%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV491+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 : n010.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 88.71s 21.70s
% Output : Refutation 89.42s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 16
% Syntax : Number of formulae : 504 ( 122 unt; 0 typ; 3 def)
% Number of atoms : 2060 ( 630 equ; 0 cnn)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 6169 (1104 ~;1017 |; 77 &;3918 @)
% ( 3 <=>; 50 =>; 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 : 16 ( 13 usr; 10 con; 0-2 aty)
% Number of variables : 652 ( 2 ^; 642 !; 5 ?; 652 :)
% ( 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(int_less_decl,type,
int_less: $i > $i > $o ).
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_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: $o ).
thf(sk4_decl,type,
sk4: $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 @ int_less ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) )
& ( ( B @ ( A @ int_less ) )
=> ( ( 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 @ int_less ) )
=> ( ( A @ ( sk1 @ a ) )
= real_zero ) )
& ( ( A @ ( sk1 @ int_less ) )
=> ( ( A @ ( sk1 @ a ) )
= real_zero ) ) ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( ^ [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 @ int_less ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) )
& ( ( B @ ( A @ int_less ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',diag) ).
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 @ int_less ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) )
& ( ( B @ ( A @ int_less ) )
=> ( ( 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 @ int_less ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) )
& ( ( B @ ( A @ int_less ) )
=> ( ( 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 )
| sk3 )
& ( ( sk1 = sk2 )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero )
| sk3 )
& ( ( ( sk2 @ ( sk1 @ a ) )
!= real_one )
| ( sk1 @ ( sk2 @ int_less ) )
| sk3 )
& ( ( sk1 = sk2 )
| ( sk1 @ ( sk2 @ int_less ) )
| sk3 )
& ( ~ sk3
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) )
& ( ~ sk3
| ( sk2 @ ( sk1 @ int_less ) ) )
& ( n @ ( sk2 @ int_leq ) )
& ( sk2 @ ( int_one @ int_leq ) )
& ( n @ ( sk1 @ int_leq ) )
& ( sk1 @ ( int_one @ int_leq ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(26,plain,
sk2 @ ( 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(68,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(69,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)],[68]) ).
thf(70,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)],[69]) ).
thf(72,plain,
! [A: $i] :
( ( A @ ( int_zero @ int_less ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(73,plain,
! [A: $i] :
( ( A @ ( int_zero @ int_less ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[72]) ).
thf(5283,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26,73]) ).
thf(5284,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[5283]) ).
thf(5285,plain,
sk2 @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[5284:[bind(A,$thf( sk2 ))]]) ).
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(59,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(60,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)],[59]) ).
thf(61,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 @ sk4 ) @ ( int_zero @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) )
& ( ( ( A @ ( B @ sk4 ) @ ( A @ plus ) )
= B )
| ~ ( B @ ( A @ int_less ) ) ) ),
inference(cnf,[status(esa)],[60]) ).
thf(64,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ int_less ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ( ( C @ ( A @ plus ) )
!= B ) ),
inference(cnfConj,[status(thm)],[61]) ).
thf(66,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ int_less ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ( ( C @ ( A @ plus ) )
!= B ) ),
inference(lifteq,[status(thm)],[64]) ).
thf(67,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) @ ( A @ int_less ) )
| ~ ( B @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[66]) ).
thf(5364,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( int_zero @ int_less ) ) )
| ( B @ ( A @ plus ) @ ( A @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5285,67]) ).
thf(5365,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( int_zero @ int_less ) ) )
| ( B @ ( A @ plus ) @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[5364]) ).
thf(5366,plain,
! [A: $i] : ( sk2 @ ( A @ plus ) @ ( A @ int_less ) ),
inference(pattern_uni,[status(thm)],[5365:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
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(32,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(33,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)],[32]) ).
thf(34,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)],[33]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[34]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[36]) ).
thf(10865,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ plus ) @ ( A @ int_less ) )
!= ( C @ ( B @ int_less ) ) )
| ( C @ ( B @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5366,39]) ).
thf(10866,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk2 @ ( A @ plus ) @ ( A @ int_less ) )
!= ( C @ ( B @ int_less ) ) )
| ( C @ ( B @ int_leq ) ) ),
inference(simp,[status(thm)],[10865]) ).
thf(10867,plain,
! [A: $i] : ( sk2 @ ( A @ plus ) @ ( A @ int_leq ) ),
inference(pattern_uni,[status(thm)],[10866:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk2 @ ( D @ plus ) ))]]) ).
thf(10915,plain,
! [A: $i] : ( sk2 @ ( A @ plus ) @ ( A @ int_leq ) ),
inference(simp,[status(thm)],[10867]) ).
thf(21066,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( B @ ( int_one @ int_leq ) ) )
| ( B @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10915,73]) ).
thf(21067,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( B @ ( int_one @ int_leq ) ) )
| ( B @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[21066]) ).
thf(21068,plain,
sk2 @ ( int_one @ plus ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[21067:[bind(A,$thf( int_one )),bind(B,$thf( sk2 @ ( int_one @ plus ) ))]]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[61]) ).
thf(21446,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21068,63]) ).
thf(21447,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[21446]) ).
thf(21448,plain,
int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[21447:[bind(A,$thf( int_zero )),bind(B,$thf( sk2 @ ( int_one @ plus ) ))]]) ).
thf(71,plain,
! [A: $i] :
( ( A @ ( int_one @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) ) ),
inference(cnfConj,[status(thm)],[70]) ).
thf(23571,plain,
! [A: $i] :
( ( ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21448,71]) ).
thf(23572,plain,
! [A: $i] :
( ( ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[23571]) ).
thf(23573,plain,
int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[23572:[bind(A,$thf( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) ))]]) ).
thf(5358,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5285,39]) ).
thf(5359,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[5358]) ).
thf(5360,plain,
sk2 @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[5359:[bind(A,$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(51,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(cnf,[status(esa)],[51]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(23,plain,
n @ ( sk2 @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
thf(7,axiom,
int_one @ ( int_zero @ int_less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_zero_one) ).
thf(50,plain,
int_one @ ( int_zero @ int_less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(19,plain,
sk1 @ ( int_one @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
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',qih) ).
thf(77,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(78,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)],[77]) ).
thf(79,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)],[78]) ).
thf(82,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)],[79]) ).
thf(83,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)],[82]) ).
thf(17,plain,
( ~ sk3
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(28,plain,
( ~ sk3
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(158,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ plus ) @ a ) )
!= ( sk2 @ ( sk1 @ a ) ) )
| ~ sk3
| ( 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)],[83,28]) ).
thf(159,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ plus ) @ a ) )
!= ( sk2 @ ( sk1 @ a ) ) )
| ~ sk3
| ~ ( 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)],[158]) ).
thf(231,plain,
! [C: $i,B: $i,A: $i] :
( ( C != sk2 )
| ( ( B @ ( C @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( 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)],[159]) ).
thf(271,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( 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)],[231]) ).
thf(282,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( 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)],[271,26]) ).
thf(283,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( 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)],[282]) ).
thf(318,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( A @ ( sk2 @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ $true
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[19,283]) ).
thf(319,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( A @ ( sk2 @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[318]) ).
thf(320,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) )
| ~ ( n @ ( sk1 @ int_leq ) )
| ~ ( n @ ( A @ ( sk1 @ plus ) @ int_leq ) )
| ~ ( A @ ( sk1 @ plus ) @ ( int_one @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[319:[bind(A,$thf( sk1 ))]]) ).
thf(389,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) )
| ~ ( n @ ( sk1 @ int_leq ) )
| ~ ( n @ ( A @ ( sk1 @ plus ) @ int_leq ) )
| ~ ( A @ ( sk1 @ plus ) @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[320]) ).
thf(21,plain,
n @ ( sk1 @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
thf(1078,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) )
| ~ $true
| ~ ( n @ ( A @ ( sk1 @ plus ) @ int_leq ) )
| ~ ( A @ ( sk1 @ plus ) @ ( int_one @ int_leq ) ) ),
inference(rewrite,[status(thm)],[389,21]) ).
