%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV492+1 : 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 : n005.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:59:37 AM UTC 2026
% Result : Theorem 209.40s 58.77s
% Output : Refutation 200.40s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 18
% Syntax : Number of formulae : 409 ( 57 unt; 0 typ; 5 def)
% Number of atoms : 1774 ( 734 equ; 0 cnn)
% Maximal formula atoms : 32 ( 4 avg)
% Number of connectives : 4675 ( 923 ~; 932 |; 81 &;2696 @)
% ( 3 <=>; 40 =>; 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 : 18 ( 15 usr; 11 con; 0-2 aty)
% Number of variables : 478 ( 2 ^; 466 !; 5 ?; 478 :)
% ( 0 !>; 0 ?*; 0 @-; 5 @+)
% Comments :
%------------------------------------------------------------------------------
thf(int_leq_decl,type,
int_leq: $i > $i > $o ).
thf(int_one_decl,type,
int_one: $i ).
thf(int_less_decl,type,
int_less: $i > $i > $o ).
thf(n_decl,type,
n: $i ).
thf(a_decl,type,
a: $i > $i > $i ).
thf(real_zero_decl,type,
real_zero: $i ).
thf(int_zero_decl,type,
int_zero: $i ).
thf(plus_decl,type,
plus: $i > $i > $i ).
thf(real_one_decl,type,
real_one: $i ).
thf(qr_decl,type,
qr: $i > $i > $i ).
thf(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i ).
thf(sk4_decl,type,
sk4: $i ).
thf(sk5_decl,type,
sk5: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( A @ int_less ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: $i] :
~ ( ( ( n @ ( A @ int_leq ) )
& ( A @ ( sk1 @ int_less ) )
& ( sk1 @ ( int_one @ int_leq ) ) )
=> ( ( A @ ( sk1 @ a ) )
= real_zero ) ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( A = B )
& ( n @ ( B @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
!= real_zero ) ) ) ) ).
thf(sk4_def,definition,
( sk4
= ( @+[A: $i] :
~ ( ( ( sk3 = A )
& ( n @ ( A @ int_leq ) )
& ( sk3 @ ( int_one @ int_leq ) ) )
=> ( ( A @ ( sk3 @ a ) )
!= real_zero ) ) ) ) ).
thf(sk5_def,definition,
( sk5
= ( ^ [A: $i,B: $i] :
@+[C: $i] :
( ( C @ ( int_zero @ int_less ) )
& ( ( C @ ( B @ plus ) )
= A ) ) ) ) ).
thf(1,conjecture,
( ! [A: $i,B: $i] :
( ( ( A = B )
& ( n @ ( B @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
!= real_zero ) )
& ! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( A @ int_less ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',lti) ).
thf(2,negated_conjecture,
~ ( ! [A: $i,B: $i] :
( ( ( A = B )
& ( n @ ( B @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
!= real_zero ) )
& ! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( A @ int_less ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(15,plain,
~ ( ! [A: $i,B: $i] :
( ( ( A = B )
& ( n @ ( B @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
!= real_zero ) )
& ! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( A @ int_less ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ( B @ ( A @ a ) )
= real_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(16,plain,
( ( ( ( sk4 @ ( sk3 @ a ) )
= real_zero )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) )
& ( ( sk3 = sk4 )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) )
& ( ( n @ ( sk4 @ int_leq ) )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) )
& ( ( sk3 @ ( int_one @ int_leq ) )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) )
& ( ( ( sk4 @ ( sk3 @ a ) )
= real_zero )
| ( n @ ( sk2 @ int_leq ) ) )
& ( ( sk3 = sk4 )
| ( n @ ( sk2 @ int_leq ) ) )
& ( ( n @ ( sk4 @ int_leq ) )
| ( n @ ( sk2 @ int_leq ) ) )
& ( ( sk3 @ ( int_one @ int_leq ) )
| ( n @ ( sk2 @ int_leq ) ) )
& ( ( ( sk4 @ ( sk3 @ a ) )
= real_zero )
| ( sk2 @ ( sk1 @ int_less ) ) )
& ( ( sk3 = sk4 )
| ( sk2 @ ( sk1 @ int_less ) ) )
& ( ( n @ ( sk4 @ int_leq ) )
| ( sk2 @ ( sk1 @ int_less ) ) )
& ( ( sk3 @ ( int_one @ int_leq ) )
| ( sk2 @ ( sk1 @ int_less ) ) )
& ( ( ( sk4 @ ( sk3 @ a ) )
= real_zero )
| ( sk1 @ ( int_one @ int_leq ) ) )
& ( ( sk3 = sk4 )
| ( sk1 @ ( int_one @ int_leq ) ) )
& ( ( n @ ( sk4 @ int_leq ) )
| ( sk1 @ ( int_one @ int_leq ) ) )
& ( ( sk3 @ ( int_one @ int_leq ) )
| ( sk1 @ ( int_one @ int_leq ) ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(18,plain,
( ( sk3 @ ( int_one @ int_leq ) )
| ( sk2 @ ( sk1 @ int_less ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ int_leq ) )
<=> ( ( A = B )
| ( B @ ( A @ int_less ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_leq) ).
thf(43,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(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(68,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(69,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)],[68]) ).
thf(30,plain,
( ( n @ ( sk4 @ int_leq ) )
| ( sk2 @ ( sk1 @ int_less ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
=> ( A != B ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_irreflexive) ).
thf(55,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(56,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[55]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[56]) ).
thf(58,plain,
! [A: $i] :
~ ( A @ ( A @ int_less ) ),
inference(simp,[status(thm)],[57]) ).
thf(1356,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ( n @ ( sk4 @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[30,58]) ).
thf(1357,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ( n @ ( sk4 @ int_leq ) ) ),
inference(simp,[status(thm)],[1356]) ).
thf(1364,plain,
! [A: $i] :
( ( sk2 != A )
| ( sk1 != A )
| ( n @ ( sk4 @ int_leq ) ) ),
inference(simp,[status(thm)],[1357]) ).
thf(1369,plain,
( ( sk2 != sk1 )
| ( n @ ( sk4 @ int_leq ) ) ),
inference(simp,[status(thm)],[1364]) ).
thf(28,plain,
( ( sk3 = sk4 )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(36,plain,
( ( n @ ( sk2 @ int_leq ) )
| ( sk4 = sk3 ) ),
inference(lifteq,[status(thm)],[28]) ).
thf(24,plain,
( ( n @ ( sk4 @ int_leq ) )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(775,plain,
( ( sk4 != sk4 )
| ( n @ ( sk3 @ int_leq ) )
| ( n @ ( sk2 @ int_leq ) )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[36,24]) ).
thf(776,plain,
( ( sk4 != sk4 )
| ( n @ ( sk3 @ int_leq ) )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(simp,[status(thm)],[775]) ).
thf(777,plain,
( ( n @ ( sk3 @ int_leq ) )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[776:[]]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( int_one @ int_leq ) )
& ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ! [C: $i] :
( ( ( B
= ( C @ ( A @ plus ) ) )
& ( C @ ( int_zero @ int_less ) ) )
=> ! [D: $i] :
( ( ( A @ ( D @ int_leq ) )
& ( D @ ( int_one @ int_leq ) ) )
=> ( ( C @ ( D @ plus ) @ ( D @ a ) )
= real_zero ) ) )
& ! [C: $i] :
( ( ( B @ ( C @ int_leq ) )
& ( C @ ( int_one @ int_leq ) ) )
=> ( ( C @ ( C @ a ) )
= real_one ) )
& ! [C: $i] :
( ( ( A
= ( C @ ( B @ plus ) ) )
& ( C @ ( int_zero @ int_less ) ) )
=> ! [D: $i] :
( ( ( B @ ( D @ int_leq ) )
& ( D @ ( int_one @ int_leq ) ) )
=> ( ( D @ ( C @ ( D @ plus ) @ a ) )
= ( D @ ( C @ ( D @ plus ) @ qr ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',qih) ).
