%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV489+3 : 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 : n014.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 08:59:36 AM UTC 2026
% Result : Theorem 139.63s 35.43s
% Output : Refutation 138.60s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 16
% Syntax : Number of formulae : 263 ( 68 unt; 0 typ; 3 def)
% Number of atoms : 928 ( 304 equ; 0 cnn)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 2490 ( 456 ~; 400 |; 68 &;1528 @)
% ( 3 <=>; 35 =>; 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 : 369 ( 2 ^; 359 !; 5 ?; 369 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(int_leq_decl,type,
int_leq: $i > $i > $o ).
thf(int_one_decl,type,
int_one: $i ).
thf(n_decl,type,
n: $i ).
thf(a_decl,type,
a: $i > $i > $i ).
thf(real_zero_decl,type,
real_zero: $i ).
thf(int_less_decl,type,
int_less: $i > $i > $o ).
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(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( A != B )
& ( n @ ( B @ int_leq ) )
& ( B @ ( int_one @ int_leq ) )
& ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( sk1 != A )
& ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) )
& ( n @ ( sk1 @ int_leq ) )
& ( sk1 @ ( int_one @ int_leq ) ) )
=> ( ( A @ ( sk1 @ a ) )
= real_zero ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ ( int_zero @ int_less ) )
& ( ( C @ ( B @ plus ) )
= A ) ) ) ) ).
thf(7,axiom,
int_one @ ( int_zero @ int_less ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_zero_one) ).
thf(43,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/sandbox/benchmark/theBenchmark.p',int_less_irreflexive) ).
thf(37,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[37]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[38]) ).
thf(40,plain,
! [A: $i] :
~ ( A @ ( A @ int_less ) ),
inference(simp,[status(thm)],[39]) ).
thf(81,plain,
! [A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,40]) ).
thf(82,plain,
! [A: $i] :
( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[81]) ).
thf(83,plain,
! [A: $i] :
( ( int_one != A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[82]) ).
thf(84,plain,
int_zero != int_one,
inference(simp,[status(thm)],[83]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( int_zero @ int_less ) )
<=> ( A @ ( int_one @ int_leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_successor_of_zero) ).
thf(61,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(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
<=> ? [C: $i] :
( ( C @ ( int_zero @ int_less ) )
& ( ( C @ ( A @ plus ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_and_inverse) ).
thf(52,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(53,plain,
( ! [A: $i,B: $i] :
( ? [C: $i] :
( ( C @ ( int_zero @ int_less ) )
& ( ( C @ ( A @ plus ) )
= B ) )
=> ( B @ ( A @ int_less ) ) )
& ! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
=> ? [C: $i] :
( ( C @ ( int_zero @ int_less ) )
& ( ( C @ ( A @ plus ) )
= B ) ) ) ),
inference(miniscope,[status(thm)],[52]) ).
thf(54,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ int_less ) )
| ~ ( E @ ( int_zero @ int_less ) )
| ( ( E @ ( C @ plus ) )
!= D ) )
& ( ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) )
& ( ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B )
| ~ ( B @ ( A @ int_less ) ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(57,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ int_less ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ( ( C @ ( A @ plus ) )
!= B ) ),
inference(cnfConj,[status(thm)],[54]) ).
thf(59,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ int_less ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ( ( C @ ( A @ plus ) )
!= B ) ),
inference(lifteq,[status(thm)],[57]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) @ ( A @ int_less ) )
| ~ ( B @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[59]) ).
