > $i ).
thf(backward_box_decl,type,
backward_box: $i > $i > $i ).
thf(c_decl,type,
c: $i > $i ).
thf(backward_diamond_decl,type,
backward_diamond: $i > $i > $i ).
thf(leq_decl,type,
leq: $i > $i > $o ).
thf(domain_difference_decl,type,
domain_difference: $i > $i > $i ).
thf(domain_decl,type,
domain: $i > $i ).
thf(forward_box_decl,type,
forward_box: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ( ( ( A @ divergence )
= zero )
=> ( ( A @ antidomain @ ( A @ star @ forward_diamond ) )
= one ) ) ) ) ).
thf(22,axiom,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_left_identity) ).
thf(99,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(100,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[99]) ).
thf(101,plain,
! [A: $i] :
( ( A @ ( one @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[100]) ).
thf(21,axiom,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiplicative_right_identity) ).
thf(96,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ coantidomain @ ( A @ coantidomain @ coantidomain @ addition ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain3) ).
thf(105,plain,
! [A: $i] :
( ( A @ coantidomain @ ( A @ coantidomain @ coantidomain @ addition ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ coantidomain @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain1) ).
thf(102,plain,
! [A: $i] :
( ( A @ coantidomain @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(103,plain,
! [A: $i] :
( ( A @ coantidomain @ ( A @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[102]) ).
thf(104,plain,
! [A: $i] :
( ( A @ coantidomain @ ( A @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[103]) ).
thf(314,plain,
! [B: $i,A: $i] :
( ( ( A @ coantidomain @ ( A @ multiplication ) )
!= ( B @ ( one @ multiplication ) ) )
| ( zero = B ) ),
inference(paramod_ordered,[status(thm)],[104,101]) ).
thf(315,plain,
( ( one @ coantidomain )
= zero ),
inference(pattern_uni,[status(thm)],[314:[bind(A,$thf( one )),bind(B,$thf( one @ coantidomain ))]]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ codomain )
= ( A @ coantidomain @ coantidomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain4) ).
thf(46,plain,
! [A: $i] :
( ( A @ codomain )
= ( A @ coantidomain @ coantidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(47,plain,
! [A: $i] :
( ( A @ codomain )
= ( A @ coantidomain @ coantidomain ) ),
inference(cnf,[status(esa)],[46]) ).
thf(48,plain,
! [A: $i] :
( ( A @ coantidomain @ coantidomain )
= ( A @ codomain ) ),
inference(lifteq,[status(thm)],[47]) ).
thf(353,plain,
! [A: $i] :
( ( ( one @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( zero @ coantidomain )
= ( A @ codomain ) ) ),
inference(paramod_ordered,[status(thm)],[315,48]) ).
thf(354,plain,
( ( zero @ coantidomain )
= ( one @ codomain ) ),
inference(pattern_uni,[status(thm)],[353:[bind(A,$thf( one ))]]) ).
thf(427,plain,
! [A: $i] :
( ( ( zero @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( one @ codomain @ coantidomain )
= ( A @ codomain ) ) ),
inference(paramod_ordered,[status(thm)],[354,48]) ).
thf(428,plain,
( ( one @ codomain @ coantidomain )
= ( zero @ codomain ) ),
inference(pattern_uni,[status(thm)],[427:[bind(A,$thf( zero ))]]) ).
thf(441,plain,
! [A: $i] :
( ( ( one @ codomain @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( zero @ codomain @ coantidomain )
= ( A @ codomain ) ) ),
inference(paramod_ordered,[status(thm)],[428,48]) ).
thf(442,plain,
( ( zero @ codomain @ coantidomain )
= ( one @ codomain @ codomain ) ),
inference(pattern_uni,[status(thm)],[441:[bind(A,$thf( one @ codomain ))]]) ).
thf(581,plain,
! [A: $i] :
( ( ( zero @ codomain @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( one @ codomain @ codomain @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[442,104]) ).
thf(582,plain,
( ( one @ codomain @ codomain @ ( zero @ codomain @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[581:[bind(A,$thf( zero @ codomain ))]]) ).
thf(29,axiom,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_identity) ).
thf(120,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(4,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(40,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)],[4]) ).
thf(41,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ addition ) @ ( C @ addition ) )
= ( A @ ( B @ ( C @ addition ) @ addition ) ) ),
inference(cnf,[status(esa)],[40]) ).