thf(88,plain,
! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( int_one @ int_leq ) )
& ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ! [C: $i] :
( ( ( B
= ( C @ ( A @ plus ) ) )
& ( C @ ( int_zero @ int_less ) ) )
=> ! [D: $i] :
( ( ( A @ ( D @ int_leq ) )
& ( D @ ( int_one @ int_leq ) ) )
=> ( ( C @ ( D @ plus ) @ ( D @ a ) )
= real_zero ) ) )
& ! [C: $i] :
( ( ( B @ ( C @ int_leq ) )
& ( C @ ( int_one @ int_leq ) ) )
=> ( ( C @ ( C @ a ) )
= real_one ) )
& ! [C: $i] :
( ( ( A
= ( C @ ( B @ plus ) ) )
& ( C @ ( int_zero @ int_less ) ) )
=> ! [D: $i] :
( ( ( B @ ( D @ int_leq ) )
& ( D @ ( int_one @ int_leq ) ) )
=> ( ( D @ ( C @ ( D @ plus ) @ a ) )
= ( D @ ( C @ ( D @ plus ) @ qr ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(25,plain,
( ( sk3 @ ( int_one @ int_leq ) )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(1155,plain,
( ~ $true
| ( ( sk3 @ ( int_one @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(eqfactor_ordered,[status(thm)],[25]) ).
thf(1158,plain,
( ( ( sk3 @ ( int_one @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1155]) ).
thf(26,plain,
( ( sk3 = sk4 )
| ( sk2 @ ( sk1 @ int_less ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(41,plain,
( ( sk2 @ ( sk1 @ int_less ) )
| ( sk4 = sk3 ) ),
inference(lifteq,[status(thm)],[26]) ).
thf(220,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ( sk4 = sk3 ) ),
inference(paramod_ordered,[status(thm)],[41,58]) ).
thf(221,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[220]) ).
thf(228,plain,
! [A: $i] :
( ( sk2 != A )
| ( sk1 != A )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[221]) ).
thf(230,plain,
( ( sk2 != sk1 )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[228]) ).
thf(1404,plain,
( ( sk4 != sk4 )
| ( sk2 != sk1 )
| ( n @ ( sk3 @ int_leq ) )
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[230,1369]) ).
thf(1405,plain,
( ( sk4 != sk4 )
| ( n @ ( sk3 @ int_leq ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[1404]) ).
thf(1406,plain,
( ( n @ ( sk3 @ int_leq ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[1405:[]]) ).
thf(89,plain,
! [G: $i,F: $i,E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( ( F @ ( G @ plus ) @ ( G @ a ) )
= real_zero )
| ~ ( A @ ( G @ int_leq ) )
| ~ ( G @ ( int_one @ int_leq ) )
| ( B
!= ( F @ ( A @ plus ) ) )
| ~ ( F @ ( int_zero @ int_less ) )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) ) )
& ( ( ( E @ ( E @ a ) )
= real_one )
| ~ ( B @ ( E @ int_leq ) )
| ~ ( E @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) ) )
& ( ( ( D @ ( C @ ( D @ plus ) @ a ) )
= ( D @ ( C @ ( D @ plus ) @ qr ) ) )
| ~ ( 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)],[88]) ).
thf(92,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)],[89]) ).
thf(97,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)],[92]) ).
thf(98,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)],[97]) ).
thf(126,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 @ ( 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(eqfactor_ordered,[status(thm)],[98]) ).
thf(136,plain,
! [B: $i,A: $i] :
( ~ ( int_one @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( ( B @ ( int_one @ plus ) @ ( int_one @ a ) )
= real_zero ) ),
inference(pattern_uni,[status(thm)],[126:[bind(A,$thf( A )),bind(B,$thf( B )),bind(C,$thf( int_one ))]]) ).
thf(7,axiom,
int_one @ ( int_zero @ int_less ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_zero_one) ).
thf(61,plain,
int_one @ ( int_zero @ int_less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
<=> ? [C: $i] :
( ( C @ ( int_zero @ int_less ) )
& ( ( C @ ( A @ plus ) )
= B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_and_inverse) ).
thf(70,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(71,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)],[70]) ).
thf(72,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 @ sk5 ) @ ( int_zero @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) )
& ( ( ( A @ ( B @ sk5 ) @ ( A @ plus ) )
= B )
| ~ ( B @ ( A @ int_less ) ) ) ),
inference(cnf,[status(esa)],[71]) ).
thf(74,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk5 ) @ ( int_zero @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[72]) ).
thf(8615,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk5 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[61,74]) ).
thf(8616,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk5 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[8615]) ).
thf(8617,plain,
int_zero @ ( int_one @ sk5 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[8616:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(8717,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ sk5 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk5 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8617,74]) ).
thf(8718,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ sk5 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk5 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[8717]) ).
thf(8719,plain,
int_zero @ ( int_zero @ ( int_one @ sk5 ) @ sk5 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[8718:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_one @ sk5 ) ))]]) ).
thf(73,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk5 ) @ ( A @ plus ) )
= B )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[72]) ).
thf(76,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ( ( A @ ( B @ sk5 ) @ ( A @ plus ) )
= B ) ),
inference(lifteq,[status(thm)],[73]) ).
thf(9225,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ~ $true
| ( ( A @ ( B @ sk5 ) @ ( A @ plus ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[61,76]) ).
thf(9226,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( ( A @ ( B @ sk5 ) @ ( A @ plus ) )
= B ) ),
inference(simp,[status(thm)],[9225]) ).
thf(9227,plain,
( ( int_zero @ ( int_one @ sk5 ) @ ( int_zero @ plus ) )
= int_one ),
inference(pattern_uni,[status(thm)],[9226:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_commutative) ).
thf(62,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(63,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(cnf,[status(esa)],[62]) ).
thf(64,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(lifteq,[status(thm)],[63]) ).
thf(9,axiom,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',plus_zero) ).
thf(65,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(66,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(cnf,[status(esa)],[65]) ).
thf(67,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(lifteq,[status(thm)],[66]) ).
thf(260,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_zero @ ( C @ plus ) ) )
| ( ( A @ ( B @ plus ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[64,67]) ).
thf(261,plain,
! [A: $i] :
( ( A @ ( int_zero @ plus ) )
= A ),
inference(pattern_uni,[status(thm)],[260:[bind(A,$thf( A )),bind(B,$thf( int_zero )),bind(C,$thf( A ))]]) ).
thf(9392,plain,
( ( int_zero @ ( int_one @ sk5 ) )
= int_one ),
inference(rewrite,[status(thm)],[9227,261]) ).
thf(9416,plain,
int_zero @ ( int_one @ sk5 ) @ ( int_zero @ int_less ),
inference(rewrite,[status(thm)],[8719,9392]) ).
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(79,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(80,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)],[79]) ).
thf(81,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)],[80]) ).
thf(82,plain,
! [A: $i] :
( ( A @ ( int_one @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(10056,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ sk5 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9416,82]) ).
thf(10057,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ sk5 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[10056]) ).
thf(10058,plain,
int_zero @ ( int_one @ sk5 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[10057:[bind(A,$thf( int_zero @ ( int_one @ sk5 ) ))]]) ).
thf(10102,plain,
int_one @ ( int_one @ int_leq ),
inference(rewrite,[status(thm)],[10058,9392]) ).
thf(16618,plain,
! [B: $i,A: $i] :
( ~ $true
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( ( B @ ( int_one @ plus ) @ ( int_one @ a ) )
= real_zero ) ),
inference(rewrite,[status(thm)],[136,10102]) ).
thf(16619,plain,
! [B: $i,A: $i] :
( ~ ( 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 @ ( int_one @ plus ) @ ( int_one @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[16618]) ).
thf(75,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ int_less ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ( ( C @ ( A @ plus ) )
!= B ) ),
inference(cnfConj,[status(thm)],[72]) ).
thf(77,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ int_less ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ( ( C @ ( A @ plus ) )
!= B ) ),
inference(lifteq,[status(thm)],[75]) ).
thf(78,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) @ ( A @ int_less ) )
| ~ ( B @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[77]) ).
thf(9644,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)],[61,78]) ).
thf(9645,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)],[9644]) ).
thf(9646,plain,
! [A: $i] : ( int_one @ ( A @ plus ) @ ( A @ int_less ) ),
inference(pattern_uni,[status(thm)],[9645:[bind(A,$thf( A )),bind(B,$thf( int_one ))]]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ int_less ) )
& ( B @ ( A @ int_less ) ) )
=> ( C @ ( A @ int_less ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',int_less_transitive) ).
thf(53,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(54,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ int_less ) )
| ~ ( C @ ( B @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[53]) ).
thf(7103,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ int_less ) )
!= ( D @ ( D @ int_less ) ) )
| ~ $true
| ~ ( C @ ( B @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[54,58]) ).
