%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV490+3 : 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 : n011.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 136.82s 36.00s
% Output : Refutation 137.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 16
% Syntax : Number of formulae : 276 ( 63 unt; 0 typ; 3 def)
% Number of atoms : 1166 ( 397 equ; 0 cnn)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 3263 ( 604 ~; 565 |; 70 &;1976 @)
% ( 3 <=>; 45 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 7 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 : 406 ( 2 ^; 396 !; 5 ?; 406 :)
% ( 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] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( int_one @ int_leq ) )
& ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( ( A = B )
=> ( ( B @ ( A @ a ) )
!= real_zero ) )
& ( ( 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_zero ) )
& ( ( 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(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(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(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(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(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(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(3370,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(3371,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)],[3370]) ).
thf(3372,plain,
! [A: $i] : ( int_one @ ( A @ plus ) @ ( A @ int_less ) ),
inference(pattern_uni,[status(thm)],[3371:[bind(A,$thf( A )),bind(B,$thf( int_one ))]]) ).
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(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(1450,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(1451,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)],[1450]) ).
thf(1452,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ~ ( A @ ( B @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[1451:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(1483,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ~ ( A @ ( B @ int_less ) ) ),
inference(simp,[status(thm)],[1452]) ).
thf(1505,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)],[47,1483]) ).
thf(1506,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[1505]) ).
thf(1507,plain,
~ ( int_zero @ ( int_one @ int_less ) ),
inference(pattern_uni,[status(thm)],[1506:[bind(A,$thf( int_one )),bind(B,$thf( int_zero ))]]) ).
thf(1564,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ int_less ) ) )
| ~ $true
| ~ ( C @ ( B @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[40,1507]) ).
thf(1565,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ int_less ) ) )
| ~ ( C @ ( B @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[1564]) ).
thf(1566,plain,
! [A: $i] :
( ~ ( int_zero @ ( A @ int_less ) )
| ~ ( A @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[1565:[bind(A,$thf( int_one )),bind(B,$thf( B )),bind(C,$thf( int_zero ))]]) ).
thf(1577,plain,
! [A: $i] :
( ~ ( int_zero @ ( A @ int_less ) )
| ~ ( A @ ( int_one @ int_less ) ) ),
inference(simp,[status(thm)],[1566]) ).
thf(3919,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( B @ ( int_one @ int_less ) ) )
| ~ ( int_zero @ ( B @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3372,1577]) ).
thf(3920,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( B @ ( int_one @ int_less ) ) )
| ~ ( int_zero @ ( B @ int_less ) ) ),
inference(simp,[status(thm)],[3919]) ).
thf(3921,plain,
~ ( int_zero @ ( int_one @ ( int_one @ plus ) @ int_less ) ),
inference(pattern_uni,[status(thm)],[3920:[bind(A,$thf( int_one )),bind(B,$thf( int_one @ ( int_one @ plus ) ))]]) ).
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(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(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(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_zero ) )
& ( ( A != B )
=> ( ( B @ ( A @ a ) )
= real_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',di) ).
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_zero ) )
& ( ( 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_zero ) )
& ( ( A != B )
=> ( ( B @ ( A @ a ) )
= real_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
( ( ( ( sk2 @ ( sk1 @ a ) )
= real_zero )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) )
& ( ( sk1 = sk2 )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) )
& ( ( ( sk2 @ ( sk1 @ a ) )
= real_zero )
| ( 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(18,plain,
( ( sk1 = sk2 )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(28,plain,
( ( sk2 = sk1 )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ plus ) @ a ) )
!= ( sk2 @ ( sk1 @ a ) ) )
| ( sk2 = sk1 )
| ( 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)],[80,28]) ).
thf(210,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ plus ) @ a ) )
!= ( sk2 @ ( sk1 @ a ) ) )
| ( sk2 = 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)],[209]) ).
thf(214,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 ) )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[210]) ).
thf(215,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 ) )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[214]) ).
thf(21,plain,
sk2 @ ( int_one @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
thf(449,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 ) )
| ( sk2 = sk1 ) ),
inference(rewrite,[status(thm)],[215,21]) ).
thf(450,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 ) )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[449]) ).