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 ) )
= real_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qii) ).
thf(70,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 ) )
= real_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(71,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 ) )
= real_zero )
| ~ ( 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)],[70]) ).
thf(72,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( D @ plus ) @ a ) )
= real_zero )
| ~ ( 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(cnfConj,[status(thm)],[71]) ).
thf(75,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ~ ( B @ ( 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 ) )
| ( ( D @ ( C @ ( D @ plus ) @ a ) )
= real_zero )
| ( A
!= ( C @ ( B @ plus ) ) ) ),
inference(lifteq,[status(thm)],[72]) ).
thf(76,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[75]) ).
thf(1,conjecture,
! [A: $i,B: $i] :
( ( ( A != B )
& ( n @ ( B @ int_leq ) )
& ( B @ ( int_one @ int_leq ) )
& ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',d) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( A != B )
& ( n @ ( B @ int_leq ) )
& ( B @ ( int_one @ int_leq ) )
& ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
~ ! [A: $i,B: $i] :
( ( ( A != B )
& ( n @ ( B @ int_leq ) )
& ( B @ ( int_one @ int_leq ) )
& ( n @ ( A @ int_leq ) )
& ( 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 )
& ( sk1 != sk2 )
& ( n @ ( sk2 @ int_leq ) )
& ( sk2 @ ( int_one @ int_leq ) )
& ( n @ ( sk1 @ int_leq ) )
& ( sk1 @ ( int_one @ int_leq ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(18,plain,
( ( sk2 @ ( sk1 @ a ) )
!= real_zero ),
inference(cnfConj,[status(thm)],[16]) ).
thf(23,plain,
( ( sk2 @ ( sk1 @ a ) )
!= real_zero ),
inference(lifteq,[status(thm)],[18]) ).
thf(358,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ plus ) @ a ) )
!= ( sk2 @ ( sk1 @ a ) ) )
| ( real_zero != real_zero )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[76,23]) ).
thf(359,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ plus ) @ a ) )
!= ( sk2 @ ( sk1 @ a ) ) )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[358]) ).
thf(369,plain,
! [C: $i,B: $i,A: $i] :
( ( C != sk2 )
| ( ( B @ ( C @ plus ) )
!= sk1 )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[359]) ).
thf(444,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( A @ ( sk2 @ int_leq ) )
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[369]) ).
thf(20,plain,
sk2 @ ( int_one @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
thf(460,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( A @ ( sk2 @ int_leq ) )
| ~ $true
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) ),
inference(rewrite,[status(thm)],[444,20]) ).
thf(461,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( A @ ( sk2 @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[460]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ int_leq ) )
<=> ( ( A = B )
| ( B @ ( A @ int_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_leq) ).
thf(25,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(26,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)],[25]) ).
thf(27,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)],[26]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[27]) ).
thf(31,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(21,plain,
n @ ( sk1 @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( n @ ( A @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[31,21]) ).
thf(109,plain,
! [A: $i] :
( ( n @ ( A @ int_leq ) )
| ( sk1 @ ( A @ int_less ) )
| ~ ( sk1 @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[108:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(17,plain,
sk1 @ ( int_one @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
thf(123,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)],[17,31]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[123]) ).
thf(125,plain,
( ( sk1 @ ( int_one @ int_less ) )
| ( sk1 = int_one ) ),
inference(pattern_uni,[status(thm)],[124:[bind(A,$thf( int_one )),bind(B,$thf( sk1 ))]]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[20,31]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[101]) ).
thf(103,plain,
( ( sk2 @ ( int_one @ int_less ) )
| ( sk2 = int_one ) ),
inference(pattern_uni,[status(thm)],[102:[bind(A,$thf( int_one )),bind(B,$thf( sk2 ))]]) ).
thf(19,plain,
sk1 != sk2,
inference(cnfConj,[status(thm)],[16]) ).
thf(24,plain,
sk2 != sk1,
inference(lifteq,[status(thm)],[19]) ).
thf(663,plain,
( ( sk2 != sk2 )
| ( sk1 != int_one )
| ( sk2 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[103,24]) ).
thf(664,plain,
( ( sk1 != int_one )
| ( sk2 @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[663:[]]) ).
thf(977,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ( sk1 != int_one ) ),
inference(paramod_ordered,[status(thm)],[664,40]) ).
thf(978,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ( sk1 != int_one ) ),
inference(simp,[status(thm)],[977]) ).
