%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : NUM434+1 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n003.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Sep 29 12:15:10 PM UTC 2026
% Result : Theorem 2.53s 1.30s
% Output : Refutation 3.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 22
% Syntax : Number of formulae : 121 ( 31 unt; 13 def)
% Number of atoms : 382 ( 47 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 450 ( 189 ~; 200 |; 36 &)
% ( 18 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 18 ( 16 usr; 13 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-2 aty)
% Number of variables : 89 ( 0 sgn 82 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0] :
( aInteger0(X0)
=> aInteger0(smndt0(X0)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntNeg) ).
fof(f5,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> aInteger0(sdtpldt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntPlus) ).
fof(f6,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> aInteger0(sdtasdt0(X0,X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mIntMult) ).
fof(f17,axiom,
! [X0,X1] :
( ( aInteger0(X0)
& aInteger0(X1) )
=> ( sdtasdt0(X0,X1) = sz00
=> ( X0 = sz00
| X1 = sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mZeroDiv) ).
fof(f18,axiom,
! [X0] :
( aInteger0(X0)
=> ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDivisor) ).
fof(f19,axiom,
! [X0,X1,X2] :
( ( aInteger0(X0)
& aInteger0(X1)
& aInteger0(X2)
& X2 != sz00 )
=> ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEquMod) ).
fof(f23,axiom,
( aInteger0(xa)
& aInteger0(xb)
& aInteger0(xp)
& xp != sz00
& aInteger0(xq)
& xq != sz00 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__979) ).
fof(f24,axiom,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1003) ).
fof(f25,conjecture,
? [X0] :
( aInteger0(X0)
& sdtasdt0(sdtasdt0(xp,xq),X0) = sdtpldt0(xa,smndt0(xb)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
fof(f26,negated_conjecture,
~ ? [X0] :
( aInteger0(X0)
& sdtasdt0(sdtasdt0(xp,xq),X0) = sdtpldt0(xa,smndt0(xb)) ),
inference(negated_conjecture,[status(cth)],[f25]) ).
fof(f28,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f4]) ).
fof(f29,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f5]) ).
fof(f30,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f6]) ).
fof(f32,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f31]) ).
fof(f48,plain,
! [X0,X1] :
( X0 = sz00
| X1 = sz00
| sz00 != sdtasdt0(X0,X1)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(ennf_transformation,[],[f17]) ).
fof(f49,plain,
! [X0,X1] :
( X0 = sz00
| X1 = sz00
| sz00 != sdtasdt0(X0,X1)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(flattening,[],[f48]) ).
fof(f50,plain,
! [X0] :
( ! [X1] :
( aDivisorOf0(X1,X0)
<=> ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) ) )
| ~ aInteger0(X0) ),
inference(ennf_transformation,[],[f18]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(ennf_transformation,[],[f19]) ).
fof(f52,plain,
! [X0,X1,X2] :
( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
<=> aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(flattening,[],[f51]) ).
fof(f59,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(sdtasdt0(xp,xq),X0) != sdtpldt0(xa,smndt0(xb)) ),
inference(ennf_transformation,[],[f26]) ).
fof(f60,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(nnf_transformation,[],[f50]) ).
fof(f61,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& ? [X2] :
( aInteger0(X2)
& sdtasdt0(X1,X2) = X0 ) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(flattening,[],[f60]) ).
fof(f62,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& ? [X3] :
( aInteger0(X3)
& sdtasdt0(X1,X3) = X0 ) )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(rectify,[],[f61]) ).
fof(f63,plain,
! [X0] :
( ! [X1] :
( ( aDivisorOf0(X1,X0)
| ~ aInteger0(X1)
| sz00 = X1
| ! [X2] :
( ~ aInteger0(X2)
| sdtasdt0(X1,X2) != X0 ) )
& ( ( aInteger0(X1)
& X1 != sz00
& aInteger0(sK0(X0,X1))
& sdtasdt0(X1,sK0(X0,X1)) = X0 )
| ~ aDivisorOf0(X1,X0) ) )
| ~ aInteger0(X0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X3,sK0(X0,X1))],[f62]) ).
fof(f64,plain,
! [X0,X1,X2] :
( ( ( sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) )
& ( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2) ) )
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(nnf_transformation,[],[f52]) ).
