TSTP Solution File: ARI701_1 by Vampire-SAT---4.9
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%------------------------------------------------------------------------------
% File : Vampire-SAT---4.9
% Problem : ARI701_1 : TPTP v8.2.0. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire %s %d SAT
% Computer : n018.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 04:35:16 EDT 2024
% Result : Theorem 0.18s 0.43s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 72
% Syntax : Number of formulae : 174 ( 46 unt; 5 typ; 0 def)
% Number of atoms : 382 ( 95 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 380 ( 167 ~; 168 |; 0 &)
% ( 45 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number arithmetic : 584 ( 69 atm; 261 fun; 59 num; 195 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 48 ( 45 usr; 46 prp; 0-2 aty)
% Number of functors : 10 ( 5 usr; 7 con; 0-2 aty)
% Number of variables : 195 ( 195 !; 0 ?; 195 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
x: $int ).
tff(func_def_1,type,
y: $int ).
tff(func_def_2,type,
a: $int ).
tff(func_def_3,type,
z: $int ).
tff(func_def_4,type,
b: $int ).
tff(f502,plain,
$false,
inference(avatar_sat_refutation,[],[f35,f41,f45,f49,f53,f57,f61,f66,f71,f76,f80,f84,f88,f96,f100,f104,f114,f118,f130,f134,f163,f167,f210,f214,f264,f273,f286,f290,f294,f330,f334,f338,f342,f346,f393,f397,f401,f405,f476,f480,f484,f488,f492,f496,f500,f501]) ).
tff(f501,plain,
( spl0_2
| ~ spl0_8
| ~ spl0_10
| ~ spl0_13
| ~ spl0_33 ),
inference(avatar_split_clause,[],[f372,f340,f86,f73,f63,f38]) ).
tff(f38,plain,
( spl0_2
<=> ( 1 = $product(b,x) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
tff(f63,plain,
( spl0_8
<=> ( $product(a,z) = 1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
tff(f73,plain,
( spl0_10
<=> ( $product(y,z) = b ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
tff(f86,plain,
( spl0_13
<=> ! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
tff(f340,plain,
( spl0_33
<=> ! [X0: $int] : ( $product(x,$product(y,X0)) = $product(a,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
tff(f372,plain,
( ( 1 = $product(b,x) )
| ~ spl0_8
| ~ spl0_10
| ~ spl0_13
| ~ spl0_33 ),
inference(forward_demodulation,[],[f371,f65]) ).
tff(f65,plain,
( ( $product(a,z) = 1 )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f63]) ).
tff(f371,plain,
( ( $product(a,z) = $product(b,x) )
| ~ spl0_10
| ~ spl0_13
| ~ spl0_33 ),
inference(forward_demodulation,[],[f362,f87]) ).
tff(f87,plain,
( ! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f86]) ).
tff(f362,plain,
( ( $product(a,z) = $product(x,b) )
| ~ spl0_10
| ~ spl0_33 ),
inference(superposition,[],[f341,f75]) ).
tff(f75,plain,
( ( $product(y,z) = b )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f73]) ).
tff(f341,plain,
( ! [X0: $int] : ( $product(x,$product(y,X0)) = $product(a,X0) )
| ~ spl0_33 ),
inference(avatar_component_clause,[],[f340]) ).
tff(f500,plain,
( spl0_45
| ~ spl0_10
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f219,f208,f73,f498]) ).
tff(f498,plain,
( spl0_45
<=> ! [X0: $int] : ( $product(y,$sum(z,X0)) = $sum(b,$product(y,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_45])]) ).
tff(f208,plain,
( spl0_23
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
tff(f219,plain,
( ! [X0: $int] : ( $product(y,$sum(z,X0)) = $sum(b,$product(y,X0)) )
| ~ spl0_10
| ~ spl0_23 ),
inference(superposition,[],[f209,f75]) ).
tff(f209,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f208]) ).
tff(f496,plain,
( spl0_44
| ~ spl0_9
| ~ spl0_23 ),
inference(avatar_split_clause,[],[f218,f208,f68,f494]) ).
tff(f494,plain,
( spl0_44
<=> ! [X0: $int] : ( $product(x,$sum(y,X0)) = $sum(a,$product(x,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_44])]) ).