thf(1079,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ ( sk1 @ plus ) @ int_leq ) )
| ~ ( A @ ( sk1 @ plus ) @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1078]) ).
thf(1182,plain,
! [A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( ( A @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ int_leq ) )
| ~ $true
| ~ ( n @ ( A @ ( sk1 @ plus ) @ int_leq ) )
| ~ ( A @ ( sk1 @ plus ) @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[50,1079]) ).
thf(1183,plain,
! [A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( ( A @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ int_leq ) )
| ~ ( n @ ( A @ ( sk1 @ plus ) @ int_leq ) )
| ~ ( A @ ( sk1 @ plus ) @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1182]) ).
thf(1184,plain,
( ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ int_leq ) )
| ~ ( n @ ( int_one @ ( sk1 @ plus ) @ int_leq ) )
| ~ ( int_one @ ( sk1 @ plus ) @ ( int_one @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[1183:[bind(A,$thf( int_one ))]]) ).
thf(1371,plain,
( ( ( int_one @ ( sk1 @ plus ) @ ( int_one @ int_leq ) )
!= ( sk2 @ ( int_one @ int_leq ) ) )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ int_leq ) )
| ~ ( n @ ( int_one @ ( sk1 @ plus ) @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[26,1184]) ).
thf(1372,plain,
( ( ( int_one @ ( sk1 @ plus ) @ ( int_one @ int_leq ) )
!= ( sk2 @ ( int_one @ int_leq ) ) )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ int_leq ) )
| ~ ( n @ ( int_one @ ( sk1 @ plus ) @ int_leq ) ) ),
inference(simp,[status(thm)],[1371]) ).
thf(1408,plain,
( ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( int_one != int_one )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ int_leq ) )
| ~ ( n @ ( int_one @ ( sk1 @ plus ) @ int_leq ) ) ),
inference(simp,[status(thm)],[1372]) ).
thf(1416,plain,
( ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ int_leq ) )
| ~ ( n @ ( int_one @ ( sk1 @ plus ) @ int_leq ) ) ),
inference(simp,[status(thm)],[1408]) ).
thf(1932,plain,
( ( ( n @ ( int_one @ ( sk1 @ plus ) @ int_leq ) )
!= ( n @ ( sk2 @ int_leq ) ) )
| ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,1416]) ).
thf(1933,plain,
( ( ( n @ ( int_one @ ( sk1 @ plus ) @ int_leq ) )
!= ( n @ ( sk2 @ int_leq ) ) )
| ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ int_leq ) ) ),
inference(simp,[status(thm)],[1932]) ).
thf(1962,plain,
( ( n != n )
| ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ int_leq ) ) ),
inference(simp,[status(thm)],[1933]) ).
thf(1977,plain,
( ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ ( sk1 @ ( sk2 @ int_leq ) ) ),
inference(simp,[status(thm)],[1962]) ).
thf(2067,plain,
( ( ( sk1 @ ( sk2 @ int_leq ) )
!= ( n @ ( sk2 @ int_leq ) ) )
| ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,1977]) ).
thf(2068,plain,
( ( ( sk1 @ ( sk2 @ int_leq ) )
!= ( n @ ( sk2 @ int_leq ) ) )
| ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3 ),
inference(simp,[status(thm)],[2067]) ).
thf(2075,plain,
( ( sk1 != n )
| ( sk2 != sk2 )
| ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3 ),
inference(simp,[status(thm)],[2068]) ).
thf(2091,plain,
( ( sk1 != n )
| ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3 ),
inference(simp,[status(thm)],[2075]) ).
thf(2629,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_one @ ( sk2 @ plus ) ) )
| ( sk1 != n )
| ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( ( A @ ( B @ plus ) )
!= sk1 )
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[53,2091]) ).
thf(2630,plain,
( ( sk1 != n )
| ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( ( sk2 @ ( int_one @ plus ) )
!= sk1 )
| ~ sk3 ),
inference(pattern_uni,[status(thm)],[2629:[bind(A,$thf( sk2 )),bind(B,$thf( int_one ))]]) ).
thf(62,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk4 ) @ ( A @ plus ) )
= B )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[61]) ).
thf(65,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ( ( A @ ( B @ sk4 ) @ ( A @ plus ) )
= B ) ),
inference(lifteq,[status(thm)],[62]) ).
thf(4092,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ~ $true
| ( ( A @ ( B @ sk4 ) @ ( A @ plus ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[50,65]) ).
thf(4093,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( ( A @ ( B @ sk4 ) @ ( A @ plus ) )
= B ) ),
inference(simp,[status(thm)],[4092]) ).
thf(4094,plain,
( ( int_zero @ ( int_one @ sk4 ) @ ( int_zero @ plus ) )
= int_one ),
inference(pattern_uni,[status(thm)],[4093:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(9,axiom,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_zero) ).
thf(54,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(55,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(cnf,[status(esa)],[54]) ).
thf(56,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(lifteq,[status(thm)],[55]) ).
thf(439,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_zero @ ( C @ plus ) ) )
| ( ( A @ ( B @ plus ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[53,56]) ).
thf(440,plain,
! [A: $i] :
( ( A @ ( int_zero @ plus ) )
= A ),
inference(pattern_uni,[status(thm)],[439:[bind(A,$thf( A )),bind(B,$thf( int_zero )),bind(C,$thf( A ))]]) ).
thf(4169,plain,
( ( int_zero @ ( int_one @ sk4 ) )
= int_one ),
inference(rewrite,[status(thm)],[4094,440]) ).
thf(4643,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)],[50,67]) ).
thf(4644,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)],[4643]) ).
thf(4645,plain,
! [A: $i] : ( int_one @ ( A @ plus ) @ ( A @ int_less ) ),
inference(pattern_uni,[status(thm)],[4644:[bind(A,$thf( A )),bind(B,$thf( int_one ))]]) ).
thf(9429,plain,
! [C: $i,B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( C @ ( B @ int_less ) ) )
| ( C @ ( B @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4645,39]) ).
thf(9430,plain,
! [C: $i,B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( C @ ( B @ int_less ) ) )
| ( C @ ( B @ int_leq ) ) ),
inference(simp,[status(thm)],[9429]) ).
thf(9431,plain,
! [A: $i] : ( int_one @ ( A @ plus ) @ ( A @ int_leq ) ),
inference(pattern_uni,[status(thm)],[9430:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( int_one @ ( D @ plus ) ))]]) ).
thf(9467,plain,
! [A: $i] : ( int_one @ ( A @ plus ) @ ( A @ int_leq ) ),
inference(simp,[status(thm)],[9431]) ).
thf(14303,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( B @ ( int_one @ int_leq ) ) )
| ( B @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9467,73]) ).
thf(14304,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( B @ ( int_one @ int_leq ) ) )
| ( B @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[14303]) ).
thf(14305,plain,
int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[14304:[bind(A,$thf( int_one )),bind(B,$thf( int_one @ ( int_one @ plus ) ))]]) ).
thf(25,plain,
( ~ sk3
| ( sk2 @ ( sk1 @ int_less ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(1552,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[25,39]) ).
thf(1553,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ sk3 ),
inference(simp,[status(thm)],[1552]) ).
thf(1554,plain,
( ( sk2 @ ( sk1 @ int_leq ) )
| ~ sk3 ),
inference(pattern_uni,[status(thm)],[1553:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(14600,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14305,63]) ).
thf(14601,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[14600]) ).
thf(14602,plain,
int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[14601:[bind(A,$thf( int_zero )),bind(B,$thf( int_one @ ( int_one @ plus ) ))]]) ).
thf(16246,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14602,63]) ).
thf(16247,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[16246]) ).
thf(16248,plain,
int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[16247:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) ))]]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_irreflexive) ).
thf(44,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(45,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[45]) ).