fof(f67,plain,
! [X0] :
( aInteger0(smndt0(X0))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f68,plain,
! [X0,X1] :
( aInteger0(sdtpldt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f30]) ).
fof(f69,plain,
! [X0,X1] :
( aInteger0(sdtasdt0(X0,X1))
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f86,plain,
! [X0,X1] :
( sz00 = X0
| sz00 = X1
| sz00 != sdtasdt0(X0,X1)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(cnf_transformation,[],[f49]) ).
fof(f87,plain,
! [X0,X1] :
( sdtasdt0(X1,sK0(X0,X1)) = X0
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f88,plain,
! [X0,X1] :
( ~ aDivisorOf0(X1,X0)
| aInteger0(sK0(X0,X1))
| ~ aInteger0(X0) ),
inference(cnf_transformation,[],[f63]) ).
fof(f92,plain,
! [X2,X0,X1] :
( aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1)))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| sz00 = X2 ),
inference(cnf_transformation,[],[f64]) ).
fof(f97,plain,
sz00 != xq,
inference(cnf_transformation,[],[f23]) ).
fof(f98,plain,
aInteger0(xq),
inference(cnf_transformation,[],[f23]) ).
fof(f99,plain,
sz00 != xp,
inference(cnf_transformation,[],[f23]) ).
fof(f100,plain,
aInteger0(xp),
inference(cnf_transformation,[],[f23]) ).
fof(f101,plain,
aInteger0(xb),
inference(cnf_transformation,[],[f23]) ).
fof(f102,plain,
aInteger0(xa),
inference(cnf_transformation,[],[f23]) ).
fof(f103,plain,
sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)),
inference(cnf_transformation,[],[f24]) ).
fof(f104,plain,
! [X0] :
( ~ aInteger0(X0)
| sdtasdt0(sdtasdt0(xp,xq),X0) != sdtpldt0(xa,smndt0(xb)) ),
inference(cnf_transformation,[],[f59]) ).
fof(f107,definition,
! [X0,X1] :
( sQ1_eqProxy(X0,X1)
<=> X0 = X1 ),
introduced(definition,[new_symbols(definition,[sQ1_eqProxy])],[equality_proxy_definition]) ).
fof(f124,plain,
! [X0,X1] :
( ~ sQ1_eqProxy(sz00,sdtasdt0(X0,X1))
| sQ1_eqProxy(sz00,X1)
| sQ1_eqProxy(sz00,X0)
| ~ aInteger0(X0)
| ~ aInteger0(X1) ),
inference(equality_proxy_replacement,[],[f86,f107,f107,f107]) ).
fof(f126,plain,
! [X0,X1] :
( sQ1_eqProxy(sdtasdt0(X1,sK0(X0,X1)),X0)
| ~ aDivisorOf0(X1,X0)
| ~ aInteger0(X0) ),
inference(equality_proxy_replacement,[],[f87,f107]) ).
fof(f128,plain,
! [X2,X0,X1] :
( sQ1_eqProxy(sz00,X2)
| ~ sdteqdtlpzmzozddtrp0(X0,X1,X2)
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(X2)
| aDivisorOf0(X2,sdtpldt0(X0,smndt0(X1))) ),
inference(equality_proxy_replacement,[],[f92,f107]) ).
fof(f132,plain,
~ sQ1_eqProxy(sz00,xp),
inference(equality_proxy_replacement,[],[f99,f107]) ).
fof(f133,plain,
~ sQ1_eqProxy(sz00,xq),
inference(equality_proxy_replacement,[],[f97,f107]) ).
fof(f134,plain,
! [X0] :
( ~ sQ1_eqProxy(sdtasdt0(sdtasdt0(xp,xq),X0),sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(X0) ),
inference(equality_proxy_replacement,[],[f104,f107]) ).
fof(f146,definition,
( spl2_1
<=> aInteger0(xq) ),
introduced(definition,[new_symbols(definition,[spl2_1])],[avatar_definition]) ).
fof(f147,plain,
( ~ aInteger0(xq)
| spl2_1 ),
inference(avatar_component_clause,[],[f146]) ).
fof(f153,definition,
( spl2_3
<=> aInteger0(xp) ),
introduced(definition,[new_symbols(definition,[spl2_3])],[avatar_definition]) ).