tff(f68,plain,
( spl0_9
<=> ( $product(x,y) = a ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
tff(f218,plain,
( ! [X0: $int] : ( $product(x,$sum(y,X0)) = $sum(a,$product(x,X0)) )
| ~ spl0_9
| ~ spl0_23 ),
inference(superposition,[],[f209,f70]) ).
tff(f70,plain,
( ( $product(x,y) = a )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f68]) ).
tff(f492,plain,
( spl0_43
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f195,f165,f86,f490]) ).
tff(f490,plain,
( spl0_43
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product(X2,$product(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_43])]) ).
tff(f165,plain,
( spl0_22
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
tff(f195,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product(X2,$product(X0,X1)) )
| ~ spl0_13
| ~ spl0_22 ),
inference(superposition,[],[f166,f87]) ).
tff(f166,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f165]) ).
tff(f488,plain,
( spl0_42
| ~ spl0_13
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f187,f165,f86,f486]) ).
tff(f486,plain,
( spl0_42
<=> ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_42])]) ).
tff(f187,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X1,X0),X2) )
| ~ spl0_13
| ~ spl0_22 ),
inference(superposition,[],[f166,f87]) ).
tff(f484,plain,
( spl0_41
| ~ spl0_12
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f174,f161,f82,f482]) ).
tff(f482,plain,
( spl0_41
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_41])]) ).
tff(f82,plain,
( spl0_12
<=> ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
tff(f161,plain,
( spl0_21
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
tff(f174,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) )
| ~ spl0_12
| ~ spl0_21 ),
inference(superposition,[],[f162,f83]) ).
tff(f83,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f82]) ).
tff(f162,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f161]) ).
tff(f480,plain,
( spl0_40
| ~ spl0_12
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f169,f161,f82,f478]) ).
tff(f478,plain,
( spl0_40
<=> ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_40])]) ).
tff(f169,plain,
( ! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X1,X0),X2) )
| ~ spl0_12
| ~ spl0_21 ),
inference(superposition,[],[f162,f83]) ).
tff(f476,plain,
( spl0_39
| ~ spl0_14
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f119,f112,f94,f474]) ).
tff(f474,plain,
( spl0_39
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_39])]) ).
tff(f94,plain,
( spl0_14
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
tff(f112,plain,
( spl0_17
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
tff(f119,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less(X0,$sum(X2,1))
| $less(X2,X1) )
| ~ spl0_14
| ~ spl0_17 ),
inference(resolution,[],[f113,f95]) ).
tff(f95,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(X0,1))
| $less(X0,X1) )
| ~ spl0_14 ),
inference(avatar_component_clause,[],[f94]) ).
tff(f113,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X1,X2)
| ~ $less(X0,X1)
| $less(X0,X2) )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f112]) ).
tff(f405,plain,
( spl0_38
| ~ spl0_11
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f173,f161,f78,f403]) ).
tff(f403,plain,
( spl0_38
<=> ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_38])]) ).
tff(f78,plain,
( spl0_11
<=> ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
tff(f173,plain,
( ! [X0: $int,X1: $int] : ( 0 = $sum(X0,$sum(X1,$uminus($sum(X0,X1)))) )
| ~ spl0_11
| ~ spl0_21 ),
inference(superposition,[],[f162,f79]) ).
tff(f79,plain,
( ! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f78]) ).
tff(f401,plain,
( spl0_37
| ~ spl0_12
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f157,f132,f82,f399]) ).
tff(f399,plain,
( spl0_37
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_37])]) ).
tff(f132,plain,
( spl0_20
<=> ! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
tff(f157,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X2,X1),$sum(X1,X0))
| ~ $less(X2,X0) )
| ~ spl0_12
| ~ spl0_20 ),
inference(superposition,[],[f133,f83]) ).
tff(f133,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f132]) ).
tff(f397,plain,
( spl0_36
| ~ spl0_12
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f153,f132,f82,f395]) ).
tff(f395,plain,
( spl0_36
<=> ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
tff(f153,plain,
( ! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) )
| ~ spl0_12
| ~ spl0_20 ),
inference(superposition,[],[f133,f83]) ).
tff(f393,plain,
( spl0_35
| ~ spl0_12
| ~ spl0_19 ),
inference(avatar_split_clause,[],[f136,f128,f82,f391]) ).