thf(23,plain,
n @ ( sk2 @ 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(228,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(229,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[228]) ).
thf(230,plain,
( ( n @ ( sk2 @ int_less ) )
| ( sk2 = n ) ),
inference(pattern_uni,[status(thm)],[229:[bind(A,$thf( sk2 )),bind(B,$thf( n ))]]) ).
thf(1499,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)],[230,1483]) ).
thf(1500,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk2 = n ) ),
inference(simp,[status(thm)],[1499]) ).
thf(1501,plain,
( ~ ( sk2 @ ( n @ int_less ) )
| ( sk2 = n ) ),
inference(pattern_uni,[status(thm)],[1500:[bind(A,$thf( n )),bind(B,$thf( sk2 ))]]) ).
thf(3903,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3372,1507]) ).
thf(3904,plain,
! [A: $i] :
( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ int_less ) ) ),
inference(simp,[status(thm)],[3903]) ).
thf(3988,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) )
!= int_zero )
| ( A != int_one ) ),
inference(simp,[status(thm)],[3904]) ).
thf(4005,plain,
( ( int_one @ ( int_one @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[3988]) ).
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(4535,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,70]) ).
thf(4536,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[4535]) ).
thf(4537,plain,
sk2 @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[4536:[bind(A,$thf( sk2 ))]]) ).
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(4712,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4537,36]) ).
thf(4713,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[4712]) ).
thf(4714,plain,
sk2 @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[4713:[bind(A,$thf( int_zero )),bind(B,$thf( sk2 ))]]) ).
thf(1040,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(1041,plain,
! [A: $i] :
( ( A @ ( int_zero @ plus ) )
= A ),
inference(pattern_uni,[status(thm)],[1040:[bind(A,$thf( A )),bind(B,$thf( int_zero )),bind(C,$thf( A ))]]) ).
thf(1559,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)],[35,1507]) ).
thf(1560,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ int_less ) ) )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(simp,[status(thm)],[1559]) ).
thf(1561,plain,
( ~ ( int_zero @ ( int_one @ int_leq ) )
| ( int_zero = int_one ) ),
inference(pattern_uni,[status(thm)],[1560:[bind(A,$thf( int_one )),bind(B,$thf( int_zero ))]]) ).
thf(378,plain,
! [A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[47,44]) ).
thf(379,plain,
! [A: $i] :
( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[378]) ).
thf(391,plain,
! [A: $i] :
( ( int_one != A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[379]) ).
thf(394,plain,
int_zero != int_one,
inference(simp,[status(thm)],[391]) ).
thf(2233,plain,
~ ( int_zero @ ( int_one @ int_leq ) ),
inference(simplifyReflect,[status(thm)],[1561,394]) ).
thf(2238,plain,
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,2233]) ).
thf(2239,plain,
( ( sk2 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[2238]) ).
thf(2257,plain,
( ( sk2 != int_zero )
| ( int_one != int_one ) ),
inference(simp,[status(thm)],[2239]) ).
thf(2264,plain,
sk2 != int_zero,
inference(simp,[status(thm)],[2257]) ).
thf(2269,plain,
( ( sk2 != sk2 )
| ( int_zero != n )
| ~ ( sk2 @ ( n @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[1501,2264]) ).
thf(2270,plain,
( ( int_zero != n )
| ~ ( sk2 @ ( n @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[2269:[]]) ).
thf(4725,plain,
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( sk2 @ ( n @ int_less ) ) )
| ( int_zero != n )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4537,2270]) ).
thf(4726,plain,
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( sk2 @ ( n @ int_less ) ) )
| ( int_zero != n ) ),
inference(simp,[status(thm)],[4725]) ).
thf(4737,plain,
( ( sk2 != sk2 )
| ( int_zero != n )
| ( int_zero != n ) ),
inference(simp,[status(thm)],[4726]) ).
thf(4739,plain,
int_zero != n,
inference(simp,[status(thm)],[4737]) ).
thf(129,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( n @ ( B @ ( A @ plus ) @ int_leq ) )
!= ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(eqfactor_ordered,[status(thm)],[80]) ).
