%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : NUM993_5 : TPTP v9.3.1. Released v6.0.0.
% 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 08:10:35 AM UTC 2026
% Result : Theorem 148.59s 36.88s
% Output : Refutation 151.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 37
% Number of leaves : 114
% Syntax : Number of formulae : 1517 ( 594 unt; 0 typ; 3 def)
% Number of atoms : 4081 (1242 equ; 0 cnn)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 18723 (1632 ~;1200 |; 153 &;15474 @)
% ( 50 <=>; 214 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 6 con; 0-3 aty)
% Number of variables : 1707 ( 2 ^;1690 !; 12 ?;1707 :)
% ( 0 !>; 0 ?*; 0 @-; 3 @+)
% Comments :
%------------------------------------------------------------------------------
thf(bool_type,type,
bool: $tType ).
thf(int_type,type,
int: $tType ).
thf(nat_type,type,
nat: $tType ).
thf(number_decl,type,
number:
!>[TA: $tType] : $o ).
thf(ring_decl,type,
ring:
!>[TA: $tType] : $o ).
thf(semiring_decl,type,
semiring:
!>[TA: $tType] : $o ).
thf(number_ring_decl,type,
number_ring:
!>[TA: $tType] : $o ).
thf(ring_char_0_decl,type,
ring_char_0:
!>[TA: $tType] : $o ).
thf(linorder_decl,type,
linorder:
!>[TA: $tType] : $o ).
thf(linordered_idom_decl,type,
linordered_idom:
!>[TA: $tType] : $o ).
thf(linord219039673up_add_decl,type,
linord219039673up_add:
!>[TA: $tType] : $o ).
thf(minus_minus_decl,type,
minus_minus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(one_one_decl,type,
one_one:
!>[TA: $tType] : TA ).
thf(plus_plus_decl,type,
plus_plus:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(times_times_decl,type,
times_times:
!>[TA: $tType] : ( TA > TA > TA ) ).
thf(zero_zero_decl,type,
zero_zero:
!>[TA: $tType] : TA ).
thf(bit0_decl,type,
bit0: int > int ).
thf(bit1_decl,type,
bit1: int > int ).
thf(pls_decl,type,
pls: int ).
thf(number_number_of_decl,type,
number_number_of:
!>[TA: $tType] : ( int > TA ) ).
thf(semiring_1_of_nat_decl,type,
semiring_1_of_nat:
!>[TA: $tType] : ( nat > TA ) ).
thf(ord_less_decl,type,
ord_less:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(ord_less_eq_decl,type,
ord_less_eq:
!>[TA: $tType] : ( TA > TA > $o ) ).
thf(m1_decl,type,
m1: int ).
thf(n_decl,type,
n: nat ).
thf(t_decl,type,
t: int ).
thf(sk1_decl,type,
sk1: int > int > nat ).
thf(sk2_decl,type,
sk2: int > int ).
thf(sk3_decl,type,
sk3: int > int ).
thf(sk1_def,definition,
( sk1
= ( ^ [A: int,B: int] :
@+[C: nat] :
( B
= ( C @ ( int @ semiring_1_of_nat ) @ ( A @ ( int @ plus_plus ) ) ) ) ) ) ).
thf(sk2_def,definition,
( sk2
= ( @+[A: int > int] :
! [B: int] :
( ( B @ bit0 @ A )
= B ) ) ) ).
thf(sk3_def,definition,
( sk3
= ( @+[A: int > int] :
! [B: int] :
( ( B @ bit1 @ A )
= B ) ) ) ).
thf(30,axiom,
t @ ( int @ one_one @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_0_t1) ).
thf(211,plain,
t @ ( int @ one_one @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(61,axiom,
! [A: int,B: int] :
( ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_68_zle__diff1__eq) ).
thf(331,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) ) )
& ( ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(332,plain,
( ! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) ) )
& ! [A: int,B: int] :
( ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(miniscope,[status(thm)],[331]) ).
thf(333,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( int @ one_one @ ( C @ ( int @ minus_minus ) ) @ ( D @ ( int @ ord_less_eq ) ) )
| ~ ( C @ ( D @ ( int @ ord_less ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(cnf,[status(esa)],[332]) ).
thf(335,plain,
! [B: int,A: int] :
( ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[333]) ).
thf(336,plain,
! [B: int,A: int] :
( ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[335]) ).
thf(31718,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,336]) ).
thf(31719,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[31718]) ).
thf(31720,plain,
int @ one_one @ ( t @ ( int @ minus_minus ) ) @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[31719:[bind(A,$thf( t )),bind(B,$thf( int @ one_one ))]]) ).
thf(13,axiom,
int @ number_ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
thf(139,plain,
int @ number_ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(25,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_14_numeral__1__eq__1) ).
thf(190,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(191,plain,
! [TA: $tType] :
( ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) )
| ~ ( TA @ number_ring ) ),
inference(cnf,[status(esa)],[190]) ).
thf(192,plain,
! [TA: $tType] :
( ~ ( TA @ number_ring )
| ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(lifteq,[status(thm)],[191]) ).
thf(11332,plain,
! [TA: $tType] :
( ( ( int @ number_ring )
!= ( TA @ number_ring ) )
| ~ $true
| ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[139,192]) ).
thf(11333,plain,
! [TA: $tType] :
( ( ( int @ number_ring )
!= ( TA @ number_ring ) )
| ( ( pls @ bit1 @ ( TA @ number_number_of ) )
= ( TA @ one_one ) ) ),
inference(simp,[status(thm)],[11332]) ).
thf(11334,plain,
( ( pls @ bit1 @ ( int @ number_number_of ) )
= ( int @ one_one ) ),
inference(pattern_uni,[status(thm)],[11333:[bind_type(TA,$thf( int ))]]) ).
thf(42,axiom,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_97_number__of__is__id) ).
thf(253,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(254,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(cnf,[status(esa)],[253]) ).
thf(255,plain,
! [A: int] :
( ( A @ ( int @ number_number_of ) )
= A ),
inference(lifteq,[status(thm)],[254]) ).
thf(18097,plain,
( ( pls @ bit1 )
= ( int @ one_one ) ),
inference(rewrite,[status(thm)],[11334,255]) ).
thf(67,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_43_number__of__Pls) ).
thf(360,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(361,plain,
! [TA: $tType] :
( ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) )
| ~ ( TA @ number_ring ) ),
inference(cnf,[status(esa)],[360]) ).
thf(362,plain,
! [TA: $tType] :
( ~ ( TA @ number_ring )
| ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(lifteq,[status(thm)],[361]) ).
thf(35181,plain,
! [TA: $tType] :
( ( ( int @ number_ring )
!= ( TA @ number_ring ) )
| ~ $true
| ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[139,362]) ).
thf(35182,plain,
! [TA: $tType] :
( ( ( int @ number_ring )
!= ( TA @ number_ring ) )
| ( ( pls @ ( TA @ number_number_of ) )
= ( TA @ zero_zero ) ) ),
inference(simp,[status(thm)],[35181]) ).
thf(35183,plain,
( ( pls @ ( int @ number_number_of ) )
= ( int @ zero_zero ) ),
inference(pattern_uni,[status(thm)],[35182:[bind_type(TA,$thf( int ))]]) ).
thf(35205,plain,
( pls
= ( int @ zero_zero ) ),
inference(rewrite,[status(thm)],[35183,255]) ).
thf(35218,plain,
( ( int @ zero_zero @ bit1 )
= ( int @ one_one ) ),
inference(rewrite,[status(thm)],[18097,35205]) ).
thf(54,axiom,
t @ ( int @ one_one @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_18_tpos) ).
thf(302,plain,
t @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(75,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_57_rel__simps_I32_J) ).
thf(401,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(402,plain,
( ! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(miniscope,[status(thm)],[401]) ).
thf(403,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( C @ bit1 @ ( D @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ ( C @ ( D @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ) ),
inference(cnf,[status(esa)],[402]) ).
thf(405,plain,
! [B: int,A: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[403]) ).
thf(406,plain,
! [B: int,A: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[405]) ).
thf(39010,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[302,406]) ).
thf(39011,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[39010]) ).
thf(39012,plain,
t @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[39011:[bind(A,$thf( t )),bind(B,$thf( int @ one_one ))]]) ).
thf(56,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_9_one__add__one__is__two) ).
thf(309,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(310,plain,
! [TA: $tType] :
( ( ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) ) )
| ~ ( TA @ number_ring ) ),
inference(cnf,[status(esa)],[309]) ).
thf(311,plain,
! [TA: $tType] :
( ~ ( TA @ number_ring )
| ( ( pls @ bit1 @ bit0 @ ( TA @ number_number_of ) )
= ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) ) ) ),
inference(lifteq,[status(thm)],[310]) ).
thf(25962,plain,
! [TA: $tType] :
( ~ ( TA @ number_ring )
| ( ( int @ one_one @ bit0 @ ( TA @ number_number_of ) )
= ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) ) ) ),
inference(rewrite,[status(thm)],[311,18097]) ).
thf(26001,plain,
! [TA: $tType] :
( ( ( int @ number_ring )
!= ( TA @ number_ring ) )
| ~ $true
| ( ( int @ one_one @ bit0 @ ( TA @ number_number_of ) )
= ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[139,25962]) ).
thf(26002,plain,
! [TA: $tType] :
( ( ( int @ number_ring )
!= ( TA @ number_ring ) )
| ( ( int @ one_one @ bit0 @ ( TA @ number_number_of ) )
= ( TA @ one_one @ ( TA @ one_one @ ( TA @ plus_plus ) ) ) ) ),
inference(simp,[status(thm)],[26001]) ).
thf(26003,plain,
( ( int @ one_one @ bit0 @ ( int @ number_number_of ) )
= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ),
inference(pattern_uni,[status(thm)],[26002:[bind_type(TA,$thf( int ))]]) ).
thf(33188,plain,
( ( int @ one_one @ bit0 )
= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[26003,255]) ).
thf(39165,plain,
t @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[39012,33188]) ).
thf(57,axiom,
! [A: int,B: int] :
( ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_94_add1__zle__eq) ).
thf(312,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(313,plain,
( ! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) )
& ! [A: int,B: int] :
( ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(miniscope,[status(thm)],[312]) ).
thf(314,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( C @ ( int @ one_one @ ( D @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
| ~ ( C @ ( D @ ( int @ ord_less ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) ) ),
inference(cnf,[status(esa)],[313]) ).
thf(315,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[314]) ).
thf(39225,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( B @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39165,315]) ).
thf(39226,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[39225]) ).
thf(39227,plain,
t @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[39226:[bind(A,$thf( t @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(21,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less ) ) )
<=> ( A @ ( pls @ bit1 @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_7_less__special_I2_J) ).
thf(169,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( A @ ( pls @ bit1 @ ( int @ ord_less ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less ) ) )
=> ( A @ ( pls @ bit1 @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(170,plain,
! [TA: $tType,A: int] :
( ( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less ) ) )
| ~ ( A @ ( pls @ bit1 @ ( int @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) )
& ( ( A @ ( pls @ bit1 @ ( int @ ord_less ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ) ),
inference(cnf,[status(esa)],[169]) ).
thf(171,plain,
! [TA: $tType,A: int] :
( ( A @ ( pls @ bit1 @ ( int @ ord_less ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[170]) ).
thf(24,axiom,
! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
<=> ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_75_less__int__def) ).
thf(180,plain,
! [A: int,B: int] :
( ( ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(181,plain,
( ! [A: int,B: int] :
( ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) )
& ! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( ( B != A )
& ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(miniscope,[status(thm)],[180]) ).
thf(182,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( C @ ( D @ ( int @ ord_less ) ) )
| ( D = C )
| ~ ( C @ ( D @ ( int @ ord_less_eq ) ) ) )
& ( ( B != A )
| ~ ( A @ ( B @ ( int @ ord_less ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(cnf,[status(esa)],[181]) ).
thf(184,plain,
! [B: int,A: int] :
( ( B != A )
| ~ ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[182]) ).
thf(186,plain,
! [B: int,A: int] :
( ~ ( A @ ( B @ ( int @ ord_less ) ) )
| ( B != A ) ),
inference(lifteq,[status(thm)],[184]) ).
thf(187,plain,
! [A: int] :
~ ( A @ ( A @ ( int @ ord_less ) ) ),
inference(simp,[status(thm)],[186]) ).
thf(4272,plain,
! [TA: $tType,B: int,A: int] :
( ( ( A @ ( pls @ bit1 @ ( int @ ord_less ) ) )
!= ( B @ ( B @ ( int @ ord_less ) ) ) )
| ~ $true
| ~ ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(paramod_ordered,[status(thm)],[171,187]) ).
thf(4273,plain,
! [TA: $tType,B: int,A: int] :
( ( ( A @ ( pls @ bit1 @ ( int @ ord_less ) ) )
!= ( B @ ( B @ ( int @ ord_less ) ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(simp,[status(thm)],[4272]) ).
thf(4274,plain,
! [TA: $tType] :
( ~ ( pls @ bit1 @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(pattern_uni,[status(thm)],[4273:[bind(A,$thf( pls @ bit1 )),bind(B,$thf( pls @ bit1 ))]]) ).
thf(18113,plain,
! [A: int] :
( ( ( A @ ( int @ number_number_of ) )
!= ( pls @ bit1 @ ( int @ number_number_of ) ) )
| ~ ( A @ ( int @ one_one @ ( int @ ord_less ) ) )
| ~ ( int @ linordered_idom )
| ~ ( int @ number_ring ) ),
inference(paramod_ordered,[status(thm)],[255,4274]) ).
thf(18114,plain,
( ~ ( pls @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
| ~ ( int @ linordered_idom )
| ~ ( int @ number_ring ) ),
inference(pattern_uni,[status(thm)],[18113:[bind(A,$thf( pls @ bit1 ))]]) ).
thf(33,axiom,
int @ linordered_idom,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
thf(219,plain,
int @ linordered_idom,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(26025,plain,
( ~ ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) )
| ~ $true
| ~ $true ),
inference(rewrite,[status(thm)],[18114,18097,139,219]) ).
thf(26026,plain,
~ ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ),
inference(simp,[status(thm)],[26025]) ).
thf(39327,plain,
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39227,26026]) ).
thf(39328,plain,
( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[39327]) ).
thf(39337,plain,
( ( ( t @ bit1 )
!= ( int @ one_one ) )
| ( ( int @ one_one )
!= ( int @ one_one ) ) ),
inference(simp,[status(thm)],[39328]) ).
thf(39348,plain,
( ( t @ bit1 )
!= ( int @ one_one ) ),
inference(simp,[status(thm)],[39337]) ).
thf(39353,plain,
( ( ( t @ bit1 )
!= ( int @ zero_zero @ bit1 ) )
| ( ( int @ one_one )
!= ( int @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[35218,39348]) ).
thf(39354,plain,
( ( t @ bit1 )
!= ( int @ zero_zero @ bit1 ) ),
inference(simp,[status(thm)],[39353]) ).
thf(39365,plain,
( t
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[39354]) ).
thf(12,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_33_rel__simps_I34_J) ).
thf(133,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(134,plain,
( ! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(miniscope,[status(thm)],[133]) ).
thf(135,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( C @ bit1 @ ( D @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ ( C @ ( D @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ) ),
inference(cnf,[status(esa)],[134]) ).
thf(137,plain,
! [B: int,A: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[135]) ).
thf(138,plain,
! [B: int,A: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[137]) ).
thf(18,axiom,
pls @ ( pls @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_34_rel__simps_I19_J) ).
thf(160,plain,
pls @ ( pls @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(14,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_56_rel__simps_I22_J) ).
thf(140,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(141,plain,
( ! [A: int] :
( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) ) )
& ! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(miniscope,[status(thm)],[140]) ).
thf(142,plain,
! [B: int,A: int] :
( ( ( B @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ ( B @ ( pls @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(cnf,[status(esa)],[141]) ).
thf(144,plain,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[142]) ).
thf(145,plain,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[144]) ).
thf(1870,plain,
! [A: int] :
( ( ( pls @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( pls @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[160,145]) ).
thf(1871,plain,
! [A: int] :
( ( ( pls @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( pls @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[1870]) ).
thf(1872,plain,
pls @ bit1 @ ( pls @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[1871:[bind(A,$thf( pls ))]]) ).
thf(16,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_91_less__int__code_I14_J) ).
thf(148,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(149,plain,
( ! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) )
& ! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(miniscope,[status(thm)],[148]) ).
thf(150,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( C @ bit1 @ ( D @ bit0 @ ( int @ ord_less ) ) )
| ~ ( C @ ( D @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ) ),
inference(cnf,[status(esa)],[149]) ).
thf(152,plain,
! [B: int,A: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[150]) ).
thf(153,plain,
! [B: int,A: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[152]) ).
thf(2377,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1872,153]) ).
thf(2378,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[2377]) ).
thf(2379,plain,
pls @ bit1 @ bit1 @ ( pls @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[2378:[bind(A,$thf( pls @ bit1 )),bind(B,$thf( pls ))]]) ).
thf(37,axiom,
( ( pls @ bit0 )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_29_Bit0__Pls) ).
thf(237,plain,
( ( pls @ bit0 )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(238,plain,
( ( pls @ bit0 )
= pls ),
inference(lifteq,[status(thm)],[237]) ).
thf(2909,plain,
pls @ bit1 @ bit1 @ ( pls @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[2379,238]) ).
thf(18143,plain,
int @ one_one @ bit1 @ ( pls @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[2909,18097]) ).
thf(31689,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18143,336]) ).
thf(31690,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[31689]) ).
thf(31691,plain,
int @ one_one @ ( int @ one_one @ bit1 @ ( int @ minus_minus ) ) @ ( pls @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[31690:[bind(A,$thf( int @ one_one @ bit1 )),bind(B,$thf( pls ))]]) ).
thf(39716,plain,
int @ one_one @ ( int @ one_one @ bit1 @ ( int @ minus_minus ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[31691,35205]) ).
thf(94,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_16_diff__bin__simps_I9_J) ).
thf(479,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(41,axiom,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_24_rel__simps_I39_J) ).
thf(249,plain,
! [A: int] :
( pls
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(106,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_38_add__Bit0__Bit0) ).
thf(518,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(36,axiom,
! [A: int,B: nat,C: nat] :
( ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) @ ( C @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_83_zadd__int__left) ).
thf(234,plain,
! [A: int,B: nat,C: nat] :
( ( A @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) @ ( C @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(23,axiom,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_25_rel__simps_I50_J) ).
thf(176,plain,
! [A: int,B: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(177,plain,
~ ? [A: int,B: int] :
( ( B @ bit1 )
= ( A @ bit0 ) ),
inference(miniscope,[status(thm)],[176]) ).
thf(178,plain,
! [B: int,A: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(cnf,[status(esa)],[177]) ).
thf(179,plain,
! [B: int,A: int] :
( ( B @ bit1 )
!= ( A @ bit0 ) ),
inference(lifteq,[status(thm)],[178]) ).
thf(18227,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 )
!= ( B @ bit1 ) )
| ( ( A @ bit0 )
!= ( int @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[18097,179]) ).
thf(18228,plain,
! [A: int] :
( ( A @ bit0 )
!= ( int @ one_one ) ),
inference(pattern_uni,[status(thm)],[18227:[bind(A,$thf( A )),bind(B,$thf( pls ))]]) ).
thf(112,axiom,
! [A: nat] :
( ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_77_int__le__0__conv) ).
thf(543,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) ) )
& ( ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(544,plain,
( ! [A: nat] :
( ( A
= ( nat @ zero_zero ) )
=> ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) ) )
& ! [A: nat] :
( ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(miniscope,[status(thm)],[543]) ).
thf(545,plain,
! [B: nat,A: nat] :
( ( ( int @ zero_zero @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
| ( B
!= ( nat @ zero_zero ) ) )
& ( ( A
= ( nat @ zero_zero ) )
| ~ ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) ) ) ),
inference(cnf,[status(esa)],[544]) ).
thf(547,plain,
! [A: nat] :
( ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
| ( A
!= ( nat @ zero_zero ) ) ),
inference(cnfConj,[status(thm)],[545]) ).
thf(549,plain,
! [A: nat] :
( ( int @ zero_zero @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ) )
| ( A
!= ( nat @ zero_zero ) ) ),
inference(lifteq,[status(thm)],[547]) ).
thf(550,plain,
int @ zero_zero @ ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less_eq ) ),
inference(simp,[status(thm)],[549]) ).
thf(29,axiom,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_89_int__0) ).
thf(209,plain,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(210,plain,
( ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ),
inference(lifteq,[status(thm)],[209]) ).
thf(922,plain,
int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[550,210]) ).
thf(2439,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[922,153]) ).
thf(2440,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[2439]) ).
thf(2441,plain,
int @ zero_zero @ bit1 @ ( int @ zero_zero @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[2440:[bind(A,$thf( int @ zero_zero )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(17,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_32_rel__simps_I14_J) ).
thf(154,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(155,plain,
( ! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) )
& ! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(miniscope,[status(thm)],[154]) ).
thf(156,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( C @ bit0 @ ( D @ bit0 @ ( int @ ord_less ) ) )
| ~ ( C @ ( D @ ( int @ ord_less ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ) ),
inference(cnf,[status(esa)],[155]) ).
thf(158,plain,
! [B: int,A: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[156]) ).
thf(159,plain,
! [B: int,A: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[158]) ).
thf(3123,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ bit1 @ ( int @ zero_zero @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2441,159]) ).
thf(3124,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ bit1 @ ( int @ zero_zero @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[3123]) ).
thf(3125,plain,
int @ zero_zero @ bit1 @ bit0 @ ( int @ zero_zero @ bit0 @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[3124:[bind(A,$thf( int @ zero_zero @ bit1 )),bind(B,$thf( int @ zero_zero @ bit0 ))]]) ).
thf(35216,plain,
( ( int @ zero_zero @ bit0 )
= ( int @ zero_zero ) ),
inference(rewrite,[status(thm)],[238,35205]) ).
thf(35282,plain,
int @ zero_zero @ bit1 @ bit0 @ ( int @ zero_zero @ bit0 @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[3125,35216]) ).
thf(44363,plain,
int @ one_one @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[35282,35216,35218]) ).
thf(83,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_69_le__special_I3_J) ).
thf(438,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less_eq ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(439,plain,
! [TA: $tType,A: int] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( pls @ ( A @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) )
& ( ( pls @ ( A @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ) ),
inference(cnf,[status(esa)],[438]) ).
thf(440,plain,
! [TA: $tType,A: int] :
( ( pls @ ( A @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[439]) ).
thf(45459,plain,
! [TA: $tType,A: int] :
( ( int @ zero_zero @ ( A @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(rewrite,[status(thm)],[440,35205]) ).
thf(8,axiom,
int @ linord219039673up_add,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
thf(126,plain,
int @ linord219039673up_add,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(27,axiom,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
<=> ( A
= ( TA @ zero_zero ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_22_double__eq__0__iff) ).
thf(196,plain,
! [TA: $tType] :
( ( TA @ linord219039673up_add )
=> ! [A: TA] :
( ( ( A
= ( TA @ zero_zero ) )
=> ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) )
& ( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
=> ( A
= ( TA @ zero_zero ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(197,plain,
! [TA: $tType,A: TA] :
( ( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
| ( A
!= ( TA @ zero_zero ) )
| ~ ( TA @ linord219039673up_add ) )
& ( ( A
= ( TA @ zero_zero ) )
| ( ( A @ ( A @ ( TA @ plus_plus ) ) )
!= ( TA @ zero_zero ) )
| ~ ( TA @ linord219039673up_add ) ) ),
inference(cnf,[status(esa)],[196]) ).
thf(199,plain,
! [TA: $tType,A: TA] :
( ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
| ( A
!= ( TA @ zero_zero ) )
| ~ ( TA @ linord219039673up_add ) ),
inference(cnfConj,[status(thm)],[197]) ).
thf(201,plain,
! [TA: $tType,A: TA] :
( ~ ( TA @ linord219039673up_add )
| ( ( A @ ( A @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) )
| ( A
!= ( TA @ zero_zero ) ) ),
inference(lifteq,[status(thm)],[199]) ).
thf(202,plain,
! [TA: $tType] :
( ~ ( TA @ linord219039673up_add )
| ( ( TA @ zero_zero @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) ),
inference(simp,[status(thm)],[201]) ).
thf(13459,plain,
! [TA: $tType] :
( ( ( int @ linord219039673up_add )
!= ( TA @ linord219039673up_add ) )
| ~ $true
| ( ( TA @ zero_zero @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[126,202]) ).
