%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV491+4 : 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 : n009.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 08:59:37 AM UTC 2026
% Result : Theorem 142.00s 37.04s
% Output : Refutation 139.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 16
% Syntax : Number of formulae : 280 ( 67 unt; 0 typ; 3 def)
% Number of atoms : 1034 ( 375 equ; 0 cnn)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 2727 ( 484 ~; 457 |; 70 &;1668 @)
% ( 3 <=>; 45 =>; 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 : 375 ( 2 ^; 365 !; 5 ?; 375 :)
% ( 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(real_one_decl,type,
real_one: $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(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] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( int_one @ int_leq ) )
& ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( ( A = B )
=> ( ( B @ ( A @ a ) )
= real_one ) )
& ( ( A != B )
=> ( ( B @ ( A @ a ) )
= real_zero ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) )
& ( n @ ( sk1 @ int_leq ) )
& ( sk1 @ ( int_one @ int_leq ) ) )
=> ( ( ( sk1 = A )
=> ( ( A @ ( sk1 @ a ) )
= real_one ) )
& ( ( sk1 != A )
=> ( ( 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(1,conjecture,
! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( int_one @ int_leq ) )
& ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( ( A = B )
=> ( ( B @ ( A @ a ) )
= real_one ) )
& ( ( A != B )
=> ( ( B @ ( A @ a ) )
= real_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',id) ).
thf(2,negated_conjecture,
~ ! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( int_one @ int_leq ) )
& ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( ( A = B )
=> ( ( B @ ( A @ a ) )
= real_one ) )
& ( ( A != B )
=> ( ( B @ ( A @ a ) )
= real_zero ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
~ ! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( int_one @ int_leq ) )
& ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( ( A = B )
=> ( ( B @ ( A @ a ) )
= real_one ) )
& ( ( A != B )
=> ( ( B @ ( A @ a ) )
= real_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
( ( ( ( sk2 @ ( sk1 @ a ) )
!= real_one )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) )
& ( ( sk1 = sk2 )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) )
& ( ( ( sk2 @ ( sk1 @ a ) )
!= real_one )
| ( sk1 != sk2 ) )
& ( ( sk1 = sk2 )
| ( 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(24,plain,
( ( ( sk2 @ ( sk1 @ a ) )
!= real_one )
| ( sk1 != sk2 ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(25,plain,
( ( ( sk2 @ ( sk1 @ a ) )
!= real_one )
| ( sk2 != sk1 ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(13,axiom,
real_zero != real_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',real_constants) ).
thf(71,plain,
real_zero != real_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(72,plain,
real_zero != real_one,
inference(polarity_switch,[status(thm)],[71]) ).
thf(73,plain,
real_one != real_zero,
inference(lifteq,[status(thm)],[72]) ).
thf(20,plain,
n @ ( sk1 @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
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(29,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(30,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)],[29]) ).
thf(31,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)],[30]) ).
thf(32,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(109,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)],[20,35]) ).
thf(110,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk1 @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[109]) ).
thf(111,plain,
( ( n @ ( sk1 @ int_less ) )
| ( sk1 = n ) ),
inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( sk1 )),bind(B,$thf( n ))]]) ).
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(39,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(40,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ int_less ) )
| ~ ( C @ ( B @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[39]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_irreflexive) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(44,plain,
! [A: $i] :
~ ( A @ ( A @ int_less ) ),
inference(simp,[status(thm)],[43]) ).
thf(1086,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)],[40,44]) ).
thf(1087,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)],[1086]) ).
thf(1088,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ~ ( A @ ( B @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[1087:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(1124,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ~ ( A @ ( B @ int_less ) ) ),
inference(simp,[status(thm)],[1088]) ).
thf(1178,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)],[111,1124]) ).
thf(1179,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk1 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk1 = n ) ),
inference(simp,[status(thm)],[1178]) ).
thf(1180,plain,
( ~ ( sk1 @ ( n @ int_less ) )
| ( sk1 = n ) ),
inference(pattern_uni,[status(thm)],[1179:[bind(A,$thf( n )),bind(B,$thf( sk1 ))]]) ).