thf(985,plain,
! [A: $i] :
( ( sk2 != A )
| ( int_one != A )
| ( sk1 != int_one ) ),
inference(simp,[status(thm)],[978]) ).
thf(992,plain,
( ( sk2 != int_one )
| ( sk1 != int_one ) ),
inference(simp,[status(thm)],[985]) ).
thf(993,plain,
( ( sk1 != sk1 )
| ( sk2 != int_one )
| ( int_one != int_one )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[125,992]) ).
thf(994,plain,
( ( sk1 != sk1 )
| ( sk2 != int_one )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(simp,[status(thm)],[993]) ).
thf(995,plain,
( ( sk2 != int_one )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[994:[]]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ int_less ) )
& ( B @ ( A @ int_less ) ) )
=> ( C @ ( A @ int_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_transitive) ).
thf(35,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(36,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ int_less ) )
| ~ ( C @ ( B @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[35]) ).
thf(1054,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)],[36,40]) ).
thf(1055,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)],[1054]) ).
thf(1056,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ~ ( A @ ( B @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[1055:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(1077,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ~ ( A @ ( B @ int_less ) ) ),
inference(simp,[status(thm)],[1056]) ).
thf(1418,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true
| ( sk2 != int_one ) ),
inference(paramod_ordered,[status(thm)],[995,1077]) ).
thf(1419,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk2 != int_one ) ),
inference(simp,[status(thm)],[1418]) ).
thf(1420,plain,
( ~ ( int_one @ ( sk1 @ int_less ) )
| ( sk2 != int_one ) ),
inference(pattern_uni,[status(thm)],[1419:[bind(A,$thf( sk1 )),bind(B,$thf( int_one ))]]) ).
thf(112,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk1 @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[21,31]) ).
thf(113,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk1 @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[112]) ).
thf(114,plain,
( ( n @ ( sk1 @ int_less ) )
| ( sk1 = n ) ),
inference(pattern_uni,[status(thm)],[113:[bind(A,$thf( sk1 )),bind(B,$thf( n ))]]) ).
thf(1124,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk1 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true
| ( sk1 = n ) ),
inference(paramod_ordered,[status(thm)],[114,1077]) ).
thf(1125,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk1 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk1 = n ) ),
inference(simp,[status(thm)],[1124]) ).
thf(1126,plain,
( ~ ( sk1 @ ( n @ int_less ) )
| ( sk1 = n ) ),
inference(pattern_uni,[status(thm)],[1125:[bind(A,$thf( n )),bind(B,$thf( sk1 ))]]) ).
thf(13,axiom,
real_zero != real_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',real_constants) ).
thf(67,plain,
real_zero != real_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(68,plain,
real_zero != real_one,
inference(polarity_switch,[status(thm)],[67]) ).
thf(69,plain,
real_one != real_zero,
inference(lifteq,[status(thm)],[68]) ).
thf(62,plain,
( ! [A: $i] :
( ( A @ ( int_one @ int_leq ) )
=> ( A @ ( int_zero @ int_less ) ) )
& ! [A: $i] :
( ( A @ ( int_zero @ int_less ) )
=> ( A @ ( int_one @ int_leq ) ) ) ),
inference(miniscope,[status(thm)],[61]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( ( B @ ( int_zero @ int_less ) )
| ~ ( B @ ( int_one @ int_leq ) ) )
& ( ( A @ ( int_one @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(65,plain,
! [A: $i] :
( ( A @ ( int_zero @ int_less ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(66,plain,
! [A: $i] :
( ( A @ ( int_zero @ int_less ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[65]) ).
thf(3734,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[20,66]) ).
thf(3735,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[3734]) ).
thf(3736,plain,
sk2 @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[3735:[bind(A,$thf( sk2 ))]]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[54]) ).
thf(3853,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3736,56]) ).
thf(3854,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[3853]) ).
thf(3855,plain,
int_zero @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[3854:[bind(A,$thf( int_zero )),bind(B,$thf( sk2 ))]]) ).
thf(4818,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3855,56]) ).
thf(4819,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[4818]) ).
