TSTP Solution File: SWW653_2 by Vampire-SAT---4.9
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.9
% Problem : SWW653_2 : TPTP v8.2.0. Released v6.1.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d SAT
% Computer : n014.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 : Mon Jun 24 18:53:58 EDT 2024
% Result : Theorem 0.21s 0.46s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 23
% Syntax : Number of formulae : 131 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 554 ( 108 equ)
% Maximal formula atoms : 27 ( 4 avg)
% Number of connectives : 641 ( 218 ~; 249 |; 95 &)
% ( 28 <=>; 49 =>; 0 <=; 2 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number arithmetic : 717 ( 257 atm; 154 fun; 176 num; 130 var)
% Number of types : 9 ( 7 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 24 ( 20 usr; 15 prp; 0-7 aty)
% Number of functors : 41 ( 37 usr; 19 con; 0-4 aty)
% Number of variables : 148 ( 136 !; 12 ?; 148 :)
% Comments :
%------------------------------------------------------------------------------
tff(type_def_5,type,
uni: $tType ).
tff(type_def_6,type,
ty: $tType ).
tff(type_def_7,type,
bool1: $tType ).
tff(type_def_8,type,
tuple02: $tType ).
tff(type_def_9,type,
uf_pure1: $tType ).
tff(type_def_10,type,
uf1: $tType ).
tff(type_def_11,type,
graph1: $tType ).
tff(func_def_0,type,
witness1: ty > uni ).
tff(func_def_1,type,
int: ty ).
tff(func_def_2,type,
real: ty ).
tff(func_def_3,type,
bool: ty ).
tff(func_def_4,type,
true1: bool1 ).
tff(func_def_5,type,
false1: bool1 ).
tff(func_def_6,type,
match_bool1: ( ty * bool1 * uni * uni ) > uni ).
tff(func_def_7,type,
tuple0: ty ).
tff(func_def_8,type,
tuple03: tuple02 ).
tff(func_def_9,type,
qtmark: ty ).
tff(func_def_12,type,
ref: ty > ty ).
tff(func_def_13,type,
mk_ref: ( ty * uni ) > uni ).
tff(func_def_14,type,
contents: ( ty * uni ) > uni ).
tff(func_def_15,type,
uf_pure: ty ).
tff(func_def_16,type,
size1: uf_pure1 > $int ).
tff(func_def_17,type,
num1: uf_pure1 > $int ).
tff(func_def_19,type,
uf: ty ).
tff(func_def_20,type,
mk_uf1: uf_pure1 > uf1 ).
tff(func_def_21,type,
state1: uf1 > uf_pure1 ).
tff(func_def_22,type,
graph: ty ).
tff(func_def_25,type,
sK0: $int ).
tff(func_def_26,type,
sK1: $int ).
tff(func_def_27,type,
sK2: graph1 ).
tff(func_def_28,type,
sK3: uf_pure1 ).
tff(func_def_29,type,
sK4: $int ).
tff(func_def_30,type,
sK5: $int ).
tff(func_def_31,type,
sK6: ( uf_pure1 * $int ) > $int ).
tff(func_def_32,type,
sK7: ( graph1 * $int * $int ) > graph1 ).
tff(func_def_33,type,
sK8: ( graph1 * $int * $int ) > $int ).
tff(func_def_34,type,
sK9: ( graph1 * $int * $int ) > graph1 ).
tff(func_def_35,type,
sK10: ( graph1 * $int * $int ) > $int ).
tff(func_def_36,type,
sK11: ( graph1 * $int * $int ) > $int ).
tff(func_def_37,type,
sK12: ( graph1 * $int * $int ) > graph1 ).
tff(func_def_38,type,
sK13: ( graph1 * $int * $int ) > $int ).
tff(func_def_39,type,
sK14: ( graph1 * $int * $int ) > $int ).
tff(func_def_40,type,
sK15: ( graph1 * $int * $int ) > $int ).
tff(func_def_41,type,
sK17: ( uf_pure1 * $int * $int ) > $int ).
tff(pred_def_1,type,
sort1: ( ty * uni ) > $o ).
tff(pred_def_3,type,
repr1: ( uf_pure1 * $int * $int ) > $o ).
tff(pred_def_5,type,
same1: ( uf_pure1 * $int * $int ) > $o ).
tff(pred_def_6,type,
same_reprs1: ( uf_pure1 * uf_pure1 ) > $o ).
tff(pred_def_7,type,
path1: ( graph1 * $int * $int ) > $o ).
tff(pred_def_8,type,
sP16: ( $int * $int * $int * graph1 * $int * $int * graph1 ) > $o ).
tff(f1233,plain,
$false,
inference(avatar_sat_refutation,[],[f182,f188,f194,f200,f211,f217,f238,f881,f885,f915,f955,f957,f1175,f1217,f1231]) ).
tff(f1231,plain,
( spl18_8
| ~ spl18_30 ),
inference(avatar_contradiction_clause,[],[f1230]) ).
tff(f1230,plain,
( $false
| spl18_8
| ~ spl18_30 ),
inference(subsumption_resolution,[],[f1219,f161]) ).
tff(f161,plain,
! [X4: $int] : path1(sK2,X4,X4),
inference(equality_resolution,[],[f105]) ).
tff(f105,plain,
! [X3: $int,X4: $int] :
( path1(sK2,X3,X4)
| ( X3 != X4 ) ),
inference(cnf_transformation,[],[f72]) ).
