TSTP Solution File: NUM989_5 by Vampire-SAT---4.8
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM989_5 : TPTP v8.2.0. Released v6.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n032.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue May 21 02:15:18 EDT 2024
% Result : Theorem 3.00s 0.76s
% Output : Refutation 3.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 75
% Syntax : Number of formulae : 265 ( 68 unt; 29 typ; 0 def)
% Number of atoms : 575 ( 86 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 581 ( 242 ~; 228 |; 37 &)
% ( 51 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 7 ( 1 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 15 ( 10 >; 5 *; 0 +; 0 <<)
% Number of predicates : 21 ( 19 usr; 9 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 6 con; 0-3 aty)
% Number of variables : 305 ( 288 !; 0 ?; 305 :)
% ( 17 !>; 0 ?*; 0 @-; 0 @+)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
bool: $tType ).
tff(type_def_6,type,
int: $tType ).
tff(type_def_7,type,
nat: $tType ).
tff(func_def_0,type,
minus_minus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_1,type,
one_one:
!>[X0: $tType] : X0 ).
tff(func_def_2,type,
plus_plus:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_3,type,
times_times:
!>[X0: $tType] : ( ( X0 * X0 ) > X0 ) ).
tff(func_def_4,type,
zero_zero:
!>[X0: $tType] : X0 ).
tff(func_def_5,type,
bit0: int > int ).
tff(func_def_6,type,
bit1: int > int ).
tff(func_def_7,type,
pls: int ).
tff(func_def_8,type,
number_number_of:
!>[X0: $tType] : ( int > X0 ) ).
tff(func_def_9,type,
semiring_1_of_nat:
!>[X0: $tType] : ( nat > X0 ) ).
tff(func_def_10,type,
fFalse: bool ).
tff(func_def_11,type,
fTrue: bool ).
tff(func_def_12,type,
m1: int ).
tff(func_def_13,type,
n: nat ).
tff(func_def_14,type,
t: int ).
tff(pred_def_1,type,
number:
!>[X0: $tType] : $o ).
tff(pred_def_2,type,
ring:
!>[X0: $tType] : $o ).
tff(pred_def_3,type,
semiring:
!>[X0: $tType] : $o ).
tff(pred_def_4,type,
number_ring:
!>[X0: $tType] : $o ).
tff(pred_def_5,type,
ring_char_0:
!>[X0: $tType] : $o ).
tff(pred_def_6,type,
linorder:
!>[X0: $tType] : $o ).
tff(pred_def_7,type,
linordered_idom:
!>[X0: $tType] : $o ).
tff(pred_def_8,type,
linord219039673up_add:
!>[X0: $tType] : $o ).
tff(pred_def_9,type,
ord_less:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_10,type,
ord_less_eq:
!>[X0: $tType] : ( ( X0 * X0 ) > $o ) ).
tff(pred_def_11,type,
pp: bool > $o ).
tff(f15594,plain,
$false,
inference(avatar_sat_refutation,[],[f1442,f1512,f6560,f6581,f8324,f8325,f9358,f10842,f14761]) ).
tff(f14761,plain,
( ~ spl0_21
| ~ spl0_78 ),
inference(avatar_contradiction_clause,[],[f14760]) ).
tff(f14760,plain,
( $false
| ~ spl0_21
| ~ spl0_78 ),
inference(subsumption_resolution,[],[f1426,f8320]) ).
tff(f8320,plain,
( ! [X0: int,X1: int] : ~ ord_less(int,X1,X0)
| ~ spl0_78 ),
inference(avatar_component_clause,[],[f8319]) ).
tff(f8319,plain,
( spl0_78
<=> ! [X0: int,X1: int] : ~ ord_less(int,X1,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_78])]) ).
tff(f1426,plain,
( ord_less(int,zero_zero(int),pls)
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f1425]) ).
tff(f1425,plain,
( spl0_21
<=> ord_less(int,zero_zero(int),pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
tff(f10842,plain,
( ~ spl0_6
| ~ spl0_53 ),
inference(avatar_contradiction_clause,[],[f10841]) ).
tff(f10841,plain,
( $false
| ~ spl0_6
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f10826,f319]) ).
tff(f319,plain,
ord_less_eq(int,pls,pls),
inference(cnf_transformation,[],[f33]) ).
tff(f33,axiom,
ord_less_eq(int,pls,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_32_rel__simps_I19_J) ).
tff(f10826,plain,
( ~ ord_less_eq(int,pls,pls)
| ~ spl0_6
| ~ spl0_53 ),
inference(backward_demodulation,[],[f6610,f9908]) ).
tff(f9908,plain,
( ( pls = plus_plus(int,pls,pls) )
| ~ spl0_6 ),
inference(backward_demodulation,[],[f695,f680]) ).
tff(f680,plain,
( ( zero_zero(int) = pls )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f678]) ).
tff(f678,plain,
( spl0_6
<=> ( zero_zero(int) = pls ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
tff(f695,plain,
zero_zero(int) = plus_plus(int,zero_zero(int),zero_zero(int)),
inference(resolution,[],[f472,f304]) ).
tff(f304,plain,
linord219039673up_add(int),
inference(cnf_transformation,[],[f99]) ).
tff(f99,axiom,
linord219039673up_add(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Groups_Olinordered__ab__group__add) ).
tff(f472,plain,
! [X0: $tType] :
( ~ linord219039673up_add(X0)
| ( zero_zero(X0) = plus_plus(X0,zero_zero(X0),zero_zero(X0)) ) ),
inference(equality_resolution,[],[f334]) ).
tff(f334,plain,
! [X0: $tType,X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
| ( zero_zero(X0) != X1 )
| ~ linord219039673up_add(X0) ),
inference(cnf_transformation,[],[f245]) ).
tff(f245,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
| ( zero_zero(X0) != X1 ) )
& ( ( zero_zero(X0) = X1 )
| ( zero_zero(X0) != plus_plus(X0,X1,X1) ) ) )
| ~ linord219039673up_add(X0) ),
inference(nnf_transformation,[],[f197]) ).
tff(f197,plain,
! [X0: $tType] :
( ! [X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
<=> ( zero_zero(X0) = X1 ) )
| ~ linord219039673up_add(X0) ),
inference(ennf_transformation,[],[f121]) ).
tff(f121,plain,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X1: X0] :
( ( zero_zero(X0) = plus_plus(X0,X1,X1) )
<=> ( zero_zero(X0) = X1 ) ) ),
inference(rectify,[],[f21]) ).