thf(18,plain,
sk1 @ ( int_one @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
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(65,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(66,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)],[65]) ).
thf(67,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)],[66]) ).
thf(69,plain,
! [A: $i] :
( ( A @ ( int_zero @ int_less ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[67]) ).
thf(70,plain,
! [A: $i] :
( ( A @ ( int_zero @ int_less ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[69]) ).
thf(3671,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18,70]) ).
thf(3672,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[3671]) ).
thf(3673,plain,
sk1 @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[3672:[bind(A,$thf( sk1 ))]]) ).
thf(136,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)],[18,35]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
( ( sk1 @ ( int_one @ int_less ) )
| ( sk1 = int_one ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( int_one )),bind(B,$thf( sk1 ))]]) ).
thf(7,axiom,
int_one @ ( int_zero @ int_less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_zero_one) ).
thf(47,plain,
int_one @ ( int_zero @ int_less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(1172,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)],[47,1124]) ).
thf(1173,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[1172]) ).
thf(1174,plain,
~ ( int_zero @ ( int_one @ int_less ) ),
inference(pattern_uni,[status(thm)],[1173:[bind(A,$thf( int_one )),bind(B,$thf( int_zero ))]]) ).
thf(1200,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ int_less ) ) )
| ~ $true
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[35,1174]) ).
thf(1201,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ int_less ) ) )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(simp,[status(thm)],[1200]) ).
thf(1202,plain,
( ~ ( int_zero @ ( int_one @ int_leq ) )
| ( int_zero = int_one ) ),
inference(pattern_uni,[status(thm)],[1201:[bind(A,$thf( int_one )),bind(B,$thf( int_zero ))]]) ).
thf(229,plain,
! [A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,44]) ).
thf(230,plain,
! [A: $i] :
( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[229]) ).
thf(231,plain,
! [A: $i] :
( ( int_one != A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[230]) ).
thf(232,plain,
int_zero != int_one,
inference(simp,[status(thm)],[231]) ).
thf(1899,plain,
~ ( int_zero @ ( int_one @ int_leq ) ),
inference(simplifyReflect,[status(thm)],[1202,232]) ).
thf(19,plain,
sk2 @ ( int_one @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
thf(3694,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,70]) ).
thf(3695,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[3694]) ).
thf(3696,plain,
sk2 @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[3695:[bind(A,$thf( sk2 ))]]) ).
thf(3861,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3696,1124]) ).
thf(3862,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[3861]) ).
thf(3863,plain,
~ ( int_zero @ ( sk2 @ int_less ) ),
inference(pattern_uni,[status(thm)],[3862:[bind(A,$thf( sk2 )),bind(B,$thf( int_zero ))]]) ).
thf(23,plain,
n @ ( sk2 @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
thf(190,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)],[23,35]) ).
thf(191,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[190]) ).
thf(192,plain,
( ( n @ ( sk2 @ int_less ) )
| ( sk2 = n ) ),
inference(pattern_uni,[status(thm)],[191:[bind(A,$thf( sk2 )),bind(B,$thf( n ))]]) ).
thf(1154,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)],[192,1124]) ).
thf(1155,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk2 = n ) ),
inference(simp,[status(thm)],[1154]) ).
thf(1156,plain,
( ~ ( sk2 @ ( n @ int_less ) )
| ( sk2 = n ) ),
inference(pattern_uni,[status(thm)],[1155:[bind(A,$thf( n )),bind(B,$thf( sk2 ))]]) ).
thf(1636,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( sk2 @ ( n @ int_less ) ) )
| ~ $true
| ( sk2 = n )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[35,1156]) ).
thf(1637,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( sk2 @ ( n @ int_less ) ) )
| ( sk2 = n )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(simp,[status(thm)],[1636]) ).
thf(1638,plain,
( ( sk2 = n )
| ~ ( sk2 @ ( n @ int_leq ) )
| ( sk2 = n ) ),
inference(pattern_uni,[status(thm)],[1637:[bind(A,$thf( n )),bind(B,$thf( sk2 ))]]) ).
thf(1671,plain,
( ~ ( sk2 @ ( n @ int_leq ) )
| ( sk2 = n ) ),
inference(simp,[status(thm)],[1638]) ).