tff(f72,plain,
? [X0: $int,X1: $int,X2: graph1] :
( ? [X5: uf_pure1] :
( ( ? [X9: $int,X10: $int] :
( ( same1(X5,X9,X10)
<~> path1(X2,X9,X10) )
& $less(X10,$product(X0,X0))
& ~ $less(X10,0)
& $less(X9,$product(X0,X0))
& ~ $less(X9,0) )
| ( $product(X0,X0) != size1(X5) )
| ( size1(X5) != $sum(num1(X5),X1) )
| $less(num1(X5),1) )
& ! [X7: $int,X8: $int] :
( ( ( X7 = X8 )
& repr1(X5,X7,X7)
& repr1(X5,X7,X8) )
| ~ same1(X5,X7,X8)
| ~ $less(X8,$product(X0,X0))
| $less(X8,0)
| ~ $less(X7,$product(X0,X0))
| $less(X7,0) )
& ! [X6: $int] :
( repr1(X5,X6,X6)
| ~ $less(X6,$product(X0,X0))
| $less(X6,0) )
& ( $product(X0,X0) = size1(X5) )
& ( $product(X0,X0) = num1(X5) ) )
& ~ $less($product(X0,X0),0)
& ! [X3: $int,X4: $int] :
( ( X3 = X4 )
<=> path1(X2,X3,X4) )
& ( 0 = X1 )
& ~ $less(X0,1) ),
inference(flattening,[],[f71]) ).
tff(f71,plain,
? [X0: $int,X1: $int,X2: graph1] :
( ? [X5: uf_pure1] :
( ( ? [X9: $int,X10: $int] :
( ( same1(X5,X9,X10)
<~> path1(X2,X9,X10) )
& $less(X10,$product(X0,X0))
& ~ $less(X10,0)
& $less(X9,$product(X0,X0))
& ~ $less(X9,0) )
| ( $product(X0,X0) != size1(X5) )
| ( size1(X5) != $sum(num1(X5),X1) )
| $less(num1(X5),1) )
& ! [X7: $int,X8: $int] :
( ( ( X7 = X8 )
& repr1(X5,X7,X7)
& repr1(X5,X7,X8) )
| ~ same1(X5,X7,X8)
| ~ $less(X8,$product(X0,X0))
| $less(X8,0)
| ~ $less(X7,$product(X0,X0))
| $less(X7,0) )
& ! [X6: $int] :
( repr1(X5,X6,X6)
| ~ $less(X6,$product(X0,X0))
| $less(X6,0) )
& ( $product(X0,X0) = size1(X5) )
& ( $product(X0,X0) = num1(X5) ) )
& ~ $less($product(X0,X0),0)
& ! [X3: $int,X4: $int] :
( ( X3 = X4 )
<=> path1(X2,X3,X4) )
& ( 0 = X1 )
& ~ $less(X0,1) ),
inference(ennf_transformation,[],[f51]) ).
tff(f51,plain,
~ ! [X0: $int,X1: $int,X2: graph1] :
( ( ! [X3: $int,X4: $int] :
( ( X3 = X4 )
<=> path1(X2,X3,X4) )
& ( 0 = X1 )
& ~ $less(X0,1) )
=> ( ~ $less($product(X0,X0),0)
=> ! [X5: uf_pure1] :
( ( ! [X6: $int] :
( ( $less(X6,$product(X0,X0))
& ~ $less(X6,0) )
=> repr1(X5,X6,X6) )
& ( $product(X0,X0) = size1(X5) )
& ( $product(X0,X0) = num1(X5) ) )
=> ( ! [X7: $int,X8: $int] :
( ( $less(X7,$product(X0,X0))
& ~ $less(X7,0) )
=> ( ( $less(X8,$product(X0,X0))
& ~ $less(X8,0) )
=> ( same1(X5,X7,X8)
=> ( ( X7 = X8 )
& repr1(X5,X7,X7)
& repr1(X5,X7,X8) ) ) ) )
=> ( ! [X9: $int,X10: $int] :
( ( $less(X9,$product(X0,X0))
& ~ $less(X9,0) )
=> ( ( $less(X10,$product(X0,X0))
& ~ $less(X10,0) )
=> ( same1(X5,X9,X10)
<=> path1(X2,X9,X10) ) ) )
& ( $product(X0,X0) = size1(X5) )
& ( size1(X5) = $sum(num1(X5),X1) )
& ~ $less(num1(X5),1) ) ) ) ) ),
inference(rectify,[],[f27]) ).
tff(f27,plain,
~ ! [X14: $int,X15: $int,X16: graph1] :
( ( ! [X1: $int,X7: $int] :
( ( X1 = X7 )
<=> path1(X16,X1,X7) )
& ( 0 = X15 )
& ~ $less(X14,1) )
=> ( ~ $less($product(X14,X14),0)
=> ! [X6: uf_pure1] :
( ( ! [X1: $int] :
( ( $less(X1,$product(X14,X14))
& ~ $less(X1,0) )
=> repr1(X6,X1,X1) )
& ( size1(X6) = $product(X14,X14) )
& ( num1(X6) = $product(X14,X14) ) )
=> ( ! [X1: $int,X7: $int] :
( ( $less(X1,$product(X14,X14))
& ~ $less(X1,0) )
=> ( ( $less(X7,$product(X14,X14))
& ~ $less(X7,0) )
=> ( same1(X6,X1,X7)
=> ( ( X1 = X7 )
& repr1(X6,X1,X1)
& repr1(X6,X1,X7) ) ) ) )
=> ( ! [X1: $int,X7: $int] :
( ( $less(X1,$product(X14,X14))
& ~ $less(X1,0) )
=> ( ( $less(X7,$product(X14,X14))
& ~ $less(X7,0) )
=> ( same1(X6,X1,X7)
<=> path1(X16,X1,X7) ) ) )
& ( size1(X6) = $product(X14,X14) )
& ( size1(X6) = $sum(num1(X6),X15) )
& ~ $less(num1(X6),1) ) ) ) ) ),
inference(theory_normalization,[],[f26]) ).
