TSTP Solution File: ARI698_1 by Vampire-SAT---4.8
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- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : ARI698_1 : TPTP v8.1.2. Released v6.3.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n013.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 Apr 30 10:35:51 EDT 2024
% Result : Theorem 2.18s 0.70s
% Output : Refutation 2.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 43
% Number of leaves : 45
% Syntax : Number of formulae : 329 ( 206 unt; 7 typ; 0 def)
% Number of atoms : 530 ( 286 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 379 ( 171 ~; 183 |; 10 &)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 2 avg)
% Maximal term depth : 7 ( 2 avg)
% Number arithmetic : 2348 ( 72 atm;1454 fun; 749 num; 73 var)
% Number of types : 1 ( 0 usr; 1 ari)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 18 ( 15 usr; 16 prp; 0-2 aty)
% Number of functors : 14 ( 7 usr; 10 con; 0-2 aty)
% Number of variables : 73 ( 73 !; 0 ?; 73 :)
% Comments :
%------------------------------------------------------------------------------
tff(func_def_0,type,
n: $int ).
tff(func_def_1,type,
x6: $int ).
tff(func_def_2,type,
x5: $int ).
tff(func_def_3,type,
x4: $int ).
tff(func_def_4,type,
x3: $int ).
tff(func_def_5,type,
x2: $int ).
tff(func_def_6,type,
x1: $int ).
tff(f10790,plain,
$false,
inference(avatar_sat_refutation,[],[f88,f1963,f1964,f8476,f9616,f9618,f9628,f9631,f9946,f10208,f10403,f10473,f10544,f10556,f10557,f10789]) ).
tff(f10789,plain,
( ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f10788]) ).
tff(f10788,plain,
( $false
| ~ spl0_1
| spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(subsumption_resolution,[],[f10760,f71]) ).
tff(f71,plain,
( ( x5 != 0 )
| spl0_2 ),
inference(avatar_component_clause,[],[f69]) ).
tff(f69,plain,
( spl0_2
<=> ( x5 = 0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
tff(f10760,plain,
( ( x5 = 0 )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(evaluation,[],[f10759]) ).
tff(f10759,plain,
( ( 1000 = 0 )
| ( x5 = 0 )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f10755]) ).
tff(f10755,plain,
( ( 0 != 0 )
| ( 1000 = 0 )
| ( x5 = 0 )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[],[f601,f10720]) ).
tff(f10720,plain,
( ( 0 = $product(1000,x5) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(evaluation,[],[f10704]) ).
tff(f10704,plain,
( ( 0 = $sum(0,$product(1000,x5)) )
| ~ spl0_1
| ~ spl0_4
| ~ spl0_6 ),
inference(backward_demodulation,[],[f10630,f66]) ).
tff(f66,plain,
( ( x6 = 0 )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f65]) ).
tff(f65,plain,
( spl0_1
<=> ( x6 = 0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
tff(f10630,plain,
( ( 0 = $sum(x6,$product(1000,x5)) )
| ~ spl0_4
| ~ spl0_6 ),
inference(evaluation,[],[f10614]) ).
tff(f10614,plain,
( ( 0 = $sum(x6,$product(1000,$sum(x5,0))) )
| ~ spl0_4
| ~ spl0_6 ),
inference(backward_demodulation,[],[f10476,f86]) ).
tff(f86,plain,
( ( x1 = 0 )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
tff(f85,plain,
( spl0_6
<=> ( x1 = 0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
tff(f10476,plain,
( ( 0 = $sum(x6,$product(1000,$sum(x5,x1))) )
| ~ spl0_4 ),
inference(backward_demodulation,[],[f762,f10474]) ).
tff(f10474,plain,
( ! [X0: $int] : ( $sum(x2,X0) = X0 )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f1466,f10461]) ).
tff(f10461,plain,
( ! [X0: $int] : ( $sum(x1,$sum(x1,X0)) = X0 )
| ~ spl0_4 ),
inference(evaluation,[],[f10460]) ).
tff(f10460,plain,
( ! [X0: $int] : ( $sum($sum(x1,0),$sum(x1,X0)) = X0 )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f1094,f10406]) ).
tff(f10406,plain,
( ( 0 = $uminus(x2) )
| ~ spl0_4 ),
inference(evaluation,[],[f10405]) ).
tff(f10405,plain,
( ( 0 = $sum(0,$uminus(x2)) )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f720,f78]) ).
tff(f78,plain,
( ( x3 = 0 )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f77]) ).
tff(f77,plain,
( spl0_4
<=> ( x3 = 0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
tff(f720,plain,
0 = $sum(x3,$uminus(x2)),
inference(evaluation,[],[f719]) ).
tff(f719,plain,
0 = $sum(x3,$sum($uminus(x2),0)),
inference(forward_demodulation,[],[f718,f207]) ).
tff(f207,plain,
0 = $sum($product(1000,x6),$uminus(x1)),
inference(evaluation,[],[f206]) ).
tff(f206,plain,
0 = $sum($sum($product(1000,x6),0),$uminus(x1)),
inference(forward_demodulation,[],[f205,f172]) ).
tff(f172,plain,
! [X0: $int] : ( 0 = $product(0,X0) ),
inference(superposition,[],[f32,f35]) ).
tff(f35,plain,
! [X0: $int] : ( 0 = $product(X0,0) ),
introduced(theory_axiom_149,[]) ).
tff(f32,plain,
! [X0: $int,X1: $int] : ( $product(X0,X1) = $product(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f205,plain,
0 = $sum($sum($product(1000,x6),$product(0,x2)),$uminus(x1)),
inference(forward_demodulation,[],[f204,f21]) ).
tff(f21,plain,
! [X0: $int,X1: $int] : ( $sum(X0,X1) = $sum(X1,X0) ),
introduced(theory_axiom_135,[]) ).
tff(f204,plain,
0 = $sum($sum($product(0,x2),$product(1000,x6)),$uminus(x1)),
inference(evaluation,[],[f203]) ).
tff(f203,plain,
0 = $sum($sum($product(0,x2),$sum($product(1000,x6),0)),$uminus(x1)),
inference(forward_demodulation,[],[f202,f172]) ).
tff(f202,plain,
0 = $sum($sum($product(0,x2),$sum($product(1000,x6),$product(0,x3))),$uminus(x1)),
inference(forward_demodulation,[],[f201,f21]) ).
tff(f201,plain,
0 = $sum($sum($product(0,x2),$sum($product(0,x3),$product(1000,x6))),$uminus(x1)),
inference(evaluation,[],[f200]) ).
tff(f200,plain,
0 = $sum($sum($product(0,x2),$sum($product(0,x3),$sum($product(1000,x6),0))),$uminus(x1)),
inference(forward_demodulation,[],[f199,f172]) ).
tff(f199,plain,
0 = $sum($sum($product(0,x2),$sum($product(0,x3),$sum($product(1000,x6),$product(0,x4)))),$uminus(x1)),
inference(forward_demodulation,[],[f190,f21]) ).
tff(f190,plain,
0 = $sum($sum($product(0,x2),$sum($product(0,x3),$sum($product(0,x4),$product(1000,x6)))),$uminus(x1)),
inference(evaluation,[],[f181]) ).
tff(f181,plain,
0 = $sum($sum($product(0,x2),$sum($product(0,x3),$sum($product(0,x4),$sum($product(1000,x6),0)))),$uminus(x1)),
inference(backward_demodulation,[],[f120,f172]) ).
tff(f120,plain,
0 = $sum($sum($product(0,x2),$sum($product(0,x3),$sum($product(0,x4),$sum($product(1000,x6),$product(0,x5))))),$uminus(x1)),
inference(forward_demodulation,[],[f119,f21]) ).
