TSTP Solution File: NUM457+1 by Vampire-SAT---4.8
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Vampire-SAT---4.8
% Problem : NUM457+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% Computer : n015.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 : Sun May 5 08:28:26 EDT 2024
% Result : Theorem 0.16s 0.33s
% Output : Refutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 53
% Syntax : Number of formulae : 165 ( 38 unt; 0 def)
% Number of atoms : 509 ( 171 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 597 ( 253 ~; 252 |; 36 &)
% ( 36 <=>; 20 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 39 ( 37 usr; 37 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 179 ( 179 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f327,plain,
$false,
inference(avatar_sat_refutation,[],[f78,f83,f88,f93,f98,f103,f108,f113,f117,f121,f125,f129,f133,f137,f146,f170,f174,f191,f196,f200,f216,f220,f224,f228,f237,f241,f257,f261,f265,f269,f279,f304,f310,f315,f320,f325,f326]) ).
fof(f326,plain,
( spl0_2
| ~ spl0_6
| ~ spl0_15
| ~ spl0_31 ),
inference(avatar_split_clause,[],[f300,f277,f143,f100,f80]) ).
fof(f80,plain,
( spl0_2
<=> sz00 = xn ),
introduced(avatar_definition,[new_symbols(naming,[spl0_2])]) ).
fof(f100,plain,
( spl0_6
<=> aNaturalNumber0(sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_6])]) ).
fof(f143,plain,
( spl0_15
<=> sz00 = sdtasdt0(xm,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_15])]) ).
fof(f277,plain,
( spl0_31
<=> ! [X0] :
( sz00 != sdtasdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| xn = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_31])]) ).
fof(f300,plain,
( ~ aNaturalNumber0(sz00)
| sz00 = xn
| ~ spl0_15
| ~ spl0_31 ),
inference(trivial_inequality_removal,[],[f299]) ).
fof(f299,plain,
( sz00 != sz00
| ~ aNaturalNumber0(sz00)
| sz00 = xn
| ~ spl0_15
| ~ spl0_31 ),
inference(superposition,[],[f278,f145]) ).
fof(f145,plain,
( sz00 = sdtasdt0(xm,sz00)
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f143]) ).
fof(f278,plain,
( ! [X0] :
( sz00 != sdtasdt0(xm,X0)
| ~ aNaturalNumber0(X0)
| xn = X0 )
| ~ spl0_31 ),
inference(avatar_component_clause,[],[f277]) ).
fof(f325,plain,
( spl0_36
| ~ spl0_5
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f154,f123,f95,f322]) ).
fof(f322,plain,
( spl0_36
<=> xn = sdtpldt0(xn,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_36])]) ).
fof(f95,plain,
( spl0_5
<=> aNaturalNumber0(xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_5])]) ).
fof(f123,plain,
( spl0_11
<=> ! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_11])]) ).
fof(f154,plain,
( xn = sdtpldt0(xn,sz00)
| ~ spl0_5
| ~ spl0_11 ),
inference(resolution,[],[f124,f97]) ).
fof(f97,plain,
( aNaturalNumber0(xn)
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f95]) ).
fof(f124,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sdtpldt0(X0,sz00) = X0 )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f123]) ).
fof(f320,plain,
( spl0_35
| ~ spl0_4
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f153,f123,f90,f317]) ).
fof(f317,plain,
( spl0_35
<=> xm = sdtpldt0(xm,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_35])]) ).
fof(f90,plain,
( spl0_4
<=> aNaturalNumber0(xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_4])]) ).
fof(f153,plain,
( xm = sdtpldt0(xm,sz00)
| ~ spl0_4
| ~ spl0_11 ),
inference(resolution,[],[f124,f92]) ).
fof(f92,plain,
( aNaturalNumber0(xm)
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f90]) ).
fof(f315,plain,
( spl0_34
| ~ spl0_5
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f150,f119,f95,f312]) ).
fof(f312,plain,
( spl0_34
<=> sz00 = sdtasdt0(sz00,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_34])]) ).
fof(f119,plain,
( spl0_10
<=> ! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_10])]) ).
fof(f150,plain,
( sz00 = sdtasdt0(sz00,xn)
| ~ spl0_5
| ~ spl0_10 ),
inference(resolution,[],[f120,f97]) ).
fof(f120,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(sz00,X0) )
| ~ spl0_10 ),
inference(avatar_component_clause,[],[f119]) ).