tff(f26,negated_conjecture,
~ ! [X14: $int,X15: $int,X16: graph1] :
( ( ! [X1: $int,X7: $int] :
( ( X1 = X7 )
<=> path1(X16,X1,X7) )
& ( 0 = X15 )
& $lesseq(1,X14) )
=> ( $lesseq(0,$product(X14,X14))
=> ! [X6: uf_pure1] :
( ( ! [X1: $int] :
( ( $less(X1,$product(X14,X14))
& $lesseq(0,X1) )
=> repr1(X6,X1,X1) )
& ( size1(X6) = $product(X14,X14) )
& ( num1(X6) = $product(X14,X14) ) )
=> ( ! [X1: $int,X7: $int] :
( ( $less(X1,$product(X14,X14))
& $lesseq(0,X1) )
=> ( ( $less(X7,$product(X14,X14))
& $lesseq(0,X7) )
=> ( same1(X6,X1,X7)
=> ( ( X1 = X7 )
& repr1(X6,X1,X1)
& repr1(X6,X1,X7) ) ) ) )
=> ( ! [X1: $int,X7: $int] :
( ( $less(X1,$product(X14,X14))
& $lesseq(0,X1) )
=> ( ( $less(X7,$product(X14,X14))
& $lesseq(0,X7) )
=> ( same1(X6,X1,X7)
<=> path1(X16,X1,X7) ) ) )
& ( size1(X6) = $product(X14,X14) )
& ( size1(X6) = $sum(num1(X6),X15) )
& $lesseq(1,num1(X6)) ) ) ) ) ),
inference(negated_conjecture,[],[f25]) ).
tff(f25,conjecture,
! [X14: $int,X15: $int,X16: graph1] :
( ( ! [X1: $int,X7: $int] :
( ( X1 = X7 )
<=> path1(X16,X1,X7) )
& ( 0 = X15 )
& $lesseq(1,X14) )
=> ( $lesseq(0,$product(X14,X14))
=> ! [X6: uf_pure1] :
( ( ! [X1: $int] :
( ( $less(X1,$product(X14,X14))
& $lesseq(0,X1) )
=> repr1(X6,X1,X1) )
& ( size1(X6) = $product(X14,X14) )
& ( num1(X6) = $product(X14,X14) ) )
=> ( ! [X1: $int,X7: $int] :
( ( $less(X1,$product(X14,X14))
& $lesseq(0,X1) )
=> ( ( $less(X7,$product(X14,X14))
& $lesseq(0,X7) )
=> ( same1(X6,X1,X7)
=> ( ( X1 = X7 )
& repr1(X6,X1,X1)
& repr1(X6,X1,X7) ) ) ) )
=> ( ! [X1: $int,X7: $int] :
( ( $less(X1,$product(X14,X14))
& $lesseq(0,X1) )
=> ( ( $less(X7,$product(X14,X14))
& $lesseq(0,X7) )
=> ( same1(X6,X1,X7)
<=> path1(X16,X1,X7) ) ) )
& ( size1(X6) = $product(X14,X14) )
& ( size1(X6) = $sum(num1(X6),X15) )
& $lesseq(1,num1(X6)) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f1219,plain,
( ~ path1(sK2,sK4,sK4)
| spl18_8
| ~ spl18_30 ),
inference(backward_demodulation,[],[f210,f1172]) ).
tff(f1172,plain,
( ( sK4 = sK5 )
| ~ spl18_30 ),
inference(avatar_component_clause,[],[f1170]) ).
tff(f1170,plain,
( spl18_30
<=> ( sK4 = sK5 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_30])]) ).
tff(f210,plain,
( ~ path1(sK2,sK4,sK5)
| spl18_8 ),
inference(avatar_component_clause,[],[f208]) ).
tff(f208,plain,
( spl18_8
<=> path1(sK2,sK4,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_8])]) ).
tff(f1217,plain,
( spl18_26
| ~ spl18_5 ),
inference(avatar_split_clause,[],[f1214,f191,f1109]) ).
tff(f1109,plain,
( spl18_26
<=> $less(sK4,size1(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_26])]) ).
tff(f191,plain,
( spl18_5
<=> $less(sK4,$product(sK0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_5])]) ).
tff(f1214,plain,
( $less(sK4,size1(sK3))
| ~ spl18_5 ),
inference(backward_demodulation,[],[f193,f103]) ).
tff(f103,plain,
size1(sK3) = $product(sK0,sK0),
inference(cnf_transformation,[],[f72]) ).
tff(f193,plain,
( $less(sK4,$product(sK0,sK0))
| ~ spl18_5 ),
inference(avatar_component_clause,[],[f191]) ).
tff(f1175,plain,
( spl18_30
| ~ spl18_26
| ~ spl18_1
| spl18_4
| spl18_6
| ~ spl18_9 ),
inference(avatar_split_clause,[],[f1174,f214,f197,f185,f171,f1109,f1170]) ).
