%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SWV486+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% Computer : n008.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 08:59:35 AM UTC 2026
% Result : Theorem 61.38s 21.62s
% Output : Refutation 52.99s
% Verified :
% SZS Type : Refutation
% Derivation depth : 33
% Number of leaves : 16
% Syntax : Number of formulae : 532 ( 139 unt; 0 typ; 3 def)
% Number of atoms : 1785 ( 576 equ; 0 cnn)
% Maximal formula atoms : 25 ( 3 avg)
% Number of connectives : 5144 ( 850 ~; 748 |; 56 &;3452 @)
% ( 3 <=>; 35 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 15 ( 12 usr; 9 con; 0-2 aty)
% Number of variables : 625 ( 2 ^; 615 !; 5 ?; 625 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% 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(sk1_decl,type,
sk1: $i ).
thf(sk2_decl,type,
sk2: $i ).
thf(sk3_decl,type,
sk3: $i > $i > $i ).
thf(sk1_def,definition,
( sk1
= ( @+[A: $i] :
~ ! [B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( 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] :
@+[C: $i] :
( ( C @ ( int_zero @ int_less ) )
& ( ( C @ ( B @ plus ) )
= A ) ) ) ) ).
thf(3,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ int_leq ) )
<=> ( ( A = B )
| ( B @ ( A @ int_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_leq) ).
thf(22,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(23,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)],[22]) ).
thf(24,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)],[23]) ).
thf(25,plain,
! [B: $i,A: $i] :
( ( A = B )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(28,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) )
| ( A = B ) ),
inference(lifteq,[status(thm)],[25]) ).
thf(1,conjecture,
! [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/sandbox/benchmark/theBenchmark.p',lt) ).
thf(2,negated_conjecture,
~ ! [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] :
( ( ( 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,
( ( ( sk2 @ ( sk1 @ a ) )
!= real_zero )
& ( n @ ( sk2 @ int_leq ) )
& ( sk2 @ ( sk1 @ int_less ) )
& ( sk1 @ ( int_one @ int_leq ) ) ),
inference(cnf,[status(esa)],[15]) ).
thf(20,plain,
( ( sk2 @ ( sk1 @ a ) )
!= real_zero ),
inference(cnfConj,[status(thm)],[16]) ).
thf(21,plain,
( ( sk2 @ ( sk1 @ a ) )
!= real_zero ),
inference(lifteq,[status(thm)],[20]) ).
thf(139,plain,
! [B: $i,A: $i] :
( ( A
!= ( sk2 @ ( sk1 @ a ) ) )
| ( B != real_zero )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,21]) ).
thf(140,plain,
! [A: $i] :
( ( A != real_zero )
| ( A @ ( sk2 @ ( sk1 @ a ) @ int_less ) )
| ~ ( A @ ( sk2 @ ( sk1 @ a ) @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[139:[bind(A,$thf( sk2 @ ( sk1 @ a ) )),bind(B,$thf( B ))]]) ).
thf(153,plain,
( ( real_zero @ ( sk2 @ ( sk1 @ a ) @ int_less ) )
| ~ ( real_zero @ ( sk2 @ ( sk1 @ a ) @ int_leq ) ) ),
inference(simp,[status(thm)],[140]) ).
thf(18,plain,
sk2 @ ( sk1 @ int_less ),
inference(cnfConj,[status(thm)],[16]) ).
thf(11,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
<=> ? [C: $i] :
( ( C @ ( int_zero @ int_less ) )
& ( ( C @ ( A @ plus ) )
= B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_and_inverse) ).
thf(49,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(50,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)],[49]) ).
thf(51,plain,
! [E: $i,D: $i,C: $i,B: $i,A: $i] :
( ( ( D @ ( C @ int_less ) )
| ~ ( E @ ( int_zero @ int_less ) )
| ( ( E @ ( C @ plus ) )
!= D ) )
& ( ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) )
& ( ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B )
| ~ ( B @ ( A @ int_less ) ) ) ),
inference(cnf,[status(esa)],[50]) ).
thf(52,plain,
! [B: $i,A: $i] :
( ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[51]) ).
thf(55,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(lifteq,[status(thm)],[52]) ).
thf(2887,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ~ $true
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[18,55]) ).
thf(2888,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(simp,[status(thm)],[2887]) ).
thf(2889,plain,
( ( sk1 @ ( sk2 @ sk3 ) @ ( sk1 @ plus ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[2888:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_commutative) ).
thf(41,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(42,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(cnf,[status(esa)],[41]) ).
thf(43,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) )
= ( A @ ( B @ plus ) ) ),
inference(lifteq,[status(thm)],[42]) ).
thf(3089,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( sk1 @ plus ) )
!= ( B @ ( A @ plus ) ) )
| ( ( A @ ( B @ plus ) )
= sk2 ) ),
inference(paramod_ordered,[status(thm)],[2889,43]) ).
thf(3090,plain,
( ( sk1 @ ( sk1 @ ( sk2 @ sk3 ) @ plus ) )
= sk2 ),
inference(pattern_uni,[status(thm)],[3089:[bind(A,$thf( sk1 )),bind(B,$thf( sk1 @ ( sk2 @ sk3 ) ))]]) ).
thf(17,plain,
sk1 @ ( int_one @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ ( int_zero @ int_less ) )
<=> ( A @ ( int_one @ int_leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',one_successor_of_zero) ).
thf(58,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(59,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)],[58]) ).
thf(60,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)],[59]) ).
thf(62,plain,
! [A: $i] :
( ( A @ ( int_zero @ int_less ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(cnfConj,[status(thm)],[60]) ).
thf(63,plain,
! [A: $i] :
( ( A @ ( int_zero @ int_less ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[62]) ).
thf(4288,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17,63]) ).
thf(4289,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[4288]) ).
thf(4290,plain,
sk1 @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[4289:[bind(A,$thf( sk1 ))]]) ).
thf(54,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ int_less ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ( ( C @ ( A @ plus ) )
!= B ) ),
inference(cnfConj,[status(thm)],[51]) ).
thf(56,plain,
! [C: $i,B: $i,A: $i] :
( ( B @ ( A @ int_less ) )
| ~ ( C @ ( int_zero @ int_less ) )
| ( ( C @ ( A @ plus ) )
!= B ) ),
inference(lifteq,[status(thm)],[54]) ).
thf(57,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ plus ) @ ( A @ int_less ) )
| ~ ( B @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[56]) ).
thf(4408,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)],[4290,57]) ).
thf(4409,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)],[4408]) ).
thf(4410,plain,
! [A: $i] : ( sk1 @ ( A @ plus ) @ ( A @ int_less ) ),
inference(pattern_uni,[status(thm)],[4409:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(8438,plain,
! [A: $i] :
( ( ( sk1 @ ( sk1 @ ( sk2 @ sk3 ) @ plus ) )
!= ( sk1 @ ( A @ plus ) ) )
| ( sk2 @ ( A @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[3090,4410]) ).
thf(8439,plain,
sk2 @ ( sk1 @ ( sk2 @ sk3 ) @ int_less ),
inference(pattern_uni,[status(thm)],[8438:[bind(A,$thf( sk1 @ ( sk2 @ sk3 ) ))]]) ).
thf(53,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[51]) ).
thf(8529,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ sk3 ) @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8439,53]) ).
thf(8530,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ sk3 ) @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[8529]) ).
thf(8531,plain,
sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[8530:[bind(A,$thf( sk1 @ ( sk2 @ sk3 ) )),bind(B,$thf( sk2 ))]]) ).
thf(8958,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8531,53]) ).
thf(8959,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[8958]) ).
thf(8960,plain,
int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[8959:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) ))]]) ).
thf(7,axiom,
int_one @ ( int_zero @ int_less ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_zero_one) ).
thf(40,plain,
int_one @ ( int_zero @ int_less ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(26,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(29,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[26]) ).
thf(758,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)],[40,29]) ).
thf(759,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[758]) ).
thf(760,plain,
int_one @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[759:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(8457,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( sk1 @ ( C @ plus ) ) )
| ( A @ ( B @ plus ) @ ( C @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[43,4410]) ).
thf(8458,plain,
! [A: $i] : ( A @ ( sk1 @ plus ) @ ( A @ int_less ) ),
inference(pattern_uni,[status(thm)],[8457:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(14111,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ plus ) @ ( A @ int_less ) )
!= ( C @ ( B @ int_less ) ) )
| ( C @ ( B @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8458,29]) ).
thf(14112,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( sk1 @ plus ) @ ( A @ int_less ) )
!= ( C @ ( B @ int_less ) ) )
| ( C @ ( B @ int_leq ) ) ),
inference(simp,[status(thm)],[14111]) ).
thf(14113,plain,
! [A: $i] : ( A @ ( sk1 @ plus ) @ ( A @ int_leq ) ),
inference(pattern_uni,[status(thm)],[14112:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( sk1 @ plus ) ))]]) ).
thf(14175,plain,
! [A: $i] : ( A @ ( sk1 @ plus ) @ ( A @ int_leq ) ),
inference(simp,[status(thm)],[14113]) ).
thf(5,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
=> ( A != B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_irreflexive) ).
thf(34,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ int_less ) )
=> ( A != B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(35,plain,
! [B: $i,A: $i] :
( ( A != B )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[34]) ).
thf(36,plain,
! [B: $i,A: $i] :
( ~ ( B @ ( A @ int_less ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[35]) ).