thf(7104,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( C @ ( A @ int_less ) )
!= ( D @ ( D @ int_less ) ) )
| ~ ( C @ ( B @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[7103]) ).
thf(7105,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ~ ( A @ ( B @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[7104:[bind(A,$thf( C )),bind(B,$thf( B )),bind(C,$thf( C )),bind(D,$thf( C ))]]) ).
thf(7175,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ~ ( A @ ( B @ int_less ) ) ),
inference(simp,[status(thm)],[7105]) ).
thf(9792,plain,
! [C: $i,B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( C @ ( B @ int_less ) ) )
| ~ $true
| ~ ( B @ ( C @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[9646,7175]) ).
thf(9793,plain,
! [C: $i,B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( C @ ( B @ int_less ) ) )
| ~ ( B @ ( C @ int_less ) ) ),
inference(simp,[status(thm)],[9792]) ).
thf(9794,plain,
! [A: $i] :
~ ( A @ ( int_one @ ( A @ plus ) @ int_less ) ),
inference(pattern_uni,[status(thm)],[9793:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( int_one @ ( D @ plus ) ))]]) ).
thf(9855,plain,
! [A: $i] :
~ ( A @ ( int_one @ ( A @ plus ) @ int_less ) ),
inference(simp,[status(thm)],[9794]) ).
thf(778,plain,
( ~ $true
| ( ( n @ ( sk4 @ int_leq ) )
!= ( n @ ( sk2 @ int_leq ) ) )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(eqfactor_ordered,[status(thm)],[24]) ).
thf(796,plain,
( ( n != n )
| ( sk4 != sk2 )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(simp,[status(thm)],[778]) ).
thf(814,plain,
( ( sk4 != sk2 )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(simp,[status(thm)],[796]) ).
thf(22,plain,
( ( sk3 = sk4 )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(40,plain,
( ( sk1 @ ( int_one @ int_leq ) )
| ( sk4 = sk3 ) ),
inference(lifteq,[status(thm)],[22]) ).
thf(44,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)],[43]) ).
thf(45,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)],[44]) ).
thf(46,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[45]) ).
thf(49,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[46]) ).
thf(99,plain,
! [A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[61,58]) ).
thf(100,plain,
! [A: $i] :
( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[99]) ).
thf(101,plain,
! [A: $i] :
( ( int_one != A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[100]) ).
thf(102,plain,
int_zero != int_one,
inference(simp,[status(thm)],[101]) ).
thf(3899,plain,
! [B: $i,A: $i] :
( ( B != int_zero )
| ( A != int_one )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[49,102]) ).
thf(3900,plain,
! [A: $i] :
( ( A != int_one )
| ( int_zero @ ( A @ int_less ) )
| ~ ( int_zero @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[3899:[bind(A,$thf( A )),bind(B,$thf( int_zero ))]]) ).
thf(4558,plain,
( ( int_zero @ ( int_one @ int_less ) )
| ~ ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[3900]) ).
thf(7338,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[61,7175]) ).
thf(7339,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[7338]) ).
thf(7340,plain,
~ ( int_zero @ ( int_one @ int_less ) ),
inference(pattern_uni,[status(thm)],[7339:[bind(A,$thf( int_one )),bind(B,$thf( int_zero ))]]) ).
thf(7388,plain,
( $false
| ~ ( int_zero @ ( int_one @ int_leq ) ) ),
inference(rewrite,[status(thm)],[4558,7340]) ).
thf(7389,plain,
~ ( int_zero @ ( int_one @ int_leq ) ),
inference(simp,[status(thm)],[7388]) ).
thf(7798,plain,
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk4 = sk3 ) ),
inference(paramod_ordered,[status(thm)],[40,7389]) ).
thf(7799,plain,
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[7798]) ).
thf(7827,plain,
( ( sk1 != int_zero )
| ( int_one != int_one )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[7799]) ).
thf(7839,plain,
( ( sk1 != int_zero )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[7827]) ).
thf(23,plain,
( ( ( sk4 @ ( sk3 @ a ) )
= real_zero )
| ( sk2 @ ( sk1 @ int_less ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(42,plain,
( ( sk2 @ ( sk1 @ int_less ) )
| ( ( sk4 @ ( sk3 @ a ) )
= real_zero ) ),
inference(lifteq,[status(thm)],[23]) ).
thf(234,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ( sk3 @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[18,58]) ).
thf(235,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ( sk3 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[234]) ).
thf(237,plain,
! [A: $i] :
( ( sk2 != A )
| ( sk1 != A )
| ( sk3 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[235]) ).
thf(239,plain,
( ( sk2 != sk1 )
| ( sk3 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[237]) ).
thf(83,plain,
! [A: $i] :
( ( A @ ( int_zero @ int_less ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[81]) ).
thf(84,plain,
! [A: $i] :
( ( A @ ( int_zero @ int_less ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[83]) ).
thf(10906,plain,
! [A: $i] :
( ( ( sk3 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[239,84]) ).
thf(10907,plain,
! [A: $i] :
( ( ( sk3 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[10906]) ).
thf(10908,plain,
( ( sk3 @ ( int_zero @ int_less ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[10907:[bind(A,$thf( sk3 ))]]) ).
thf(21,plain,
( ( sk3 = sk4 )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(37,plain,
( ( sk4 = sk3 )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(lifteq,[status(thm)],[21]) ).
thf(48,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[45]) ).
thf(51,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[48]) ).
thf(52,plain,
! [A: $i] : ( A @ ( A @ int_leq ) ),
inference(simp,[status(thm)],[51]) ).
thf(7774,plain,
( ( ( sk3 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[25,7389]) ).
thf(7775,plain,
( ( ( sk3 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[7774]) ).
thf(7817,plain,
( ( sk3 != int_zero )
| ( int_one != int_one )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[7775]) ).
thf(7837,plain,
( ( sk3 != int_zero )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[7817]) ).
thf(10863,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true
| ( sk3 != int_zero ) ),
inference(paramod_ordered,[status(thm)],[7837,84]) ).
thf(10864,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ( sk3 != int_zero ) ),
inference(simp,[status(thm)],[10863]) ).
thf(10865,plain,
( ( sk1 @ ( int_zero @ int_less ) )
| ( sk3 != int_zero ) ),
inference(pattern_uni,[status(thm)],[10864:[bind(A,$thf( sk1 ))]]) ).
thf(1159,plain,
( ( sk3 != sk1 )
| ( int_one != int_one )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1155]) ).
thf(1174,plain,
( ( sk3 != sk1 )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1159]) ).
thf(7780,plain,
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk3 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1174,7389]) ).
thf(7781,plain,
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[7780]) ).
thf(7812,plain,
( ( sk1 != int_zero )
| ( int_one != int_one )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[7781]) ).
thf(7835,plain,
( ( sk1 != int_zero )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[7812]) ).
thf(47,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[45]) ).
thf(50,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[47]) ).
thf(9842,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)],[9646,50]) ).
thf(9843,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)],[9842]) ).
thf(9844,plain,
! [A: $i] : ( int_one @ ( A @ plus ) @ ( A @ int_leq ) ),
inference(pattern_uni,[status(thm)],[9843:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( int_one @ ( D @ plus ) ))]]) ).
thf(9869,plain,
! [A: $i] : ( int_one @ ( A @ plus ) @ ( A @ int_leq ) ),
inference(simp,[status(thm)],[9844]) ).
thf(13926,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)],[9869,84]) ).
thf(13927,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( B @ ( int_one @ int_leq ) ) )
| ( B @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[13926]) ).
thf(13928,plain,
int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[13927:[bind(A,$thf( int_one )),bind(B,$thf( int_one @ ( int_one @ plus ) ))]]) ).
thf(14203,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)],[13928,50]) ).
thf(14204,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[14203]) ).
thf(14205,plain,
int_one @ ( int_one @ plus ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[14204:[bind(A,$thf( int_zero )),bind(B,$thf( int_one @ ( int_one @ plus ) ))]]) ).
thf(13043,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[10908,7175]) ).
thf(13044,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[13043]) ).
thf(13045,plain,
( ~ ( int_zero @ ( sk3 @ int_less ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[13044:[bind(A,$thf( sk3 )),bind(B,$thf( int_zero ))]]) ).
thf(9777,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( B @ ( B @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9646,58]) ).
thf(9778,plain,
! [B: $i,A: $i] :
( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( B @ ( B @ int_less ) ) ),
inference(simp,[status(thm)],[9777]) ).