thf(4820,plain,
int_zero @ ( int_zero @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[4819:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( sk2 @ sk3 ) ))]]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[54]) ).
thf(58,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(lifteq,[status(thm)],[55]) ).
thf(3896,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ~ $true
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[3736,58]) ).
thf(3897,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(simp,[status(thm)],[3896]) ).
thf(3898,plain,
( ( int_zero @ ( sk2 @ sk3 ) @ ( int_zero @ plus ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[3897:[bind(A,$thf( int_zero )),bind(B,$thf( sk2 ))]]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_commutative) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(9,axiom,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_zero) ).
thf(47,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(48,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(cnf,[status(esa)],[47]) ).
thf(49,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(lifteq,[status(thm)],[48]) ).
thf(199,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_zero @ ( C @ plus ) ) )
| ( ( A @ ( B @ plus ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[46,49]) ).
thf(200,plain,
! [A: $i] :
( ( A @ ( int_zero @ plus ) )
= A ),
inference(pattern_uni,[status(thm)],[199:[bind(A,$thf( A )),bind(B,$thf( int_zero )),bind(C,$thf( A ))]]) ).
thf(7232,plain,
( ( int_zero @ ( sk2 @ sk3 ) )
= sk2 ),
inference(rewrite,[status(thm)],[3898,200]) ).
thf(7903,plain,
int_zero @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ),
inference(rewrite,[status(thm)],[4820,7232]) ).
thf(3760,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17,66]) ).
thf(3761,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[3760]) ).
thf(3762,plain,
sk1 @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[3761:[bind(A,$thf( sk1 ))]]) ).
thf(119,plain,
! [B: $i,A: $i] :
( ( B != int_one )
| ( sk1 @ ( A @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[31,17]) ).
thf(120,plain,
! [A: $i] :
( ( sk1 @ ( A @ int_leq ) )
| ( int_one @ ( A @ int_less ) )
| ~ ( int_one @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[119:[bind(A,$thf( A )),bind(B,$thf( int_one ))]]) ).
thf(2473,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ~ $true
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[43,58]) ).
thf(2474,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(simp,[status(thm)],[2473]) ).
thf(2475,plain,
( ( int_zero @ ( int_one @ sk3 ) @ ( int_zero @ plus ) )
= int_one ),
inference(pattern_uni,[status(thm)],[2474:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(2627,plain,
( ( int_zero @ ( int_one @ sk3 ) )
= int_one ),
inference(rewrite,[status(thm)],[2475,200]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_total) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[41]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[27]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[29]) ).
thf(3878,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3736,32]) ).
thf(3879,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[3878]) ).
thf(3880,plain,
sk2 @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[3879:[bind(A,$thf( int_zero )),bind(B,$thf( sk2 ))]]) ).
thf(22,plain,
n @ ( sk2 @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
thf(134,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)],[22,31]) ).
thf(135,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[134]) ).
thf(136,plain,
( ( n @ ( sk2 @ int_less ) )
| ( sk2 = n ) ),
inference(pattern_uni,[status(thm)],[135:[bind(A,$thf( sk2 )),bind(B,$thf( n ))]]) ).
thf(1130,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)],[136,1077]) ).
thf(1131,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk2 = n ) ),
inference(simp,[status(thm)],[1130]) ).
thf(1132,plain,
( ~ ( sk2 @ ( n @ int_less ) )
| ( sk2 = n ) ),
inference(pattern_uni,[status(thm)],[1131:[bind(A,$thf( n )),bind(B,$thf( sk2 ))]]) ).
thf(723,plain,
( ( sk1 != sk1 )
| ( n @ ( int_one @ int_leq ) )
| ( n @ ( sk1 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[114,17]) ).
thf(724,plain,
( ( n @ ( int_one @ int_leq ) )
| ( n @ ( sk1 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[723:[]]) ).
thf(901,plain,
( ( sk2 != sk2 )
| ( sk1 != n )
| ( n @ ( sk2 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[136,24]) ).