thf(37,plain,
! [A: $i] :
~ ( A @ ( A @ int_less ) ),
inference(simp,[status(thm)],[36]) ).
thf(4244,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)],[63,37]) ).
thf(4245,plain,
! [B: $i,A: $i] :
( ( ( A @ ( int_zero @ int_less ) )
!= ( B @ ( B @ int_less ) ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[4244]) ).
thf(4246,plain,
~ ( int_zero @ ( int_one @ int_leq ) ),
inference(pattern_uni,[status(thm)],[4245:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero ))]]) ).
thf(17745,plain,
! [A: $i] :
( ( ( A @ ( sk1 @ plus ) @ ( A @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14175,4246]) ).
thf(17746,plain,
! [A: $i] :
( ( A @ ( sk1 @ plus ) @ ( A @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[17745]) ).
thf(17832,plain,
! [A: $i] :
( ( ( A @ ( sk1 @ plus ) )
!= int_zero )
| ( A != int_one ) ),
inference(simp,[status(thm)],[17746]) ).
thf(17875,plain,
( ( int_one @ ( sk1 @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[17832]) ).
thf(2361,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18,53]) ).
thf(2362,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[2361]) ).
thf(2363,plain,
sk1 @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[2362:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(2459,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2363,37]) ).
thf(2460,plain,
! [A: $i] :
( ( sk1 @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[2459]) ).
thf(2497,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) )
!= A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[2460]) ).
thf(2499,plain,
( ( sk1 @ ( sk2 @ sk3 ) )
!= int_zero ),
inference(simp,[status(thm)],[2497]) ).
thf(10702,plain,
! [A: $i] :
( ( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8960,37]) ).
thf(10703,plain,
! [A: $i] :
( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[10702]) ).
thf(10780,plain,
! [A: $i] :
( ( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ sk3 ) )
!= A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[10703]) ).
thf(10790,plain,
( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ sk3 ) )
!= int_zero ),
inference(simp,[status(thm)],[10780]) ).
thf(19,plain,
n @ ( sk2 @ int_leq ),
inference(cnfConj,[status(thm)],[16]) ).
thf(136,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)],[19,28]) ).
thf(137,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[136]) ).
thf(138,plain,
( ( n @ ( sk2 @ int_less ) )
| ( sk2 = n ) ),
inference(pattern_uni,[status(thm)],[137:[bind(A,$thf( sk2 )),bind(B,$thf( n ))]]) ).
thf(2461,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2363,29]) ).
thf(2462,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[2461]) ).
thf(2463,plain,
sk1 @ ( sk2 @ sk3 ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[2462:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 @ ( sk2 @ sk3 ) ))]]) ).
thf(8417,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)],[4410,29]) ).
thf(8418,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)],[8417]) ).
thf(8419,plain,
! [A: $i] : ( sk1 @ ( A @ plus ) @ ( A @ int_leq ) ),
inference(pattern_uni,[status(thm)],[8418:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( sk1 @ ( D @ plus ) ))]]) ).
thf(8482,plain,
! [A: $i] : ( sk1 @ ( A @ plus ) @ ( A @ int_leq ) ),
inference(simp,[status(thm)],[8419]) ).
thf(14669,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)],[8482,63]) ).
thf(14670,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( B @ ( int_one @ int_leq ) ) )
| ( B @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[14669]) ).
thf(14671,plain,
sk1 @ ( int_one @ plus ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[14670:[bind(A,$thf( int_one )),bind(B,$thf( sk1 @ ( int_one @ plus ) ))]]) ).
thf(14887,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14671,53]) ).
thf(14888,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[14887]) ).
thf(14889,plain,
int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[14888:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 @ ( int_one @ plus ) ))]]) ).
thf(61,plain,
! [A: $i] :
( ( A @ ( int_one @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) ) ),
inference(cnfConj,[status(thm)],[60]) ).
thf(15240,plain,
! [A: $i] :
( ( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14889,61]) ).
thf(15241,plain,
! [A: $i] :
( ( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[15240]) ).
thf(15242,plain,
int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[15241:[bind(A,$thf( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) ))]]) ).
thf(78,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18,37]) ).
thf(79,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[78]) ).
thf(80,plain,
! [A: $i] :
( ( sk2 != A )
| ( sk1 != A ) ),
inference(simp,[status(thm)],[79]) ).
thf(81,plain,
sk2 != sk1,
inference(simp,[status(thm)],[80]) ).
thf(104,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( B != sk1 )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,81]) ).
thf(105,plain,
! [A: $i] :
( ( A != sk1 )
| ( A @ ( sk2 @ int_less ) )
| ~ ( A @ ( sk2 @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[104:[bind(A,$thf( sk2 ))]]) ).
thf(161,plain,
( ( sk1 @ ( sk2 @ int_less ) )
| ~ ( sk1 @ ( sk2 @ int_leq ) ) ),
inference(simp,[status(thm)],[105]) ).
thf(1390,plain,
( ( ( sk1 @ ( sk2 @ int_leq ) )
!= ( n @ ( sk2 @ int_leq ) ) )
| ( sk1 @ ( sk2 @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,161]) ).
thf(1391,plain,
( ( ( sk1 @ ( sk2 @ int_leq ) )
!= ( n @ ( sk2 @ int_leq ) ) )
| ( sk1 @ ( sk2 @ int_less ) ) ),
inference(simp,[status(thm)],[1390]) ).
thf(1395,plain,
( ( sk1 != n )
| ( sk2 != sk2 )
| ( sk1 @ ( sk2 @ int_less ) ) ),
inference(simp,[status(thm)],[1391]) ).
thf(1406,plain,
( ( sk1 != n )
| ( sk1 @ ( sk2 @ int_less ) ) ),
inference(simp,[status(thm)],[1395]) ).
thf(101,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ~ $true
| ( A = B ) ),
inference(paramod_ordered,[status(thm)],[17,28]) ).
thf(102,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( B @ ( A @ int_leq ) ) )
| ( B @ ( A @ int_less ) )
| ( A = B ) ),
inference(simp,[status(thm)],[101]) ).
thf(103,plain,
( ( sk1 @ ( int_one @ int_less ) )
| ( sk1 = int_one ) ),
inference(pattern_uni,[status(thm)],[102:[bind(A,$thf( int_one )),bind(B,$thf( sk1 ))]]) ).
thf(755,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18,29]) ).
thf(756,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[755]) ).
thf(757,plain,
sk2 @ ( sk1 @ int_leq ),
inference(pattern_uni,[status(thm)],[756:[bind(A,$thf( sk1 )),bind(B,$thf( sk2 ))]]) ).
thf(793,plain,
( ( sk1 != sk1 )
| ( sk2 @ ( int_one @ int_leq ) )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[103,757]) ).
thf(794,plain,
( ( sk2 @ ( int_one @ int_leq ) )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[793:[]]) ).
thf(3612,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ( sk2 @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[794,37]) ).
thf(3613,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ( sk2 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[3612]) ).
thf(3647,plain,
! [A: $i] :
( ( sk1 != A )
| ( int_one != A )
| ( sk2 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[3613]) ).
thf(3656,plain,
( ( sk1 != int_one )
| ( sk2 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[3647]) ).
thf(4234,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true
| ( sk1 != int_one ) ),
inference(paramod_ordered,[status(thm)],[3656,63]) ).
thf(4235,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ( sk1 != int_one ) ),
inference(simp,[status(thm)],[4234]) ).
thf(4236,plain,
( ( sk2 @ ( int_zero @ int_less ) )
| ( sk1 != int_one ) ),
inference(pattern_uni,[status(thm)],[4235:[bind(A,$thf( sk2 ))]]) ).
thf(6439,plain,
( ( sk1 != sk1 )
| ( sk2 @ ( int_zero @ int_less ) )
| ( int_one != int_one )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[103,4236]) ).
thf(6440,plain,
( ( sk1 != sk1 )
| ( sk2 @ ( int_zero @ int_less ) )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(simp,[status(thm)],[6439]) ).
thf(6441,plain,
( ( sk2 @ ( int_zero @ int_less ) )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[6440:[]]) ).
thf(9,axiom,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_zero) ).
thf(44,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(45,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(cnf,[status(esa)],[44]) ).
thf(46,plain,
! [A: $i] :
( ( int_zero @ ( A @ plus ) )
= A ),
inference(lifteq,[status(thm)],[45]) ).
thf(184,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_zero @ ( C @ plus ) ) )
| ( ( A @ ( B @ plus ) )
= C ) ),
inference(paramod_ordered,[status(thm)],[43,46]) ).
thf(185,plain,
! [A: $i] :
( ( A @ ( int_zero @ plus ) )
= A ),
inference(pattern_uni,[status(thm)],[184:[bind(A,$thf( A )),bind(B,$thf( int_zero )),bind(C,$thf( A ))]]) ).
thf(1384,plain,
( ( ( sk1 @ ( sk2 @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( sk1 @ ( sk2 @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17,161]) ).
thf(1385,plain,
( ( ( sk1 @ ( sk2 @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( sk1 @ ( sk2 @ int_less ) ) ),
inference(simp,[status(thm)],[1384]) ).
thf(1397,plain,
( ( sk1 != sk1 )
| ( sk2 != int_one )
| ( sk1 @ ( sk2 @ int_less ) ) ),
inference(simp,[status(thm)],[1385]) ).
thf(1409,plain,
( ( sk2 != int_one )
| ( sk1 @ ( sk2 @ int_less ) ) ),
inference(simp,[status(thm)],[1397]) ).