thf(9854,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[9778]) ).
thf(9880,plain,
! [A: $i] :
( ( int_one @ ( A @ plus ) )
!= A ),
inference(simp,[status(thm)],[9854]) ).
thf(10966,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_one @ ( C @ plus ) ) )
| ( ( A @ ( B @ plus ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[64,9880]) ).
thf(10967,plain,
! [A: $i] :
( ( A @ ( int_one @ plus ) )
!= A ),
inference(pattern_uni,[status(thm)],[10966:[bind(A,$thf( A )),bind(B,$thf( int_one )),bind(C,$thf( A ))]]) ).
thf(10797,plain,
! [A: $i] :
( ( ( sk3 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[25,84]) ).
thf(10798,plain,
! [A: $i] :
( ( ( sk3 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[10797]) ).
thf(10799,plain,
( ( sk3 @ ( int_zero @ int_less ) )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[10798:[bind(A,$thf( sk3 ))]]) ).
thf(16345,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[10799,50]) ).
thf(16346,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[16345]) ).
thf(16347,plain,
( ( sk3 @ ( int_zero @ int_leq ) )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[16346:[bind(A,$thf( int_zero )),bind(B,$thf( sk3 ))]]) ).
thf(13,axiom,
real_zero != real_one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',real_constants) ).
thf(85,plain,
real_zero != real_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(86,plain,
real_zero != real_one,
inference(polarity_switch,[status(thm)],[85]) ).
thf(87,plain,
real_one != real_zero,
inference(lifteq,[status(thm)],[86]) ).
thf(4234,plain,
! [B: $i,A: $i] :
( ( B != real_one )
| ( A != real_zero )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[49,87]) ).
thf(4235,plain,
! [A: $i] :
( ( A != real_zero )
| ( real_one @ ( A @ int_less ) )
| ~ ( real_one @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[4234:[bind(A,$thf( A )),bind(B,$thf( real_one ))]]) ).
thf(4400,plain,
( ( real_one @ ( real_zero @ int_less ) )
| ~ ( real_one @ ( real_zero @ int_leq ) ) ),
inference(simp,[status(thm)],[4235]) ).
thf(8131,plain,
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk3 != int_zero ) ),
inference(paramod_ordered,[status(thm)],[7837,7389]) ).
thf(8132,plain,
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ( sk3 != int_zero ) ),
inference(simp,[status(thm)],[8131]) ).
thf(8212,plain,
( ( sk1 != int_zero )
| ( int_one != int_one )
| ( sk3 != int_zero ) ),
inference(simp,[status(thm)],[8132]) ).
thf(8229,plain,
( ( sk1 != int_zero )
| ( sk3 != int_zero ) ),
inference(simp,[status(thm)],[8212]) ).
thf(865,plain,
( ( sk4 != sk4 )
| ( sk3 != sk2 )
| ( n @ ( sk2 @ int_leq ) )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[36,814]) ).
thf(866,plain,
( ( sk4 != sk4 )
| ( sk3 != sk2 )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(simp,[status(thm)],[865]) ).
thf(867,plain,
( ( sk3 != sk2 )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[866:[]]) ).
thf(7806,plain,
( ( ( n @ ( sk2 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk3 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[867,7389]) ).
thf(7807,plain,
( ( ( n @ ( sk2 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[7806]) ).
thf(7818,plain,
( ( int_zero != n )
| ( sk2 != int_one )
| ( sk3 != sk2 ) ),
inference(simp,[status(thm)],[7807]) ).
thf(4232,plain,
! [B: $i,A: $i] :
( ( A != real_one )
| ( B != real_zero )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[49,87]) ).
thf(4233,plain,
! [A: $i] :
( ( A != real_zero )
| ( A @ ( real_one @ int_less ) )
| ~ ( A @ ( real_one @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[4232:[bind(A,$thf( real_one ))]]) ).
thf(4399,plain,
( ( real_zero @ ( real_one @ int_less ) )
| ~ ( real_zero @ ( real_one @ int_leq ) ) ),
inference(simp,[status(thm)],[4233]) ).
thf(7374,plain,
! [B: $i,A: $i] :
( ( ( real_zero @ ( real_one @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true
| ~ ( real_zero @ ( real_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[4399,7175]) ).
thf(7375,plain,
! [B: $i,A: $i] :
( ( ( real_zero @ ( real_one @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ ( real_zero @ ( real_one @ int_leq ) ) ),
inference(simp,[status(thm)],[7374]) ).
thf(7376,plain,
( ~ ( real_one @ ( real_zero @ int_less ) )
| ~ ( real_zero @ ( real_one @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[7375:[bind(A,$thf( real_zero )),bind(B,$thf( real_one ))]]) ).
thf(1856,plain,
( ( sk4 != sk4 )
| ( sk2 @ ( sk1 @ int_less ) )
| ( ( sk3 @ ( sk3 @ a ) )
= real_zero )
| ( sk2 @ ( sk1 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[41,42]) ).
thf(1857,plain,
( ( sk4 != sk4 )
| ( ( sk3 @ ( sk3 @ a ) )
= real_zero )
| ( sk2 @ ( sk1 @ int_less ) ) ),
inference(simp,[status(thm)],[1856]) ).
thf(1858,plain,
( ( ( sk3 @ ( sk3 @ a ) )
= real_zero )
| ( sk2 @ ( sk1 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[1857:[]]) ).
thf(19,plain,
( ( n @ ( sk4 @ int_leq ) )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(589,plain,
( ( sk4 != sk4 )
| ( n @ ( sk3 @ int_leq ) )
| ( sk1 @ ( int_one @ int_leq ) )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[40,19]) ).
thf(590,plain,
( ( sk4 != sk4 )
| ( n @ ( sk3 @ int_leq ) )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[589]) ).
thf(591,plain,
( ( n @ ( sk3 @ int_leq ) )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[590:[]]) ).
thf(12996,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ( sk3 != int_zero ) ),
inference(paramod_ordered,[status(thm)],[10865,50]) ).
thf(12997,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ( sk3 != int_zero ) ),
inference(simp,[status(thm)],[12996]) ).
thf(12998,plain,
( ( sk1 @ ( int_zero @ int_leq ) )
| ( sk3 != int_zero ) ),
inference(pattern_uni,[status(thm)],[12997:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 ))]]) ).
thf(8631,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk5 ) @ ( int_zero @ int_less ) )
| ~ $true
| ( sk4 = sk3 ) ),
inference(paramod_ordered,[status(thm)],[41,74]) ).
thf(8632,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk5 ) @ ( int_zero @ int_less ) )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[8631]) ).
thf(8633,plain,
( ( sk1 @ ( sk2 @ sk5 ) @ ( int_zero @ int_less ) )
| ( sk4 = sk3 ) ),
inference(pattern_uni,[status(thm)],[8632:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(10440,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ sk5 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ( sk4 = sk3 ) ),
inference(paramod_ordered,[status(thm)],[8633,50]) ).
thf(10441,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ sk5 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[10440]) ).
thf(10442,plain,
( ( sk1 @ ( sk2 @ sk5 ) @ ( int_zero @ int_leq ) )
| ( sk4 = sk3 ) ),
inference(pattern_uni,[status(thm)],[10441:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 @ ( sk2 @ sk5 ) ))]]) ).
thf(5399,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ( sk4 = sk3 ) ),
inference(paramod_ordered,[status(thm)],[41,50]) ).
thf(5400,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[5399]) ).
thf(5401,plain,
( ( sk2 @ ( sk1 @ int_leq ) )
| ( sk4 = sk3 ) ),
inference(pattern_uni,[status(thm)],[5400:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(124,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 ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( ( B @ ( C @ plus ) @ ( C @ a ) )
= real_zero ) ),
inference(eqfactor_ordered,[status(thm)],[98]) ).
thf(132,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 ) )
| ~ ( 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)],[124]) ).