tff(f119,plain,
0 = $sum($sum($product(0,x2),$sum($product(0,x3),$sum($product(0,x4),$sum($product(0,x5),$product(1000,x6))))),$uminus(x1)),
inference(forward_demodulation,[],[f118,f32]) ).
tff(f118,plain,
0 = $sum($sum($product(0,x2),$sum($product(0,x3),$sum($product(0,x4),$sum($product(0,x5),$product(x6,1000))))),$uminus(x1)),
inference(forward_demodulation,[],[f117,f45]) ).
tff(f45,plain,
n = 1000,
inference(cnf_transformation,[],[f1]) ).
tff(f1,axiom,
n = 1000,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq1) ).
tff(f117,plain,
0 = $sum($sum($product(0,x2),$sum($product(0,x3),$sum($product(0,x4),$sum($product(0,x5),$product(x6,n))))),$uminus(x1)),
inference(forward_demodulation,[],[f116,f32]) ).
tff(f116,plain,
0 = $sum($sum($product(0,x2),$sum($product(0,x3),$sum($product(0,x4),$sum($product(0,x5),$product(n,x6))))),$uminus(x1)),
inference(forward_demodulation,[],[f115,f21]) ).
tff(f115,plain,
0 = $sum($sum($product(0,x2),$sum($product(0,x3),$sum($product(0,x4),$sum($product(n,x6),$product(0,x5))))),$uminus(x1)),
inference(forward_demodulation,[],[f114,f21]) ).
tff(f114,plain,
0 = $sum($sum($product(0,x2),$sum($product(0,x3),$sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)))),$uminus(x1)),
inference(forward_demodulation,[],[f113,f21]) ).
tff(f113,plain,
0 = $sum($sum($product(0,x2),$sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3))),$uminus(x1)),
inference(forward_demodulation,[],[f50,f21]) ).
tff(f50,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$product(0,x2)),$uminus(x1)),
inference(cnf_transformation,[],[f18]) ).
tff(f18,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$product(0,x2)),$uminus(x1)),
inference(theory_normalization,[],[f11]) ).
tff(f11,axiom,
0 = $difference($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$product(0,x2)),x1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq11) ).
tff(f718,plain,
0 = $sum(x3,$sum($uminus(x2),$sum($product(1000,x6),$uminus(x1)))),
inference(forward_demodulation,[],[f717,f435]) ).
tff(f435,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum(X2,$sum(X0,X1)) ),
inference(superposition,[],[f22,f21]) ).
tff(f22,plain,
! [X2: $int,X0: $int,X1: $int] : ( $sum(X0,$sum(X1,X2)) = $sum($sum(X0,X1),X2) ),
introduced(theory_axiom_136,[]) ).
tff(f717,plain,
0 = $sum(x3,$sum($uminus(x1),$sum($uminus(x2),$product(1000,x6)))),
inference(forward_demodulation,[],[f707,f21]) ).
tff(f707,plain,
0 = $sum(x3,$sum($sum($uminus(x2),$product(1000,x6)),$uminus(x1))),
inference(superposition,[],[f486,f22]) ).
tff(f486,plain,
0 = $sum($sum(x3,$sum($uminus(x2),$product(1000,x6))),$uminus(x1)),
inference(forward_demodulation,[],[f466,f21]) ).
tff(f466,plain,
0 = $sum($sum(x3,$sum($product(1000,x6),$uminus(x2))),$uminus(x1)),
inference(backward_demodulation,[],[f198,f435]) ).
tff(f198,plain,
0 = $sum($sum($uminus(x2),$sum(x3,$product(1000,x6))),$uminus(x1)),
inference(evaluation,[],[f197]) ).
tff(f197,plain,
0 = $sum($sum($uminus(x2),$sum(x3,$sum($product(1000,x6),0))),$uminus(x1)),
inference(forward_demodulation,[],[f196,f172]) ).
tff(f196,plain,
0 = $sum($sum($uminus(x2),$sum(x3,$sum($product(1000,x6),$product(0,x4)))),$uminus(x1)),
inference(forward_demodulation,[],[f191,f21]) ).
tff(f191,plain,
0 = $sum($sum($uminus(x2),$sum(x3,$sum($product(0,x4),$product(1000,x6)))),$uminus(x1)),
inference(evaluation,[],[f180]) ).
tff(f180,plain,
0 = $sum($sum($uminus(x2),$sum(x3,$sum($product(0,x4),$sum($product(1000,x6),0)))),$uminus(x1)),
inference(backward_demodulation,[],[f112,f172]) ).
tff(f112,plain,
0 = $sum($sum($uminus(x2),$sum(x3,$sum($product(0,x4),$sum($product(1000,x6),$product(0,x5))))),$uminus(x1)),
inference(forward_demodulation,[],[f111,f21]) ).
tff(f111,plain,
0 = $sum($sum($uminus(x2),$sum(x3,$sum($product(0,x4),$sum($product(0,x5),$product(1000,x6))))),$uminus(x1)),
inference(forward_demodulation,[],[f110,f32]) ).
tff(f110,plain,
0 = $sum($sum($uminus(x2),$sum(x3,$sum($product(0,x4),$sum($product(0,x5),$product(x6,1000))))),$uminus(x1)),
inference(forward_demodulation,[],[f109,f45]) ).
tff(f109,plain,
0 = $sum($sum($uminus(x2),$sum(x3,$sum($product(0,x4),$sum($product(0,x5),$product(x6,n))))),$uminus(x1)),
inference(forward_demodulation,[],[f108,f32]) ).
tff(f108,plain,
0 = $sum($sum($uminus(x2),$sum(x3,$sum($product(0,x4),$sum($product(0,x5),$product(n,x6))))),$uminus(x1)),
inference(forward_demodulation,[],[f107,f21]) ).
tff(f107,plain,
0 = $sum($sum($uminus(x2),$sum(x3,$sum($product(0,x4),$sum($product(n,x6),$product(0,x5))))),$uminus(x1)),
inference(forward_demodulation,[],[f106,f21]) ).
tff(f106,plain,
0 = $sum($sum($uminus(x2),$sum(x3,$sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)))),$uminus(x1)),
inference(forward_demodulation,[],[f105,f21]) ).
tff(f105,plain,
0 = $sum($sum($uminus(x2),$sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),x3)),$uminus(x1)),
inference(forward_demodulation,[],[f62,f21]) ).
tff(f62,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),x3),$uminus(x2)),$uminus(x1)),
inference(evaluation,[],[f49]) ).
tff(f49,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(1,x3)),$uminus(x2)),$uminus(x1)),
inference(cnf_transformation,[],[f42]) ).
tff(f42,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(1,x3)),$uminus(x2)),$uminus(x1)),
inference(theory_normalization,[],[f17]) ).
tff(f17,plain,
0 = $sum($difference($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(1,x3)),x2),$uminus(x1)),
inference(theory_normalization,[],[f8]) ).
tff(f8,axiom,
0 = $difference($difference($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(1,x3)),x2),x1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq8) ).
tff(f1094,plain,
! [X0: $int] : ( $sum($sum(x1,$uminus(x2)),$sum(x1,X0)) = X0 ),
inference(forward_demodulation,[],[f1061,f21]) ).
tff(f1061,plain,
! [X0: $int] : ( $sum($sum($uminus(x2),x1),$sum(x1,X0)) = X0 ),
inference(backward_demodulation,[],[f455,f1044]) ).
tff(f1044,plain,
x1 = $product(1000,x6),
inference(evaluation,[],[f979]) ).
tff(f979,plain,
$product(1000,x6) = $sum(x1,0),
inference(superposition,[],[f458,f244]) ).
tff(f244,plain,
0 = $sum($uminus(x1),$product(1000,x6)),
inference(superposition,[],[f207,f21]) ).
tff(f458,plain,
! [X0: $int,X1: $int] : ( $sum(X0,$sum($uminus(X0),X1)) = X1 ),
inference(evaluation,[],[f422]) ).