thf(42,plain,
! [C: $i,B: $i,A: $i] :
( ( A @ ( B @ ( C @ addition ) @ addition ) )
= ( A @ ( B @ addition ) @ ( C @ addition ) ) ),
inference(lifteq,[status(thm)],[41]) ).
thf(3,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(37,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)],[3]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ backward_box ) )
= ( B @ c @ ( A @ backward_diamond ) @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',backward_box) ).
thf(52,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ backward_box ) )
= ( B @ c @ ( A @ backward_diamond ) @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(586,plain,
! [A: $i] :
( ( ( zero @ codomain @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( one @ codomain @ codomain @ coantidomain )
= ( A @ codomain ) ) ),
inference(paramod_ordered,[status(thm)],[442,48]) ).
thf(587,plain,
( ( one @ codomain @ codomain @ coantidomain )
= ( zero @ codomain @ codomain ) ),
inference(pattern_uni,[status(thm)],[586:[bind(A,$thf( zero @ codomain ))]]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_annihilation) ).
thf(93,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(18,axiom,
! [A: $i] :
( ( A @ ( A @ antidomain @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain1) ).
thf(87,plain,
! [A: $i] :
( ( A @ ( A @ antidomain @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(88,plain,
! [A: $i] :
( ( A @ ( A @ antidomain @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[87]) ).
thf(89,plain,
! [A: $i] :
( ( A @ ( A @ antidomain @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[88]) ).
thf(97,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(cnf,[status(esa)],[96]) ).
thf(98,plain,
! [A: $i] :
( ( one @ ( A @ multiplication ) )
= A ),
inference(lifteq,[status(thm)],[97]) ).
thf(283,plain,
! [B: $i,A: $i] :
( ( ( A @ ( A @ antidomain @ multiplication ) )
!= ( one @ ( B @ multiplication ) ) )
| ( zero = B ) ),
inference(paramod_ordered,[status(thm)],[89,98]) ).
thf(284,plain,
( ( one @ antidomain )
= zero ),
inference(pattern_uni,[status(thm)],[283:[bind(A,$thf( one )),bind(B,$thf( one @ antidomain ))]]) ).
thf(15,axiom,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_annihilation) ).
thf(78,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(79,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[78]) ).
thf(80,plain,
! [A: $i] :
( ( zero @ ( A @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[79]) ).
thf(142,plain,
! [B: $i,A: $i] :
( ( ( zero @ ( A @ multiplication ) )
!= ( one @ ( B @ multiplication ) ) )
| ( zero = B ) ),
inference(paramod_ordered,[status(thm)],[80,98]) ).
thf(144,plain,
! [B: $i,A: $i] :
( ( one != zero )
| ( A != B )
| ( zero = B ) ),
inference(simp,[status(thm)],[142]) ).
thf(145,plain,
! [A: $i] :
( ( one != zero )
| ( zero = A ) ),
inference(simp,[status(thm)],[144]) ).
thf(1,conjecture,
! [A: $i] :
( ( ( A @ divergence )
= zero )
=> ( ( A @ antidomain @ ( A @ star @ forward_diamond ) )
= one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).
thf(2,negated_conjecture,
~ ! [A: $i] :
( ( ( A @ divergence )
= zero )
=> ( ( A @ antidomain @ ( A @ star @ forward_diamond ) )
= one ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(31,plain,
~ ! [A: $i] :
( ( ( A @ divergence )
= zero )
=> ( ( A @ antidomain @ ( A @ star @ forward_diamond ) )
= one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(32,plain,
( ( ( sk1 @ antidomain @ ( sk1 @ star @ forward_diamond ) )
!= one )
& ( ( sk1 @ divergence )
= zero ) ),
inference(cnf,[status(esa)],[31]) ).
thf(34,plain,
( ( sk1 @ antidomain @ ( sk1 @ star @ forward_diamond ) )
!= one ),
inference(cnfConj,[status(thm)],[32]) ).
thf(36,plain,
( ( sk1 @ antidomain @ ( sk1 @ star @ forward_diamond ) )
!= one ),
inference(lifteq,[status(thm)],[34]) ).
thf(162,plain,
! [A: $i] :
( ( A
!= ( sk1 @ antidomain @ ( sk1 @ star @ forward_diamond ) ) )
| ( one != zero )
| ( one != zero ) ),
inference(paramod_ordered,[status(thm)],[145,36]) ).