fof(f310,plain,
( spl0_33
| ~ spl0_4
| ~ spl0_10 ),
inference(avatar_split_clause,[],[f149,f119,f90,f307]) ).
fof(f307,plain,
( spl0_33
<=> sz00 = sdtasdt0(sz00,xm) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_33])]) ).
fof(f149,plain,
( sz00 = sdtasdt0(sz00,xm)
| ~ spl0_4
| ~ spl0_10 ),
inference(resolution,[],[f120,f92]) ).
fof(f304,plain,
( ~ spl0_5
| spl0_2
| ~ spl0_4
| spl0_32
| ~ spl0_3
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f280,f259,f85,f302,f90,f80,f95]) ).
fof(f302,plain,
( spl0_32
<=> ! [X0] :
( sz00 != sdtasdt0(X0,xn)
| ~ aNaturalNumber0(X0)
| xm = X0 ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_32])]) ).
fof(f85,plain,
( spl0_3
<=> sz00 = sdtasdt0(xm,xn) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_3])]) ).
fof(f259,plain,
( spl0_28
<=> ! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_28])]) ).
fof(f280,plain,
( ! [X0] :
( sz00 != sdtasdt0(X0,xn)
| xm = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xm)
| sz00 = xn
| ~ aNaturalNumber0(xn) )
| ~ spl0_3
| ~ spl0_28 ),
inference(superposition,[],[f260,f87]) ).
fof(f87,plain,
( sz00 = sdtasdt0(xm,xn)
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f85]) ).
fof(f260,plain,
( ! [X2,X0,X1] :
( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| X1 = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f259]) ).
fof(f279,plain,
( ~ spl0_4
| spl0_1
| ~ spl0_5
| spl0_31
| ~ spl0_3
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f270,f255,f85,f277,f95,f75,f90]) ).
fof(f75,plain,
( spl0_1
<=> sz00 = xm ),
introduced(avatar_definition,[new_symbols(naming,[spl0_1])]) ).
fof(f255,plain,
( spl0_27
<=> ! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_27])]) ).
fof(f270,plain,
( ! [X0] :
( sz00 != sdtasdt0(xm,X0)
| xn = X0
| ~ aNaturalNumber0(X0)
| ~ aNaturalNumber0(xn)
| sz00 = xm
| ~ aNaturalNumber0(xm) )
| ~ spl0_3
| ~ spl0_27 ),
inference(superposition,[],[f256,f87]) ).
fof(f256,plain,
( ! [X2,X0,X1] :
( sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| X1 = X2
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f255]) ).
fof(f269,plain,
spl0_30,
inference(avatar_split_clause,[],[f71,f267]) ).
fof(f267,plain,
( spl0_30
<=> ! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_30])]) ).
fof(f71,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f42]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f13]) ).
fof(f13,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sdtasdt0(sdtpldt0(X1,X2),X0) = sdtpldt0(sdtasdt0(X1,X0),sdtasdt0(X2,X0))
& sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAMDistr) ).
fof(f265,plain,
spl0_29,
inference(avatar_split_clause,[],[f70,f263]) ).
fof(f263,plain,
( spl0_29
<=> ! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_29])]) ).
fof(f70,plain,
! [X2,X0,X1] :
( sdtasdt0(X0,sdtpldt0(X1,X2)) = sdtpldt0(sdtasdt0(X0,X1),sdtasdt0(X0,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f43]) ).
fof(f261,plain,
spl0_28,
inference(avatar_split_clause,[],[f61,f259]) ).
fof(f61,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f27,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f26]) ).
fof(f26,plain,
! [X0] :
( ! [X1,X2] :
( X1 = X2
| ( sdtasdt0(X1,X0) != sdtasdt0(X2,X0)
& sdtasdt0(X0,X1) != sdtasdt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1) )
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f15]) ).
fof(f15,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 != X0
=> ! [X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1) )
=> ( ( sdtasdt0(X1,X0) = sdtasdt0(X2,X0)
| sdtasdt0(X0,X1) = sdtasdt0(X0,X2) )
=> X1 = X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulCanc) ).
fof(f257,plain,
spl0_27,
inference(avatar_split_clause,[],[f60,f255]) ).
fof(f60,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtasdt0(X0,X1) != sdtasdt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| sz00 = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f241,plain,
spl0_26,
inference(avatar_split_clause,[],[f69,f239]) ).
fof(f239,plain,
( spl0_26
<=> ! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_26])]) ).
fof(f69,plain,
! [X2,X0,X1] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f41]) ).
fof(f41,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f40]) ).