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(56,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(1142,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)],[138,1124]) ).
thf(1143,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[1142]) ).
thf(1144,plain,
( ~ ( int_one @ ( sk1 @ int_less ) )
| ( sk1 = int_one ) ),
inference(pattern_uni,[status(thm)],[1143:[bind(A,$thf( sk1 )),bind(B,$thf( int_one ))]]) ).
thf(1286,plain,
( ( sk1 != sk1 )
| ( ( sk2 @ ( int_one @ a ) )
!= real_one )
| ( sk2 != sk1 )
| ~ ( int_one @ ( sk1 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[1144,25]) ).
thf(1287,plain,
( ( ( sk2 @ ( int_one @ a ) )
!= real_one )
| ( sk2 != sk1 )
| ~ ( int_one @ ( sk1 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[1286:[]]) ).
thf(17,plain,
( ( sk1 = sk2 )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(27,plain,
( ( sk2 = sk1 )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( sk2 = sk1 )
| ( ( sk2 @ ( A @ a ) )
!= real_zero )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[35,27]) ).
thf(125,plain,
! [A: $i] :
( ( sk2 = sk1 )
| ( ( sk2 @ ( A @ a ) )
!= real_zero )
| ( sk1 @ ( A @ int_less ) )
| ~ ( sk1 @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[124:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
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(45,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[45]) ).
thf(1914,plain,
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18,1899]) ).
thf(1915,plain,
( ( sk1 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1914]) ).
thf(1924,plain,
( ( sk1 != int_zero )
| ( int_one != int_one ) ),
inference(simp,[status(thm)],[1915]) ).
thf(1931,plain,
sk1 != int_zero,
inference(simp,[status(thm)],[1924]) ).
thf(105,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( n @ ( A @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[35,20]) ).
thf(106,plain,
! [A: $i] :
( ( n @ ( A @ int_leq ) )
| ( sk1 @ ( A @ int_less ) )
| ~ ( sk1 @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[105:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
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/sandbox2/benchmark/theBenchmark.p',qii) ).
thf(74,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(75,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)],[74]) ).
thf(78,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)],[75]) ).
thf(83,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)],[78]) ).
thf(84,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)],[83]) ).
thf(132,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)],[35,18]) ).
thf(133,plain,
! [A: $i] :
( ( sk1 @ ( A @ int_leq ) )
| ( int_one @ ( A @ int_less ) )
| ~ ( int_one @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( A )),bind(B,$thf( int_one ))]]) ).
thf(57,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)],[56]) ).
thf(58,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)],[57]) ).
thf(59,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[58]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(lifteq,[status(thm)],[59]) ).
thf(3903,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)],[3696,62]) ).
thf(3904,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(simp,[status(thm)],[3903]) ).
thf(3905,plain,
( ( int_zero @ ( sk2 @ sk3 ) @ ( int_zero @ plus ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[3904:[bind(A,$thf( int_zero )),bind(B,$thf( sk2 ))]]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_commutative) ).
thf(48,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(cnf,[status(esa)],[48]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(lifteq,[status(thm)],[49]) ).
thf(9,axiom,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_zero) ).
thf(51,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(52,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(cnf,[status(esa)],[51]) ).
thf(53,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(lifteq,[status(thm)],[52]) ).
thf(907,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_zero @ ( C @ plus ) ) )
| ( ( A @ ( B @ plus ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[50,53]) ).
thf(908,plain,
! [A: $i] :
( ( A @ ( int_zero @ plus ) )
= A ),
inference(pattern_uni,[status(thm)],[907:[bind(A,$thf( A )),bind(B,$thf( int_zero )),bind(C,$thf( A ))]]) ).