tff(f171,plain,
( spl18_1
<=> $less(sK5,$product(sK0,sK0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_1])]) ).
tff(f185,plain,
( spl18_4
<=> $less(sK5,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_4])]) ).
tff(f197,plain,
( spl18_6
<=> $less(sK4,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_6])]) ).
tff(f214,plain,
( spl18_9
<=> same1(sK3,sK4,sK5) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_9])]) ).
tff(f1174,plain,
( ~ $less(sK4,size1(sK3))
| ( sK4 = sK5 )
| ~ spl18_1
| spl18_4
| spl18_6
| ~ spl18_9 ),
inference(subsumption_resolution,[],[f1167,f199]) ).
tff(f199,plain,
( ~ $less(sK4,0)
| spl18_6 ),
inference(avatar_component_clause,[],[f197]) ).
tff(f1167,plain,
( $less(sK4,0)
| ~ $less(sK4,size1(sK3))
| ( sK4 = sK5 )
| ~ spl18_1
| spl18_4
| ~ spl18_9 ),
inference(subsumption_resolution,[],[f1166,f187]) ).
tff(f187,plain,
( ~ $less(sK5,0)
| spl18_4 ),
inference(avatar_component_clause,[],[f185]) ).
tff(f1166,plain,
( $less(sK4,0)
| $less(sK5,0)
| ~ $less(sK4,size1(sK3))
| ( sK4 = sK5 )
| ~ spl18_1
| ~ spl18_9 ),
inference(subsumption_resolution,[],[f1154,f1043]) ).
tff(f1043,plain,
( $less(sK5,size1(sK3))
| ~ spl18_1 ),
inference(backward_demodulation,[],[f173,f103]) ).
tff(f173,plain,
( $less(sK5,$product(sK0,sK0))
| ~ spl18_1 ),
inference(avatar_component_clause,[],[f171]) ).
tff(f1154,plain,
( ~ $less(sK5,size1(sK3))
| $less(sK4,0)
| $less(sK5,0)
| ~ $less(sK4,size1(sK3))
| ( sK4 = sK5 )
| ~ spl18_9 ),
inference(resolution,[],[f216,f473]) ).
tff(f473,plain,
! [X8: $int,X7: $int] :
( ~ same1(sK3,X7,X8)
| ~ $less(X8,size1(sK3))
| $less(X7,0)
| $less(X8,0)
| ~ $less(X7,size1(sK3))
| ( X7 = X8 ) ),
inference(backward_demodulation,[],[f396,f103]) ).
tff(f396,plain,
! [X8: $int,X7: $int] :
( ~ $less(X8,size1(sK3))
| $less(X7,0)
| ~ $less(X7,$product(sK0,sK0))
| $less(X8,0)
| ~ same1(sK3,X7,X8)
| ( X7 = X8 ) ),
inference(backward_demodulation,[],[f100,f103]) ).
tff(f100,plain,
! [X8: $int,X7: $int] :
( $less(X7,0)
| ~ $less(X7,$product(sK0,sK0))
| $less(X8,0)
| ~ $less(X8,$product(sK0,sK0))
| ~ same1(sK3,X7,X8)
| ( X7 = X8 ) ),
inference(cnf_transformation,[],[f72]) ).
tff(f216,plain,
( same1(sK3,sK4,sK5)
| ~ spl18_9 ),
inference(avatar_component_clause,[],[f214]) ).
tff(f957,plain,
spl18_7,
inference(avatar_contradiction_clause,[],[f956]) ).
tff(f956,plain,
( $false
| spl18_7 ),
inference(subsumption_resolution,[],[f206,f747]) ).
tff(f747,plain,
! [X0: uf_pure1,X1: $int] : same1(X0,X1,X1),
inference(subsumption_resolution,[],[f746,f150]) ).
tff(f150,plain,
! [X2: $int,X0: uf_pure1,X1: $int] :
( ~ repr1(X0,X1,sK17(X0,X1,X2))
| ~ repr1(X0,X2,sK17(X0,X1,X2))
| same1(X0,X1,X2) ),
inference(cnf_transformation,[],[f68]) ).
tff(f68,plain,
! [X0: uf_pure1,X1: $int,X2: $int] :
( same1(X0,X1,X2)
<=> ! [X3: $int] :
( repr1(X0,X1,X3)
<=> repr1(X0,X2,X3) ) ),
inference(rectify,[],[f15]) ).
tff(f15,axiom,
! [X6: uf_pure1,X1: $int,X7: $int] :
( same1(X6,X1,X7)
<=> ! [X8: $int] :
( repr1(X6,X1,X8)
<=> repr1(X6,X7,X8) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f746,plain,
! [X0: uf_pure1,X1: $int] :
( repr1(X0,X1,sK17(X0,X1,X1))
| same1(X0,X1,X1) ),
inference(factoring,[],[f149]) ).
tff(f149,plain,
! [X2: $int,X0: uf_pure1,X1: $int] :
( repr1(X0,X2,sK17(X0,X1,X2))
| repr1(X0,X1,sK17(X0,X1,X2))
| same1(X0,X1,X2) ),
inference(cnf_transformation,[],[f68]) ).
tff(f206,plain,
( ~ same1(sK3,sK4,sK4)
| spl18_7 ),
inference(avatar_component_clause,[],[f204]) ).
tff(f204,plain,
( spl18_7
<=> same1(sK3,sK4,sK4) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_7])]) ).
tff(f955,plain,
~ spl18_16,
inference(avatar_contradiction_clause,[],[f954]) ).