thf(47,plain,
! [A: $i] :
~ ( A @ ( A @ int_less ) ),
inference(simp,[status(thm)],[46]) ).
thf(18098,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16248,47]) ).
thf(18099,plain,
! [A: $i] :
( ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[18098]) ).
thf(18111,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ sk4 ) )
!= A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[18099]) ).
thf(18129,plain,
( ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ sk4 ) )
!= int_zero ),
inference(simp,[status(thm)],[18111]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[34]) ).
thf(38,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(695,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk1 @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[21,38]) ).
thf(696,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk1 @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[695]) ).
thf(697,plain,
( ( n @ ( sk1 @ int_less ) )
| ( sk1 = n ) ),
inference(pattern_uni,[status(thm)],[696:[bind(A,$thf( sk1 )),bind(B,$thf( n ))]]) ).
thf(940,plain,
( ( sk1 != sk1 )
| ( n @ ( int_one @ int_leq ) )
| ( n @ ( sk1 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[697,19]) ).
thf(941,plain,
( ( n @ ( int_one @ int_leq ) )
| ( n @ ( sk1 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[940:[]]) ).
thf(203,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)],[83]) ).
thf(217,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)],[203]) ).
thf(16276,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14602,47]) ).
thf(16277,plain,
! [A: $i] :
( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[16276]) ).
thf(16287,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) )
!= A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[16277]) ).
thf(16308,plain,
( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) )
!= int_zero ),
inference(simp,[status(thm)],[16287]) ).
thf(1525,plain,
! [A: $i] :
( ( ( n @ ( sk1 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ( n @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[941,47]) ).
thf(1526,plain,
! [A: $i] :
( ( ( n @ ( sk1 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ( n @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1525]) ).
thf(1540,plain,
! [A: $i] :
( ( n != A )
| ( sk1 != A )
| ( n @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1526]) ).
thf(1544,plain,
( ( sk1 != n )
| ( n @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1540]) ).
thf(773,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)],[23,38]) ).
thf(774,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[773]) ).
thf(775,plain,
( ( n @ ( sk2 @ int_less ) )
| ( sk2 = n ) ),
inference(pattern_uni,[status(thm)],[774:[bind(A,$thf( sk2 )),bind(B,$thf( n ))]]) ).
thf(5613,plain,
( ( sk2 != sk2 )
| ( n @ ( int_zero @ int_leq ) )
| ( n @ ( sk2 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[775,5360]) ).
thf(5614,plain,
( ( n @ ( int_zero @ int_leq ) )
| ( n @ ( sk2 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[5613:[]]) ).
thf(5296,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,73]) ).
thf(5297,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[5296]) ).
thf(5298,plain,
sk1 @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[5297:[bind(A,$thf( sk1 ))]]) ).
thf(5434,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( int_zero @ int_less ) ) )
| ( B @ ( A @ plus ) @ ( A @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5298,67]) ).
thf(5435,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( int_zero @ int_less ) ) )
| ( B @ ( A @ plus ) @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[5434]) ).
thf(5436,plain,
! [A: $i] : ( sk1 @ ( A @ plus ) @ ( A @ int_less ) ),
inference(pattern_uni,[status(thm)],[5435:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(12096,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( sk1 @ ( C @ plus ) ) )
| ( A @ ( B @ plus ) @ ( C @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[53,5436]) ).
thf(12097,plain,
! [A: $i] : ( A @ ( sk1 @ plus ) @ ( A @ int_less ) ),
inference(pattern_uni,[status(thm)],[12096:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(9426,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( B @ ( int_zero @ int_less ) ) )
| ( B @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4645,71]) ).
thf(9427,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( B @ ( int_zero @ int_less ) ) )
| ( B @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[9426]) ).
thf(9428,plain,
int_one @ ( int_zero @ plus ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[9427:[bind(A,$thf( int_zero )),bind(B,$thf( int_one @ ( int_zero @ plus ) ))]]) ).
thf(9481,plain,
int_one @ ( int_one @ int_leq ),
inference(rewrite,[status(thm)],[9428,440]) ).
thf(183,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)],[26,83]) ).
thf(184,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)],[183]) ).
thf(185,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( sk2 @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( ( sk2 @ ( B @ ( sk2 @ plus ) @ a ) )
= real_zero ) ),
inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk2 ))]]) ).
thf(796,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)],[19,38]) ).
thf(797,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[796]) ).
thf(798,plain,
( ( sk1 @ ( int_one @ int_less ) )
| ( sk1 = int_one ) ),
inference(pattern_uni,[status(thm)],[797:[bind(A,$thf( int_one )),bind(B,$thf( sk1 ))]]) ).
thf(762,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)],[26,38]) ).
thf(763,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[762]) ).
thf(764,plain,
( ( sk2 @ ( int_one @ int_less ) )
| ( sk2 = int_one ) ),
inference(pattern_uni,[status(thm)],[763:[bind(A,$thf( int_one )),bind(B,$thf( sk2 ))]]) ).
thf(88,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[25,47]) ).
thf(89,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ sk3 ),
inference(simp,[status(thm)],[88]) ).
thf(90,plain,
! [A: $i] :
( ( sk2 != A )
| ( sk1 != A )
| ~ sk3 ),
inference(simp,[status(thm)],[89]) ).
thf(91,plain,
( ( sk2 != sk1 )
| ~ sk3 ),
inference(simp,[status(thm)],[90]) ).
thf(992,plain,
( ( sk2 != sk2 )
| ( sk1 != int_one )
| ~ sk3
| ( sk2 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[764,91]) ).
thf(993,plain,
( ( sk1 != int_one )
| ~ sk3
| ( sk2 @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[992:[]]) ).
thf(2836,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ( sk1 != int_one )
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[993,47]) ).
thf(2837,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ( sk1 != int_one )
| ~ sk3 ),
inference(simp,[status(thm)],[2836]) ).
thf(2842,plain,
! [A: $i] :
( ( sk2 != A )
| ( int_one != A )
| ( sk1 != int_one )
| ~ sk3 ),
inference(simp,[status(thm)],[2837]) ).
thf(2850,plain,
( ( sk2 != int_one )
| ( sk1 != int_one )
| ~ sk3 ),
inference(simp,[status(thm)],[2842]) ).
thf(3234,plain,
( ( sk1 != sk1 )
| ( sk2 != int_one )
| ( int_one != int_one )
| ~ sk3
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[798,2850]) ).
thf(3235,plain,
( ( sk1 != sk1 )
| ( sk2 != int_one )
| ~ sk3
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(simp,[status(thm)],[3234]) ).
thf(3236,plain,
( ( sk2 != int_one )
| ~ sk3
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[3235:[]]) ).
thf(1059,plain,
( ( sk2 != sk2 )
| ( n @ ( int_one @ int_leq ) )
| ( n @ ( sk2 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[775,26]) ).
thf(1060,plain,
( ( n @ ( int_one @ int_leq ) )
| ( n @ ( sk2 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[1059:[]]) ).
thf(3287,plain,
! [A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ( n @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[1060,47]) ).
thf(3288,plain,
! [A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ( n @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[3287]) ).
thf(3296,plain,
! [A: $i] :
( ( n != A )
| ( sk2 != A )
| ( n @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[3288]) ).
thf(3297,plain,
( ( sk2 != n )
| ( n @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[3296]) ).
thf(5250,plain,
! [A: $i] :
( ( ( n @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true
| ( sk2 != n ) ),
inference(paramod_ordered,[status(thm)],[3297,73]) ).
thf(5251,plain,
! [A: $i] :
( ( ( n @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ( sk2 != n ) ),
inference(simp,[status(thm)],[5250]) ).
thf(5252,plain,
( ( n @ ( int_zero @ int_less ) )
| ( sk2 != n ) ),
inference(pattern_uni,[status(thm)],[5251:[bind(A,$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(42,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(12106,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ plus ) @ ( A @ int_less ) )
!= ( C @ ( B @ int_less ) ) )
| ( C @ ( B @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5436,39]) ).