tff(f422,plain,
! [X0: $int,X1: $int] : ( $sum(0,X1) = $sum(X0,$sum($uminus(X0),X1)) ),
inference(superposition,[],[f22,f25]) ).
tff(f25,plain,
! [X0: $int] : ( 0 = $sum(X0,$uminus(X0)) ),
introduced(theory_axiom_140,[]) ).
tff(f455,plain,
! [X0: $int] : ( $sum($sum($uminus(x2),$product(1000,x6)),$sum(x1,X0)) = X0 ),
inference(evaluation,[],[f427]) ).
tff(f427,plain,
! [X0: $int] : ( $sum(0,X0) = $sum($sum($uminus(x2),$product(1000,x6)),$sum(x1,X0)) ),
inference(superposition,[],[f22,f213]) ).
tff(f213,plain,
0 = $sum($sum($uminus(x2),$product(1000,x6)),x1),
inference(evaluation,[],[f212]) ).
tff(f212,plain,
0 = $sum($sum($uminus(x2),$sum($product(1000,x6),0)),x1),
inference(forward_demodulation,[],[f211,f172]) ).
tff(f211,plain,
0 = $sum($sum($uminus(x2),$sum($product(1000,x6),$product(0,x3))),x1),
inference(forward_demodulation,[],[f210,f21]) ).
tff(f210,plain,
0 = $sum($sum($uminus(x2),$sum($product(0,x3),$product(1000,x6))),x1),
inference(evaluation,[],[f209]) ).
tff(f209,plain,
0 = $sum($sum($uminus(x2),$sum($product(0,x3),$sum($product(1000,x6),0))),x1),
inference(forward_demodulation,[],[f208,f172]) ).
tff(f208,plain,
0 = $sum($sum($uminus(x2),$sum($product(0,x3),$sum($product(1000,x6),$product(0,x4)))),x1),
inference(forward_demodulation,[],[f189,f21]) ).
tff(f189,plain,
0 = $sum($sum($uminus(x2),$sum($product(0,x3),$sum($product(0,x4),$product(1000,x6)))),x1),
inference(evaluation,[],[f182]) ).
tff(f182,plain,
0 = $sum($sum($uminus(x2),$sum($product(0,x3),$sum($product(0,x4),$sum($product(1000,x6),0)))),x1),
inference(backward_demodulation,[],[f128,f172]) ).
tff(f128,plain,
0 = $sum($sum($uminus(x2),$sum($product(0,x3),$sum($product(0,x4),$sum($product(1000,x6),$product(0,x5))))),x1),
inference(forward_demodulation,[],[f127,f21]) ).
tff(f127,plain,
0 = $sum($sum($uminus(x2),$sum($product(0,x3),$sum($product(0,x4),$sum($product(0,x5),$product(1000,x6))))),x1),
inference(forward_demodulation,[],[f126,f32]) ).
tff(f126,plain,
0 = $sum($sum($uminus(x2),$sum($product(0,x3),$sum($product(0,x4),$sum($product(0,x5),$product(x6,1000))))),x1),
inference(forward_demodulation,[],[f125,f45]) ).
tff(f125,plain,
0 = $sum($sum($uminus(x2),$sum($product(0,x3),$sum($product(0,x4),$sum($product(0,x5),$product(x6,n))))),x1),
inference(forward_demodulation,[],[f124,f32]) ).
tff(f124,plain,
0 = $sum($sum($uminus(x2),$sum($product(0,x3),$sum($product(0,x4),$sum($product(0,x5),$product(n,x6))))),x1),
inference(forward_demodulation,[],[f123,f21]) ).
tff(f123,plain,
0 = $sum($sum($uminus(x2),$sum($product(0,x3),$sum($product(0,x4),$sum($product(n,x6),$product(0,x5))))),x1),
inference(forward_demodulation,[],[f122,f21]) ).
tff(f122,plain,
0 = $sum($sum($uminus(x2),$sum($product(0,x3),$sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)))),x1),
inference(forward_demodulation,[],[f121,f21]) ).
tff(f121,plain,
0 = $sum($sum($uminus(x2),$sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3))),x1),
inference(forward_demodulation,[],[f61,f21]) ).
tff(f61,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$uminus(x2)),x1),
inference(evaluation,[],[f51]) ).
tff(f51,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$uminus(x2)),$product(1,x1)),
inference(cnf_transformation,[],[f19]) ).
tff(f19,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$uminus(x2)),$product(1,x1)),
inference(theory_normalization,[],[f10]) ).
tff(f10,axiom,
0 = $sum($difference($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),x2),$product(1,x1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq10) ).
tff(f1466,plain,
! [X0: $int] : ( $sum(x1,$sum(x1,X0)) = $sum(x2,X0) ),
inference(superposition,[],[f22,f1454]) ).
tff(f1454,plain,
x2 = $sum(x1,x1),
inference(evaluation,[],[f1449]) ).
tff(f1449,plain,
$sum(x1,x1) = $sum(x2,0),
inference(superposition,[],[f458,f1065]) ).
tff(f1065,plain,
0 = $sum($uminus(x2),$sum(x1,x1)),
inference(backward_demodulation,[],[f462,f1044]) ).
tff(f462,plain,
0 = $sum($uminus(x2),$sum(x1,$product(1000,x6))),
inference(forward_demodulation,[],[f432,f21]) ).
tff(f432,plain,
0 = $sum($uminus(x2),$sum($product(1000,x6),x1)),
inference(superposition,[],[f22,f213]) ).
tff(f762,plain,
0 = $sum(x6,$product(1000,$sum(x5,$sum(x2,x1)))),
inference(forward_demodulation,[],[f761,f435]) ).
tff(f761,plain,
0 = $sum(x6,$product(1000,$sum(x2,$sum(x1,x5)))),
inference(forward_demodulation,[],[f760,f435]) ).
tff(f760,plain,
0 = $sum(x6,$product(1000,$sum(x1,$sum(x5,x2)))),
inference(forward_demodulation,[],[f759,f21]) ).
tff(f759,plain,
0 = $sum(x6,$product(1000,$sum($sum(x5,x2),x1))),
inference(forward_demodulation,[],[f749,f36]) ).
tff(f36,plain,
! [X2: $int,X0: $int,X1: $int] : ( $product(X0,$sum(X1,X2)) = $sum($product(X0,X1),$product(X0,X2)) ),
introduced(theory_axiom_150,[]) ).
tff(f749,plain,
0 = $sum(x6,$sum($product(1000,$sum(x5,x2)),$product(1000,x1))),
inference(superposition,[],[f693,f22]) ).
tff(f693,plain,
0 = $sum($sum(x6,$product(1000,$sum(x5,x2))),$product(1000,x1)),
inference(backward_demodulation,[],[f481,f692]) ).
tff(f692,plain,
! [X0: $int] : ( $sum(x4,$sum(x3,X0)) = X0 ),
inference(evaluation,[],[f689]) ).
tff(f689,plain,
! [X0: $int] : ( $sum(0,X0) = $sum(x4,$sum(x3,X0)) ),
inference(superposition,[],[f22,f681]) ).
tff(f681,plain,
0 = $sum(x4,x3),
inference(evaluation,[],[f680]) ).
tff(f680,plain,
0 = $sum(x4,$sum(x3,0)),
inference(forward_demodulation,[],[f679,f461]) ).
tff(f461,plain,
0 = $sum(x2,$sum(x1,$product(1000,x6))),
inference(forward_demodulation,[],[f431,f21]) ).
tff(f431,plain,
0 = $sum(x2,$sum($product(1000,x6),x1)),
inference(superposition,[],[f22,f219]) ).
tff(f219,plain,
0 = $sum($sum(x2,$product(1000,x6)),x1),
inference(evaluation,[],[f218]) ).