fof(f40,plain,
! [X0,X1,X2] :
( sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f10]) ).
fof(f10,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(sdtasdt0(X0,X1),X2) = sdtasdt0(X0,sdtasdt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulAsso) ).
fof(f237,plain,
spl0_25,
inference(avatar_split_clause,[],[f68,f235]) ).
fof(f235,plain,
( spl0_25
<=> ! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_25])]) ).
fof(f68,plain,
! [X2,X0,X1] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f39]) ).
fof(f39,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f38]) ).
fof(f38,plain,
! [X0,X1,X2] :
( sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2))
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f7,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(sdtpldt0(X0,X1),X2) = sdtpldt0(X0,sdtpldt0(X1,X2)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddAsso) ).
fof(f228,plain,
spl0_24,
inference(avatar_split_clause,[],[f73,f226]) ).
fof(f226,plain,
( spl0_24
<=> ! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_24])]) ).
fof(f73,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f45,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f44]) ).
fof(f44,plain,
! [X0,X1,X2] :
( X1 = X2
| ( sdtpldt0(X1,X0) != sdtpldt0(X2,X0)
& sdtpldt0(X0,X1) != sdtpldt0(X0,X2) )
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f14,axiom,
! [X0,X1,X2] :
( ( aNaturalNumber0(X2)
& aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( ( sdtpldt0(X1,X0) = sdtpldt0(X2,X0)
| sdtpldt0(X0,X1) = sdtpldt0(X0,X2) )
=> X1 = X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddCanc) ).
fof(f224,plain,
spl0_23,
inference(avatar_split_clause,[],[f72,f222]) ).
fof(f222,plain,
( spl0_23
<=> ! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_23])]) ).
fof(f72,plain,
! [X2,X0,X1] :
( X1 = X2
| sdtpldt0(X0,X1) != sdtpldt0(X0,X2)
| ~ aNaturalNumber0(X2)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f45]) ).
fof(f220,plain,
spl0_22,
inference(avatar_split_clause,[],[f67,f218]) ).
fof(f218,plain,
( spl0_22
<=> ! [X0,X1] :
( sz00 = X1
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_22])]) ).
fof(f67,plain,
! [X0,X1] :
( sz00 = X1
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f37,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f36]) ).
fof(f36,plain,
! [X0,X1] :
( ( sz00 = X1
& sz00 = X0 )
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f16]) ).
fof(f16,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> ( sz00 = sdtpldt0(X0,X1)
=> ( sz00 = X1
& sz00 = X0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroAdd) ).
fof(f216,plain,
spl0_21,
inference(avatar_split_clause,[],[f66,f214]) ).
fof(f214,plain,
( spl0_21
<=> ! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_21])]) ).
fof(f66,plain,
! [X0,X1] :
( sz00 = X0
| sz00 != sdtpldt0(X0,X1)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f37]) ).
fof(f200,plain,
spl0_20,
inference(avatar_split_clause,[],[f65,f198]) ).
fof(f198,plain,
( spl0_20
<=> ! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_20])]) ).
fof(f65,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f35,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f34]) ).
fof(f34,plain,
! [X0,X1] :
( sdtasdt0(X0,X1) = sdtasdt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f9,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtasdt0(X0,X1) = sdtasdt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mMulComm) ).
fof(f196,plain,
( spl0_19
| ~ spl0_5
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f141,f115,f95,f193]) ).
fof(f193,plain,
( spl0_19
<=> sz00 = sdtasdt0(xn,sz00) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_19])]) ).
fof(f115,plain,
( spl0_9
<=> ! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_9])]) ).
fof(f141,plain,
( sz00 = sdtasdt0(xn,sz00)
| ~ spl0_5
| ~ spl0_9 ),
inference(resolution,[],[f116,f97]) ).
fof(f116,plain,
( ! [X0] :
( ~ aNaturalNumber0(X0)
| sz00 = sdtasdt0(X0,sz00) )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f115]) ).
fof(f191,plain,
spl0_18,
inference(avatar_split_clause,[],[f64,f189]) ).
fof(f189,plain,
( spl0_18
<=> ! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_18])]) ).
fof(f64,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f33]) ).
fof(f33,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f32]) ).
fof(f32,plain,
! [X0,X1] :
( sdtpldt0(X0,X1) = sdtpldt0(X1,X0)
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f6]) ).
fof(f6,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> sdtpldt0(X0,X1) = sdtpldt0(X1,X0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mAddComm) ).
fof(f174,plain,
spl0_17,
inference(avatar_split_clause,[],[f63,f172]) ).