tff(f21,axiom,
! [X0: $tType] :
( linord219039673up_add(X0)
=> ! [X9: X0] :
( ( zero_zero(X0) = plus_plus(X0,X9,X9) )
<=> ( zero_zero(X0) = X9 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_20_double__eq__0__iff) ).
tff(f6610,plain,
( ~ ord_less_eq(int,plus_plus(int,pls,pls),pls)
| ~ spl0_53 ),
inference(forward_demodulation,[],[f6609,f318]) ).
tff(f318,plain,
pls = bit0(pls),
inference(cnf_transformation,[],[f28]) ).
tff(f28,axiom,
pls = bit0(pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_27_Bit0__Pls) ).
tff(f6609,plain,
( ~ ord_less_eq(int,plus_plus(int,pls,bit0(pls)),pls)
| ~ spl0_53 ),
inference(forward_demodulation,[],[f6605,f1086]) ).
tff(f1086,plain,
! [X0: int] : ( plus_plus(int,pls,bit0(X0)) = times_times(int,bit0(bit1(pls)),X0) ),
inference(forward_demodulation,[],[f1085,f761]) ).
tff(f761,plain,
! [X0: int] : ( bit0(plus_plus(int,pls,X0)) = plus_plus(int,pls,bit0(X0)) ),
inference(superposition,[],[f415,f318]) ).
tff(f415,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
inference(cnf_transformation,[],[f167]) ).
tff(f167,plain,
! [X0: int,X1: int] : ( plus_plus(int,bit0(X1),bit0(X0)) = bit0(plus_plus(int,X1,X0)) ),
inference(rectify,[],[f37]) ).
tff(f37,axiom,
! [X5: int,X6: int] : ( plus_plus(int,bit0(X6),bit0(X5)) = bit0(plus_plus(int,X6,X5)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_36_add__Bit0__Bit0) ).
tff(f1085,plain,
! [X0: int] : ( bit0(plus_plus(int,pls,X0)) = times_times(int,bit0(bit1(pls)),X0) ),
inference(superposition,[],[f409,f1011]) ).
tff(f1011,plain,
! [X0: int] : ( plus_plus(int,pls,X0) = times_times(int,bit1(pls),X0) ),
inference(forward_demodulation,[],[f1000,f330]) ).
tff(f330,plain,
! [X0: int] : ( pls = times_times(int,pls,X0) ),
inference(cnf_transformation,[],[f118]) ).
tff(f118,plain,
! [X0: int] : ( pls = times_times(int,pls,X0) ),
inference(rectify,[],[f35]) ).
tff(f35,axiom,
! [X1: int] : ( pls = times_times(int,pls,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_34_mult__Pls) ).
tff(f1000,plain,
! [X0: int] : ( times_times(int,bit1(pls),X0) = plus_plus(int,times_times(int,pls,X0),X0) ),
inference(superposition,[],[f485,f318]) ).
tff(f485,plain,
! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,times_times(int,bit0(X1),X0),X0) ),
inference(forward_demodulation,[],[f416,f409]) ).
tff(f416,plain,
! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,bit0(times_times(int,X1,X0)),X0) ),
inference(cnf_transformation,[],[f168]) ).
tff(f168,plain,
! [X0: int,X1: int] : ( times_times(int,bit1(X1),X0) = plus_plus(int,bit0(times_times(int,X1,X0)),X0) ),
inference(rectify,[],[f10]) ).
tff(f10,axiom,
! [X5: int,X6: int] : ( times_times(int,bit1(X6),X5) = plus_plus(int,bit0(times_times(int,X6,X5)),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_9_mult__Bit1) ).
tff(f409,plain,
! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
inference(cnf_transformation,[],[f161]) ).
tff(f161,plain,
! [X0: int,X1: int] : ( bit0(times_times(int,X1,X0)) = times_times(int,bit0(X1),X0) ),
inference(rectify,[],[f36]) ).
tff(f36,axiom,
! [X5: int,X6: int] : ( bit0(times_times(int,X6,X5)) = times_times(int,bit0(X6),X5) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_35_mult__Bit0) ).
tff(f6605,plain,
( ~ ord_less_eq(int,times_times(int,bit0(bit1(pls)),pls),pls)
| ~ spl0_53 ),
inference(resolution,[],[f6604,f617]) ).
tff(f617,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,times_times(int,bit0(X0),X1),pls)
| ~ ord_less_eq(int,times_times(int,X0,X1),pls) ),
inference(superposition,[],[f388,f409]) ).
tff(f388,plain,
! [X0: int] :
( ord_less_eq(int,bit0(X0),pls)
| ~ ord_less_eq(int,X0,pls) ),
inference(cnf_transformation,[],[f265]) ).
tff(f265,plain,
! [X0: int] :
( ( ord_less_eq(int,bit0(X0),pls)
| ~ ord_less_eq(int,X0,pls) )
& ( ord_less_eq(int,X0,pls)
| ~ ord_less_eq(int,bit0(X0),pls) ) ),
inference(nnf_transformation,[],[f149]) ).
tff(f149,plain,
! [X0: int] :
( ord_less_eq(int,bit0(X0),pls)
<=> ord_less_eq(int,X0,pls) ),
inference(rectify,[],[f56]) ).
tff(f56,axiom,
! [X8: int] :
( ord_less_eq(int,bit0(X8),pls)
<=> ord_less_eq(int,X8,pls) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_55_rel__simps_I27_J) ).
tff(f6604,plain,
( ~ ord_less_eq(int,times_times(int,bit0(bit0(bit1(pls))),pls),pls)
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f6603,f309]) ).
tff(f309,plain,
number_ring(int),
inference(cnf_transformation,[],[f103]) ).
tff(f103,axiom,
number_ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber__ring) ).
tff(f6603,plain,
( ~ ord_less_eq(int,times_times(int,bit0(bit0(bit1(pls))),pls),pls)
| ~ number_ring(int)
| ~ spl0_53 ),
inference(subsumption_resolution,[],[f6602,f308]) ).
tff(f308,plain,
linordered_idom(int),
inference(cnf_transformation,[],[f100]) ).
tff(f100,axiom,
linordered_idom(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Olinordered__idom) ).
tff(f6602,plain,
( ~ ord_less_eq(int,times_times(int,bit0(bit0(bit1(pls))),pls),pls)
| ~ linordered_idom(int)
| ~ number_ring(int)
| ~ spl0_53 ),
inference(resolution,[],[f6598,f356]) ).
tff(f356,plain,
! [X0: $tType,X1: int] :
( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ ord_less_eq(int,X1,pls)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f251]) ).