thf(142,plain,
! [C: $i,B: $i,A: $i] :
( ( ( n @ ( B @ ( A @ plus ) @ int_leq ) )
!= ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[129]) ).
thf(1704,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)],[35,1501]) ).
thf(1705,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( sk2 @ ( n @ int_less ) ) )
| ( sk2 = n )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(simp,[status(thm)],[1704]) ).
thf(1706,plain,
( ( sk2 = n )
| ~ ( sk2 @ ( n @ int_leq ) )
| ( sk2 = n ) ),
inference(pattern_uni,[status(thm)],[1705:[bind(A,$thf( n )),bind(B,$thf( sk2 ))]]) ).
thf(1722,plain,
( ~ ( sk2 @ ( n @ int_leq ) )
| ( sk2 = n ) ),
inference(simp,[status(thm)],[1706]) ).
thf(2644,plain,
( ( ( sk2 @ ( n @ int_leq ) )
!= ( sk2 @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk2 = n ) ),
inference(paramod_ordered,[status(thm)],[21,1722]) ).
thf(2645,plain,
( ( ( sk2 @ ( n @ int_leq ) )
!= ( sk2 @ ( int_one @ int_leq ) ) )
| ( sk2 = n ) ),
inference(simp,[status(thm)],[2644]) ).
thf(2697,plain,
( ( sk2 != sk2 )
| ( n != int_one )
| ( sk2 = n ) ),
inference(simp,[status(thm)],[2645]) ).
thf(2703,plain,
( ( n != int_one )
| ( sk2 = n ) ),
inference(simp,[status(thm)],[2697]) ).
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(19,plain,
sk1 @ ( int_one @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
thf(4587,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,70]) ).
thf(4588,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[4587]) ).
thf(4589,plain,
sk1 @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[4588:[bind(A,$thf( sk1 ))]]) ).
thf(4828,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4589,36]) ).
thf(4829,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[4828]) ).
thf(4830,plain,
sk1 @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[4829:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 ))]]) ).
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(4722,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)],[4537,62]) ).
thf(4723,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(simp,[status(thm)],[4722]) ).
thf(4724,plain,
( ( int_zero @ ( sk2 @ sk3 ) @ ( int_zero @ plus ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[4723:[bind(A,$thf( int_zero )),bind(B,$thf( sk2 ))]]) ).
thf(10871,plain,
( ( int_zero @ ( sk2 @ sk3 ) )
= sk2 ),
inference(rewrite,[status(thm)],[4724,1041]) ).
thf(262,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)],[21,35]) ).
thf(263,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[262]) ).
thf(264,plain,
( ( sk2 @ ( int_one @ int_less ) )
| ( sk2 = int_one ) ),
inference(pattern_uni,[status(thm)],[263:[bind(A,$thf( int_one )),bind(B,$thf( sk2 ))]]) ).
thf(1517,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)],[264,1483]) ).
thf(1518,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk2 = int_one ) ),
inference(simp,[status(thm)],[1517]) ).
thf(1519,plain,
( ~ ( int_one @ ( sk2 @ int_less ) )
| ( sk2 = int_one ) ),
inference(pattern_uni,[status(thm)],[1518:[bind(A,$thf( sk2 )),bind(B,$thf( int_one ))]]) ).
thf(1960,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)],[35,1519]) ).
thf(1961,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( int_one @ ( sk2 @ int_less ) ) )
| ( sk2 = int_one )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(simp,[status(thm)],[1960]) ).
thf(1962,plain,
( ( sk2 = int_one )
| ~ ( int_one @ ( sk2 @ int_leq ) )
| ( sk2 = int_one ) ),
inference(pattern_uni,[status(thm)],[1961:[bind(A,$thf( sk2 )),bind(B,$thf( int_one ))]]) ).
thf(1978,plain,
( ~ ( int_one @ ( sk2 @ int_leq ) )
| ( sk2 = int_one ) ),
inference(simp,[status(thm)],[1962]) ).