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(59,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(60,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[59]) ).
thf(20,plain,
( ( ( sk4 @ ( sk3 @ a ) )
= real_zero )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(34,plain,
( ( sk1 @ ( int_one @ int_leq ) )
| ( ( sk4 @ ( sk3 @ a ) )
= real_zero ) ),
inference(lifteq,[status(thm)],[20]) ).
thf(1766,plain,
( ( sk4 != sk4 )
| ( sk1 @ ( int_one @ int_leq ) )
| ( ( sk3 @ ( sk3 @ a ) )
= real_zero )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[40,34]) ).
thf(1767,plain,
( ( sk4 != sk4 )
| ( ( sk3 @ ( sk3 @ a ) )
= real_zero )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1766]) ).
thf(1768,plain,
( ( ( sk3 @ ( sk3 @ a ) )
= real_zero )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[1767:[]]) ).
thf(7758,plain,
( ( ( n @ ( sk2 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk4 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[814,7389]) ).
thf(7759,plain,
( ( ( n @ ( sk2 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[7758]) ).
thf(7834,plain,
( ( int_zero != n )
| ( sk2 != int_one )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[7759]) ).
thf(4301,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ~ $true
| ( A = B )
| ( sk4 = sk3 ) ),
inference(paramod_ordered,[status(thm)],[36,49]) ).
thf(4302,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[4301]) ).
thf(4303,plain,
( ( n @ ( sk2 @ int_less ) )
| ( sk2 = n )
| ( sk4 = sk3 ) ),
inference(pattern_uni,[status(thm)],[4302:[bind(A,$thf( sk2 )),bind(B,$thf( n ))]]) ).
thf(7344,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true
| ( sk4 = sk3 ) ),
inference(paramod_ordered,[status(thm)],[41,7175]) ).
thf(7345,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[7344]) ).
thf(7346,plain,
( ~ ( sk1 @ ( sk2 @ int_less ) )
| ( sk4 = sk3 ) ),
inference(pattern_uni,[status(thm)],[7345:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(7683,plain,
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( n @ ( sk2 @ int_less ) ) )
| ~ $true
| ( sk4 = sk3 )
| ( sk2 = n )
| ( sk4 = sk3 ) ),
inference(paramod_ordered,[status(thm)],[4303,7346]) ).
thf(7684,plain,
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( n @ ( sk2 @ int_less ) ) )
| ( sk2 = n )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[7683]) ).
thf(7701,plain,
( ( sk1 != n )
| ( sk2 != sk2 )
| ( sk2 = n )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[7684]) ).
thf(7710,plain,
( ( sk1 != n )
| ( sk2 = n )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[7701]) ).
thf(122,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 ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( ( B @ ( C @ plus ) @ ( C @ a ) )
= real_zero ) ),
inference(eqfactor_ordered,[status(thm)],[98]) ).
thf(137,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 ) )
| ~ ( 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)],[122]) ).
thf(31,plain,
( ( n @ ( sk4 @ int_leq ) )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(33,plain,
( ( n @ ( sk4 @ int_leq ) )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(lifteq,[status(thm)],[31]) ).
thf(32,plain,
( ( ( sk4 @ ( sk3 @ a ) )
= real_zero )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(38,plain,
( ( ( sk4 @ ( sk3 @ a ) )
= real_zero )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(lifteq,[status(thm)],[32]) ).
thf(7810,plain,
( ( ( sk3 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[239,7389]) ).
thf(7811,plain,
( ( ( sk3 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[7810]) ).
thf(7831,plain,
( ( sk3 != int_zero )
| ( int_one != int_one )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[7811]) ).
thf(7842,plain,
( ( sk3 != int_zero )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[7831]) ).
thf(14149,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk5 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13928,74]) ).
thf(14150,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk5 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[14149]) ).
thf(14151,plain,
int_zero @ ( int_one @ ( int_one @ plus ) @ sk5 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[14150:[bind(A,$thf( int_zero )),bind(B,$thf( int_one @ ( int_one @ plus ) ))]]) ).
thf(19650,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk5 ) @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14151,7175]) ).
thf(19651,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk5 ) @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[19650]) ).
thf(19652,plain,
~ ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk5 ) @ int_less ) ),
inference(pattern_uni,[status(thm)],[19651:[bind(A,$thf( int_zero @ ( int_one @ ( int_one @ plus ) @ sk5 ) )),bind(B,$thf( int_zero ))]]) ).
thf(606,plain,
( ~ $true
| ( ( n @ ( sk4 @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(eqfactor_ordered,[status(thm)],[19]) ).
thf(610,plain,
( ( sk1 != n )
| ( sk4 != int_one )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[606]) ).
thf(7782,plain,
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk1 != n )
| ( sk4 != int_one ) ),
inference(paramod_ordered,[status(thm)],[610,7389]) ).
thf(7783,plain,
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ( sk1 != n )
| ( sk4 != int_one ) ),
inference(simp,[status(thm)],[7782]) ).
thf(7822,plain,
( ( sk1 != int_zero )
| ( int_one != int_one )
| ( sk1 != n )
| ( sk4 != int_one ) ),
inference(simp,[status(thm)],[7783]) ).
thf(7838,plain,
( ( sk1 != int_zero )
| ( sk1 != n )
| ( sk4 != int_one ) ),
inference(simp,[status(thm)],[7822]) ).
thf(13097,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[10908,50]) ).
thf(13098,plain,
! [B: $i,A: $i] :
( ( ( sk3 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[13097]) ).
thf(13099,plain,
( ( sk3 @ ( int_zero @ int_leq ) )
| ( sk2 != sk1 ) ),
inference(pattern_uni,[status(thm)],[13098:[bind(A,$thf( int_zero )),bind(B,$thf( sk3 ))]]) ).
thf(10886,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true
| ( sk4 = sk3 ) ),
inference(paramod_ordered,[status(thm)],[40,84]) ).
thf(10887,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[10886]) ).
thf(10888,plain,
( ( sk1 @ ( int_zero @ int_less ) )
| ( sk4 = sk3 ) ),
inference(pattern_uni,[status(thm)],[10887:[bind(A,$thf( sk1 ))]]) ).
thf(11128,plain,
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( sk1 @ ( int_zero @ int_less ) ) )
| ~ $true
| ( sk4 = sk3 )
| ( sk4 = sk3 ) ),
inference(paramod_ordered,[status(thm)],[10888,7346]) ).
thf(11129,plain,
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( sk1 @ ( int_zero @ int_less ) ) )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[11128]) ).
thf(11274,plain,
( ( sk1 != sk1 )
| ( sk2 != int_zero )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[11129]) ).
thf(11278,plain,
( ( sk2 != int_zero )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[11274]) ).
thf(14140,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13928,7175]) ).
thf(14141,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[14140]) ).
thf(14142,plain,
~ ( int_zero @ ( int_one @ ( int_one @ plus ) @ int_less ) ),
inference(pattern_uni,[status(thm)],[14141:[bind(A,$thf( int_one @ ( int_one @ plus ) )),bind(B,$thf( int_zero ))]]) ).
thf(5408,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ( n @ ( sk4 @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[30,50]) ).
thf(5409,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ( n @ ( sk4 @ int_leq ) ) ),
inference(simp,[status(thm)],[5408]) ).
thf(5410,plain,
( ( sk2 @ ( sk1 @ int_leq ) )
| ( n @ ( sk4 @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[5409:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(6761,plain,
( ( sk4 != sk4 )
| ( sk2 @ ( sk1 @ int_leq ) )
| ( n @ ( sk3 @ int_leq ) )
| ( sk2 @ ( sk1 @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[5401,5410]) ).
thf(6762,plain,
( ( sk4 != sk4 )
| ( n @ ( sk3 @ int_leq ) )
| ( sk2 @ ( sk1 @ int_leq ) ) ),
inference(simp,[status(thm)],[6761]) ).
thf(6763,plain,
( ( n @ ( sk3 @ int_leq ) )
| ( sk2 @ ( sk1 @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[6762:[]]) ).
thf(10827,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true
| ( sk3 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1174,84]) ).
thf(10828,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[10827]) ).
thf(10829,plain,
( ( sk1 @ ( int_zero @ int_less ) )
| ( sk3 != sk1 ) ),
inference(pattern_uni,[status(thm)],[10828:[bind(A,$thf( sk1 ))]]) ).
thf(11440,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true
| ( sk3 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[10829,7175]) ).
thf(11441,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[11440]) ).
thf(11442,plain,
( ~ ( int_zero @ ( sk1 @ int_less ) )
| ( sk3 != sk1 ) ),
inference(pattern_uni,[status(thm)],[11441:[bind(A,$thf( sk1 )),bind(B,$thf( int_zero ))]]) ).
thf(91,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)],[89]) ).
thf(95,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)],[91]) ).
thf(96,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)],[95]) ).