tff(f391,plain,
( spl0_35
<=> ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
tff(f128,plain,
( spl0_19
<=> ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
tff(f136,plain,
( ! [X0: $int,X1: $int] : ( $sum($uminus(X1),$uminus(X0)) = $uminus($sum(X1,X0)) )
| ~ spl0_12
| ~ spl0_19 ),
inference(superposition,[],[f129,f83]) ).
tff(f129,plain,
( ! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f128]) ).
tff(f346,plain,
( spl0_34
| ~ spl0_10
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f190,f165,f73,f344]) ).
tff(f344,plain,
( spl0_34
<=> ! [X0: $int] : ( $product(y,$product(z,X0)) = $product(b,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
tff(f190,plain,
( ! [X0: $int] : ( $product(y,$product(z,X0)) = $product(b,X0) )
| ~ spl0_10
| ~ spl0_22 ),
inference(superposition,[],[f166,f75]) ).
tff(f342,plain,
( spl0_33
| ~ spl0_9
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f189,f165,f68,f340]) ).
tff(f189,plain,
( ! [X0: $int] : ( $product(x,$product(y,X0)) = $product(a,X0) )
| ~ spl0_9
| ~ spl0_22 ),
inference(superposition,[],[f166,f70]) ).
tff(f338,plain,
( spl0_32
| ~ spl0_12
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f267,f262,f82,f336]) ).
tff(f336,plain,
( spl0_32
<=> ! [X0: $int] : $less(X0,$sum(1,X0)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
tff(f262,plain,
( spl0_25
<=> ! [X0: $int] : $less(X0,$sum(X0,1)) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
tff(f267,plain,
( ! [X0: $int] : $less(X0,$sum(1,X0))
| ~ spl0_12
| ~ spl0_25 ),
inference(superposition,[],[f263,f83]) ).
tff(f263,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f262]) ).
tff(f334,plain,
( spl0_31
| ~ spl0_11
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f156,f132,f78,f332]) ).
tff(f332,plain,
( spl0_31
<=> ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
tff(f156,plain,
( ! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) )
| ~ spl0_11
| ~ spl0_20 ),
inference(superposition,[],[f133,f79]) ).
tff(f330,plain,
( spl0_30
| ~ spl0_11
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f152,f132,f78,f328]) ).
tff(f328,plain,
( spl0_30
<=> ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
tff(f152,plain,
( ! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) )
| ~ spl0_11
| ~ spl0_20 ),
inference(superposition,[],[f133,f79]) ).
tff(f294,plain,
( spl0_29
| ~ spl0_11
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f183,f161,f78,f292]) ).
tff(f292,plain,
( spl0_29
<=> ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
tff(f183,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 )
| ~ spl0_11
| ~ spl0_21 ),
inference(evaluation,[],[f168]) ).
tff(f168,plain,
( ! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = $sum(0,X1) )
| ~ spl0_11
| ~ spl0_21 ),
inference(superposition,[],[f162,f79]) ).
tff(f290,plain,
( spl0_28
| ~ spl0_12
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f109,f102,f82,f288]) ).
tff(f288,plain,
( spl0_28
<=> ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
tff(f102,plain,
( spl0_16
<=> ! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
tff(f109,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) )
| ~ spl0_12
| ~ spl0_16 ),
inference(superposition,[],[f103,f83]) ).
tff(f103,plain,
( ! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f102]) ).
tff(f286,plain,
( spl0_27
| ~ spl0_12
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f106,f94,f82,f284]) ).
tff(f284,plain,
( spl0_27
<=> ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
tff(f106,plain,
( ! [X0: $int,X1: $int] :
( $less(X1,$sum(1,X0))
| $less(X0,X1) )
| ~ spl0_12
| ~ spl0_14 ),
inference(superposition,[],[f95,f83]) ).
tff(f273,plain,
( spl0_26
| ~ spl0_8
| ~ spl0_22 ),
inference(avatar_split_clause,[],[f200,f165,f63,f271]) ).
tff(f271,plain,
( spl0_26
<=> ! [X0: $int] : ( $product(a,$product(z,X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
tff(f200,plain,
( ! [X0: $int] : ( $product(a,$product(z,X0)) = X0 )
| ~ spl0_8
| ~ spl0_22 ),
inference(evaluation,[],[f191]) ).