tff(f218,plain,
0 = $sum($sum(x2,$sum($product(1000,x6),0)),x1),
inference(forward_demodulation,[],[f217,f172]) ).
tff(f217,plain,
0 = $sum($sum(x2,$sum($product(1000,x6),$product(0,x3))),x1),
inference(forward_demodulation,[],[f216,f21]) ).
tff(f216,plain,
0 = $sum($sum(x2,$sum($product(0,x3),$product(1000,x6))),x1),
inference(evaluation,[],[f215]) ).
tff(f215,plain,
0 = $sum($sum(x2,$sum($product(0,x3),$sum($product(1000,x6),0))),x1),
inference(forward_demodulation,[],[f214,f172]) ).
tff(f214,plain,
0 = $sum($sum(x2,$sum($product(0,x3),$sum($product(1000,x6),$product(0,x4)))),x1),
inference(forward_demodulation,[],[f186,f21]) ).
tff(f186,plain,
0 = $sum($sum(x2,$sum($product(0,x3),$sum($product(0,x4),$product(1000,x6)))),x1),
inference(evaluation,[],[f185]) ).
tff(f185,plain,
0 = $sum($sum(x2,$sum($product(0,x3),$sum($product(0,x4),$sum($product(1000,x6),0)))),x1),
inference(backward_demodulation,[],[f152,f172]) ).
tff(f152,plain,
0 = $sum($sum(x2,$sum($product(0,x3),$sum($product(0,x4),$sum($product(1000,x6),$product(0,x5))))),x1),
inference(forward_demodulation,[],[f151,f21]) ).
tff(f151,plain,
0 = $sum($sum(x2,$sum($product(0,x3),$sum($product(0,x4),$sum($product(0,x5),$product(1000,x6))))),x1),
inference(forward_demodulation,[],[f150,f32]) ).
tff(f150,plain,
0 = $sum($sum(x2,$sum($product(0,x3),$sum($product(0,x4),$sum($product(0,x5),$product(x6,1000))))),x1),
inference(forward_demodulation,[],[f149,f45]) ).
tff(f149,plain,
0 = $sum($sum(x2,$sum($product(0,x3),$sum($product(0,x4),$sum($product(0,x5),$product(x6,n))))),x1),
inference(forward_demodulation,[],[f148,f32]) ).
tff(f148,plain,
0 = $sum($sum(x2,$sum($product(0,x3),$sum($product(0,x4),$sum($product(0,x5),$product(n,x6))))),x1),
inference(forward_demodulation,[],[f147,f21]) ).
tff(f147,plain,
0 = $sum($sum(x2,$sum($product(0,x3),$sum($product(0,x4),$sum($product(n,x6),$product(0,x5))))),x1),
inference(forward_demodulation,[],[f146,f21]) ).
tff(f146,plain,
0 = $sum($sum(x2,$sum($product(0,x3),$sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)))),x1),
inference(forward_demodulation,[],[f145,f21]) ).
tff(f145,plain,
0 = $sum($sum(x2,$sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3))),x1),
inference(forward_demodulation,[],[f58,f21]) ).
tff(f58,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),x2),x1),
inference(evaluation,[],[f54]) ).
tff(f54,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$product(1,x2)),$product(1,x1)),
inference(cnf_transformation,[],[f9]) ).
tff(f9,axiom,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(0,x4)),$product(0,x3)),$product(1,x2)),$product(1,x1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq9) ).
tff(f679,plain,
0 = $sum(x4,$sum(x3,$sum(x2,$sum(x1,$product(1000,x6))))),
inference(forward_demodulation,[],[f678,f21]) ).
tff(f678,plain,
0 = $sum(x4,$sum(x3,$sum(x2,$sum($product(1000,x6),x1)))),
inference(forward_demodulation,[],[f677,f435]) ).
tff(f677,plain,
0 = $sum(x4,$sum(x3,$sum(x1,$sum(x2,$product(1000,x6))))),
inference(forward_demodulation,[],[f676,f21]) ).
tff(f676,plain,
0 = $sum(x4,$sum(x3,$sum($sum(x2,$product(1000,x6)),x1))),
inference(forward_demodulation,[],[f675,f435]) ).
tff(f675,plain,
0 = $sum(x4,$sum(x1,$sum(x3,$sum(x2,$product(1000,x6))))),
inference(forward_demodulation,[],[f665,f21]) ).
tff(f665,plain,
0 = $sum(x4,$sum($sum(x3,$sum(x2,$product(1000,x6))),x1)),
inference(superposition,[],[f484,f22]) ).
tff(f484,plain,
0 = $sum($sum(x4,$sum(x3,$sum(x2,$product(1000,x6)))),x1),
inference(forward_demodulation,[],[f483,f435]) ).
tff(f483,plain,
0 = $sum($sum(x4,$sum(x2,$sum($product(1000,x6),x3))),x1),
inference(forward_demodulation,[],[f482,f21]) ).
tff(f482,plain,
0 = $sum($sum(x4,$sum($sum($product(1000,x6),x3),x2)),x1),
inference(forward_demodulation,[],[f464,f435]) ).
tff(f464,plain,
0 = $sum($sum(x2,$sum(x4,$sum($product(1000,x6),x3))),x1),
inference(backward_demodulation,[],[f187,f435]) ).
tff(f187,plain,
0 = $sum($sum(x2,$sum(x3,$sum(x4,$product(1000,x6)))),x1),
inference(evaluation,[],[f184]) ).
tff(f184,plain,
0 = $sum($sum(x2,$sum(x3,$sum(x4,$sum($product(1000,x6),0)))),x1),
inference(backward_demodulation,[],[f144,f172]) ).
tff(f144,plain,
0 = $sum($sum(x2,$sum(x3,$sum(x4,$sum($product(1000,x6),$product(0,x5))))),x1),
inference(forward_demodulation,[],[f143,f21]) ).
tff(f143,plain,
0 = $sum($sum(x2,$sum(x3,$sum(x4,$sum($product(0,x5),$product(1000,x6))))),x1),
inference(forward_demodulation,[],[f142,f32]) ).
tff(f142,plain,
0 = $sum($sum(x2,$sum(x3,$sum(x4,$sum($product(0,x5),$product(x6,1000))))),x1),
inference(forward_demodulation,[],[f141,f45]) ).
tff(f141,plain,
0 = $sum($sum(x2,$sum(x3,$sum(x4,$sum($product(0,x5),$product(x6,n))))),x1),
inference(forward_demodulation,[],[f140,f32]) ).
tff(f140,plain,
0 = $sum($sum(x2,$sum(x3,$sum(x4,$sum($product(0,x5),$product(n,x6))))),x1),
inference(forward_demodulation,[],[f139,f21]) ).
tff(f139,plain,
0 = $sum($sum(x2,$sum(x3,$sum(x4,$sum($product(n,x6),$product(0,x5))))),x1),
inference(forward_demodulation,[],[f138,f21]) ).
tff(f138,plain,
0 = $sum($sum(x2,$sum(x3,$sum($sum($product(n,x6),$product(0,x5)),x4))),x1),
inference(forward_demodulation,[],[f137,f21]) ).
tff(f137,plain,
0 = $sum($sum(x2,$sum($sum($sum($product(n,x6),$product(0,x5)),x4),x3)),x1),
inference(forward_demodulation,[],[f59,f21]) ).
tff(f59,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),x4),x3),x2),x1),
inference(evaluation,[],[f53]) ).
tff(f53,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(1,x4)),$product(1,x3)),$product(1,x2)),$product(1,x1)),
inference(cnf_transformation,[],[f5]) ).
tff(f5,axiom,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$product(1,x4)),$product(1,x3)),$product(1,x2)),$product(1,x1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq5) ).
tff(f481,plain,
0 = $sum($sum(x6,$product(1000,$sum(x5,$sum(x4,$sum(x3,x2))))),$product(1000,x1)),
inference(forward_demodulation,[],[f480,f36]) ).