thf(2306,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,53]) ).
thf(2307,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[2306]) ).
thf(2308,plain,
int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[2307:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(2384,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2308,53]) ).
thf(2385,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[2384]) ).
thf(2386,plain,
int_zero @ ( int_zero @ ( int_one @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[2385:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_one @ sk3 ) ))]]) ).
thf(2896,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ~ $true
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[40,55]) ).
thf(2897,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(simp,[status(thm)],[2896]) ).
thf(2898,plain,
( ( int_zero @ ( int_one @ sk3 ) @ ( int_zero @ plus ) )
= int_one ),
inference(pattern_uni,[status(thm)],[2897:[bind(A,$thf( int_zero )),bind(B,$thf( int_one ))]]) ).
thf(3139,plain,
( ( int_zero @ ( int_one @ sk3 ) )
= int_one ),
inference(rewrite,[status(thm)],[2898,185]) ).
thf(3495,plain,
int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ),
inference(rewrite,[status(thm)],[2386,3139]) ).
thf(3436,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)],[40,57]) ).
thf(3437,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)],[3436]) ).
thf(3438,plain,
! [A: $i] : ( int_one @ ( A @ plus ) @ ( A @ int_less ) ),
inference(pattern_uni,[status(thm)],[3437:[bind(A,$thf( A )),bind(B,$thf( int_one ))]]) ).
thf(7293,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)],[43,3438]) ).
thf(7294,plain,
! [A: $i] : ( A @ ( int_one @ plus ) @ ( A @ int_less ) ),
inference(pattern_uni,[status(thm)],[7293:[bind(A,$thf( A )),bind(B,$thf( int_one )),bind(C,$thf( A ))]]) ).
thf(124,plain,
! [B: $i,A: $i] :
( ( B != int_zero )
| ( int_one @ ( A @ int_less ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,40]) ).
thf(125,plain,
! [A: $i] :
( ( int_one @ ( A @ int_less ) )
| ( int_zero @ ( A @ int_less ) )
| ~ ( int_zero @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[124:[bind(A,$thf( A )),bind(B,$thf( int_zero ))]]) ).
thf(7259,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)],[3438,29]) ).
thf(7260,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)],[7259]) ).
thf(7261,plain,
! [A: $i] : ( int_one @ ( A @ plus ) @ ( A @ int_leq ) ),
inference(pattern_uni,[status(thm)],[7260:[bind(A,$thf( D )),bind(B,$thf( D )),bind(C,$thf( int_one @ ( D @ plus ) ))]]) ).
thf(7319,plain,
! [A: $i] : ( int_one @ ( A @ plus ) @ ( A @ int_leq ) ),
inference(simp,[status(thm)],[7261]) ).
thf(11836,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)],[7319,63]) ).
thf(11837,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( B @ ( int_one @ int_leq ) ) )
| ( B @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[11836]) ).
thf(11838,plain,
int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[11837:[bind(A,$thf( int_one )),bind(B,$thf( int_one @ ( int_one @ plus ) ))]]) ).
thf(12048,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[11838,53]) ).
thf(12049,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[12048]) ).
thf(12050,plain,
int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[12049:[bind(A,$thf( int_zero )),bind(B,$thf( int_one @ ( int_one @ plus ) ))]]) ).
thf(12553,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12050,53]) ).
thf(12554,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[12553]) ).
thf(12555,plain,
int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[12554:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) ))]]) ).
thf(13273,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12555,29]) ).
thf(13274,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[13273]) ).
thf(13275,plain,
int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[13274:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ sk3 ) ))]]) ).
thf(14676,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8482,4246]) ).
thf(14677,plain,
! [A: $i] :
( ( sk1 @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[14676]) ).
thf(14734,plain,
! [A: $i] :
( ( ( sk1 @ ( A @ plus ) )
!= int_zero )
| ( A != int_one ) ),
inference(simp,[status(thm)],[14677]) ).
thf(14773,plain,
( ( sk1 @ ( int_one @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[14734]) ).
thf(130,plain,
! [B: $i,A: $i] :
( ( A != n )
| ( B @ ( sk2 @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,19]) ).
thf(131,plain,
! [A: $i] :
( ( A @ ( sk2 @ int_leq ) )
| ( A @ ( n @ int_less ) )
| ~ ( A @ ( n @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[130:[bind(A,$thf( n ))]]) ).
thf(152,plain,
! [A: $i] :
( ( A @ ( sk2 @ int_leq ) )
| ( A @ ( n @ int_less ) )
| ~ ( A @ ( n @ int_leq ) ) ),
inference(simp,[status(thm)],[131]) ).
thf(14857,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)],[14671,29]) ).
thf(14858,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[14857]) ).
thf(14859,plain,
sk1 @ ( int_one @ plus ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[14858:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 @ ( int_one @ plus ) ))]]) ).
thf(2451,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2363,53]) ).
thf(2452,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[2451]) ).
thf(2453,plain,
int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[2452:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 @ ( sk2 @ sk3 ) ))]]) ).
thf(4027,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2453,53]) ).
thf(4028,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[4027]) ).
thf(4029,plain,
int_zero @ ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[4028:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) ))]]) ).
thf(6597,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4029,61]) ).
thf(6598,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[6597]) ).
thf(6599,plain,
int_zero @ ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ sk3 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[6598:[bind(A,$thf( int_zero @ ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ sk3 ) ))]]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( ( n @ ( B @ int_leq ) )
& ( B @ ( int_one @ int_leq ) )
& ( n @ ( A @ int_leq ) )
& ( A @ ( int_one @ int_leq ) ) )
=> ( ! [C: $i] :
( ( ( B
= ( C @ ( A @ plus ) ) )
& ( C @ ( int_zero @ int_less ) ) )
=> ! [D: $i] :
( ( ( A @ ( D @ int_leq ) )
& ( D @ ( int_one @ int_leq ) ) )
=> ( ( C @ ( D @ plus ) @ ( D @ a ) )
= real_zero ) ) )
& ! [C: $i] :
( ( ( B @ ( C @ int_leq ) )
& ( C @ ( int_one @ int_leq ) ) )
=> ( ( C @ ( C @ a ) )
= real_one ) )
& ! [C: $i] :
( ( ( A
= ( C @ ( B @ plus ) ) )
& ( C @ ( int_zero @ int_less ) ) )
=> ! [D: $i] :
( ( ( B @ ( D @ int_leq ) )
& ( D @ ( int_one @ int_leq ) ) )
=> ( ( D @ ( C @ ( D @ plus ) @ a ) )
= real_zero ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',qii) ).
thf(67,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(68,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)],[67]) ).
thf(69,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)],[68]) ).
thf(72,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)],[69]) ).
thf(73,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)],[72]) ).
thf(347,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ plus ) @ a ) )
!= ( sk2 @ ( sk1 @ a ) ) )
| ( real_zero != real_zero )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[73,21]) ).
thf(348,plain,
! [C: $i,B: $i,A: $i] :
( ( ( C @ ( B @ ( C @ plus ) @ a ) )
!= ( sk2 @ ( sk1 @ a ) ) )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[347]) ).
thf(363,plain,
! [C: $i,B: $i,A: $i] :
( ( C != sk2 )
| ( ( B @ ( C @ plus ) )
!= sk1 )
| ~ ( A @ ( C @ int_leq ) )
| ~ ( C @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[348]) ).
thf(422,plain,
! [B: $i,A: $i] :
( ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( A @ ( sk2 @ int_leq ) )
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( n @ ( A @ int_leq ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[363]) ).
thf(550,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_leq ) )
!= ( n @ ( A @ int_leq ) ) )
| ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( A @ ( sk2 @ int_leq ) )
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ $true
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[19,422]) ).
thf(551,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk2 @ int_leq ) )
!= ( n @ ( A @ int_leq ) ) )
| ( ( B @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( A @ ( sk2 @ int_leq ) )
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ ( B @ ( int_zero @ int_less ) )
| ~ ( A @ ( int_one @ int_leq ) )
| ~ ( n @ ( B @ ( A @ plus ) @ int_leq ) )
| ~ ( B @ ( A @ plus ) @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[550]) ).
thf(552,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( sk2 @ ( sk2 @ int_leq ) )
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) )
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ ( sk2 @ plus ) @ int_leq ) )
| ~ ( A @ ( sk2 @ plus ) @ ( int_one @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[551:[bind(A,$thf( sk2 ))]]) ).
thf(604,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( sk2 @ ( sk2 @ int_leq ) )
| ~ ( A @ ( int_zero @ int_less ) )
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ ( sk2 @ plus ) @ int_leq ) )
| ~ ( A @ ( sk2 @ plus ) @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[552]) ).
thf(27,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ( A != B ) ),
inference(cnfConj,[status(thm)],[24]) ).
thf(30,plain,
! [B: $i,A: $i] :
( ( B @ ( A @ int_leq ) )
| ( A != B ) ),
inference(lifteq,[status(thm)],[27]) ).
thf(31,plain,
! [A: $i] : ( A @ ( A @ int_leq ) ),
inference(simp,[status(thm)],[30]) ).
thf(905,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ plus ) )
!= sk1 )
| ~ $true
| ~ ( A @ ( int_zero @ int_less ) )
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ ( sk2 @ plus ) @ int_leq ) )
| ~ ( A @ ( sk2 @ plus ) @ ( int_one @ int_leq ) ) ),
inference(rewrite,[status(thm)],[604,31]) ).