tff(f954,plain,
( $false
| ~ spl18_16 ),
inference(subsumption_resolution,[],[f951,f106]) ).
tff(f106,plain,
~ $less(sK0,1),
inference(cnf_transformation,[],[f72]) ).
tff(f951,plain,
( $less(sK0,1)
| ~ spl18_16 ),
inference(evaluation,[],[f945]) ).
tff(f945,plain,
( $less(0,0)
| $less(sK0,1)
| ~ spl18_16 ),
inference(resolution,[],[f914,f794]) ).
tff(f794,plain,
! [X0: $int] :
( $less(X0,1)
| $less(0,X0) ),
inference(superposition,[],[f271,f35]) ).
tff(f35,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_145,[]) ).
tff(f271,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ),
inference(superposition,[],[f42,f33]) ).
tff(f33,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_143,[]) ).
tff(f42,plain,
! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) ),
introduced(theory_axiom_155,[]) ).
tff(f914,plain,
( ! [X1: $int] :
( ~ $less(X1,sK0)
| $less(X1,0) )
| ~ spl18_16 ),
inference(avatar_component_clause,[],[f913]) ).
tff(f913,plain,
( spl18_16
<=> ! [X1: $int] :
( $less(X1,0)
| ~ $less(X1,sK0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_16])]) ).
tff(f915,plain,
( spl18_16
| spl18_16
| ~ spl18_12 ),
inference(avatar_split_clause,[],[f911,f322,f913,f913]) ).
tff(f322,plain,
( spl18_12
<=> ( 0 = size1(sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_12])]) ).
tff(f911,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X0,sK0)
| $less(X1,0)
| ~ $less(X1,sK0)
| $less(X0,0) )
| ~ spl18_12 ),
inference(subsumption_resolution,[],[f908,f219]) ).
tff(f219,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less($sum($product(X1,X0),X2),0)
| ~ $less(X1,X0)
| $less(X2,0)
| ~ $less(X2,X0)
| $less(X1,0) ),
inference(subsumption_resolution,[],[f125,f39]) ).
tff(f39,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) ),
introduced(theory_axiom_151,[]) ).
tff(f125,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,0)
| $less(X1,0)
| ~ $less(X1,X0)
| $less(X2,0)
| ~ $less(X2,X0)
| ~ $less($sum($product(X1,X0),X2),0) ),
inference(cnf_transformation,[],[f82]) ).
tff(f82,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( $less($sum($product(X1,X0),X2),$product(X0,X0))
& ~ $less($sum($product(X1,X0),X2),0) )
| ~ $less(X2,X0)
| $less(X2,0)
| ~ $less(X1,X0)
| $less(X1,0)
| $less(X0,0) ),
inference(flattening,[],[f81]) ).
tff(f81,plain,
! [X0: $int,X1: $int,X2: $int] :
( ( $less($sum($product(X1,X0),X2),$product(X0,X0))
& ~ $less($sum($product(X1,X0),X2),0) )
| ~ $less(X2,X0)
| $less(X2,0)
| ~ $less(X1,X0)
| $less(X1,0)
| $less(X0,0) ),
inference(ennf_transformation,[],[f63]) ).
tff(f63,plain,
! [X0: $int,X1: $int,X2: $int] :
( ~ $less(X0,0)
=> ( ( $less(X1,X0)
& ~ $less(X1,0) )
=> ( ( $less(X2,X0)
& ~ $less(X2,0) )
=> ( $less($sum($product(X1,X0),X2),$product(X0,X0))
& ~ $less($sum($product(X1,X0),X2),0) ) ) ) ),
inference(rectify,[],[f31]) ).
tff(f31,plain,
! [X14: $int,X1: $int,X7: $int] :
( ~ $less(X14,0)
=> ( ( $less(X1,X14)
& ~ $less(X1,0) )
=> ( ( $less(X7,X14)
& ~ $less(X7,0) )
=> ( $less($sum($product(X1,X14),X7),$product(X14,X14))
& ~ $less($sum($product(X1,X14),X7),0) ) ) ) ),
inference(theory_normalization,[],[f24]) ).
tff(f24,axiom,
! [X14: $int,X1: $int,X7: $int] :
( $lesseq(0,X14)
=> ( ( $less(X1,X14)
& $lesseq(0,X1) )
=> ( ( $less(X7,X14)
& $lesseq(0,X7) )
=> ( $less($sum($product(X1,X14),X7),$product(X14,X14))
& $lesseq(0,$sum($product(X1,X14),X7)) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',unknown) ).
tff(f908,plain,
( ! [X0: $int,X1: $int] :
( $less($sum($product(X0,sK0),X1),0)
| ~ $less(X0,sK0)
| $less(X1,0)
| ~ $less(X1,sK0)
| $less(X0,0) )
| ~ spl18_12 ),
inference(backward_demodulation,[],[f835,f324]) ).
tff(f324,plain,
( ( 0 = size1(sK3) )
| ~ spl18_12 ),
inference(avatar_component_clause,[],[f322]) ).
tff(f835,plain,
! [X0: $int,X1: $int] :
( $less($sum($product(X0,sK0),X1),size1(sK3))
| ~ $less(X0,sK0)
| $less(X1,0)
| ~ $less(X1,sK0)
| $less(X0,0) ),
inference(superposition,[],[f218,f103]) ).
tff(f218,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum($product(X1,X0),X2),$product(X0,X0))
| ~ $less(X1,X0)
| $less(X2,0)
| ~ $less(X2,X0)
| $less(X1,0) ),
inference(subsumption_resolution,[],[f126,f39]) ).