thf(12107,plain,
! [C: $i,B: $i,A: $i] :
( ( ( sk1 @ ( A @ plus ) @ ( A @ int_less ) )
!= ( C @ ( B @ int_less ) ) )
| ( C @ ( B @ int_leq ) ) ),
inference(simp,[status(thm)],[12106]) ).
thf(12108,plain,
! [A: $i] : ( sk1 @ ( A @ plus ) @ ( A @ int_leq ) ),
inference(pattern_uni,[status(thm)],[12107:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk1 @ ( D @ plus ) ))]]) ).
thf(12143,plain,
! [A: $i] : ( sk1 @ ( A @ plus ) @ ( A @ int_leq ) ),
inference(simp,[status(thm)],[12108]) ).
thf(29364,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( B @ ( int_one @ int_leq ) ) )
| ( B @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12143,73]) ).
thf(29365,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( B @ ( int_one @ int_leq ) ) )
| ( B @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[29364]) ).
thf(29366,plain,
sk1 @ ( int_one @ plus ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[29365:[bind(A,$thf( int_one )),bind(B,$thf( sk1 @ ( int_one @ plus ) ))]]) ).
thf(1570,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)],[50,39]) ).
thf(1571,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[1570]) ).
thf(1572,plain,
int_one @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[1571:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(13,axiom,
real_zero != real_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',real_constants) ).
thf(74,plain,
real_zero != real_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(75,plain,
real_zero != real_one,
inference(polarity_switch,[status(thm)],[74]) ).
thf(76,plain,
real_one != real_zero,
inference(lifteq,[status(thm)],[75]) ).
thf(714,plain,
! [B: $i,A: $i] :
( ( A != real_one )
| ( B != real_zero )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[38,76]) ).
thf(715,plain,
! [A: $i] :
( ( A != real_zero )
| ( A @ ( real_one @ int_less ) )
| ~ ( A @ ( real_one @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[714:[bind(A,$thf( real_one ))]]) ).
thf(881,plain,
( ( real_zero @ ( real_one @ int_less ) )
| ~ ( real_zero @ ( real_one @ int_leq ) ) ),
inference(simp,[status(thm)],[715]) ).
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(57,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(3540,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,63]) ).
thf(3541,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[3540]) ).
thf(3542,plain,
int_zero @ ( int_one @ sk4 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[3541:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(3608,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3542,63]) ).
thf(3609,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[3608]) ).
thf(3610,plain,
int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[3609:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_one @ sk4 ) ))]]) ).
thf(3779,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3610,63]) ).
thf(3780,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[3779]) ).
thf(3781,plain,
int_zero @ ( int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[3780:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) ))]]) ).
thf(4719,plain,
int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ),
inference(rewrite,[status(thm)],[3781,4169]) ).
thf(4774,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4719,47]) ).
thf(4775,plain,
! [A: $i] :
( ( int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[4774]) ).
thf(4779,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) )
!= A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[4775]) ).
thf(4786,plain,
( ( int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) )
!= int_zero ),
inference(simp,[status(thm)],[4779]) ).
thf(4793,plain,
( ( int_zero @ ( int_one @ sk4 ) )
!= int_zero ),
inference(rewrite,[status(thm)],[4786,4169]) ).
thf(22,plain,
( ( ( sk2 @ ( sk1 @ a ) )
!= real_one )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero )
| sk3 ),
inference(cnfConj,[status(thm)],[16]) ).
thf(29,plain,
( sk3
| ( ( sk2 @ ( sk1 @ a ) )
!= real_one )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(5378,plain,
( ( sk2 != sk2 )
| ( n @ ( int_zero @ int_less ) )
| ( n @ ( sk2 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[775,5285]) ).
thf(5379,plain,
( ( n @ ( int_zero @ int_less ) )
| ( n @ ( sk2 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[5378:[]]) ).
thf(29820,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29366,63]) ).
thf(29821,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[29820]) ).
thf(29822,plain,
int_zero @ ( sk1 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[29821:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 @ ( int_one @ plus ) ))]]) ).
thf(31488,plain,
! [A: $i] :
( ( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29822,71]) ).
thf(31489,plain,
! [A: $i] :
( ( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[31488]) ).
thf(31490,plain,
int_zero @ ( sk1 @ ( int_one @ plus ) @ sk4 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[31489:[bind(A,$thf( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk4 ) ))]]) ).
thf(209,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( A @ ( C @ int_leq ) )
!= ( A @ ( int_one @ 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(eqfactor_ordered,[status(thm)],[83]) ).
thf(232,plain,
! [B: $i,A: $i] :
( ~ ( int_one @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( ( int_one @ ( B @ ( int_one @ plus ) @ a ) )
= real_zero ) ),
inference(pattern_uni,[status(thm)],[209:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( int_one ))]]) ).
thf(18841,plain,
! [B: $i,A: $i] :
( ~ $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 ) )
| ( ( int_one @ ( B @ ( int_one @ plus ) @ a ) )
= real_zero ) ),
inference(rewrite,[status(thm)],[232,9481]) ).
thf(18842,plain,
! [B: $i,A: $i] :
( ~ ( 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 ) )
| ( ( int_one @ ( B @ ( int_one @ plus ) @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[18841]) ).
thf(189,plain,
! [C: $i,B: $i,A: $i] :
( ( ( n @ ( sk2 @ 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 ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ $true
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(paramod_ordered,[status(thm)],[23,83]) ).
thf(190,plain,
! [C: $i,B: $i,A: $i] :
( ( ( n @ ( sk2 @ 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 ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[189]) ).
thf(243,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= n )
| ( sk2 != 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 ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[190]) ).
thf(5345,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ~ $true
| ( ( A @ ( B @ sk4 ) @ ( A @ plus ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[5285,65]) ).
thf(5346,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( ( A @ ( B @ sk4 ) @ ( A @ plus ) )
= B ) ),
inference(simp,[status(thm)],[5345]) ).
thf(5347,plain,
( ( int_zero @ ( sk2 @ sk4 ) @ ( int_zero @ plus ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[5346:[bind(A,$thf( int_zero )),bind(B,$thf( sk2 ))]]) ).
thf(7758,plain,
( ( int_zero @ ( sk2 @ sk4 ) )
= sk2 ),
inference(rewrite,[status(thm)],[5347,440]) ).
thf(5302,plain,
! [B: $i,A: $i] :
( ( ( A @ ( int_zero @ int_less ) )
!= ( B @ ( B @ int_less ) ) )
| ~ $true
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[73,47]) ).
thf(5303,plain,
! [B: $i,A: $i] :
( ( ( A @ ( int_zero @ int_less ) )
!= ( B @ ( B @ int_less ) ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[5302]) ).
thf(5304,plain,
~ ( int_zero @ ( int_one @ int_leq ) ),
inference(pattern_uni,[status(thm)],[5303:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero ))]]) ).
thf(29436,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12143,5304]) ).
thf(29437,plain,
! [A: $i] :
( ( sk1 @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[29436]) ).
thf(29580,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ plus ) )
!= int_zero )
| ( A != int_one ) ),
inference(simp,[status(thm)],[29437]) ).
thf(29682,plain,
( ( sk1 @ ( int_one @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[29580]) ).
thf(80,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)],[78]) ).
thf(84,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)],[80]) ).
thf(85,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)],[84]) ).
thf(21443,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21068,39]) ).
thf(21444,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[21443]) ).
thf(21445,plain,
sk2 @ ( int_one @ plus ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[21444:[bind(A,$thf( int_zero )),bind(B,$thf( sk2 @ ( int_one @ plus ) ))]]) ).
thf(23579,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21448,39]) ).
thf(23580,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[23579]) ).
thf(23581,plain,
int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[23580:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) ))]]) ).
thf(23582,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21448,63]) ).
thf(23583,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[23582]) ).
thf(23584,plain,
int_zero @ ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[23583:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) ))]]) ).