fof(f172,plain,
( spl0_17
<=> ! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_17])]) ).
fof(f63,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f31]) ).
fof(f31,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f30]) ).
fof(f30,plain,
! [X0,X1] :
( aNaturalNumber0(sdtasdt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f5]) ).
fof(f5,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
fof(f170,plain,
spl0_16,
inference(avatar_split_clause,[],[f62,f168]) ).
fof(f168,plain,
( spl0_16
<=> ! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_16])]) ).
fof(f62,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f29,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(flattening,[],[f28]) ).
fof(f28,plain,
! [X0,X1] :
( aNaturalNumber0(sdtpldt0(X0,X1))
| ~ aNaturalNumber0(X1)
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f4,axiom,
! [X0,X1] :
( ( aNaturalNumber0(X1)
& aNaturalNumber0(X0) )
=> aNaturalNumber0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
fof(f146,plain,
( spl0_15
| ~ spl0_4
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f140,f115,f90,f143]) ).
fof(f140,plain,
( sz00 = sdtasdt0(xm,sz00)
| ~ spl0_4
| ~ spl0_9 ),
inference(resolution,[],[f116,f92]) ).
fof(f137,plain,
spl0_14,
inference(avatar_split_clause,[],[f59,f135]) ).
fof(f135,plain,
( spl0_14
<=> ! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_14])]) ).
fof(f59,plain,
! [X0] :
( sdtasdt0(sz10,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f25,plain,
! [X0] :
( ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f11]) ).
fof(f11,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtasdt0(sz10,X0) = X0
& sdtasdt0(X0,sz10) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulUnit) ).
fof(f133,plain,
spl0_13,
inference(avatar_split_clause,[],[f58,f131]) ).
fof(f131,plain,
( spl0_13
<=> ! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_13])]) ).
fof(f58,plain,
! [X0] :
( sdtasdt0(X0,sz10) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f25]) ).
fof(f129,plain,
spl0_12,
inference(avatar_split_clause,[],[f57,f127]) ).
fof(f127,plain,
( spl0_12
<=> ! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_12])]) ).
fof(f57,plain,
! [X0] :
( sdtpldt0(sz00,X0) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f24,plain,
! [X0] :
( ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f8]) ).
fof(f8,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sdtpldt0(sz00,X0) = X0
& sdtpldt0(X0,sz00) = X0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_AddZero) ).
fof(f125,plain,
spl0_11,
inference(avatar_split_clause,[],[f56,f123]) ).
fof(f56,plain,
! [X0] :
( sdtpldt0(X0,sz00) = X0
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f24]) ).
fof(f121,plain,
spl0_10,
inference(avatar_split_clause,[],[f55,f119]) ).
fof(f55,plain,
! [X0] :
( sz00 = sdtasdt0(sz00,X0)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f23,plain,
! [X0] :
( ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) )
| ~ aNaturalNumber0(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f12,axiom,
! [X0] :
( aNaturalNumber0(X0)
=> ( sz00 = sdtasdt0(sz00,X0)
& sz00 = sdtasdt0(X0,sz00) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m_MulZero) ).
fof(f117,plain,
spl0_9,
inference(avatar_split_clause,[],[f54,f115]) ).
fof(f54,plain,
! [X0] :
( sz00 = sdtasdt0(X0,sz00)
| ~ aNaturalNumber0(X0) ),
inference(cnf_transformation,[],[f23]) ).
fof(f113,plain,
~ spl0_8,
inference(avatar_split_clause,[],[f53,f110]) ).
fof(f110,plain,
( spl0_8
<=> sz00 = sz10 ),
introduced(avatar_definition,[new_symbols(naming,[spl0_8])]) ).
fof(f53,plain,
sz00 != sz10,
inference(cnf_transformation,[],[f3]) ).
fof(f3,axiom,
( sz00 != sz10
& aNaturalNumber0(sz10) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC_01) ).
fof(f108,plain,
spl0_7,
inference(avatar_split_clause,[],[f52,f105]) ).
fof(f105,plain,
( spl0_7
<=> aNaturalNumber0(sz10) ),
introduced(avatar_definition,[new_symbols(naming,[spl0_7])]) ).
fof(f52,plain,
aNaturalNumber0(sz10),
inference(cnf_transformation,[],[f3]) ).
fof(f103,plain,
spl0_6,
inference(avatar_split_clause,[],[f51,f100]) ).
fof(f51,plain,
aNaturalNumber0(sz00),
inference(cnf_transformation,[],[f2]) ).