tff(f480,plain,
0 = $sum($sum(x6,$sum($product(1000,x5),$product(1000,$sum(x4,$sum(x3,x2))))),$product(1000,x1)),
inference(forward_demodulation,[],[f479,f36]) ).
tff(f479,plain,
0 = $sum($sum(x6,$sum($product(1000,x5),$sum($product(1000,x4),$product(1000,$sum(x3,x2))))),$product(1000,x1)),
inference(forward_demodulation,[],[f478,f36]) ).
tff(f478,plain,
0 = $sum($sum(x6,$sum($product(1000,x5),$sum($product(1000,x4),$sum($product(1000,x3),$product(1000,x2))))),$product(1000,x1)),
inference(forward_demodulation,[],[f477,f435]) ).
tff(f477,plain,
0 = $sum($sum(x6,$sum($product(1000,x5),$sum($product(1000,x3),$sum($product(1000,x2),$product(1000,x4))))),$product(1000,x1)),
inference(forward_demodulation,[],[f476,f21]) ).
tff(f476,plain,
0 = $sum($sum(x6,$sum($product(1000,x5),$sum($sum($product(1000,x2),$product(1000,x4)),$product(1000,x3)))),$product(1000,x1)),
inference(forward_demodulation,[],[f475,f21]) ).
tff(f475,plain,
0 = $sum($sum(x6,$sum($sum($sum($product(1000,x2),$product(1000,x4)),$product(1000,x3)),$product(1000,x5))),$product(1000,x1)),
inference(forward_demodulation,[],[f474,f435]) ).
tff(f474,plain,
0 = $sum($sum($product(1000,x5),$sum(x6,$sum($sum($product(1000,x2),$product(1000,x4)),$product(1000,x3)))),$product(1000,x1)),
inference(forward_demodulation,[],[f473,f435]) ).
tff(f473,plain,
0 = $sum($sum($product(1000,x5),$sum($product(1000,x3),$sum(x6,$sum($product(1000,x2),$product(1000,x4))))),$product(1000,x1)),
inference(forward_demodulation,[],[f472,f435]) ).
tff(f472,plain,
0 = $sum($sum($product(1000,x5),$sum($product(1000,x3),$sum($product(1000,x2),$sum($product(1000,x4),x6)))),$product(1000,x1)),
inference(forward_demodulation,[],[f471,f21]) ).
tff(f471,plain,
0 = $sum($sum($product(1000,x5),$sum($product(1000,x3),$sum($sum($product(1000,x4),x6),$product(1000,x2)))),$product(1000,x1)),
inference(forward_demodulation,[],[f470,f21]) ).
tff(f470,plain,
0 = $sum($sum($product(1000,x5),$sum($sum($sum($product(1000,x4),x6),$product(1000,x2)),$product(1000,x3))),$product(1000,x1)),
inference(forward_demodulation,[],[f469,f435]) ).
tff(f469,plain,
0 = $sum($sum($product(1000,x3),$sum($product(1000,x5),$sum($sum($product(1000,x4),x6),$product(1000,x2)))),$product(1000,x1)),
inference(forward_demodulation,[],[f468,f435]) ).
tff(f468,plain,
0 = $sum($sum($product(1000,x3),$sum($product(1000,x2),$sum($product(1000,x5),$sum($product(1000,x4),x6)))),$product(1000,x1)),
inference(forward_demodulation,[],[f467,f21]) ).
tff(f467,plain,
0 = $sum($sum($product(1000,x3),$sum($sum($product(1000,x5),$sum($product(1000,x4),x6)),$product(1000,x2))),$product(1000,x1)),
inference(forward_demodulation,[],[f463,f435]) ).
tff(f463,plain,
0 = $sum($sum($product(1000,x2),$sum($product(1000,x3),$sum($product(1000,x5),$sum($product(1000,x4),x6)))),$product(1000,x1)),
inference(backward_demodulation,[],[f158,f435]) ).
tff(f158,plain,
0 = $sum($sum($product(1000,x2),$sum($product(1000,x3),$sum($product(1000,x4),$sum(x6,$product(1000,x5))))),$product(1000,x1)),
inference(forward_demodulation,[],[f157,f21]) ).
tff(f157,plain,
0 = $sum($sum($product(1000,x2),$sum($product(1000,x3),$sum($sum(x6,$product(1000,x5)),$product(1000,x4)))),$product(1000,x1)),
inference(forward_demodulation,[],[f156,f21]) ).
tff(f156,plain,
0 = $sum($sum($product(1000,x2),$sum($sum($sum(x6,$product(1000,x5)),$product(1000,x4)),$product(1000,x3))),$product(1000,x1)),
inference(forward_demodulation,[],[f155,f21]) ).
tff(f155,plain,
0 = $sum($sum($sum($sum($sum(x6,$product(1000,x5)),$product(1000,x4)),$product(1000,x3)),$product(1000,x2)),$product(1000,x1)),
inference(forward_demodulation,[],[f154,f32]) ).
tff(f154,plain,
0 = $sum($sum($sum($sum($sum(x6,$product(1000,x5)),$product(1000,x4)),$product(1000,x3)),$product(1000,x2)),$product(x1,1000)),
inference(forward_demodulation,[],[f153,f45]) ).
tff(f153,plain,
0 = $sum($sum($sum($sum($sum(x6,$product(n,x5)),$product(n,x4)),$product(n,x3)),$product(n,x2)),$product(x1,n)),
inference(forward_demodulation,[],[f57,f32]) ).
tff(f57,plain,
0 = $sum($sum($sum($sum($sum(x6,$product(n,x5)),$product(n,x4)),$product(n,x3)),$product(n,x2)),$product(n,x1)),
inference(evaluation,[],[f55]) ).
tff(f55,plain,
$sum($sum($sum($sum($sum($product(1,x6),$product(n,x5)),$product(n,x4)),$product(n,x3)),$product(n,x2)),$product(n,x1)) = 0,
inference(cnf_transformation,[],[f2]) ).
tff(f2,axiom,
$sum($sum($sum($sum($sum($product(1,x6),$product(n,x5)),$product(n,x4)),$product(n,x3)),$product(n,x2)),$product(n,x1)) = 0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq2) ).
tff(f601,plain,
! [X0: $int,X1: $int] :
( ( 0 != $product(X0,X1) )
| ( 0 = X0 )
| ( 0 = X1 ) ),
inference(superposition,[],[f56,f35]) ).
tff(f56,plain,
! [X2: $int,X3: $int,X0: $int] :
( ( $product(X0,X2) != $product(X0,X3) )
| ( 0 = X0 )
| ( X2 = X3 ) ),
inference(equality_resolution,[],[f37]) ).
tff(f37,plain,
! [X2: $int,X3: $int,X0: $int,X1: $int] :
( ( 0 = X0 )
| ( $product(X0,X2) != X1 )
| ( $product(X0,X3) != X1 )
| ( X2 = X3 ) ),
introduced(theory_axiom_151,[]) ).
tff(f10557,plain,
( spl0_1
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f4010,f85,f65]) ).
tff(f4010,plain,
( ( x1 != 0 )
| ( x6 = 0 ) ),
inference(evaluation,[],[f4006]) ).
tff(f4006,plain,
( ( x1 != 0 )
| ( 1000 = 0 )
| ( x6 = 0 ) ),
inference(superposition,[],[f601,f1044]) ).
tff(f10556,plain,
( ~ spl0_3
| ~ spl0_23
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[],[f10555]) ).
tff(f10555,plain,
( $false
| ~ spl0_3
| ~ spl0_23
| ~ spl0_29 ),
inference(subsumption_resolution,[],[f10551,f10545]) ).
tff(f10545,plain,
( $less(0,x1)
| ~ spl0_3
| ~ spl0_29 ),
inference(forward_demodulation,[],[f9144,f74]) ).