thf(25800,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23584,71]) ).
thf(25801,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[25800]) ).
thf(25802,plain,
int_zero @ ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[25801:[bind(A,$thf( int_zero @ ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ sk4 ) ))]]) ).
thf(23615,plain,
! [A: $i] :
( ( ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21448,47]) ).
thf(23616,plain,
! [A: $i] :
( ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[23615]) ).
thf(23629,plain,
! [A: $i] :
( ( ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) )
!= A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[23616]) ).
thf(23639,plain,
( ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) )
!= int_zero ),
inference(simp,[status(thm)],[23629]) ).
thf(20,plain,
( ( sk1 = sk2 )
| ( sk1 @ ( sk2 @ int_less ) )
| sk3 ),
inference(cnfConj,[status(thm)],[16]) ).
thf(27,plain,
( ( sk1 @ ( sk2 @ int_less ) )
| sk3
| ( sk2 = sk1 ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(1558,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| sk3
| ( sk2 = sk1 ) ),
inference(paramod_ordered,[status(thm)],[27,39]) ).
thf(1559,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| sk3
| ( sk2 = sk1 ) ),
inference(simp,[status(thm)],[1558]) ).
thf(1560,plain,
( ( sk1 @ ( sk2 @ int_leq ) )
| sk3
| ( sk2 = sk1 ) ),
inference(pattern_uni,[status(thm)],[1559:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(160,plain,
! [C: $i,B: $i,A: $i] :
( ( ( n @ ( sk1 @ 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 ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ $true
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(paramod_ordered,[status(thm)],[21,83]) ).
thf(161,plain,
! [C: $i,B: $i,A: $i] :
( ( ( n @ ( sk1 @ 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 ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[160]) ).
thf(229,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= n )
| ( sk1 != 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 ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ( ( C @ ( B @ ( C @ plus ) @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[161]) ).
thf(1465,plain,
( ( sk1 != sk1 )
| ( n @ ( int_one @ int_leq ) )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[798,21]) ).
thf(1466,plain,
( ( n @ ( int_one @ int_leq ) )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[1465:[]]) ).
thf(3884,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ( n @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[1466,47]) ).
thf(3885,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ( n @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[3884]) ).
thf(3889,plain,
! [A: $i] :
( ( sk1 != A )
| ( int_one != A )
| ( n @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[3885]) ).
thf(3894,plain,
( ( sk1 != int_one )
| ( n @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[3889]) ).
thf(9422,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_one @ ( C @ plus ) ) )
| ( A @ ( B @ plus ) @ ( C @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[53,4645]) ).
thf(9423,plain,
! [A: $i] : ( A @ ( int_one @ plus ) @ ( A @ int_less ) ),
inference(pattern_uni,[status(thm)],[9422:[bind(A,$thf( A )),bind(B,$thf( int_one )),bind(C,$thf( A ))]]) ).
thf(10889,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( A @ plus ) @ ( A @ int_less ) )
!= ( B @ ( B @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5366,47]) ).
thf(10890,plain,
! [B: $i,A: $i] :
( ( sk2 @ ( A @ plus ) @ ( A @ int_less ) )
!= ( B @ ( B @ int_less ) ) ),
inference(simp,[status(thm)],[10889]) ).
thf(10898,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( A @ plus ) )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[10890]) ).
thf(10907,plain,
! [A: $i] :
( ( sk2 @ ( A @ plus ) )
!= A ),
inference(simp,[status(thm)],[10898]) ).
thf(2069,plain,
( ( ( sk1 @ ( sk2 @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,1977]) ).
thf(2070,plain,
( ( ( sk1 @ ( sk2 @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3 ),
inference(simp,[status(thm)],[2069]) ).
thf(2090,plain,
( ( sk1 != sk1 )
| ( sk2 != int_one )
| ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3 ),
inference(simp,[status(thm)],[2070]) ).
thf(2100,plain,
( ( sk2 != int_one )
| ( ( int_one @ ( sk1 @ plus ) )
!= sk2 )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3 ),
inference(simp,[status(thm)],[2090]) ).
thf(16240,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14602,71]) ).
thf(16241,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[16240]) ).
thf(16242,plain,
int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[16241:[bind(A,$thf( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) ))]]) ).
thf(9453,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( B @ ( B @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4645,47]) ).
thf(9454,plain,
! [B: $i,A: $i] :
( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( B @ ( B @ int_less ) ) ),
inference(simp,[status(thm)],[9453]) ).
thf(9459,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[9454]) ).
thf(9477,plain,
! [A: $i] :
( ( int_one @ ( A @ plus ) )
!= A ),
inference(simp,[status(thm)],[9459]) ).
thf(206,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)],[83]) ).
thf(212,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)],[206]) ).
thf(5361,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5285,63]) ).
thf(5362,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[5361]) ).
thf(5363,plain,
int_zero @ ( sk2 @ sk4 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[5362:[bind(A,$thf( int_zero )),bind(B,$thf( sk2 ))]]) ).
thf(6295,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk2 @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5363,63]) ).
thf(6296,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk2 @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[6295]) ).
thf(6297,plain,
int_zero @ ( int_zero @ ( sk2 @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[6296:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( sk2 @ sk4 ) ))]]) ).
thf(7878,plain,
int_zero @ ( sk2 @ sk4 ) @ ( int_zero @ int_less ),
inference(rewrite,[status(thm)],[6297,7758]) ).
thf(37,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[34]) ).
thf(40,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[37]) ).
thf(41,plain,
! [A: $i] : ( A @ ( A @ int_leq ) ),
inference(simp,[status(thm)],[40]) ).
thf(5473,plain,
( ( ( n @ ( sk1 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[21,5304]) ).
thf(5474,plain,
( ( n @ ( sk1 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[5473]) ).
thf(5514,plain,
( ( int_zero != n )
| ( sk1 != int_one ) ),
inference(simp,[status(thm)],[5474]) ).
thf(5745,plain,
( ( sk1 != sk1 )
| ( int_zero != n )
| ( int_one != int_one )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[798,5514]) ).
thf(5746,plain,
( ( sk1 != sk1 )
| ( int_zero != n )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(simp,[status(thm)],[5745]) ).
thf(5747,plain,
( ( int_zero != n )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[5746:[]]) ).
thf(12133,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ plus ) @ ( A @ int_less ) )
!= ( B @ ( B @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5436,47]) ).
thf(12134,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( A @ plus ) @ ( A @ int_less ) )
!= ( B @ ( B @ int_less ) ) ),
inference(simp,[status(thm)],[12133]) ).
thf(12139,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ plus ) )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[12134]) ).
thf(12155,plain,
! [A: $i] :
( ( sk1 @ ( A @ plus ) )
!= A ),
inference(simp,[status(thm)],[12139]) ).
thf(5485,plain,
( ( ( int_zero @ ( int_one @ int_leq ) )
!= ( n @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk2 != n ) ),
inference(paramod_ordered,[status(thm)],[3297,5304]) ).
thf(5486,plain,
( ( ( int_zero @ ( int_one @ int_leq ) )
!= ( n @ ( int_one @ int_leq ) ) )
| ( sk2 != n ) ),
inference(simp,[status(thm)],[5485]) ).
thf(5512,plain,
( ( int_zero != n )
| ( int_one != int_one )
| ( sk2 != n ) ),
inference(simp,[status(thm)],[5486]) ).
thf(5525,plain,
( ( int_zero != n )
| ( sk2 != n ) ),
inference(simp,[status(thm)],[5512]) ).
thf(18062,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16248,71]) ).
thf(18063,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[18062]) ).
thf(18064,plain,
int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[18063:[bind(A,$thf( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ sk4 ) ))]]) ).
thf(12010,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( sk2 @ ( C @ plus ) ) )
| ( ( A @ ( B @ plus ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[53,10907]) ).
thf(12011,plain,
! [A: $i] :
( ( A @ ( sk2 @ plus ) )
!= A ),
inference(pattern_uni,[status(thm)],[12010:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(998,plain,
( ( sk2 != sk2 )
| ( n @ ( int_one @ int_leq ) )
| ( sk2 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[764,23]) ).
thf(999,plain,
( ( n @ ( int_one @ int_leq ) )
| ( sk2 @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[998:[]]) ).
thf(2684,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ( n @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[999,47]) ).
thf(2685,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ( n @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[2684]) ).
thf(2691,plain,
! [A: $i] :
( ( sk2 != A )
| ( int_one != A )
| ( n @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[2685]) ).
thf(2695,plain,
( ( sk2 != int_one )
| ( n @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[2691]) ).