thf(7230,plain,
( ( int_zero @ ( sk2 @ sk3 ) )
= sk2 ),
inference(rewrite,[status(thm)],[3905,908]) ).
thf(33,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[33]) ).
thf(3897,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3696,36]) ).
thf(3898,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[3897]) ).
thf(3899,plain,
sk2 @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[3898:[bind(A,$thf( int_zero )),bind(B,$thf( sk2 ))]]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[58]) ).
thf(61,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ int_less ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ( ( C @ ( A @ plus ) )
!= B ) ),
inference(cnfConj,[status(thm)],[58]) ).
thf(63,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ int_less ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ( ( C @ ( A @ plus ) )
!= B ) ),
inference(lifteq,[status(thm)],[61]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) @ ( A @ int_less ) )
| ~ ( B @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[63]) ).
thf(2937,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)],[47,64]) ).
thf(2938,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)],[2937]) ).
thf(2939,plain,
! [A: $i] : ( int_one @ ( A @ plus ) @ ( A @ int_less ) ),
inference(pattern_uni,[status(thm)],[2938:[bind(A,$thf( A )),bind(B,$thf( int_one ))]]) ).
thf(3761,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3673,1124]) ).
thf(3762,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[3761]) ).
thf(3763,plain,
~ ( int_zero @ ( sk1 @ int_less ) ),
inference(pattern_uni,[status(thm)],[3762:[bind(A,$thf( sk1 )),bind(B,$thf( int_zero ))]]) ).
thf(3925,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( sk1 @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2939,3763]) ).
thf(3926,plain,
! [A: $i] :
( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( sk1 @ int_less ) ) ),
inference(simp,[status(thm)],[3925]) ).
thf(3978,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) )
!= int_zero )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[3926]) ).
thf(3989,plain,
( ( int_one @ ( sk1 @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[3978]) ).
thf(1315,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( int_one @ ( sk1 @ int_less ) ) )
| ~ $true
| ( sk1 = int_one )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[35,1144]) ).
thf(1316,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( int_one @ ( sk1 @ int_less ) ) )
| ( sk1 = int_one )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(simp,[status(thm)],[1315]) ).
thf(1317,plain,
( ( sk1 = int_one )
| ~ ( int_one @ ( sk1 @ int_leq ) )
| ( sk1 = int_one ) ),
inference(pattern_uni,[status(thm)],[1316:[bind(A,$thf( sk1 )),bind(B,$thf( int_one ))]]) ).
thf(1350,plain,
( ~ ( int_one @ ( sk1 @ int_leq ) )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[1317]) ).
thf(2330,plain,
( ( ( n @ ( sk1 @ int_leq ) )
!= ( int_one @ ( sk1 @ int_leq ) ) )
| ~ $true
| ( sk1 = int_one ) ),
inference(paramod_ordered,[status(thm)],[20,1350]) ).
thf(2331,plain,
( ( ( n @ ( sk1 @ int_leq ) )
!= ( int_one @ ( sk1 @ int_leq ) ) )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[2330]) ).
thf(2389,plain,
( ( n != int_one )
| ( sk1 != sk1 )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[2331]) ).
thf(2396,plain,
( ( n != int_one )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[2389]) ).
thf(34,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[31]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[34]) ).
thf(38,plain,
! [A: $i] : ( A @ ( A @ int_leq ) ),
inference(simp,[status(thm)],[37]) ).
thf(845,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)],[47,36]) ).
thf(846,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[845]) ).
thf(847,plain,
int_one @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[846:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(3797,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3673,36]) ).
thf(3798,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[3797]) ).
thf(3799,plain,
sk1 @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[3798:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 ))]]) ).
thf(2522,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)],[47,62]) ).
thf(2523,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(simp,[status(thm)],[2522]) ).
thf(2524,plain,
( ( int_zero @ ( int_one @ sk3 ) @ ( int_zero @ plus ) )
= int_one ),
inference(pattern_uni,[status(thm)],[2523:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(2631,plain,
( ( int_zero @ ( int_one @ sk3 ) )
= int_one ),
inference(rewrite,[status(thm)],[2524,908]) ).