thf(2302,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( ( B @ ( A @ plus ) )
!= n )
| ( ( B @ ( A @ plus ) )
!= int_one )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ $true
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( ( B @ ( C @ plus ) @ ( C @ a ) )
= real_zero )
| ( sk1 != n )
| ( sk4 != int_one ) ),
inference(paramod_ordered,[status(thm)],[610,132]) ).
thf(2303,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( ( 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 @ ( C @ plus ) @ ( C @ a ) )
= real_zero )
| ( sk1 != n )
| ( sk4 != int_one ) ),
inference(simp,[status(thm)],[2302]) ).
thf(2343,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= sk1 )
| ( int_one != int_one )
| ( ( 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 ) )
| ( sk1 != n )
| ( sk4 != int_one )
| ( ( B @ ( C @ plus ) @ ( C @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[2303]) ).
thf(2361,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= sk1 )
| ( ( 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 ) )
| ( sk1 != n )
| ( sk4 != int_one )
| ( ( B @ ( C @ plus ) @ ( C @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[2343]) ).
thf(2603,plain,
! [C: $i,B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( ( B @ ( A @ plus ) )
!= sk1 )
| ( ( 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 ) )
| ~ $true
| ( sk1 != n )
| ( sk4 != int_one )
| ( ( B @ ( C @ plus ) @ ( C @ a ) )
= real_zero )
| ( sk4 != sk2 ) ),
inference(paramod_ordered,[status(thm)],[814,2361]) ).
thf(2604,plain,
! [C: $i,B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( ( B @ ( A @ plus ) )
!= sk1 )
| ( ( 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 ) )
| ( sk1 != n )
| ( sk4 != int_one )
| ( ( B @ ( C @ plus ) @ ( C @ a ) )
= real_zero )
| ( sk4 != sk2 ) ),
inference(simp,[status(thm)],[2603]) ).
thf(2889,plain,
! [C: $i,B: $i,A: $i] :
( ( n != A )
| ( sk2 != int_one )
| ( ( B @ ( A @ plus ) )
!= sk1 )
| ( ( 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 ) )
| ( sk1 != n )
| ( sk4 != int_one )
| ( sk4 != sk2 )
| ( ( B @ ( C @ plus ) @ ( C @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[2604]) ).
thf(2958,plain,
! [B: $i,A: $i] :
( ( sk2 != int_one )
| ( ( A @ ( n @ plus ) )
!= sk1 )
| ( ( A @ ( n @ plus ) )
!= n )
| ( ( A @ ( n @ plus ) )
!= int_one )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) )
| ~ ( n @ ( n @ int_leq ) )
| ( sk1 != n )
| ( sk4 != int_one )
| ( sk4 != sk2 )
| ( ( A @ ( B @ plus ) @ ( B @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[2889]) ).
thf(3004,plain,
! [B: $i,A: $i] :
( ( sk2 != int_one )
| ( ( A @ ( n @ plus ) )
!= sk1 )
| ( ( A @ ( n @ plus ) )
!= n )
| ( ( A @ ( n @ plus ) )
!= int_one )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) )
| ~ $true
| ( sk1 != n )
| ( sk4 != int_one )
| ( sk4 != sk2 )
| ( ( A @ ( B @ plus ) @ ( B @ a ) )
= real_zero ) ),
inference(rewrite,[status(thm)],[2958,52]) ).
thf(3005,plain,
! [B: $i,A: $i] :
( ( sk2 != int_one )
| ( ( A @ ( n @ plus ) )
!= sk1 )
| ( ( A @ ( n @ plus ) )
!= n )
| ( ( A @ ( n @ plus ) )
!= int_one )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) )
| ( sk1 != n )
| ( sk4 != int_one )
| ( sk4 != sk2 )
| ( ( A @ ( B @ plus ) @ ( B @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[3004]) ).
thf(4267,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ~ $true
| ( A = B )
| ( sk4 = sk3 ) ),
inference(paramod_ordered,[status(thm)],[40,49]) ).
thf(4268,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[4267]) ).
thf(4269,plain,
( ( sk1 @ ( int_one @ int_less ) )
| ( sk1 = int_one )
| ( sk4 = sk3 ) ),
inference(pattern_uni,[status(thm)],[4268:[bind(A,$thf( int_one )),bind(B,$thf( sk1 ))]]) ).
thf(7622,plain,
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( sk1 @ ( int_one @ int_less ) ) )
| ~ $true
| ( sk4 = sk3 )
| ( sk1 = int_one )
| ( sk4 = sk3 ) ),
inference(paramod_ordered,[status(thm)],[4269,7346]) ).
thf(7623,plain,
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( sk1 @ ( int_one @ int_less ) ) )
| ( sk1 = int_one )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[7622]) ).
thf(7695,plain,
( ( sk1 != sk1 )
| ( sk2 != int_one )
| ( sk1 = int_one )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[7623]) ).
thf(7706,plain,
( ( sk2 != int_one )
| ( sk1 = int_one )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[7695]) ).
thf(7380,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true
| ( n @ ( sk4 @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[30,7175]) ).
thf(7381,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( n @ ( sk4 @ int_leq ) ) ),
inference(simp,[status(thm)],[7380]) ).
thf(7382,plain,
( ~ ( sk1 @ ( sk2 @ int_less ) )
| ( n @ ( sk4 @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[7381:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(11224,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ( sk4 = sk3 ) ),
inference(paramod_ordered,[status(thm)],[10888,50]) ).
thf(11225,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[11224]) ).
thf(11226,plain,
( ( sk1 @ ( int_zero @ int_leq ) )
| ( sk4 = sk3 ) ),
inference(pattern_uni,[status(thm)],[11225:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 ))]]) ).
thf(7770,plain,
( ( ( n @ ( sk3 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1406,7389]) ).
thf(7771,plain,
( ( ( n @ ( sk3 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[7770]) ).
thf(7815,plain,
( ( int_zero != n )
| ( sk3 != int_one )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[7771]) ).
thf(27,plain,
( ( sk3 @ ( int_one @ int_leq ) )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(1611,plain,
( ~ $true
| ( ( n @ ( sk3 @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(eqfactor_ordered,[status(thm)],[591]) ).
thf(1629,plain,
( ( sk1 != n )
| ( sk3 != int_one )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1611]) ).
thf(4682,plain,
! [B: $i,A: $i] :
( ( ( real_zero @ ( real_one @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( sk2 != int_one )
| ( ( A @ ( n @ plus ) )
!= sk1 )
| ( ( A @ ( n @ plus ) )
!= n )
| ( ( A @ ( n @ plus ) )
!= int_one )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ~ $true
| ( sk1 != n )
| ( sk4 != int_one )
| ( sk4 != sk2 )
| ( ( A @ ( B @ plus ) @ ( B @ a ) )
= real_zero )
| ~ ( real_zero @ ( real_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[4399,3005]) ).
thf(4683,plain,
! [B: $i,A: $i] :
( ( ( real_zero @ ( real_one @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( sk2 != int_one )
| ( ( A @ ( n @ plus ) )
!= sk1 )
| ( ( A @ ( n @ plus ) )
!= n )
| ( ( A @ ( n @ plus ) )
!= int_one )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ( sk1 != n )
| ( sk4 != int_one )
| ( sk4 != sk2 )
| ( ( A @ ( B @ plus ) @ ( B @ a ) )
= real_zero )
| ~ ( real_zero @ ( real_one @ int_leq ) ) ),
inference(simp,[status(thm)],[4682]) ).
thf(4720,plain,
! [B: $i,A: $i] :
( ( real_zero != A )
| ( real_one != int_zero )
| ( sk2 != int_one )
| ( ( A @ ( n @ plus ) )
!= sk1 )
| ( ( A @ ( n @ plus ) )
!= n )
| ( ( A @ ( n @ plus ) )
!= int_one )
| ~ ( n @ ( B @ int_leq ) )
| ~ ( B @ ( int_one @ int_leq ) )
| ( sk1 != n )
| ( sk4 != int_one )
| ( sk4 != sk2 )
| ~ ( real_zero @ ( real_one @ int_leq ) )
| ( ( A @ ( B @ plus ) @ ( B @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[4683]) ).
thf(4734,plain,
! [A: $i] :
( ( real_one != int_zero )
| ( sk2 != int_one )
| ( ( real_zero @ ( n @ plus ) )
!= sk1 )
| ( ( real_zero @ ( n @ plus ) )
!= n )
| ( ( real_zero @ ( n @ plus ) )
!= int_one )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( sk1 != n )
| ( sk4 != int_one )
| ( sk4 != sk2 )
| ~ ( real_zero @ ( real_one @ int_leq ) )
| ( ( real_zero @ ( A @ plus ) @ ( A @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[4720]) ).