tff(f74,plain,
( ( x4 = 0 )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f73]) ).
tff(f73,plain,
( spl0_3
<=> ( x4 = 0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
tff(f9144,plain,
( $less(x4,x1)
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f9143]) ).
tff(f9143,plain,
( spl0_29
<=> $less(x4,x1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
tff(f10551,plain,
( ~ $less(0,x1)
| ~ spl0_3
| ~ spl0_23 ),
inference(resolution,[],[f10498,f248]) ).
tff(f248,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,X1)
| ~ $less(X1,X0) ),
inference(resolution,[],[f27,f26]) ).
tff(f26,plain,
! [X0: $int] : ~ $less(X0,X0),
introduced(theory_axiom_142,[]) ).
tff(f27,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less(X0,X2)
| ~ $less(X1,X2)
| ~ $less(X0,X1) ),
introduced(theory_axiom_143,[]) ).
tff(f10498,plain,
( $less(x1,0)
| ~ spl0_3
| ~ spl0_23 ),
inference(forward_demodulation,[],[f8474,f74]) ).
tff(f8474,plain,
( $less(x1,x4)
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f8473]) ).
tff(f8473,plain,
( spl0_23
<=> $less(x1,x4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
tff(f10544,plain,
( ~ spl0_3
| spl0_22
| spl0_29 ),
inference(avatar_contradiction_clause,[],[f10543]) ).
tff(f10543,plain,
( $false
| ~ spl0_3
| spl0_22
| spl0_29 ),
inference(subsumption_resolution,[],[f10542,f8471]) ).
tff(f8471,plain,
( ~ $less(x1,1)
| spl0_22 ),
inference(avatar_component_clause,[],[f8469]) ).
tff(f8469,plain,
( spl0_22
<=> $less(x1,1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
tff(f10542,plain,
( $less(x1,1)
| ~ spl0_3
| spl0_29 ),
inference(evaluation,[],[f10541]) ).
tff(f10541,plain,
( $less(x1,$sum(0,1))
| ~ spl0_3
| spl0_29 ),
inference(resolution,[],[f9837,f30]) ).
tff(f30,plain,
! [X0: $int,X1: $int] :
( $less(X0,X1)
| $less(X1,$sum(X0,1)) ),
introduced(theory_axiom_147,[]) ).
tff(f9837,plain,
( ~ $less(0,x1)
| ~ spl0_3
| spl0_29 ),
inference(backward_demodulation,[],[f9145,f74]) ).
tff(f9145,plain,
( ~ $less(x4,x1)
| spl0_29 ),
inference(avatar_component_clause,[],[f9143]) ).
tff(f10473,plain,
( spl0_5
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f10472,f77,f81]) ).
tff(f81,plain,
( spl0_5
<=> ( x2 = 0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
tff(f10472,plain,
( ( x2 = 0 )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f1454,f10453]) ).
tff(f10453,plain,
( ( 0 = $sum(x1,x1) )
| ~ spl0_4 ),
inference(evaluation,[],[f10452]) ).
tff(f10452,plain,
( ( 0 = $sum($sum(x1,0),x1) )
| ~ spl0_4 ),
inference(forward_demodulation,[],[f1090,f10406]) ).
tff(f1090,plain,
0 = $sum($sum(x1,$uminus(x2)),x1),
inference(forward_demodulation,[],[f1050,f21]) ).
tff(f1050,plain,
0 = $sum($sum($uminus(x2),x1),x1),
inference(backward_demodulation,[],[f213,f1044]) ).
tff(f10403,plain,
( ~ spl0_5
| ~ spl0_4
| spl0_11 ),
inference(avatar_split_clause,[],[f10402,f1616,f77,f81]) ).
tff(f1616,plain,
( spl0_11
<=> ( x3 = x2 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
tff(f10402,plain,
( ( x2 != 0 )
| ~ spl0_4
| spl0_11 ),
inference(forward_demodulation,[],[f1617,f78]) ).
tff(f1617,plain,
( ( x3 != x2 )
| spl0_11 ),
inference(avatar_component_clause,[],[f1616]) ).
tff(f10208,plain,
( ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_11
| spl0_23 ),
inference(avatar_contradiction_clause,[],[f10207]) ).
tff(f10207,plain,
( $false
| ~ spl0_3
| spl0_6
| ~ spl0_7
| ~ spl0_11
| spl0_23 ),
inference(subsumption_resolution,[],[f10206,f87]) ).
tff(f87,plain,
( ( x1 != 0 )
| spl0_6 ),
inference(avatar_component_clause,[],[f85]) ).
tff(f10206,plain,
( ( x1 = 0 )
| ~ spl0_3
| ~ spl0_7
| ~ spl0_11
| spl0_23 ),
inference(subsumption_resolution,[],[f10203,f9581]) ).
tff(f9581,plain,
( ~ $less(0,x1)
| ~ spl0_7
| ~ spl0_11
| spl0_23 ),
inference(subsumption_resolution,[],[f9561,f8475]) ).
tff(f8475,plain,
( ~ $less(x1,x4)
| spl0_23 ),
inference(avatar_component_clause,[],[f8473]) ).
tff(f9561,plain,
( $less(x1,x4)
| ~ $less(0,x1)
| ~ spl0_7
| ~ spl0_11 ),
inference(superposition,[],[f2556,f2016]) ).
tff(f2016,plain,
( ( x4 = $sum(x1,x1) )
| ~ spl0_7
| ~ spl0_11 ),
inference(backward_demodulation,[],[f1671,f1532]) ).
tff(f1532,plain,
( ( x4 = x3 )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f1530]) ).
tff(f1530,plain,
( spl0_7
<=> ( x4 = x3 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
tff(f1671,plain,
( ( x3 = $sum(x1,x1) )
| ~ spl0_11 ),
inference(backward_demodulation,[],[f1454,f1618]) ).
tff(f1618,plain,
( ( x3 = x2 )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f1616]) ).
tff(f2556,plain,
! [X0: $int,X1: $int] :
( $less(X0,$sum(X1,X0))
| ~ $less(0,X1) ),
inference(superposition,[],[f361,f23]) ).
tff(f23,plain,
! [X0: $int] : ( $sum(X0,0) = X0 ),
introduced(theory_axiom_137,[]) ).
tff(f361,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X1,X0),$sum(X2,X1))
| ~ $less(X0,X2) ),
inference(superposition,[],[f29,f21]) ).
tff(f29,plain,
! [X2: $int,X0: $int,X1: $int] :
( $less($sum(X0,X2),$sum(X1,X2))
| ~ $less(X0,X1) ),
introduced(theory_axiom_145,[]) ).
tff(f10203,plain,
( $less(0,x1)
| ( x1 = 0 )
| ~ spl0_3
| spl0_23 ),
inference(resolution,[],[f9823,f28]) ).
tff(f28,plain,
! [X0: $int,X1: $int] :
( $less(X1,X0)
| $less(X0,X1)
| ( X0 = X1 ) ),
introduced(theory_axiom_144,[]) ).
tff(f9823,plain,
( ~ $less(x1,0)
| ~ spl0_3
| spl0_23 ),
inference(backward_demodulation,[],[f8475,f74]) ).
tff(f9946,plain,
( spl0_4
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f9632,f1530,f73,f77]) ).
tff(f9632,plain,
( ( x3 = 0 )
| ~ spl0_3
| ~ spl0_7 ),
inference(backward_demodulation,[],[f1532,f74]) ).
tff(f9631,plain,
( ~ spl0_16
| ~ spl0_19
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f9125,f1530,f8456,f7992]) ).
tff(f7992,plain,
( spl0_16
<=> $less(x4,0) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
tff(f8456,plain,
( spl0_19
<=> $less(x4,1) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
tff(f9125,plain,
( ~ $less(x4,1)
| ~ $less(x4,0)
| ~ spl0_7 ),
inference(resolution,[],[f1969,f235]) ).