tff(f251,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
| ~ ord_less_eq(int,X1,pls) )
& ( ord_less_eq(int,X1,pls)
| ~ ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f218]) ).
tff(f218,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less_eq(int,X1,pls) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f217]) ).
tff(f217,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less_eq(int,X1,pls) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f131]) ).
tff(f131,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int] :
( ord_less_eq(X0,number_number_of(X0,X1),zero_zero(X0))
<=> ord_less_eq(int,X1,pls) ) ),
inference(rectify,[],[f9]) ).
tff(f9,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X4: int] :
( ord_less_eq(X0,number_number_of(X0,X4),zero_zero(X0))
<=> ord_less_eq(int,X4,pls) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_8_le__special_I3_J) ).
tff(f6598,plain,
( ~ ord_less_eq(int,number_number_of(int,times_times(int,bit0(bit0(bit1(pls))),pls)),zero_zero(int))
| ~ spl0_53 ),
inference(forward_demodulation,[],[f6593,f3705]) ).
tff(f3705,plain,
! [X0: int] : ( number_number_of(int,times_times(int,X0,pls)) = times_times(int,number_number_of(int,X0),zero_zero(int)) ),
inference(superposition,[],[f1463,f498]) ).
tff(f498,plain,
zero_zero(int) = number_number_of(int,pls),
inference(resolution,[],[f337,f309]) ).
tff(f337,plain,
! [X0: $tType] :
( ~ number_ring(X0)
| ( zero_zero(X0) = number_number_of(X0,pls) ) ),
inference(cnf_transformation,[],[f199]) ).
tff(f199,plain,
! [X0: $tType] :
( ( zero_zero(X0) = number_number_of(X0,pls) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f41]) ).
tff(f41,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( zero_zero(X0) = number_number_of(X0,pls) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_40_number__of__Pls) ).
tff(f1463,plain,
! [X0: int,X1: int] : ( number_number_of(int,times_times(int,X0,X1)) = times_times(int,number_number_of(int,X0),number_number_of(int,X1)) ),
inference(resolution,[],[f342,f309]) ).
tff(f342,plain,
! [X0: $tType,X2: int,X1: int] :
( ~ number_ring(X0)
| ( number_number_of(X0,times_times(int,X2,X1)) = times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) ),
inference(cnf_transformation,[],[f204]) ).
tff(f204,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] : ( number_number_of(X0,times_times(int,X2,X1)) = times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f47]) ).
tff(f47,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ! [X1: int,X2: int] : ( number_number_of(X0,times_times(int,X2,X1)) = times_times(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_46_arith__simps_I32_J) ).
tff(f6593,plain,
( ~ ord_less_eq(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),zero_zero(int)),zero_zero(int))
| ~ spl0_53 ),
inference(backward_demodulation,[],[f1636,f5036]) ).
tff(f5036,plain,
( ( zero_zero(int) = minus_minus(int,semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n)),m1) )
| ~ spl0_53 ),
inference(avatar_component_clause,[],[f5034]) ).
tff(f5034,plain,
( spl0_53
<=> ( zero_zero(int) = minus_minus(int,semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n)),m1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_53])]) ).
tff(f1636,plain,
~ ord_less_eq(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),minus_minus(int,semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n)),m1)),zero_zero(int)),
inference(backward_demodulation,[],[f1158,f1634]) ).
tff(f1634,plain,
! [X2: int,X0: int,X1: int] : ( times_times(int,number_number_of(int,X0),minus_minus(int,X1,X2)) = minus_minus(int,times_times(int,number_number_of(int,X0),X1),times_times(int,number_number_of(int,X0),X2)) ),
inference(subsumption_resolution,[],[f1625,f307]) ).
tff(f307,plain,
ring(int),
inference(cnf_transformation,[],[f105]) ).
tff(f105,axiom,
ring(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Rings_Oring) ).
tff(f1625,plain,
! [X2: int,X0: int,X1: int] :
( ~ ring(int)
| ( times_times(int,number_number_of(int,X0),minus_minus(int,X1,X2)) = minus_minus(int,times_times(int,number_number_of(int,X0),X1),times_times(int,number_number_of(int,X0),X2)) ) ),
inference(resolution,[],[f369,f313]) ).
tff(f313,plain,
number(int),
inference(cnf_transformation,[],[f106]) ).
tff(f106,axiom,
number(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Int_Onumber) ).
tff(f369,plain,
! [X0: $tType,X2: X0,X3: int,X1: X0] :
( ~ number(X0)
| ~ ring(X0)
| ( times_times(X0,number_number_of(X0,X3),minus_minus(X0,X2,X1)) = minus_minus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) ) ),
inference(cnf_transformation,[],[f232]) ).
tff(f232,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: int] : ( times_times(X0,number_number_of(X0,X3),minus_minus(X0,X2,X1)) = minus_minus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) )
| ~ ring(X0)
| ~ number(X0) ),
inference(flattening,[],[f231]) ).
tff(f231,plain,
! [X0: $tType] :
( ! [X1: X0,X2: X0,X3: int] : ( times_times(X0,number_number_of(X0,X3),minus_minus(X0,X2,X1)) = minus_minus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) )
| ~ ring(X0)
| ~ number(X0) ),
inference(ennf_transformation,[],[f138]) ).
tff(f138,plain,
! [X0: $tType] :
( ( ring(X0)
& number(X0) )
=> ! [X1: X0,X2: X0,X3: int] : ( times_times(X0,number_number_of(X0,X3),minus_minus(X0,X2,X1)) = minus_minus(X0,times_times(X0,number_number_of(X0,X3),X2),times_times(X0,number_number_of(X0,X3),X1)) ) ),
inference(rectify,[],[f43]) ).
tff(f43,axiom,
! [X10: $tType] :
( ( ring(X10)
& number(X10) )
=> ! [X13: X10,X11: X10,X2: int] : ( times_times(X10,number_number_of(X10,X2),minus_minus(X10,X11,X13)) = minus_minus(X10,times_times(X10,number_number_of(X10,X2),X11),times_times(X10,number_number_of(X10,X2),X13)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_42_right__diff__distrib__number__of) ).
tff(f1158,plain,
~ ord_less_eq(int,minus_minus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n))),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m1)),zero_zero(int)),
inference(backward_demodulation,[],[f302,f1152]) ).
tff(f1152,plain,
! [X0: nat] : ( semiring_1_of_nat(int,plus_plus(nat,one_one(nat),X0)) = plus_plus(int,one_one(int),semiring_1_of_nat(int,X0)) ),
inference(superposition,[],[f417,f323]) ).