thf(902,plain,
( ( sk1 != n )
| ( n @ ( sk2 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[901:[]]) ).
thf(73,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( C @ a ) )
= real_one )
| ~ ( B @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[71]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( ( C @ ( C @ a ) )
= real_one ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(78,plain,
! [C: $i,B: $i,A: $i] :
( ~ ( B @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( ( C @ ( C @ a ) )
= real_one ) ),
inference(simp,[status(thm)],[77]) ).
thf(2024,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,56]) ).
thf(2025,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[2024]) ).
thf(2026,plain,
int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[2025:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(2114,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2026,56]) ).
thf(2115,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[2114]) ).
thf(2116,plain,
int_zero @ ( int_zero @ ( int_one @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[2115:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_one @ sk3 ) ))]]) ).
thf(2651,plain,
int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ),
inference(rewrite,[status(thm)],[2116,2627]) ).
thf(64,plain,
! [A: $i] :
( ( A @ ( int_one @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) ) ),
inference(cnfConj,[status(thm)],[63]) ).
thf(3234,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2651,64]) ).
thf(3235,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[3234]) ).
thf(3236,plain,
int_zero @ ( int_one @ sk3 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[3235:[bind(A,$thf( int_zero @ ( int_one @ sk3 ) ))]]) ).
thf(3261,plain,
int_one @ ( int_one @ int_leq ),
inference(rewrite,[status(thm)],[3236,2627]) ).
thf(2854,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( int_zero @ int_less ) ) )
| ( B @ ( A @ plus ) @ ( A @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[43,60]) ).
thf(2855,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( int_zero @ int_less ) ) )
| ( B @ ( A @ plus ) @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[2854]) ).
thf(2856,plain,
! [A: $i] : ( int_one @ ( A @ plus ) @ ( A @ int_less ) ),
inference(pattern_uni,[status(thm)],[2855:[bind(A,$thf( A )),bind(B,$thf( int_one ))]]) ).
thf(4010,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3762,1077]) ).
thf(4011,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[4010]) ).
thf(4012,plain,
~ ( int_zero @ ( sk1 @ int_less ) ),
inference(pattern_uni,[status(thm)],[4011:[bind(A,$thf( sk1 )),bind(B,$thf( int_zero ))]]) ).
thf(4679,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( sk1 @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2856,4012]) ).
thf(4680,plain,
! [A: $i] :
( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( sk1 @ int_less ) ) ),
inference(simp,[status(thm)],[4679]) ).
thf(4703,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) )
!= int_zero )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[4680]) ).
thf(4719,plain,
( ( int_one @ ( sk1 @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[4703]) ).
thf(5454,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_one @ ( sk1 @ plus ) ) )
| ( ( A @ ( B @ plus ) )
!= int_zero ) ),
inference(paramod_ordered,[status(thm)],[46,4719]) ).
thf(5455,plain,
( ( sk1 @ ( int_one @ plus ) )
!= int_zero ),
inference(pattern_uni,[status(thm)],[5454:[bind(A,$thf( sk1 )),bind(B,$thf( int_one ))]]) ).
thf(3780,plain,
! [B: $i,A: $i] :
( ( ( A @ ( int_zero @ int_less ) )
!= ( B @ ( B @ int_less ) ) )
| ~ $true
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[66,40]) ).
thf(3781,plain,
! [B: $i,A: $i] :
( ( ( A @ ( int_zero @ int_less ) )
!= ( B @ ( B @ int_less ) ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[3780]) ).
thf(3782,plain,
~ ( int_zero @ ( int_one @ int_leq ) ),
inference(pattern_uni,[status(thm)],[3781:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero ))]]) ).
thf(1295,plain,
! [A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ( sk1 != n ) ),
inference(paramod_ordered,[status(thm)],[902,40]) ).
thf(1296,plain,
! [A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ( sk1 != n ) ),
inference(simp,[status(thm)],[1295]) ).