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(4670,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4537,1483]) ).
thf(4671,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[4670]) ).
thf(4672,plain,
~ ( int_zero @ ( sk2 @ int_less ) ),
inference(pattern_uni,[status(thm)],[4671:[bind(A,$thf( sk2 )),bind(B,$thf( int_zero ))]]) ).
thf(4888,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( sk2 @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3372,4672]) ).
thf(4889,plain,
! [A: $i] :
( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( sk2 @ int_less ) ) ),
inference(simp,[status(thm)],[4888]) ).
thf(4918,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) )
!= int_zero )
| ( A != sk2 ) ),
inference(simp,[status(thm)],[4889]) ).
thf(4935,plain,
( ( int_one @ ( sk2 @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[4918]) ).
thf(5571,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_one @ ( sk2 @ plus ) ) )
| ( ( A @ ( B @ plus ) )
!= int_zero ) ),
inference(paramod_ordered,[status(thm)],[50,4935]) ).
thf(5572,plain,
( ( sk2 @ ( int_one @ plus ) )
!= int_zero ),
inference(pattern_uni,[status(thm)],[5571:[bind(A,$thf( sk2 )),bind(B,$thf( int_one ))]]) ).
thf(131,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( n @ ( B @ ( A @ plus ) @ int_leq ) )
!= ( n @ ( A @ int_leq ) ) )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(eqfactor_ordered,[status(thm)],[80]) ).
thf(147,plain,
! [C: $i,B: $i,A: $i] :
( ( ( n @ ( B @ ( A @ plus ) @ int_leq ) )
!= ( n @ ( A @ int_leq ) ) )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[131]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[58]) ).
thf(22,plain,
n @ ( sk1 @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
thf(239,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)],[19,35]) ).
thf(240,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[239]) ).
thf(241,plain,
( ( sk1 @ ( int_one @ int_less ) )
| ( sk1 = int_one ) ),
inference(pattern_uni,[status(thm)],[240:[bind(A,$thf( int_one )),bind(B,$thf( sk1 ))]]) ).
thf(1529,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)],[241,1483]) ).
thf(1530,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[1529]) ).
thf(1531,plain,
( ~ ( int_one @ ( sk1 @ int_less ) )
| ( sk1 = int_one ) ),
inference(pattern_uni,[status(thm)],[1530:[bind(A,$thf( sk1 )),bind(B,$thf( int_one ))]]) ).
thf(2200,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)],[35,1531]) ).
thf(2201,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( int_one @ ( sk1 @ int_less ) ) )
| ( sk1 = int_one )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(simp,[status(thm)],[2200]) ).
thf(2202,plain,
( ( sk1 = int_one )
| ~ ( int_one @ ( sk1 @ int_leq ) )
| ( sk1 = int_one ) ),
inference(pattern_uni,[status(thm)],[2201:[bind(A,$thf( sk1 )),bind(B,$thf( int_one ))]]) ).
thf(2228,plain,
( ~ ( int_one @ ( sk1 @ int_leq ) )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[2202]) ).
thf(11647,plain,
( ( ( n @ ( sk1 @ int_leq ) )
!= ( int_one @ ( sk1 @ int_leq ) ) )
| ~ $true
| ( sk1 = int_one ) ),
inference(paramod_ordered,[status(thm)],[22,2228]) ).
thf(11648,plain,
( ( ( n @ ( sk1 @ int_leq ) )
!= ( int_one @ ( sk1 @ int_leq ) ) )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[11647]) ).
thf(11737,plain,
( ( n != int_one )
| ( sk1 != sk1 )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[11648]) ).
thf(11751,plain,
( ( n != int_one )
| ( sk1 = int_one ) ),
inference(simp,[status(thm)],[11737]) ).
thf(471,plain,
! [B: $i,A: $i] :
( ( ( n @ ( B @ ( A @ plus ) @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( A @ ( sk2 @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ $true
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( sk2 = sk1 ) ),
inference(paramod_ordered,[status(thm)],[19,450]) ).
thf(472,plain,
! [B: $i,A: $i] :
( ( ( n @ ( B @ ( A @ plus ) @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( A @ ( sk2 @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[471]) ).
thf(572,plain,
! [B: $i,A: $i] :
( ( sk1 != n )
| ( ( B @ ( A @ plus ) )
!= int_one )
| ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( A @ ( sk2 @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[472]) ).