thf(13460,plain,
! [TA: $tType] :
( ( ( int @ linord219039673up_add )
!= ( TA @ linord219039673up_add ) )
| ( ( TA @ zero_zero @ ( TA @ zero_zero @ ( TA @ plus_plus ) ) )
= ( TA @ zero_zero ) ) ),
inference(simp,[status(thm)],[13459]) ).
thf(13461,plain,
( ( int @ zero_zero @ ( int @ zero_zero @ ( int @ plus_plus ) ) )
= ( int @ zero_zero ) ),
inference(pattern_uni,[status(thm)],[13460:[bind_type(TA,$thf( int ))]]) ).
thf(22,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_60_add__Bit1__Bit0) ).
thf(173,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(174,plain,
! [B: int,A: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
inference(cnf,[status(esa)],[173]) ).
thf(175,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 )
= ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) ) ),
inference(lifteq,[status(thm)],[174]) ).
thf(13596,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ ( int @ zero_zero @ ( int @ plus_plus ) ) )
!= ( A @ ( B @ ( int @ plus_plus ) ) ) )
| ( ( int @ zero_zero @ bit1 )
= ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13461,175]) ).
thf(13597,plain,
( ( int @ zero_zero @ bit0 @ ( int @ zero_zero @ bit1 @ ( int @ plus_plus ) ) )
= ( int @ zero_zero @ bit1 ) ),
inference(pattern_uni,[status(thm)],[13596:[bind(A,$thf( int @ zero_zero )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(26,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_61_add__Bit0__Bit1) ).
thf(193,plain,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(194,plain,
! [B: int,A: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 ) ),
inference(cnf,[status(esa)],[193]) ).
thf(195,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ bit1 )
= ( A @ bit1 @ ( B @ bit0 @ ( int @ plus_plus ) ) ) ),
inference(lifteq,[status(thm)],[194]) ).
thf(12219,plain,
! [B: int,A: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) )
= ( A @ bit1 @ ( B @ bit0 @ ( int @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[195,175]) ).
thf(17345,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ bit0 @ ( int @ zero_zero @ bit1 @ ( int @ plus_plus ) ) )
!= ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) ) )
| ( ( int @ zero_zero @ bit1 )
= ( A @ bit1 @ ( B @ bit0 @ ( int @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[13597,12219]) ).
thf(17346,plain,
( ( int @ zero_zero @ bit1 @ ( int @ zero_zero @ bit0 @ ( int @ plus_plus ) ) )
= ( int @ zero_zero @ bit1 ) ),
inference(pattern_uni,[status(thm)],[17345:[bind(A,$thf( int @ zero_zero )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(35288,plain,
( ( int @ zero_zero @ bit1 @ ( int @ zero_zero @ ( int @ plus_plus ) ) )
= ( int @ zero_zero @ bit1 ) ),
inference(rewrite,[status(thm)],[17346,35216]) ).
thf(44870,plain,
( ( int @ one_one @ ( int @ zero_zero @ ( int @ plus_plus ) ) )
= ( int @ one_one ) ),
inference(rewrite,[status(thm)],[35288,35218]) ).
thf(38,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_53_rel__simps_I16_J) ).
thf(239,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(240,plain,
( ! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) ) )
& ! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(miniscope,[status(thm)],[239]) ).
thf(241,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( C @ bit0 @ ( D @ bit1 @ ( int @ ord_less ) ) )
| ~ ( C @ ( D @ ( int @ ord_less ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ) ),
inference(cnf,[status(esa)],[240]) ).
thf(243,plain,
! [B: int,A: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[241]) ).
thf(244,plain,
! [B: int,A: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[243]) ).
thf(19047,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,244]) ).
thf(19048,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[19047]) ).
thf(19049,plain,
t @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[19048:[bind(A,$thf( t )),bind(B,$thf( int @ one_one ))]]) ).
thf(22277,plain,
! [A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19049,187]) ).
thf(22278,plain,
! [A: int] :
( ( t @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[22277]) ).
thf(22309,plain,
! [A: int] :
( ( ( t @ bit0 )
!= A )
| ( ( int @ one_one @ bit1 )
!= A ) ),
inference(simp,[status(thm)],[22278]) ).
thf(22328,plain,
( ( int @ one_one @ bit1 )
!= ( t @ bit0 ) ),
inference(simp,[status(thm)],[22309]) ).
thf(7,axiom,
! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
<=> ? [C: nat] :
( A
= ( C @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_86_zle__iff__zadd) ).
thf(118,plain,
! [A: int,B: int] :
( ( ? [C: nat] :
( A
= ( C @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ? [C: nat] :
( A
= ( C @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(119,plain,
( ! [A: int,B: int] :
( ? [C: nat] :
( A
= ( C @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
& ! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ? [C: nat] :
( A
= ( C @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) ) ) ) ),
inference(miniscope,[status(thm)],[118]) ).
thf(120,plain,
! [E: nat,D: int,C: int,B: int,A: int] :
( ( ( C @ ( D @ ( int @ ord_less_eq ) ) )
| ( C
!= ( E @ ( int @ semiring_1_of_nat ) @ ( D @ ( int @ plus_plus ) ) ) ) )
& ( ( A
= ( A @ ( B @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(cnf,[status(esa)],[119]) ).
thf(121,plain,
! [B: int,A: int] :
( ( A
= ( A @ ( B @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(123,plain,
! [B: int,A: int] :
( ~ ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ( ( A @ ( B @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) )
= A ) ),
inference(lifteq,[status(thm)],[121]) ).
thf(792,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ~ $true
| ( ( A @ ( B @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[302,123]) ).
thf(793,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( ( A @ ( B @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) )
= A ) ),
inference(simp,[status(thm)],[792]) ).
thf(794,plain,
( ( t @ ( int @ one_one @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) )
= t ),
inference(pattern_uni,[status(thm)],[793:[bind(A,$thf( t )),bind(B,$thf( int @ one_one ))]]) ).
thf(46,axiom,
~ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( m1 @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_1__096_126_Am1_A_060_A1_A_L_Aint_An_096) ).
thf(274,plain,
~ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( m1 @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(275,plain,
~ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( m1 @ ( int @ ord_less ) ) ),
inference(polarity_switch,[status(thm)],[274]) ).
thf(1274,plain,
( ( ( t @ ( int @ one_one @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) )
| ~ ( t @ ( m1 @ ( int @ ord_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[794,275]) ).
thf(1289,plain,
( ( ( t @ ( int @ one_one @ sk1 ) @ ( int @ semiring_1_of_nat ) )
!= ( n @ ( int @ semiring_1_of_nat ) ) )
| ( ( int @ one_one )
!= ( int @ one_one ) )
| ~ ( t @ ( m1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[1274]) ).
thf(1316,plain,
( ( ( t @ ( int @ one_one @ sk1 ) @ ( int @ semiring_1_of_nat ) )
!= ( n @ ( int @ semiring_1_of_nat ) ) )
| ~ ( t @ ( m1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[1289]) ).
thf(1767,plain,
( ( ( t @ ( int @ one_one @ sk1 ) )
!= n )
| ~ ( t @ ( m1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[1316]) ).
thf(63,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_90_less__eq__int__code_I15_J) ).
thf(347,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(1952,plain,
! [A: int] :
( ( ( pls @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( pls @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1872,145]) ).
thf(1953,plain,
! [A: int] :
( ( ( pls @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( pls @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[1952]) ).
thf(1954,plain,
pls @ bit1 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[1953:[bind(A,$thf( pls @ bit1 ))]]) ).
thf(1978,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( pls @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1954,145]) ).
thf(1979,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( pls @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[1978]) ).
thf(1980,plain,
pls @ bit1 @ bit1 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[1979:[bind(A,$thf( pls @ bit1 @ bit1 ))]]) ).
thf(2031,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit1 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( pls @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1980,145]) ).
thf(2032,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit1 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( pls @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[2031]) ).
thf(2033,plain,
pls @ bit1 @ bit1 @ bit1 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[2032:[bind(A,$thf( pls @ bit1 @ bit1 @ bit1 ))]]) ).
thf(18144,plain,
int @ one_one @ bit1 @ bit1 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[2033,18097]) ).
thf(35236,plain,
int @ one_one @ bit1 @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[18144,35205]) ).
thf(1970,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1954,138]) ).
thf(1971,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[1970]) ).
thf(1972,plain,
pls @ bit1 @ bit1 @ bit1 @ ( pls @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[1971:[bind(A,$thf( pls @ bit1 @ bit1 )),bind(B,$thf( pls ))]]) ).
thf(18165,plain,
int @ one_one @ bit1 @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[1972,18097]) ).
thf(480,plain,
! [B: int,A: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit1 ) ),
inference(cnf,[status(esa)],[479]) ).
thf(481,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ bit1 )
= ( A @ bit0 @ ( B @ bit1 @ ( int @ minus_minus ) ) ) ),
inference(lifteq,[status(thm)],[480]) ).
thf(48,axiom,
n @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_17_n0) ).
thf(278,plain,
n @ ( nat @ zero_zero @ ( nat @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(58,axiom,
! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
<=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_78_zero__less__int__conv) ).
thf(318,plain,
! [A: nat] :
( ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(319,plain,
( ! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
& ! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ) ),
inference(miniscope,[status(thm)],[318]) ).
thf(320,plain,
! [B: nat,A: nat] :
( ( ( B @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ ( B @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ~ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ) ),
inference(cnf,[status(esa)],[319]) ).
thf(322,plain,
! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[320]) ).
thf(323,plain,
! [A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) ),
inference(simp,[status(thm)],[322]) ).
thf(28795,plain,
! [A: nat] :
( ( ( n @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
!= ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
| ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[278,323]) ).
thf(28796,plain,
! [A: nat] :
( ( ( n @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
!= ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) ) )
| ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[28795]) ).
thf(28797,plain,
n @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[28796:[bind(A,$thf( n ))]]) ).
thf(28944,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28797,159]) ).
thf(28945,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[28944]) ).
thf(28946,plain,
n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ zero_zero @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[28945:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(38160,plain,
n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[28946,35216]) ).
thf(38202,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38160,187]) ).
thf(38203,plain,
! [A: int] :
( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[38202]) ).
thf(38247,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[38203]) ).
thf(38259,plain,
( ( n @ ( int @ semiring_1_of_nat ) @ bit0 )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[38247]) ).
thf(4,axiom,
nat @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Int_Onumber) ).
thf(115,plain,
nat @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(19,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_74_less__eq__int__code_I13_J) ).
thf(161,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(162,plain,
( ! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(miniscope,[status(thm)],[161]) ).
thf(163,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( C @ bit0 @ ( D @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ ( C @ ( D @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ) ),
inference(cnf,[status(esa)],[162]) ).
thf(165,plain,
! [B: int,A: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[163]) ).
thf(166,plain,
! [B: int,A: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[165]) ).
thf(3884,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[302,166]) ).
thf(3885,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[3884]) ).
thf(3886,plain,
t @ bit0 @ ( int @ one_one @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[3885:[bind(A,$thf( t )),bind(B,$thf( int @ one_one ))]]) ).
thf(33263,plain,
t @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[3886,33188]) ).
thf(42702,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( B @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33263,315]) ).
thf(42703,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[42702]) ).
thf(42704,plain,
t @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[42703:[bind(A,$thf( t @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(183,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[182]) ).
thf(42811,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42704,183]) ).
thf(42812,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[42811]) ).
thf(42813,plain,
t @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[42812:[bind(A,$thf( t @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(47,axiom,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_95_le__imp__0__less) ).
thf(276,plain,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
=> ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(19616,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18143,244]) ).
thf(19617,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[19616]) ).
thf(19618,plain,
int @ one_one @ bit1 @ bit0 @ ( pls @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[19617:[bind(A,$thf( int @ one_one @ bit1 )),bind(B,$thf( pls ))]]) ).
thf(28117,plain,
int @ one_one @ bit1 @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[19618,18097]) ).
thf(28203,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28117,183]) ).
thf(28204,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[28203]) ).
thf(28205,plain,
int @ one_one @ bit1 @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[28204:[bind(A,$thf( int @ one_one @ bit1 @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(6143,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ bit1 @ bit0 @ ( int @ zero_zero @ bit0 @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3125,183]) ).
thf(6144,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ bit1 @ bit0 @ ( int @ zero_zero @ bit0 @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[6143]) ).
thf(6145,plain,
int @ zero_zero @ bit1 @ bit0 @ ( int @ zero_zero @ bit0 @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[6144:[bind(A,$thf( int @ zero_zero @ bit1 @ bit0 )),bind(B,$thf( int @ zero_zero @ bit0 @ bit0 ))]]) ).
thf(35302,plain,
int @ zero_zero @ bit1 @ bit0 @ ( int @ zero_zero @ bit0 @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[6145,35216]) ).
thf(45719,plain,
int @ one_one @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[35302,35216,35218]) ).
thf(277,plain,
! [A: int] :
( ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
inference(cnf,[status(esa)],[276]) ).
thf(45785,plain,
! [A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45719,277]) ).
thf(45786,plain,
! [A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[45785]) ).
thf(45787,plain,
int @ one_one @ bit0 @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[45786:[bind(A,$thf( int @ one_one @ bit0 ))]]) ).
thf(58666,plain,
int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[45787,33188]) ).
thf(86,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_47_le__number__of) ).
thf(447,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(448,plain,
! [TA: $tType,B: int,A: int] :
( ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) )
& ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ) ),
inference(cnf,[status(esa)],[447]) ).
thf(449,plain,
! [TA: $tType,B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[448]) ).
thf(20,axiom,
( ( nat @ one_one @ ( int @ semiring_1_of_nat ) )
= ( int @ one_one ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_87_int__1) ).
thf(167,plain,
( ( nat @ one_one @ ( int @ semiring_1_of_nat ) )
= ( int @ one_one ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(168,plain,
( ( nat @ one_one @ ( int @ semiring_1_of_nat ) )
= ( int @ one_one ) ),
inference(lifteq,[status(thm)],[167]) ).
thf(603,plain,
( ( ( n @ ( int @ semiring_1_of_nat ) )
!= ( nat @ one_one @ ( int @ semiring_1_of_nat ) ) )
| ~ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( m1 @ ( int @ ord_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[168,275]) ).
thf(614,plain,
( ( n
!= ( nat @ one_one ) )
| ~ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( m1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[603]) ).
thf(2382,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1954,153]) ).
thf(2383,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[2382]) ).
thf(2384,plain,
pls @ bit1 @ bit1 @ bit1 @ ( pls @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[2383:[bind(A,$thf( pls @ bit1 @ bit1 )),bind(B,$thf( pls ))]]) ).
thf(3409,plain,
pls @ bit1 @ bit1 @ bit1 @ ( pls @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[2384,238]) ).
thf(18140,plain,
int @ one_one @ bit1 @ bit1 @ ( pls @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[3409,18097]) ).
thf(35222,plain,
int @ one_one @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[18140,35205]) ).
thf(77,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) )
<=> ( A @ ( pls @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_55_rel__simps_I4_J) ).
thf(413,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) ) )
& ( ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(414,plain,
( ! [A: int] :
( ( A @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) ) )
& ! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ),
inference(miniscope,[status(thm)],[413]) ).
thf(415,plain,
! [B: int,A: int] :
( ( ( B @ bit0 @ ( pls @ ( int @ ord_less ) ) )
| ~ ( B @ ( pls @ ( int @ ord_less ) ) ) )
& ( ( A @ ( pls @ ( int @ ord_less ) ) )
| ~ ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) ) ) ),
inference(cnf,[status(esa)],[414]) ).
thf(417,plain,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) )
| ~ ( A @ ( pls @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[415]) ).
thf(418,plain,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) )
| ~ ( A @ ( pls @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[417]) ).
thf(40526,plain,
! [A: int] :
( ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(rewrite,[status(thm)],[418,35205]) ).
thf(40531,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35222,40526]) ).
thf(40532,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[40531]) ).
thf(40533,plain,
int @ one_one @ bit1 @ bit1 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[40532:[bind(A,$thf( int @ one_one @ bit1 @ bit1 ))]]) ).
thf(50592,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit1 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40533,187]) ).
thf(50593,plain,
! [A: int] :
( ( int @ one_one @ bit1 @ bit1 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[50592]) ).
thf(50640,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit1 @ bit0 )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[50593]) ).
thf(50660,plain,
( ( int @ one_one @ bit1 @ bit1 @ bit0 )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[50640]) ).
thf(43120,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42813,153]) ).
thf(43121,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[43120]) ).
thf(43122,plain,
t @ bit0 @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[43121:[bind(A,$thf( t @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(52895,plain,
t @ bit0 @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[43122,33188]) ).
thf(52964,plain,
! [A: int] :
( ( ( t @ bit0 @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52895,187]) ).
thf(52965,plain,
! [A: int] :
( ( t @ bit0 @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[52964]) ).
thf(53042,plain,
! [A: int] :
( ( ( t @ bit0 @ bit1 )
!= A )
| ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= A ) ),
inference(simp,[status(thm)],[52965]) ).
thf(53054,plain,
( ( t @ bit0 @ bit1 )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[53042]) ).
thf(39324,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39227,183]) ).
thf(39325,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[39324]) ).
thf(39326,plain,
t @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[39325:[bind(A,$thf( t @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(39408,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39326,406]) ).
thf(39409,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[39408]) ).
thf(39410,plain,
t @ bit1 @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[39409:[bind(A,$thf( t @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(49832,plain,
t @ bit1 @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[39410,33188]) ).
thf(49916,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( B @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49832,315]) ).
thf(49917,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[49916]) ).
thf(49918,plain,
t @ bit1 @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[49917:[bind(A,$thf( t @ bit1 @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(50050,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49918,183]) ).
thf(50051,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[50050]) ).
thf(50052,plain,
t @ bit1 @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[50051:[bind(A,$thf( t @ bit1 @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(103,axiom,
! [A: int] :
( ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_92_int__one__le__iff__zero__less) ).
thf(507,plain,
! [A: int] :
( ( ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
=> ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(508,plain,
( ! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
=> ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
& ! [A: int] :
( ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
=> ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ) ),
inference(miniscope,[status(thm)],[507]) ).
thf(509,plain,
! [B: int,A: int] :
( ( ( B @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
| ~ ( B @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) ) ),
inference(cnf,[status(esa)],[508]) ).
thf(510,plain,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[509]) ).
thf(68174,plain,
! [A: int] :
( ( ( t @ bit1 @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[50052,510]) ).
thf(68175,plain,
! [A: int] :
( ( ( t @ bit1 @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[68174]) ).
thf(68176,plain,
t @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[68175:[bind(A,$thf( t @ bit1 @ bit1 ))]]) ).
thf(102,axiom,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_19_eq__number__of) ).
thf(500,plain,
! [TA: $tType] :
( ( ( TA @ ring_char_0 )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) ) )
& ( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
=> ( B = A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(79,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
<=> ( pls @ bit1 @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_71_le__special_I4_J) ).
thf(422,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( pls @ bit1 @ ( A @ ( int @ ord_less_eq ) ) )
=> ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
=> ( pls @ bit1 @ ( A @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(423,plain,
! [TA: $tType,A: int] :
( ( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( pls @ bit1 @ ( A @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) )
& ( ( pls @ bit1 @ ( A @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ) ),
inference(cnf,[status(esa)],[422]) ).
thf(425,plain,
! [TA: $tType,A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( pls @ bit1 @ ( A @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[423]) ).
thf(42207,plain,
! [TA: $tType,A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( int @ zero_zero @ bit1 @ ( A @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(rewrite,[status(thm)],[425,35205]) ).
thf(101,axiom,
int @ zero_zero @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_4__0962_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_A_060_A0_096) ).
thf(499,plain,
int @ zero_zero @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(61058,plain,
int @ zero_zero @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[499,255]) ).
thf(1446,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[302,138]) ).
thf(1447,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[1446]) ).
thf(1448,plain,
t @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[1447:[bind(A,$thf( t )),bind(B,$thf( int @ one_one ))]]) ).
thf(2457,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1448,153]) ).
thf(2458,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[2457]) ).
thf(2459,plain,
t @ bit1 @ bit1 @ ( int @ one_one @ bit1 @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[2458:[bind(A,$thf( t @ bit1 )),bind(B,$thf( int @ one_one @ bit1 ))]]) ).
thf(316,plain,
! [B: int,A: int] :
( ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[314]) ).
thf(317,plain,
! [B: int,A: int] :
( ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[316]) ).
thf(27092,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,317]) ).
thf(27093,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[27092]) ).
thf(27094,plain,
t @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[27093:[bind(A,$thf( t )),bind(B,$thf( int @ one_one ))]]) ).
thf(39405,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39326,166]) ).
thf(39406,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[39405]) ).
thf(39407,plain,
t @ bit1 @ bit0 @ ( int @ one_one @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[39406:[bind(A,$thf( t @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(49183,plain,
t @ bit1 @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[39407,33188]) ).
thf(2409,plain,
! [B: int,A: int] :
( ( ( pls @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[160,153]) ).
thf(2410,plain,
! [B: int,A: int] :
( ( ( pls @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[2409]) ).
thf(2411,plain,
pls @ bit1 @ ( pls @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[2410:[bind(A,$thf( pls )),bind(B,$thf( pls ))]]) ).
thf(2588,plain,
pls @ bit1 @ ( pls @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[2411,238]) ).
thf(3166,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2588,159]) ).
thf(3167,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[3166]) ).
thf(3168,plain,
pls @ bit1 @ bit0 @ ( pls @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[3167:[bind(A,$thf( pls @ bit1 )),bind(B,$thf( pls ))]]) ).
thf(3306,plain,
pls @ bit1 @ bit0 @ ( pls @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[3168,238]) ).
thf(18141,plain,
int @ one_one @ bit0 @ ( pls @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[3306,18097]) ).
thf(31836,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18141,336]) ).
thf(31837,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[31836]) ).
thf(31838,plain,
int @ one_one @ ( int @ one_one @ bit0 @ ( int @ minus_minus ) ) @ ( pls @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[31837:[bind(A,$thf( int @ one_one @ bit0 )),bind(B,$thf( pls ))]]) ).
thf(39885,plain,
int @ one_one @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ minus_minus ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[31838,33188,35205]) ).
thf(18123,plain,
int @ one_one @ bit1 @ ( pls @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[1954,18097]) ).
thf(35217,plain,
int @ one_one @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[18123,35205]) ).
thf(73,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_73_less__eq__int__code_I16_J) ).
thf(385,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(72,axiom,
! [TA: $tType] :
( ( ( TA @ linorder )
& ( TA @ number ) )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
<=> ~ ( B @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_80_le__number__of__eq__not__less) ).
thf(381,plain,
! [TA: $tType] :
( ( ( TA @ linorder )
& ( TA @ number ) )
=> ! [A: int,B: int] :
( ( ~ ( B @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
=> ~ ( B @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(382,plain,
! [TA: $tType,B: int,A: int] :
( ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ( B @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ linorder )
| ~ ( TA @ number ) )
& ( ~ ( B @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( TA @ linorder )
| ~ ( TA @ number ) ) ),
inference(cnf,[status(esa)],[381]) ).
thf(384,plain,
! [TA: $tType,B: int,A: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ( B @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ linorder )
| ~ ( TA @ number ) ),
inference(cnfConj,[status(thm)],[382]) ).
thf(71417,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68176,183]) ).
thf(71418,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[71417]) ).
thf(71419,plain,
t @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[71418:[bind(A,$thf( t @ bit1 @ bit1 )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(404,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[403]) ).
thf(15,axiom,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_82_zero__zle__int) ).
thf(146,plain,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(147,plain,
! [A: nat] : ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ),
inference(cnf,[status(esa)],[146]) ).
thf(1130,plain,
! [A: nat] :
( ( ( nat @ one_one @ ( int @ semiring_1_of_nat ) )
!= ( A @ ( int @ semiring_1_of_nat ) ) )
| ( int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
inference(paramod_ordered,[status(thm)],[168,147]) ).
thf(1131,plain,
int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[1130:[bind(A,$thf( nat @ one_one ))]]) ).
thf(22606,plain,
! [A: int] :
( ( ( int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1131,277]) ).
thf(22607,plain,
! [A: int] :
( ( ( int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[22606]) ).
thf(22608,plain,
int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[22607:[bind(A,$thf( int @ one_one ))]]) ).
thf(23110,plain,
! [A: int] :
( ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22608,187]) ).
thf(23111,plain,
! [A: int] :
( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[23110]) ).
thf(23154,plain,
! [A: int] :
( ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[23111]) ).