tff(f323,plain,
one_one(int) = semiring_1_of_nat(int,one_one(nat)),
inference(cnf_transformation,[],[f87]) ).
tff(f87,axiom,
one_one(int) = semiring_1_of_nat(int,one_one(nat)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_86_int__1) ).
tff(f417,plain,
! [X0: nat,X1: nat] : ( semiring_1_of_nat(int,plus_plus(nat,X1,X0)) = plus_plus(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ),
inference(cnf_transformation,[],[f169]) ).
tff(f169,plain,
! [X0: nat,X1: nat] : ( semiring_1_of_nat(int,plus_plus(nat,X1,X0)) = plus_plus(int,semiring_1_of_nat(int,X1),semiring_1_of_nat(int,X0)) ),
inference(rectify,[],[f85]) ).
tff(f85,axiom,
! [X22: nat,X23: nat] : ( semiring_1_of_nat(int,plus_plus(nat,X23,X22)) = plus_plus(int,semiring_1_of_nat(int,X23),semiring_1_of_nat(int,X22)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_84_zadd__int) ).
tff(f302,plain,
~ ord_less_eq(int,minus_minus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m1)),zero_zero(int)),
inference(cnf_transformation,[],[f115]) ).
tff(f115,plain,
~ ord_less_eq(int,minus_minus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m1)),zero_zero(int)),
inference(flattening,[],[f114]) ).
tff(f114,negated_conjecture,
~ ord_less_eq(int,minus_minus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m1)),zero_zero(int)),
inference(negated_conjecture,[],[f113]) ).
tff(f113,conjecture,
ord_less_eq(int,minus_minus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m1)),zero_zero(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj_0) ).
tff(f9358,plain,
( ~ spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f9357,f678,f674]) ).
tff(f674,plain,
( spl0_5
<=> ord_less_eq(int,pls,zero_zero(int)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
tff(f9357,plain,
( ( zero_zero(int) = pls )
| ~ ord_less_eq(int,pls,zero_zero(int)) ),
inference(forward_demodulation,[],[f9356,f318]) ).
tff(f9356,plain,
( ~ ord_less_eq(int,pls,zero_zero(int))
| ( zero_zero(int) = bit0(pls) ) ),
inference(subsumption_resolution,[],[f5095,f320]) ).
tff(f320,plain,
~ ord_less(int,pls,zero_zero(int)),
inference(cnf_transformation,[],[f78]) ).
tff(f78,axiom,
~ ord_less(int,pls,zero_zero(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_77_bin__less__0__simps_I1_J) ).
tff(f5095,plain,
( ~ ord_less_eq(int,pls,zero_zero(int))
| ( zero_zero(int) = bit0(pls) )
| ord_less(int,pls,zero_zero(int)) ),
inference(superposition,[],[f655,f318]) ).
tff(f655,plain,
! [X0: int] :
( ~ ord_less_eq(int,bit0(X0),zero_zero(int))
| ( zero_zero(int) = bit0(X0) )
| ord_less(int,X0,zero_zero(int)) ),
inference(resolution,[],[f426,f401]) ).
tff(f401,plain,
! [X0: int] :
( ~ ord_less(int,bit0(X0),zero_zero(int))
| ord_less(int,X0,zero_zero(int)) ),
inference(cnf_transformation,[],[f272]) ).
tff(f272,plain,
! [X0: int] :
( ( ord_less(int,bit0(X0),zero_zero(int))
| ~ ord_less(int,X0,zero_zero(int)) )
& ( ord_less(int,X0,zero_zero(int))
| ~ ord_less(int,bit0(X0),zero_zero(int)) ) ),
inference(nnf_transformation,[],[f156]) ).
tff(f156,plain,
! [X0: int] :
( ord_less(int,bit0(X0),zero_zero(int))
<=> ord_less(int,X0,zero_zero(int)) ),
inference(rectify,[],[f79]) ).
tff(f79,axiom,
! [X16: int] :
( ord_less(int,bit0(X16),zero_zero(int))
<=> ord_less(int,X16,zero_zero(int)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_78_bin__less__0__simps_I3_J) ).
tff(f426,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
| ( X0 = X1 )
| ~ ord_less_eq(int,X1,X0) ),
inference(cnf_transformation,[],[f279]) ).
tff(f279,plain,
! [X0: int,X1: int] :
( ( ord_less(int,X1,X0)
| ( X0 = X1 )
| ~ ord_less_eq(int,X1,X0) )
& ( ( ( X0 != X1 )
& ord_less_eq(int,X1,X0) )
| ~ ord_less(int,X1,X0) ) ),
inference(flattening,[],[f278]) ).
tff(f278,plain,
! [X0: int,X1: int] :
( ( ord_less(int,X1,X0)
| ( X0 = X1 )
| ~ ord_less_eq(int,X1,X0) )
& ( ( ( X0 != X1 )
& ord_less_eq(int,X1,X0) )
| ~ ord_less(int,X1,X0) ) ),
inference(nnf_transformation,[],[f173]) ).
tff(f173,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
<=> ( ( X0 != X1 )
& ord_less_eq(int,X1,X0) ) ),
inference(rectify,[],[f72]) ).
tff(f72,axiom,
! [X16: int,X15: int] :
( ord_less(int,X15,X16)
<=> ( ( X15 != X16 )
& ord_less_eq(int,X15,X16) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_71_less__int__def) ).
tff(f8325,plain,
( spl0_24
| spl0_5 ),
inference(avatar_split_clause,[],[f8080,f674,f1439]) ).
tff(f1439,plain,
( spl0_24
<=> ord_less_eq(int,zero_zero(int),pls) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
tff(f8080,plain,
( ord_less_eq(int,zero_zero(int),pls)
| spl0_5 ),
inference(resolution,[],[f6915,f676]) ).
tff(f676,plain,
( ~ ord_less_eq(int,pls,zero_zero(int))
| spl0_5 ),
inference(avatar_component_clause,[],[f674]) ).
tff(f6915,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ord_less_eq(int,X0,X1) ),
inference(subsumption_resolution,[],[f6914,f309]) ).
tff(f6914,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X0,X1)
| ~ number_ring(int)
| ord_less_eq(int,X1,X0) ),
inference(subsumption_resolution,[],[f6913,f308]) ).
tff(f6913,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X0,X1)
| ~ linordered_idom(int)
| ~ number_ring(int)
| ord_less_eq(int,X1,X0) ),
inference(subsumption_resolution,[],[f6912,f313]) ).