thf(5126,plain,
! [A: $i] :
( ( ( real_zero @ ( real_one @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( real_one != int_zero )
| ( sk2 != int_one )
| ( ( real_zero @ ( n @ plus ) )
!= sk1 )
| ( ( real_zero @ ( n @ plus ) )
!= n )
| ( ( real_zero @ ( n @ plus ) )
!= int_one )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( sk1 != n )
| ( sk4 != int_one )
| ( sk4 != sk2 )
| ~ $true
| ( ( real_zero @ ( A @ plus ) @ ( A @ a ) )
= real_zero )
| ( sk1 != n )
| ( sk3 != int_one ) ),
inference(paramod_ordered,[status(thm)],[1629,4734]) ).
thf(5127,plain,
! [A: $i] :
( ( ( real_zero @ ( real_one @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( real_one != int_zero )
| ( sk2 != int_one )
| ( ( real_zero @ ( n @ plus ) )
!= sk1 )
| ( ( real_zero @ ( n @ plus ) )
!= n )
| ( ( real_zero @ ( n @ plus ) )
!= int_one )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( sk4 != int_one )
| ( sk4 != sk2 )
| ( ( real_zero @ ( A @ plus ) @ ( A @ a ) )
= real_zero )
| ( sk1 != n )
| ( sk3 != int_one ) ),
inference(simp,[status(thm)],[5126]) ).
thf(5158,plain,
! [A: $i] :
( ( sk1 != real_zero )
| ( real_one != int_one )
| ( real_one != int_zero )
| ( sk2 != int_one )
| ( ( real_zero @ ( n @ plus ) )
!= sk1 )
| ( ( real_zero @ ( n @ plus ) )
!= n )
| ( ( real_zero @ ( n @ plus ) )
!= int_one )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( sk4 != int_one )
| ( sk4 != sk2 )
| ( sk1 != n )
| ( sk3 != int_one )
| ( ( real_zero @ ( A @ plus ) @ ( A @ a ) )
= real_zero ) ),
inference(simp,[status(thm)],[5127]) ).
thf(14132,plain,
! [A: $i] :
( ( ( int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_one @ ( A @ plus ) @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[13928,9855]) ).
thf(14133,plain,
! [A: $i] :
( ( int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_one @ ( A @ plus ) @ int_less ) ) ),
inference(simp,[status(thm)],[14132]) ).
thf(14225,plain,
! [A: $i] :
( ( ( int_one @ ( int_one @ plus ) )
!= A )
| ( ( int_one @ ( A @ plus ) )
!= int_zero ) ),
inference(simp,[status(thm)],[14133]) ).
thf(14233,plain,
( ( int_one @ ( int_one @ ( int_one @ plus ) @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[14225]) ).
thf(7326,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true
| ( sk3 @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[18,7175]) ).
thf(7327,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk3 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[7326]) ).
thf(7328,plain,
( ~ ( sk1 @ ( sk2 @ int_less ) )
| ( sk3 @ ( int_one @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[7327:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(17,plain,
( ( sk3 @ ( int_one @ int_leq ) )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(39,plain,
( ( sk3 @ ( int_one @ int_leq ) )
| ( ( sk2 @ ( sk1 @ a ) )
!= real_zero ) ),
inference(lifteq,[status(thm)],[17]) ).
thf(609,plain,
( ( ( n @ ( sk4 @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( sk1 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[606]) ).
thf(125,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 ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( ( B @ ( C @ plus ) @ ( C @ a ) )
= real_zero ) ),
inference(eqfactor_ordered,[status(thm)],[98]) ).
thf(140,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 ) )
| ~ ( 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)],[125]) ).
thf(5390,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ( sk3 @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[18,50]) ).
thf(5391,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ( sk3 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[5390]) ).
thf(5392,plain,
( ( sk2 @ ( sk1 @ int_leq ) )
| ( sk3 @ ( int_one @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[5391:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(9803,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9646,7340]) ).
thf(9804,plain,
! [A: $i] :
( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ int_less ) ) ),
inference(simp,[status(thm)],[9803]) ).
thf(9848,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) )
!= int_zero )
| ( A != int_one ) ),
inference(simp,[status(thm)],[9804]) ).
thf(9873,plain,
( ( int_one @ ( int_one @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[9848]) ).
thf(7332,plain,
! [B: $i,A: $i] :
( ( ( real_one @ ( real_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true
| ~ ( real_one @ ( real_zero @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[4400,7175]) ).
thf(7333,plain,
! [B: $i,A: $i] :
( ( ( real_one @ ( real_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ ( real_one @ ( real_zero @ int_leq ) ) ),
inference(simp,[status(thm)],[7332]) ).
thf(7334,plain,
( ~ ( real_zero @ ( real_one @ int_less ) )
| ~ ( real_one @ ( real_zero @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[7333:[bind(A,$thf( real_one )),bind(B,$thf( real_zero ))]]) ).
thf(29,plain,
( ( ( sk4 @ ( sk3 @ a ) )
= real_zero )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[16]) ).
thf(35,plain,
( ( n @ ( sk2 @ int_leq ) )
| ( ( sk4 @ ( sk3 @ a ) )
= real_zero ) ),
inference(lifteq,[status(thm)],[29]) ).
thf(795,plain,
( ( ( n @ ( sk4 @ int_leq ) )
!= ( n @ ( sk2 @ int_leq ) ) )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(simp,[status(thm)],[778]) ).
thf(19731,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk5 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14151,58]) ).
thf(19732,plain,
! [A: $i] :
( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk5 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[19731]) ).
thf(19752,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk5 ) )
!= A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[19732]) ).
thf(19770,plain,
( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk5 ) )
!= int_zero ),
inference(simp,[status(thm)],[19752]) ).
thf(9808,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)],[64,9646]) ).
thf(9809,plain,
! [A: $i] : ( A @ ( int_one @ plus ) @ ( A @ int_less ) ),
inference(pattern_uni,[status(thm)],[9808:[bind(A,$thf( A )),bind(B,$thf( int_one )),bind(C,$thf( A ))]]) ).
thf(1308,plain,
( ~ $true
| ( ( n @ ( sk2 @ int_leq ) )
!= ( sk3 @ ( int_one @ int_leq ) ) )
| ( sk3 @ ( int_one @ int_leq ) ) ),
inference(eqfactor_ordered,[status(thm)],[27]) ).
thf(1321,plain,
( ( sk3 != n )
| ( sk2 != int_one )
| ( sk3 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1308]) ).
thf(7802,plain,
( ( ( n @ ( sk2 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk4 = sk3 ) ),
inference(paramod_ordered,[status(thm)],[36,7389]) ).
thf(7803,plain,
( ( ( n @ ( sk2 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[7802]) ).
thf(7816,plain,
( ( int_zero != n )
| ( sk2 != int_one )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[7803]) ).
thf(14307,plain,
! [A: $i] :
( ( ( A @ ( int_one @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ ( int_one @ plus ) @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[9809,14142]) ).
thf(14308,plain,
! [A: $i] :
( ( A @ ( int_one @ plus ) @ ( A @ int_less ) )
!= ( int_zero @ ( int_one @ ( int_one @ plus ) @ int_less ) ) ),
inference(simp,[status(thm)],[14307]) ).
thf(14317,plain,
! [A: $i] :
( ( ( A @ ( int_one @ plus ) )
!= int_zero )
| ( A
!= ( int_one @ ( int_one @ plus ) ) ) ),
inference(simp,[status(thm)],[14308]) ).
thf(14344,plain,
( ( int_one @ ( int_one @ plus ) @ ( int_one @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[14317]) ).
thf(5396,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)],[61,50]) ).
thf(5397,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[5396]) ).
thf(5398,plain,
int_one @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[5397:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(11492,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ( sk3 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[10829,50]) ).
thf(11493,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ( sk3 != sk1 ) ),
inference(simp,[status(thm)],[11492]) ).
thf(11494,plain,
( ( sk1 @ ( int_zero @ int_leq ) )
| ( sk3 != sk1 ) ),
inference(pattern_uni,[status(thm)],[11493:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 ))]]) ).