thf(23184,plain,
( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[23154]) ).
thf(99,axiom,
! [A: int] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_54_rel__simps_I10_J) ).
thf(492,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(493,plain,
( ! [A: int] :
( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) ) )
& ! [A: int] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(miniscope,[status(thm)],[492]) ).
thf(494,plain,
! [B: int,A: int] :
( ( ( pls @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ ( pls @ ( B @ ( int @ ord_less ) ) ) )
& ( ( pls @ ( A @ ( int @ ord_less ) ) )
| ~ ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) ) ) ),
inference(cnf,[status(esa)],[493]) ).
thf(496,plain,
! [A: int] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) )
| ~ ( pls @ ( A @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[494]) ).
thf(497,plain,
! [A: int] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) )
| ~ ( pls @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[496]) ).
thf(60462,plain,
! [A: int] :
( ( int @ zero_zero @ ( A @ bit0 @ ( int @ ord_less ) ) )
| ~ ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) ) ),
inference(rewrite,[status(thm)],[497,35205]) ).
thf(35953,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35217,277]) ).
thf(35954,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[35953]) ).
thf(35955,plain,
int @ one_one @ bit1 @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[35954:[bind(A,$thf( int @ one_one @ bit1 ))]]) ).
thf(47066,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35955,187]) ).
thf(47067,plain,
! [A: int] :
( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[47066]) ).
thf(47127,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[47067]) ).
thf(47141,plain,
( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[47127]) ).
thf(53,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_30_rel__simps_I17_J) ).
thf(296,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(297,plain,
( ! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) )
& ! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(miniscope,[status(thm)],[296]) ).
thf(298,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( C @ bit1 @ ( D @ bit1 @ ( int @ ord_less ) ) )
| ~ ( C @ ( D @ ( int @ ord_less ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ) ),
inference(cnf,[status(esa)],[297]) ).
thf(300,plain,
! [B: int,A: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[298]) ).
thf(301,plain,
! [B: int,A: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[300]) ).
thf(28932,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28797,317]) ).
thf(28933,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[28932]) ).
thf(28934,plain,
n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ zero_zero @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[28933:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(44874,plain,
n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[28934,44870]) ).
thf(45142,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44874,166]) ).
thf(45143,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[45142]) ).
thf(45144,plain,
n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ one_one @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[45143:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) )),bind(B,$thf( int @ one_one ))]]) ).
thf(57434,plain,
n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[45144,33188]) ).
thf(62,axiom,
! [A: int,B: int] :
( ( ( B @ bit0 )
= ( A @ bit0 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_21_rel__simps_I48_J) ).
thf(337,plain,
! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ bit0 )
= ( A @ bit0 ) ) )
& ( ( ( B @ bit0 )
= ( A @ bit0 ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(338,plain,
( ! [A: int,B: int] :
( ( B = A )
=> ( ( B @ bit0 )
= ( A @ bit0 ) ) )
& ! [A: int,B: int] :
( ( ( B @ bit0 )
= ( A @ bit0 ) )
=> ( B = A ) ) ),
inference(miniscope,[status(thm)],[337]) ).
thf(339,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( ( D @ bit0 )
= ( C @ bit0 ) )
| ( D != C ) )
& ( ( B = A )
| ( ( B @ bit0 )
!= ( A @ bit0 ) ) ) ),
inference(cnf,[status(esa)],[338]) ).
thf(340,plain,
! [B: int,A: int] :
( ( B = A )
| ( ( B @ bit0 )
!= ( A @ bit0 ) ) ),
inference(cnfConj,[status(thm)],[339]) ).
thf(342,plain,
! [B: int,A: int] :
( ( B = A )
| ( ( B @ bit0 )
!= ( A @ bit0 ) ) ),
inference(lifteq,[status(thm)],[340]) ).
thf(343,plain,
? [A: int > int] :
! [B: int] :
( ( B @ bit0 @ A )
= B ),
inference(detectInverse,[status(thm)],[342]) ).
thf(344,plain,
! [A: int] :
( ( A @ bit0 @ sk2 )
= A ),
inference(cnf,[status(esa)],[343]) ).
thf(33068,plain,
! [A: int] :
( ( A @ bit0 @ sk2 )
= A ),
inference(lifteq,[status(thm)],[344]) ).
thf(60,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_65_rel__simps_I33_J) ).
thf(325,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(326,plain,
( ! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(miniscope,[status(thm)],[325]) ).
thf(327,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( C @ bit0 @ ( D @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ ( C @ ( D @ ( int @ ord_less ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ) ),
inference(cnf,[status(esa)],[326]) ).
thf(329,plain,
! [B: int,A: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[327]) ).
thf(330,plain,
! [B: int,A: int] :
( ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[329]) ).
thf(30225,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18143,330]) ).
thf(30226,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[30225]) ).
thf(30227,plain,
int @ one_one @ bit1 @ bit0 @ ( pls @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[30226:[bind(A,$thf( int @ one_one @ bit1 )),bind(B,$thf( pls ))]]) ).
thf(38747,plain,
int @ one_one @ bit1 @ bit0 @ ( int @ zero_zero @ bit1 @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[30227,35205]) ).
thf(82,axiom,
! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_93_zless__imp__add1__zle) ).
thf(436,plain,
! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(3856,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1872,166]) ).
thf(3857,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[3856]) ).
thf(3858,plain,
pls @ bit1 @ bit0 @ ( pls @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[3857:[bind(A,$thf( pls @ bit1 )),bind(B,$thf( pls ))]]) ).
thf(4124,plain,
pls @ bit1 @ bit0 @ ( pls @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[3858,238]) ).
thf(4128,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4124,153]) ).
thf(4129,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[4128]) ).
thf(4130,plain,
pls @ bit1 @ bit0 @ bit1 @ ( pls @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[4129:[bind(A,$thf( pls @ bit1 @ bit0 )),bind(B,$thf( pls ))]]) ).
thf(12660,plain,
pls @ bit1 @ bit0 @ bit1 @ ( pls @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[4130,238]) ).
thf(18145,plain,
int @ one_one @ bit0 @ bit1 @ ( pls @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[12660,18097]) ).
thf(33214,plain,
int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 @ ( pls @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[18145,33188]) ).
thf(40987,plain,
int @ one_one @ bit0 @ ( int @ one_one @ bit1 @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[33214,35205,175]) ).
thf(43115,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42813,138]) ).
thf(43116,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[43115]) ).
thf(43117,plain,
t @ bit0 @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[43116:[bind(A,$thf( t @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(18160,plain,
int @ one_one @ ( pls @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[2588,18097]) ).
thf(19123,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18160,244]) ).
thf(19124,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[19123]) ).
thf(19125,plain,
int @ one_one @ bit0 @ ( pls @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[19124:[bind(A,$thf( int @ one_one )),bind(B,$thf( pls ))]]) ).
thf(22348,plain,
int @ one_one @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[19125,18097]) ).
thf(31705,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22348,336]) ).
thf(31706,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[31705]) ).
thf(31707,plain,
int @ one_one @ ( int @ one_one @ bit0 @ ( int @ minus_minus ) ) @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[31706:[bind(A,$thf( int @ one_one @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(39788,plain,
int @ one_one @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ minus_minus ) ) @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[31707,33188]) ).
thf(50055,plain,
( ( ( t @ bit1 @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49918,26026]) ).
thf(50056,plain,
( ( t @ bit1 @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[50055]) ).
thf(50063,plain,
( ( ( t @ bit1 @ bit1 )
!= ( int @ one_one ) )
| ( ( int @ one_one )
!= ( int @ one_one ) ) ),
inference(simp,[status(thm)],[50056]) ).
thf(50085,plain,
( ( t @ bit1 @ bit1 )
!= ( int @ one_one ) ),
inference(simp,[status(thm)],[50063]) ).
thf(50089,plain,
( ( ( t @ bit1 @ bit1 )
!= ( int @ zero_zero @ bit1 ) )
| ( ( int @ one_one )
!= ( int @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[35218,50085]) ).
thf(50090,plain,
( ( t @ bit1 @ bit1 )
!= ( int @ zero_zero @ bit1 ) ),
inference(simp,[status(thm)],[50089]) ).
thf(50109,plain,
( ( t @ bit1 )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[50090]) ).
thf(24480,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18141,301]) ).
thf(24481,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[24480]) ).
thf(24482,plain,
int @ one_one @ bit0 @ bit1 @ ( pls @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[24481:[bind(A,$thf( int @ one_one @ bit0 )),bind(B,$thf( pls ))]]) ).
thf(31501,plain,
int @ one_one @ bit0 @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[24482,18097]) ).
thf(31589,plain,
( ( ( int @ one_one @ bit0 @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31501,26026]) ).
thf(31590,plain,
( ( int @ one_one @ bit0 @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[31589]) ).
thf(31599,plain,
( ( ( int @ one_one @ bit0 @ bit1 )
!= ( int @ one_one ) )
| ( ( int @ one_one )
!= ( int @ one_one ) ) ),
inference(simp,[status(thm)],[31590]) ).
thf(31632,plain,
( ( int @ one_one @ bit0 @ bit1 )
!= ( int @ one_one ) ),
inference(simp,[status(thm)],[31599]) ).
thf(33197,plain,
( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 )
!= ( int @ one_one ) ),
inference(rewrite,[status(thm)],[31632,33188]) ).
thf(33568,plain,
( ( int @ one_one @ bit0 @ ( int @ one_one @ bit1 @ ( int @ plus_plus ) ) )
!= ( int @ one_one ) ),
inference(rewrite,[status(thm)],[33197,175]) ).
thf(98,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_62_diff__bin__simps_I10_J) ).
thf(489,plain,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(490,plain,
! [B: int,A: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(cnf,[status(esa)],[489]) ).
thf(491,plain,
! [B: int,A: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(lifteq,[status(thm)],[490]) ).
thf(78,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_39_diff__bin__simps_I7_J) ).
thf(419,plain,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(420,plain,
! [B: int,A: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ minus_minus ) ) )
= ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(cnf,[status(esa)],[419]) ).
thf(421,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ minus_minus ) ) @ bit0 )
= ( A @ bit0 @ ( B @ bit0 @ ( int @ minus_minus ) ) ) ),
inference(lifteq,[status(thm)],[420]) ).
thf(59259,plain,
! [B: int,A: int] :
( ( A @ bit1 @ ( B @ bit1 @ ( int @ minus_minus ) ) )
= ( A @ bit0 @ ( B @ bit0 @ ( int @ minus_minus ) ) ) ),
inference(rewrite,[status(thm)],[491,421]) ).
thf(1944,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1872,138]) ).
thf(1945,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[1944]) ).
thf(1946,plain,
pls @ bit1 @ bit1 @ ( pls @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[1945:[bind(A,$thf( pls @ bit1 )),bind(B,$thf( pls ))]]) ).
thf(18132,plain,
int @ one_one @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[1946,18097]) ).
thf(19295,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18132,153]) ).
thf(19296,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[19295]) ).
thf(19297,plain,
int @ one_one @ bit1 @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[19296:[bind(A,$thf( int @ one_one @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(26883,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19297,183]) ).
thf(26884,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[26883]) ).
thf(26885,plain,
int @ one_one @ bit1 @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[26884:[bind(A,$thf( int @ one_one @ bit1 @ bit1 )),bind(B,$thf( int @ one_one @ bit0 ))]]) ).
thf(34896,plain,
int @ one_one @ bit1 @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[26885,33188]) ).
thf(3936,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1448,166]) ).
thf(3937,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[3936]) ).
thf(3938,plain,
t @ bit1 @ bit0 @ ( int @ one_one @ bit1 @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[3937:[bind(A,$thf( t @ bit1 )),bind(B,$thf( int @ one_one @ bit1 ))]]) ).
thf(43149,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42813,166]) ).
thf(43150,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[43149]) ).
thf(43151,plain,
t @ bit0 @ bit0 @ ( int @ one_one @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[43150:[bind(A,$thf( t @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(53359,plain,
t @ bit0 @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[43151,33188]) ).
thf(53447,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( B @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[53359,315]) ).
thf(53448,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[53447]) ).
thf(53449,plain,
t @ bit0 @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[53448:[bind(A,$thf( t @ bit0 @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(33077,plain,
! [A: int] :
( ( ( pls @ bit0 )
!= ( A @ bit0 ) )
| ( ( pls @ sk2 )
= A ) ),
inference(paramod_ordered,[status(thm)],[238,33068]) ).
thf(33078,plain,
( ( pls @ sk2 )
= pls ),
inference(pattern_uni,[status(thm)],[33077:[bind(A,$thf( pls ))]]) ).
thf(35229,plain,
( ( int @ zero_zero @ sk2 )
= ( int @ zero_zero ) ),
inference(rewrite,[status(thm)],[33078,35205]) ).
thf(44,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
<=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_10_less__special_I1_J) ).
thf(262,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(263,plain,
! [TA: $tType,A: int] :
( ( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( A @ ( pls @ ( int @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) )
& ( ( A @ ( pls @ ( int @ ord_less ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ) ),
inference(cnf,[status(esa)],[262]) ).
thf(264,plain,
! [TA: $tType,A: int] :
( ( A @ ( pls @ ( int @ ord_less ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[263]) ).
thf(21483,plain,
! [TA: $tType,B: int,A: int] :
( ( ( A @ ( pls @ ( int @ ord_less ) ) )
!= ( B @ ( B @ ( int @ ord_less ) ) ) )
| ~ $true
| ~ ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(paramod_ordered,[status(thm)],[264,187]) ).
thf(21484,plain,
! [TA: $tType,B: int,A: int] :
( ( ( A @ ( pls @ ( int @ ord_less ) ) )
!= ( B @ ( B @ ( int @ ord_less ) ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(simp,[status(thm)],[21483]) ).
thf(21485,plain,
! [TA: $tType] :
( ~ ( pls @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(pattern_uni,[status(thm)],[21484:[bind(A,$thf( pls )),bind(B,$thf( pls ))]]) ).
thf(32207,plain,
! [TA: $tType] :
( ( ( int @ linordered_idom )
!= ( TA @ linordered_idom ) )
| ~ ( pls @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ $true
| ~ ( TA @ number_ring ) ),
inference(paramod_ordered,[status(thm)],[219,21485]) ).
thf(32208,plain,
! [TA: $tType] :
( ( ( int @ linordered_idom )
!= ( TA @ linordered_idom ) )
| ~ ( pls @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( TA @ number_ring ) ),
inference(simp,[status(thm)],[32207]) ).
thf(32209,plain,
( ~ ( pls @ ( int @ number_number_of ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ ( int @ number_ring ) ),
inference(pattern_uni,[status(thm)],[32208:[bind_type(TA,$thf( int ))]]) ).
thf(32711,plain,
( ~ ( pls @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(rewrite,[status(thm)],[32209,139,255]) ).
thf(32712,plain,
~ ( pls @ ( int @ zero_zero @ ( int @ ord_less ) ) ),
inference(simp,[status(thm)],[32711]) ).
thf(32761,plain,
( ( ( int @ one_one @ bit0 @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( pls @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18145,32712]) ).
thf(32762,plain,
( ( int @ one_one @ bit0 @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( pls @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[32761]) ).
thf(32845,plain,
( ( ( int @ one_one @ bit0 @ bit1 )
!= pls )
| ( pls
!= ( int @ zero_zero ) ) ),
inference(simp,[status(thm)],[32762]) ).
thf(59200,plain,
( ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 )
!= ( int @ zero_zero ) )
| ( ( int @ zero_zero )
!= ( int @ zero_zero ) ) ),
inference(rewrite,[status(thm)],[32845,33188,35205]) ).
thf(59201,plain,
( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[59200]) ).
thf(501,plain,
! [TA: $tType,B: int,A: int] :
( ( ( ( B @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) ) )
| ( B != A )
| ~ ( TA @ ring_char_0 )
| ~ ( TA @ number_ring ) )
& ( ( B = A )
| ( ( B @ ( TA @ number_number_of ) )
!= ( A @ ( TA @ number_number_of ) ) )
| ~ ( TA @ ring_char_0 )
| ~ ( TA @ number_ring ) ) ),
inference(cnf,[status(esa)],[500]) ).
thf(502,plain,
! [TA: $tType,B: int,A: int] :
( ( B = A )
| ( ( B @ ( TA @ number_number_of ) )
!= ( A @ ( TA @ number_number_of ) ) )
| ~ ( TA @ ring_char_0 )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[501]) ).
thf(504,plain,
! [TA: $tType,B: int,A: int] :
( ~ ( TA @ ring_char_0 )
| ~ ( TA @ number_ring )
| ( B = A )
| ( ( B @ ( TA @ number_number_of ) )
!= ( A @ ( TA @ number_number_of ) ) ) ),
inference(lifteq,[status(thm)],[502]) ).
thf(2406,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[302,153]) ).
thf(2407,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[2406]) ).
thf(2408,plain,
t @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[2407:[bind(A,$thf( t )),bind(B,$thf( int @ one_one ))]]) ).
thf(33226,plain,
t @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[2408,33188]) ).
thf(88,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ ( A @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_6_add__special_I3_J) ).
thf(455,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ ( A @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(456,plain,
! [TA: $tType,A: int] :
( ( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( pls @ bit1 @ ( A @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) )
| ~ ( TA @ number_ring ) ),
inference(cnf,[status(esa)],[455]) ).
thf(457,plain,
! [TA: $tType,A: int] :
( ~ ( TA @ number_ring )
| ( ( pls @ bit1 @ ( A @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) )
= ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
inference(lifteq,[status(thm)],[456]) ).
thf(51122,plain,
! [TA: $tType,A: int] :
( ~ ( TA @ number_ring )
| ( ( int @ zero_zero @ bit1 @ ( A @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) )
= ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
inference(rewrite,[status(thm)],[457,35205]) ).
thf(122,plain,
! [C: nat,B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ( A
!= ( C @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) ) ) ),
inference(cnfConj,[status(thm)],[120]) ).
thf(124,plain,
! [C: nat,B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ( A
!= ( C @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) ) ) ),
inference(lifteq,[status(thm)],[122]) ).
thf(125,plain,
! [B: nat,A: int] : ( B @ ( int @ semiring_1_of_nat ) @ ( A @ ( int @ plus_plus ) ) @ ( A @ ( int @ ord_less_eq ) ) ),
inference(simp,[status(thm)],[124]) ).
thf(4541,plain,
! [A: int] :
( ( ( int @ zero_zero @ bit1 @ bit0 @ ( int @ zero_zero @ bit0 @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3125,187]) ).
thf(4542,plain,
! [A: int] :
( ( int @ zero_zero @ bit1 @ bit0 @ ( int @ zero_zero @ bit0 @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[4541]) ).
thf(4576,plain,
! [A: int] :
( ( ( int @ zero_zero @ bit1 @ bit0 )
!= A )
| ( ( int @ zero_zero @ bit0 @ bit0 )
!= A ) ),
inference(simp,[status(thm)],[4542]) ).
thf(4597,plain,
( ( int @ zero_zero @ bit1 @ bit0 )
!= ( int @ zero_zero @ bit0 @ bit0 ) ),
inference(simp,[status(thm)],[4576]) ).
thf(35301,plain,
( ( int @ zero_zero @ bit1 @ bit0 )
!= ( int @ zero_zero @ bit0 ) ),
inference(rewrite,[status(thm)],[4597,35216]) ).
thf(37173,plain,
( ( int @ one_one @ bit0 )
!= ( int @ zero_zero ) ),
inference(rewrite,[status(thm)],[35301,35216,35218]) ).
thf(157,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[156]) ).
thf(185,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
| ( B = A )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[182]) ).
thf(188,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ( B = A ) ),
inference(lifteq,[status(thm)],[185]) ).
thf(189,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ( B = A ) ),
inference(simp,[status(thm)],[188]) ).
thf(7976,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( B @ ( int @ ord_less ) ) )
| ~ $true
| ( B = A ) ),
inference(paramod_ordered,[status(thm)],[1131,189]) ).
thf(7977,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( B @ ( int @ ord_less ) ) )
| ( B = A ) ),
inference(simp,[status(thm)],[7976]) ).
thf(7978,plain,
( ( int @ one_one @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ( ( int @ zero_zero )
= ( int @ one_one ) ) ),
inference(pattern_uni,[status(thm)],[7977:[bind(A,$thf( int @ one_one )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(23221,plain,
( ( ( int @ zero_zero @ ( int @ zero_zero @ ( int @ plus_plus ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) )
| ( ( int @ zero_zero )
!= ( int @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[13461,23184]) ).
thf(23222,plain,
( ( int @ zero_zero @ ( int @ zero_zero @ ( int @ plus_plus ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[23221]) ).
thf(23228,plain,
( ( ( int @ zero_zero )
!= ( int @ one_one ) )
| ( ( int @ zero_zero )
!= ( int @ one_one ) ) ),
inference(simp,[status(thm)],[23222]) ).
thf(23247,plain,
( ( int @ zero_zero )
!= ( int @ one_one ) ),
inference(simp,[status(thm)],[23228]) ).
thf(23250,plain,
int @ one_one @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(simplifyReflect,[status(thm)],[7978,23247]) ).
thf(31753,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[23250,336]) ).
thf(31754,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[31753]) ).
thf(31755,plain,
int @ one_one @ ( int @ one_one @ ( int @ minus_minus ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[31754:[bind(A,$thf( int @ one_one )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(90,axiom,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_64_rel__simps_I5_J) ).
thf(464,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) ) )
& ( ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(465,plain,
( ! [A: int] :
( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) ) )
& ! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(miniscope,[status(thm)],[464]) ).
thf(466,plain,
! [B: int,A: int] :
( ( ( B @ bit1 @ ( pls @ ( int @ ord_less ) ) )
| ~ ( B @ ( pls @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) ) ) ),
inference(cnf,[status(esa)],[465]) ).
thf(468,plain,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) )
| ~ ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[466]) ).
thf(469,plain,
! [A: int] :
( ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) )
| ~ ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[468]) ).
thf(53815,plain,
! [A: int] :
( ( A @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
inference(rewrite,[status(thm)],[469,35205]) ).
thf(54003,plain,
! [A: int] :
( ( ( int @ one_one @ ( int @ one_one @ ( int @ minus_minus ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31755,53815]) ).
thf(54004,plain,
! [A: int] :
( ( ( int @ one_one @ ( int @ one_one @ ( int @ minus_minus ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[54003]) ).
thf(54005,plain,
int @ one_one @ ( int @ one_one @ ( int @ minus_minus ) ) @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[54004:[bind(A,$thf( int @ one_one @ ( int @ one_one @ ( int @ minus_minus ) ) ))]]) ).
thf(59639,plain,
int @ one_one @ bit0 @ ( int @ one_one @ bit1 @ ( int @ minus_minus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[54005,481]) ).
thf(59707,plain,
! [A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ one_one @ bit1 @ ( int @ minus_minus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[59639,187]) ).
thf(59708,plain,
! [A: int] :
( ( int @ one_one @ bit0 @ ( int @ one_one @ bit1 @ ( int @ minus_minus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[59707]) ).
thf(59769,plain,
! [A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ one_one @ bit1 @ ( int @ minus_minus ) ) )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[59708]) ).
thf(59791,plain,
( ( int @ one_one @ bit0 @ ( int @ one_one @ bit1 @ ( int @ minus_minus ) ) )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[59769]) ).
thf(61429,plain,
( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ bit1 @ ( int @ minus_minus ) ) )
!= ( int @ zero_zero ) ),
inference(rewrite,[status(thm)],[59791,33188]) ).
thf(24477,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18160,301]) ).
thf(24478,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[24477]) ).
thf(24479,plain,
int @ one_one @ bit1 @ ( pls @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[24478:[bind(A,$thf( int @ one_one )),bind(B,$thf( pls ))]]) ).
thf(24825,plain,
int @ one_one @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[24479,18097]) ).
thf(24869,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24825,244]) ).
thf(24870,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[24869]) ).
thf(24871,plain,
int @ one_one @ bit1 @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[24870:[bind(A,$thf( int @ one_one @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(18162,plain,
int @ one_one @ bit1 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[1980,18097]) ).
thf(35261,plain,
int @ one_one @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[18162,35205]) ).
thf(43152,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42813,406]) ).
thf(43153,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[43152]) ).
thf(43154,plain,
t @ bit0 @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[43153:[bind(A,$thf( t @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(54498,plain,
t @ bit0 @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[43154,33188]) ).
thf(54587,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( B @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54498,315]) ).
thf(54588,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[54587]) ).