fof(f154,plain,
( ~ aInteger0(xp)
| spl2_3 ),
inference(avatar_component_clause,[],[f153]) ).
fof(f159,plain,
( ~ aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| ~ aInteger0(sK0(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))) ),
inference(resolution,[],[f126,f134]) ).
fof(f161,definition,
( spl2_5
<=> aInteger0(sK0(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq))) ),
introduced(definition,[new_symbols(definition,[spl2_5])],[avatar_definition]) ).
fof(f162,plain,
( ~ aInteger0(sK0(sdtpldt0(xa,smndt0(xb)),sdtasdt0(xp,xq)))
| spl2_5 ),
inference(avatar_component_clause,[],[f161]) ).
fof(f164,definition,
( spl2_6
<=> aInteger0(sdtpldt0(xa,smndt0(xb))) ),
introduced(definition,[new_symbols(definition,[spl2_6])],[avatar_definition]) ).
fof(f165,plain,
( ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| spl2_6 ),
inference(avatar_component_clause,[],[f164]) ).
fof(f167,definition,
( spl2_7
<=> aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb))) ),
introduced(definition,[new_symbols(definition,[spl2_7])],[avatar_definition]) ).
fof(f168,plain,
( ~ aDivisorOf0(sdtasdt0(xp,xq),sdtpldt0(xa,smndt0(xb)))
| spl2_7 ),
inference(avatar_component_clause,[],[f167]) ).
fof(f169,plain,
( ~ spl2_5
| ~ spl2_6
| ~ spl2_7 ),
inference(avatar_split_clause,[],[f159,f167,f164,f161]) ).
fof(f170,plain,
( $false
| spl2_1 ),
inference(resolution,[],[f147,f98]) ).
fof(f171,plain,
spl2_1,
inference(avatar_contradiction_clause,[],[f170]) ).
fof(f172,plain,
( $false
| spl2_3 ),
inference(resolution,[],[f154,f100]) ).
fof(f173,plain,
spl2_3,
inference(avatar_contradiction_clause,[],[f172]) ).
fof(f238,plain,
! [X2,X3,X0,X1] :
( aDivisorOf0(sdtasdt0(X2,X3),sdtpldt0(X0,smndt0(X1)))
| ~ aInteger0(X0)
| ~ aInteger0(X1)
| ~ aInteger0(sdtasdt0(X2,X3))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(X2,X3))
| sQ1_eqProxy(sz00,X3)
| sQ1_eqProxy(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X3) ),
inference(resolution,[],[f128,f124]) ).
fof(f294,plain,
! [X2,X3,X0,X1] :
( aInteger0(sK0(sdtpldt0(X0,smndt0(X1)),sdtasdt0(X2,X3)))
| ~ aInteger0(X1)
| ~ aInteger0(sdtasdt0(X2,X3))
| ~ sdteqdtlpzmzozddtrp0(X0,X1,sdtasdt0(X2,X3))
| sQ1_eqProxy(sz00,X3)
| sQ1_eqProxy(sz00,X2)
| ~ aInteger0(X2)
| ~ aInteger0(X3)
| ~ aInteger0(X0)
| ~ aInteger0(sdtpldt0(X0,smndt0(X1))) ),
inference(resolution,[],[f238,f88]) ).
fof(f296,plain,
( ~ aInteger0(xb)
| ~ aInteger0(sdtasdt0(xp,xq))
| ~ sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
| sQ1_eqProxy(sz00,xq)
| sQ1_eqProxy(sz00,xp)
| ~ aInteger0(xp)
| ~ aInteger0(xq)
| ~ aInteger0(xa)
| ~ aInteger0(sdtpldt0(xa,smndt0(xb)))
| spl2_5 ),
inference(resolution,[],[f294,f162]) ).
fof(f298,definition,
( spl2_20
<=> aInteger0(xa) ),
introduced(definition,[new_symbols(definition,[spl2_20])],[avatar_definition]) ).
fof(f299,plain,
( ~ aInteger0(xa)
| spl2_20 ),
inference(avatar_component_clause,[],[f298]) ).
fof(f301,definition,
( spl2_21
<=> sQ1_eqProxy(sz00,xp) ),
introduced(definition,[new_symbols(definition,[spl2_21])],[avatar_definition]) ).