tff(f191,plain,
( ! [X0: $int] : ( $product(a,$product(z,X0)) = $product(1,X0) )
| ~ spl0_8
| ~ spl0_22 ),
inference(superposition,[],[f166,f65]) ).
tff(f264,plain,
( spl0_25
| ~ spl0_3
| ~ spl0_14 ),
inference(avatar_split_clause,[],[f105,f94,f43,f262]) ).
tff(f43,plain,
( spl0_3
<=> ! [X0: $int] : ~ $less(X0,X0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
tff(f105,plain,
( ! [X0: $int] : $less(X0,$sum(X0,1))
| ~ spl0_3
| ~ spl0_14 ),
inference(resolution,[],[f95,f44]) ).
tff(f44,plain,
( ! [X0: $int] : ~ $less(X0,X0)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f43]) ).
tff(f214,plain,
spl0_24,
inference(avatar_split_clause,[],[f29,f212]) ).
tff(f212,plain,
( spl0_24
<=> ! [X2: $int,X0: $int,X3: $int] :
( ( 0 = X0 )
| ( $product(X0,X2) != $product(X0,X3) )
| ( X2 = X3 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
tff(f29,plain,
! [X2: $int,X3: $int,X0: $int] :
( ( 0 = X0 )
| ( $product(X0,X2) != $product(X0,X3) )
| ( X2 = X3 ) ),
inference(equality_resolution,[],[f22]) ).
tff(f22,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ( 0 = X0 )
| ( $product(X0,X2) != X1 )
| ( $product(X0,X3) != X1 )
| ( X2 = X3 ) ),
introduced(theory_axiom_159,[]) ).
tff(f210,plain,
spl0_23,
inference(avatar_split_clause,[],[f21,f208]) ).
tff(f21,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ),
introduced(theory_axiom_158,[]) ).
tff(f167,plain,
spl0_22,
inference(avatar_split_clause,[],[f18,f165]) ).
tff(f18,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$product(X1,X2)) = $product($product(X0,X1),X2) ),
introduced(theory_axiom_144,[]) ).
tff(f163,plain,
spl0_21,
inference(avatar_split_clause,[],[f7,f161]) ).
tff(f7,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_144,[]) ).
tff(f134,plain,
spl0_20,
inference(avatar_split_clause,[],[f14,f132]) ).
tff(f14,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| $less($sum(X0,X2),$sum(X1,X2)) ),
introduced(theory_axiom_153,[]) ).
tff(f130,plain,
spl0_19,
inference(avatar_split_clause,[],[f9,f128]) ).
tff(f9,plain,
! [X0: $int,X1: $int] : ( $uminus($sum(X0,X1)) = $sum($uminus(X1),$uminus(X0)) ),
introduced(theory_axiom_147,[]) ).
tff(f118,plain,
spl0_18,
inference(avatar_split_clause,[],[f13,f116]) ).
tff(f116,plain,
( spl0_18
<=> ! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
tff(f13,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,X0)
| ( X0 = X1 ) ),
introduced(theory_axiom_152,[]) ).
tff(f114,plain,
spl0_17,
inference(avatar_split_clause,[],[f12,f112]) ).
tff(f12,plain,
! [X2: $int,X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X2)
| $less(X0,X2) ),
introduced(theory_axiom_151,[]) ).
tff(f104,plain,
spl0_16,
inference(avatar_split_clause,[],[f23,f102]) ).
tff(f23,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_169,[]) ).
tff(f100,plain,
( spl0_15
| ~ spl0_7
| ~ spl0_13 ),
inference(avatar_split_clause,[],[f89,f86,f59,f98]) ).
tff(f98,plain,
( spl0_15
<=> ! [X0: $int] : ( 0 = $product(0,X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
tff(f59,plain,
( spl0_7
<=> ! [X0: $int] : ( 0 = $product(X0,0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
tff(f89,plain,
( ! [X0: $int] : ( 0 = $product(0,X0) )
| ~ spl0_7
| ~ spl0_13 ),
inference(superposition,[],[f87,f60]) ).
tff(f60,plain,
( ! [X0: $int] : ( 0 = $product(X0,0) )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f59]) ).