thf(54589,plain,
t @ bit0 @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[54588:[bind(A,$thf( t @ bit0 @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(54737,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54589,183]) ).
thf(54738,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[54737]) ).
thf(54739,plain,
t @ bit0 @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[54738:[bind(A,$thf( t @ bit0 @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(68129,plain,
! [A: int] :
( ( ( t @ bit0 @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54739,510]) ).
thf(68130,plain,
! [A: int] :
( ( ( t @ bit0 @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[68129]) ).
thf(68131,plain,
t @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[68130:[bind(A,$thf( t @ bit0 @ bit1 ))]]) ).
thf(70552,plain,
! [A: int] :
( ( ( t @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68131,187]) ).
thf(70553,plain,
! [A: int] :
( ( t @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[70552]) ).
thf(70616,plain,
! [A: int] :
( ( ( t @ bit0 @ bit1 )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[70553]) ).
thf(70631,plain,
( ( t @ bit0 @ bit1 )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[70616]) ).
thf(12715,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit0 @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[12660,187]) ).
thf(12716,plain,
! [A: int] :
( ( pls @ bit1 @ bit0 @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[12715]) ).
thf(12752,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit0 @ bit1 )
!= A )
| ( pls != A ) ),
inference(simp,[status(thm)],[12716]) ).
thf(12786,plain,
( ( pls @ bit1 @ bit0 @ bit1 )
!= pls ),
inference(simp,[status(thm)],[12752]) ).
thf(18167,plain,
( ( int @ one_one @ bit0 @ bit1 )
!= pls ),
inference(rewrite,[status(thm)],[12786,18097]) ).
thf(33231,plain,
( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 )
!= pls ),
inference(rewrite,[status(thm)],[18167,33188]) ).
thf(34495,plain,
( ( int @ one_one @ bit0 @ ( int @ one_one @ bit1 @ ( int @ plus_plus ) ) )
!= pls ),
inference(rewrite,[status(thm)],[33231,175]) ).
thf(34532,plain,
! [B: int,A: int] :
( ( ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) )
!= ( int @ one_one @ bit0 @ ( int @ one_one @ bit1 @ ( int @ plus_plus ) ) ) )
| ( ( A @ bit1 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
!= pls ) ),
inference(paramod_ordered,[status(thm)],[12219,34495]) ).
thf(34533,plain,
( ( int @ one_one @ bit1 @ ( int @ one_one @ bit0 @ ( int @ plus_plus ) ) )
!= pls ),
inference(pattern_uni,[status(thm)],[34532:[bind(A,$thf( int @ one_one )),bind(B,$thf( int @ one_one ))]]) ).
thf(43620,plain,
( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
inference(rewrite,[status(thm)],[34533,33188,35205]) ).
thf(39375,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39326,138]) ).
thf(39376,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[39375]) ).
thf(39377,plain,
t @ bit1 @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[39376:[bind(A,$thf( t @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(49268,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( B @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49183,315]) ).
thf(49269,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( B @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( B @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[49268]) ).
thf(49270,plain,
t @ bit1 @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[49269:[bind(A,$thf( t @ bit1 @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(49404,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49270,183]) ).
thf(49405,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[49404]) ).
thf(49406,plain,
t @ bit1 @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[49405:[bind(A,$thf( t @ bit1 @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(33206,plain,
int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[22348,33188]) ).
thf(3144,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2909,159]) ).
thf(3145,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[3144]) ).
thf(3146,plain,
pls @ bit1 @ bit1 @ bit0 @ ( pls @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[3145:[bind(A,$thf( pls @ bit1 @ bit1 )),bind(B,$thf( pls ))]]) ).
thf(4854,plain,
pls @ bit1 @ bit1 @ bit0 @ ( pls @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[3146,238]) ).
thf(18151,plain,
int @ one_one @ bit1 @ bit0 @ ( pls @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[4854,18097]) ).
thf(35225,plain,
int @ one_one @ bit1 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[18151,35205]) ).
thf(40567,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35225,40526]) ).
thf(40568,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[40567]) ).
thf(40569,plain,
int @ one_one @ bit1 @ bit0 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[40568:[bind(A,$thf( int @ one_one @ bit1 @ bit0 ))]]) ).
thf(53881,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35261,53815]) ).
thf(53882,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[53881]) ).
thf(53883,plain,
int @ one_one @ bit1 @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[53882:[bind(A,$thf( int @ one_one @ bit1 @ bit1 ))]]) ).
thf(59553,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[53883,187]) ).
thf(59554,plain,
! [A: int] :
( ( int @ one_one @ bit1 @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[59553]) ).
thf(59601,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit1 @ bit1 )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[59554]) ).
thf(59629,plain,
( ( int @ one_one @ bit1 @ bit1 @ bit1 )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[59601]) ).
thf(93,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_11_less__special_I3_J) ).
thf(475,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(33640,plain,
( ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( m1 @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( int @ ord_less ) ) ) )
| ( n
!= ( nat @ one_one ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[33206,614]) ).
thf(33641,plain,
( ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( m1 @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( int @ ord_less ) ) ) )
| ( n
!= ( nat @ one_one ) ) ),
inference(simp,[status(thm)],[33640]) ).
thf(33762,plain,
( ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) )
| ( m1
!= ( int @ one_one ) )
| ( n
!= ( nat @ one_one ) ) ),
inference(simp,[status(thm)],[33641]) ).
thf(33786,plain,
( ( m1
!= ( int @ one_one ) )
| ( n
!= ( nat @ one_one ) ) ),
inference(simp,[status(thm)],[33762]) ).
thf(321,plain,
! [A: nat] :
( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ~ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[320]) ).
thf(96,axiom,
int @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Osemiring) ).
thf(485,plain,
int @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(1149,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ~ $true
| ( ( A @ ( B @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[1131,123]) ).
thf(1150,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( ( A @ ( B @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) )
= A ) ),
inference(simp,[status(thm)],[1149]) ).
thf(1151,plain,
( ( int @ one_one @ ( int @ zero_zero @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ plus_plus ) ) )
= ( int @ one_one ) ),
inference(pattern_uni,[status(thm)],[1150:[bind(A,$thf( int @ one_one )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(24339,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[18143,301]) ).
thf(24340,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[24339]) ).
thf(24341,plain,
int @ one_one @ bit1 @ bit1 @ ( pls @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[24340:[bind(A,$thf( int @ one_one @ bit1 )),bind(B,$thf( pls ))]]) ).
thf(30708,plain,
int @ one_one @ bit1 @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[24341,18097]) ).
thf(30770,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[30708,187]) ).
thf(30771,plain,
! [A: int] :
( ( int @ one_one @ bit1 @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[30770]) ).
thf(30818,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit1 )
!= A )
| ( ( int @ one_one )
!= A ) ),
inference(simp,[status(thm)],[30771]) ).
thf(30838,plain,
( ( int @ one_one @ bit1 @ bit1 )
!= ( int @ one_one ) ),
inference(simp,[status(thm)],[30818]) ).
thf(32,axiom,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_44_left__diff__distrib__number__of) ).
thf(216,plain,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(164,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[163]) ).
thf(49,axiom,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_36_mult__Pls) ).
thf(279,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(280,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(cnf,[status(esa)],[279]) ).
thf(281,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ times_times ) ) )
= pls ),
inference(lifteq,[status(thm)],[280]) ).
thf(1,conjecture,
int @ zero_zero @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( int @ zero_zero @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( int @ ord_less ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(113,plain,
~ ( int @ zero_zero @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(1183,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ times_times ) ) )
!= ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) ) )
| ~ ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) ) ),
inference(paramod_ordered,[status(thm)],[281,113]) ).
thf(1198,plain,
! [A: int] :
( ( A
!= ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) ) )
| ( pls
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) )
| ~ ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[1183]) ).
thf(1239,plain,
( ( pls
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) )
| ~ ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[1198]) ).
thf(2616,plain,
( ( ( pls @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) ) )
| ( pls
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2588,1239]) ).
thf(2617,plain,
( ( ( pls @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) ) )
| ( pls
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) ) ),
inference(simp,[status(thm)],[2616]) ).
thf(2644,plain,
( ( ( pls @ bit1 )
!= ( int @ zero_zero ) )
| ( pls != pls )
| ( pls
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) ) ),
inference(simp,[status(thm)],[2617]) ).
thf(2661,plain,
( ( ( pls @ bit1 )
!= ( int @ zero_zero ) )
| ( pls
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) ) ),
inference(simp,[status(thm)],[2644]) ).
thf(18159,plain,
( ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( pls
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) ) ),
inference(rewrite,[status(thm)],[2661,18097]) ).
thf(18545,plain,
( ( ( int @ zero_zero @ ( int @ zero_zero @ ( int @ plus_plus ) ) )
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( pls
!= ( int @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[13461,18159]) ).
thf(18556,plain,
( ( ( n @ ( int @ semiring_1_of_nat ) )
!= ( int @ zero_zero ) )
| ( ( int @ zero_zero )
!= ( int @ one_one ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( pls
!= ( int @ zero_zero ) ) ),
inference(simp,[status(thm)],[18545]) ).
thf(18583,plain,
( ( ( n @ ( int @ semiring_1_of_nat ) )
!= ( int @ zero_zero ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( pls
!= ( int @ zero_zero ) ) ),
inference(simp,[status(thm)],[18556]) ).
thf(18609,plain,
( ( ( n @ ( int @ semiring_1_of_nat ) )
!= ( nat @ one_one @ ( int @ semiring_1_of_nat ) ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( pls
!= ( int @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[168,18583]) ).
thf(18610,plain,
( ( ( n @ ( int @ semiring_1_of_nat ) )
!= ( nat @ one_one @ ( int @ semiring_1_of_nat ) ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( pls
!= ( int @ zero_zero ) ) ),
inference(simp,[status(thm)],[18609]) ).
thf(18613,plain,
( ( n
!= ( nat @ one_one ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( pls
!= ( int @ zero_zero ) ) ),
inference(simp,[status(thm)],[18610]) ).
thf(18950,plain,
! [B: int,A: int] :
( ( B
!= ( int @ one_one ) )
| ( n
!= ( nat @ one_one ) )
| ( A
!= ( int @ zero_zero ) )
| ( pls
!= ( int @ zero_zero ) )
| ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(paramod_ordered,[status(thm)],[189,18613]) ).
thf(18951,plain,
! [A: int] :
( ( n
!= ( nat @ one_one ) )
| ( A
!= ( int @ zero_zero ) )
| ( pls
!= ( int @ zero_zero ) )
| ( A @ ( int @ one_one @ ( int @ ord_less ) ) )
| ~ ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) ),
inference(pattern_uni,[status(thm)],[18950:[bind(A,$thf( A )),bind(B,$thf( int @ one_one ))]]) ).
thf(18969,plain,
( ( n
!= ( nat @ one_one ) )
| ( pls
!= ( int @ zero_zero ) )
| ( int @ zero_zero @ ( int @ one_one @ ( int @ ord_less ) ) )
| ~ ( int @ zero_zero @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[18951]) ).
thf(50840,plain,
( ( n
!= ( nat @ one_one ) )
| ( ( int @ zero_zero )
!= ( int @ zero_zero ) )
| ( int @ zero_zero @ ( int @ one_one @ ( int @ ord_less ) ) )
| ~ ( int @ zero_zero @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) ),
inference(rewrite,[status(thm)],[18969,35205]) ).
thf(50841,plain,
( ( n
!= ( nat @ one_one ) )
| ( int @ zero_zero @ ( int @ one_one @ ( int @ ord_less ) ) )
| ~ ( int @ zero_zero @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[50840]) ).
thf(64,axiom,
! [A: int,B: int] :
( ( A @ ( B @ bit0 @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_37_mult__Bit0) ).
thf(353,plain,
! [A: int,B: int] :
( ( A @ ( B @ bit0 @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(28937,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28797,244]) ).
thf(28938,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[28937]) ).
thf(28939,plain,
n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ zero_zero @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[28938:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(37937,plain,
n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[28939,35218]) ).
thf(52,axiom,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_42_right__distrib__number__of) ).
thf(293,plain,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(87,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_46_less__number__of) ).
thf(451,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(452,plain,
! [TA: $tType,B: int,A: int] :
( ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) )
& ( ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ) ),
inference(cnf,[status(esa)],[451]) ).
thf(453,plain,
! [TA: $tType,B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[452]) ).
thf(11,axiom,
! [A: nat,B: int,C: int] :
( ( B @ ( C @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ times_times ) ) @ ( C @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ times_times ) ) @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_79_zmult__zless__mono2__lemma) ).
thf(131,plain,
! [A: nat,B: int,C: int] :
( ( B @ ( C @ ( int @ ord_less ) ) )
=> ( ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
=> ( B @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ times_times ) ) @ ( C @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ times_times ) ) @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(132,plain,
! [C: int,B: int,A: nat] :
( ( B @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ times_times ) ) @ ( C @ ( A @ ( int @ semiring_1_of_nat ) @ ( int @ times_times ) ) @ ( int @ ord_less ) ) )
| ~ ( A @ ( nat @ zero_zero @ ( nat @ ord_less ) ) )
| ~ ( B @ ( C @ ( int @ ord_less ) ) ) ),
inference(cnf,[status(esa)],[131]) ).
thf(74,axiom,
! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_20_rel__simps_I51_J) ).
thf(391,plain,
! [A: int,B: int] :
( ( ( B = A )
=> ( ( B @ bit1 )
= ( A @ bit1 ) ) )
& ( ( ( B @ bit1 )
= ( A @ bit1 ) )
=> ( B = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(392,plain,
( ! [A: int,B: int] :
( ( B = A )
=> ( ( B @ bit1 )
= ( A @ bit1 ) ) )
& ! [A: int,B: int] :
( ( ( B @ bit1 )
= ( A @ bit1 ) )
=> ( B = A ) ) ),
inference(miniscope,[status(thm)],[391]) ).
thf(393,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( ( D @ bit1 )
= ( C @ bit1 ) )
| ( D != C ) )
& ( ( B = A )
| ( ( B @ bit1 )
!= ( A @ bit1 ) ) ) ),
inference(cnf,[status(esa)],[392]) ).
thf(394,plain,
! [B: int,A: int] :
( ( B = A )
| ( ( B @ bit1 )
!= ( A @ bit1 ) ) ),
inference(cnfConj,[status(thm)],[393]) ).
thf(396,plain,
! [B: int,A: int] :
( ( B = A )
| ( ( B @ bit1 )
!= ( A @ bit1 ) ) ),
inference(lifteq,[status(thm)],[394]) ).
thf(650,plain,
( ( ( t @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( m1 @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,275]) ).
thf(651,plain,
( ( t @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( m1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[650]) ).
thf(660,plain,
( ( t
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) )
| ( m1
!= ( int @ one_one ) ) ),
inference(simp,[status(thm)],[651]) ).
thf(5,axiom,
nat @ semiring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Rings_Osemiring) ).
thf(116,plain,
nat @ semiring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(3859,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1954,166]) ).
thf(3860,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[3859]) ).
thf(3861,plain,
pls @ bit1 @ bit1 @ bit0 @ ( pls @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[3860:[bind(A,$thf( pls @ bit1 @ bit1 )),bind(B,$thf( pls ))]]) ).
thf(5606,plain,
pls @ bit1 @ bit1 @ bit0 @ ( pls @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[3861,238]) ).
thf(18173,plain,
int @ one_one @ bit1 @ bit0 @ ( pls @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[5606,18097]) ).
thf(35248,plain,
int @ one_one @ bit1 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[18173,35205]) ).
thf(54027,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35248,53815]) ).
thf(54028,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[54027]) ).
thf(54029,plain,
int @ one_one @ bit1 @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[54028:[bind(A,$thf( int @ one_one @ bit1 @ bit0 ))]]) ).
thf(60137,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54029,187]) ).
thf(60138,plain,
! [A: int] :
( ( int @ one_one @ bit1 @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[60137]) ).
thf(60194,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit0 @ bit1 )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[60138]) ).
thf(60217,plain,
( ( int @ one_one @ bit1 @ bit0 @ bit1 )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[60194]) ).
thf(68054,plain,
! [A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42813,510]) ).
thf(68055,plain,
! [A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[68054]) ).
thf(68056,plain,
t @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[68055:[bind(A,$thf( t @ bit0 ))]]) ).
thf(28901,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28797,301]) ).
thf(28902,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[28901]) ).
thf(28903,plain,
n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ zero_zero @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[28902:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(37639,plain,
n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[28903,35218]) ).
thf(37709,plain,
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[37639,26026]) ).
thf(37710,plain,
( ( n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[37709]) ).
thf(37718,plain,
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit1 )
!= ( int @ one_one ) )
| ( ( int @ one_one )
!= ( int @ one_one ) ) ),
inference(simp,[status(thm)],[37710]) ).
thf(37733,plain,
( ( n @ ( int @ semiring_1_of_nat ) @ bit1 )
!= ( int @ one_one ) ),
inference(simp,[status(thm)],[37718]) ).
thf(84,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
<=> ( pls @ bit1 @ ( A @ ( int @ ord_less ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_8_less__special_I4_J) ).
thf(442,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( pls @ bit1 @ ( A @ ( int @ ord_less ) ) )
=> ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) ) )
& ( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
=> ( pls @ bit1 @ ( A @ ( int @ ord_less ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(443,plain,
! [TA: $tType,A: int] :
( ( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( pls @ bit1 @ ( A @ ( int @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) )
& ( ( pls @ bit1 @ ( A @ ( int @ ord_less ) ) )
| ~ ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ) ),
inference(cnf,[status(esa)],[442]) ).
thf(444,plain,
! [TA: $tType,A: int] :
( ( pls @ bit1 @ ( A @ ( int @ ord_less ) ) )
| ~ ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[443]) ).
thf(46481,plain,
! [TA: $tType,A: int] :
( ( int @ zero_zero @ bit1 @ ( A @ ( int @ ord_less ) ) )
| ~ ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(rewrite,[status(thm)],[444,35205]) ).
thf(108,axiom,
int @ ring_char_0,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Oring__char__0) ).
thf(527,plain,
int @ ring_char_0,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(42789,plain,
! [A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42704,187]) ).
thf(42790,plain,
! [A: int] :
( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[42789]) ).
thf(42827,plain,
! [A: int] :
( ( ( t @ bit0 )
!= A )
| ( ( int @ one_one )
!= A ) ),
inference(simp,[status(thm)],[42790]) ).
thf(42844,plain,
( ( t @ bit0 )
!= ( int @ one_one ) ),
inference(simp,[status(thm)],[42827]) ).
thf(68122,plain,
! [A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[302,510]) ).
thf(68123,plain,
! [A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[68122]) ).
thf(68124,plain,
t @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[68123:[bind(A,$thf( t ))]]) ).
thf(51,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_49_arith__simps_I32_J) ).
thf(290,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(291,plain,
! [TA: $tType,B: int,A: int] :
( ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) ) )
| ~ ( TA @ number_ring ) ),
inference(cnf,[status(esa)],[290]) ).
thf(292,plain,
! [TA: $tType,B: int,A: int] :
( ~ ( TA @ number_ring )
| ( ( A @ ( B @ ( int @ times_times ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(lifteq,[status(thm)],[291]) ).
thf(40,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_51_add__number__of__eq) ).
thf(246,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int,B: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(247,plain,
! [TA: $tType,B: int,A: int] :
( ( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) )
| ~ ( TA @ number_ring ) ),
inference(cnf,[status(esa)],[246]) ).
thf(248,plain,
! [TA: $tType,B: int,A: int] :
( ~ ( TA @ number_ring )
| ( ( A @ ( B @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
inference(lifteq,[status(thm)],[247]) ).
thf(511,plain,
! [A: int] :
( ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[509]) ).
thf(512,plain,
! [A: int] :
( ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[511]) ).
thf(1457,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[922,138]) ).
thf(1458,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[1457]) ).
thf(1459,plain,
int @ zero_zero @ bit1 @ ( int @ zero_zero @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[1458:[bind(A,$thf( int @ zero_zero )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(2454,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ bit1 @ ( int @ zero_zero @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1459,153]) ).
thf(2455,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ bit1 @ ( int @ zero_zero @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[2454]) ).
thf(2456,plain,
int @ zero_zero @ bit1 @ bit1 @ ( int @ zero_zero @ bit1 @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[2455:[bind(A,$thf( int @ zero_zero @ bit1 )),bind(B,$thf( int @ zero_zero @ bit1 ))]]) ).
thf(6146,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ bit1 @ bit1 @ ( int @ zero_zero @ bit1 @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2456,183]) ).
thf(6147,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ bit1 @ bit1 @ ( int @ zero_zero @ bit1 @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[6146]) ).
thf(6148,plain,
int @ zero_zero @ bit1 @ bit1 @ ( int @ zero_zero @ bit1 @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[6147:[bind(A,$thf( int @ zero_zero @ bit1 @ bit1 )),bind(B,$thf( int @ zero_zero @ bit1 @ bit0 ))]]) ).
thf(35427,plain,
int @ one_one @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[6148,35218]) ).
thf(37192,plain,
int @ one_one @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[35427,33188]) ).
thf(925,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ~ $true
| ( ( A @ ( B @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) )
= A ) ),
inference(paramod_ordered,[status(thm)],[922,123]) ).
thf(926,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( ( A @ ( B @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) )
= A ) ),
inference(simp,[status(thm)],[925]) ).
thf(927,plain,
( ( int @ zero_zero @ ( int @ zero_zero @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ plus_plus ) ) )
= ( int @ zero_zero ) ),
inference(pattern_uni,[status(thm)],[926:[bind(A,$thf( int @ zero_zero )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(35235,plain,
( ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( ( int @ zero_zero )
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) ) ),
inference(rewrite,[status(thm)],[18159,35205]) ).
thf(35691,plain,
( ( ( int @ zero_zero @ ( int @ zero_zero @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ plus_plus ) ) )
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( ( int @ zero_zero )
!= ( int @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[927,35235]) ).
thf(35692,plain,
( ( ( int @ zero_zero @ ( int @ zero_zero @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ plus_plus ) ) )
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) ) ),
inference(simp,[status(thm)],[35691]) ).
thf(35707,plain,
( ( ( int @ zero_zero @ ( int @ zero_zero @ sk1 ) @ ( int @ semiring_1_of_nat ) )
!= ( n @ ( int @ semiring_1_of_nat ) ) )
| ( ( int @ zero_zero )
!= ( int @ one_one ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) ) ),
inference(simp,[status(thm)],[35692]) ).
thf(35729,plain,
( ( ( int @ zero_zero @ ( int @ zero_zero @ sk1 ) @ ( int @ semiring_1_of_nat ) )
!= ( n @ ( int @ semiring_1_of_nat ) ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) ) ),
inference(simp,[status(thm)],[35707]) ).
thf(45116,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44874,153]) ).
thf(45117,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[45116]) ).
thf(45118,plain,
n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[45117:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) )),bind(B,$thf( int @ one_one ))]]) ).
thf(57263,plain,
n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[45118,33188]) ).
thf(39297,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39227,244]) ).
thf(39298,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[39297]) ).
thf(39299,plain,
t @ bit1 @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[39298:[bind(A,$thf( t @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(81,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_59_rel__simps_I21_J) ).
thf(430,plain,
! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(431,plain,
( ! [A: int] :
( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) ) )
& ! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(miniscope,[status(thm)],[430]) ).
thf(432,plain,
! [B: int,A: int] :
( ( ( B @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ ( B @ ( pls @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
inference(cnf,[status(esa)],[431]) ).
thf(434,plain,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[432]) ).
thf(435,plain,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[434]) ).
thf(44466,plain,
! [A: int] :
( ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
inference(rewrite,[status(thm)],[435,35205]) ).
thf(44538,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35261,44466]) ).
thf(44539,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[44538]) ).
thf(44540,plain,
int @ one_one @ bit1 @ bit1 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[44539:[bind(A,$thf( int @ one_one @ bit1 @ bit1 ))]]) ).
thf(110,axiom,
! [A: int,B: int] :
( ( A @ ( B @ bit1 @ ( int @ times_times ) ) )
= ( A @ ( A @ ( B @ ( int @ times_times ) ) @ bit0 @ ( int @ plus_plus ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_13_mult__Bit1) ).
thf(534,plain,
! [A: int,B: int] :
( ( A @ ( B @ bit1 @ ( int @ times_times ) ) )
= ( A @ ( A @ ( B @ ( int @ times_times ) ) @ bit0 @ ( int @ plus_plus ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(71,axiom,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_41_left__distrib__number__of) ).