thf(1304,plain,
! [A: $i] :
( ( n != A )
| ( sk2 != A )
| ( sk1 != n ) ),
inference(simp,[status(thm)],[1296]) ).
thf(1312,plain,
( ( sk2 != n )
| ( sk1 != n ) ),
inference(simp,[status(thm)],[1304]) ).
thf(1326,plain,
( ( sk1 != sk1 )
| ( sk2 != n )
| ( n != n )
| ( n @ ( sk1 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[114,1312]) ).
thf(1327,plain,
( ( sk1 != sk1 )
| ( sk2 != n )
| ( n @ ( sk1 @ int_less ) ) ),
inference(simp,[status(thm)],[1326]) ).
thf(1328,plain,
( ( sk2 != n )
| ( n @ ( sk1 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[1327:[]]) ).
thf(1094,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true
| ( sk1 = int_one ) ),
inference(paramod_ordered,[status(thm)],[125,1077]) ).
thf(1095,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[1094]) ).
thf(1096,plain,
( ~ ( int_one @ ( sk1 @ int_less ) )
| ( sk1 = int_one ) ),
inference(pattern_uni,[status(thm)],[1095:[bind(A,$thf( sk1 )),bind(B,$thf( int_one ))]]) ).
thf(1136,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true
| ( sk1 != int_one ) ),
inference(paramod_ordered,[status(thm)],[664,1077]) ).
thf(1137,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk1 != int_one ) ),
inference(simp,[status(thm)],[1136]) ).
thf(1138,plain,
( ~ ( int_one @ ( sk2 @ int_less ) )
| ( sk1 != int_one ) ),
inference(pattern_uni,[status(thm)],[1137:[bind(A,$thf( sk2 )),bind(B,$thf( int_one ))]]) ).
thf(1112,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)],[43,1077]) ).
thf(1113,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[1112]) ).
thf(1114,plain,
~ ( int_zero @ ( int_one @ int_less ) ),
inference(pattern_uni,[status(thm)],[1113:[bind(A,$thf( int_one )),bind(B,$thf( int_zero ))]]) ).
thf(1945,plain,
( ( sk1 != sk1 )
| ( sk2 != n )
| ( n != n )
| ~ ( sk1 @ ( n @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[1126,1312]) ).
thf(1946,plain,
( ( sk1 != sk1 )
| ( sk2 != n )
| ~ ( sk1 @ ( n @ int_less ) ) ),
inference(simp,[status(thm)],[1945]) ).
thf(1947,plain,
( ( sk2 != n )
| ~ ( sk1 @ ( n @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[1946:[]]) ).
thf(4007,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ~ $true
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[3762,58]) ).
thf(4008,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(simp,[status(thm)],[4007]) ).
thf(4009,plain,
( ( int_zero @ ( sk1 @ sk3 ) @ ( int_zero @ plus ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[4008:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 ))]]) ).
thf(7289,plain,
( ( int_zero @ ( sk1 @ sk3 ) )
= sk1 ),
inference(rewrite,[status(thm)],[4009,200]) ).
thf(792,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)],[43,32]) ).
thf(793,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[792]) ).
thf(794,plain,
int_one @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[793:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(1276,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true
| ( sk1 != n ) ),
inference(paramod_ordered,[status(thm)],[902,1077]) ).
thf(1277,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk1 != n ) ),
inference(simp,[status(thm)],[1276]) ).
thf(1278,plain,
( ~ ( sk2 @ ( n @ int_less ) )
| ( sk1 != n ) ),
inference(pattern_uni,[status(thm)],[1277:[bind(A,$thf( n )),bind(B,$thf( sk2 ))]]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[27]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[30]) ).
thf(34,plain,
! [A: $i] : ( A @ ( A @ int_leq ) ),
inference(simp,[status(thm)],[33]) ).
thf(4003,plain,
! [A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3762,40]) ).
thf(4004,plain,
! [A: $i] :
( ( sk1 @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[4003]) ).
thf(4026,plain,
! [A: $i] :
( ( sk1 != A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[4004]) ).