thf(685,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk1 @ int_leq ) )
!= ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) )
| ( sk1 != n )
| ( ( B @ ( A @ plus ) )
!= int_one )
| ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( A @ ( sk2 @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ $true
| ( sk2 = sk1 ) ),
inference(paramod_ordered,[status(thm)],[22,572]) ).
thf(686,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk1 @ int_leq ) )
!= ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) )
| ( sk1 != n )
| ( ( B @ ( A @ plus ) )
!= int_one )
| ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( A @ ( sk2 @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[685]) ).
thf(746,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= n )
| ( sk1 != int_one )
| ( sk1 != n )
| ( ( B @ ( A @ plus ) )
!= int_one )
| ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( A @ ( sk2 @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[686]) ).
thf(2856,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(2857,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(simp,[status(thm)],[2856]) ).
thf(2858,plain,
( ( int_zero @ ( int_one @ sk3 ) @ ( int_zero @ plus ) )
= int_one ),
inference(pattern_uni,[status(thm)],[2857:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(2986,plain,
( ( int_zero @ ( int_one @ sk3 ) )
= int_one ),
inference(rewrite,[status(thm)],[2858,1041]) ).
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(273,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)],[22,35]) ).
thf(274,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk1 @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[273]) ).
thf(275,plain,
( ( n @ ( sk1 @ int_less ) )
| ( sk1 = n ) ),
inference(pattern_uni,[status(thm)],[274:[bind(A,$thf( sk1 )),bind(B,$thf( n ))]]) ).
thf(2369,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(2370,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[2369]) ).
thf(2371,plain,
int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[2370:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(2457,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)],[2371,60]) ).
thf(2458,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[2457]) ).
thf(2459,plain,
int_zero @ ( int_zero @ ( int_one @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[2458:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_one @ sk3 ) ))]]) ).
thf(3010,plain,
int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ),
inference(rewrite,[status(thm)],[2459,2986]) ).
thf(4836,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)],[4589,62]) ).
thf(4837,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(simp,[status(thm)],[4836]) ).
thf(4838,plain,
( ( int_zero @ ( sk1 @ sk3 ) @ ( int_zero @ plus ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[4837:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 ))]]) ).
thf(10936,plain,
( ( int_zero @ ( sk1 @ sk3 ) )
= sk1 ),
inference(rewrite,[status(thm)],[4838,1041]) ).
thf(94,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( C @ ( int_one @ int_leq ) ) )
| ~ ( A @ ( C @ 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 ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(paramod_ordered,[status(thm)],[21,80]) ).
thf(95,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( C @ ( int_one @ int_leq ) ) )
| ~ ( A @ ( C @ 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)],[94]) ).
thf(96,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( sk2 @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( ( sk2 @ ( B @ ( sk2 @ plus ) @ a ) )
= real_zero ) ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
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(68,plain,
! [A: $i] :
( ( A @ ( int_one @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) ) ),
inference(cnfConj,[status(thm)],[67]) ).
thf(3759,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)],[3010,68]) ).
thf(3760,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[3759]) ).
thf(3761,plain,
int_zero @ ( int_one @ sk3 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[3760:[bind(A,$thf( int_zero @ ( int_one @ sk3 ) ))]]) ).
thf(3802,plain,
int_one @ ( int_one @ int_leq ),
inference(rewrite,[status(thm)],[3761,2986]) ).
thf(17,plain,
( ( ( sk2 @ ( sk1 @ a ) )
= real_zero )
| ( sk1 != sk2 ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(27,plain,
( ( ( sk2 @ ( sk1 @ a ) )
= real_zero )
| ( sk2 != sk1 ) ),
inference(lifteq,[status(thm)],[17]) ).