thf(378,plain,
! [TA: $tType] :
( ( ( TA @ semiring )
& ( TA @ number ) )
=> ! [A: int,B: TA,C: TA] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(379,plain,
! [TA: $tType,C: TA,B: TA,A: int] :
( ( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
| ~ ( TA @ semiring )
| ~ ( TA @ number ) ),
inference(cnf,[status(esa)],[378]) ).
thf(380,plain,
! [TA: $tType,C: TA,B: TA,A: int] :
( ~ ( TA @ semiring )
| ~ ( TA @ number )
| ( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ plus_plus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(lifteq,[status(thm)],[379]) ).
thf(6,axiom,
bool @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_HOL_Obool___Orderings_Olinorder) ).
thf(117,plain,
bool @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(35238,plain,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ times_times ) ) )
= ( int @ zero_zero ) ),
inference(rewrite,[status(thm)],[281,35205]) ).
thf(4143,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( pls @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4124,145]) ).
thf(4144,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( pls @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[4143]) ).
thf(4145,plain,
pls @ bit1 @ bit0 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[4144:[bind(A,$thf( pls @ bit1 @ bit0 ))]]) ).
thf(18161,plain,
int @ one_one @ bit0 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[4145,18097]) ).
thf(33195,plain,
int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 @ ( pls @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[18161,33188]) ).
thf(40416,plain,
int @ one_one @ bit0 @ ( int @ one_one @ bit1 @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[33195,35205,175]) ).
thf(34,axiom,
! [A: int,B: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_35_rel__simps_I31_J) ).
thf(220,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(68,axiom,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_26_rel__simps_I49_J) ).
thf(363,plain,
! [A: int,B: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(364,plain,
~ ? [A: int,B: int] :
( ( B @ bit0 )
= ( A @ bit1 ) ),
inference(miniscope,[status(thm)],[363]) ).
thf(365,plain,
! [B: int,A: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(cnf,[status(esa)],[364]) ).
thf(366,plain,
! [B: int,A: int] :
( ( B @ bit0 )
!= ( A @ bit1 ) ),
inference(lifteq,[status(thm)],[365]) ).
thf(42749,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42704,301]) ).
thf(42750,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[42749]) ).
thf(42751,plain,
t @ bit0 @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[42750:[bind(A,$thf( t @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(42793,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42704,330]) ).
thf(42794,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[42793]) ).
thf(42795,plain,
t @ bit0 @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[42794:[bind(A,$thf( t @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(39300,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39227,159]) ).
thf(39301,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[39300]) ).
thf(39302,plain,
t @ bit1 @ bit0 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[39301:[bind(A,$thf( t @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(48191,plain,
t @ bit1 @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[39302,33188]) ).
thf(48256,plain,
! [A: int] :
( ( ( t @ bit1 @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[48191,187]) ).
thf(48257,plain,
! [A: int] :
( ( t @ bit1 @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[48256]) ).
thf(48302,plain,
! [A: int] :
( ( ( t @ bit1 @ bit0 )
!= A )
| ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= A ) ),
inference(simp,[status(thm)],[48257]) ).
thf(48333,plain,
( ( t @ bit1 @ bit0 )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[48302]) ).
thf(100,axiom,
n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_3_n1pos) ).
thf(498,plain,
n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(2250,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[498,187]) ).
thf(2251,plain,
! [A: int] :
( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[2250]) ).
thf(2255,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[2251]) ).
thf(2258,plain,
( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[2255]) ).
thf(2259,plain,
( ( ( int @ one_one @ ( int @ zero_zero @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ plus_plus ) ) )
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[1151,2258]) ).
thf(2269,plain,
( ( ( int @ one_one @ ( int @ zero_zero @ sk1 ) @ ( int @ semiring_1_of_nat ) )
!= ( n @ ( int @ semiring_1_of_nat ) ) )
| ( ( int @ zero_zero )
!= ( int @ one_one ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) ) ),
inference(simp,[status(thm)],[2259]) ).
thf(2277,plain,
( ( ( int @ one_one @ ( int @ zero_zero @ sk1 ) @ ( int @ semiring_1_of_nat ) )
!= ( n @ ( int @ semiring_1_of_nat ) ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) ) ),
inference(simp,[status(thm)],[2269]) ).
thf(5625,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit1 @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( pls @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[5606,145]) ).
thf(5626,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit1 @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( pls @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[5625]) ).
thf(5627,plain,
pls @ bit1 @ bit1 @ bit0 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[5626:[bind(A,$thf( pls @ bit1 @ bit1 @ bit0 ))]]) ).
thf(18148,plain,
int @ one_one @ bit1 @ bit0 @ bit1 @ ( pls @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[5627,18097]) ).
thf(35220,plain,
int @ one_one @ bit1 @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[18148,35205]) ).
thf(334,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[333]) ).
thf(76,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_66_rel__simps_I15_J) ).
thf(407,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) )
& ( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(68507,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68124,183]) ).
thf(68508,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[68507]) ).
thf(68509,plain,
t @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[68508:[bind(A,$thf( t )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(92,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_70_le__special_I1_J) ).
thf(471,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( pls @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(472,plain,
! [TA: $tType,A: int] :
( ( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
| ~ ( A @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) )
& ( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ) ),
inference(cnf,[status(esa)],[471]) ).
thf(474,plain,
! [TA: $tType,A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
| ~ ( A @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[472]) ).
thf(55433,plain,
! [TA: $tType,A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
| ~ ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(rewrite,[status(thm)],[474,35205]) ).
thf(24876,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24825,159]) ).
thf(24877,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[24876]) ).
thf(24878,plain,
int @ one_one @ bit1 @ bit0 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[24877:[bind(A,$thf( int @ one_one @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(32993,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit0 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24878,187]) ).
thf(32994,plain,
! [A: int] :
( ( int @ one_one @ bit1 @ bit0 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[32993]) ).
thf(33033,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit0 )
!= A )
| ( ( int @ one_one @ bit0 )
!= A ) ),
inference(simp,[status(thm)],[32994]) ).
thf(33060,plain,
( ( int @ one_one @ bit1 @ bit0 )
!= ( int @ one_one @ bit0 ) ),
inference(simp,[status(thm)],[33033]) ).
thf(33540,plain,
( ( int @ one_one @ bit1 @ bit0 )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[33060,33188]) ).
thf(95,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_48_mult__number__of__left) ).
thf(482,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(483,plain,
! [TA: $tType,C: int,B: int,A: TA] :
( ( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) )
| ~ ( TA @ number_ring ) ),
inference(cnf,[status(esa)],[482]) ).
thf(484,plain,
! [TA: $tType,C: int,B: int,A: TA] :
( ~ ( TA @ number_ring )
| ( ( A @ ( B @ ( C @ ( int @ times_times ) ) @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) ) ) ),
inference(lifteq,[status(thm)],[483]) ).
thf(4889,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit1 @ bit0 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4854,187]) ).
thf(4890,plain,
! [A: int] :
( ( pls @ bit1 @ bit1 @ bit0 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[4889]) ).
thf(4923,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit1 @ bit0 )
!= A )
| ( pls != A ) ),
inference(simp,[status(thm)],[4890]) ).
thf(4952,plain,
( ( pls @ bit1 @ bit1 @ bit0 )
!= pls ),
inference(simp,[status(thm)],[4923]) ).
thf(18129,plain,
( ( int @ one_one @ bit1 @ bit0 )
!= pls ),
inference(rewrite,[status(thm)],[4952,18097]) ).
thf(35206,plain,
( ( int @ one_one @ bit1 @ bit0 )
!= ( int @ zero_zero ) ),
inference(rewrite,[status(thm)],[18129,35205]) ).
thf(35162,plain,
! [TB: $tType] :
( ( ( pls @ ( TB @ number_number_of ) )
!= ( pls @ ( TB @ number_number_of ) ) )
| ~ ( TB @ zero_zero @ ( TB @ zero_zero @ ( TB @ ord_less ) ) )
| ~ ( TB @ linordered_idom )
| ~ ( TB @ number_ring )
| ~ ( TB @ number_ring ) ),
inference(paramod_ordered,[status(thm)],[362,21485]) ).
thf(35163,plain,
! [TB: $tType] :
( ( ( pls @ ( TB @ number_number_of ) )
!= ( pls @ ( TB @ number_number_of ) ) )
| ~ ( TB @ zero_zero @ ( TB @ zero_zero @ ( TB @ ord_less ) ) )
| ~ ( TB @ linordered_idom )
| ~ ( TB @ number_ring ) ),
inference(simp,[status(thm)],[35162]) ).
thf(35164,plain,
! [TB: $tType] :
( ~ ( TB @ zero_zero @ ( TB @ zero_zero @ ( TB @ ord_less ) ) )
| ~ ( TB @ linordered_idom )
| ~ ( TB @ number_ring ) ),
inference(pattern_uni,[status(thm)],[35163:[]]) ).
thf(35203,plain,
! [TA: $tType] :
( ~ ( TA @ zero_zero @ ( TA @ zero_zero @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(simp,[status(thm)],[35164]) ).
thf(89,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( nat @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_85_zless__int) ).
thf(458,plain,
! [A: nat,B: nat] :
( ( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ) )
& ( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(459,plain,
( ! [A: nat,B: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
=> ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ) )
& ! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( nat @ ord_less ) ) ) ) ),
inference(miniscope,[status(thm)],[458]) ).
thf(460,plain,
! [D: nat,C: nat,B: nat,A: nat] :
( ( ( C @ ( int @ semiring_1_of_nat ) @ ( D @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
| ~ ( C @ ( D @ ( nat @ ord_less ) ) ) )
& ( ( A @ ( B @ ( nat @ ord_less ) ) )
| ~ ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ) ) ),
inference(cnf,[status(esa)],[459]) ).
thf(461,plain,
! [B: nat,A: nat] :
( ( A @ ( B @ ( nat @ ord_less ) ) )
| ~ ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[460]) ).
thf(107,axiom,
! [A: int,B: int] :
( ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_67_zle__add1__eq__le) ).
thf(521,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) ) )
& ( ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(522,plain,
( ! [A: int,B: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) ) )
& ! [A: int,B: int] :
( ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(miniscope,[status(thm)],[521]) ).
thf(523,plain,
! [D: int,C: int,B: int,A: int] :
( ( ( int @ one_one @ ( C @ ( int @ plus_plus ) ) @ ( D @ ( int @ ord_less ) ) )
| ~ ( C @ ( D @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) ) ) ),
inference(cnf,[status(esa)],[522]) ).
thf(525,plain,
! [B: int,A: int] :
( ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[523]) ).
thf(526,plain,
! [B: int,A: int] :
( ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[525]) ).
thf(72328,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[302,526]) ).
thf(72329,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[72328]) ).
thf(72330,plain,
int @ one_one @ ( t @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[72329:[bind(A,$thf( t )),bind(B,$thf( int @ one_one ))]]) ).
thf(53596,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[53449,183]) ).
thf(53597,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[53596]) ).
thf(53598,plain,
t @ bit0 @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[53597:[bind(A,$thf( t @ bit0 @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(68271,plain,
! [A: int] :
( ( ( t @ bit0 @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[53598,510]) ).
thf(68272,plain,
! [A: int] :
( ( ( t @ bit0 @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[68271]) ).
thf(68273,plain,
t @ bit0 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[68272:[bind(A,$thf( t @ bit0 @ bit0 ))]]) ).
thf(59,axiom,
int @ zero_zero @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_12__0964_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_A_060_061_A0_096) ).
thf(324,plain,
int @ zero_zero @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(39378,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39326,153]) ).
thf(39379,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[39378]) ).
thf(39380,plain,
t @ bit1 @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[39379:[bind(A,$thf( t @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(49030,plain,
t @ bit1 @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[39380,33188]) ).
thf(22418,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22348,183]) ).
thf(22419,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[22418]) ).
thf(22420,plain,
int @ one_one @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[22419:[bind(A,$thf( int @ one_one @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(33210,plain,
int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[22420,33188]) ).
thf(65,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( A @ ( pls @ bit1 @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_5_add__special_I2_J) ).
thf(356,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( A @ ( pls @ bit1 @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(357,plain,
! [TA: $tType,A: int] :
( ( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) )
= ( A @ ( pls @ bit1 @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) ) )
| ~ ( TA @ number_ring ) ),
inference(cnf,[status(esa)],[356]) ).
thf(358,plain,
! [TA: $tType,A: int] :
( ~ ( TA @ number_ring )
| ( ( A @ ( pls @ bit1 @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) ) ) ),
inference(lifteq,[status(thm)],[357]) ).
thf(34754,plain,
! [TA: $tType,A: int] :
( ~ ( TA @ number_ring )
| ( ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) )
= ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ plus_plus ) ) ) ) ),
inference(rewrite,[status(thm)],[358,18097]) ).
thf(38227,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38160,183]) ).
thf(38228,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[38227]) ).
thf(38229,plain,
n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[38228:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) @ bit0 )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(44645,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38229,44466]) ).
thf(44646,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[44645]) ).
thf(44647,plain,
n @ ( int @ semiring_1_of_nat ) @ bit0 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[44646:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) @ bit0 ))]]) ).
thf(38007,plain,
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[37937,26026]) ).
thf(38008,plain,
( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[38007]) ).
thf(38026,plain,
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 )
!= ( int @ one_one ) )
| ( ( int @ one_one )
!= ( int @ one_one ) ) ),
inference(simp,[status(thm)],[38008]) ).
thf(38036,plain,
( ( n @ ( int @ semiring_1_of_nat ) @ bit0 )
!= ( int @ one_one ) ),
inference(simp,[status(thm)],[38026]) ).
thf(80,axiom,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
<=> ( A @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_72_le__special_I2_J) ).
thf(426,plain,
! [TA: $tType] :
( ( ( TA @ linordered_idom )
& ( TA @ number_ring ) )
=> ! [A: int] :
( ( ( A @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) ) )
& ( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
=> ( A @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(427,plain,
! [TA: $tType,A: int] :
( ( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
| ~ ( A @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) )
& ( ( A @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ) ),
inference(cnf,[status(esa)],[426]) ).
thf(428,plain,
! [TA: $tType,A: int] :
( ( A @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[427]) ).
thf(42850,plain,
! [TA: $tType,A: int] :
( ( A @ ( int @ zero_zero @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(rewrite,[status(thm)],[428,35205]) ).
thf(37706,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[37639,183]) ).
thf(37707,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[37706]) ).
thf(37708,plain,
n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[37707:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(97,axiom,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_84_zadd__int) ).
thf(486,plain,
! [A: nat,B: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(487,plain,
! [B: nat,A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) ) ),
inference(cnf,[status(esa)],[486]) ).
thf(488,plain,
! [B: nat,A: nat] :
( ( A @ ( B @ ( nat @ plus_plus ) ) @ ( int @ semiring_1_of_nat ) )
= ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ plus_plus ) ) ) ),
inference(lifteq,[status(thm)],[487]) ).
thf(35254,plain,
( ( int @ one_one @ bit0 @ ( int @ one_one @ bit1 @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
inference(rewrite,[status(thm)],[34495,35205]) ).
thf(44269,plain,
( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ bit1 @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
inference(rewrite,[status(thm)],[35254,33188]) ).
thf(4125,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[4124,138]) ).
thf(4126,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[4125]) ).
thf(4127,plain,
pls @ bit1 @ bit0 @ bit1 @ ( pls @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[4126:[bind(A,$thf( pls @ bit1 @ bit0 )),bind(B,$thf( pls ))]]) ).
thf(18150,plain,
int @ one_one @ bit0 @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[4127,18097]) ).
thf(33233,plain,
int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[18150,33188]) ).
thf(41956,plain,
int @ one_one @ bit0 @ ( int @ one_one @ bit1 @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[33233,175]) ).
thf(1768,plain,
( ( ( t @ ( m1 @ ( int @ ord_less ) ) )
!= ( t @ ( int @ one_one @ ( int @ ord_less ) ) ) )
| ( ( t @ ( int @ one_one @ sk1 ) @ ( int @ semiring_1_of_nat ) )
!= ( n @ ( int @ semiring_1_of_nat ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,1316]) ).
thf(1769,plain,
( ( ( t @ ( m1 @ ( int @ ord_less ) ) )
!= ( t @ ( int @ one_one @ ( int @ ord_less ) ) ) )
| ( ( t @ ( int @ one_one @ sk1 ) @ ( int @ semiring_1_of_nat ) )
!= ( n @ ( int @ semiring_1_of_nat ) ) ) ),
inference(simp,[status(thm)],[1768]) ).
thf(1789,plain,
( ( t != t )
| ( m1
!= ( int @ one_one ) )
| ( ( t @ ( int @ one_one @ sk1 ) )
!= n ) ),
inference(simp,[status(thm)],[1769]) ).
thf(1791,plain,
( ( m1
!= ( int @ one_one ) )
| ( ( t @ ( int @ one_one @ sk1 ) )
!= n ) ),
inference(simp,[status(thm)],[1789]) ).
thf(49409,plain,
( ( ( t @ bit1 @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49270,26026]) ).
thf(49410,plain,
( ( t @ bit1 @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[49409]) ).
thf(49420,plain,
( ( ( t @ bit1 @ bit0 )
!= ( int @ one_one ) )
| ( ( int @ one_one )
!= ( int @ one_one ) ) ),
inference(simp,[status(thm)],[49410]) ).
thf(49442,plain,
( ( t @ bit1 @ bit0 )
!= ( int @ one_one ) ),
inference(simp,[status(thm)],[49420]) ).
thf(31,axiom,
! [A: int] :
( ( A @ bit1 )
!= pls ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_23_rel__simps_I46_J) ).
thf(212,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(328,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[327]) ).
thf(43,axiom,
! [A: int] :
( ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_58_rel__simps_I27_J) ).
thf(256,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( pls @ ( A @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( A @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(111,axiom,
! [A: int,B: int] :
( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_76_less__eq__number__of__int__code) ).
thf(537,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ ( int @ number_number_of ) @ ( B @ ( int @ number_number_of ) @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(24879,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24825,187]) ).
thf(24880,plain,
! [A: int] :
( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[24879]) ).
thf(24917,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 )
!= A )
| ( ( int @ one_one )
!= A ) ),
inference(simp,[status(thm)],[24880]) ).
thf(24931,plain,
( ( int @ one_one @ bit1 )
!= ( int @ one_one ) ),
inference(simp,[status(thm)],[24917]) ).
thf(3446,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit1 @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3409,187]) ).
thf(3447,plain,
! [A: int] :
( ( pls @ bit1 @ bit1 @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[3446]) ).
thf(3488,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit1 @ bit1 )
!= A )
| ( pls != A ) ),
inference(simp,[status(thm)],[3447]) ).
thf(3497,plain,
( ( pls @ bit1 @ bit1 @ bit1 )
!= pls ),
inference(simp,[status(thm)],[3488]) ).
thf(18171,plain,
( ( int @ one_one @ bit1 @ bit1 )
!= pls ),
inference(rewrite,[status(thm)],[3497,18097]) ).
thf(35211,plain,
( ( int @ one_one @ bit1 @ bit1 )
!= ( int @ zero_zero ) ),
inference(rewrite,[status(thm)],[18171,35205]) ).
thf(68143,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[37708,510]) ).
thf(68144,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[68143]) ).
thf(68145,plain,
n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[68144:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) @ bit1 ))]]) ).
thf(71213,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68145,183]) ).
thf(71214,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[71213]) ).
thf(71215,plain,
n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[71214:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) @ bit1 )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(104,axiom,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_50_add__number__of__left) ).
thf(513,plain,
! [TA: $tType] :
( ( TA @ number_ring )
=> ! [A: TA,B: int,C: int] :
( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(514,plain,
! [TA: $tType,C: int,B: int,A: TA] :
( ( ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) )
| ~ ( TA @ number_ring ) ),
inference(cnf,[status(esa)],[513]) ).
thf(515,plain,
! [TA: $tType,C: int,B: int,A: TA] :
( ~ ( TA @ number_ring )
| ( ( A @ ( B @ ( C @ ( int @ plus_plus ) ) @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) )
= ( A @ ( B @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ plus_plus ) ) ) ) ),
inference(lifteq,[status(thm)],[514]) ).
thf(45764,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45719,406]) ).
thf(45765,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[45764]) ).
thf(45766,plain,
int @ one_one @ bit0 @ bit1 @ ( int @ zero_zero @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[45765:[bind(A,$thf( int @ one_one @ bit0 )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(58377,plain,
int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[45766,35216,33188]) ).
thf(28947,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28797,187]) ).
thf(28948,plain,
! [A: int] :
( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[28947]) ).
thf(28980,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[28948]) ).
thf(29008,plain,
( ( n @ ( int @ semiring_1_of_nat ) )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[28980]) ).
thf(29019,plain,
( ( ( n @ ( int @ semiring_1_of_nat ) )
!= ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) ) )
| ( ( int @ zero_zero )
!= ( int @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[210,29008]) ).
thf(29020,plain,
( ( n @ ( int @ semiring_1_of_nat ) )
!= ( nat @ zero_zero @ ( int @ semiring_1_of_nat ) ) ),
inference(simp,[status(thm)],[29019]) ).
thf(29022,plain,
( n
!= ( nat @ zero_zero ) ),
inference(simp,[status(thm)],[29020]) ).
thf(45,axiom,
! [A: int] :
( ( ( A @ bit0 )
= pls )
<=> ( A = pls ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_27_rel__simps_I44_J) ).
thf(266,plain,
! [A: int] :
( ( ( A = pls )
=> ( ( A @ bit0 )
= pls ) )
& ( ( ( A @ bit0 )
= pls )
=> ( A = pls ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(39265,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39227,301]) ).
thf(39266,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[39265]) ).
thf(39267,plain,
t @ bit1 @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[39266:[bind(A,$thf( t @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(433,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ ( A @ bit0 @ ( pls @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[432]) ).
thf(44009,plain,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
| ~ ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
inference(rewrite,[status(thm)],[433,35205]) ).
thf(68039,plain,
! [A: int] :
( ( ( int @ one_one @ ( t @ ( int @ minus_minus ) ) @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31720,510]) ).
thf(68040,plain,
! [A: int] :
( ( ( int @ one_one @ ( t @ ( int @ minus_minus ) ) @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[68039]) ).
thf(68041,plain,
int @ one_one @ ( t @ ( int @ minus_minus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[68040:[bind(A,$thf( int @ one_one @ ( t @ ( int @ minus_minus ) ) ))]]) ).
thf(70126,plain,
! [A: int] :
( ( ( int @ one_one @ ( t @ ( int @ minus_minus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68041,187]) ).
thf(70127,plain,
! [A: int] :
( ( int @ one_one @ ( t @ ( int @ minus_minus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[70126]) ).
thf(70189,plain,
! [A: int] :
( ( ( int @ one_one @ ( t @ ( int @ minus_minus ) ) )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[70127]) ).
thf(70198,plain,
( ( int @ one_one @ ( t @ ( int @ minus_minus ) ) )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[70189]) ).
thf(42800,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42704,336]) ).
thf(42801,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[42800]) ).
thf(42802,plain,
int @ one_one @ ( t @ bit0 @ ( int @ minus_minus ) ) @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[42801:[bind(A,$thf( t @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(2995,plain,
( ( ( int @ one_one @ ( int @ zero_zero @ sk1 ) )
!= n )
| ( ( int @ one_one )
!= ( int @ zero_zero ) ) ),
inference(simp,[status(thm)],[2277]) ).
thf(44368,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44363,301]) ).
thf(44369,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[44368]) ).
thf(44370,plain,
int @ one_one @ bit0 @ bit1 @ ( int @ zero_zero @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[44369:[bind(A,$thf( int @ one_one @ bit0 )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(55275,plain,
int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[44370,35218,33188]) ).
thf(68107,plain,
! [A: int] :
( ( ( t @ bit1 @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49406,510]) ).
thf(68108,plain,
! [A: int] :
( ( ( t @ bit1 @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[68107]) ).
thf(68109,plain,
t @ bit1 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[68108:[bind(A,$thf( t @ bit1 @ bit0 ))]]) ).
thf(68634,plain,
! [A: int] :
( ( ( t @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68509,44466]) ).
thf(68635,plain,
! [A: int] :
( ( ( t @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[68634]) ).
thf(68636,plain,
t @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[68635:[bind(A,$thf( t ))]]) ).
thf(42781,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42704,244]) ).
thf(42782,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[42781]) ).
thf(42783,plain,
t @ bit0 @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[42782:[bind(A,$thf( t @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(52030,plain,
! [A: int] :
( ( ( t @ bit0 @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42783,187]) ).