tff(f6912,plain,
! [X0: int,X1: int] :
( ~ number(int)
| ord_less_eq(int,X0,X1)
| ~ linordered_idom(int)
| ~ number_ring(int)
| ord_less_eq(int,X1,X0) ),
inference(subsumption_resolution,[],[f6894,f316]) ).
tff(f316,plain,
linorder(int),
inference(cnf_transformation,[],[f101]) ).
tff(f101,axiom,
linorder(int),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',arity_Int_Oint___Orderings_Olinorder) ).
tff(f6894,plain,
! [X0: int,X1: int] :
( ~ linorder(int)
| ~ number(int)
| ord_less_eq(int,X0,X1)
| ~ linordered_idom(int)
| ~ number_ring(int)
| ord_less_eq(int,X1,X0) ),
inference(resolution,[],[f1557,f1333]) ).
tff(f1333,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,number_number_of(int,X0),number_number_of(int,X1))
| ord_less_eq(int,X0,X1) ),
inference(subsumption_resolution,[],[f1332,f309]) ).
tff(f1332,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X0,X1)
| ~ number_ring(int)
| ~ ord_less(int,number_number_of(int,X0),number_number_of(int,X1)) ),
inference(subsumption_resolution,[],[f1326,f308]) ).
tff(f1326,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X0,X1)
| ~ linordered_idom(int)
| ~ number_ring(int)
| ~ ord_less(int,number_number_of(int,X0),number_number_of(int,X1)) ),
inference(resolution,[],[f365,f424]) ).
tff(f424,plain,
! [X0: int,X1: int] :
( ord_less_eq(int,X1,X0)
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f279]) ).
tff(f365,plain,
! [X0: $tType,X2: int,X1: int] :
( ~ ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ord_less_eq(int,X2,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f256]) ).
tff(f256,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ~ ord_less_eq(int,X2,X1) )
& ( ord_less_eq(int,X2,X1)
| ~ ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f228]) ).
tff(f228,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less_eq(int,X2,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f227]) ).
tff(f227,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less_eq(int,X2,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f136]) ).
tff(f136,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ord_less_eq(int,X2,X1) ) ),
inference(rectify,[],[f45]) ).
tff(f45,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X3: int,X4: int] :
( ord_less_eq(X0,number_number_of(X0,X4),number_number_of(X0,X3))
<=> ord_less_eq(int,X4,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_44_le__number__of) ).
tff(f1557,plain,
! [X0: $tType,X2: int,X1: int] :
( ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ linorder(X0)
| ~ number(X0)
| ord_less_eq(int,X2,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(resolution,[],[f374,f365]) ).
tff(f374,plain,
! [X0: $tType,X2: int,X1: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ linorder(X0)
| ~ number(X0) ),
inference(cnf_transformation,[],[f258]) ).
tff(f258,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
| ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2)) )
& ( ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2))
| ~ ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1)) ) )
| ~ linorder(X0)
| ~ number(X0) ),
inference(nnf_transformation,[],[f240]) ).
tff(f240,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2)) )
| ~ linorder(X0)
| ~ number(X0) ),
inference(flattening,[],[f239]) ).
tff(f239,plain,
! [X0: $tType] :
( ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2)) )
| ~ linorder(X0)
| ~ number(X0) ),
inference(ennf_transformation,[],[f142]) ).
tff(f142,plain,
! [X0: $tType] :
( ( linorder(X0)
& number(X0) )
=> ! [X1: int,X2: int] :
( ord_less_eq(X0,number_number_of(X0,X2),number_number_of(X0,X1))
<=> ~ ord_less(X0,number_number_of(X0,X1),number_number_of(X0,X2)) ) ),
inference(rectify,[],[f75]) ).
tff(f75,axiom,
! [X0: $tType] :
( ( linorder(X0)
& number(X0) )
=> ! [X16: int,X19: int] :
( ord_less_eq(X0,number_number_of(X0,X19),number_number_of(X0,X16))
<=> ~ ord_less(X0,number_number_of(X0,X16),number_number_of(X0,X19)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_74_le__number__of__eq__not__less) ).
tff(f8324,plain,
( spl0_78
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f8323,f1425,f8319]) ).
tff(f8323,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,zero_zero(int),pls)
| ~ ord_less(int,X0,X1) ),
inference(subsumption_resolution,[],[f8322,f317]) ).
tff(f317,plain,
~ ord_less(int,pls,pls),
inference(cnf_transformation,[],[f30]) ).
tff(f30,axiom,
~ ord_less(int,pls,pls),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_29_rel__simps_I2_J) ).
tff(f8322,plain,
! [X0: int,X1: int] :
( ord_less(int,pls,pls)
| ~ ord_less(int,zero_zero(int),pls)
| ~ ord_less(int,X0,X1) ),
inference(forward_demodulation,[],[f1498,f330]) ).
tff(f1498,plain,
! [X0: int,X1: int] :
( ord_less(int,pls,times_times(int,pls,X1))
| ~ ord_less(int,zero_zero(int),pls)
| ~ ord_less(int,X0,X1) ),
inference(superposition,[],[f471,f330]) ).
tff(f471,plain,
! [X2: int,X0: int,X1: int] :
( ord_less(int,times_times(int,X0,X2),times_times(int,X0,X1))
| ~ ord_less(int,zero_zero(int),X0)
| ~ ord_less(int,X2,X1) ),
inference(cnf_transformation,[],[f244]) ).
tff(f244,plain,
! [X0: int,X1: int,X2: int] :
( ord_less(int,times_times(int,X0,X2),times_times(int,X0,X1))
| ~ ord_less(int,zero_zero(int),X0)
| ~ ord_less(int,X2,X1) ),
inference(flattening,[],[f243]) ).
tff(f243,plain,
! [X0: int,X1: int,X2: int] :
( ord_less(int,times_times(int,X0,X2),times_times(int,X0,X1))
| ~ ord_less(int,zero_zero(int),X0)
| ~ ord_less(int,X2,X1) ),
inference(ennf_transformation,[],[f196]) ).
tff(f196,plain,
! [X0: int,X1: int,X2: int] :
( ord_less(int,X2,X1)
=> ( ord_less(int,zero_zero(int),X0)
=> ord_less(int,times_times(int,X0,X2),times_times(int,X0,X1)) ) ),
inference(rectify,[],[f80]) ).
tff(f80,axiom,
! [X6: int,X20: int,X21: int] :
( ord_less(int,X21,X20)
=> ( ord_less(int,zero_zero(int),X6)
=> ord_less(int,times_times(int,X6,X21),times_times(int,X6,X20)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_79_zmult__zless__mono2) ).