thf(906,plain,
! [A: $i] :
( ( ( A @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( A @ ( int_zero @ int_less ) )
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ ( sk2 @ plus ) @ int_leq ) )
| ~ ( A @ ( sk2 @ plus ) @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[905]) ).
thf(923,plain,
! [A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( ( A @ ( sk2 @ plus ) )
!= sk1 )
| ~ $true
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ ( sk2 @ plus ) @ int_leq ) )
| ~ ( A @ ( sk2 @ plus ) @ ( int_one @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[40,906]) ).
thf(924,plain,
! [A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( ( A @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ ( n @ ( A @ ( sk2 @ plus ) @ int_leq ) )
| ~ ( A @ ( sk2 @ plus ) @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[923]) ).
thf(925,plain,
( ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ ( n @ ( int_one @ ( sk2 @ plus ) @ int_leq ) )
| ~ ( int_one @ ( sk2 @ plus ) @ ( int_one @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[924:[bind(A,$thf( int_one ))]]) ).
thf(1263,plain,
( ( ( int_one @ ( sk2 @ plus ) @ ( int_one @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ ( n @ ( int_one @ ( sk2 @ plus ) @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17,925]) ).
thf(1264,plain,
( ( ( int_one @ ( sk2 @ plus ) @ ( int_one @ int_leq ) )
!= ( sk1 @ ( int_one @ int_leq ) ) )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ ( n @ ( int_one @ ( sk2 @ plus ) @ int_leq ) ) ),
inference(simp,[status(thm)],[1263]) ).
thf(1300,plain,
( ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ( int_one != int_one )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ ( n @ ( int_one @ ( sk2 @ plus ) @ int_leq ) ) ),
inference(simp,[status(thm)],[1264]) ).
thf(1320,plain,
( ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ ( n @ ( int_one @ ( sk2 @ plus ) @ int_leq ) ) ),
inference(simp,[status(thm)],[1300]) ).
thf(1538,plain,
( ( ( n @ ( int_one @ ( sk2 @ plus ) @ int_leq ) )
!= ( sk2 @ ( sk1 @ int_leq ) ) )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( sk2 @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[757,1320]) ).
thf(1539,plain,
( ( ( n @ ( int_one @ ( sk2 @ plus ) @ int_leq ) )
!= ( sk2 @ ( sk1 @ int_leq ) ) )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( sk2 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1538]) ).
thf(1623,plain,
( ( sk2 != n )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( sk2 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1539]) ).
thf(1635,plain,
( ( sk2 != n )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ ( sk2 @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[1623]) ).
thf(2152,plain,
( ( ( sk2 @ ( sk1 @ int_leq ) )
!= ( sk2 @ ( int_one @ int_leq ) ) )
| ( sk2 != n )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[757,1635]) ).
thf(2153,plain,
( ( ( sk2 @ ( sk1 @ int_leq ) )
!= ( sk2 @ ( int_one @ int_leq ) ) )
| ( sk2 != n )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 ) ),
inference(simp,[status(thm)],[2152]) ).
thf(2173,plain,
( ( sk2 != sk2 )
| ( sk1 != int_one )
| ( sk2 != n )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 ) ),
inference(simp,[status(thm)],[2153]) ).
thf(2190,plain,
( ( sk1 != int_one )
| ( sk2 != n )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 ) ),
inference(simp,[status(thm)],[2173]) ).
thf(132,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( n @ ( A @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,19]) ).
thf(133,plain,
! [A: $i] :
( ( n @ ( A @ int_leq ) )
| ( sk2 @ ( A @ int_less ) )
| ~ ( sk2 @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[132:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(4411,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4290,29]) ).
thf(4412,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[4411]) ).
thf(4413,plain,
sk1 @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[4412:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 ))]]) ).
thf(4485,plain,
( ( ( sk1 @ ( sk2 @ int_leq ) )
!= ( sk1 @ ( int_zero @ int_leq ) ) )
| ( sk1 @ ( sk2 @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4413,161]) ).
thf(4486,plain,
( ( ( sk1 @ ( sk2 @ int_leq ) )
!= ( sk1 @ ( int_zero @ int_leq ) ) )
| ( sk1 @ ( sk2 @ int_less ) ) ),
inference(simp,[status(thm)],[4485]) ).
thf(4516,plain,
( ( sk1 != sk1 )
| ( sk2 != int_zero )
| ( sk1 @ ( sk2 @ int_less ) ) ),
inference(simp,[status(thm)],[4486]) ).
thf(4536,plain,
( ( sk2 != int_zero )
| ( sk1 @ ( sk2 @ int_less ) ) ),
inference(simp,[status(thm)],[4516]) ).
thf(4359,plain,
( ( ( sk1 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17,4246]) ).
thf(4360,plain,
( ( sk1 @ ( int_one @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[4359]) ).
thf(4383,plain,
( ( sk1 != int_zero )
| ( int_one != int_one ) ),
inference(simp,[status(thm)],[4360]) ).
thf(4394,plain,
sk1 != int_zero,
inference(simp,[status(thm)],[4383]) ).
thf(4395,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B != int_zero )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,4394]) ).
thf(4396,plain,
! [A: $i] :
( ( A != int_zero )
| ( A @ ( sk1 @ int_less ) )
| ~ ( A @ ( sk1 @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[4395:[bind(A,$thf( sk1 ))]]) ).
thf(4401,plain,
( ( int_zero @ ( sk1 @ int_less ) )
| ~ ( int_zero @ ( sk1 @ int_leq ) ) ),
inference(simp,[status(thm)],[4396]) ).
thf(14229,plain,
( ( ( sk2 @ ( sk1 @ int_leq ) )
!= ( int_zero @ ( sk1 @ int_leq ) ) )
| ( int_zero @ ( sk1 @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[757,4401]) ).
thf(14230,plain,
( ( ( sk2 @ ( sk1 @ int_leq ) )
!= ( int_zero @ ( sk1 @ int_leq ) ) )
| ( int_zero @ ( sk1 @ int_less ) ) ),
inference(simp,[status(thm)],[14229]) ).
thf(14313,plain,
( ( sk2 != int_zero )
| ( sk1 != sk1 )
| ( int_zero @ ( sk1 @ int_less ) ) ),
inference(simp,[status(thm)],[14230]) ).
thf(14360,plain,
( ( sk2 != int_zero )
| ( int_zero @ ( sk1 @ int_less ) ) ),
inference(simp,[status(thm)],[14313]) ).
thf(15163,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ( sk2 != int_zero ) ),
inference(paramod_ordered,[status(thm)],[14360,29]) ).
thf(15164,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ( sk2 != int_zero ) ),
inference(simp,[status(thm)],[15163]) ).
thf(15165,plain,
( ( int_zero @ ( sk1 @ int_leq ) )
| ( sk2 != int_zero ) ),
inference(pattern_uni,[status(thm)],[15164:[bind(A,$thf( sk1 )),bind(B,$thf( int_zero ))]]) ).
thf(4442,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ~ $true
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(paramod_ordered,[status(thm)],[4290,55]) ).
thf(4443,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( ( A @ ( B @ sk3 ) @ ( A @ plus ) )
= B ) ),
inference(simp,[status(thm)],[4442]) ).
thf(4444,plain,
( ( int_zero @ ( sk1 @ sk3 ) @ ( int_zero @ plus ) )
= sk1 ),
inference(pattern_uni,[status(thm)],[4443:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 ))]]) ).
thf(5328,plain,
( ( int_zero @ ( sk1 @ sk3 ) )
= sk1 ),
inference(rewrite,[status(thm)],[4444,185]) ).
thf(8412,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ plus ) @ ( A @ int_less ) )
!= ( B @ ( B @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4410,37]) ).
thf(8413,plain,
! [B: $i,A: $i] :
( ( sk1 @ ( A @ plus ) @ ( A @ int_less ) )
!= ( B @ ( B @ int_less ) ) ),
inference(simp,[status(thm)],[8412]) ).
thf(8468,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( A @ plus ) )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[8413]) ).
thf(8477,plain,
! [A: $i] :
( ( sk1 @ ( A @ plus ) )
!= A ),
inference(simp,[status(thm)],[8468]) ).
thf(9588,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( sk1 @ ( C @ plus ) ) )
| ( ( A @ ( B @ plus ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[43,8477]) ).
thf(9589,plain,
! [A: $i] :
( ( A @ ( sk1 @ plus ) )
!= A ),
inference(pattern_uni,[status(thm)],[9588:[bind(A,$thf( A )),bind(B,$thf( sk1 )),bind(C,$thf( A ))]]) ).
thf(116,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( sk2 @ ( A @ int_less ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,18]) ).
thf(117,plain,
! [A: $i] :
( ( sk2 @ ( A @ int_less ) )
| ( sk1 @ ( A @ int_less ) )
| ~ ( sk1 @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[116:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(82,plain,
! [A: $i] :
( ( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40,37]) ).
thf(83,plain,
! [A: $i] :
( ( int_one @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[82]) ).
thf(84,plain,
! [A: $i] :
( ( int_one != A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[83]) ).
thf(85,plain,
int_zero != int_one,
inference(simp,[status(thm)],[84]) ).
thf(680,plain,
( ( sk2 != sk2 )
| ( n @ ( sk1 @ int_less ) )
| ( n @ ( sk2 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[138,18]) ).
thf(681,plain,
( ( n @ ( sk1 @ int_less ) )
| ( n @ ( sk2 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[680:[]]) ).
thf(2197,plain,
! [A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ( n @ ( sk1 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[681,37]) ).