thf(52031,plain,
! [A: int] :
( ( t @ bit0 @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[52030]) ).
thf(52094,plain,
! [A: int] :
( ( ( t @ bit0 @ bit0 )
!= A )
| ( ( int @ one_one @ bit1 )
!= A ) ),
inference(simp,[status(thm)],[52031]) ).
thf(52107,plain,
( ( int @ one_one @ bit1 )
!= ( t @ bit0 @ bit0 ) ),
inference(simp,[status(thm)],[52094]) ).
thf(213,plain,
~ ? [A: int] :
( ( A @ bit1 )
= pls ),
inference(miniscope,[status(thm)],[212]) ).
thf(214,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(cnf,[status(esa)],[213]) ).
thf(215,plain,
! [A: int] :
( ( A @ bit1 )
!= pls ),
inference(lifteq,[status(thm)],[214]) ).
thf(35268,plain,
! [A: int] :
( ( A @ bit1 )
!= ( int @ zero_zero ) ),
inference(rewrite,[status(thm)],[215,35205]) ).
thf(22294,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[19049,183]) ).
thf(22295,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[22294]) ).
thf(22296,plain,
t @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[22295:[bind(A,$thf( t @ bit0 )),bind(B,$thf( int @ one_one @ bit1 ))]]) ).
thf(70,axiom,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_45_right__diff__distrib__number__of) ).
thf(375,plain,
! [TA: $tType] :
( ( ( TA @ ring )
& ( TA @ number ) )
=> ! [A: TA,B: TA,C: int] :
( ( A @ ( B @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(31872,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24825,336]) ).
thf(31873,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[31872]) ).
thf(31874,plain,
int @ one_one @ ( int @ one_one @ bit1 @ ( int @ minus_minus ) ) @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[31873:[bind(A,$thf( int @ one_one @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(44618,plain,
! [A: int] :
( ( ( int @ one_one @ ( int @ one_one @ ( int @ minus_minus ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[31755,44466]) ).
thf(44619,plain,
! [A: int] :
( ( ( int @ one_one @ ( int @ one_one @ ( int @ minus_minus ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[44618]) ).
thf(44620,plain,
int @ one_one @ ( int @ one_one @ ( int @ minus_minus ) ) @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[44619:[bind(A,$thf( int @ one_one @ ( int @ one_one @ ( int @ minus_minus ) ) ))]]) ).
thf(56354,plain,
int @ one_one @ bit0 @ ( int @ one_one @ bit0 @ ( int @ minus_minus ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[44620,421]) ).
thf(3103,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,159]) ).
thf(3104,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[3103]) ).
thf(3105,plain,
t @ bit0 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[3104:[bind(A,$thf( t )),bind(B,$thf( int @ one_one ))]]) ).
thf(3252,plain,
! [A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3105,187]) ).
thf(3253,plain,
! [A: int] :
( ( t @ bit0 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[3252]) ).
thf(3270,plain,
! [A: int] :
( ( ( t @ bit0 )
!= A )
| ( ( int @ one_one @ bit0 )
!= A ) ),
inference(simp,[status(thm)],[3253]) ).
thf(3300,plain,
( ( t @ bit0 )
!= ( int @ one_one @ bit0 ) ),
inference(simp,[status(thm)],[3270]) ).
thf(33208,plain,
( ( t @ bit0 )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[3300,33188]) ).
thf(35423,plain,
int @ one_one @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[2456,35218]) ).
thf(36854,plain,
int @ one_one @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[35423,33188]) ).
thf(70588,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68131,183]) ).
thf(70589,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[70588]) ).
thf(70590,plain,
t @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[70589:[bind(A,$thf( t @ bit0 @ bit1 )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(85,axiom,
int @ zero_zero @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( int @ ord_less ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_2__096_I1_A_L_Aint_An_J_A_K_A_I2_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_J_A_060_A_I1_A_L_Aint_An_J_A_K_A0_096) ).
thf(446,plain,
int @ zero_zero @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( int @ ord_less ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(47214,plain,
int @ zero_zero @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ times_times ) ) @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[446,255]) ).
thf(33601,plain,
! [B: int,A: int] :
( ( ( A @ bit0 @ ( B @ bit1 @ ( int @ plus_plus ) ) )
!= ( int @ one_one @ bit0 @ ( int @ one_one @ bit1 @ ( int @ plus_plus ) ) ) )
| ( ( A @ bit1 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
!= ( int @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[12219,33568]) ).
thf(33602,plain,
( ( int @ one_one @ bit1 @ ( int @ one_one @ bit0 @ ( int @ plus_plus ) ) )
!= ( int @ one_one ) ),
inference(pattern_uni,[status(thm)],[33601:[bind(A,$thf( int @ one_one )),bind(B,$thf( int @ one_one ))]]) ).
thf(43190,plain,
( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ plus_plus ) ) )
!= ( int @ one_one ) ),
inference(rewrite,[status(thm)],[33602,33188]) ).
thf(1452,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1131,138]) ).
thf(1453,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[1452]) ).
thf(1454,plain,
int @ one_one @ bit1 @ ( int @ zero_zero @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[1453:[bind(A,$thf( int @ one_one )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(2368,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ zero_zero @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1454,153]) ).
thf(2369,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ zero_zero @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[2368]) ).
thf(2370,plain,
int @ one_one @ bit1 @ bit1 @ ( int @ zero_zero @ bit1 @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[2369:[bind(A,$thf( int @ one_one @ bit1 )),bind(B,$thf( int @ zero_zero @ bit1 ))]]) ).
thf(3035,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit1 @ ( int @ zero_zero @ bit1 @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2370,187]) ).
thf(3036,plain,
! [A: int] :
( ( int @ one_one @ bit1 @ bit1 @ ( int @ zero_zero @ bit1 @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[3035]) ).
thf(3055,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit1 )
!= A )
| ( ( int @ zero_zero @ bit1 @ bit0 )
!= A ) ),
inference(simp,[status(thm)],[3036]) ).
thf(3082,plain,
( ( int @ one_one @ bit1 @ bit1 )
!= ( int @ zero_zero @ bit1 @ bit0 ) ),
inference(simp,[status(thm)],[3055]) ).
thf(35431,plain,
( ( int @ one_one @ bit1 @ bit1 )
!= ( int @ one_one @ bit0 ) ),
inference(rewrite,[status(thm)],[3082,35218]) ).
thf(37395,plain,
( ( int @ one_one @ bit1 @ bit1 )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[35431,33188]) ).
thf(71382,plain,
! [A: int] :
( ( ( t @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68176,187]) ).
thf(71383,plain,
! [A: int] :
( ( t @ bit1 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[71382]) ).
thf(71444,plain,
! [A: int] :
( ( ( t @ bit1 @ bit1 )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[71383]) ).
thf(71458,plain,
( ( t @ bit1 @ bit1 )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[71444]) ).
thf(473,plain,
! [TA: $tType,A: int] :
( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[472]) ).
thf(54784,plain,
! [TA: $tType,A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( TA @ zero_zero @ ( TA @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(rewrite,[status(thm)],[473,35205]) ).
thf(6902,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( B @ ( int @ ord_less ) ) )
| ~ $true
| ( B = A ) ),
inference(paramod_ordered,[status(thm)],[1872,189]) ).
thf(6903,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( B @ ( int @ ord_less ) ) )
| ( B = A ) ),
inference(simp,[status(thm)],[6902]) ).
thf(6904,plain,
( ( pls @ bit1 @ ( pls @ ( int @ ord_less ) ) )
| ( ( pls @ bit1 )
= pls ) ),
inference(pattern_uni,[status(thm)],[6903:[bind(A,$thf( pls @ bit1 )),bind(B,$thf( pls ))]]) ).
thf(61578,plain,
( ( int @ zero_zero @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ( ( int @ zero_zero @ bit1 )
= ( int @ zero_zero ) ) ),
inference(rewrite,[status(thm)],[6904,35205]) ).
thf(61579,plain,
int @ zero_zero @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(simplifyReflect,[status(thm)],[61578,35268]) ).
thf(47788,plain,
! [A: int] :
( ( ( t @ bit1 @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39299,187]) ).
thf(47789,plain,
! [A: int] :
( ( t @ bit1 @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[47788]) ).
thf(47834,plain,
! [A: int] :
( ( ( t @ bit1 @ bit0 )
!= A )
| ( ( int @ one_one @ bit1 )
!= A ) ),
inference(simp,[status(thm)],[47789]) ).
thf(47855,plain,
( ( t @ bit1 @ bit0 )
!= ( int @ one_one @ bit1 ) ),
inference(simp,[status(thm)],[47834]) ).
thf(44972,plain,
( ( ( int @ one_one @ ( int @ zero_zero @ ( int @ plus_plus ) ) )
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[44870,2258]) ).
thf(45023,plain,
( ( ( n @ ( int @ semiring_1_of_nat ) )
!= ( int @ one_one ) )
| ( ( int @ zero_zero )
!= ( int @ one_one ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) ) ),
inference(simp,[status(thm)],[44972]) ).
thf(45084,plain,
( ( ( n @ ( int @ semiring_1_of_nat ) )
!= ( int @ one_one ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) ) ),
inference(simp,[status(thm)],[45023]) ).
thf(47638,plain,
! [A: int] :
( ( ( t @ bit1 @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39267,187]) ).
thf(47639,plain,
! [A: int] :
( ( t @ bit1 @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[47638]) ).
thf(47677,plain,
! [A: int] :
( ( ( t @ bit1 @ bit1 )
!= A )
| ( ( int @ one_one @ bit1 )
!= A ) ),
inference(simp,[status(thm)],[47639]) ).
thf(47703,plain,
( ( t @ bit1 @ bit1 )
!= ( int @ one_one @ bit1 ) ),
inference(simp,[status(thm)],[47677]) ).
thf(71176,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68145,187]) ).
thf(71177,plain,
! [A: int] :
( ( n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[71176]) ).
thf(71249,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit1 )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[71177]) ).
thf(71258,plain,
( ( n @ ( int @ semiring_1_of_nat ) @ bit1 )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[71249]) ).
thf(429,plain,
! [TA: $tType,A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
| ~ ( A @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[427]) ).
thf(43275,plain,
! [TA: $tType,A: int] :
( ( A @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less_eq ) ) )
| ~ ( A @ ( int @ zero_zero @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(rewrite,[status(thm)],[429,35205]) ).
thf(47094,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35955,183]) ).
thf(47095,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[47094]) ).
thf(47096,plain,
int @ one_one @ bit1 @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[47095:[bind(A,$thf( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ plus_plus ) ) )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(445,plain,
! [TA: $tType,A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( pls @ bit1 @ ( A @ ( int @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[443]) ).
thf(46715,plain,
! [TA: $tType,A: int] :
( ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( int @ zero_zero @ bit1 @ ( A @ ( int @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(rewrite,[status(thm)],[445,35205]) ).
thf(39,axiom,
int @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
thf(245,plain,
int @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(55,axiom,
! [A: int] :
( ( pls @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_63_rel__simps_I29_J) ).
thf(303,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ bit1 @ ( int @ ord_less_eq ) ) ) )
& ( ( pls @ ( A @ bit1 @ ( int @ ord_less_eq ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(68496,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68124,336]) ).
thf(68497,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[68496]) ).
thf(68498,plain,
int @ one_one @ ( t @ ( int @ minus_minus ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[68497:[bind(A,$thf( t )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(376,plain,
! [TA: $tType,C: int,B: TA,A: TA] :
( ( ( A @ ( B @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) )
| ~ ( TA @ ring )
| ~ ( TA @ number ) ),
inference(cnf,[status(esa)],[375]) ).
thf(377,plain,
! [TA: $tType,C: int,B: TA,A: TA] :
( ~ ( TA @ ring )
| ~ ( TA @ number )
| ( ( A @ ( B @ ( TA @ minus_minus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
inference(lifteq,[status(thm)],[376]) ).
thf(2245,plain,
! [A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,187]) ).
thf(2246,plain,
! [A: int] :
( ( t @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[2245]) ).
thf(2254,plain,
! [A: int] :
( ( t != A )
| ( ( int @ one_one )
!= A ) ),
inference(simp,[status(thm)],[2246]) ).
thf(2257,plain,
( t
!= ( int @ one_one ) ),
inference(simp,[status(thm)],[2254]) ).
thf(1449,plain,
! [B: int,A: int] :
( ( ( pls @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[160,138]) ).
thf(1450,plain,
! [B: int,A: int] :
( ( ( pls @ ( pls @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[1449]) ).
thf(1451,plain,
pls @ bit1 @ ( pls @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[1450:[bind(A,$thf( pls )),bind(B,$thf( pls ))]]) ).
thf(1499,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1451,138]) ).
thf(1500,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[1499]) ).
thf(1501,plain,
pls @ bit1 @ bit1 @ ( pls @ bit1 @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[1500:[bind(A,$thf( pls @ bit1 )),bind(B,$thf( pls @ bit1 ))]]) ).
thf(18118,plain,
int @ one_one @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[1501,18097]) ).
thf(57327,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[57263,187]) ).
thf(57328,plain,
! [A: int] :
( ( n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[57327]) ).
thf(57393,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit1 )
!= A )
| ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= A ) ),
inference(simp,[status(thm)],[57328]) ).
thf(57417,plain,
( ( n @ ( int @ semiring_1_of_nat ) @ bit1 )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[57393]) ).
thf(69,axiom,
! [A: int] :
( ( pls
= ( A @ bit0 ) )
<=> ( pls = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_28_rel__simps_I38_J) ).
thf(367,plain,
! [A: int] :
( ( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(54708,plain,
! [A: int] :
( ( ( t @ bit0 @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54589,187]) ).
thf(54709,plain,
! [A: int] :
( ( t @ bit0 @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[54708]) ).
thf(54752,plain,
! [A: int] :
( ( ( t @ bit0 @ bit1 )
!= A )
| ( ( int @ one_one )
!= A ) ),
inference(simp,[status(thm)],[54709]) ).
thf(54780,plain,
( ( t @ bit0 @ bit1 )
!= ( int @ one_one ) ),
inference(simp,[status(thm)],[54752]) ).
thf(519,plain,
! [B: int,A: int] :
( ( A @ bit0 @ ( B @ bit0 @ ( int @ plus_plus ) ) )
= ( A @ ( B @ ( int @ plus_plus ) ) @ bit0 ) ),
inference(cnf,[status(esa)],[518]) ).
thf(520,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ plus_plus ) ) @ bit0 )
= ( A @ bit0 @ ( B @ bit0 @ ( int @ plus_plus ) ) ) ),
inference(lifteq,[status(thm)],[519]) ).
thf(36562,plain,
( ( ( int @ zero_zero @ ( int @ zero_zero @ sk1 ) )
!= n )
| ( ( int @ one_one )
!= ( int @ zero_zero ) ) ),
inference(simp,[status(thm)],[35729]) ).
thf(39313,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39227,336]) ).
thf(39314,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[39313]) ).
thf(39315,plain,
int @ one_one @ ( t @ bit1 @ ( int @ minus_minus ) ) @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[39314:[bind(A,$thf( t @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(476,plain,
! [TA: $tType,A: int] :
( ( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( pls @ ( A @ ( int @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) )
& ( ( pls @ ( A @ ( int @ ord_less ) ) )
| ~ ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ) ),
inference(cnf,[status(esa)],[475]) ).
thf(478,plain,
! [TA: $tType,A: int] :
( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( pls @ ( A @ ( int @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[476]) ).
thf(56485,plain,
! [TA: $tType,A: int] :
( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(rewrite,[status(thm)],[478,35205]) ).
thf(958,plain,
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( m1 @ ( int @ ord_less ) ) )
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[498,275]) ).
thf(959,plain,
( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( m1 @ ( int @ ord_less ) ) )
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[958]) ).
thf(971,plain,
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) )
| ( m1
!= ( int @ zero_zero ) ) ),
inference(simp,[status(thm)],[959]) ).
thf(983,plain,
( m1
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[971]) ).
thf(24834,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24825,301]) ).
thf(24835,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[24834]) ).
thf(24836,plain,
int @ one_one @ bit1 @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[24835:[bind(A,$thf( int @ one_one @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(32436,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24836,187]) ).
thf(32437,plain,
! [A: int] :
( ( int @ one_one @ bit1 @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[32436]) ).
thf(32481,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit1 )
!= A )
| ( ( int @ one_one @ bit1 )
!= A ) ),
inference(simp,[status(thm)],[32437]) ).
thf(32509,plain,
( ( int @ one_one @ bit1 @ bit1 )
!= ( int @ one_one @ bit1 ) ),
inference(simp,[status(thm)],[32481]) ).
thf(35,axiom,
! [A: nat] :
( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
<=> ( A
= ( nat @ zero_zero ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_88_int__eq__0__conv) ).
thf(226,plain,
! [A: nat] :
( ( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ) )
& ( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(70335,plain,
! [A: int] :
( ( ( t @ bit1 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68109,187]) ).
thf(70336,plain,
! [A: int] :
( ( t @ bit1 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[70335]) ).
thf(70401,plain,
! [A: int] :
( ( ( t @ bit1 @ bit0 )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[70336]) ).
thf(70412,plain,
( ( t @ bit1 @ bit0 )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[70401]) ).
thf(10,axiom,
int @ number,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
thf(130,plain,
int @ number,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(33221,plain,
t @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[3105,33188]) ).
thf(299,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[298]) ).
thf(441,plain,
! [TA: $tType,A: int] :
( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( pls @ ( A @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[439]) ).
thf(45945,plain,
! [TA: $tType,A: int] :
( ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( int @ zero_zero @ ( A @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(rewrite,[status(thm)],[441,35205]) ).
thf(467,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ ord_less_eq ) ) )
| ~ ( A @ bit1 @ ( pls @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[466]) ).
thf(53062,plain,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
| ~ ( A @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(rewrite,[status(thm)],[467,35205]) ).
thf(354,plain,
! [B: int,A: int] :
( ( A @ ( B @ bit0 @ ( int @ times_times ) ) )
= ( A @ ( B @ ( int @ times_times ) ) @ bit0 ) ),
inference(cnf,[status(esa)],[353]) ).
thf(355,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ times_times ) ) @ bit0 )
= ( A @ ( B @ bit0 @ ( int @ times_times ) ) ) ),
inference(lifteq,[status(thm)],[354]) ).
thf(35212,plain,
int @ one_one @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[18143,35205]) ).
thf(477,plain,
! [TA: $tType,A: int] :
( ( pls @ ( A @ ( int @ ord_less ) ) )
| ~ ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[476]) ).
thf(55923,plain,
! [TA: $tType,A: int] :
( ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) )
| ~ ( TA @ zero_zero @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(rewrite,[status(thm)],[477,35205]) ).
thf(29018,plain,
( ( ( n @ ( int @ semiring_1_of_nat ) )
!= ( nat @ one_one @ ( int @ semiring_1_of_nat ) ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) ) ),
inference(paramod_ordered,[status(thm)],[168,29008]) ).
thf(29021,plain,
( ( n
!= ( nat @ one_one ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) ) ),
inference(simp,[status(thm)],[29018]) ).
thf(24350,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22348,301]) ).
thf(24351,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[24350]) ).
thf(24352,plain,
int @ one_one @ bit0 @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[24351:[bind(A,$thf( int @ one_one @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(31396,plain,
! [A: int] :
( ( ( int @ one_one @ bit0 @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24352,187]) ).
thf(31397,plain,
! [A: int] :
( ( int @ one_one @ bit0 @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[31396]) ).
thf(31432,plain,
! [A: int] :
( ( ( int @ one_one @ bit0 @ bit1 )
!= A )
| ( ( int @ one_one @ bit1 )
!= A ) ),
inference(simp,[status(thm)],[31397]) ).
thf(31460,plain,
( ( int @ one_one @ bit0 @ bit1 )
!= ( int @ one_one @ bit1 ) ),
inference(simp,[status(thm)],[31432]) ).
thf(33248,plain,
( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 )
!= ( int @ one_one @ bit1 ) ),
inference(rewrite,[status(thm)],[31460,33188]) ).
thf(42560,plain,
( ( int @ one_one @ bit0 @ ( int @ one_one @ bit1 @ ( int @ plus_plus ) ) )
!= ( int @ one_one @ bit1 ) ),
inference(rewrite,[status(thm)],[33248,175]) ).
thf(105,axiom,
~ ( pls @ ( pls @ ( int @ ord_less ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_31_rel__simps_I2_J) ).
thf(516,plain,
~ ( pls @ ( pls @ ( int @ ord_less ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(33284,plain,
! [A: int] :
( ( ( int @ one_one @ bit0 )
!= ( A @ bit0 ) )
| ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ sk2 )
= A ) ),
inference(paramod_ordered,[status(thm)],[33188,33068]) ).
thf(33285,plain,
( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ sk2 )
= ( int @ one_one ) ),
inference(pattern_uni,[status(thm)],[33284:[bind(A,$thf( int @ one_one ))]]) ).
thf(368,plain,
( ! [A: int] :
( ( pls = A )
=> ( pls
= ( A @ bit0 ) ) )
& ! [A: int] :
( ( pls
= ( A @ bit0 ) )
=> ( pls = A ) ) ),
inference(miniscope,[status(thm)],[367]) ).
thf(369,plain,
! [B: int,A: int] :
( ( ( pls
= ( B @ bit0 ) )
| ( pls != B ) )
& ( ( pls = A )
| ( pls
!= ( A @ bit0 ) ) ) ),
inference(cnf,[status(esa)],[368]) ).
thf(370,plain,
! [A: int] :
( ( pls = A )
| ( pls
!= ( A @ bit0 ) ) ),
inference(cnfConj,[status(thm)],[369]) ).
thf(372,plain,
! [A: int] :
( ( pls = A )
| ( ( A @ bit0 )
!= pls ) ),
inference(lifteq,[status(thm)],[370]) ).
thf(35875,plain,
! [A: int] :
( ( ( int @ zero_zero )
= A )
| ( ( A @ bit0 )
!= ( int @ zero_zero ) ) ),
inference(rewrite,[status(thm)],[372,35205]) ).
thf(294,plain,
! [TA: $tType,C: int,B: TA,A: TA] :
( ( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) )
| ~ ( TA @ semiring )
| ~ ( TA @ number ) ),
inference(cnf,[status(esa)],[293]) ).
thf(295,plain,
! [TA: $tType,C: int,B: TA,A: TA] :
( ~ ( TA @ semiring )
| ~ ( TA @ number )
| ( ( A @ ( B @ ( TA @ plus_plus ) ) @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) )
= ( A @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( B @ ( C @ ( TA @ number_number_of ) @ ( TA @ times_times ) ) @ ( TA @ plus_plus ) ) ) ) ),
inference(lifteq,[status(thm)],[294]) ).
thf(50,axiom,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( B @ ( TA @ number_number_of ) )
= A )
<=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_96_number__of__reorient) ).
thf(282,plain,
! [TA: $tType] :
( ( TA @ number )
=> ! [A: TA,B: int] :
( ( ( A
= ( B @ ( TA @ number_number_of ) ) )
=> ( ( B @ ( TA @ number_number_of ) )
= A ) )
& ( ( ( B @ ( TA @ number_number_of ) )
= A )
=> ( A
= ( B @ ( TA @ number_number_of ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(68637,plain,
! [A: int] :
( ( ( t @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68509,277]) ).
thf(68638,plain,
! [A: int] :
( ( ( t @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[68637]) ).
thf(68639,plain,
t @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[68638:[bind(A,$thf( t ))]]) ).
thf(72772,plain,
! [A: int] :
( ( ( t @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68639,187]) ).
thf(72773,plain,
! [A: int] :
( ( t @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[72772]) ).
thf(72838,plain,
! [A: int] :
( ( ( t @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[72773]) ).
thf(72860,plain,
( ( t @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[72838]) ).
thf(68154,plain,
! [A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39326,510]) ).
thf(68155,plain,
! [A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[68154]) ).
thf(68156,plain,
t @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[68155:[bind(A,$thf( t @ bit1 ))]]) ).
thf(2943,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2909,187]) ).
thf(2944,plain,
! [A: int] :
( ( pls @ bit1 @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[2943]) ).
thf(2985,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit1 )
!= A )
| ( pls != A ) ),
inference(simp,[status(thm)],[2944]) ).
thf(2994,plain,
( ( pls @ bit1 @ bit1 )
!= pls ),
inference(simp,[status(thm)],[2985]) ).