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(48,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[48]) ).
thf(176,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)],[26,83]) ).
thf(177,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)],[176]) ).
thf(236,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)],[177]) ).
thf(18065,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[16248,39]) ).
thf(18066,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[18065]) ).
thf(18067,plain,
int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[18066:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ sk4 ) ))]]) ).
thf(110,plain,
! [A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50,47]) ).
thf(111,plain,
! [A: $i] :
( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[110]) ).
thf(112,plain,
! [A: $i] :
( ( int_one != A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[111]) ).
thf(113,plain,
int_zero != int_one,
inference(simp,[status(thm)],[112]) ).
thf(5495,plain,
( ( ( n @ ( sk2 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23,5304]) ).
thf(5496,plain,
( ( n @ ( sk2 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[5495]) ).
thf(5506,plain,
( ( int_zero != n )
| ( sk2 != int_one ) ),
inference(simp,[status(thm)],[5496]) ).
thf(1055,plain,
( ( sk2 != sk2 )
| ( sk1 != n )
| ~ sk3
| ( n @ ( sk2 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[775,91]) ).
thf(1056,plain,
( ( sk1 != n )
| ~ sk3
| ( n @ ( sk2 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[1055:[]]) ).
thf(3449,plain,
! [A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ( sk1 != n )
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[1056,47]) ).
thf(3450,plain,
! [A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ( sk1 != n )
| ~ sk3 ),
inference(simp,[status(thm)],[3449]) ).
thf(3455,plain,
! [A: $i] :
( ( n != A )
| ( sk2 != A )
| ( sk1 != n )
| ~ sk3 ),
inference(simp,[status(thm)],[3450]) ).
thf(3468,plain,
( ( sk2 != n )
| ( sk1 != n )
| ~ sk3 ),
inference(simp,[status(thm)],[3455]) ).
thf(126,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ int_leq ) )
!= ( B @ ( int_one @ int_leq ) ) )
| ~ ( B @ ( D @ int_leq ) )
| ~ ( D @ ( int_one @ int_leq ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ~ ( n @ ( B @ int_leq ) )
| ~ $true
| ~ ( n @ ( C @ ( B @ plus ) @ int_leq ) )
| ~ ( C @ ( B @ plus ) @ ( int_one @ int_leq ) )
| ( ( D @ ( C @ ( D @ plus ) @ a ) )
= real_zero ) ),
inference(paramod_ordered,[status(thm)],[41,83]) ).
thf(127,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ int_leq ) )
!= ( B @ ( int_one @ int_leq ) ) )
| ~ ( B @ ( D @ int_leq ) )
| ~ ( D @ ( int_one @ int_leq ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( n @ ( C @ ( B @ plus ) @ int_leq ) )
| ~ ( C @ ( B @ plus ) @ ( int_one @ int_leq ) )
| ( ( D @ ( C @ ( D @ plus ) @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[126]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ~ ( int_one @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) )
| ~ ( n @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ ( int_one @ plus ) @ int_leq ) )
| ~ ( A @ ( int_one @ plus ) @ ( int_one @ int_leq ) )
| ( ( B @ ( A @ ( B @ plus ) @ a ) )
= real_zero ) ),
inference(pattern_uni,[status(thm)],[127:[bind(A,$thf( int_one )),bind(B,$thf( int_one ))]]) ).
thf(245,plain,
! [B: $i,A: $i] :
( ~ ( int_one @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) )
| ~ ( n @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ ( int_one @ plus ) @ int_leq ) )
| ~ ( A @ ( int_one @ plus ) @ ( int_one @ int_leq ) )
| ( ( B @ ( A @ ( B @ plus ) @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[128]) ).
thf(5265,plain,
! [A: $i] :
( ( ( n @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true
| ( sk2 != int_one ) ),
inference(paramod_ordered,[status(thm)],[2695,73]) ).
thf(5266,plain,
! [A: $i] :
( ( ( n @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ( sk2 != int_one ) ),
inference(simp,[status(thm)],[5265]) ).
thf(5267,plain,
( ( n @ ( int_zero @ int_less ) )
| ( sk2 != int_one ) ),
inference(pattern_uni,[status(thm)],[5266:[bind(A,$thf( n ))]]) ).
thf(2631,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_one @ ( sk1 @ plus ) ) )
| ( sk1 != n )
| ( ( A @ ( B @ plus ) )
!= sk2 )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3 ),
inference(paramod_ordered,[status(thm)],[53,2091]) ).
thf(2632,plain,
( ( sk1 != n )
| ( ( sk1 @ ( int_one @ plus ) )
!= sk2 )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ sk3 ),
inference(pattern_uni,[status(thm)],[2631:[bind(A,$thf( sk1 )),bind(B,$thf( int_one ))]]) ).
thf(18,plain,
( ( ( sk2 @ ( sk1 @ a ) )
!= real_one )
| ( sk1 @ ( sk2 @ int_less ) )
| sk3 ),
inference(cnfConj,[status(thm)],[16]) ).
thf(30,plain,
( ( sk1 @ ( sk2 @ int_less ) )
| sk3
| ( ( sk2 @ ( sk1 @ a ) )
!= real_one ) ),
inference(lifteq,[status(thm)],[18]) ).
thf(518,plain,
( ( sk2 != sk2 )
| ( sk1 @ ( sk2 @ int_less ) )
| sk3
| ( ( sk1 @ ( sk1 @ a ) )
!= real_one )
| ( sk1 @ ( sk2 @ int_less ) )
| sk3 ),
inference(paramod_ordered,[status(thm)],[27,30]) ).
thf(519,plain,
( ( sk2 != sk2 )
| ( ( sk1 @ ( sk1 @ a ) )
!= real_one )
| ( sk1 @ ( sk2 @ int_less ) )
| sk3 ),
inference(simp,[status(thm)],[518]) ).
thf(520,plain,
( ( ( sk1 @ ( sk1 @ a ) )
!= real_one )
| ( sk1 @ ( sk2 @ int_less ) )
| sk3 ),
inference(pattern_uni,[status(thm)],[519:[]]) ).
thf(21130,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[10915,5304]) ).
thf(21131,plain,
! [A: $i] :
( ( sk2 @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[21130]) ).
thf(21252,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ plus ) )
!= int_zero )
| ( A != int_one ) ),
inference(simp,[status(thm)],[21131]) ).
thf(21259,plain,
( ( sk2 @ ( int_one @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[21252]) ).
thf(31539,plain,
! [A: $i] :
( ( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29822,47]) ).
thf(31540,plain,
! [A: $i] :
( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[31539]) ).
thf(31548,plain,
! [A: $i] :
( ( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk4 ) )
!= A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[31540]) ).
thf(31567,plain,
( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk4 ) )
!= int_zero ),
inference(simp,[status(thm)],[31548]) ).
thf(10851,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( sk2 @ ( C @ plus ) ) )
| ( A @ ( B @ plus ) @ ( C @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[53,5366]) ).
thf(10852,plain,
! [A: $i] : ( A @ ( sk2 @ plus ) @ ( A @ int_less ) ),
inference(pattern_uni,[status(thm)],[10851:[bind(A,$thf( A )),bind(B,$thf( sk2 )),bind(C,$thf( A ))]]) ).
thf(10781,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_one @ ( C @ plus ) ) )
| ( ( A @ ( B @ plus ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[53,9477]) ).