thf(2198,plain,
! [A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ( n @ ( sk1 @ int_less ) ) ),
inference(simp,[status(thm)],[2197]) ).
thf(2226,plain,
! [A: $i] :
( ( n != A )
| ( sk2 != A )
| ( n @ ( sk1 @ int_less ) ) ),
inference(simp,[status(thm)],[2198]) ).
thf(2234,plain,
( ( sk2 != n )
| ( n @ ( sk1 @ int_less ) ) ),
inference(simp,[status(thm)],[2226]) ).
thf(2247,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ( sk2 != n ) ),
inference(paramod_ordered,[status(thm)],[2234,29]) ).
thf(2248,plain,
! [B: $i,A: $i] :
( ( ( n @ ( sk1 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ( sk2 != n ) ),
inference(simp,[status(thm)],[2247]) ).
thf(2249,plain,
( ( n @ ( sk1 @ int_leq ) )
| ( sk2 != n ) ),
inference(pattern_uni,[status(thm)],[2248:[bind(A,$thf( sk1 )),bind(B,$thf( n ))]]) ).
thf(95,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( B @ ( int_one @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,17]) ).
thf(96,plain,
! [A: $i] :
( ( A @ ( int_one @ int_leq ) )
| ( A @ ( sk1 @ int_less ) )
| ~ ( A @ ( sk1 @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[95:[bind(A,$thf( sk1 ))]]) ).
thf(160,plain,
! [A: $i] :
( ( A @ ( int_one @ int_leq ) )
| ( A @ ( sk1 @ int_less ) )
| ~ ( A @ ( sk1 @ int_leq ) ) ),
inference(simp,[status(thm)],[96]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( C @ ( B @ int_less ) )
& ( B @ ( A @ int_less ) ) )
=> ( C @ ( A @ int_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_transitive) ).
thf(32,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(33,plain,
! [C: $i,B: $i,A: $i] :
( ( C @ ( A @ int_less ) )
| ~ ( C @ ( B @ int_less ) )
| ~ ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[32]) ).
thf(6,axiom,
! [A: $i,B: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',int_less_total) ).
thf(38,plain,
! [A: $i,B: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15275,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14889,53]) ).
thf(15276,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[15275]) ).
thf(15277,plain,
int_zero @ ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[15276:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) ))]]) ).
thf(16070,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15277,61]) ).
thf(16071,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[16070]) ).
thf(16072,plain,
int_zero @ ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[16071:[bind(A,$thf( int_zero @ ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ sk3 ) ))]]) ).
thf(643,plain,
( ( sk1 != sk1 )
| ( sk2 @ ( int_one @ int_less ) )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[103,18]) ).
thf(644,plain,
( ( sk2 @ ( int_one @ int_less ) )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[643:[]]) ).
thf(1653,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[644,37]) ).
thf(1654,plain,
! [A: $i] :
( ( ( sk2 @ ( int_one @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(simp,[status(thm)],[1653]) ).
thf(1681,plain,
! [A: $i] :
( ( sk2 != A )
| ( int_one != A )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(simp,[status(thm)],[1654]) ).
thf(1687,plain,
( ( sk2 != int_one )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(simp,[status(thm)],[1681]) ).
thf(4032,plain,
! [A: $i] :
( ( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2453,37]) ).
thf(4033,plain,
! [A: $i] :
( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[4032]) ).
thf(4092,plain,
! [A: $i] :
( ( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) )
!= A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[4033]) ).
thf(4104,plain,
( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) )
!= int_zero ),
inference(simp,[status(thm)],[4092]) ).
thf(12018,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)],[11838,29]) ).
thf(12019,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( int_one @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[12018]) ).
thf(12020,plain,
int_one @ ( int_one @ plus ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[12019:[bind(A,$thf( int_zero )),bind(B,$thf( int_one @ ( int_one @ plus ) ))]]) ).
thf(8501,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ sk3 ) @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8439,29]) ).
thf(8502,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ sk3 ) @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[8501]) ).
thf(8503,plain,
sk2 @ ( sk1 @ ( sk2 @ sk3 ) @ int_leq ),
inference(pattern_uni,[status(thm)],[8502:[bind(A,$thf( sk1 @ ( sk2 @ sk3 ) )),bind(B,$thf( sk2 ))]]) ).
thf(7254,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( B @ ( B @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3438,37]) ).
thf(7255,plain,
! [B: $i,A: $i] :
( ( int_one @ ( A @ plus ) @ ( A @ int_less ) )
!= ( B @ ( B @ int_less ) ) ),
inference(simp,[status(thm)],[7254]) ).
thf(7307,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( A @ plus ) )
!= B )
| ( A != B ) ),
inference(simp,[status(thm)],[7255]) ).
thf(7315,plain,
! [A: $i] :
( ( int_one @ ( A @ plus ) )
!= A ),
inference(simp,[status(thm)],[7307]) ).
thf(7539,plain,
! [C: $i,B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_one @ ( C @ plus ) ) )
| ( ( A @ ( B @ plus ) )
!= C ) ),
inference(paramod_ordered,[status(thm)],[43,7315]) ).
thf(7540,plain,
! [A: $i] :
( ( A @ ( int_one @ plus ) )
!= A ),
inference(pattern_uni,[status(thm)],[7539:[bind(A,$thf( A )),bind(B,$thf( int_one )),bind(C,$thf( A ))]]) ).
thf(145,plain,
! [B: $i,A: $i] :
( ( B
!= ( sk2 @ ( sk1 @ a ) ) )
| ( A != real_zero )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,21]) ).
thf(146,plain,
! [A: $i] :
( ( A != real_zero )
| ( sk2 @ ( sk1 @ a ) @ ( A @ int_less ) )
| ~ ( sk2 @ ( sk1 @ a ) @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[145:[bind(A,$thf( A )),bind(B,$thf( sk2 @ ( sk1 @ a ) ))]]) ).
thf(156,plain,
( ( sk2 @ ( sk1 @ a ) @ ( real_zero @ int_less ) )
| ~ ( sk2 @ ( sk1 @ a ) @ ( real_zero @ int_leq ) ) ),
inference(simp,[status(thm)],[146]) ).
thf(9572,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( sk1 @ plus ) )
!= ( sk1 @ ( A @ plus ) ) )
| ( sk2 != A ) ),
inference(paramod_ordered,[status(thm)],[2889,8477]) ).
thf(9593,plain,
( ( sk1 @ ( sk2 @ sk3 ) @ ( sk1 @ plus ) )
!= ( sk1 @ ( sk2 @ plus ) ) ),
inference(simp,[status(thm)],[9572]) ).
thf(9608,plain,
( ( sk1 @ ( sk2 @ plus ) )
!= sk2 ),
inference(rewrite,[status(thm)],[9593,2889]) ).
thf(15236,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14889,29]) ).
thf(15237,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[15236]) ).
thf(15238,plain,
int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[15237:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) ))]]) ).
thf(8497,plain,
! [A: $i] :
( ( ( sk2 @ ( sk1 @ ( sk2 @ sk3 ) @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8439,37]) ).
thf(8498,plain,
! [A: $i] :
( ( sk2 @ ( sk1 @ ( sk2 @ sk3 ) @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[8497]) ).
thf(8555,plain,
! [A: $i] :
( ( sk2 != A )
| ( ( sk1 @ ( sk2 @ sk3 ) )
!= A ) ),
inference(simp,[status(thm)],[8498]) ).
thf(8567,plain,
( ( sk1 @ ( sk2 @ sk3 ) )
!= sk2 ),
inference(simp,[status(thm)],[8555]) ).
thf(16066,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15277,29]) ).
thf(16067,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[16066]) ).
thf(16068,plain,
int_zero @ ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[16067:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ sk3 ) ))]]) ).
thf(71,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)],[68]) ).
thf(76,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)],[71]) ).
thf(77,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)],[76]) ).
thf(1422,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ( sk1 != n ) ),
inference(paramod_ordered,[status(thm)],[1406,29]) ).
thf(1423,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ( sk1 != n ) ),
inference(simp,[status(thm)],[1422]) ).
thf(1424,plain,
( ( sk1 @ ( sk2 @ int_leq ) )
| ( sk1 != n ) ),
inference(pattern_uni,[status(thm)],[1423:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(678,plain,
( ( sk2 != sk2 )
| ( sk1 != n )
| ( n @ ( sk2 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[138,81]) ).
thf(679,plain,
( ( sk1 != n )
| ( n @ ( sk2 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[678:[]]) ).
thf(7666,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ( sk2 != int_zero ) ),
inference(paramod_ordered,[status(thm)],[4536,29]) ).
thf(7667,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ( sk2 != int_zero ) ),
inference(simp,[status(thm)],[7666]) ).
thf(7668,plain,
( ( sk1 @ ( sk2 @ int_leq ) )
| ( sk2 != int_zero ) ),
inference(pattern_uni,[status(thm)],[7667:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(8915,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8531,37]) ).
thf(8916,plain,
! [A: $i] :
( ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[8915]) ).
thf(8983,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) )
!= A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[8916]) ).
thf(8989,plain,
( ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) )
!= int_zero ),
inference(simp,[status(thm)],[8983]) ).
thf(2164,plain,
( ( ( n @ ( sk2 @ int_leq ) )
!= ( sk2 @ ( int_one @ int_leq ) ) )
| ( sk2 != n )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,1635]) ).