tff(f126,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,0)
| $less(X1,0)
| ~ $less(X1,X0)
| $less(X2,0)
| ~ $less(X2,X0)
| $less($sum($product(X1,X0),X2),$product(X0,X0)) ),
inference(cnf_transformation,[],[f82]) ).
tff(f885,plain,
( spl18_12
| spl18_13 ),
inference(avatar_split_clause,[],[f399,f326,f322]) ).
tff(f326,plain,
( spl18_13
<=> $less(0,size1(sK3)) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_13])]) ).
tff(f399,plain,
( $less(0,size1(sK3))
| ( 0 = size1(sK3) ) ),
inference(resolution,[],[f168,f40]) ).
tff(f40,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_152,[]) ).
tff(f168,plain,
~ $less(size1(sK3),0),
inference(backward_demodulation,[],[f108,f103]) ).
tff(f108,plain,
~ $less($product(sK0,sK0),0),
inference(cnf_transformation,[],[f72]) ).
tff(f881,plain,
( ~ spl18_2
| ~ spl18_3
| ~ spl18_13 ),
inference(avatar_contradiction_clause,[],[f880]) ).
tff(f880,plain,
( $false
| ~ spl18_2
| ~ spl18_3
| ~ spl18_13 ),
inference(subsumption_resolution,[],[f863,f239]) ).
tff(f239,plain,
( $less(size1(sK3),1)
| ~ spl18_2
| ~ spl18_3 ),
inference(backward_demodulation,[],[f181,f176]) ).
tff(f176,plain,
( ( num1(sK3) = size1(sK3) )
| ~ spl18_2 ),
inference(avatar_component_clause,[],[f175]) ).
tff(f175,plain,
( spl18_2
<=> ( num1(sK3) = size1(sK3) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_2])]) ).
tff(f181,plain,
( $less(num1(sK3),1)
| ~ spl18_3 ),
inference(avatar_component_clause,[],[f179]) ).
tff(f179,plain,
( spl18_3
<=> $less(num1(sK3),1) ),
introduced(avatar_definition,[new_symbols(naming,[spl18_3])]) ).
tff(f863,plain,
( ~ $less(size1(sK3),1)
| ~ spl18_13 ),
inference(resolution,[],[f855,f328]) ).
tff(f328,plain,
( $less(0,size1(sK3))
| ~ spl18_13 ),
inference(avatar_component_clause,[],[f326]) ).
tff(f855,plain,
! [X0: $int] :
( ~ $less(0,X0)
| ~ $less(X0,1) ),
inference(superposition,[],[f276,f35]) ).
tff(f276,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ),
inference(superposition,[],[f50,f33]) ).
tff(f50,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(theory_axiom_169,[]) ).
tff(f238,plain,
spl18_2,
inference(avatar_split_clause,[],[f233,f175]) ).
tff(f233,plain,
num1(sK3) = size1(sK3),
inference(superposition,[],[f102,f103]) ).
tff(f102,plain,
num1(sK3) = $product(sK0,sK0),
inference(cnf_transformation,[],[f72]) ).
tff(f217,plain,
( spl18_9
| spl18_8
| ~ spl18_2
| spl18_3 ),
inference(avatar_split_clause,[],[f212,f179,f175,f208,f214]) ).
tff(f212,plain,
( $less(num1(sK3),1)
| ( num1(sK3) != size1(sK3) )
| path1(sK2,sK4,sK5)
| same1(sK3,sK4,sK5) ),
inference(subsumption_resolution,[],[f162,f103]) ).
tff(f162,plain,
( $less(num1(sK3),1)
| ( num1(sK3) != size1(sK3) )
| ( size1(sK3) != $product(sK0,sK0) )
| path1(sK2,sK4,sK5)
| same1(sK3,sK4,sK5) ),
inference(evaluation,[],[f159]) ).
tff(f159,plain,
( $less(num1(sK3),1)
| ( size1(sK3) != $sum(num1(sK3),0) )
| ( size1(sK3) != $product(sK0,sK0) )
| path1(sK2,sK4,sK5)
| same1(sK3,sK4,sK5) ),
inference(definition_unfolding,[],[f92,f107]) ).
tff(f107,plain,
0 = sK1,
inference(cnf_transformation,[],[f72]) ).
tff(f92,plain,
( $less(num1(sK3),1)
| ( size1(sK3) != $sum(num1(sK3),sK1) )
| ( size1(sK3) != $product(sK0,sK0) )
| path1(sK2,sK4,sK5)
| same1(sK3,sK4,sK5) ),
inference(cnf_transformation,[],[f72]) ).
tff(f211,plain,
( ~ spl18_7
| ~ spl18_8
| ~ spl18_2
| spl18_3 ),
inference(avatar_split_clause,[],[f202,f179,f175,f208,f204]) ).
tff(f202,plain,
( $less(num1(sK3),1)
| ( num1(sK3) != size1(sK3) )
| ~ path1(sK2,sK4,sK5)
| ~ same1(sK3,sK4,sK4) ),
inference(forward_subsumption_demodulation,[],[f201,f104]) ).
tff(f104,plain,
! [X3: $int,X4: $int] :
( ~ path1(sK2,X3,X4)
| ( X3 = X4 ) ),
inference(cnf_transformation,[],[f72]) ).
