%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV486+2 : 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 : n016.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 08:59:35 AM UTC 2026
% Result : Theorem 10.39s 3.96s
% Output : Refutation 11.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 15
% Syntax : Number of formulae : 121 ( 35 unt; 0 typ; 2 def)
% Number of atoms : 442 ( 140 equ; 0 cnn)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 1228 ( 209 ~; 181 |; 48 &; 756 @)
% ( 3 <=>; 31 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 188 ( 0 ^; 183 !; 3 ?; 188 :)
% ( 0 !>; 0 ?*; 0 @-; 2 @+)
% Comments :
%------------------------------------------------------------------------------
thf(int_leq_decl,type,
int_leq: $i > $i > $o ).
thf(int_one_decl,type,
int_one: $i ).
thf(int_less_decl,type,
int_less: $i > $i > $o ).
thf(n_decl,type,
n: $i ).
thf(a_decl,type,
a: $i > $i > $i ).
thf(real_zero_decl,type,
real_zero: $i ).
thf(int_zero_decl,type,
int_zero: $i ).
thf(plus_decl,type,
plus: $i > $i > $i ).
thf(real_one_decl,type,
real_one: $i ).
thf(lu_decl,type,
lu: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( A @ int_less ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( n @ ( A @ int_leq ) )
& ( A @ ( sk1 @ int_less ) )
& ( sk1 @ ( int_one @ int_leq ) ) )
=> ( ( A @ ( sk1 @ a ) )
= real_zero ) ) ) ) ).
thf(7,axiom,
int_one @ ( int_zero @ int_less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_zero_one) ).
thf(40,plain,
int_one @ ( int_zero @ int_less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_irreflexive) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(37,plain,
! [A: $i] :
~ ( A @ ( A @ int_less ) ),
inference(simp,[status(thm)],[36]) ).
thf(82,plain,
! [A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,37]) ).
thf(83,plain,
! [A: $i] :
( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[82]) ).
thf(84,plain,
! [A: $i] :
( ( int_one != A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[83]) ).
thf(85,plain,
int_zero != int_one,
inference(simp,[status(thm)],[84]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( int_one @ int_leq ) )
& ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ! [C: $i] :
( ( ( B
= ( C @ ( A @ plus ) ) )
& ( C @ ( int_zero @ int_less ) ) )
=> ! [D: $i] :
( ( ( A @ ( D @ int_leq ) )
& ( D @ ( int_one @ int_leq ) ) )
=> ( ( C @ ( D @ plus ) @ ( D @ a ) )
= real_zero ) ) )
& ! [C: $i] :
( ( ( B @ ( C @ int_leq ) )
& ( C @ ( int_one @ int_leq ) ) )
=> ( ( C @ ( C @ a ) )
= real_one ) )
& ! [C: $i] :
( ( ( A
= ( C @ ( B @ plus ) ) )
& ( C @ ( int_zero @ int_less ) ) )
=> ! [D: $i] :
( ( ( B @ ( D @ int_leq ) )
& ( D @ ( int_one @ int_leq ) ) )
=> ( ( D @ ( C @ ( D @ plus ) @ a ) )
= ( D @ ( C @ ( D @ plus ) @ lu ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qil) ).
thf(67,plain,
! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( int_one @ int_leq ) )
& ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ! [C: $i] :
( ( ( B
= ( C @ ( A @ plus ) ) )
& ( C @ ( int_zero @ int_less ) ) )
=> ! [D: $i] :
( ( ( A @ ( D @ int_leq ) )
& ( D @ ( int_one @ int_leq ) ) )
=> ( ( C @ ( D @ plus ) @ ( D @ a ) )
= real_zero ) ) )
& ! [C: $i] :
( ( ( B @ ( C @ int_leq ) )
& ( C @ ( int_one @ int_leq ) ) )
=> ( ( C @ ( C @ a ) )
= real_one ) )
& ! [C: $i] :
( ( ( A
= ( C @ ( B @ plus ) ) )
& ( C @ ( int_zero @ int_less ) ) )
=> ! [D: $i] :
( ( ( B @ ( D @ int_leq ) )
& ( D @ ( int_one @ int_leq ) ) )
=> ( ( D @ ( C @ ( D @ plus ) @ a ) )
= ( D @ ( C @ ( D @ plus ) @ lu ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(68,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( F @ ( G @ plus ) @ ( G @ a ) )
= real_zero )
| ~ ( A @ ( G @ int_leq ) )
| ~ ( G @ ( int_one @ int_leq ) )
| ( B
!= ( F @ ( A @ plus ) ) )
| ~ ( F @ ( int_zero @ int_less ) )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) ) )
& ( ( ( E @ ( E @ a ) )
= real_one )
| ~ ( B @ ( E @ int_leq ) )
| ~ ( E @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) ) )
& ( ( ( D @ ( C @ ( D @ plus ) @ a ) )
= ( D @ ( C @ ( D @ plus ) @ lu ) ) )
| ~ ( B @ ( D @ int_leq ) )
| ~ ( D @ ( int_one @ int_leq ) )
| ( A
!= ( C @ ( B @ plus ) ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) ) ) ),
inference(cnf,[status(esa)],[67]) ).