thf(2165,plain,
( ( ( n @ ( sk2 @ int_leq ) )
!= ( sk2 @ ( int_one @ int_leq ) ) )
| ( sk2 != n )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 ) ),
inference(simp,[status(thm)],[2164]) ).
thf(2171,plain,
( ( sk2 != n )
| ( sk2 != int_one )
| ( sk2 != n )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 ) ),
inference(simp,[status(thm)],[2165]) ).
thf(2189,plain,
( ( sk2 != int_one )
| ( sk2 != n )
| ( ( int_one @ ( sk2 @ plus ) )
!= sk1 ) ),
inference(simp,[status(thm)],[2171]) ).
thf(4353,plain,
( ( ( sk2 @ ( sk1 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[757,4246]) ).
thf(4354,plain,
( ( sk2 @ ( sk1 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[4353]) ).
thf(4381,plain,
( ( sk2 != int_zero )
| ( sk1 != int_one ) ),
inference(simp,[status(thm)],[4354]) ).
thf(4570,plain,
( ( sk1 != sk1 )
| ( sk2 != int_zero )
| ( int_one != int_one )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[103,4381]) ).
thf(4571,plain,
( ( sk1 != sk1 )
| ( sk2 != int_zero )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(simp,[status(thm)],[4570]) ).
thf(4572,plain,
( ( sk2 != int_zero )
| ( sk1 @ ( int_one @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[4571:[]]) ).
thf(4367,plain,
( ( ( n @ ( sk2 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,4246]) ).
thf(4368,plain,
( ( n @ ( sk2 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[4367]) ).
thf(4380,plain,
( ( int_zero != n )
| ( sk2 != int_one ) ),
inference(simp,[status(thm)],[4368]) ).
thf(2555,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_one @ ( sk2 @ plus ) ) )
| ( sk2 != int_one )
| ( sk2 != n )
| ( ( A @ ( B @ plus ) )
!= sk1 ) ),
inference(paramod_ordered,[status(thm)],[43,2189]) ).
thf(2556,plain,
( ( sk2 != int_one )
| ( sk2 != n )
| ( ( sk2 @ ( int_one @ plus ) )
!= sk1 ) ),
inference(pattern_uni,[status(thm)],[2555:[bind(A,$thf( sk2 )),bind(B,$thf( int_one ))]]) ).
thf(147,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( ( sk2 @ ( A @ a ) )
!= real_zero )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,21]) ).
thf(148,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ a ) )
!= real_zero )
| ( sk1 @ ( A @ int_less ) )
| ~ ( sk1 @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[147:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(13,axiom,
real_zero != real_one,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',real_constants) ).
thf(64,plain,
real_zero != real_one,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(10707,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8960,29]) ).
thf(10708,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[10707]) ).
thf(10709,plain,
int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[10708:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ sk3 ) ))]]) ).
thf(4305,plain,
! [A: $i] :
( ( ( n @ ( sk2 @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19,63]) ).
thf(4306,plain,
! [A: $i] :
( ( ( n @ ( sk2 @ int_leq ) )
!= ( A @ ( int_one @ int_leq ) ) )
| ( A @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[4305]) ).
thf(4319,plain,
! [A: $i] :
( ( n != A )
| ( sk2 != int_one )
| ( A @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[4306]) ).
thf(4328,plain,
( ( sk2 != int_one )
| ( n @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[4319]) ).
thf(7345,plain,
! [A: $i] :
( ( ( n @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true
| ( sk2 != int_one ) ),
inference(paramod_ordered,[status(thm)],[4328,61]) ).
thf(7346,plain,
! [A: $i] :
( ( ( n @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ( sk2 != int_one ) ),
inference(simp,[status(thm)],[7345]) ).
thf(7347,plain,
( ( n @ ( int_one @ int_leq ) )
| ( sk2 != int_one ) ),
inference(pattern_uni,[status(thm)],[7346:[bind(A,$thf( n ))]]) ).
thf(93,plain,
! [B: $i,A: $i] :
( ( A != int_one )
| ( sk1 @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,17]) ).
thf(94,plain,
! [A: $i] :
( ( sk1 @ ( A @ int_leq ) )
| ( A @ ( int_one @ int_less ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[93:[bind(A,$thf( int_one ))]]) ).
thf(159,plain,
! [A: $i] :
( ( sk1 @ ( A @ int_leq ) )
| ( A @ ( int_one @ int_less ) )
| ~ ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[94]) ).
thf(39,plain,
! [B: $i,A: $i] :
( ( A @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) ) ),
inference(cnf,[status(esa)],[38]) ).
thf(97,plain,
! [B: $i,A: $i] :
( ( B != int_one )
| ( sk1 @ ( A @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,17]) ).
thf(98,plain,
! [A: $i] :
( ( sk1 @ ( A @ int_leq ) )
| ( int_one @ ( A @ int_less ) )
| ~ ( int_one @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[97:[bind(A,$thf( A )),bind(B,$thf( int_one ))]]) ).
thf(7526,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( sk1 @ plus ) )
!= ( int_one @ ( A @ plus ) ) )
| ( sk2 != A ) ),
inference(paramod_ordered,[status(thm)],[2889,7315]) ).
thf(7546,plain,
( ( sk1 @ ( sk2 @ sk3 ) @ ( sk1 @ plus ) )
!= ( int_one @ ( sk2 @ plus ) ) ),
inference(simp,[status(thm)],[7526]) ).
thf(7561,plain,
( ( int_one @ ( sk2 @ plus ) )
!= sk2 ),
inference(rewrite,[status(thm)],[7546,2889]) ).
thf(7566,plain,
! [A: $i] :
( ( ( A @ ( int_zero @ plus ) )
!= ( int_one @ ( sk2 @ plus ) ) )
| ( A != sk2 ) ),
inference(paramod_ordered,[status(thm)],[185,7561]) ).
thf(7594,plain,
( ( sk2 != int_one )
| ( sk2 != int_zero ) ),
inference(simp,[status(thm)],[7566]) ).
thf(65,plain,
real_zero != real_one,
inference(polarity_switch,[status(thm)],[64]) ).
thf(66,plain,
real_one != real_zero,
inference(lifteq,[status(thm)],[65]) ).
thf(143,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( ( B @ ( sk1 @ a ) )
!= real_zero )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,21]) ).
thf(144,plain,
! [A: $i] :
( ( ( A @ ( sk1 @ a ) )
!= real_zero )
| ( A @ ( sk2 @ int_less ) )
| ~ ( A @ ( sk2 @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[143:[bind(A,$thf( sk2 ))]]) ).
thf(155,plain,
! [A: $i] :
( ( ( A @ ( sk1 @ a ) )
!= real_zero )
| ( A @ ( sk2 @ int_less ) )
| ~ ( A @ ( sk2 @ int_leq ) ) ),
inference(simp,[status(thm)],[144]) ).
thf(767,plain,
( ( sk2 != sk2 )
| ( n @ ( sk1 @ int_leq ) )
| ( n @ ( sk2 @ int_less ) ) ),
inference(paramod_ordered,[status(thm)],[138,757]) ).
thf(768,plain,
( ( n @ ( sk1 @ int_leq ) )
| ( n @ ( sk2 @ int_less ) ) ),
inference(pattern_uni,[status(thm)],[767:[]]) ).
thf(4343,plain,
( ( ( n @ ( sk1 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true
| ( sk2 != n ) ),
inference(paramod_ordered,[status(thm)],[2249,4246]) ).
thf(4344,plain,
( ( ( n @ ( sk1 @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ( sk2 != n ) ),
inference(simp,[status(thm)],[4343]) ).
thf(4373,plain,
( ( int_zero != n )
| ( sk1 != int_one )
| ( sk2 != n ) ),
inference(simp,[status(thm)],[4344]) ).
thf(134,plain,
! [B: $i,A: $i] :
( ( B != n )
| ( A @ ( sk2 @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,19]) ).
thf(135,plain,
! [A: $i] :
( ( A @ ( sk2 @ int_leq ) )
| ( n @ ( A @ int_less ) )
| ~ ( n @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[134:[bind(A,$thf( A )),bind(B,$thf( n ))]]) ).
thf(8920,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8531,29]) ).
thf(8921,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[8920]) ).
thf(8922,plain,
sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[8921:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) ))]]) ).
thf(6589,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4029,37]) ).
thf(6590,plain,
! [A: $i] :
( ( int_zero @ ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[6589]) ).
thf(6667,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ sk3 ) )
!= A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[6590]) ).
thf(6672,plain,
( ( int_zero @ ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ sk3 ) )
!= int_zero ),
inference(simp,[status(thm)],[6667]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( D @ ( C @ int_leq ) )
& ( B @ ( A @ int_less ) ) )
=> ( D @ ( B @ plus ) @ ( C @ ( A @ plus ) @ int_leq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',plus_and_order1) ).
thf(47,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(48,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)],[47]) ).
thf(149,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( ( A @ ( sk1 @ a ) )
!= real_zero )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,21]) ).
thf(150,plain,
! [A: $i] :
( ( ( A @ ( sk1 @ a ) )
!= real_zero )
| ( sk2 @ ( A @ int_less ) )
| ~ ( sk2 @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[149:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(13268,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12555,37]) ).
thf(13269,plain,
! [A: $i] :
( ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[13268]) ).
thf(13351,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ sk3 ) )
!= A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[13269]) ).
thf(13367,plain,
( ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ sk3 ) )
!= int_zero ),
inference(simp,[status(thm)],[13351]) ).
thf(6594,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4029,29]) ).