tff(f6581,plain,
spl0_26,
inference(avatar_contradiction_clause,[],[f6580]) ).
tff(f6580,plain,
( $false
| spl0_26 ),
inference(subsumption_resolution,[],[f6578,f2206]) ).
tff(f2206,plain,
ord_less(int,pls,bit0(bit1(pls))),
inference(resolution,[],[f2205,f2088]) ).
tff(f2088,plain,
! [X0: int] :
( ~ ord_less(int,bit1(pls),X0)
| ord_less(int,pls,X0) ),
inference(resolution,[],[f2082,f424]) ).
tff(f2082,plain,
! [X0: int] :
( ~ ord_less_eq(int,bit1(pls),X0)
| ord_less(int,pls,X0) ),
inference(subsumption_resolution,[],[f2081,f309]) ).
tff(f2081,plain,
! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less_eq(int,bit1(pls),X0)
| ~ number_ring(int) ),
inference(subsumption_resolution,[],[f2078,f308]) ).
tff(f2078,plain,
! [X0: int] :
( ord_less(int,pls,X0)
| ~ ord_less_eq(int,bit1(pls),X0)
| ~ linordered_idom(int)
| ~ number_ring(int) ),
inference(resolution,[],[f1107,f350]) ).
tff(f350,plain,
! [X0: $tType,X1: int] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less_eq(int,bit1(pls),X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f248]) ).
tff(f248,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less_eq(int,bit1(pls),X1) )
& ( ord_less_eq(int,bit1(pls),X1)
| ~ ord_less_eq(X0,one_one(X0),number_number_of(X0,X1)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f212]) ).
tff(f212,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,bit1(pls),X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f211]) ).
tff(f211,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,bit1(pls),X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f128]) ).
tff(f128,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less_eq(int,bit1(pls),X1) ) ),
inference(rectify,[],[f5]) ).
tff(f5,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X3: int] :
( ord_less_eq(X0,one_one(X0),number_number_of(X0,X3))
<=> ord_less_eq(int,bit1(pls),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_4_le__special_I2_J) ).
tff(f1107,plain,
! [X0: int] :
( ~ ord_less_eq(int,one_one(int),number_number_of(int,X0))
| ord_less(int,pls,X0) ),
inference(subsumption_resolution,[],[f1106,f309]) ).
tff(f1106,plain,
! [X0: int] :
( ord_less(int,pls,X0)
| ~ number_ring(int)
| ~ ord_less_eq(int,one_one(int),number_number_of(int,X0)) ),
inference(subsumption_resolution,[],[f1102,f308]) ).
tff(f1102,plain,
! [X0: int] :
( ord_less(int,pls,X0)
| ~ linordered_idom(int)
| ~ number_ring(int)
| ~ ord_less_eq(int,one_one(int),number_number_of(int,X0)) ),
inference(resolution,[],[f359,f383]) ).
tff(f383,plain,
! [X0: int] :
( ord_less(int,zero_zero(int),X0)
| ~ ord_less_eq(int,one_one(int),X0) ),
inference(cnf_transformation,[],[f263]) ).
tff(f263,plain,
! [X0: int] :
( ( ord_less_eq(int,one_one(int),X0)
| ~ ord_less(int,zero_zero(int),X0) )
& ( ord_less(int,zero_zero(int),X0)
| ~ ord_less_eq(int,one_one(int),X0) ) ),
inference(nnf_transformation,[],[f147]) ).
tff(f147,plain,
! [X0: int] :
( ord_less_eq(int,one_one(int),X0)
<=> ord_less(int,zero_zero(int),X0) ),
inference(rectify,[],[f92]) ).
tff(f92,axiom,
! [X15: int] :
( ord_less_eq(int,one_one(int),X15)
<=> ord_less(int,zero_zero(int),X15) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_91_int__one__le__iff__zero__less) ).
tff(f359,plain,
! [X0: $tType,X1: int] :
( ~ ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
| ord_less(int,pls,X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f253]) ).
tff(f253,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
| ~ ord_less(int,pls,X1) )
& ( ord_less(int,pls,X1)
| ~ ord_less(X0,zero_zero(X0),number_number_of(X0,X1)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f222]) ).
tff(f222,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less(int,pls,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f221]) ).
tff(f221,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less(int,pls,X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f133]) ).
tff(f133,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X1))
<=> ord_less(int,pls,X1) ) ),
inference(rectify,[],[f67]) ).
tff(f67,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X3: int] :
( ord_less(X0,zero_zero(X0),number_number_of(X0,X3))
<=> ord_less(int,pls,X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_66_less__special_I1_J) ).
tff(f2205,plain,
ord_less(int,bit1(pls),bit0(bit1(pls))),
inference(subsumption_resolution,[],[f2204,f309]) ).
tff(f2204,plain,
( ord_less(int,bit1(pls),bit0(bit1(pls)))
| ~ number_ring(int) ),
inference(subsumption_resolution,[],[f2203,f308]) ).
tff(f2203,plain,
( ord_less(int,bit1(pls),bit0(bit1(pls)))
| ~ linordered_idom(int)
| ~ number_ring(int) ),
inference(resolution,[],[f2193,f357]) ).
tff(f357,plain,
! [X0: $tType,X1: int] :
( ~ ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ord_less(int,bit1(pls),X1)
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(cnf_transformation,[],[f252]) ).
tff(f252,plain,
! [X0: $tType] :
( ! [X1: int] :
( ( ord_less(X0,one_one(X0),number_number_of(X0,X1))
| ~ ord_less(int,bit1(pls),X1) )
& ( ord_less(int,bit1(pls),X1)
| ~ ord_less(X0,one_one(X0),number_number_of(X0,X1)) ) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(nnf_transformation,[],[f220]) ).
tff(f220,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less(int,bit1(pls),X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(flattening,[],[f219]) ).
tff(f219,plain,
! [X0: $tType] :
( ! [X1: int] :
( ord_less(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less(int,bit1(pls),X1) )
| ~ linordered_idom(X0)
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f132]) ).
tff(f132,plain,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X1: int] :
( ord_less(X0,one_one(X0),number_number_of(X0,X1))
<=> ord_less(int,bit1(pls),X1) ) ),
inference(rectify,[],[f69]) ).
tff(f69,axiom,
! [X0: $tType] :
( ( linordered_idom(X0)
& number_ring(X0) )
=> ! [X3: int] :
( ord_less(X0,one_one(X0),number_number_of(X0,X3))
<=> ord_less(int,bit1(pls),X3) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_68_less__special_I2_J) ).