tff(f201,plain,
( $less(num1(sK3),1)
| ( num1(sK3) != size1(sK3) )
| ~ path1(sK2,sK4,sK5)
| ~ same1(sK3,sK4,sK5) ),
inference(subsumption_resolution,[],[f163,f103]) ).
tff(f163,plain,
( $less(num1(sK3),1)
| ( num1(sK3) != size1(sK3) )
| ( size1(sK3) != $product(sK0,sK0) )
| ~ path1(sK2,sK4,sK5)
| ~ same1(sK3,sK4,sK5) ),
inference(evaluation,[],[f158]) ).
tff(f158,plain,
( $less(num1(sK3),1)
| ( size1(sK3) != $sum(num1(sK3),0) )
| ( size1(sK3) != $product(sK0,sK0) )
| ~ path1(sK2,sK4,sK5)
| ~ same1(sK3,sK4,sK5) ),
inference(definition_unfolding,[],[f93,f107]) ).
tff(f93,plain,
( $less(num1(sK3),1)
| ( size1(sK3) != $sum(num1(sK3),sK1) )
| ( size1(sK3) != $product(sK0,sK0) )
| ~ path1(sK2,sK4,sK5)
| ~ same1(sK3,sK4,sK5) ),
inference(cnf_transformation,[],[f72]) ).
tff(f200,plain,
( ~ spl18_6
| ~ spl18_2
| spl18_3 ),
inference(avatar_split_clause,[],[f195,f179,f175,f197]) ).
tff(f195,plain,
( $less(num1(sK3),1)
| ( num1(sK3) != size1(sK3) )
| ~ $less(sK4,0) ),
inference(subsumption_resolution,[],[f164,f103]) ).
tff(f164,plain,
( $less(num1(sK3),1)
| ( num1(sK3) != size1(sK3) )
| ( size1(sK3) != $product(sK0,sK0) )
| ~ $less(sK4,0) ),
inference(evaluation,[],[f157]) ).
tff(f157,plain,
( $less(num1(sK3),1)
| ( size1(sK3) != $sum(num1(sK3),0) )
| ( size1(sK3) != $product(sK0,sK0) )
| ~ $less(sK4,0) ),
inference(definition_unfolding,[],[f94,f107]) ).
tff(f94,plain,
( $less(num1(sK3),1)
| ( size1(sK3) != $sum(num1(sK3),sK1) )
| ( size1(sK3) != $product(sK0,sK0) )
| ~ $less(sK4,0) ),
inference(cnf_transformation,[],[f72]) ).
tff(f194,plain,
( spl18_5
| ~ spl18_2
| spl18_3 ),
inference(avatar_split_clause,[],[f189,f179,f175,f191]) ).
tff(f189,plain,
( $less(num1(sK3),1)
| ( num1(sK3) != size1(sK3) )
| $less(sK4,$product(sK0,sK0)) ),
inference(subsumption_resolution,[],[f165,f103]) ).
tff(f165,plain,
( $less(num1(sK3),1)
| ( num1(sK3) != size1(sK3) )
| ( size1(sK3) != $product(sK0,sK0) )
| $less(sK4,$product(sK0,sK0)) ),
inference(evaluation,[],[f156]) ).
tff(f156,plain,
( $less(num1(sK3),1)
| ( size1(sK3) != $sum(num1(sK3),0) )
| ( size1(sK3) != $product(sK0,sK0) )
| $less(sK4,$product(sK0,sK0)) ),
inference(definition_unfolding,[],[f95,f107]) ).
tff(f95,plain,
( $less(num1(sK3),1)
| ( size1(sK3) != $sum(num1(sK3),sK1) )
| ( size1(sK3) != $product(sK0,sK0) )
| $less(sK4,$product(sK0,sK0)) ),
inference(cnf_transformation,[],[f72]) ).
tff(f188,plain,
( ~ spl18_4
| ~ spl18_2
| spl18_3 ),
inference(avatar_split_clause,[],[f183,f179,f175,f185]) ).
tff(f183,plain,
( $less(num1(sK3),1)
| ( num1(sK3) != size1(sK3) )
| ~ $less(sK5,0) ),
inference(subsumption_resolution,[],[f166,f103]) ).
tff(f166,plain,
( $less(num1(sK3),1)
| ( num1(sK3) != size1(sK3) )
| ( size1(sK3) != $product(sK0,sK0) )
| ~ $less(sK5,0) ),
inference(evaluation,[],[f155]) ).
tff(f155,plain,
( $less(num1(sK3),1)
| ( size1(sK3) != $sum(num1(sK3),0) )
| ( size1(sK3) != $product(sK0,sK0) )
| ~ $less(sK5,0) ),
inference(definition_unfolding,[],[f96,f107]) ).
tff(f96,plain,
( $less(num1(sK3),1)
| ( size1(sK3) != $sum(num1(sK3),sK1) )
| ( size1(sK3) != $product(sK0,sK0) )
| ~ $less(sK5,0) ),
inference(cnf_transformation,[],[f72]) ).
tff(f182,plain,
( spl18_1
| ~ spl18_2
| spl18_3 ),
inference(avatar_split_clause,[],[f169,f179,f175,f171]) ).
tff(f169,plain,
( $less(num1(sK3),1)
| ( num1(sK3) != size1(sK3) )
| $less(sK5,$product(sK0,sK0)) ),
inference(subsumption_resolution,[],[f167,f103]) ).
tff(f167,plain,
( $less(num1(sK3),1)
| ( num1(sK3) != size1(sK3) )
| ( size1(sK3) != $product(sK0,sK0) )
| $less(sK5,$product(sK0,sK0)) ),
inference(evaluation,[],[f154]) ).
tff(f154,plain,
( $less(num1(sK3),1)
| ( size1(sK3) != $sum(num1(sK3),0) )
| ( size1(sK3) != $product(sK0,sK0) )
| $less(sK5,$product(sK0,sK0)) ),
inference(definition_unfolding,[],[f97,f107]) ).
tff(f97,plain,
( $less(num1(sK3),1)
| ( size1(sK3) != $sum(num1(sK3),sK1) )
| ( size1(sK3) != $product(sK0,sK0) )
| $less(sK5,$product(sK0,sK0)) ),
inference(cnf_transformation,[],[f72]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : SWW653_2 : TPTP v8.2.0. Released v6.1.0.