thf(12942,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true
| ( sk3 != int_zero ) ),
inference(paramod_ordered,[status(thm)],[10865,7175]) ).
thf(12943,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk3 != int_zero ) ),
inference(simp,[status(thm)],[12942]) ).
thf(12944,plain,
( ~ ( int_zero @ ( sk1 @ int_less ) )
| ( sk3 != int_zero ) ),
inference(pattern_uni,[status(thm)],[12943:[bind(A,$thf( sk1 )),bind(B,$thf( int_zero ))]]) ).
thf(11097,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ~ $true
| ( sk4 = sk3 ) ),
inference(paramod_ordered,[status(thm)],[10888,7175]) ).
thf(11098,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( A @ ( B @ int_less ) ) )
| ~ ( B @ ( A @ int_less ) )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[11097]) ).
thf(11099,plain,
( ~ ( int_zero @ ( sk1 @ int_less ) )
| ( sk4 = sk3 ) ),
inference(pattern_uni,[status(thm)],[11098:[bind(A,$thf( sk1 )),bind(B,$thf( int_zero ))]]) ).
thf(90,plain,
! [D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ ( D @ plus ) @ a ) )
= ( D @ ( C @ ( D @ plus ) @ qr ) ) )
| ~ ( 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)],[89]) ).
thf(93,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 ) @ qr ) )
= ( D @ ( C @ ( D @ plus ) @ a ) ) )
| ( A
!= ( C @ ( B @ plus ) ) ) ),
inference(lifteq,[status(thm)],[90]) ).
thf(94,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 ) @ qr ) )
= ( C @ ( B @ ( C @ plus ) @ a ) ) ) ),
inference(simp,[status(thm)],[93]) ).
thf(7766,plain,
( ( ( n @ ( sk4 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk2 != sk1 ) ),
inference(paramod_ordered,[status(thm)],[1369,7389]) ).
thf(7767,plain,
( ( ( n @ ( sk4 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[7766]) ).
thf(7819,plain,
( ( int_zero != n )
| ( sk4 != int_one )
| ( sk2 != sk1 ) ),
inference(simp,[status(thm)],[7767]) ).
thf(1827,plain,
( ( sk4 != sk4 )
| ( n @ ( sk2 @ int_leq ) )
| ( ( sk3 @ ( sk3 @ a ) )
= real_zero )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[36,35]) ).
thf(1828,plain,
( ( sk4 != sk4 )
| ( ( sk3 @ ( sk3 @ a ) )
= real_zero )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(simp,[status(thm)],[1827]) ).
thf(1829,plain,
( ( ( sk3 @ ( sk3 @ a ) )
= real_zero )
| ( n @ ( sk2 @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[1828:[]]) ).
thf(5847,plain,
! [A: $i] :
( ( ( real_zero @ ( A @ plus ) @ ( A @ a ) )
!= ( sk2 @ ( sk1 @ a ) ) )
| ( sk4 = sk3 )
| ( real_zero != real_zero )
| ( sk1 != real_zero )
| ( real_one != int_one )
| ( real_one != int_zero )
| ( sk2 != int_one )
| ( ( real_zero @ ( n @ plus ) )
!= sk1 )
| ( ( real_zero @ ( n @ plus ) )
!= n )
| ( ( real_zero @ ( n @ plus ) )
!= int_one )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( sk4 != int_one )
| ( sk4 != sk2 )
| ( sk1 != n )
| ( sk3 != int_one ) ),
inference(paramod_ordered,[status(thm)],[5158,37]) ).
thf(5848,plain,
! [A: $i] :
( ( ( real_zero @ ( A @ plus ) @ ( A @ a ) )
!= ( sk2 @ ( sk1 @ a ) ) )
| ( sk4 = sk3 )
| ( sk1 != real_zero )
| ( real_one != int_one )
| ( real_one != int_zero )
| ( sk2 != int_one )
| ( ( real_zero @ ( n @ plus ) )
!= sk1 )
| ( ( real_zero @ ( n @ plus ) )
!= n )
| ( ( real_zero @ ( n @ plus ) )
!= int_one )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( sk4 != int_one )
| ( sk4 != sk2 )
| ( sk1 != n )
| ( sk3 != int_one ) ),
inference(simp,[status(thm)],[5847]) ).
thf(6126,plain,
! [A: $i] :
( ( ( real_zero @ ( A @ plus ) )
!= sk2 )
| ( A != sk1 )
| ( sk1 != real_zero )
| ( real_one != int_one )
| ( real_one != int_zero )
| ( sk2 != int_one )
| ( ( real_zero @ ( n @ plus ) )
!= sk1 )
| ( ( real_zero @ ( n @ plus ) )
!= n )
| ( ( real_zero @ ( n @ plus ) )
!= int_one )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ( sk4 != int_one )
| ( sk4 != sk2 )
| ( sk1 != n )
| ( sk3 != int_one )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[5848]) ).
thf(6209,plain,
( ( ( real_zero @ ( sk1 @ plus ) )
!= sk2 )
| ( sk1 != real_zero )
| ( real_one != int_one )
| ( real_one != int_zero )
| ( sk2 != int_one )
| ( ( real_zero @ ( n @ plus ) )
!= sk1 )
| ( ( real_zero @ ( n @ plus ) )
!= n )
| ( ( real_zero @ ( n @ plus ) )
!= int_one )
| ~ ( n @ ( sk1 @ int_leq ) )
| ~ ( sk1 @ ( int_one @ int_leq ) )
| ( sk4 != int_one )
| ( sk4 != sk2 )
| ( sk1 != n )
| ( sk3 != int_one )
| ( sk4 = sk3 ) ),
inference(simp,[status(thm)],[6126]) ).
thf(131,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 ) )
| ~ ( 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)],[124]) ).
thf(1320,plain,
( ( ( n @ ( sk2 @ int_leq ) )
!= ( sk3 @ ( int_one @ int_leq ) ) )
| ( sk3 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1308]) ).
thf(200256,plain,
$false,
inference(e,[status(thm)],[18,43,69,1369,777,88,1158,1406,16619,9855,814,7839,42,10908,24,37,25,52,10865,7835,14205,13045,10967,9869,261,16347,78,4400,8229,7818,7376,1858,84,7175,591,12998,10799,10442,5401,61,132,74,60,85,102,1768,7834,7710,70,10102,137,33,1174,38,65,7842,7346,19652,7389,7838,53,13099,610,11278,13928,14142,6763,11442,9392,96,7340,41,3005,9416,34,7706,64,7382,4269,11226,59,7815,27,54,49,5158,14151,2361,14233,7837,7328,230,76,98,10888,39,8633,609,140,5392,5410,9873,7334,35,9646,10829,795,19770,50,67,9809,87,1321,7816,14344,40,1629,55,58,82,4399,36,30,19,867,5398,239,4303,79,11494,12944,11099,94,7819,1829,6209,131,15,68,62,1320,9880,4734]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV492+1 : 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
% 0.13/0.40 % Computer : n005.cluster.edu
% 0.13/0.40 % Model : x86_64 x86_64
% 0.13/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.40 % Memory : 8046.5625MB
% 0.13/0.40 % OS : Linux 6.8.0-71-generic
% 0.13/0.41 % CPULimit : 300
% 0.13/0.41 % WCLimit : 300
% 0.13/0.41 % DateTime : Sat Sep 26 13:58:32 UTC 2026
% 0.13/0.41 % CPUTime :
% 0.13/0.41 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.88/1.00 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 1.40/1.20 % [INFO] Parsing done (202ms).
% 1.40/1.22 % [INFO] Running in sequential loop mode.
% 2.04/1.63 % [INFO] eprover registered as external prover.
% 2.04/1.64 % [INFO] Scanning for conjecture ...
% 2.26/1.75 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.26/1.79 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.44/1.83 % [INFO] Problem is first-order (TPTP FOF).
% 2.44/1.83 % [INFO] Type checking passed.
% 2.44/1.84 % [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 ...
% 209.40/58.76 % External prover 'e' found a proof!
% 209.40/58.76 % [INFO] Killing All external provers ...
% 209.40/58.76 % Time passed: 58217ms (effective reasoning time: 57542ms)
% 209.40/58.76 % 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)>
% 209.40/58.77 % 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
% 209.40/58.77 % No. of inferences in proof: 404
% 209.40/58.77 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 58217 ms resp. 57542 ms w/o parsing
% 200.40/58.91 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 200.40/58.91 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------