thf(163,plain,
! [A: $i] :
( ( A
!= ( sk1 @ antidomain @ ( sk1 @ star @ forward_diamond ) ) )
| ( one != zero ) ),
inference(simp,[status(thm)],[162]) ).
thf(164,plain,
one != zero,
inference(pattern_uni,[status(thm)],[163:[bind(A,$thf( sk1 @ antidomain @ ( sk1 @ star @ forward_diamond ) ))]]) ).
thf(17,axiom,
! [A: $i] :
( ( A @ antidomain @ ( A @ antidomain @ antidomain @ addition ) )
= one ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain3) ).
thf(84,plain,
! [A: $i] :
( ( A @ antidomain @ ( A @ antidomain @ antidomain @ addition ) )
= one ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_commutativity) ).
thf(61,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ addition ) )
= ( A @ ( B @ addition ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(13,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ leq ) )
<=> ( ( B @ ( A @ addition ) )
= B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',order) ).
thf(67,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)],[13]) ).
thf(68,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)],[67]) ).
thf(69,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)],[68]) ).
thf(71,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
!= B ) ),
inference(simp,[status(thm)],[73]) ).
thf(28,axiom,
! [A: $i] :
( ( A @ c )
= ( A @ domain @ antidomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',complement) ).
thf(117,plain,
! [A: $i] :
( ( A @ c )
= ( A @ domain @ antidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(438,plain,
! [A: $i] :
( ( ( one @ codomain @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( zero @ codomain @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[428,104]) ).
thf(439,plain,
( ( zero @ codomain @ ( one @ codomain @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[438:[bind(A,$thf( one @ codomain ))]]) ).
thf(5,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',left_distributivity) ).
thf(43,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)],[5]) ).
thf(44,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) ) ),
inference(cnf,[status(esa)],[43]) ).
thf(45,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) )
= ( C @ ( B @ ( A @ addition ) @ multiplication ) ) ),
inference(lifteq,[status(thm)],[44]) ).
thf(7,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain @ ( B @ ( A @ multiplication ) @ coantidomain @ addition ) )
= ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',codomain2) ).
thf(49,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain @ ( B @ ( A @ multiplication ) @ coantidomain @ addition ) )
= ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain @ ( B @ ( A @ multiplication ) @ coantidomain @ addition ) )
= ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain ) ),
inference(cnf,[status(esa)],[49]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain @ ( B @ ( A @ multiplication ) @ coantidomain @ addition ) )
= ( B @ ( A @ coantidomain @ coantidomain @ multiplication ) @ coantidomain ) ),
inference(lifteq,[status(thm)],[50]) ).
thf(496,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ codomain @ multiplication ) @ coantidomain @ ( B @ ( A @ multiplication ) @ coantidomain @ addition ) )
= ( B @ ( A @ codomain @ multiplication ) @ coantidomain ) ),
inference(rewrite,[status(thm)],[51,48]) ).
thf(509,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ multiplication ) @ ( C @ ( A @ multiplication ) @ addition ) )
!= ( E @ ( D @ codomain @ multiplication ) @ coantidomain @ ( E @ ( D @ multiplication ) @ coantidomain @ addition ) ) )
| ( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( E @ ( D @ codomain @ multiplication ) @ coantidomain ) ) ),
inference(paramod_ordered,[status(thm)],[45,496]) ).
thf(552,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ multiplication ) )
!= ( E @ ( D @ codomain @ multiplication ) @ coantidomain ) )
| ( ( C @ ( A @ multiplication ) )
!= ( E @ ( D @ multiplication ) @ coantidomain ) )
| ( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
= ( E @ ( D @ codomain @ multiplication ) @ coantidomain ) ) ),
inference(simp,[status(thm)],[509]) ).
thf(783,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( A @ addition ) @ multiplication ) )
!= ( J @ ( I @ codomain @ multiplication ) ) )
| ( ( H @ ( G @ multiplication ) )
!= ( J @ ( I @ codomain @ multiplication ) @ coantidomain ) )
| ( ( H @ ( F @ multiplication ) )
!= ( J @ ( I @ multiplication ) @ coantidomain ) )
| ( ( E @ ( D @ codomain @ multiplication ) @ coantidomain @ coantidomain )
= ( H @ ( G @ ( F @ addition ) @ multiplication ) ) )
| ( ( C @ ( B @ multiplication ) )
!= ( E @ ( D @ codomain @ multiplication ) @ coantidomain ) )
| ( ( C @ ( A @ multiplication ) )
!= ( E @ ( D @ multiplication ) @ coantidomain ) ) ),
inference(paramod_ordered,[status(thm)],[552,552]) ).