thf(71,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( D @ plus ) @ ( D @ a ) )
= real_zero )
| ~ ( A @ ( D @ int_leq ) )
| ~ ( D @ ( int_one @ int_leq ) )
| ( B
!= ( C @ ( A @ plus ) ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[68]) ).
thf(76,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( A @ ( D @ int_leq ) )
| ~ ( D @ ( int_one @ int_leq ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( ( C @ ( D @ plus ) @ ( D @ a ) )
= real_zero )
| ( B
!= ( C @ ( A @ plus ) ) ) ),
inference(lifteq,[status(thm)],[71]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( ( B @ ( C @ plus ) @ ( C @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[76]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_commutative) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ int_less ) )
& ( B @ ( A @ int_less ) ) )
=> ( C @ ( A @ int_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_transitive) ).
thf(32,plain,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ int_less ) )
& ( B @ ( A @ int_less ) ) )
=> ( C @ ( A @ int_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(33,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ int_less ) )
| ~ ( C @ ( B @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(908,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ int_less ) )
!= ( D @ ( D @ int_less ) ) )
| ~ $true
| ~ ( C @ ( B @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[33,37]) ).
thf(909,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ int_less ) )
!= ( D @ ( D @ int_less ) ) )
| ~ ( C @ ( B @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[908]) ).
thf(910,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ~ ( A @ ( B @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[909:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(938,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ~ ( A @ ( B @ int_less ) ) ),
inference(simp,[status(thm)],[910]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( A @ int_less ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lt) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( A @ int_less ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
~ ! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( A @ int_less ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
( ( ( sk2 @ ( sk1 @ a ) )
!= real_zero )
& ( n @ ( sk2 @ int_leq ) )
& ( sk2 @ ( sk1 @ int_less ) )
& ( sk1 @ ( int_one @ int_leq ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(20,plain,
( ( sk2 @ ( sk1 @ a ) )
!= real_zero ),
inference(cnfConj,[status(thm)],[16]) ).
thf(21,plain,
( ( sk2 @ ( sk1 @ a ) )
!= real_zero ),
inference(lifteq,[status(thm)],[20]) ).
thf(347,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ plus ) @ ( C @ a ) )
!= ( sk2 @ ( sk1 @ a ) ) )
| ( real_zero != real_zero )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[77,21]) ).
thf(348,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ plus ) @ ( C @ a ) )
!= ( sk2 @ ( sk1 @ a ) ) )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[347]) ).
thf(361,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( C @ plus ) )
!= sk2 )
| ( C != sk1 )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[348]) ).
thf(419,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk1 @ plus ) )
!= sk2 )
| ~ ( A @ ( sk1 @ int_leq ) )
| ~ ( sk1 @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[361]) ).
thf(17,plain,
sk1 @ ( int_one @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
thf(437,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk1 @ plus ) )
!= sk2 )
| ~ ( A @ ( sk1 @ int_leq ) )
| ~ $true
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(rewrite,[status(thm)],[419,17]) ).
thf(438,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk1 @ plus ) )
!= sk2 )
| ~ ( A @ ( sk1 @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[437]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ int_leq ) )
<=> ( ( A = B )
| ( B @ ( A @ int_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_leq) ).
thf(22,plain,
! [A: $i,B: $i] :
( ( ( ( A = B )
| ( B @ ( A @ int_less ) ) )
=> ( B @ ( A @ int_leq ) ) )
& ( ( B @ ( A @ int_leq ) )
=> ( ( A = B )
| ( B @ ( A @ int_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(23,plain,
( ! [A: $i,B: $i] :
( ( ( A = B )
| ( B @ ( A @ int_less ) ) )
=> ( B @ ( A @ int_leq ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ int_leq ) )
=> ( ( A = B )
| ( B @ ( A @ int_less ) ) ) ) ),
inference(miniscope,[status(thm)],[22]) ).
thf(24,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ int_leq ) )
| ( C != D ) )
& ( ( D @ ( C @ int_leq ) )
| ~ ( D @ ( C @ int_less ) ) )
& ( ( A = B )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ) ),
inference(cnf,[status(esa)],[23]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[17,28]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[101]) ).