tff(f2193,plain,
ord_less(int,one_one(int),number_number_of(int,bit0(bit1(pls)))),
inference(superposition,[],[f483,f968]) ).
tff(f968,plain,
plus_plus(int,one_one(int),one_one(int)) = number_number_of(int,bit0(bit1(pls))),
inference(resolution,[],[f339,f309]) ).
tff(f339,plain,
! [X0: $tType] :
( ~ number_ring(X0)
| ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) ) ),
inference(cnf_transformation,[],[f201]) ).
tff(f201,plain,
! [X0: $tType] :
( ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) )
| ~ number_ring(X0) ),
inference(ennf_transformation,[],[f7]) ).
tff(f7,axiom,
! [X0: $tType] :
( number_ring(X0)
=> ( plus_plus(X0,one_one(X0),one_one(X0)) = number_number_of(X0,bit0(bit1(pls))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_6_one__add__one__is__two) ).
tff(f483,plain,
! [X1: int] : ord_less(int,X1,plus_plus(int,X1,one_one(int))),
inference(equality_resolution,[],[f467]) ).
tff(f467,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ( X0 != X1 ) ),
inference(cnf_transformation,[],[f300]) ).
tff(f300,plain,
! [X0: int,X1: int] :
( ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ( ( X0 != X1 )
& ~ ord_less(int,X1,X0) ) )
& ( ( X0 = X1 )
| ord_less(int,X1,X0)
| ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ) ),
inference(flattening,[],[f299]) ).
tff(f299,plain,
! [X0: int,X1: int] :
( ( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
| ( ( X0 != X1 )
& ~ ord_less(int,X1,X0) ) )
& ( ( X0 = X1 )
| ord_less(int,X1,X0)
| ~ ord_less(int,X1,plus_plus(int,X0,one_one(int))) ) ),
inference(nnf_transformation,[],[f193]) ).
tff(f193,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,plus_plus(int,X0,one_one(int)))
<=> ( ( X0 = X1 )
| ord_less(int,X1,X0) ) ),
inference(rectify,[],[f81]) ).
tff(f81,axiom,
! [X15: int,X16: int] :
( ord_less(int,X16,plus_plus(int,X15,one_one(int)))
<=> ( ( X15 = X16 )
| ord_less(int,X16,X15) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_80_zless__add1__eq) ).
tff(f6578,plain,
( ~ ord_less(int,pls,bit0(bit1(pls)))
| spl0_26 ),
inference(resolution,[],[f6565,f392]) ).
tff(f392,plain,
! [X0: int] :
( ord_less(int,pls,bit0(X0))
| ~ ord_less(int,pls,X0) ),
inference(cnf_transformation,[],[f267]) ).
tff(f267,plain,
! [X0: int] :
( ( ord_less(int,pls,bit0(X0))
| ~ ord_less(int,pls,X0) )
& ( ord_less(int,pls,X0)
| ~ ord_less(int,pls,bit0(X0)) ) ),
inference(nnf_transformation,[],[f151]) ).
tff(f151,plain,
! [X0: int] :
( ord_less(int,pls,bit0(X0))
<=> ord_less(int,pls,X0) ),
inference(rectify,[],[f53]) ).
tff(f53,axiom,
! [X8: int] :
( ord_less(int,pls,bit0(X8))
<=> ord_less(int,pls,X8) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_52_rel__simps_I4_J) ).
tff(f6565,plain,
( ~ ord_less(int,pls,bit0(bit0(bit1(pls))))
| spl0_26 ),
inference(resolution,[],[f1511,f934]) ).
tff(f934,plain,
! [X0: int] :
( ord_less(int,zero_zero(int),number_number_of(int,X0))
| ~ ord_less(int,pls,X0) ),
inference(superposition,[],[f469,f498]) ).
tff(f469,plain,
! [X0: int,X1: int] :
( ord_less(int,number_number_of(int,X1),number_number_of(int,X0))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f301]) ).
tff(f301,plain,
! [X0: int,X1: int] :
( ( ord_less(int,number_number_of(int,X1),number_number_of(int,X0))
| ~ ord_less(int,X1,X0) )
& ( ord_less(int,X1,X0)
| ~ ord_less(int,number_number_of(int,X1),number_number_of(int,X0)) ) ),
inference(nnf_transformation,[],[f194]) ).
tff(f194,plain,
! [X0: int,X1: int] :
( ord_less(int,number_number_of(int,X1),number_number_of(int,X0))
<=> ord_less(int,X1,X0) ),
inference(rectify,[],[f73]) ).
tff(f73,axiom,
! [X7: int,X8: int] :
( ord_less(int,number_number_of(int,X8),number_number_of(int,X7))
<=> ord_less(int,X8,X7) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_72_less__number__of__int__code) ).
tff(f1511,plain,
( ~ ord_less(int,zero_zero(int),number_number_of(int,bit0(bit0(bit1(pls)))))
| spl0_26 ),
inference(avatar_component_clause,[],[f1509]) ).
tff(f1509,plain,
( spl0_26
<=> ord_less(int,zero_zero(int),number_number_of(int,bit0(bit0(bit1(pls))))) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
tff(f6560,plain,
( spl0_25
| spl0_53 ),
inference(avatar_split_clause,[],[f6533,f5034,f1505]) ).
tff(f1505,plain,
( spl0_25
<=> ord_less(int,semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n)),m1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
tff(f6533,plain,
( ( zero_zero(int) = minus_minus(int,semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n)),m1) )
| ord_less(int,semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n)),m1) ),
inference(resolution,[],[f802,f1161]) ).
tff(f1161,plain,
ord_less_eq(int,minus_minus(int,semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n)),m1),zero_zero(int)),
inference(backward_demodulation,[],[f327,f1152]) ).
tff(f327,plain,
ord_less_eq(int,minus_minus(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1),zero_zero(int)),
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
ord_less_eq(int,minus_minus(int,plus_plus(int,one_one(int),semiring_1_of_nat(int,n)),m1),zero_zero(int)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_0__0961_A_L_Aint_An_A_N_Am1_A_060_061_A0_096) ).
tff(f802,plain,
! [X0: int,X1: int] :
( ~ ord_less_eq(int,minus_minus(int,X0,X1),zero_zero(int))
| ( zero_zero(int) = minus_minus(int,X0,X1) )
| ord_less(int,X0,X1) ),
inference(resolution,[],[f423,f426]) ).