tff(f96,plain,
spl0_14,
inference(avatar_split_clause,[],[f15,f94]) ).
tff(f15,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_155,[]) ).
tff(f88,plain,
spl0_13,
inference(avatar_split_clause,[],[f17,f86]) ).
tff(f17,plain,
! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(theory_axiom_143,[]) ).
tff(f84,plain,
spl0_12,
inference(avatar_split_clause,[],[f6,f82]) ).
tff(f6,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_143,[]) ).
tff(f80,plain,
spl0_11,
inference(avatar_split_clause,[],[f10,f78]) ).
tff(f10,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_148,[]) ).
tff(f76,plain,
spl0_10,
inference(avatar_split_clause,[],[f28,f73]) ).
tff(f28,plain,
$product(y,z) = b,
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
$product(y,z) = b,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
tff(f71,plain,
spl0_9,
inference(avatar_split_clause,[],[f27,f68]) ).
tff(f27,plain,
$product(x,y) = a,
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
$product(x,y) = a,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
tff(f66,plain,
spl0_8,
inference(avatar_split_clause,[],[f26,f63]) ).
tff(f26,plain,
$product(a,z) = 1,
inference(cnf_transformation,[],[f3]) ).
tff(f3,axiom,
$product(a,z) = 1,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
tff(f61,plain,
spl0_7,
inference(avatar_split_clause,[],[f20,f59]) ).
tff(f20,plain,
! [X0: $int] : ( 0 = $product(X0,0) ),
introduced(theory_axiom_157,[]) ).
tff(f57,plain,
spl0_6,
inference(avatar_split_clause,[],[f19,f55]) ).
tff(f55,plain,
( spl0_6
<=> ! [X0: $int] : ( $product(X0,1) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
tff(f19,plain,
! [X0: $int] : ( $product(X0,1) = X0 ),
introduced(theory_axiom_145,[]) ).
tff(f53,plain,
spl0_5,
inference(avatar_split_clause,[],[f16,f51]) ).
tff(f51,plain,
( spl0_5
<=> ! [X0: $int] : ( $uminus($uminus(X0)) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
tff(f16,plain,
! [X0: $int] : ( $uminus($uminus(X0)) = X0 ),
introduced(theory_axiom_156,[]) ).
tff(f49,plain,
spl0_4,
inference(avatar_split_clause,[],[f8,f47]) ).
tff(f47,plain,
( spl0_4
<=> ! [X0: $int] : ( $sum(X0,0) = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
tff(f8,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_145,[]) ).
tff(f45,plain,
spl0_3,
inference(avatar_split_clause,[],[f11,f43]) ).
tff(f11,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_150,[]) ).
tff(f41,plain,
( ~ spl0_2
| spl0_1 ),
inference(avatar_split_clause,[],[f36,f32,f38]) ).
tff(f32,plain,
( spl0_1
<=> ( 1 = $product($product(y,z),x) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
tff(f36,plain,
( ( 1 != $product(b,x) )
| spl0_1 ),
inference(forward_demodulation,[],[f34,f28]) ).
tff(f34,plain,
( ( 1 != $product($product(y,z),x) )
| spl0_1 ),
inference(avatar_component_clause,[],[f32]) ).
tff(f35,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f30,f32]) ).
tff(f30,plain,
1 != $product($product(y,z),x),
inference(forward_demodulation,[],[f25,f17]) ).
tff(f25,plain,
1 != $product($product(z,y),x),
inference(cnf_transformation,[],[f24]) ).
tff(f24,plain,
1 != $product($product(z,y),x),
inference(flattening,[],[f5]) ).
tff(f5,negated_conjecture,
( ~ 1 = $product($product(z,y),x) ),
inference(negated_conjecture,[],[f4]) ).
tff(f4,conjecture,
1 = $product($product(z,y),x),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',unknown) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : ARI701_1 : TPTP v8.2.0. Released v6.3.0.