thf(147,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)],[19,35]) ).
thf(148,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[147]) ).
thf(149,plain,
( ( sk2 @ ( int_one @ int_less ) )
| ( sk2 = int_one ) ),
inference(pattern_uni,[status(thm)],[148:[bind(A,$thf( int_one )),bind(B,$thf( sk2 ))]]) ).
thf(1148,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)],[149,1124]) ).
thf(1149,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk2 = int_one ) ),
inference(simp,[status(thm)],[1148]) ).
thf(1150,plain,
( ~ ( int_one @ ( sk2 @ int_less ) )
| ( sk2 = int_one ) ),
inference(pattern_uni,[status(thm)],[1149:[bind(A,$thf( sk2 )),bind(B,$thf( int_one ))]]) ).
thf(3803,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)],[3673,62]) ).
thf(3804,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(simp,[status(thm)],[3803]) ).
thf(3805,plain,
( ( int_zero @ ( sk1 @ sk3 ) @ ( int_zero @ plus ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[3804:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 ))]]) ).
thf(7169,plain,
( ( int_zero @ ( sk1 @ sk3 ) )
= sk1 ),
inference(rewrite,[status(thm)],[3805,908]) ).
thf(3741,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3673,60]) ).
thf(3742,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[3741]) ).
thf(3743,plain,
int_zero @ ( sk1 @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[3742:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 ))]]) ).
thf(4686,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3743,60]) ).
thf(4687,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[4686]) ).
thf(4688,plain,
int_zero @ ( int_zero @ ( sk1 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[4687:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( sk1 @ sk3 ) ))]]) ).
thf(8164,plain,
int_zero @ ( sk1 @ sk3 ) @ ( int_zero @ int_less ),
inference(rewrite,[status(thm)],[4688,7169]) ).
thf(742,plain,
( ( sk1 != sk1 )
| ( n @ ( int_one @ int_leq ) )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[138,20]) ).
thf(743,plain,
( ( n @ ( int_one @ int_leq ) )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[742:[]]) ).
thf(4611,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_one @ ( sk1 @ plus ) ) )
| ( ( A @ ( B @ plus ) )
!= int_zero ) ),
inference(paramod_ordered,[status(thm)],[50,3989]) ).
thf(4612,plain,
( ( sk1 @ ( int_one @ plus ) )
!= int_zero ),
inference(pattern_uni,[status(thm)],[4611:[bind(A,$thf( sk1 )),bind(B,$thf( int_one ))]]) ).
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(54,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(143,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)],[35,19]) ).
thf(144,plain,
! [A: $i] :
( ( sk2 @ ( A @ int_leq ) )
| ( int_one @ ( A @ int_less ) )
| ~ ( int_one @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( A )),bind(B,$thf( int_one ))]]) ).
thf(3283,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2939,1174]) ).
thf(3284,plain,
! [A: $i] :
( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ int_less ) ) ),
inference(simp,[status(thm)],[3283]) ).
thf(3341,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) )
!= int_zero )
| ( A != int_one ) ),
inference(simp,[status(thm)],[3284]) ).
thf(3355,plain,
( ( int_one @ ( int_one @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[3341]) ).
thf(3509,plain,
( ( ( sk2 @ ( n @ int_leq ) )
!= ( sk2 @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk2 = n ) ),
inference(paramod_ordered,[status(thm)],[19,1671]) ).
thf(3510,plain,
( ( ( sk2 @ ( n @ int_leq ) )
!= ( sk2 @ ( int_one @ int_leq ) ) )
| ( sk2 = n ) ),
inference(simp,[status(thm)],[3509]) ).
thf(3519,plain,
( ( sk2 != sk2 )
| ( n != int_one )
| ( sk2 = n ) ),
inference(simp,[status(thm)],[3510]) ).
thf(3532,plain,
( ( n != int_one )
| ( sk2 = n ) ),
inference(simp,[status(thm)],[3519]) ).