thf(18157,plain,
( ( int @ one_one @ bit1 )
!= pls ),
inference(rewrite,[status(thm)],[2994,18097]) ).
thf(35263,plain,
( ( int @ one_one @ bit1 )
!= ( int @ zero_zero ) ),
inference(rewrite,[status(thm)],[18157,35205]) ).
thf(495,plain,
! [A: int] :
( ( pls @ ( A @ ( int @ ord_less ) ) )
| ~ ( pls @ ( A @ bit0 @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[494]) ).
thf(59798,plain,
! [A: int] :
( ( int @ zero_zero @ ( A @ ( int @ ord_less ) ) )
| ~ ( int @ zero_zero @ ( A @ bit0 @ ( int @ ord_less ) ) ) ),
inference(rewrite,[status(thm)],[495,35205]) ).
thf(24363,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[211,301]) ).
thf(24364,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[24363]) ).
thf(24365,plain,
t @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[24364:[bind(A,$thf( t )),bind(B,$thf( int @ one_one ))]]) ).
thf(24608,plain,
! [A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24365,187]) ).
thf(24609,plain,
! [A: int] :
( ( t @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[24608]) ).
thf(24632,plain,
! [A: int] :
( ( ( t @ bit1 )
!= A )
| ( ( int @ one_one @ bit1 )
!= A ) ),
inference(simp,[status(thm)],[24609]) ).
thf(24661,plain,
( ( t @ bit1 )
!= ( int @ one_one @ bit1 ) ),
inference(simp,[status(thm)],[24632]) ).
thf(31860,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28797,336]) ).
thf(31861,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( int @ one_one @ ( A @ ( int @ minus_minus ) ) @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[31860]) ).
thf(31862,plain,
int @ one_one @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ minus_minus ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[31861:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(28199,plain,
( ( ( int @ one_one @ bit1 @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[28117,26026]) ).
thf(28200,plain,
( ( int @ one_one @ bit1 @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[28199]) ).
thf(28226,plain,
( ( ( int @ one_one @ bit1 @ bit0 )
!= ( int @ one_one ) )
| ( ( int @ one_one )
!= ( int @ one_one ) ) ),
inference(simp,[status(thm)],[28200]) ).
thf(28240,plain,
( ( int @ one_one @ bit1 @ bit0 )
!= ( int @ one_one ) ),
inference(simp,[status(thm)],[28226]) ).
thf(462,plain,
! [B: nat,A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( nat @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[460]) ).
thf(463,plain,
! [B: nat,A: nat] :
( ( A @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ semiring_1_of_nat ) @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( nat @ ord_less ) ) ) ),
inference(simp,[status(thm)],[462]) ).
thf(9,axiom,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ minus_minus ) ) )
= ( A @ ( pls @ ( int @ minus_minus ) ) @ bit0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_15_diff__bin__simps_I3_J) ).
thf(127,plain,
! [A: int] :
( ( A @ bit0 @ ( pls @ ( int @ minus_minus ) ) )
= ( A @ ( pls @ ( int @ minus_minus ) ) @ bit0 ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(49095,plain,
! [A: int] :
( ( ( t @ bit1 @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[49030,187]) ).
thf(49096,plain,
! [A: int] :
( ( t @ bit1 @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[49095]) ).
thf(49143,plain,
! [A: int] :
( ( ( t @ bit1 @ bit1 )
!= A )
| ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= A ) ),
inference(simp,[status(thm)],[49096]) ).
thf(49177,plain,
( ( t @ bit1 @ bit1 )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[49143]) ).
thf(66,axiom,
int @ ring,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
thf(359,plain,
int @ ring,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(42786,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42704,159]) ).
thf(42787,plain,
! [B: int,A: int] :
( ( ( t @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[42786]) ).
thf(42788,plain,
t @ bit0 @ bit0 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[42787:[bind(A,$thf( t @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(52123,plain,
t @ bit0 @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[42788,33188]) ).
thf(23136,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22608,183]) ).
thf(23137,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[23136]) ).
thf(23138,plain,
int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[23137:[bind(A,$thf( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(1788,plain,
( ( t != t )
| ( m1
!= ( int @ one_one ) )
| ( ( t @ ( int @ one_one @ sk1 ) @ ( int @ semiring_1_of_nat ) )
!= ( n @ ( int @ semiring_1_of_nat ) ) ) ),
inference(simp,[status(thm)],[1769]) ).
thf(1790,plain,
( ( m1
!= ( int @ one_one ) )
| ( ( t @ ( int @ one_one @ sk1 ) @ ( int @ semiring_1_of_nat ) )
!= ( n @ ( int @ semiring_1_of_nat ) ) ) ),
inference(simp,[status(thm)],[1788]) ).
thf(53865,plain,
! [A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45719,53815]) ).
thf(53866,plain,
! [A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[53865]) ).
thf(53867,plain,
int @ one_one @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[53866:[bind(A,$thf( int @ one_one @ bit0 ))]]) ).
thf(54266,plain,
int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[53867,33188]) ).
thf(54331,plain,
! [A: int] :
( ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54266,187]) ).
thf(54332,plain,
! [A: int] :
( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[54331]) ).
thf(54392,plain,
! [A: int] :
( ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[54332]) ).
thf(54420,plain,
( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[54392]) ).
thf(54424,plain,
( ( int @ one_one @ bit0 @ ( int @ one_one @ bit1 @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
inference(rewrite,[status(thm)],[54420,175]) ).
thf(73920,plain,
( ( ( int @ one_one @ ( t @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72330,26026]) ).
thf(73921,plain,
( ( int @ one_one @ ( t @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( int @ one_one @ ( int @ one_one @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[73920]) ).
thf(73945,plain,
( ( ( int @ one_one @ ( t @ ( int @ plus_plus ) ) )
!= ( int @ one_one ) )
| ( ( int @ one_one )
!= ( int @ one_one ) ) ),
inference(simp,[status(thm)],[73921]) ).
thf(73968,plain,
( ( int @ one_one @ ( t @ ( int @ plus_plus ) ) )
!= ( int @ one_one ) ),
inference(simp,[status(thm)],[73945]) ).
thf(397,plain,
? [A: int > int] :
! [B: int] :
( ( B @ bit1 @ A )
= B ),
inference(detectInverse,[status(thm)],[396]) ).
thf(398,plain,
! [A: int] :
( ( A @ bit1 @ sk3 )
= A ),
inference(cnf,[status(esa)],[397]) ).
thf(38128,plain,
! [A: int] :
( ( A @ bit1 @ sk3 )
= A ),
inference(lifteq,[status(thm)],[398]) ).
thf(91,axiom,
int @ zero_zero @ ( m1 @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ minus_minus ) ) @ ( int @ ord_less_eq ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_40__0961_A_L_Aint_An_A_N_Am1_A_060_061_A0_096) ).
thf(470,plain,
int @ zero_zero @ ( m1 @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ minus_minus ) ) @ ( int @ ord_less_eq ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(55107,plain,
( ( ( t @ bit0 @ bit1 )
!= ( int @ zero_zero @ bit1 ) )
| ( ( int @ one_one )
!= ( int @ one_one ) ) ),
inference(paramod_ordered,[status(thm)],[35218,54780]) ).
thf(55108,plain,
( ( t @ bit0 @ bit1 )
!= ( int @ zero_zero @ bit1 ) ),
inference(simp,[status(thm)],[55107]) ).
thf(55129,plain,
( ( t @ bit0 )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[55108]) ).
thf(6191,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[498,183]) ).
thf(6192,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[6191]) ).
thf(6193,plain,
n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[6192:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(32610,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24871,187]) ).
thf(32611,plain,
! [A: int] :
( ( int @ one_one @ bit1 @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[32610]) ).
thf(32654,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit0 )
!= A )
| ( ( int @ one_one @ bit1 )
!= A ) ),
inference(simp,[status(thm)],[32611]) ).
thf(32677,plain,
( ( int @ one_one @ bit1 @ bit0 )
!= ( int @ one_one @ bit1 ) ),
inference(simp,[status(thm)],[32654]) ).
thf(54033,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38229,53815]) ).
thf(54034,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[54033]) ).
thf(54035,plain,
n @ ( int @ semiring_1_of_nat ) @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[54034:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) @ bit0 ))]]) ).
thf(60365,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54035,183]) ).
thf(60366,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[60365]) ).
thf(60367,plain,
n @ ( int @ semiring_1_of_nat ) @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[60366:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) @ bit0 @ bit1 )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(40587,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[38160,40526]) ).
thf(40588,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[40587]) ).
thf(40589,plain,
n @ ( int @ semiring_1_of_nat ) @ bit0 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[40588:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) @ bit0 ))]]) ).
thf(51414,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40589,187]) ).
thf(51415,plain,
! [A: int] :
( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[51414]) ).
thf(51477,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ bit0 )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[51415]) ).
thf(51486,plain,
( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ bit0 )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[51477]) ).
thf(72334,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68509,526]) ).
thf(72335,plain,
! [B: int,A: int] :
( ( ( t @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[72334]) ).
thf(72336,plain,
int @ one_one @ ( t @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[72335:[bind(A,$thf( t )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(30403,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[24825,330]) ).
thf(30404,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[30403]) ).
thf(30405,plain,
int @ one_one @ bit1 @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[30404:[bind(A,$thf( int @ one_one @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(18179,plain,
! [TA: $tType] :
( ~ ( int @ one_one @ ( TA @ number_number_of ) @ ( TA @ one_one @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(rewrite,[status(thm)],[4274,18097]) ).
thf(33227,plain,
int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[31501,33188]) ).
thf(41578,plain,
int @ one_one @ bit0 @ ( int @ one_one @ bit1 @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[33227,175]) ).
thf(524,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( int @ one_one @ ( A @ ( int @ plus_plus ) ) @ ( B @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[523]) ).
thf(45147,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44874,406]) ).
thf(45148,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[45147]) ).
thf(45149,plain,
n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[45148:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) )),bind(B,$thf( int @ one_one ))]]) ).
thf(58071,plain,
n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[45149,33188]) ).
thf(217,plain,
! [TA: $tType,C: TA,B: TA,A: int] :
( ( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) )
| ~ ( TA @ ring )
| ~ ( TA @ number ) ),
inference(cnf,[status(esa)],[216]) ).
thf(218,plain,
! [TA: $tType,C: TA,B: TA,A: int] :
( ~ ( TA @ ring )
| ~ ( TA @ number )
| ( ( A @ ( TA @ number_number_of ) @ ( B @ ( C @ ( TA @ minus_minus ) ) @ ( TA @ times_times ) ) )
= ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ times_times ) ) @ ( A @ ( TA @ number_number_of ) @ ( C @ ( TA @ times_times ) ) @ ( TA @ minus_minus ) ) ) ) ),
inference(lifteq,[status(thm)],[217]) ).
thf(53566,plain,
! [A: int] :
( ( ( t @ bit0 @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[53449,187]) ).
thf(53567,plain,
! [A: int] :
( ( t @ bit0 @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[53566]) ).
thf(53622,plain,
! [A: int] :
( ( ( t @ bit0 @ bit0 )
!= A )
| ( ( int @ one_one )
!= A ) ),
inference(simp,[status(thm)],[53567]) ).
thf(53644,plain,
( ( t @ bit0 @ bit0 )
!= ( int @ one_one ) ),
inference(simp,[status(thm)],[53622]) ).
thf(227,plain,
( ! [A: nat] :
( ( A
= ( nat @ zero_zero ) )
=> ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) ) )
& ! [A: nat] :
( ( ( A @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
=> ( A
= ( nat @ zero_zero ) ) ) ),
inference(miniscope,[status(thm)],[226]) ).
thf(228,plain,
! [B: nat,A: nat] :
( ( ( ( B @ ( int @ semiring_1_of_nat ) )
= ( int @ zero_zero ) )
| ( B
!= ( nat @ zero_zero ) ) )
& ( ( A
= ( nat @ zero_zero ) )
| ( ( A @ ( int @ semiring_1_of_nat ) )
!= ( int @ zero_zero ) ) ) ),
inference(cnf,[status(esa)],[227]) ).
thf(229,plain,
! [A: nat] :
( ( A
= ( nat @ zero_zero ) )
| ( ( A @ ( int @ semiring_1_of_nat ) )
!= ( int @ zero_zero ) ) ),
inference(cnfConj,[status(thm)],[228]) ).
thf(231,plain,
! [A: nat] :
( ( A
= ( nat @ zero_zero ) )
| ( ( A @ ( int @ semiring_1_of_nat ) )
!= ( int @ zero_zero ) ) ),
inference(lifteq,[status(thm)],[229]) ).
thf(450,plain,
! [TA: $tType,B: int,A: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[448]) ).
thf(28,axiom,
! [A: int] :
( ( pls @ ( A @ bit1 @ ( int @ ord_less ) ) )
<=> ( pls @ ( A @ ( int @ ord_less ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_52_rel__simps_I12_J) ).
thf(203,plain,
! [A: int] :
( ( ( pls @ ( A @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ bit1 @ ( int @ ord_less ) ) ) )
& ( ( pls @ ( A @ bit1 @ ( int @ ord_less ) ) )
=> ( pls @ ( A @ ( int @ ord_less ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(50761,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit0 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[40569,187]) ).
thf(50762,plain,
! [A: int] :
( ( int @ one_one @ bit1 @ bit0 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[50761]) ).
thf(50812,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit0 @ bit0 )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[50762]) ).
thf(50836,plain,
( ( int @ one_one @ bit1 @ bit0 @ bit0 )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[50812]) ).
thf(38129,plain,
! [A: int] :
( ( ( int @ zero_zero @ bit1 )
!= ( A @ bit1 ) )
| ( ( int @ one_one @ sk3 )
= A ) ),
inference(paramod_ordered,[status(thm)],[35218,38128]) ).
thf(38130,plain,
( ( int @ one_one @ sk3 )
= ( int @ zero_zero ) ),
inference(pattern_uni,[status(thm)],[38129:[bind(A,$thf( int @ zero_zero ))]]) ).
thf(1479,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1448,138]) ).
thf(1480,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[1479]) ).
thf(1481,plain,
t @ bit1 @ bit1 @ ( int @ one_one @ bit1 @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[1480:[bind(A,$thf( t @ bit1 )),bind(B,$thf( int @ one_one @ bit1 ))]]) ).
thf(1996,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ bit1 @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1946,138]) ).
thf(1997,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ bit1 @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[1996]) ).
thf(1998,plain,
pls @ bit1 @ bit1 @ bit1 @ ( pls @ bit1 @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[1997:[bind(A,$thf( pls @ bit1 @ bit1 )),bind(B,$thf( pls @ bit1 ))]]) ).
thf(18166,plain,
int @ one_one @ bit1 @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[1998,18097]) ).
thf(68913,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68156,183]) ).
thf(68914,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[68913]) ).
thf(68915,plain,
t @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[68914:[bind(A,$thf( t @ bit1 )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(69580,plain,
! [A: int] :
( ( ( t @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68915,44466]) ).
thf(69581,plain,
! [A: int] :
( ( ( t @ bit1 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[69580]) ).
thf(69582,plain,
t @ bit1 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[69581:[bind(A,$thf( t @ bit1 ))]]) ).
thf(3,axiom,
nat @ linorder,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',arity_Nat_Onat___Orderings_Olinorder) ).
thf(114,plain,
nat @ linorder,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(38004,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[37937,183]) ).
thf(38005,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[38004]) ).
thf(38006,plain,
n @ ( int @ semiring_1_of_nat ) @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[38005:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(72070,plain,
! [A: int] :
( ( ( t @ bit0 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68273,187]) ).
thf(72071,plain,
! [A: int] :
( ( t @ bit0 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[72070]) ).
thf(72142,plain,
! [A: int] :
( ( ( t @ bit0 @ bit0 )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[72071]) ).
thf(72163,plain,
( ( t @ bit0 @ bit0 )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[72142]) ).
thf(535,plain,
! [B: int,A: int] :
( ( A @ ( B @ bit1 @ ( int @ times_times ) ) )
= ( A @ ( A @ ( B @ ( int @ times_times ) ) @ bit0 @ ( int @ plus_plus ) ) ) ),
inference(cnf,[status(esa)],[534]) ).
thf(536,plain,
! [B: int,A: int] :
( ( A @ ( B @ bit1 @ ( int @ times_times ) ) )
= ( A @ ( A @ ( B @ ( int @ times_times ) ) @ bit0 @ ( int @ plus_plus ) ) ) ),
inference(lifteq,[status(thm)],[535]) ).
thf(73115,plain,
! [B: int,A: int] :
( ( A @ ( B @ bit1 @ ( int @ times_times ) ) )
= ( A @ ( A @ ( B @ bit0 @ ( int @ times_times ) ) @ ( int @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[536,355]) ).
thf(45720,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[45719,138]) ).
thf(45721,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[45720]) ).
thf(45722,plain,
int @ one_one @ bit0 @ bit1 @ ( int @ zero_zero @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[45721:[bind(A,$thf( int @ one_one @ bit0 )),bind(B,$thf( int @ zero_zero ))]]) ).
thf(58224,plain,
int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[45722,35218,33188]) ).
thf(11337,plain,
! [TB: $tType] :
( ( ( pls @ bit1 @ ( TB @ number_number_of ) )
!= ( pls @ bit1 @ ( TB @ number_number_of ) ) )
| ~ ( TB @ one_one @ ( TB @ one_one @ ( TB @ ord_less ) ) )
| ~ ( TB @ linordered_idom )
| ~ ( TB @ number_ring )
| ~ ( TB @ number_ring ) ),
inference(paramod_ordered,[status(thm)],[192,4274]) ).
thf(11338,plain,
! [TB: $tType] :
( ( ( pls @ bit1 @ ( TB @ number_number_of ) )
!= ( pls @ bit1 @ ( TB @ number_number_of ) ) )
| ~ ( TB @ one_one @ ( TB @ one_one @ ( TB @ ord_less ) ) )
| ~ ( TB @ linordered_idom )
| ~ ( TB @ number_ring ) ),
inference(simp,[status(thm)],[11337]) ).
thf(11339,plain,
! [TB: $tType] :
( ~ ( TB @ one_one @ ( TB @ one_one @ ( TB @ ord_less ) ) )
| ~ ( TB @ linordered_idom )
| ~ ( TB @ number_ring ) ),
inference(pattern_uni,[status(thm)],[11338:[]]) ).
thf(11366,plain,
! [TA: $tType] :
( ~ ( TA @ one_one @ ( TA @ one_one @ ( TA @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(simp,[status(thm)],[11339]) ).
thf(69455,plain,
! [A: int] :
( ( ( t @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[68636,44466]) ).
thf(69456,plain,
! [A: int] :
( ( ( t @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[69455]) ).
thf(69457,plain,
t @ bit0 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[69456:[bind(A,$thf( t @ bit0 ))]]) ).
thf(35430,plain,
int @ one_one @ bit1 @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[2370,35218]) ).
thf(46330,plain,
int @ one_one @ bit1 @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ),
inference(rewrite,[status(thm)],[35430,33188]) ).
thf(3340,plain,
( ( ( pls @ bit1 @ bit0 @ ( pls @ ( int @ ord_less ) ) )
!= ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) ) )
| ( pls
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[3306,1239]) ).
thf(3341,plain,
( ( ( pls @ bit1 @ bit0 @ ( pls @ ( int @ ord_less ) ) )
!= ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) ) )
| ( pls
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) ) ),
inference(simp,[status(thm)],[3340]) ).
thf(3391,plain,
( ( ( pls @ bit1 @ bit0 )
!= ( int @ zero_zero ) )
| ( pls != pls )
| ( pls
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) ) ),
inference(simp,[status(thm)],[3341]) ).
thf(3398,plain,
( ( ( pls @ bit1 @ bit0 )
!= ( int @ zero_zero ) )
| ( pls
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) ) ),
inference(simp,[status(thm)],[3391]) ).
thf(18164,plain,
( ( ( int @ one_one @ bit0 )
!= ( int @ zero_zero ) )
| ( pls
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) ) ),
inference(rewrite,[status(thm)],[3398,18097]) ).
thf(21794,plain,
( ( ( n @ ( int @ semiring_1_of_nat ) )
!= ( nat @ one_one @ ( int @ semiring_1_of_nat ) ) )
| ( ( int @ one_one @ bit0 )
!= ( int @ zero_zero ) )
| ( pls
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ) ),
inference(paramod_ordered,[status(thm)],[168,18164]) ).
thf(21802,plain,
( ( n
!= ( nat @ one_one ) )
| ( ( int @ one_one @ bit0 )
!= ( int @ zero_zero ) )
| ( pls
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ) ),
inference(simp,[status(thm)],[21794]) ).
thf(39439,plain,
( ( n
!= ( nat @ one_one ) )
| ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) )
| ( ( int @ zero_zero )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ) ),
inference(rewrite,[status(thm)],[21802,33188,35205]) ).
thf(39440,plain,
( ( n
!= ( nat @ one_one ) )
| ( ( int @ zero_zero )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ) ),
inference(simp,[status(thm)],[39439]) ).
thf(383,plain,
! [TA: $tType,B: int,A: int] :
( ~ ( B @ ( TA @ number_number_of ) @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( TA @ linorder )
| ~ ( TA @ number ) ),
inference(cnfConj,[status(thm)],[382]) ).
thf(52192,plain,
! [A: int] :
( ( ( t @ bit0 @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[52123,187]) ).
thf(52193,plain,
! [A: int] :
( ( t @ bit0 @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[52192]) ).
thf(52268,plain,
! [A: int] :
( ( ( t @ bit0 @ bit0 )
!= A )
| ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= A ) ),
inference(simp,[status(thm)],[52193]) ).
thf(52284,plain,
( ( t @ bit0 @ bit0 )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ),
inference(simp,[status(thm)],[52268]) ).
thf(22400,plain,
! [A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22348,187]) ).
thf(22401,plain,
! [A: int] :
( ( int @ one_one @ bit0 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[22400]) ).
thf(22427,plain,
! [A: int] :
( ( ( int @ one_one @ bit0 )
!= A )
| ( ( int @ one_one )
!= A ) ),
inference(simp,[status(thm)],[22401]) ).
thf(22447,plain,
( ( int @ one_one @ bit0 )
!= ( int @ one_one ) ),
inference(simp,[status(thm)],[22427]) ).
thf(33216,plain,
( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= ( int @ one_one ) ),
inference(rewrite,[status(thm)],[22447,33188]) ).
thf(552,plain,
! [B: int,A: int] :
( ( ( A @ ( B @ sk1 ) @ ( int @ semiring_1_of_nat ) @ ( B @ ( int @ plus_plus ) ) )
!= ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) ) )
| ~ ( int @ zero_zero @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( A @ ( int @ times_times ) ) @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(paramod_ordered,[status(thm)],[123,113]) ).
thf(555,plain,
! [B: int,A: int] :
( ( ( A @ ( B @ sk1 ) @ ( int @ semiring_1_of_nat ) )
!= ( n @ ( int @ semiring_1_of_nat ) ) )
| ( B
!= ( int @ one_one ) )
| ~ ( int @ zero_zero @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( A @ ( int @ times_times ) ) @ ( int @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[552]) ).
thf(558,plain,
! [A: int] :
( ( ( A @ ( int @ one_one @ sk1 ) @ ( int @ semiring_1_of_nat ) )
!= ( n @ ( int @ semiring_1_of_nat ) ) )
| ~ ( int @ zero_zero @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( A @ ( int @ times_times ) ) @ ( int @ ord_less ) ) )
| ~ ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[555]) ).
thf(560,plain,
! [A: int] :
( ( ( A @ ( int @ one_one @ sk1 ) )
!= n )
| ~ ( int @ zero_zero @ ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( A @ ( int @ times_times ) ) @ ( int @ ord_less ) ) )
| ~ ( A @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[558]) ).
thf(1192,plain,
! [B: int,A: int] :
( ( ( A @ ( pls @ ( int @ times_times ) ) )
!= ( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) @ ( B @ ( int @ times_times ) ) ) )
| ( ( B @ ( int @ one_one @ sk1 ) )
!= n )
| ~ ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) )
| ~ ( B @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) ),
inference(paramod_ordered,[status(thm)],[281,560]) ).
thf(1193,plain,
( ( ( pls @ ( int @ one_one @ sk1 ) )
!= n )
| ~ ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) )
| ~ ( pls @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) ),
inference(pattern_uni,[status(thm)],[1192:[bind(A,$thf( m1 @ ( pls @ bit1 @ bit0 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( pls @ bit1 @ bit0 @ ( int @ number_number_of ) @ ( int @ times_times ) ) @ ( int @ minus_minus ) ) )),bind(B,$thf( pls ))]]) ).