% 0.02/0.12 % Command : run_vampire %s %d SAT
% 0.11/0.33 % Computer : n018.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 21 05:01:08 EDT 2024
% 0.11/0.33 % CPUTime :
% 0.11/0.35 This is a TF0_THM_EQU_ARI problem
% 0.11/0.35 Running first-order model finding
% 0.11/0.35 Running /export/starexec/sandbox/solver/bin/vampire --mode casc_sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.41 % (25300)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.41 % (25305)ott+21_1:1_sil=4000:i=104:fsd=on:fd=off:newcnf=on_0 on theBenchmark for (3000ds/104Mi)
% 0.18/0.41 % (25300)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.41 % (25302)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)
% 0.18/0.41 % (25300)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.41 % (25306)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)
% 0.18/0.41 % (25300)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.41 % (25303)fmb+10_1:1_sil=256000:fmbes=contour:i=214858:bce=on_0 on theBenchmark for (3000ds/214858Mi)
% 0.18/0.41 % (25300)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.41 % (25307)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)
% 0.18/0.41 % (25303)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.18/0.41 % (25303)Terminated due to inappropriate strategy.
% 0.18/0.41 % (25303)------------------------------
% 0.18/0.41 % (25303)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.18/0.41 % (25303)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.18/0.41 % (25303)Termination reason: Inappropriate
% 0.18/0.41
% 0.18/0.41 % (25303)Memory used [KB]: 670
% 0.18/0.41 % (25303)Time elapsed: 0.003 s
% 0.18/0.41 % (25303)Instructions burned: 2 (million)
% 0.18/0.41 % (25300)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.41 % (25304)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)
% 0.18/0.41 % (25303)------------------------------
% 0.18/0.41 % (25303)------------------------------
% 0.18/0.41 % (25304)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.18/0.41 % (25304)Terminated due to inappropriate strategy.
% 0.18/0.41 % (25304)------------------------------
% 0.18/0.41 % (25304)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.18/0.41 % (25304)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.18/0.41 % (25304)Termination reason: Inappropriate
% 0.18/0.41
% 0.18/0.41 % (25304)Memory used [KB]: 671
% 0.18/0.41 % (25304)Time elapsed: 0.002 s
% 0.18/0.41 % (25304)Instructions burned: 2 (million)
% 0.18/0.41 % (25300)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.41 % (25301)fmb+10_1:1_sil=256000:i=98885:tgt=full:fmbsr=1.3:fmbss=10_0 on theBenchmark for (3000ds/98885Mi)
% 0.18/0.41 % (25304)------------------------------
% 0.18/0.41 % (25304)------------------------------
% 0.18/0.41 % (25301)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.18/0.41 % (25301)Terminated due to inappropriate strategy.
% 0.18/0.41 % (25301)------------------------------
% 0.18/0.41 % (25301)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.18/0.41 % (25301)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.18/0.41 % (25301)Termination reason: Inappropriate
% 0.18/0.41
% 0.18/0.41 % (25301)Memory used [KB]: 671
% 0.18/0.41 % (25301)Time elapsed: 0.002 s
% 0.18/0.41 % (25301)Instructions burned: 2 (million)
% 0.18/0.41 % (25301)------------------------------
% 0.18/0.41 % (25301)------------------------------
% 0.18/0.43 % (25302)First to succeed.
% 0.18/0.43 % (25302)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-25300"
% 0.18/0.43 % (25300)Running in auto input_syntax mode. Trying TPTP
% 0.18/0.43 % (25302)Refutation found. Thanks to Tanya!
% 0.18/0.43 % SZS status Theorem for theBenchmark
% 0.18/0.43 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.43 % (25302)------------------------------
% 0.18/0.43 % (25302)Version: Vampire 4.9 (commit 18c118a85 on 2024-06-08 21:14:20 +0100)
% 0.18/0.43 % (25302)Linked with Z3 4.12.3.0 79bbbf76d0c123481c8ca05cd3a98939270074d3 z3-4.8.4-7980-g79bbbf76d
% 0.18/0.43 % (25302)Termination reason: Refutation
% 0.18/0.43
% 0.18/0.43 % (25302)Memory used [KB]: 991
% 0.18/0.43 % (25302)Time elapsed: 0.017 s
% 0.18/0.43 % (25302)Instructions burned: 24 (million)
% 0.18/0.43 % (25302)------------------------------
% 0.18/0.43 % (25302)------------------------------
% 0.18/0.43 % (25300)Success in time 0.073 s
%------------------------------------------------------------------------------