tff(f235,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(1,X0))
| ~ $less(X0,X1) ),
inference(superposition,[],[f38,f21]) ).
tff(f38,plain,
! [X0: $int,X1: $int] :
( ~ $less(X1,$sum(X0,1))
| ~ $less(X0,X1) ),
introduced(theory_axiom_161,[]) ).
tff(f1969,plain,
( ! [X0: $int] :
( $less(0,$sum(X0,x4))
| ~ $less(x4,X0) )
| ~ spl0_7 ),
inference(backward_demodulation,[],[f691,f1532]) ).
tff(f691,plain,
! [X0: $int] :
( $less(0,$sum(X0,x3))
| ~ $less(x4,X0) ),
inference(superposition,[],[f29,f681]) ).
tff(f9628,plain,
( ~ spl0_18
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f9627,f1530,f8001]) ).
tff(f8001,plain,
( spl0_18
<=> $less(0,x4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
tff(f9627,plain,
( ~ $less(0,x4)
| ~ spl0_7 ),
inference(subsumption_resolution,[],[f9557,f248]) ).
tff(f9557,plain,
( $less(x4,0)
| ~ $less(0,x4)
| ~ spl0_7 ),
inference(superposition,[],[f2556,f1967]) ).
tff(f1967,plain,
( ( 0 = $sum(x4,x4) )
| ~ spl0_7 ),
inference(backward_demodulation,[],[f681,f1532]) ).
tff(f9618,plain,
( spl0_18
| spl0_19 ),
inference(avatar_contradiction_clause,[],[f9617]) ).
tff(f9617,plain,
( $false
| spl0_18
| spl0_19 ),
inference(subsumption_resolution,[],[f9615,f8458]) ).
tff(f8458,plain,
( ~ $less(x4,1)
| spl0_19 ),
inference(avatar_component_clause,[],[f8456]) ).
tff(f9615,plain,
( $less(x4,1)
| spl0_18 ),
inference(evaluation,[],[f9614]) ).
tff(f9614,plain,
( $less(x4,$sum(0,1))
| spl0_18 ),
inference(resolution,[],[f8002,f30]) ).
tff(f8002,plain,
( ~ $less(0,x4)
| spl0_18 ),
inference(avatar_component_clause,[],[f8001]) ).
tff(f9616,plain,
( spl0_3
| spl0_16
| spl0_18 ),
inference(avatar_split_clause,[],[f9612,f8001,f7992,f73]) ).
tff(f9612,plain,
( $less(x4,0)
| ( x4 = 0 )
| spl0_18 ),
inference(resolution,[],[f8002,f28]) ).
tff(f8476,plain,
( ~ spl0_22
| ~ spl0_23
| ~ spl0_7
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f8438,f1616,f1530,f8473,f8469]) ).
tff(f8438,plain,
( ~ $less(x1,x4)
| ~ $less(x1,1)
| ~ spl0_7
| ~ spl0_11 ),
inference(superposition,[],[f925,f2016]) ).
tff(f925,plain,
! [X0: $int,X1: $int] :
( ~ $less(X0,$sum(X1,X0))
| ~ $less(X1,1) ),
inference(resolution,[],[f235,f29]) ).
tff(f1964,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f1594,f1534,f1530]) ).
tff(f1534,plain,
( spl0_8
<=> $less(x3,x4) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
tff(f1594,plain,
( $less(x3,x4)
| ( x4 = x3 ) ),
inference(resolution,[],[f1523,f28]) ).
tff(f1523,plain,
~ $less(x4,x3),
inference(evaluation,[],[f1512]) ).
tff(f1512,plain,
( $less(0,0)
| ~ $less(x4,x3) ),
inference(superposition,[],[f360,f1390]) ).
tff(f1390,plain,
0 = $sum(x3,$uminus(x4)),
inference(backward_demodulation,[],[f1100,f1389]) ).
tff(f1389,plain,
! [X0: $int] : ( $sum(x2,$sum(x1,$sum(x1,X0))) = X0 ),
inference(forward_demodulation,[],[f1388,f22]) ).
tff(f1388,plain,
! [X0: $int] : ( $sum(x2,$sum($sum(x1,x1),X0)) = X0 ),
inference(evaluation,[],[f1385]) ).
tff(f1385,plain,
! [X0: $int] : ( $sum(0,X0) = $sum(x2,$sum($sum(x1,x1),X0)) ),
inference(superposition,[],[f22,f1064]) ).
tff(f1064,plain,
0 = $sum(x2,$sum(x1,x1)),
inference(backward_demodulation,[],[f461,f1044]) ).
tff(f1100,plain,
0 = $sum(x3,$sum(x2,$sum(x1,$sum(x1,$uminus(x4))))),
inference(forward_demodulation,[],[f1076,f435]) ).
tff(f1076,plain,
0 = $sum(x3,$sum(x2,$sum(x1,$sum($uminus(x4),x1)))),
inference(backward_demodulation,[],[f792,f1044]) ).
tff(f792,plain,
0 = $sum(x3,$sum(x2,$sum(x1,$sum($uminus(x4),$product(1000,x6))))),
inference(forward_demodulation,[],[f791,f435]) ).
tff(f791,plain,
0 = $sum(x3,$sum(x2,$sum($uminus(x4),$sum($product(1000,x6),x1)))),
inference(forward_demodulation,[],[f790,f22]) ).
tff(f790,plain,
0 = $sum(x3,$sum(x2,$sum($sum($uminus(x4),$product(1000,x6)),x1))),
inference(forward_demodulation,[],[f780,f22]) ).
tff(f780,plain,
0 = $sum(x3,$sum($sum(x2,$sum($uminus(x4),$product(1000,x6))),x1)),
inference(superposition,[],[f485,f22]) ).
tff(f485,plain,
0 = $sum($sum(x3,$sum(x2,$sum($uminus(x4),$product(1000,x6)))),x1),
inference(forward_demodulation,[],[f465,f21]) ).
tff(f465,plain,
0 = $sum($sum(x3,$sum($sum($uminus(x4),$product(1000,x6)),x2)),x1),
inference(backward_demodulation,[],[f188,f435]) ).
tff(f188,plain,
0 = $sum($sum(x2,$sum(x3,$sum($uminus(x4),$product(1000,x6)))),x1),
inference(evaluation,[],[f183]) ).
tff(f183,plain,
0 = $sum($sum(x2,$sum(x3,$sum($uminus(x4),$sum($product(1000,x6),0)))),x1),
inference(backward_demodulation,[],[f136,f172]) ).
tff(f136,plain,
0 = $sum($sum(x2,$sum(x3,$sum($uminus(x4),$sum($product(1000,x6),$product(0,x5))))),x1),
inference(forward_demodulation,[],[f135,f21]) ).
tff(f135,plain,
0 = $sum($sum(x2,$sum(x3,$sum($uminus(x4),$sum($product(0,x5),$product(1000,x6))))),x1),
inference(forward_demodulation,[],[f134,f32]) ).
tff(f134,plain,
0 = $sum($sum(x2,$sum(x3,$sum($uminus(x4),$sum($product(0,x5),$product(x6,1000))))),x1),
inference(forward_demodulation,[],[f133,f45]) ).
tff(f133,plain,
0 = $sum($sum(x2,$sum(x3,$sum($uminus(x4),$sum($product(0,x5),$product(x6,n))))),x1),
inference(forward_demodulation,[],[f132,f32]) ).
tff(f132,plain,
0 = $sum($sum(x2,$sum(x3,$sum($uminus(x4),$sum($product(0,x5),$product(n,x6))))),x1),
inference(forward_demodulation,[],[f131,f21]) ).
tff(f131,plain,
0 = $sum($sum(x2,$sum(x3,$sum($uminus(x4),$sum($product(n,x6),$product(0,x5))))),x1),
inference(forward_demodulation,[],[f130,f21]) ).