tff(f423,plain,
! [X0: int,X1: int] :
( ~ ord_less(int,minus_minus(int,X1,X0),zero_zero(int))
| ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f277,plain,
! [X0: int,X1: int] :
( ( ord_less(int,X1,X0)
| ~ ord_less(int,minus_minus(int,X1,X0),zero_zero(int)) )
& ( ord_less(int,minus_minus(int,X1,X0),zero_zero(int))
| ~ ord_less(int,X1,X0) ) ),
inference(nnf_transformation,[],[f172]) ).
tff(f172,plain,
! [X0: int,X1: int] :
( ord_less(int,X1,X0)
<=> ord_less(int,minus_minus(int,X1,X0),zero_zero(int)) ),
inference(rectify,[],[f82]) ).
tff(f82,axiom,
! [X7: int,X8: int] :
( ord_less(int,X8,X7)
<=> ord_less(int,minus_minus(int,X8,X7),zero_zero(int)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fact_81_less__bin__lemma) ).
tff(f1512,plain,
( ~ spl0_25
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f1496,f1509,f1505]) ).
tff(f1496,plain,
( ~ ord_less(int,zero_zero(int),number_number_of(int,bit0(bit0(bit1(pls)))))
| ~ ord_less(int,semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n)),m1) ),
inference(resolution,[],[f471,f1164]) ).
tff(f1164,plain,
~ ord_less(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),semiring_1_of_nat(int,plus_plus(nat,one_one(nat),n))),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m1)),
inference(backward_demodulation,[],[f786,f1152]) ).
tff(f786,plain,
~ ord_less(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m1)),
inference(resolution,[],[f422,f499]) ).
tff(f499,plain,
~ ord_less(int,minus_minus(int,times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),plus_plus(int,one_one(int),semiring_1_of_nat(int,n))),times_times(int,number_number_of(int,bit0(bit0(bit1(pls)))),m1)),zero_zero(int)),
inference(resolution,[],[f424,f302]) ).
tff(f422,plain,
! [X0: int,X1: int] :
( ord_less(int,minus_minus(int,X1,X0),zero_zero(int))
| ~ ord_less(int,X1,X0) ),
inference(cnf_transformation,[],[f277]) ).
tff(f1442,plain,
( ~ spl0_24
| spl0_6
| spl0_21 ),
inference(avatar_split_clause,[],[f1437,f1425,f678,f1439]) ).
tff(f1437,plain,
( ( zero_zero(int) = pls )
| ~ ord_less_eq(int,zero_zero(int),pls)
| spl0_21 ),
inference(resolution,[],[f1427,f426]) ).
tff(f1427,plain,
( ~ ord_less(int,zero_zero(int),pls)
| spl0_21 ),
inference(avatar_component_clause,[],[f1425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.08 % Problem : NUM989_5 : TPTP v8.2.0. Released v6.0.0.
% 0.00/0.09 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 300
% 0.08/0.28 % DateTime : Mon May 20 05:55:07 EDT 2024
% 0.08/0.28 % CPUTime :
% 0.08/0.28 % (9818)Running in auto input_syntax mode. Trying TPTP
% 0.12/0.30 % (9822)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.12/0.30 % (9824)ott-10_8_av=off:bd=preordered:bs=on:fsd=off:fsr=off:fde=unused:irw=on:lcm=predicate:lma=on:nm=4:nwc=1.7:sp=frequency_522 on theBenchmark for (522ds/0Mi)
% 0.12/0.30 % (9823)ott+10_10:1_add=off:afr=on:amm=off:anc=all:bd=off:bs=on:fsr=off:irw=on:lma=on:msp=off:nm=4:nwc=4.0:sac=on:sp=reverse_frequency_531 on theBenchmark for (531ds/0Mi)
% 0.12/0.30 % Exception at run slice level
% 0.12/0.30 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.30 % (9819)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.12/0.30 % (9820)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.12/0.30 % (9821)WARNING: value z3 for option sas not known
% 0.12/0.30 % (9821)dis+2_11_add=large:afr=on:amm=off:bd=off:bce=on:fsd=off:fde=none:gs=on:gsaa=full_model:gsem=off:irw=on:msp=off:nm=4:nwc=1.3:sas=z3:sims=off:sac=on:sp=reverse_arity_569 on theBenchmark for (569ds/0Mi)
% 0.12/0.30 % Exception at run slice level
% 0.12/0.30 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.30 % (9825)ott+1_64_av=off:bd=off:bce=on:fsd=off:fde=unused:gsp=on:irw=on:lcm=predicate:lma=on:nm=2:nwc=1.1:sims=off:urr=on_497 on theBenchmark for (497ds/0Mi)
% 0.12/0.30 % Exception at run slice level
% 0.12/0.30 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.30 % (9825)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.31 % (9829)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.12/0.31 % (9829)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.31 % Exception at run slice level
% 0.12/0.31 User error: Finite model buillding is currently not compatible with polymorphism or higher-order constructs
% 0.12/0.31 % (9830)ott+1_9_av=off:bd=off:bs=on:gsp=on:lcm=predicate:nm=4:sp=weighted_frequency:urr=on_382 on theBenchmark for (382ds/0Mi)
% 0.12/0.31 % (9831)lrs-11_2:5_fsd=off:fde=none:nm=4:nwc=5.0:sims=off:sp=reverse_weighted_frequency:stl=62_367 on theBenchmark for (367ds/0Mi)
% 0.12/0.31 % (9830)WARNING: Not using GeneralSplitting currently not compatible with polymorphic/higher-order inputs.
% 0.12/0.32 % (9836)ott+4_64_acc=on:anc=none:bs=on:bsr=on:fsd=off:gs=on:gsem=off:irw=on:msp=off:nwc=2.5:nicw=on:sims=off_354 on theBenchmark for (354ds/0Mi)
% 3.00/0.75 % (9831)First to succeed.
% 3.00/0.75 % (9831)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-9818"
% 3.00/0.76 % (9831)Refutation found. Thanks to Tanya!
% 3.00/0.76 % SZS status Theorem for theBenchmark
% 3.00/0.76 % SZS output start Proof for theBenchmark
% See solution above
% 3.00/0.76 % (9831)------------------------------
% 3.00/0.76 % (9831)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 3.00/0.76 % (9831)Termination reason: Refutation
% 3.00/0.76
% 3.00/0.76 % (9831)Memory used [KB]: 5921
% 3.00/0.76 % (9831)Time elapsed: 0.441 s
% 3.00/0.76 % (9831)Instructions burned: 1403 (million)
% 3.00/0.76 % (9818)Success in time 0.471 s
%------------------------------------------------------------------------------