thf(3839,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)],[3696,60]) ).
thf(3840,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[3839]) ).
thf(3841,plain,
int_zero @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[3840:[bind(A,$thf( int_zero )),bind(B,$thf( sk2 ))]]) ).
thf(5323,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)],[3841,60]) ).
thf(5324,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[5323]) ).
thf(5325,plain,
int_zero @ ( int_zero @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[5324:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( sk2 @ sk3 ) ))]]) ).
thf(8445,plain,
int_zero @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ),
inference(rewrite,[status(thm)],[5325,7230]) ).
thf(1403,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( int_one @ ( sk2 @ int_less ) ) )
| ~ $true
| ( sk2 = int_one )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[35,1150]) ).
thf(1404,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( int_one @ ( sk2 @ int_less ) ) )
| ( sk2 = int_one )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(simp,[status(thm)],[1403]) ).
thf(1405,plain,
( ( sk2 = int_one )
| ~ ( int_one @ ( sk2 @ int_leq ) )
| ( sk2 = int_one ) ),
inference(pattern_uni,[status(thm)],[1404:[bind(A,$thf( sk2 )),bind(B,$thf( int_one ))]]) ).
thf(1440,plain,
( ~ ( int_one @ ( sk2 @ int_leq ) )
| ( sk2 = int_one ) ),
inference(simp,[status(thm)],[1405]) ).
thf(2831,plain,
( ( ( n @ ( sk2 @ int_leq ) )
!= ( int_one @ ( sk2 @ int_leq ) ) )
| ~ $true
| ( sk2 = int_one ) ),
inference(paramod_ordered,[status(thm)],[23,1440]) ).
thf(2832,plain,
( ( ( n @ ( sk2 @ int_leq ) )
!= ( int_one @ ( sk2 @ int_leq ) ) )
| ( sk2 = int_one ) ),
inference(simp,[status(thm)],[2831]) ).
thf(2852,plain,
( ( n != int_one )
| ( sk2 != sk2 )
| ( sk2 = int_one ) ),
inference(simp,[status(thm)],[2832]) ).
thf(2856,plain,
( ( n != int_one )
| ( sk2 = int_one ) ),
inference(simp,[status(thm)],[2852]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( ( sk2 @ ( A @ a ) )
!= real_one )
| ( sk2 != sk1 )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[35,25]) ).
thf(98,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ a ) )
!= real_one )
| ( sk2 != sk1 )
| ( sk1 @ ( A @ int_less ) )
| ~ ( sk1 @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(2072,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)],[47,60]) ).
thf(2073,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[2072]) ).
thf(2074,plain,
int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[2073:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(2104,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)],[2074,60]) ).
thf(2105,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[2104]) ).
thf(2106,plain,
int_zero @ ( int_zero @ ( int_one @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[2105:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_one @ sk3 ) ))]]) ).
thf(2655,plain,
int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ),
inference(rewrite,[status(thm)],[2106,2631]) ).
thf(68,plain,
! [A: $i] :
( ( A @ ( int_one @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) ) ),
inference(cnfConj,[status(thm)],[67]) ).
thf(3178,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)],[2655,68]) ).
thf(3179,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[3178]) ).
thf(3180,plain,
int_zero @ ( int_one @ sk3 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[3179:[bind(A,$thf( int_zero @ ( int_one @ sk3 ) ))]]) ).
thf(3197,plain,
int_one @ ( int_one @ int_leq ),
inference(rewrite,[status(thm)],[3180,2631]) ).
thf(699,plain,
( ( sk1 != sk1 )
| ( n @ ( int_one @ int_leq ) )
| ( n @ ( sk1 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[111,18]) ).
thf(700,plain,
( ( n @ ( int_one @ int_leq ) )
| ( n @ ( sk1 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[699:[]]) ).
thf(107,plain,
! [B: $i,A: $i] :
( ( B != n )
| ( A @ ( sk1 @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[35,20]) ).