tff(f130,plain,
0 = $sum($sum(x2,$sum(x3,$sum($sum($product(n,x6),$product(0,x5)),$uminus(x4)))),x1),
inference(forward_demodulation,[],[f129,f21]) ).
tff(f129,plain,
0 = $sum($sum(x2,$sum($sum($sum($product(n,x6),$product(0,x5)),$uminus(x4)),x3)),x1),
inference(forward_demodulation,[],[f60,f21]) ).
tff(f60,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$uminus(x4)),x3),x2),x1),
inference(evaluation,[],[f52]) ).
tff(f52,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$uminus(x4)),$product(1,x3)),$product(1,x2)),$product(1,x1)),
inference(cnf_transformation,[],[f20]) ).
tff(f20,plain,
0 = $sum($sum($sum($sum($sum($product(n,x6),$product(0,x5)),$uminus(x4)),$product(1,x3)),$product(1,x2)),$product(1,x1)),
inference(theory_normalization,[],[f6]) ).
tff(f6,axiom,
0 = $sum($sum($sum($difference($sum($product(n,x6),$product(0,x5)),x4),$product(1,x3)),$product(1,x2)),$product(1,x1)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',eq6) ).
tff(f360,plain,
! [X0: $int,X1: $int] :
( $less(0,$sum(X1,$uminus(X0)))
| ~ $less(X0,X1) ),
inference(superposition,[],[f29,f25]) ).
tff(f1963,plain,
~ spl0_8,
inference(avatar_split_clause,[],[f1959,f1534]) ).
tff(f1959,plain,
~ $less(x3,x4),
inference(evaluation,[],[f1948]) ).
tff(f1948,plain,
( $less(0,0)
| ~ $less(x3,x4) ),
inference(superposition,[],[f368,f1390]) ).
tff(f368,plain,
! [X0: $int,X1: $int] :
( $less($sum(X1,$uminus(X0)),0)
| ~ $less(X1,X0) ),
inference(superposition,[],[f29,f25]) ).
tff(f88,plain,
( ~ spl0_1
| ~ spl0_2
| ~ spl0_3
| ~ spl0_4
| ~ spl0_5
| ~ spl0_6 ),
inference(avatar_split_clause,[],[f44,f85,f81,f77,f73,f69,f65]) ).
tff(f44,plain,
( ( x1 != 0 )
| ( x2 != 0 )
| ( x3 != 0 )
| ( x4 != 0 )
| ( x5 != 0 )
| ( x6 != 0 ) ),
inference(cnf_transformation,[],[f43]) ).
tff(f43,plain,
( ( x1 != 0 )
| ( x2 != 0 )
| ( x3 != 0 )
| ( x4 != 0 )
| ( x5 != 0 )
| ( x6 != 0 ) ),
inference(ennf_transformation,[],[f13]) ).
tff(f13,negated_conjecture,
~ ( ( x1 = 0 )
& ( x2 = 0 )
& ( x3 = 0 )
& ( x4 = 0 )
& ( x5 = 0 )
& ( x6 = 0 ) ),
inference(negated_conjecture,[],[f12]) ).
tff(f12,conjecture,
( ( x1 = 0 )
& ( x2 = 0 )
& ( x3 = 0 )
& ( x4 = 0 )
& ( x5 = 0 )
& ( x6 = 0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',conj) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : ARI698_1 : TPTP v8.1.2. Released v6.3.0.
% 0.14/0.15 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.15/0.36 % Computer : n013.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Tue Apr 30 05:31:49 EDT 2024
% 0.15/0.36 % CPUTime :
% 0.21/0.36 % (6431)Running in auto input_syntax mode. Trying TPTP
% 0.21/0.38 % (6434)WARNING: value z3 for option sas not known
% 0.21/0.38 % (6432)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.21/0.38 % (6435)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.21/0.38 % (6433)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.21/0.38 % (6434)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)
% 0.21/0.38 % (6436)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)
% 0.21/0.38 % (6437)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)
% 0.21/0.38 % (6438)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)
% 0.21/0.38 % (6433)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.38 % (6433)Terminated due to inappropriate strategy.
% 0.21/0.38 % (6433)------------------------------
% 0.21/0.38 % (6433)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.38 % (6433)Termination reason: Inappropriate
% 0.21/0.38
% 0.21/0.38 % (6433)Memory used [KB]: 731
% 0.21/0.38 % (6433)Time elapsed: 0.003 s
% 0.21/0.38 % (6433)Instructions burned: 4 (million)
% 0.21/0.38 % (6433)------------------------------
% 0.21/0.38 % (6433)------------------------------
% 0.21/0.38 % (6435)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.38 % (6435)Terminated due to inappropriate strategy.
% 0.21/0.38 % (6435)------------------------------
% 0.21/0.38 % (6435)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.38 % (6435)Termination reason: Inappropriate
% 0.21/0.38
% 0.21/0.38 % (6435)Memory used [KB]: 732
% 0.21/0.38 % (6435)Time elapsed: 0.003 s
% 0.21/0.38 % (6435)Instructions burned: 4 (million)
% 0.21/0.38 % (6435)------------------------------
% 0.21/0.38 % (6435)------------------------------
% 0.21/0.38 % (6432)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.38 % (6432)Terminated due to inappropriate strategy.
% 0.21/0.38 % (6432)------------------------------
% 0.21/0.38 % (6432)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.38 % (6432)Termination reason: Inappropriate
% 0.21/0.38
% 0.21/0.38 % (6432)Memory used [KB]: 731
% 0.21/0.38 % (6432)Time elapsed: 0.003 s
% 0.21/0.38 % (6432)Instructions burned: 4 (million)
% 0.21/0.38 % (6432)------------------------------
% 0.21/0.38 % (6432)------------------------------
% 0.21/0.40 % (6439)fmb+10_1_fmbas=expand:fmbsr=1.1:gsp=on:nm=4_411 on theBenchmark for (411ds/0Mi)
% 0.21/0.40 % (6441)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)
% 0.21/0.40 % (6440)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)
% 0.21/0.40 % (6439)WARNING: trying to run FMB on interpreted or otherwise provably infinite-domain problem!
% 0.21/0.40 % (6439)Terminated due to inappropriate strategy.
% 0.21/0.40 % (6439)------------------------------
% 0.21/0.40 % (6439)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 0.21/0.40 % (6439)Termination reason: Inappropriate
% 0.21/0.40
% 0.21/0.40 % (6439)Memory used [KB]: 732
% 0.21/0.40 % (6439)Time elapsed: 0.002 s
% 0.21/0.40 % (6439)Instructions burned: 4 (million)
% 0.21/0.40 % (6439)------------------------------
% 0.21/0.40 % (6439)------------------------------
% 0.21/0.42 % (6450)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)
% 2.18/0.69 % (6441)First to succeed.
% 2.18/0.70 % (6441)Refutation found. Thanks to Tanya!
% 2.18/0.70 % SZS status Theorem for theBenchmark
% 2.18/0.70 % SZS output start Proof for theBenchmark
% See solution above
% 2.18/0.70 % (6441)------------------------------
% 2.18/0.70 % (6441)Version: Vampire 4.8 (commit 8e9376e55 on 2024-01-18 13:49:33 +0100)
% 2.18/0.70 % (6441)Termination reason: Refutation
% 2.18/0.70
% 2.18/0.70 % (6441)Memory used [KB]: 4522
% 2.18/0.70 % (6441)Time elapsed: 0.298 s
% 2.18/0.70 % (6441)Instructions burned: 792 (million)
% 2.18/0.70 % (6441)------------------------------
% 2.18/0.70 % (6441)------------------------------
% 2.18/0.70 % (6431)Success in time 0.328 s
%------------------------------------------------------------------------------