thf(937,plain,
! [J: $i,I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( C != J )
| ( ( B @ ( A @ addition ) )
!= ( I @ codomain ) )
| ( ( H @ ( G @ multiplication ) )
!= ( J @ ( I @ codomain @ multiplication ) @ coantidomain ) )
| ( ( H @ ( F @ multiplication ) )
!= ( J @ ( I @ multiplication ) @ coantidomain ) )
| ( ( C @ ( B @ multiplication ) )
!= ( E @ ( D @ codomain @ multiplication ) @ coantidomain ) )
| ( ( C @ ( A @ multiplication ) )
!= ( E @ ( D @ multiplication ) @ coantidomain ) )
| ( ( E @ ( D @ codomain @ multiplication ) @ coantidomain @ coantidomain )
= ( H @ ( G @ ( F @ addition ) @ multiplication ) ) ) ),
inference(simp,[status(thm)],[783]) ).
thf(1024,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( H @ codomain ) )
| ( ( G @ ( F @ multiplication ) )
!= ( I @ ( H @ codomain @ multiplication ) @ coantidomain ) )
| ( ( G @ ( E @ multiplication ) )
!= ( I @ ( H @ multiplication ) @ coantidomain ) )
| ( ( I @ ( B @ multiplication ) )
!= ( D @ ( C @ codomain @ multiplication ) @ coantidomain ) )
| ( ( I @ ( A @ multiplication ) )
!= ( D @ ( C @ multiplication ) @ coantidomain ) )
| ( ( D @ ( C @ codomain @ multiplication ) @ coantidomain @ coantidomain )
= ( G @ ( F @ ( E @ addition ) @ multiplication ) ) ) ),
inference(simp,[status(thm)],[937]) ).
thf(1047,plain,
! [I: $i,H: $i,G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
!= ( H @ codomain ) )
| ( ( G @ ( F @ multiplication ) )
!= ( I @ ( H @ codomain @ multiplication ) @ coantidomain ) )
| ( ( G @ ( E @ multiplication ) )
!= ( I @ ( H @ multiplication ) @ coantidomain ) )
| ( ( I @ ( B @ multiplication ) )
!= ( D @ ( C @ codomain @ multiplication ) @ coantidomain ) )
| ( ( I @ ( A @ multiplication ) )
!= ( D @ ( C @ multiplication ) @ coantidomain ) )
| ( ( D @ ( C @ codomain @ multiplication ) @ codomain )
= ( G @ ( F @ ( E @ addition ) @ multiplication ) ) ) ),
inference(rewrite,[status(thm)],[1024,48]) ).
thf(12,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',right_distributivity) ).
thf(64,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)],[12]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ backward_box ) )
= ( B @ c @ ( A @ backward_diamond ) @ c ) ),
inference(cnf,[status(esa)],[52]) ).
thf(54,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ backward_box ) )
= ( B @ c @ ( A @ backward_diamond ) @ c ) ),
inference(lifteq,[status(thm)],[53]) ).
thf(662,plain,
! [A: $i] :
( ( ( one @ codomain @ codomain @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( zero @ codomain @ codomain @ coantidomain )
= ( A @ codomain ) ) ),
inference(paramod_ordered,[status(thm)],[587,48]) ).
thf(663,plain,
( ( zero @ codomain @ codomain @ coantidomain )
= ( one @ codomain @ codomain @ codomain ) ),
inference(pattern_uni,[status(thm)],[662:[bind(A,$thf( one @ codomain @ codomain ))]]) ).
thf(1637,plain,
! [A: $i] :
( ( ( zero @ codomain @ codomain @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( one @ codomain @ codomain @ codomain @ coantidomain )
= ( A @ codomain ) ) ),
inference(paramod_ordered,[status(thm)],[663,48]) ).
thf(1638,plain,
( ( one @ codomain @ codomain @ codomain @ coantidomain )
= ( zero @ codomain @ codomain @ codomain ) ),
inference(pattern_uni,[status(thm)],[1637:[bind(A,$thf( zero @ codomain @ codomain ))]]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ forward_diamond ) )
= ( B @ domain @ ( A @ multiplication ) @ domain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_diamond) ).