fof(f2,axiom,
aNaturalNumber0(sz00),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsC) ).
fof(f98,plain,
spl0_5,
inference(avatar_split_clause,[],[f50,f95]) ).
fof(f50,plain,
aNaturalNumber0(xn),
inference(cnf_transformation,[],[f17]) ).
fof(f17,axiom,
( aNaturalNumber0(xn)
& aNaturalNumber0(xm) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__624) ).
fof(f93,plain,
spl0_4,
inference(avatar_split_clause,[],[f49,f90]) ).
fof(f49,plain,
aNaturalNumber0(xm),
inference(cnf_transformation,[],[f17]) ).
fof(f88,plain,
spl0_3,
inference(avatar_split_clause,[],[f46,f85]) ).
fof(f46,plain,
sz00 = sdtasdt0(xm,xn),
inference(cnf_transformation,[],[f22]) ).
fof(f22,plain,
( sz00 != xn
& sz00 != xm
& sz00 = sdtasdt0(xm,xn) ),
inference(flattening,[],[f21]) ).
fof(f21,plain,
( sz00 != xn
& sz00 != xm
& sz00 = sdtasdt0(xm,xn) ),
inference(ennf_transformation,[],[f19]) ).
fof(f19,negated_conjecture,
~ ( sz00 = sdtasdt0(xm,xn)
=> ( sz00 = xn
| sz00 = xm ) ),
inference(negated_conjecture,[],[f18]) ).
fof(f18,conjecture,
( sz00 = sdtasdt0(xm,xn)
=> ( sz00 = xn
| sz00 = xm ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f83,plain,
~ spl0_2,
inference(avatar_split_clause,[],[f48,f80]) ).
fof(f48,plain,
sz00 != xn,
inference(cnf_transformation,[],[f22]) ).
fof(f78,plain,
~ spl0_1,
inference(avatar_split_clause,[],[f47,f75]) ).
fof(f47,plain,
sz00 != xm,
inference(cnf_transformation,[],[f22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.09 % Problem : NUM457+1 : TPTP v8.1.2. Released v4.0.0.
% 0.05/0.11 % Command : vampire --mode casc_sat -m 16384 --cores 7 -t %d %s
% 0.10/0.31 % Computer : n015.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Fri May 3 14:34:52 EDT 2024
% 0.10/0.31 % CPUTime :
% 0.16/0.31 % (16312)Running in auto input_syntax mode. Trying TPTP
% 0.16/0.32 % (16317)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)
% 0.16/0.33 % (16316)fmb+10_1_bce=on:fmbsr=1.5:nm=32_533 on theBenchmark for (533ds/0Mi)
% 0.16/0.33 % (16319)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)
% 0.16/0.33 % (16315)WARNING: value z3 for option sas not known
% 0.16/0.33 % (16313)fmb+10_1_bce=on:fmbas=function:fmbsr=1.2:fde=unused:nm=0_846 on theBenchmark for (846ds/0Mi)
% 0.16/0.33 % (16314)fmb+10_1_bce=on:fmbdsb=on:fmbes=contour:fmbswr=3:fde=none:nm=0_793 on theBenchmark for (793ds/0Mi)
% 0.16/0.33 % (16318)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)
% 0.16/0.33 TRYING [1]
% 0.16/0.33 % (16315)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)
% 0.16/0.33 TRYING [2]
% 0.16/0.33 TRYING [1]
% 0.16/0.33 TRYING [2]
% 0.16/0.33 TRYING [3]
% 0.16/0.33 TRYING [3]
% 0.16/0.33 % (16317)First to succeed.
% 0.16/0.33 % (16317)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-16312"
% 0.16/0.33 % (16317)Refutation found. Thanks to Tanya!
% 0.16/0.33 % SZS status Theorem for theBenchmark
% 0.16/0.33 % SZS output start Proof for theBenchmark
% See solution above
% 0.16/0.33 % (16317)------------------------------
% 0.16/0.33 % (16317)Version: Vampire 4.8 (commit 3a798227e on 2024-05-03 07:42:47 +0200)
% 0.16/0.33 % (16317)Termination reason: Refutation
% 0.16/0.33
% 0.16/0.33 % (16317)Memory used [KB]: 967
% 0.16/0.33 % (16317)Time elapsed: 0.009 s
% 0.16/0.33 % (16317)Instructions burned: 15 (million)
% 0.16/0.33 % (16312)Success in time 0.022 s
%------------------------------------------------------------------------------