thf(6595,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[6594]) ).
thf(6596,plain,
int_zero @ ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[6595:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ sk3 ) ))]]) ).
thf(3766,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3495,61]) ).
thf(3767,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[3766]) ).
thf(3768,plain,
int_zero @ ( int_one @ sk3 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[3767:[bind(A,$thf( int_zero @ ( int_one @ sk3 ) ))]]) ).
thf(3940,plain,
int_one @ ( int_one @ int_leq ),
inference(rewrite,[status(thm)],[3768,3139]) ).
thf(4403,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4290,53]) ).
thf(4404,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[4403]) ).
thf(4405,plain,
int_zero @ ( sk1 @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[4404:[bind(A,$thf( int_zero )),bind(B,$thf( sk1 ))]]) ).
thf(4577,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4405,53]) ).
thf(4578,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( A @ ( B @ sk3 ) @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[4577]) ).
thf(4579,plain,
int_zero @ ( int_zero @ ( sk1 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[4578:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( sk1 @ sk3 ) ))]]) ).
thf(6298,plain,
int_zero @ ( sk1 @ sk3 ) @ ( int_zero @ int_less ),
inference(rewrite,[status(thm)],[4579,5328]) ).
thf(126,plain,
! [B: $i,A: $i] :
( ( B != int_one )
| ( A @ ( int_zero @ int_less ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,40]) ).
thf(127,plain,
! [A: $i] :
( ( A @ ( int_zero @ int_less ) )
| ( int_one @ ( A @ int_less ) )
| ~ ( int_one @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[126:[bind(A,$thf( A )),bind(B,$thf( int_one ))]]) ).
thf(7582,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( int_one @ ( sk2 @ plus ) ) )
| ( ( A @ ( B @ plus ) )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[43,7561]) ).
thf(7583,plain,
( ( sk2 @ ( int_one @ plus ) )
!= sk2 ),
inference(pattern_uni,[status(thm)],[7582:[bind(A,$thf( sk2 )),bind(B,$thf( int_one ))]]) ).
thf(721,plain,
! [A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ( sk1 != n ) ),
inference(paramod_ordered,[status(thm)],[679,37]) ).
thf(722,plain,
! [A: $i] :
( ( ( n @ ( sk2 @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ( sk1 != n ) ),
inference(simp,[status(thm)],[721]) ).
thf(740,plain,
! [A: $i] :
( ( n != A )
| ( sk2 != A )
| ( sk1 != n ) ),
inference(simp,[status(thm)],[722]) ).
thf(744,plain,
( ( sk2 != n )
| ( sk1 != n ) ),
inference(simp,[status(thm)],[740]) ).
thf(141,plain,
! [B: $i,A: $i] :
( ( A != sk1 )
| ( ( sk2 @ ( B @ a ) )
!= real_zero )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,21]) ).
thf(142,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ a ) )
!= real_zero )
| ( A @ ( sk1 @ int_less ) )
| ~ ( A @ ( sk1 @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[141:[bind(A,$thf( sk1 ))]]) ).
thf(154,plain,
! [A: $i] :
( ( ( sk2 @ ( A @ a ) )
!= real_zero )
| ( A @ ( sk1 @ int_less ) )
| ~ ( A @ ( sk1 @ int_leq ) ) ),
inference(simp,[status(thm)],[142]) ).
thf(9631,plain,
! [B: $i,A: $i] :
( ( ( B @ ( A @ plus ) )
!= ( sk1 @ ( sk2 @ plus ) ) )
| ( ( A @ ( B @ plus ) )
!= sk2 ) ),
inference(paramod_ordered,[status(thm)],[43,9608]) ).
thf(9632,plain,
( ( sk2 @ ( sk1 @ plus ) )
!= sk2 ),
inference(pattern_uni,[status(thm)],[9631:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(11843,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7319,4246]) ).
thf(11844,plain,
! [A: $i] :
( ( int_one @ ( A @ plus ) @ ( A @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[11843]) ).
thf(11897,plain,
! [A: $i] :
( ( ( int_one @ ( A @ plus ) )
!= int_zero )
| ( A != int_one ) ),
inference(simp,[status(thm)],[11844]) ).
thf(11967,plain,
( ( int_one @ ( int_one @ plus ) )
!= int_zero ),
inference(simp,[status(thm)],[11897]) ).
thf(17738,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk1 @ plus ) @ ( A @ int_leq ) )
!= ( B @ ( int_one @ int_leq ) ) )
| ( B @ ( int_zero @ int_less ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14175,63]) ).
thf(17739,plain,
! [B: $i,A: $i] :
( ( ( A @ ( sk1 @ plus ) @ ( A @ int_leq ) )
!= ( B @ ( int_one @ int_leq ) ) )
| ( B @ ( int_zero @ int_less ) ) ),
inference(simp,[status(thm)],[17738]) ).
thf(17740,plain,
int_one @ ( sk1 @ plus ) @ ( int_zero @ int_less ),
inference(pattern_uni,[status(thm)],[17739:[bind(A,$thf( int_one )),bind(B,$thf( int_one @ ( sk1 @ plus ) ))]]) ).
thf(17932,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( sk1 @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[17740,29]) ).
thf(17933,plain,
! [B: $i,A: $i] :
( ( ( int_one @ ( sk1 @ plus ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[17932]) ).
thf(17934,plain,
int_one @ ( sk1 @ plus ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[17933:[bind(A,$thf( int_zero )),bind(B,$thf( int_one @ ( sk1 @ plus ) ))]]) ).
thf(10710,plain,
! [A: $i] :
( ( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8960,61]) ).
thf(10711,plain,
! [A: $i] :
( ( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[10710]) ).
thf(10712,plain,
int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[10711:[bind(A,$thf( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ sk3 ) ))]]) ).
thf(6406,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ( sk1 != int_one ) ),
inference(paramod_ordered,[status(thm)],[4236,29]) ).
thf(6407,plain,
! [B: $i,A: $i] :
( ( ( sk2 @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ( sk1 != int_one ) ),
inference(simp,[status(thm)],[6406]) ).
thf(6408,plain,
( ( sk2 @ ( int_zero @ int_leq ) )
| ( sk1 != int_one ) ),
inference(pattern_uni,[status(thm)],[6407:[bind(A,$thf( int_zero )),bind(B,$thf( sk2 ))]]) ).
thf(16061,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[15277,37]) ).
thf(16062,plain,
! [A: $i] :
( ( int_zero @ ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[16061]) ).
thf(16147,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ sk3 ) )
!= A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[16062]) ).
thf(16161,plain,
( ( int_zero @ ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ sk3 ) )
!= int_zero ),
inference(simp,[status(thm)],[16147]) ).
thf(7342,plain,
! [B: $i,A: $i] :
( ( ( n @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ( sk2 != int_one ) ),
inference(paramod_ordered,[status(thm)],[4328,29]) ).
thf(7343,plain,
! [B: $i,A: $i] :
( ( ( n @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ( sk2 != int_one ) ),
inference(simp,[status(thm)],[7342]) ).
thf(7344,plain,
( ( n @ ( int_zero @ int_leq ) )
| ( sk2 != int_one ) ),
inference(pattern_uni,[status(thm)],[7343:[bind(A,$thf( int_zero )),bind(B,$thf( n ))]]) ).
thf(12514,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12050,29]) ).
thf(12515,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[12514]) ).
thf(12516,plain,
int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[12515:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) ))]]) ).
thf(4040,plain,
! [A: $i] :
( ( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2453,61]) ).
thf(4041,plain,
! [A: $i] :
( ( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[4040]) ).
thf(4042,plain,
int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[4041:[bind(A,$thf( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) ))]]) ).
thf(15231,plain,
! [A: $i] :
( ( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[14889,37]) ).
thf(15232,plain,
! [A: $i] :
( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[15231]) ).
thf(15308,plain,
! [A: $i] :
( ( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) )
!= A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[15232]) ).
thf(15315,plain,
( ( int_zero @ ( sk1 @ ( int_one @ plus ) @ sk3 ) )
!= int_zero ),
inference(simp,[status(thm)],[15308]) ).
thf(70,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)],[68]) ).
thf(74,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)],[70]) ).
thf(75,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)],[74]) ).
thf(8923,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8531,61]) ).
thf(8924,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[8923]) ).
thf(8925,plain,
sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[8924:[bind(A,$thf( sk1 @ ( sk2 @ sk3 ) @ ( sk2 @ sk3 ) ))]]) ).
thf(3759,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2363,61]) ).
thf(3760,plain,
! [A: $i] :
( ( ( sk1 @ ( sk2 @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[3759]) ).
thf(3761,plain,
sk1 @ ( sk2 @ sk3 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[3760:[bind(A,$thf( sk1 @ ( sk2 @ sk3 ) ))]]) ).
thf(118,plain,
! [B: $i,A: $i] :
( ( B != sk2 )
| ( A @ ( sk1 @ int_less ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,18]) ).
thf(119,plain,
! [A: $i] :
( ( A @ ( sk1 @ int_less ) )
| ( sk2 @ ( A @ int_less ) )
| ~ ( sk2 @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[118:[bind(A,$thf( A )),bind(B,$thf( sk2 ))]]) ).
thf(128,plain,
! [B: $i,A: $i] :
( ( A != sk2 )
| ( n @ ( B @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,19]) ).
thf(129,plain,
! [A: $i] :
( ( n @ ( A @ int_leq ) )
| ( A @ ( sk2 @ int_less ) )
| ~ ( A @ ( sk2 @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[128:[bind(A,$thf( sk2 ))]]) ).