% 0.04/0.12 % Command : run_vampire %s %d SAT
% 0.12/0.33 % Computer : n014.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Wed Jun 19 05:52:24 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.35 This is a TF0_THM_EQU_ARI problem
% 0.12/0.35 Running first-order model finding
% 0.12/0.35 Running /export/starexec/sandbox2/solver/bin/vampire --mode casc_sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.21/0.42 % (13037)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (13041)fmb+10_1:1_sil=256000:fmbss=23:fmbes=contour:newcnf=on:fmbsr=1.14:i=152523:nm=2:gsp=on:rp=on_0 on theBenchmark for (3000ds/152523Mi)
% 0.21/0.42 % (13037)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (13038)fmb+10_1:1_sil=256000:i=98885:tgt=full:fmbsr=1.3:fmbss=10_0 on theBenchmark for (3000ds/98885Mi)
% 0.21/0.42 % (13037)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (13042)ott+21_1:1_sil=4000:i=104:fsd=on:fd=off:newcnf=on_0 on theBenchmark for (3000ds/104Mi)
% 0.21/0.42 % (13037)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (13040)fmb+10_1:1_sil=256000:fmbes=contour:i=214858:bce=on_0 on theBenchmark for (3000ds/214858Mi)
% 0.21/0.42 % (13037)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (13043)ott+11_8:59_sil=16000:sp=occurrence:lsd=20:abs=on:i=146:aac=none:nm=16:fdi=10:rawr=on:nicw=on_0 on theBenchmark for (3000ds/146Mi)
% 0.21/0.42 % (13037)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (13039)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:i=99418_0 on theBenchmark for (3000ds/99418Mi)
% 0.21/0.42 % (13037)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.42 % (13044)ott-4_1:1_sil=4000:sp=reverse_arity:lcm=predicate:newcnf=on:i=115:bce=on:fd=off:fs=off:fsr=off_0 on theBenchmark for (3000ds/115Mi)
% 0.21/0.42 % (13038)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.42 % (13038)Terminated due to inappropriate strategy.
% 0.21/0.42 % (13038)------------------------------
% 0.21/0.42 % (13038)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.42 % (13041)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.42 % (13041)Terminated due to inappropriate strategy.
% 0.21/0.42 % (13041)------------------------------
% 0.21/0.42 % (13041)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.42 % (13041)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.42 % (13041)Termination reason: Inappropriate
% 0.21/0.42
% 0.21/0.42 % (13041)Memory used [KB]: 776
% 0.21/0.42 % (13041)Time elapsed: 0.005 s
% 0.21/0.42 % (13041)Instructions burned: 5 (million)
% 0.21/0.42 % (13038)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.42 % (13038)Termination reason: Inappropriate
% 0.21/0.42
% 0.21/0.42 % (13038)Memory used [KB]: 801
% 0.21/0.42 % (13038)Time elapsed: 0.005 s
% 0.21/0.42 % (13038)Instructions burned: 5 (million)
% 0.21/0.42 % (13040)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.42 % (13040)Terminated due to inappropriate strategy.
% 0.21/0.42 % (13040)------------------------------
% 0.21/0.42 % (13040)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.42 % (13040)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.42 % (13040)Termination reason: Inappropriate
% 0.21/0.42
% 0.21/0.42 % (13040)Memory used [KB]: 859
% 0.21/0.42 % (13041)------------------------------
% 0.21/0.42 % (13041)------------------------------
% 0.21/0.42 % (13040)Time elapsed: 0.005 s
% 0.21/0.42 % (13040)Instructions burned: 6 (million)
% 0.21/0.42 % (13038)------------------------------
% 0.21/0.42 % (13038)------------------------------
% 0.21/0.42 % (13040)------------------------------
% 0.21/0.42 % (13040)------------------------------
% 0.21/0.46 % (13042)First to succeed.
% 0.21/0.46 % (13042)Solution written to "/export/starexec/sandbox2/tmp/vampire-proof-13037"
% 0.21/0.46 % (13037)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.46 % (13042)Refutation found. Thanks to Tanya!
% 0.21/0.46 % SZS status Theorem for theBenchmark
% 0.21/0.46 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.46 % (13042)------------------------------
% 0.21/0.46 % (13042)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.21/0.46 % (13042)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.21/0.46 % (13042)Termination reason: Refutation
% 0.21/0.46
% 0.21/0.46 % (13042)Memory used [KB]: 1282
% 0.21/0.46 % (13042)Time elapsed: 0.044 s
% 0.21/0.46 % (13042)Instructions burned: 66 (million)
% 0.21/0.46 % (13042)------------------------------
% 0.21/0.46 % (13042)------------------------------
% 0.21/0.46 % (13037)Success in time 0.095 s
%------------------------------------------------------------------------------