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(1511,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)],[275,1483]) ).
thf(1512,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk1 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk1 = n ) ),
inference(simp,[status(thm)],[1511]) ).
thf(1513,plain,
( ~ ( sk1 @ ( n @ int_less ) )
| ( sk1 = n ) ),
inference(pattern_uni,[status(thm)],[1512:[bind(A,$thf( n )),bind(B,$thf( sk1 ))]]) ).
thf(1777,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)],[35,1513]) ).
thf(1778,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( sk1 @ ( n @ int_less ) ) )
| ( sk1 = n )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(simp,[status(thm)],[1777]) ).
thf(1779,plain,
( ( sk1 = n )
| ~ ( sk1 @ ( n @ int_leq ) )
| ( sk1 = n ) ),
inference(pattern_uni,[status(thm)],[1778:[bind(A,$thf( n )),bind(B,$thf( sk1 ))]]) ).
thf(1806,plain,
( ~ ( sk1 @ ( n @ int_leq ) )
| ( sk1 = n ) ),
inference(simp,[status(thm)],[1779]) ).
thf(3194,plain,
( ( ( sk1 @ ( n @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk1 = n ) ),
inference(paramod_ordered,[status(thm)],[19,1806]) ).
thf(3195,plain,
( ( ( sk1 @ ( n @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( sk1 = n ) ),
inference(simp,[status(thm)],[3194]) ).
thf(3198,plain,
( ( sk1 != sk1 )
| ( n != int_one )
| ( sk1 = n ) ),
inference(simp,[status(thm)],[3195]) ).
thf(3208,plain,
( ( n != int_one )
| ( sk1 = n ) ),
inference(simp,[status(thm)],[3198]) ).
thf(4788,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4589,1483]) ).
thf(4789,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[4788]) ).
thf(4790,plain,
~ ( int_zero @ ( sk1 @ int_less ) ),
inference(pattern_uni,[status(thm)],[4789:[bind(A,$thf( sk1 )),bind(B,$thf( int_zero ))]]) ).
thf(862,plain,
( ( sk1 != sk1 )
| ( n @ ( int_one @ int_leq ) )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[241,22]) ).
thf(863,plain,
( ( n @ ( int_one @ int_leq ) )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[862:[]]) ).
thf(962,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(963,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[962]) ).
thf(964,plain,
int_one @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[963:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(4962,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( sk1 @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3372,4790]) ).
thf(4963,plain,
! [A: $i] :
( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( sk1 @ int_less ) ) ),
inference(simp,[status(thm)],[4962]) ).
thf(4997,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) )
!= int_zero )
| ( A != sk1 ) ),
inference(simp,[status(thm)],[4963]) ).
thf(5007,plain,
( ( int_one @ ( sk1 @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[4997]) ).
thf(6626,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ ( int_one @ plus ) @ int_less ) ) )
| ~ $true
| ( A @ ( B @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[46,3921]) ).
thf(6627,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ ( int_one @ plus ) @ int_less ) ) )
| ( A @ ( B @ int_leq ) ) ),
inference(simp,[status(thm)],[6626]) ).
thf(6628,plain,
int_one @ ( int_one @ plus ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[6627:[bind(A,$thf( int_one @ ( int_one @ plus ) )),bind(B,$thf( int_zero ))]]) ).
thf(87,plain,
! [C: $i,B: $i,A: $i] :
( ( ( n @ ( B @ ( A @ plus ) @ int_leq ) )
!= ( sk2 @ ( int_one @ int_leq ) ) )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ $true
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(paramod_ordered,[status(thm)],[21,80]) ).
thf(88,plain,
! [C: $i,B: $i,A: $i] :
( ( ( n @ ( B @ ( A @ plus ) @ int_leq ) )
!= ( sk2 @ ( int_one @ int_leq ) ) )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[87]) ).
thf(150,plain,
! [C: $i,B: $i,A: $i] :
( ( sk2 != n )
| ( ( B @ ( A @ plus ) )
!= int_one )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[88]) ).
thf(4361,plain,
( ( ( n @ ( sk2 @ int_leq ) )
!= ( int_one @ ( sk2 @ int_leq ) ) )
| ~ $true
| ( sk2 = int_one ) ),
inference(paramod_ordered,[status(thm)],[23,1978]) ).
thf(4362,plain,
( ( ( n @ ( sk2 @ int_leq ) )
!= ( int_one @ ( sk2 @ int_leq ) ) )
| ( sk2 = int_one ) ),
inference(simp,[status(thm)],[4361]) ).
thf(4384,plain,
( ( n != int_one )
| ( sk2 != sk2 )
| ( sk2 = int_one ) ),
inference(simp,[status(thm)],[4362]) ).