thf(10782,plain,
! [A: $i] :
( ( A @ ( int_one @ plus ) )
!= A ),
inference(pattern_uni,[status(thm)],[10781:[bind(A,$thf( A )),bind(B,$thf( int_one )),bind(C,$thf( A ))]]) ).
thf(3776,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3610,39]) ).
thf(3777,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[3776]) ).
thf(3778,plain,
int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[3777:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) ))]]) ).
thf(4196,plain,
int_zero @ ( int_one @ sk4 ) @ ( int_zero @ int_leq ),
inference(rewrite,[status(thm)],[3778,4169]) ).
thf(14597,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14305,39]) ).
thf(14598,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[14597]) ).
thf(14599,plain,
int_one @ ( int_one @ plus ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[14598:[bind(A,$thf( int_zero )),bind(B,$thf( int_one @ ( int_one @ plus ) ))]]) ).
thf(5423,plain,
( ( sk1 != sk1 )
| ( n @ ( int_zero @ int_less ) )
| ( n @ ( sk1 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[697,5298]) ).
thf(5424,plain,
( ( n @ ( int_zero @ int_less ) )
| ( n @ ( sk1 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[5423:[]]) ).
thf(5469,plain,
( ( ( int_zero @ ( int_one @ int_leq ) )
!= ( n @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk1 != n ) ),
inference(paramod_ordered,[status(thm)],[1544,5304]) ).
thf(5470,plain,
( ( ( int_zero @ ( int_one @ int_leq ) )
!= ( n @ ( int_one @ int_leq ) ) )
| ( sk1 != n ) ),
inference(simp,[status(thm)],[5469]) ).
thf(5503,plain,
( ( int_zero != n )
| ( int_one != int_one )
| ( sk1 != n ) ),
inference(simp,[status(thm)],[5470]) ).
thf(5528,plain,
( ( int_zero != n )
| ( sk1 != n ) ),
inference(simp,[status(thm)],[5503]) ).
thf(25808,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23584,39]) ).
thf(25809,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[25808]) ).
thf(25810,plain,
int_zero @ ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[25809:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ sk4 ) ))]]) ).
thf(25847,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23584,47]) ).
thf(25848,plain,
! [A: $i] :
( ( int_zero @ ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[25847]) ).
thf(25863,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ sk4 ) )
!= A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[25848]) ).
thf(25873,plain,
( ( int_zero @ ( int_zero @ ( sk2 @ ( int_one @ plus ) @ sk4 ) @ sk4 ) )
!= int_zero ),
inference(simp,[status(thm)],[25863]) ).
thf(5443,plain,
! [A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5298,47]) ).
thf(5444,plain,
! [A: $i] :
( ( sk1 @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[5443]) ).
thf(5448,plain,
! [A: $i] :
( ( sk1 != A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[5444]) ).
thf(5452,plain,
sk1 != int_zero,
inference(simp,[status(thm)],[5448]) ).
thf(5541,plain,
( ( sk2 != sk2 )
| ( int_zero != n )
| ( int_one != int_one )
| ( sk2 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[764,5506]) ).
thf(5542,plain,
( ( sk2 != sk2 )
| ( int_zero != n )
| ( sk2 @ ( int_one @ int_less ) ) ),
inference(simp,[status(thm)],[5541]) ).
thf(5543,plain,
( ( int_zero != n )
| ( sk2 @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[5542:[]]) ).
thf(24,plain,
( ( sk1 = sk2 )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero )
| sk3 ),
inference(cnfConj,[status(thm)],[16]) ).
thf(31,plain,
( sk3
| ( sk2 = sk1 )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(lifteq,[status(thm)],[24]) ).
thf(14349,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9467,5304]) ).
thf(14350,plain,
! [A: $i] :
( ( int_one @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[14349]) ).
thf(14440,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) )
!= int_zero )
| ( A != int_one ) ),
inference(simp,[status(thm)],[14350]) ).
thf(14512,plain,
( ( int_one @ ( int_one @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[14440]) ).
thf(152,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)],[19,83]) ).
thf(153,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)],[152]) ).
thf(154,plain,
! [B: $i,A: $i] :
( ~ ( A @ ( sk1 @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ( ( sk1 @ ( B @ ( sk1 @ plus ) @ a ) )
= real_zero ) ),
inference(pattern_uni,[status(thm)],[153:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( sk1 ))]]) ).
thf(5431,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5298,63]) ).
thf(5432,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[5431]) ).
thf(5433,plain,
int_zero @ ( sk1 @ sk4 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[5432:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 ))]]) ).
thf(6391,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5433,63]) ).
thf(6392,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk4 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[6391]) ).
thf(6393,plain,
int_zero @ ( int_zero @ ( sk1 @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[6392:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( sk1 @ sk4 ) ))]]) ).
thf(5417,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ~ $true
| ( ( A @ ( B @ sk4 ) @ ( A @ plus ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[5298,65]) ).
thf(5418,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( ( A @ ( B @ sk4 ) @ ( A @ plus ) )
= B ) ),
inference(simp,[status(thm)],[5417]) ).
thf(5419,plain,
( ( int_zero @ ( sk1 @ sk4 ) @ ( int_zero @ plus ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[5418:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 ))]]) ).
thf(7823,plain,
( ( int_zero @ ( sk1 @ sk4 ) )
= sk1 ),
inference(rewrite,[status(thm)],[5419,440]) ).
thf(8552,plain,
int_zero @ ( sk1 @ sk4 ) @ ( int_zero @ int_less ),
inference(rewrite,[status(thm)],[6393,7823]) ).
thf(43,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ int_less ) )
| ~ ( C @ ( B @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[42]) ).
thf(81,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)],[78]) ).
thf(86,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)],[81]) ).
thf(87,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)],[86]) ).
thf(16243,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14602,39]) ).
thf(16244,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[16243]) ).
thf(16245,plain,
int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[16244:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_one @ ( int_one @ plus ) @ sk4 ) ))]]) ).
thf(218,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)],[203]) ).
thf(31497,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29822,39]) ).
thf(31498,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[31497]) ).
thf(31499,plain,
int_zero @ ( sk1 @ ( int_one @ plus ) @ sk4 ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[31498:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk4 ) ))]]) ).
thf(5373,plain,
! [A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5285,47]) ).
thf(5374,plain,
! [A: $i] :
( ( sk2 @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[5373]) ).
thf(5380,plain,
! [A: $i] :
( ( sk2 != A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[5374]) ).
thf(5382,plain,
sk2 != int_zero,
inference(simp,[status(thm)],[5380]) ).
thf(13187,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( sk1 @ ( C @ plus ) ) )
| ( ( A @ ( B @ plus ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[53,12155]) ).
thf(13188,plain,
! [A: $i] :
( ( A @ ( sk1 @ plus ) )
!= A ),
inference(pattern_uni,[status(thm)],[13187:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(58,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)],[57]) ).
thf(129,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ int_leq ) )
!= ( n @ ( B @ int_leq ) ) )
| ~ ( B @ ( D @ int_leq ) )
| ~ ( D @ ( int_one @ int_leq ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ~ $true
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( n @ ( C @ ( B @ plus ) @ int_leq ) )
| ~ ( C @ ( B @ plus ) @ ( int_one @ int_leq ) )
| ( ( D @ ( C @ ( D @ plus ) @ a ) )
= real_zero ) ),
inference(paramod_ordered,[status(thm)],[41,83]) ).
thf(130,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( A @ ( A @ int_leq ) )
!= ( n @ ( B @ int_leq ) ) )
| ~ ( B @ ( D @ int_leq ) )
| ~ ( D @ ( int_one @ int_leq ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( n @ ( C @ ( B @ plus ) @ int_leq ) )
| ~ ( C @ ( B @ plus ) @ ( int_one @ int_leq ) )
| ( ( D @ ( C @ ( D @ plus ) @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[129]) ).