fof(f302,plain,
( sQ1_eqProxy(sz00,xp)
| ~ spl2_21 ),
inference(avatar_component_clause,[],[f301]) ).
fof(f304,definition,
( spl2_22
<=> sQ1_eqProxy(sz00,xq) ),
introduced(definition,[new_symbols(definition,[spl2_22])],[avatar_definition]) ).
fof(f305,plain,
( sQ1_eqProxy(sz00,xq)
| ~ spl2_22 ),
inference(avatar_component_clause,[],[f304]) ).
fof(f307,definition,
( spl2_23
<=> sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq)) ),
introduced(definition,[new_symbols(definition,[spl2_23])],[avatar_definition]) ).
fof(f308,plain,
( ~ sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
| spl2_23 ),
inference(avatar_component_clause,[],[f307]) ).
fof(f310,definition,
( spl2_24
<=> aInteger0(sdtasdt0(xp,xq)) ),
introduced(definition,[new_symbols(definition,[spl2_24])],[avatar_definition]) ).
fof(f311,plain,
( ~ aInteger0(sdtasdt0(xp,xq))
| spl2_24 ),
inference(avatar_component_clause,[],[f310]) ).
fof(f313,definition,
( spl2_25
<=> aInteger0(xb) ),
introduced(definition,[new_symbols(definition,[spl2_25])],[avatar_definition]) ).
fof(f314,plain,
( ~ aInteger0(xb)
| spl2_25 ),
inference(avatar_component_clause,[],[f313]) ).
fof(f315,plain,
( ~ spl2_6
| ~ spl2_20
| ~ spl2_1
| ~ spl2_3
| spl2_21
| spl2_22
| ~ spl2_23
| ~ spl2_24
| ~ spl2_25
| spl2_5 ),
inference(avatar_split_clause,[],[f296,f161,f313,f310,f307,f304,f301,f153,f146,f298,f164]) ).
fof(f316,plain,
( ~ aInteger0(xa)
| ~ aInteger0(smndt0(xb))
| spl2_6 ),
inference(resolution,[],[f165,f68]) ).
fof(f318,definition,
( spl2_26
<=> aInteger0(smndt0(xb)) ),
introduced(definition,[new_symbols(definition,[spl2_26])],[avatar_definition]) ).
fof(f319,plain,
( ~ aInteger0(smndt0(xb))
| spl2_26 ),
inference(avatar_component_clause,[],[f318]) ).
fof(f320,plain,
( ~ spl2_26
| ~ spl2_20
| spl2_6 ),
inference(avatar_split_clause,[],[f316,f164,f298,f318]) ).
fof(f321,plain,
( $false
| spl2_20 ),
inference(resolution,[],[f299,f102]) ).
fof(f322,plain,
spl2_20,
inference(avatar_contradiction_clause,[],[f321]) ).
fof(f323,plain,
( ~ aInteger0(xb)
| spl2_26 ),
inference(resolution,[],[f319,f67]) ).
fof(f324,plain,
( ~ spl2_25
| spl2_26 ),
inference(avatar_split_clause,[],[f323,f318,f313]) ).
fof(f325,plain,
( $false
| spl2_25 ),
inference(resolution,[],[f314,f101]) ).
fof(f326,plain,
spl2_25,
inference(avatar_contradiction_clause,[],[f325]) ).
fof(f327,plain,
( $false
| spl2_23 ),
inference(resolution,[],[f308,f103]) ).
fof(f331,plain,
spl2_23,
inference(avatar_contradiction_clause,[],[f327]) ).
fof(f341,plain,
( ~ aInteger0(xp)
| ~ aInteger0(xq)
| spl2_24 ),
inference(resolution,[],[f311,f69]) ).
fof(f342,plain,
( ~ spl2_1
| ~ spl2_3
| spl2_24 ),
inference(avatar_split_clause,[],[f341,f310,f153,f146]) ).
fof(f343,plain,
( $false
| ~ spl2_21 ),
inference(resolution,[],[f302,f132]) ).
fof(f344,plain,
~ spl2_21,
inference(avatar_contradiction_clause,[],[f343]) ).
fof(f345,plain,
( $false
| ~ spl2_22 ),
inference(resolution,[],[f305,f133]) ).
fof(f346,plain,
~ spl2_22,
inference(avatar_contradiction_clause,[],[f345]) ).