thf(81,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ forward_diamond ) )
= ( B @ domain @ ( A @ multiplication ) @ domain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(38,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ multiplication ) @ ( A @ multiplication ) )
= ( C @ ( B @ ( A @ multiplication ) @ multiplication ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( B @ ( A @ multiplication ) @ multiplication ) )
= ( C @ ( B @ multiplication ) @ ( A @ multiplication ) ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ domain @ ( A @ domain @ ( B @ forward_diamond ) @ addition ) @ ( A @ domain @ addition ) )
= ( C @ domain @ ( A @ domain @ ( B @ forward_diamond ) @ addition ) ) )
=> ( ( C @ domain @ ( B @ star @ forward_diamond ) @ ( B @ divergence @ addition ) @ ( A @ domain @ addition ) )
= ( C @ domain @ ( B @ star @ forward_diamond ) @ ( B @ divergence @ addition ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence2) ).
thf(108,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ domain @ ( A @ domain @ ( B @ forward_diamond ) @ addition ) @ ( A @ domain @ addition ) )
= ( C @ domain @ ( A @ domain @ ( B @ forward_diamond ) @ addition ) ) )
=> ( ( C @ domain @ ( B @ star @ forward_diamond ) @ ( B @ divergence @ addition ) @ ( A @ domain @ addition ) )
= ( C @ domain @ ( B @ star @ forward_diamond ) @ ( B @ divergence @ addition ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(33,plain,
( ( sk1 @ divergence )
= zero ),
inference(cnfConj,[status(thm)],[32]) ).
thf(35,plain,
( ( sk1 @ divergence )
= zero ),
inference(lifteq,[status(thm)],[33]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ divergence @ ( A @ forward_diamond ) )
= ( A @ divergence ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',divergence1) ).
thf(123,plain,
! [A: $i] :
( ( A @ divergence @ ( A @ forward_diamond ) )
= ( A @ divergence ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(94,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(cnf,[status(esa)],[93]) ).
thf(95,plain,
! [A: $i] :
( ( A @ ( zero @ multiplication ) )
= zero ),
inference(lifteq,[status(thm)],[94]) ).
thf(655,plain,
! [A: $i] :
( ( ( one @ codomain @ codomain @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( zero @ codomain @ codomain @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[587,104]) ).
thf(656,plain,
( ( zero @ codomain @ codomain @ ( one @ codomain @ codomain @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[655:[bind(A,$thf( one @ codomain @ codomain ))]]) ).
thf(70,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ addition ) )
= B )
| ~ ( B @ ( A @ leq ) ) ),
inference(cnfConj,[status(thm)],[69]) ).
thf(72,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ leq ) )
| ( ( B @ ( A @ addition ) )
= B ) ),
inference(lifteq,[status(thm)],[70]) ).
thf(9,axiom,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',additive_idempotence) ).
thf(55,plain,
! [A: $i] :
( ( A @ ( A @ addition ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(27,axiom,
! [A: $i] :
( ( A @ domain )
= ( A @ antidomain @ antidomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain4) ).
thf(114,plain,
! [A: $i] :
( ( A @ domain )
= ( A @ antidomain @ antidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ domain_difference ) )
= ( B @ antidomain @ ( A @ domain @ multiplication ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_difference) ).
thf(75,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ domain_difference ) )
= ( B @ antidomain @ ( A @ domain @ multiplication ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(10,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ backward_diamond ) )
= ( A @ ( B @ codomain @ multiplication ) @ codomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',backward_diamond) ).
thf(58,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ backward_diamond ) )
= ( A @ ( B @ codomain @ multiplication ) @ codomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(121,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(cnf,[status(esa)],[120]) ).
thf(122,plain,
! [A: $i] :
( ( zero @ ( A @ addition ) )
= A ),
inference(lifteq,[status(thm)],[121]) ).
thf(240,plain,
! [C: $i,B: $i,A: $i] :
( ( ( zero @ ( A @ addition ) )
!= ( C @ ( B @ addition ) ) )
| ( C @ ( B @ leq ) )
| ( A != C ) ),
inference(paramod_ordered,[status(thm)],[122,74]) ).
thf(241,plain,
! [A: $i] :
( ( zero @ ( A @ leq ) )
| ( A != zero ) ),
inference(pattern_uni,[status(thm)],[240:[bind(A,$thf( A )),bind(B,$thf( A )),bind(C,$thf( zero ))]]) ).