thf(103,plain,
( ( sk1 @ ( int_one @ int_less ) )
| ( sk1 = int_one ) ),
inference(pattern_uni,[status(thm)],[102:[bind(A,$thf( int_one )),bind(B,$thf( sk1 ))]]) ).
thf(18,plain,
sk2 @ ( sk1 @ int_less ),
inference(cnfConj,[status(thm)],[16]) ).
thf(626,plain,
( ( sk1 != sk1 )
| ( sk2 @ ( int_one @ int_less ) )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[103,18]) ).
thf(627,plain,
( ( sk2 @ ( int_one @ int_less ) )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[626:[]]) ).
thf(19,plain,
n @ ( sk2 @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[19,28]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
( ( n @ ( sk2 @ int_less ) )
| ( sk2 = n ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( sk2 )),bind(B,$thf( n ))]]) ).
thf(953,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true
| ( sk2 = n ) ),
inference(paramod_ordered,[status(thm)],[138,938]) ).
thf(954,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk2 = n ) ),
inference(simp,[status(thm)],[953]) ).
thf(955,plain,
( ~ ( sk2 @ ( n @ int_less ) )
| ( sk2 = n ) ),
inference(pattern_uni,[status(thm)],[954:[bind(A,$thf( n )),bind(B,$thf( sk2 ))]]) ).
thf(78,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18,37]) ).
thf(79,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[78]) ).
thf(80,plain,
! [A: $i] :
( ( sk2 != A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[79]) ).
thf(81,plain,
sk2 != sk1,
inference(simp,[status(thm)],[80]) ).
thf(659,plain,
( ( sk2 != sk2 )
| ( sk1 != n )
| ( n @ ( sk2 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[138,81]) ).
thf(660,plain,
( ( sk1 != n )
| ( n @ ( sk2 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[659:[]]) ).
thf(965,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18,938]) ).
thf(966,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[965]) ).
thf(967,plain,
~ ( sk1 @ ( sk2 @ int_less ) ),
inference(pattern_uni,[status(thm)],[966:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(1001,plain,
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( n @ ( sk2 @ int_less ) ) )
| ~ $true
| ( sk1 != n ) ),
inference(paramod_ordered,[status(thm)],[660,967]) ).
thf(1002,plain,
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( n @ ( sk2 @ int_less ) ) )
| ( sk1 != n ) ),
inference(simp,[status(thm)],[1001]) ).
thf(1026,plain,
( ( sk1 != n )
| ( sk2 != sk2 )
| ( sk1 != n ) ),
inference(simp,[status(thm)],[1002]) ).
thf(1031,plain,
sk1 != n,
inference(simp,[status(thm)],[1026]) ).
thf(9,axiom,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_zero) ).
thf(44,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(45,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(lifteq,[status(thm)],[45]) ).
thf(184,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_zero @ ( C @ plus ) ) )
| ( ( A @ ( B @ plus ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[43,46]) ).
thf(185,plain,
! [A: $i] :
( ( A @ ( int_zero @ plus ) )
= A ),
inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( A )),bind(B,$thf( int_zero )),bind(C,$thf( A ))]]) ).
thf(971,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,938]) ).
thf(972,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[971]) ).
thf(973,plain,
~ ( int_zero @ ( int_one @ int_less ) ),
inference(pattern_uni,[status(thm)],[972:[bind(A,$thf( int_one )),bind(B,$thf( int_zero ))]]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_total) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(13,axiom,
real_zero != real_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',real_constants) ).
thf(64,plain,
real_zero != real_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(730,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18,29]) ).
thf(731,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[730]) ).
thf(732,plain,
sk2 @ ( sk1 @ int_leq ),
inference(pattern_uni,[status(thm)],[731:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(1101,plain,
( ( ( sk1 @ ( int_one @ int_less ) )
!= ( int_zero @ ( int_one @ int_less ) ) )
| ~ $true
| ( sk1 = int_one ) ),
inference(paramod_ordered,[status(thm)],[103,973]) ).
thf(1102,plain,
( ( ( sk1 @ ( int_one @ int_less ) )
!= ( int_zero @ ( int_one @ int_less ) ) )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[1101]) ).
thf(1105,plain,
( ( sk1 != int_zero )
| ( int_one != int_one )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[1102]) ).
thf(1107,plain,
( ( sk1 != int_zero )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[1105]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
<=> ? [C: $i] :
( ( C @ ( int_zero @ int_less ) )
& ( ( C @ ( A @ plus ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_and_inverse) ).