thf(151,plain,
! [A: $i] :
( ( n @ ( A @ int_leq ) )
| ( A @ ( sk2 @ int_less ) )
| ~ ( A @ ( sk2 @ int_leq ) ) ),
inference(simp,[status(thm)],[129]) ).
thf(4037,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2453,29]) ).
thf(4038,plain,
! [B: $i,A: $i] :
( ( ( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) ) ),
inference(simp,[status(thm)],[4037]) ).
thf(4039,plain,
int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) @ ( int_zero @ int_leq ),
inference(pattern_uni,[status(thm)],[4038:[bind(A,$thf( int_zero )),bind(B,$thf( int_zero @ ( sk1 @ ( sk2 @ sk3 ) @ sk3 ) ))]]) ).
thf(12518,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12050,61]) ).
thf(12519,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[12518]) ).
thf(12520,plain,
int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[12519:[bind(A,$thf( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) ))]]) ).
thf(11516,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( int_one @ plus ) @ ( A @ int_less ) )
!= ( C @ ( B @ int_less ) ) )
| ( C @ ( B @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[7294,29]) ).
thf(11517,plain,
! [C: $i,B: $i,A: $i] :
( ( ( A @ ( int_one @ plus ) @ ( A @ int_less ) )
!= ( C @ ( B @ int_less ) ) )
| ( C @ ( B @ int_leq ) ) ),
inference(simp,[status(thm)],[11516]) ).
thf(11518,plain,
! [A: $i] : ( A @ ( int_one @ plus ) @ ( A @ int_leq ) ),
inference(pattern_uni,[status(thm)],[11517:[bind(A,$thf( E )),bind(B,$thf( E )),bind(C,$thf( E @ ( int_one @ plus ) ))]]) ).
thf(11589,plain,
! [A: $i] : ( A @ ( int_one @ plus ) @ ( A @ int_leq ) ),
inference(simp,[status(thm)],[11518]) ).
thf(2052,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true
| ( sk2 != int_one ) ),
inference(paramod_ordered,[status(thm)],[1687,37]) ).
thf(2053,plain,
! [A: $i] :
( ( ( sk1 @ ( int_one @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ( sk2 != int_one ) ),
inference(simp,[status(thm)],[2052]) ).
thf(2086,plain,
! [A: $i] :
( ( sk1 != A )
| ( int_one != A )
| ( sk2 != int_one ) ),
inference(simp,[status(thm)],[2053]) ).
thf(2091,plain,
( ( sk1 != int_one )
| ( sk2 != int_one ) ),
inference(simp,[status(thm)],[2086]) ).
thf(1498,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ~ $true
| ( sk2 != int_one ) ),
inference(paramod_ordered,[status(thm)],[1409,29]) ).
thf(1499,plain,
! [B: $i,A: $i] :
( ( ( sk1 @ ( sk2 @ int_less ) )
!= ( B @ ( A @ int_less ) ) )
| ( B @ ( A @ int_leq ) )
| ( sk2 != int_one ) ),
inference(simp,[status(thm)],[1498]) ).
thf(1500,plain,
( ( sk1 @ ( sk2 @ int_leq ) )
| ( sk2 != int_one ) ),
inference(pattern_uni,[status(thm)],[1499:[bind(A,$thf( sk2 )),bind(B,$thf( sk1 ))]]) ).
thf(8672,plain,
( ( ( sk2 @ ( sk1 @ ( sk2 @ sk3 ) @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[8503,4246]) ).
thf(8673,plain,
( ( sk2 @ ( sk1 @ ( sk2 @ sk3 ) @ int_leq ) )
!= ( int_zero @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[8672]) ).
thf(8730,plain,
( ( sk2 != int_zero )
| ( ( sk1 @ ( sk2 @ sk3 ) )
!= int_one ) ),
inference(simp,[status(thm)],[8673]) ).
thf(13277,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12555,61]) ).
thf(13278,plain,
! [A: $i] :
( ( ( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( int_zero @ int_less ) ) )
| ( A @ ( int_one @ int_leq ) ) ),
inference(simp,[status(thm)],[13277]) ).
thf(13279,plain,
int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ sk3 ) @ ( int_one @ int_leq ),
inference(pattern_uni,[status(thm)],[13278:[bind(A,$thf( int_zero @ ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ sk3 ) ))]]) ).
thf(108,plain,
! [B: $i,A: $i] :
( ( A != real_one )
| ( B != real_zero )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,66]) ).
thf(109,plain,
! [A: $i] :
( ( A != real_zero )
| ( A @ ( real_one @ int_less ) )
| ~ ( A @ ( real_one @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[108:[bind(A,$thf( real_one ))]]) ).
thf(163,plain,
( ( real_zero @ ( real_one @ int_less ) )
| ~ ( real_zero @ ( real_one @ int_leq ) ) ),
inference(simp,[status(thm)],[109]) ).
thf(99,plain,
! [B: $i,A: $i] :
( ( B != sk1 )
| ( A @ ( int_one @ int_leq ) )
| ( B @ ( A @ int_less ) )
| ~ ( B @ ( A @ int_leq ) ) ),
inference(paramod_ordered,[status(thm)],[28,17]) ).
thf(100,plain,
! [A: $i] :
( ( A @ ( int_one @ int_leq ) )
| ( sk1 @ ( A @ int_less ) )
| ~ ( sk1 @ ( A @ int_leq ) ) ),
inference(pattern_uni,[status(thm)],[99:[bind(A,$thf( A )),bind(B,$thf( sk1 ))]]) ).
thf(12509,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12050,37]) ).
thf(12510,plain,
! [A: $i] :
( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) @ ( int_zero @ int_less ) )
!= ( A @ ( A @ int_less ) ) ),
inference(simp,[status(thm)],[12509]) ).
thf(12583,plain,
! [A: $i] :
( ( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) )
!= A )
| ( int_zero != A ) ),
inference(simp,[status(thm)],[12510]) ).
thf(12594,plain,
( ( int_zero @ ( int_one @ ( int_one @ plus ) @ sk3 ) )
!= int_zero ),
inference(simp,[status(thm)],[12583]) ).
thf(30226,plain,
$false,
inference(e,[status(thm)],[153,8960,760,17875,4290,2499,10790,138,2889,2463,15242,2363,1406,6441,185,37,1409,3495,7294,125,13275,14773,152,14859,57,29,46,6599,3438,11838,61,2190,133,4536,15165,5328,9589,117,85,2249,160,21,33,28,38,16072,14889,1687,757,4104,12020,3090,8503,7540,156,9608,15238,53,8567,16068,77,1424,679,7668,8439,41,8458,3656,73,8482,8989,2189,794,4572,906,4380,2556,8531,148,161,64,17,32,34,22,44,10709,4328,4381,4236,1635,4413,49,7347,14360,7315,159,81,39,98,681,7594,4401,103,66,155,7561,768,4373,135,8922,4394,6672,2234,14175,8477,48,63,18,150,13367,6596,67,3940,14671,6298,127,7583,7319,31,744,4246,154,9632,43,11967,17934,10712,3139,6408,15277,16161,40,7344,12516,4042,15315,55,12050,75,17740,8925,3761,119,58,151,4039,12520,11589,19,422,4029,2091,12555,644,47,15,1500,8730,4410,13279,163,1320,2453,100,12594]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SWV486+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.07 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.11/0.42 % Computer : n008.cluster.edu
% 0.11/0.42 % Model : x86_64 x86_64
% 0.11/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.42 % Memory : 8046.5625MB
% 0.11/0.42 % OS : Linux 6.8.0-71-generic
% 0.11/0.42 % CPULimit : 300
% 0.11/0.42 % WCLimit : 300
% 0.11/0.42 % DateTime : Sat Sep 26 13:58:39 UTC 2026
% 0.11/0.42 % CPUTime :
% 0.11/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox/solver/bin/leo3.jar /export/starexec/sandbox/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox/solver/bin/externals/eprover --instantiate 39
% 0.85/1.15 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 1.08/1.35 % [INFO] Parsing done (193ms).
% 1.08/1.37 % [INFO] Running in sequential loop mode.
% 1.74/1.88 % [INFO] eprover registered as external prover.
% 1.74/1.89 % [INFO] Scanning for conjecture ...
% 2.00/2.02 % [INFO] Found a conjecture (or negated_conjecture) and 12 axioms. Running axiom selection ...
% 2.00/2.08 % [INFO] Axiom selection finished. Selected 12 axioms (removed 0 axioms).
% 2.00/2.12 % [INFO] Problem is first-order (TPTP FOF).
% 2.00/2.14 % [INFO] Type checking passed.
% 2.00/2.15 % [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 ...
% 61.15/21.60 % External prover 'e' found a proof!
% 61.15/21.60 % [INFO] Killing All external provers ...
% 61.38/21.61 % Time passed: 21021ms (effective reasoning time: 20234ms)
% 61.38/21.61 % 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)>
% 61.38/21.62 % Axioms used in derivation (12): plus_and_order1, qii, int_less_total, int_leq, int_less_transitive, int_zero_one, plus_and_inverse, int_less_irreflexive, plus_commutative, real_constants, plus_zero, one_successor_of_zero
% 61.38/21.62 % No. of inferences in proof: 529
% 61.38/21.62 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 21021 ms resp. 20234 ms w/o parsing
% 52.99/21.81 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 52.99/21.82 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------