thf(4041,plain,
sk1 != int_zero,
inference(simp,[status(thm)],[4026]) ).
thf(3856,plain,
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( sk2 @ ( n @ int_less ) ) )
| ~ $true
| ( sk2 = n ) ),
inference(paramod_ordered,[status(thm)],[3736,1132]) ).
thf(3857,plain,
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( sk2 @ ( n @ int_less ) ) )
| ( sk2 = n ) ),
inference(simp,[status(thm)],[3856]) ).
thf(3924,plain,
( ( sk2 != sk2 )
| ( int_zero != n )
| ( sk2 = n ) ),
inference(simp,[status(thm)],[3857]) ).
thf(3933,plain,
( ( int_zero != n )
| ( sk2 = n ) ),
inference(simp,[status(thm)],[3924]) ).
thf(3894,plain,
! [A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3736,40]) ).
thf(3895,plain,
! [A: $i] :
( ( sk2 @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[3894]) ).
thf(3923,plain,
! [A: $i] :
( ( sk2 != A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[3895]) ).
thf(3932,plain,
sk2 != int_zero,
inference(simp,[status(thm)],[3923]) ).
thf(4956,plain,
( ( sk2 != sk2 )
| ( int_zero != n )
| ( int_zero != n ) ),
inference(paramod_ordered,[status(thm)],[3933,3932]) ).
thf(4957,plain,
( ( sk2 != sk2 )
| ( int_zero != n ) ),
inference(simp,[status(thm)],[4956]) ).
thf(4958,plain,
int_zero != n,
inference(pattern_uni,[status(thm)],[4957:[]]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( B != int_one )
| ( sk2 @ ( A @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[31,20]) ).
thf(98,plain,
! [A: $i] :
( ( sk2 @ ( A @ int_leq ) )
| ( int_one @ ( A @ int_less ) )
| ~ ( int_one @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( A )),bind(B,$thf( int_one ))]]) ).
thf(1100,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true
| ( sk2 = int_one ) ),
inference(paramod_ordered,[status(thm)],[103,1077]) ).
thf(1101,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk2 = int_one ) ),
inference(simp,[status(thm)],[1100]) ).
thf(1102,plain,
( ~ ( int_one @ ( sk2 @ int_less ) )
| ( sk2 = int_one ) ),
inference(pattern_uni,[status(thm)],[1101:[bind(A,$thf( sk2 )),bind(B,$thf( int_one ))]]) ).
thf(74,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)],[71]) ).
thf(79,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)],[74]) ).
thf(80,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)],[79]) ).
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/sandbox/benchmark/theBenchmark.p',plus_and_order1) ).
thf(50,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(672,plain,
( ( sk2 != sk2 )
| ( n @ ( int_one @ int_leq ) )
| ( sk2 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[103,22]) ).
thf(673,plain,
( ( n @ ( int_one @ int_leq ) )
| ( sk2 @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[672:[]]) ).
thf(3989,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3762,32]) ).
thf(3990,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[3989]) ).
thf(3991,plain,
sk1 @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[3990:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 ))]]) ).
thf(3899,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3736,1077]) ).
thf(3900,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[3899]) ).
thf(3901,plain,
~ ( int_zero @ ( sk2 @ int_less ) ),
inference(pattern_uni,[status(thm)],[3900:[bind(A,$thf( sk2 )),bind(B,$thf( int_zero ))]]) ).
thf(4132,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( sk2 @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2856,3901]) ).
thf(4133,plain,
! [A: $i] :
( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( sk2 @ int_less ) ) ),
inference(simp,[status(thm)],[4132]) ).
thf(4165,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) )
!= int_zero )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[4133]) ).
thf(4174,plain,
( ( int_one @ ( sk2 @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[4165]) ).
thf(4744,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_one @ ( sk2 @ plus ) ) )
| ( ( A @ ( B @ plus ) )
!= int_zero ) ),
inference(paramod_ordered,[status(thm)],[46,4174]) ).