thf(2591,plain,
( ( ( pls @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) ) )
| ( ( pls @ ( int @ one_one @ sk1 ) )
!= n )
| ~ $true
| ~ ( pls @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) ),
inference(paramod_ordered,[status(thm)],[2588,1193]) ).
thf(2592,plain,
( ( ( pls @ bit1 @ ( pls @ ( int @ ord_less ) ) )
!= ( int @ zero_zero @ ( pls @ ( int @ ord_less ) ) ) )
| ( ( pls @ ( int @ one_one @ sk1 ) )
!= n )
| ~ ( pls @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[2591]) ).
thf(2659,plain,
( ( ( pls @ bit1 )
!= ( int @ zero_zero ) )
| ( pls != pls )
| ( ( pls @ ( int @ one_one @ sk1 ) )
!= n )
| ~ ( pls @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[2592]) ).
thf(2666,plain,
( ( ( pls @ bit1 )
!= ( int @ zero_zero ) )
| ( ( pls @ ( int @ one_one @ sk1 ) )
!= n )
| ~ ( pls @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[2659]) ).
thf(18138,plain,
( ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( ( pls @ ( int @ one_one @ sk1 ) )
!= n )
| ~ ( pls @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) ),
inference(rewrite,[status(thm)],[2666,18097]) ).
thf(28489,plain,
( ( ( int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( pls @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( ( pls @ ( int @ one_one @ sk1 ) )
!= n )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[922,18138]) ).
thf(28490,plain,
( ( ( int @ zero_zero @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( pls @ ( int @ one_one @ ( int @ ord_less_eq ) ) ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( ( pls @ ( int @ one_one @ sk1 ) )
!= n ) ),
inference(simp,[status(thm)],[28489]) ).
thf(28566,plain,
( ( pls
!= ( int @ zero_zero ) )
| ( ( int @ zero_zero )
!= ( int @ one_one ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( ( pls @ ( int @ one_one @ sk1 ) )
!= n ) ),
inference(simp,[status(thm)],[28490]) ).
thf(28638,plain,
( ( pls
!= ( int @ zero_zero ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( ( pls @ ( int @ one_one @ sk1 ) )
!= n ) ),
inference(simp,[status(thm)],[28566]) ).
thf(35265,plain,
( ( ( int @ zero_zero )
!= ( int @ zero_zero ) )
| ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( ( int @ zero_zero @ ( int @ one_one @ sk1 ) )
!= n ) ),
inference(rewrite,[status(thm)],[28638,35205]) ).
thf(35266,plain,
( ( ( int @ one_one )
!= ( int @ zero_zero ) )
| ( ( int @ zero_zero @ ( int @ one_one @ sk1 ) )
!= n ) ),
inference(simp,[status(thm)],[35265]) ).
thf(45111,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[44874,138]) ).
thf(45112,plain,
! [B: int,A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[45111]) ).
thf(45113,plain,
n @ ( int @ semiring_1_of_nat ) @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[45112:[bind(A,$thf( n @ ( int @ semiring_1_of_nat ) )),bind(B,$thf( int @ one_one ))]]) ).
thf(151,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[150]) ).
thf(416,plain,
! [A: int] :
( ( A @ ( pls @ ( int @ ord_less ) ) )
| ~ ( A @ bit0 @ ( pls @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[415]) ).
thf(40125,plain,
! [A: int] :
( ( A @ ( int @ zero_zero @ ( int @ ord_less ) ) )
| ~ ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less ) ) ) ),
inference(rewrite,[status(thm)],[416,35205]) ).
thf(22474,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22420,153]) ).
thf(22475,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ ( int @ one_one @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[22474]) ).
thf(22476,plain,
int @ one_one @ bit0 @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[22475:[bind(A,$thf( int @ one_one @ bit0 )),bind(B,$thf( int @ one_one ))]]) ).
thf(30538,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[22476,183]) ).
thf(30539,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit0 @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[30538]) ).
thf(30540,plain,
int @ one_one @ bit0 @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[30539:[bind(A,$thf( int @ one_one @ bit0 @ bit1 )),bind(B,$thf( int @ one_one @ bit0 ))]]) ).
thf(39584,plain,
int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ bit1 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[30540,33188]) ).
thf(39307,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[39227,330]) ).
thf(39308,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[39307]) ).
thf(39309,plain,
t @ bit1 @ bit0 @ ( int @ one_one @ bit1 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[39308:[bind(A,$thf( t @ bit1 )),bind(B,$thf( int @ one_one ))]]) ).
thf(60326,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[54035,187]) ).
thf(60327,plain,
! [A: int] :
( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ bit1 @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[60326]) ).
thf(60388,plain,
! [A: int] :
( ( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ bit1 )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[60327]) ).
thf(60414,plain,
( ( n @ ( int @ semiring_1_of_nat ) @ bit0 @ bit1 )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[60388]) ).
thf(3933,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ bit1 @ ( int @ zero_zero @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1459,166]) ).
thf(3934,plain,
! [B: int,A: int] :
( ( ( int @ zero_zero @ bit1 @ ( int @ zero_zero @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[3933]) ).
thf(3935,plain,
int @ zero_zero @ bit1 @ bit0 @ ( int @ zero_zero @ bit1 @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[3934:[bind(A,$thf( int @ zero_zero @ bit1 )),bind(B,$thf( int @ zero_zero @ bit1 ))]]) ).
thf(35429,plain,
int @ one_one @ bit0 @ ( int @ one_one @ bit0 @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[3935,35218]) ).
thf(37282,plain,
int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[35429,33188]) ).
thf(3792,plain,
! [A: int] :
( ( ( t @ bit1 @ bit1 @ ( int @ one_one @ bit1 @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2459,187]) ).
thf(3793,plain,
! [A: int] :
( ( t @ bit1 @ bit1 @ ( int @ one_one @ bit1 @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[3792]) ).
thf(3839,plain,
! [A: int] :
( ( ( t @ bit1 @ bit1 )
!= A )
| ( ( int @ one_one @ bit1 @ bit0 )
!= A ) ),
inference(simp,[status(thm)],[3793]) ).
thf(3843,plain,
( ( t @ bit1 @ bit1 )
!= ( int @ one_one @ bit1 @ bit0 ) ),
inference(simp,[status(thm)],[3839]) ).
thf(242,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( A @ bit0 @ ( B @ bit1 @ ( int @ ord_less ) ) ) ),
inference(cnfConj,[status(thm)],[241]) ).
thf(424,plain,
! [TA: $tType,A: int] :
( ( pls @ bit1 @ ( A @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[423]) ).
thf(41723,plain,
! [TA: $tType,A: int] :
( ( int @ zero_zero @ bit1 @ ( A @ ( int @ ord_less_eq ) ) )
| ~ ( TA @ one_one @ ( A @ ( TA @ number_number_of ) @ ( TA @ ord_less_eq ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(rewrite,[status(thm)],[424,35205]) ).
thf(136,plain,
! [B: int,A: int] :
( ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ ( A @ bit1 @ ( B @ bit1 @ ( int @ ord_less_eq ) ) ) ),
inference(cnfConj,[status(thm)],[135]) ).
thf(35291,plain,
( ( int @ zero_zero @ ( int @ zero_zero @ bit1 @ ( int @ plus_plus ) ) )
= ( int @ zero_zero @ bit1 ) ),
inference(rewrite,[status(thm)],[13597,35216]) ).
thf(45218,plain,
( ( int @ zero_zero @ ( int @ one_one @ ( int @ plus_plus ) ) )
= ( int @ one_one ) ),
inference(rewrite,[status(thm)],[35291,35218]) ).
thf(109,axiom,
! [A: int,B: int] :
( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
<=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_81_less__eq__int__code_I14_J) ).
thf(528,plain,
! [A: int,B: int] :
( ( ( A @ ( B @ ( int @ ord_less_eq ) ) )
=> ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) )
& ( ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
=> ( A @ ( B @ ( int @ ord_less_eq ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(51859,plain,
! [A: int] :
( ( ( t @ bit0 @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[42751,187]) ).
thf(51860,plain,
! [A: int] :
( ( t @ bit0 @ bit1 @ ( int @ one_one @ bit1 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[51859]) ).
thf(51916,plain,
! [A: int] :
( ( ( t @ bit0 @ bit1 )
!= A )
| ( ( int @ one_one @ bit1 )
!= A ) ),
inference(simp,[status(thm)],[51860]) ).
thf(51926,plain,
( ( t @ bit0 @ bit1 )
!= ( int @ one_one @ bit1 ) ),
inference(simp,[status(thm)],[51916]) ).
thf(74126,plain,
! [A: int] :
( ( ( int @ one_one @ ( t @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[72336,187]) ).
thf(74127,plain,
! [A: int] :
( ( int @ one_one @ ( t @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[74126]) ).
thf(74189,plain,
! [A: int] :
( ( ( int @ one_one @ ( t @ ( int @ plus_plus ) ) )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[74127]) ).
thf(74215,plain,
( ( int @ one_one @ ( t @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[74189]) ).
thf(6134,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ bit1 @ ( int @ one_one @ bit1 @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2459,183]) ).
thf(6135,plain,
! [B: int,A: int] :
( ( ( t @ bit1 @ bit1 @ ( int @ one_one @ bit1 @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( B @ ( int @ ord_less ) ) ) )
| ( A @ ( B @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[6134]) ).
thf(6136,plain,
t @ bit1 @ bit1 @ ( int @ one_one @ bit1 @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[6135:[bind(A,$thf( t @ bit1 @ bit1 )),bind(B,$thf( int @ one_one @ bit1 @ bit0 ))]]) ).
thf(44639,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[35248,44466]) ).
thf(44640,plain,
! [A: int] :
( ( ( int @ one_one @ bit1 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) )
!= ( A @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[44639]) ).
thf(44641,plain,
int @ one_one @ bit1 @ bit0 @ bit0 @ ( int @ zero_zero @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[44640:[bind(A,$thf( int @ one_one @ bit1 @ bit0 ))]]) ).
thf(3853,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ zero_zero @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1454,166]) ).
thf(3854,plain,
! [B: int,A: int] :
( ( ( int @ one_one @ bit1 @ ( int @ zero_zero @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit0 @ ( B @ bit0 @ ( int @ ord_less_eq ) ) ) ),
inference(simp,[status(thm)],[3853]) ).
thf(3855,plain,
int @ one_one @ bit1 @ bit0 @ ( int @ zero_zero @ bit1 @ bit0 @ ( int @ ord_less_eq ) ),
inference(pattern_uni,[status(thm)],[3854:[bind(A,$thf( int @ one_one @ bit1 )),bind(B,$thf( int @ zero_zero @ bit1 ))]]) ).
thf(35422,plain,
int @ one_one @ bit1 @ bit0 @ ( int @ one_one @ bit0 @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[3855,35218]) ).
thf(45809,plain,
int @ one_one @ bit1 @ bit0 @ ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[35422,33188]) ).
thf(198,plain,
! [TA: $tType,A: TA] :
( ( A
= ( TA @ zero_zero ) )
| ( ( A @ ( A @ ( TA @ plus_plus ) ) )
!= ( TA @ zero_zero ) )
| ~ ( TA @ linord219039673up_add ) ),
inference(cnfConj,[status(thm)],[197]) ).
thf(200,plain,
! [TA: $tType,A: TA] :
( ~ ( TA @ linord219039673up_add )
| ( A
= ( TA @ zero_zero ) )
| ( ( A @ ( A @ ( TA @ plus_plus ) ) )
!= ( TA @ zero_zero ) ) ),
inference(lifteq,[status(thm)],[198]) ).
thf(18139,plain,
int @ one_one @ ( int @ one_one @ ( int @ ord_less_eq ) ),
inference(rewrite,[status(thm)],[1451,18097]) ).
thf(2542,plain,
! [A: int] :
( ( ( t @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2408,187]) ).
thf(2543,plain,
! [A: int] :
( ( t @ bit1 @ ( int @ one_one @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[2542]) ).
thf(2584,plain,
! [A: int] :
( ( ( t @ bit1 )
!= A )
| ( ( int @ one_one @ bit0 )
!= A ) ),
inference(simp,[status(thm)],[2543]) ).
thf(2587,plain,
( ( t @ bit1 )
!= ( int @ one_one @ bit0 ) ),
inference(simp,[status(thm)],[2584]) ).
thf(33257,plain,
( ( t @ bit1 )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[2587,33188]) ).
thf(2419,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[1451,153]) ).
thf(2420,plain,
! [B: int,A: int] :
( ( ( pls @ bit1 @ ( pls @ bit1 @ ( int @ ord_less_eq ) ) )
!= ( A @ ( B @ ( int @ ord_less_eq ) ) ) )
| ( A @ bit1 @ ( B @ bit0 @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[2419]) ).
thf(2421,plain,
pls @ bit1 @ bit1 @ ( pls @ bit1 @ bit0 @ ( int @ ord_less ) ),
inference(pattern_uni,[status(thm)],[2420:[bind(A,$thf( pls @ bit1 )),bind(B,$thf( pls @ bit1 ))]]) ).
thf(3620,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit1 @ ( pls @ bit1 @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[2421,187]) ).
thf(3621,plain,
! [A: int] :
( ( pls @ bit1 @ bit1 @ ( pls @ bit1 @ bit0 @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[3620]) ).
thf(3645,plain,
! [A: int] :
( ( ( pls @ bit1 @ bit1 )
!= A )
| ( ( pls @ bit1 @ bit0 )
!= A ) ),
inference(simp,[status(thm)],[3621]) ).
thf(3671,plain,
( ( pls @ bit1 @ bit1 )
!= ( pls @ bit1 @ bit0 ) ),
inference(simp,[status(thm)],[3645]) ).
thf(18137,plain,
( ( int @ one_one @ bit1 )
!= ( int @ one_one @ bit0 ) ),
inference(rewrite,[status(thm)],[3671,18097]) ).
thf(33224,plain,
( ( int @ one_one @ bit1 )
!= ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) ) ),
inference(rewrite,[status(thm)],[18137,33188]) ).
thf(58739,plain,
! [A: int] :
( ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) )
| ~ $true ),
inference(paramod_ordered,[status(thm)],[58666,187]) ).
thf(58740,plain,
! [A: int] :
( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ zero_zero @ ( int @ ord_less ) ) )
!= ( A @ ( A @ ( int @ ord_less ) ) ) ),
inference(simp,[status(thm)],[58739]) ).
thf(58820,plain,
! [A: int] :
( ( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= A )
| ( ( int @ zero_zero )
!= A ) ),
inference(simp,[status(thm)],[58740]) ).
thf(58843,plain,
( ( int @ one_one @ ( int @ one_one @ ( int @ plus_plus ) ) @ ( int @ one_one @ ( int @ plus_plus ) ) )
!= ( int @ zero_zero ) ),
inference(simp,[status(thm)],[58820]) ).
thf(454,plain,
! [TA: $tType,B: int,A: int] :
( ( A @ ( TA @ number_number_of ) @ ( B @ ( TA @ number_number_of ) @ ( TA @ ord_less ) ) )
| ~ ( A @ ( B @ ( int @ ord_less ) ) )
| ~ ( TA @ linordered_idom )
| ~ ( TA @ number_ring ) ),
inference(cnfConj,[status(thm)],[452]) ).
thf(82629,plain,
$false,
inference(e,[status(thm)],[31720,39365,138,39716,479,249,518,234,18228,44363,45459,44870,22328,1767,347,35236,18165,481,38259,115,42813,276,28205,58666,449,614,50660,53054,202,68176,500,42207,35222,61058,2459,27094,49183,153,39885,35217,385,384,71419,404,23184,60462,47141,35955,301,57434,33068,38747,436,40987,43117,39788,45719,50109,33568,59259,34896,35218,196,3938,53449,35229,59201,504,33226,51122,125,37173,157,61429,421,325,24871,35261,70631,43620,39377,189,49406,33206,49832,40569,59629,475,179,33786,321,485,1151,30838,216,492,164,35225,22608,211,253,50841,353,147,37937,293,453,132,396,133,660,116,60217,68056,54589,507,37733,46481,527,42844,312,68124,292,248,512,37192,35729,57263,381,39299,44540,534,380,117,35238,40416,220,366,42751,42795,48333,2277,302,160,35220,35235,334,23250,407,68509,275,55433,33540,54739,38160,484,30708,35206,33263,40533,35203,461,72330,68273,324,49030,39348,33210,34754,44647,49270,356,169,38036,499,53815,42850,317,37708,488,18132,54498,44269,41956,526,489,1791,49442,39326,212,328,471,256,193,537,24931,35211,71215,515,1131,173,19049,58377,29022,237,266,360,39267,40526,53359,794,52895,44009,70198,244,42802,44874,2995,55275,68109,68636,52107,166,68041,148,35268,161,279,22296,375,513,430,31874,56354,180,296,50052,176,50085,33208,36854,70590,413,47214,43190,35205,118,37395,71458,391,54784,498,61579,47855,45084,47703,159,71258,43275,187,406,113,219,47096,46715,419,245,318,303,274,68498,377,2257,18118,451,57417,367,54780,140,520,36562,39315,330,42783,56485,323,983,278,31755,455,32509,226,39227,438,70412,521,59639,130,33221,299,45945,922,167,53062,927,255,209,355,458,35212,426,55923,29021,37639,42560,516,33285,342,123,35875,295,282,72860,39165,12219,68156,35263,59798,35216,331,24661,31862,38229,28240,463,127,49177,359,52123,23138,1790,54424,35248,73968,54029,38128,470,55129,68145,13461,6193,175,446,32677,336,53883,29008,154,60367,51486,68639,363,72336,30405,18179,41578,524,58071,218,1448,53644,231,1316,450,482,203,68131,50836,38130,1481,18166,24365,69582,114,401,139,49918,38006,72163,73115,510,28117,58224,11366,69457,46330,28797,24836,290,378,39440,246,383,52284,42704,447,315,33216,146,35266,190,183,23247,45113,2258,26026,151,168,262,422,40125,210,39584,39309,60414,37282,3843,24825,239,242,41723,126,136,45218,44466,54035,53598,33188,528,131,51926,277,74215,6136,464,44641,68915,45809,200,54266,442,18139,486,33257,337,40589,309,543,33224,58843,454,48191]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM993_5 : TPTP v9.3.1. Released v6.0.0.
% 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
% 0.15/0.40 % Computer : n008.cluster.edu
% 0.15/0.40 % Model : x86_64 x86_64
% 0.15/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.40 % Memory : 8046.5625MB
% 0.15/0.40 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 04:25:39 UTC 2026
% 0.15/0.41 % CPUTime :
% 0.15/0.41 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
% 0.68/0.72 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 0.90/0.89 % [INFO] Parsing done (164ms).
% 1.30/0.90 % [INFO] Running in sequential loop mode.
% 1.81/1.11 % [INFO] eprover registered as external prover.
% 1.81/1.11 % [INFO] Scanning for conjecture ...
% 2.08/1.20 % [INFO] Found a conjecture (or negated_conjecture) and 112 axioms. Running axiom selection ...
% 2.25/1.26 % [INFO] Axiom selection finished. Selected 110 axioms (removed 2 axioms).
% 2.63/1.36 % [INFO] Problem is typed first-order (TPTP TFF).
% 2.63/1.37 % [INFO] Type checking passed.
% 2.63/1.38 % [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 ...
% 148.59/36.87 % External prover 'e' found a proof!
% 148.59/36.87 % [INFO] Killing All external provers ...
% 148.59/36.87 % Time passed: 36359ms (effective reasoning time: 35970ms)
% 148.59/36.87 % 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)>
% 148.59/36.88 % Axioms used in derivation (110): fact_57_rel__simps_I32_J, fact_33_rel__simps_I34_J, fact_97_number__of__is__id, fact_47_le__number__of, fact_36_mult__Pls, fact_40__0961_A_L_Aint_An_A_N_Am1_A_060_061_A0_096, fact_16_diff__bin__simps_I9_J, fact_69_le__special_I3_J, fact_10_less__special_I1_J, fact_62_diff__bin__simps_I10_J, fact_68_zle__diff1__eq, fact_20_rel__simps_I51_J, fact_87_int__1, fact_51_add__number__of__eq, fact_17_n0, fact_24_rel__simps_I39_J, fact_48_mult__number__of__left, arity_Int_Oint___Rings_Olinordered__idom, fact_86_zle__iff__zadd, arity_Int_Oint___Int_Oring__char__0, fact_3_n1pos, fact_6_add__special_I3_J, fact_7_less__special_I2_J, fact_15_diff__bin__simps_I3_J, fact_35_rel__simps_I31_J, fact_31_rel__simps_I2_J, fact_28_rel__simps_I38_J, fact_56_rel__simps_I22_J, fact_2__096_I1_A_L_Aint_An_J_A_K_A_I2_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_J_A_060_A_I1_A_L_Aint_An_J_A_K_A0_096, fact_73_less__eq__int__code_I16_J, fact_61_add__Bit0__Bit1, fact_85_zless__int, arity_Int_Oint___Rings_Oring, fact_44_left__diff__distrib__number__of, fact_77_int__le__0__conv, fact_14_numeral__1__eq__1, fact_91_less__int__code_I14_J, arity_Int_Oint___Int_Onumber__ring, fact_22_double__eq__0__iff, fact_39_diff__bin__simps_I7_J, fact_45_right__diff__distrib__number__of, fact_1__096_126_Am1_A_060_A1_A_L_Aint_An_096, arity_HOL_Obool___Orderings_Olinorder, fact_74_less__eq__int__code_I13_J, fact_30_rel__simps_I17_J, fact_13_mult__Bit1, fact_72_le__special_I2_J, fact_93_zless__imp__add1__zle, fact_50_add__number__of__left, fact_34_rel__simps_I19_J, fact_26_rel__simps_I49_J, arity_Nat_Onat___Orderings_Olinorder, fact_76_less__eq__number__of__int__code, fact_12__0964_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_A_060_061_A0_096, fact_8_less__special_I4_J, fact_9_one__add__one__is__two, fact_90_less__eq__int__code_I15_J, fact_82_zero__zle__int, fact_42_right__distrib__number__of, fact_96_number__of__reorient, fact_78_zero__less__int__conv, fact_84_zadd__int, fact_54_rel__simps_I10_J, fact_89_int__0, arity_Int_Oint___Orderings_Olinorder, fact_43_number__of__Pls, fact_75_less__int__def, fact_25_rel__simps_I50_J, fact_81_less__eq__int__code_I14_J, arity_Int_Oint___Rings_Osemiring, fact_79_zmult__zless__mono2__lemma, fact_46_less__number__of, fact_5_add__special_I2_J, fact_27_rel__simps_I44_J, fact_67_zle__add1__eq__le, fact_19_eq__number__of, fact_4__0962_A_K_A_I1_A_L_Aint_An_J_A_N_A4_A_K_Am1_A_060_A0_096, fact_41_left__distrib__number__of, fact_52_rel__simps_I12_J, fact_65_rel__simps_I33_J, fact_11_less__special_I3_J, fact_60_add__Bit1__Bit0, fact_49_arith__simps_I32_J, fact_55_rel__simps_I4_J, fact_94_add1__zle__eq, fact_18_tpos, fact_38_add__Bit0__Bit0, arity_Nat_Onat___Int_Onumber, fact_0_t1, fact_95_le__imp__0__less, fact_32_rel__simps_I14_J, fact_58_rel__simps_I27_J, fact_71_le__special_I4_J, fact_29_Bit0__Pls, fact_23_rel__simps_I46_J, fact_21_rel__simps_I48_J, arity_Nat_Onat___Rings_Osemiring, fact_80_le__number__of__eq__not__less, fact_70_le__special_I1_J, arity_Int_Oint___Int_Onumber, arity_Int_Oint___Groups_Olinordered__ab__group__add, fact_83_zadd__int__left, fact_88_int__eq__0__conv, fact_59_rel__simps_I21_J, fact_92_int__one__le__iff__zero__less, fact_66_rel__simps_I15_J, fact_37_mult__Bit0, fact_53_rel__simps_I16_J, fact_63_rel__simps_I29_J, fact_64_rel__simps_I5_J
% 148.59/36.88 % No. of inferences in proof: 1514
% 148.59/36.88 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 36359 ms resp. 35970 ms w/o parsing
% 151.16/37.26 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 151.16/37.27 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------