thf(49,plain,
! [A: $i,B: $i] :
( ( ? [C: $i] :
( ( C @ ( int_zero @ int_less ) )
& ( ( C @ ( A @ plus ) )
= B ) )
=> ( B @ ( A @ int_less ) ) )
& ( ( B @ ( A @ int_less ) )
=> ? [C: $i] :
( ( C @ ( int_zero @ int_less ) )
& ( ( C @ ( A @ plus ) )
= B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(65,plain,
real_zero != real_one,
inference(polarity_switch,[status(thm)],[64]) ).
thf(66,plain,
real_one != real_zero,
inference(lifteq,[status(thm)],[65]) ).
thf(1005,plain,
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( int_one @ ( int_zero @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,967]) ).
thf(1006,plain,
( ( sk1 @ ( sk2 @ int_less ) )
!= ( int_one @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[1005]) ).
thf(1029,plain,
( ( sk1 != int_one )
| ( sk2 != int_zero ) ),
inference(simp,[status(thm)],[1006]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ int_leq ) )
& ( B @ ( A @ int_less ) ) )
=> ( D @ ( B @ plus ) @ ( C @ ( A @ plus ) @ int_leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_and_order1) ).
thf(47,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ int_leq ) )
& ( B @ ( A @ int_less ) ) )
=> ( D @ ( B @ plus ) @ ( C @ ( A @ plus ) @ int_leq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(48,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( D @ ( B @ plus ) @ ( C @ ( A @ plus ) @ int_leq ) )
| ~ ( D @ ( C @ int_leq ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[47]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(31,plain,
! [A: $i] : ( A @ ( A @ int_leq ) ),
inference(simp,[status(thm)],[30]) ).
thf(1023,plain,
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( sk1 @ ( int_one @ int_less ) ) )
| ~ $true
| ( sk1 = int_one ) ),
inference(paramod_ordered,[status(thm)],[103,967]) ).
thf(1024,plain,
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( sk1 @ ( int_one @ int_less ) ) )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[1023]) ).
thf(1025,plain,
( ( sk1 != sk1 )
| ( sk2 != int_one )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[1024]) ).
thf(1030,plain,
( ( sk2 != int_one )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[1025]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( int_zero @ int_less ) )
<=> ( A @ ( int_one @ int_leq ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',one_successor_of_zero) ).
thf(58,plain,
! [A: $i] :
( ( ( A @ ( int_one @ int_leq ) )
=> ( A @ ( int_zero @ int_less ) ) )
& ( ( A @ ( int_zero @ int_less ) )
=> ( A @ ( int_one @ int_leq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(733,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,29]) ).
thf(734,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[733]) ).
thf(735,plain,
int_one @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[734:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(1567,plain,
$false,
inference(e,[status(thm)],[85,77,41,938,438,43,627,40,955,138,1031,185,973,37,46,29,21,33,28,38,64,17,32,34,732,22,44,1107,49,81,39,103,66,1029,48,18,67,31,1030,58,967,19,735,47,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV486+2 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % 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
% 0.16/0.42 % Computer : n016.cluster.edu
% 0.16/0.42 % Model : x86_64 x86_64
% 0.16/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.42 % Memory : 8046.5625MB
% 0.16/0.42 % OS : Linux 6.8.0-71-generic
% 0.16/0.42 % CPULimit : 300
% 0.16/0.42 % WCLimit : 300
% 0.16/0.42 % DateTime : Sat Sep 26 14:02:50 UTC 2026
% 0.16/0.42 % CPUTime :
% 0.16/0.42 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
% 0.84/1.01 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.32/1.21 % [INFO] Parsing done (197ms).
% 1.32/1.22 % [INFO] Running in sequential loop mode.
% 1.93/1.62 % [INFO] eprover registered as external prover.
% 1.93/1.63 % [INFO] Scanning for conjecture ...
% 2.09/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.09/1.79 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.24/1.82 % [INFO] Problem is first-order (TPTP FOF).
% 2.24/1.83 % [INFO] Type checking passed.
% 2.24/1.83 % [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 ...
% 10.39/3.95 % External prover 'e' found a proof!
% 10.39/3.95 % [INFO] Killing All external provers ...
% 10.39/3.96 % Time passed: 3391ms (effective reasoning time: 2726ms)
% 10.39/3.96 % 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)>
% 10.39/3.96 % Axioms used in derivation (12): plus_and_order1, qil, int_less_total, int_leq, int_less_transitive, int_zero_one, plus_and_inverse, int_less_irreflexive, plus_commutative, real_constants, plus_zero, one_successor_of_zero
% 10.39/3.96 % No. of inferences in proof: 119
% 10.39/3.96 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3391 ms resp. 2726 ms w/o parsing
% 11.18/4.04 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 11.18/4.05 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------