thf(108,plain,
! [A: $i] :
( ( A @ ( sk1 @ int_leq ) )
| ( n @ ( A @ int_less ) )
| ~ ( n @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[107:[bind(A,$thf( A )),bind(B,$thf( n ))]]) ).
thf(134,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)],[35,18]) ).
thf(135,plain,
! [A: $i] :
( ( A @ ( int_one @ int_leq ) )
| ( sk1 @ ( A @ int_less ) )
| ~ ( sk1 @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(76,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)],[75]) ).
thf(79,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)],[76]) ).
thf(80,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)],[79]) ).
thf(4003,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( sk2 @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2939,3863]) ).
thf(4004,plain,
! [A: $i] :
( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( sk2 @ int_less ) ) ),
inference(simp,[status(thm)],[4003]) ).
thf(4057,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) )
!= int_zero )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[4004]) ).
thf(4071,plain,
( ( int_one @ ( sk2 @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[4057]) ).
thf(4657,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_one @ ( sk2 @ plus ) ) )
| ( ( A @ ( B @ plus ) )
!= int_zero ) ),
inference(paramod_ordered,[status(thm)],[50,4071]) ).
thf(4658,plain,
( ( sk2 @ ( int_one @ plus ) )
!= int_zero ),
inference(pattern_uni,[status(thm)],[4657:[bind(A,$thf( sk2 )),bind(B,$thf( int_one ))]]) ).
thf(1853,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( sk1 @ ( n @ int_less ) ) )
| ~ $true
| ( sk1 = n )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[35,1180]) ).
thf(1854,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( sk1 @ ( n @ int_less ) ) )
| ( sk1 = n )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(simp,[status(thm)],[1853]) ).
thf(1855,plain,
( ( sk1 = n )
| ~ ( sk1 @ ( n @ int_leq ) )
| ( sk1 = n ) ),
inference(pattern_uni,[status(thm)],[1854:[bind(A,$thf( n )),bind(B,$thf( sk1 ))]]) ).
thf(1898,plain,
( ~ ( sk1 @ ( n @ int_leq ) )
| ( sk1 = n ) ),
inference(simp,[status(thm)],[1855]) ).
thf(7683,plain,
( ( ( sk1 @ ( n @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk1 = n ) ),
inference(paramod_ordered,[status(thm)],[18,1898]) ).
thf(7684,plain,
( ( ( sk1 @ ( n @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( sk1 = n ) ),
inference(simp,[status(thm)],[7683]) ).
thf(7719,plain,
( ( sk1 != sk1 )
| ( n != int_one )
| ( sk1 = n ) ),
inference(simp,[status(thm)],[7684]) ).
thf(7724,plain,
( ( n != int_one )
| ( sk1 = n ) ),
inference(simp,[status(thm)],[7719]) ).
thf(1951,plain,
( ( sk1 != sk1 )
| ( int_zero != n )
| ~ ( sk1 @ ( n @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[1180,1931]) ).
thf(1952,plain,
( ( int_zero != n )
| ~ ( sk1 @ ( n @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[1951:[]]) ).
thf(3746,plain,
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( sk1 @ ( n @ int_less ) ) )
| ( int_zero != n )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3673,1952]) ).
thf(3747,plain,
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( sk1 @ ( n @ int_less ) ) )
| ( int_zero != n ) ),
inference(simp,[status(thm)],[3746]) ).
thf(3812,plain,
( ( sk1 != sk1 )
| ( int_zero != n )
| ( int_zero != n ) ),
inference(simp,[status(thm)],[3747]) ).
thf(3823,plain,
int_zero != n,
inference(simp,[status(thm)],[3812]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( sk2 = sk1 )
| ( ( A @ ( sk1 @ a ) )
!= real_zero )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[35,27]) ).
thf(127,plain,
! [A: $i] :
( ( sk2 = sk1 )
| ( ( A @ ( sk1 @ a ) )
!= real_zero )
| ( sk2 @ ( A @ int_less ) )
| ~ ( sk2 @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[126:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(21,plain,
( ( ( sk2 @ ( sk1 @ a ) )
!= real_one )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(26,plain,
( ( ( sk2 @ ( sk1 @ a ) )
!= real_one )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(55,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)],[54]) ).