thf(4392,plain,
( ( n != int_one )
| ( sk2 = int_one ) ),
inference(simp,[status(thm)],[4384]) ).
thf(143,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= n )
| ( ( B @ ( A @ plus ) )
!= int_one )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[129]) ).
thf(2254,plain,
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,2233]) ).
thf(2255,plain,
( ( sk1 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[2254]) ).
thf(2259,plain,
( ( sk1 != int_zero )
| ( int_one != int_one ) ),
inference(simp,[status(thm)],[2255]) ).
thf(2266,plain,
sk1 != int_zero,
inference(simp,[status(thm)],[2259]) ).
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(132,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( n @ ( B @ ( A @ plus ) @ int_leq ) )
!= ( C @ ( int_one @ int_leq ) ) )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(eqfactor_ordered,[status(thm)],[80]) ).
thf(151,plain,
! [C: $i,B: $i,A: $i] :
( ( ( n @ ( B @ ( A @ plus ) @ int_leq ) )
!= ( C @ ( int_one @ int_leq ) ) )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[132]) ).
thf(817,plain,
( ( sk2 != sk2 )
| ( n @ ( int_one @ int_leq ) )
| ( n @ ( sk2 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[230,21]) ).
thf(818,plain,
( ( n @ ( int_one @ int_leq ) )
| ( n @ ( sk2 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[817:[]]) ).
thf(109,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( C @ ( int_one @ int_leq ) ) )
| ~ ( A @ ( C @ 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 ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(paramod_ordered,[status(thm)],[19,80]) ).
thf(110,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( C @ ( int_one @ int_leq ) ) )
| ~ ( A @ ( C @ 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)],[109]) ).
thf(111,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( sk1 @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( ( sk1 @ ( B @ ( sk1 @ plus ) @ a ) )
= real_zero ) ),
inference(pattern_uni,[status(thm)],[110:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(5617,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_one @ ( sk1 @ plus ) ) )
| ( ( A @ ( B @ plus ) )
!= int_zero ) ),
inference(paramod_ordered,[status(thm)],[50,5007]) ).
thf(5618,plain,
( ( sk1 @ ( int_one @ plus ) )
!= int_zero ),
inference(pattern_uni,[status(thm)],[5617:[bind(A,$thf( sk1 )),bind(B,$thf( int_one ))]]) ).
thf(108111,plain,
$false,
inference(e,[status(thm)],[53,41,3921,50,450,1501,4005,4714,1041,56,4739,142,1507,1577,2703,46,4830,29,10871,1978,84,5572,147,4935,74,60,4589,2264,11751,746,1519,70,2986,28,38,275,21,65,2228,3010,10936,96,73,3802,1483,264,45,64,3372,22,44,27,54,572,3208,4672,4537,71,4790,1806,230,1722,39,863,964,5007,6628,394,35,241,80,48,150,1531,4392,143,2266,40,55,23,1513,82,151,36,2233,51,818,19,47,15,68,62,111,5618]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV490+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.14/0.40 % Computer : n011.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.40 % WCLimit : 300
% 0.14/0.40 % DateTime : Sat Sep 26 13:58:14 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 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
% 0.88/0.97 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.29/1.17 % [INFO] Parsing done (200ms).
% 1.29/1.19 % [INFO] Running in sequential loop mode.
% 1.91/1.58 % [INFO] eprover registered as external prover.
% 1.91/1.59 % [INFO] Scanning for conjecture ...
% 2.30/1.70 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.30/1.74 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.30/1.77 % [INFO] Problem is first-order (TPTP FOF).
% 2.30/1.78 % [INFO] Type checking passed.
% 2.30/1.79 % [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 ...
% 136.82/35.99 % External prover 'e' found a proof!
% 136.82/35.99 % [INFO] Killing All external provers ...
% 136.82/35.99 % Time passed: 35447ms (effective reasoning time: 34797ms)
% 136.82/35.99 % 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)>
% 136.82/36.00 % 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
% 136.82/36.00 % No. of inferences in proof: 273
% 136.82/36.00 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 35447 ms resp. 34797 ms w/o parsing
% 137.37/36.12 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 137.37/36.13 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------