thf(246,plain,
zero @ ( zero @ leq ),
inference(simp,[status(thm)],[241]) ).
thf(1624,plain,
! [A: $i] :
( ( ( zero @ codomain @ codomain @ coantidomain )
!= ( A @ coantidomain ) )
| ( ( one @ codomain @ codomain @ codomain @ ( A @ multiplication ) )
= zero ) ),
inference(paramod_ordered,[status(thm)],[663,104]) ).
thf(1625,plain,
( ( one @ codomain @ codomain @ codomain @ ( zero @ codomain @ codomain @ multiplication ) )
= zero ),
inference(pattern_uni,[status(thm)],[1624:[bind(A,$thf( zero @ codomain @ codomain ))]]) ).
thf(306,plain,
( ( ( sk1 @ antidomain )
!= ( one @ antidomain ) )
| ( ( zero @ ( sk1 @ star @ forward_diamond ) )
!= one ) ),
inference(paramod_ordered,[status(thm)],[284,36]) ).
thf(309,plain,
( ( sk1 != one )
| ( ( zero @ ( sk1 @ star @ forward_diamond ) )
!= one ) ),
inference(simp,[status(thm)],[306]) ).
thf(19,axiom,
! [A: $i,B: $i] :
( ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain @ ( B @ ( A @ multiplication ) @ antidomain @ addition ) )
= ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain2) ).
thf(90,plain,
! [A: $i,B: $i] :
( ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain @ ( B @ ( A @ multiplication ) @ antidomain @ addition ) )
= ( B @ antidomain @ antidomain @ ( A @ multiplication ) @ antidomain ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ forward_box ) )
= ( B @ c @ ( A @ forward_diamond ) @ c ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',forward_box) ).
thf(111,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ forward_box ) )
= ( B @ c @ ( A @ forward_diamond ) @ c ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(3156,plain,
$false,
inference(e,[status(thm)],[101,96,105,442,582,120,42,37,52,587,46,93,284,78,164,84,61,89,428,74,117,439,102,1047,45,64,54,49,1638,81,39,98,552,108,80,35,663,123,48,95,67,31,656,72,43,99,87,104,40,55,114,75,58,246,315,36,1625,122,354,309,496,90,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : KLE135+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.10 % 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
% 0.10/0.40 % Computer : n003.cluster.edu
% 0.10/0.40 % Model : x86_64 x86_64
% 0.10/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.40 % Memory : 8046.5625MB
% 0.10/0.40 % OS : Linux 6.8.0-71-generic
% 0.10/0.40 % CPULimit : 300
% 0.10/0.40 % WCLimit : 300
% 0.10/0.40 % DateTime : Fri Sep 25 19:27:08 UTC 2026
% 0.10/0.40 % CPUTime :
% 0.10/0.40 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
% 0.73/1.13 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.09/1.39 % [INFO] Parsing done (254ms).
% 1.09/1.40 % [INFO] Running in sequential loop mode.
% 1.90/1.74 % [INFO] eprover registered as external prover.
% 1.90/1.76 % [INFO] Scanning for conjecture ...
% 2.09/1.82 % [INFO] Found a conjecture (or negated_conjecture) and 28 axioms. Running axiom selection ...
% 2.09/1.89 % [INFO] Axiom selection finished. Selected 28 axioms (removed 0 axioms).
% 2.27/1.99 % [INFO] Problem is first-order (TPTP FOF).
% 2.43/2.00 % [INFO] Type checking passed.
% 2.43/2.01 % [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 ...
% 24.89/10.14 % External prover 'e' found a proof!
% 24.89/10.14 % [INFO] Killing All external provers ...
% 24.89/10.14 % Time passed: 9548ms (effective reasoning time: 8742ms)
% 24.89/10.15 % 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)>
% 24.89/10.15 % Axioms used in derivation (28): forward_box, additive_identity, domain4, backward_box, domain3, codomain2, complement, right_annihilation, backward_diamond, forward_diamond, codomain4, left_annihilation, codomain1, additive_idempotence, additive_associativity, right_distributivity, domain2, divergence2, multiplicative_right_identity, order, additive_commutativity, domain_difference, multiplicative_left_identity, codomain3, domain1, divergence1, multiplicative_associativity, left_distributivity
% 24.89/10.15 % No. of inferences in proof: 140
% 24.89/10.15 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 9548 ms resp. 8742 ms w/o parsing
% 25.82/10.31 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.82/10.31 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------