thf(77,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)],[75]) ).
thf(81,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)],[77]) ).
thf(82,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)],[81]) ).
thf(1920,plain,
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,1899]) ).
thf(1921,plain,
( ( sk2 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1920]) ).
thf(1923,plain,
( ( sk2 != int_zero )
| ( int_one != int_one ) ),
inference(simp,[status(thm)],[1921]) ).
thf(1930,plain,
sk2 != int_zero,
inference(simp,[status(thm)],[1923]) ).
thf(366,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ plus ) @ a ) )
!= ( sk2 @ ( sk1 @ a ) ) )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_one )
| ( 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)],[80,26]) ).
thf(367,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ plus ) @ a ) )
!= ( sk2 @ ( sk1 @ a ) ) )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_one )
| ~ ( 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)],[366]) ).
thf(412,plain,
! [C: $i,B: $i,A: $i] :
( ( C != sk2 )
| ( ( B @ ( C @ plus ) )
!= sk1 )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_one )
| ~ ( 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)],[367]) ).
thf(446,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_one )
| ~ ( 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)],[412]) ).
thf(485,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_one )
| ~ ( 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)],[446,19]) ).
thf(486,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_one )
| ~ ( 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)],[485]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( ( A @ ( sk1 @ a ) )
!= real_one )
| ( sk2 != sk1 )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[35,25]) ).
thf(100,plain,
! [A: $i] :
( ( ( A @ ( sk1 @ a ) )
!= real_one )
| ( sk2 != sk1 )
| ( sk2 @ ( A @ int_less ) )
| ~ ( sk2 @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(112539,plain,
$false,
inference(e,[status(thm)],[25,73,1180,3673,138,1899,3863,1671,56,1287,125,20,46,1931,29,106,84,133,74,7230,3899,60,70,3989,192,2396,1174,38,847,65,3763,3799,1350,2631,53,1150,7169,41,8164,45,64,3696,149,44,743,4612,1124,27,71,54,144,3355,3532,8445,1144,2856,98,3197,39,700,108,135,80,35,4658,48,18,1156,7724,50,3823,127,1898,2939,40,26,55,23,1440,82,36,51,19,1930,908,47,15,68,62,4071,111,486,232,100,2655]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SWV491+4 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.11 % 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
% 0.23/0.59 % Computer : n009.cluster.edu
% 0.23/0.59 % Model : x86_64 x86_64
% 0.23/0.59 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.23/0.59 % Memory : 8046.5625MB
% 0.23/0.59 % OS : Linux 6.8.0-71-generic
% 0.23/0.59 % CPULimit : 300
% 0.23/0.59 % WCLimit : 300
% 0.23/0.59 % DateTime : Sat Sep 26 13:58:45 UTC 2026
% 0.23/0.59 % CPUTime :
% 0.23/0.59 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
% 0.99/1.16 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.23/1.35 % [INFO] Parsing done (189ms).
% 1.23/1.36 % [INFO] Running in sequential loop mode.
% 1.91/1.77 % [INFO] eprover registered as external prover.
% 1.91/1.78 % [INFO] Scanning for conjecture ...
% 2.10/1.88 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.25/1.92 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.25/1.95 % [INFO] Problem is first-order (TPTP FOF).
% 2.25/1.96 % [INFO] Type checking passed.
% 2.25/1.96 % [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 ...
% 142.00/37.04 % External prover 'e' found a proof!
% 142.00/37.04 % [INFO] Killing All external provers ...
% 142.00/37.04 % Time passed: 36308ms (effective reasoning time: 35668ms)
% 142.00/37.04 % 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)>
% 142.00/37.04 % 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
% 142.00/37.04 % No. of inferences in proof: 277
% 142.00/37.04 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 36308 ms resp. 35668 ms w/o parsing
% 139.31/37.16 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 139.31/37.16 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------