thf(4745,plain,
( ( sk2 @ ( int_one @ plus ) )
!= int_zero ),
inference(pattern_uni,[status(thm)],[4744:[bind(A,$thf( sk2 )),bind(B,$thf( int_one ))]]) ).
thf(3322,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2856,1114]) ).
thf(3323,plain,
! [A: $i] :
( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ int_less ) ) ),
inference(simp,[status(thm)],[3322]) ).
thf(3405,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) )
!= int_zero )
| ( A != int_one ) ),
inference(simp,[status(thm)],[3323]) ).
thf(3420,plain,
( ( int_one @ ( int_one @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[3405]) ).
thf(51,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)],[50]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( n @ ( A @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[31,22]) ).
thf(131,plain,
! [A: $i] :
( ( n @ ( A @ int_leq ) )
| ( sk2 @ ( A @ int_less ) )
| ~ ( sk2 @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[130:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(121,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( A @ ( int_one @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[31,17]) ).
thf(122,plain,
! [A: $i] :
( ( A @ ( int_one @ int_leq ) )
| ( sk1 @ ( A @ int_less ) )
| ~ ( sk1 @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[121:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( A @ ( int_one @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[31,20]) ).
thf(100,plain,
! [A: $i] :
( ( A @ ( int_one @ int_leq ) )
| ( sk2 @ ( A @ int_less ) )
| ~ ( sk2 @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( B != n )
| ( A @ ( sk1 @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[31,21]) ).
thf(111,plain,
! [A: $i] :
( ( A @ ( sk1 @ int_leq ) )
| ( n @ ( A @ int_less ) )
| ~ ( n @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( A )),bind(B,$thf( n ))]]) ).
thf(129111,plain,
$false,
inference(e,[status(thm)],[84,61,60,461,109,1420,43,1126,69,7903,3762,120,56,2627,42,24,3880,37,25,125,1132,52,724,902,20,46,78,3261,5455,70,21,3782,1328,1096,1138,4012,1114,1947,41,7289,794,1278,64,17,32,34,4041,22,44,3736,1312,49,76,4958,2856,98,103,3932,66,1102,80,7232,35,50,67,673,31,40,3991,114,23,995,4745,58,1077,3420,36,51,4719,136,664,2651,992,15,200,131,47,122,4174,100,3901,111]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV489+3 : 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
% 0.14/0.39 % Computer : n014.cluster.edu
% 0.14/0.39 % Model : x86_64 x86_64
% 0.14/0.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.39 % Memory : 8046.5625MB
% 0.14/0.39 % OS : Linux 6.8.0-71-generic
% 0.14/0.39 % CPULimit : 300
% 0.14/0.39 % WCLimit : 300
% 0.14/0.39 % DateTime : Sat Sep 26 13:58:02 UTC 2026
% 0.14/0.39 % CPUTime :
% 0.14/0.39 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
% 0.88/0.98 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.27/1.18 % [INFO] Parsing done (198ms).
% 1.27/1.20 % [INFO] Running in sequential loop mode.
% 2.07/1.62 % [INFO] eprover registered as external prover.
% 2.07/1.63 % [INFO] Scanning for conjecture ...
% 2.28/1.74 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.28/1.78 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.46/1.82 % [INFO] Problem is first-order (TPTP FOF).
% 2.46/1.82 % [INFO] Type checking passed.
% 2.46/1.83 % [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 ...
% 139.63/35.42 % External prover 'e' found a proof!
% 139.63/35.42 % [INFO] Killing All external provers ...
% 139.63/35.42 % Time passed: 34887ms (effective reasoning time: 34219ms)
% 139.63/35.42 % 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)>
% 139.63/35.42 % Axioms used in derivation (12): plus_and_order1, qii, 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
% 139.63/35.42 % No. of inferences in proof: 260
% 139.63/35.43 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 34887 ms resp. 34219 ms w/o parsing
% 138.60/35.54 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 138.60/35.54 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------