thf(131,plain,
! [B: $i,A: $i] :
( ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) )
| ~ ( n @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ ( n @ plus ) @ int_leq ) )
| ~ ( A @ ( n @ plus ) @ ( int_one @ int_leq ) )
| ( ( B @ ( A @ ( B @ plus ) @ a ) )
= real_zero ) ),
inference(pattern_uni,[status(thm)],[130:[bind(A,$thf( n )),bind(B,$thf( n ))]]) ).
thf(246,plain,
! [B: $i,A: $i] :
( ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) )
| ~ ( n @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ ( n @ plus ) @ int_leq ) )
| ~ ( A @ ( n @ plus ) @ ( int_one @ int_leq ) )
| ( ( B @ ( A @ ( B @ plus ) @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[131]) ).
thf(4989,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4719,71]) ).
thf(4990,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[4989]) ).
thf(4991,plain,
int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[4990:[bind(A,$thf( int_zero @ ( int_zero @ ( int_one @ sk4 ) @ sk4 ) ))]]) ).
thf(5040,plain,
int_zero @ ( int_one @ sk4 ) @ ( int_one @ int_leq ),
inference(rewrite,[status(thm)],[4991,4169]) ).
thf(204,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( n @ ( B @ ( A @ plus ) @ int_leq ) )
!= ( A @ ( 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)],[83]) ).
thf(214,plain,
! [C: $i,B: $i,A: $i] :
( ( ( n @ ( B @ ( A @ plus ) @ int_leq ) )
!= ( A @ ( 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)],[204]) ).
thf(5397,plain,
( ( sk2 != sk2 )
| ( int_zero != n )
| ( n @ ( sk2 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[775,5382]) ).
thf(5398,plain,
( ( int_zero != n )
| ( n @ ( sk2 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[5397:[]]) ).
thf(5230,plain,
! [A: $i] :
( ( ( n @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true
| ( sk1 != n ) ),
inference(paramod_ordered,[status(thm)],[1544,73]) ).
thf(5231,plain,
! [A: $i] :
( ( ( n @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ( sk1 != n ) ),
inference(simp,[status(thm)],[5230]) ).
thf(5232,plain,
( ( n @ ( int_zero @ int_less ) )
| ( sk1 != n ) ),
inference(pattern_uni,[status(thm)],[5231:[bind(A,$thf( n ))]]) ).
thf(5428,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5298,39]) ).
thf(5429,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[5428]) ).
thf(5430,plain,
sk1 @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[5429:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 ))]]) ).
thf(5461,plain,
( ( sk1 != sk1 )
| ( int_zero != n )
| ( n @ ( sk1 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[697,5452]) ).
thf(5462,plain,
( ( int_zero != n )
| ( n @ ( sk1 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[5461:[]]) ).
thf(207,plain,
! [C: $i,B: $i,A: $i] :
( ~ $true
| ( ( A @ ( C @ int_leq ) )
!= ( B @ ( A @ plus ) @ ( int_one @ 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(eqfactor_ordered,[status(thm)],[83]) ).
thf(239,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( C @ int_leq ) )
!= ( B @ ( A @ plus ) @ ( int_one @ 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)],[207]) ).
thf(145,plain,
! [C: $i,B: $i,A: $i] :
( ( ( n @ ( B @ ( A @ plus ) @ int_leq ) )
!= ( sk1 @ ( 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)],[19,83]) ).
thf(146,plain,
! [C: $i,B: $i,A: $i] :
( ( ( n @ ( B @ ( A @ plus ) @ int_leq ) )
!= ( sk1 @ ( 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)],[145]) ).
thf(242,plain,
! [C: $i,B: $i,A: $i] :
( ( sk1 != 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)],[146]) ).
thf(29817,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[29366,39]) ).
thf(29818,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[29817]) ).
thf(29819,plain,
sk1 @ ( int_one @ plus ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[29818:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 @ ( int_one @ plus ) ))]]) ).
thf(205,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)],[83]) ).
thf(227,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)],[205]) ).
thf(716,plain,
! [B: $i,A: $i] :
( ( B != real_one )
| ( A != real_zero )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[38,76]) ).
thf(717,plain,
! [A: $i] :
( ( A != real_zero )
| ( real_one @ ( A @ int_less ) )
| ~ ( real_one @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[716:[bind(A,$thf( A )),bind(B,$thf( real_one ))]]) ).
thf(882,plain,
( ( real_one @ ( real_zero @ int_less ) )
| ~ ( real_one @ ( real_zero @ int_leq ) ) ),
inference(simp,[status(thm)],[717]) ).
thf(5253,plain,
! [A: $i] :
( ( ( n @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true
| ( sk1 != int_one ) ),
inference(paramod_ordered,[status(thm)],[3894,73]) ).
thf(5254,plain,
! [A: $i] :
( ( ( n @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ( sk1 != int_one ) ),
inference(simp,[status(thm)],[5253]) ).
thf(5255,plain,
( ( n @ ( int_zero @ int_less ) )
| ( sk1 != int_one ) ),
inference(pattern_uni,[status(thm)],[5254:[bind(A,$thf( n ))]]) ).
thf(57771,plain,
$false,
inference(e,[status(thm)],[23573,5360,2630,4169,14305,1554,16248,18129,941,217,16308,1544,440,5614,56,14602,12097,9481,185,3236,5252,42,29366,25,1572,881,57,4793,29,5379,31490,18842,243,7758,74,5298,29682,85,798,21445,23581,25802,23639,5366,21,1560,28,38,229,65,3297,3894,9423,1079,10907,5285,697,2100,53,16242,77,9477,212,7878,1060,41,1466,21448,73,5747,12155,32,5525,18064,44,12143,59,12011,2695,27,71,54,49,236,29822,4645,764,18067,113,5506,3468,76,245,39,23584,5267,2632,91,520,21259,31567,10852,10782,4196,14599,5424,5528,25810,25873,5452,48,63,5514,9467,2850,993,50,67,5543,31,14512,10915,154,8552,43,87,16245,218,31499,5382,26,13188,23,5304,58,246,5040,21068,214,999,30,19,5398,51,5232,4719,5430,5462,1056,2091,283,239,242,1977,47,15,68,29819,227,83,1184,5436,7823,882,775,5255]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV491+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
% 0.16/0.41 % Computer : n010.cluster.edu
% 0.16/0.41 % Model : x86_64 x86_64
% 0.16/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.41 % Memory : 8046.5625MB
% 0.16/0.41 % OS : Linux 6.8.0-71-generic
% 0.16/0.41 % CPULimit : 300
% 0.16/0.41 % WCLimit : 300
% 0.16/0.41 % DateTime : Sat Sep 26 13:59:15 UTC 2026
% 0.16/0.41 % CPUTime :
% 0.16/0.41 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
% 0.82/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.18/1.19 % [INFO] Parsing done (194ms).
% 1.32/1.21 % [INFO] Running in sequential loop mode.
% 1.95/1.61 % [INFO] eprover registered as external prover.
% 1.95/1.62 % [INFO] Scanning for conjecture ...
% 2.13/1.73 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.13/1.77 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.30/1.80 % [INFO] Problem is first-order (TPTP FOF).
% 2.30/1.80 % [INFO] Type checking passed.
% 2.30/1.81 % [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 ...
% 90.26/21.69 % External prover 'e' found a proof!
% 90.26/21.69 % [INFO] Killing All external provers ...
% 88.71/21.70 % Time passed: 21142ms (effective reasoning time: 20482ms)
% 88.71/21.70 % 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)>
% 88.71/21.70 % Axioms used in derivation (12): plus_and_order1, int_less_total, qih, int_leq, int_less_transitive, int_zero_one, plus_and_inverse, int_less_irreflexive, plus_commutative, real_constants, plus_zero, one_successor_of_zero
% 88.71/21.70 % No. of inferences in proof: 501
% 88.71/21.70 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 21142 ms resp. 20482 ms w/o parsing
% 89.08/21.89 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 89.42/21.90 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------