fof(f347,plain,
( ~ aInteger0(xa)
| ~ aInteger0(xb)
| ~ aInteger0(sdtasdt0(xp,xq))
| ~ sdteqdtlpzmzozddtrp0(xa,xb,sdtasdt0(xp,xq))
| sQ1_eqProxy(sz00,xq)
| sQ1_eqProxy(sz00,xp)
| ~ aInteger0(xp)
| ~ aInteger0(xq)
| spl2_7 ),
inference(resolution,[],[f168,f238]) ).
fof(f348,plain,
( ~ spl2_1
| ~ spl2_3
| spl2_21
| spl2_22
| ~ spl2_23
| ~ spl2_24
| ~ spl2_25
| ~ spl2_20
| spl2_7 ),
inference(avatar_split_clause,[],[f347,f167,f298,f313,f310,f307,f304,f301,f153,f146]) ).
cnf(s3,plain,
( ~ spl2_5
| ~ spl2_6
| ~ spl2_7 ),
inference(sat_conversion,[],[f169]) ).
cnf(s4,plain,
spl2_1,
inference(sat_conversion,[],[f171]) ).
cnf(s5,plain,
spl2_3,
inference(sat_conversion,[],[f173]) ).
cnf(s18,plain,
( ~ spl2_1
| ~ spl2_3
| spl2_5
| ~ spl2_6
| ~ spl2_20
| spl2_21
| spl2_22
| ~ spl2_23
| ~ spl2_24
| ~ spl2_25 ),
inference(sat_conversion,[],[f315]) ).
cnf(s19,plain,
( spl2_6
| ~ spl2_20
| ~ spl2_26 ),
inference(sat_conversion,[],[f320]) ).
cnf(s20,plain,
spl2_20,
inference(sat_conversion,[],[f322]) ).
cnf(s21,plain,
( ~ spl2_25
| spl2_26 ),
inference(sat_conversion,[],[f324]) ).
cnf(s22,plain,
spl2_25,
inference(sat_conversion,[],[f326]) ).
cnf(s23,plain,
spl2_23,
inference(sat_conversion,[],[f331]) ).
cnf(s27,plain,
( ~ spl2_1
| ~ spl2_3
| spl2_24 ),
inference(sat_conversion,[],[f342]) ).
cnf(s28,plain,
~ spl2_21,
inference(sat_conversion,[],[f344]) ).
cnf(s29,plain,
~ spl2_22,
inference(sat_conversion,[],[f346]) ).
cnf(s30,plain,
( ~ spl2_1
| ~ spl2_3
| spl2_7
| ~ spl2_20
| spl2_21
| spl2_22
| ~ spl2_23
| ~ spl2_24
| ~ spl2_25 ),
inference(sat_conversion,[],[f348]) ).
cnf(s34,plain,
spl2_26,
inference(rat,[],[s21,s22]) ).
cnf(s35,plain,
spl2_6,
inference(rat,[],[s19,s34,s20]) ).
cnf(s36,plain,
( ~ spl2_1
| ~ spl2_3
| spl2_5
| ~ spl2_24 ),
inference(rat,[],[s18,s22,s23,s29,s28,s20,s35]) ).
cnf(s43,plain,
spl2_24,
inference(rat,[],[s27,s5,s4]) ).
cnf(s44,plain,
spl2_5,
inference(rat,[],[s36,s43,s5,s4]) ).
cnf(s50,plain,
spl2_7,
inference(rat,[],[s30,s22,s4,s23,s29,s28,s20,s5,s43]) ).
cnf(s51,plain,
$false,
inference(rat,[],[s3,s50,s35,s44]) ).
fof(f349,plain,
$false,
inference(avatar_sat_refutation,[],[s51]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM434+1 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.09/0.37 % Computer : n003.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Sun Sep 27 19:55:26 UTC 2026
% 0.09/0.38 % CPUTime :
% 0.09/0.38 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.15/0.41 Running first-order theorem proving
% 0.15/0.41 Running: /export/starexec/sandbox/solver/bin/vampire --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.53/1.30 % (885632)Detected formulas, will run a generic FOF schedule.
% 2.53/1.30 % (885658)lrs+1010_1_to=lpo:sil=32000:sos=on:spb=goal_then_units:bce=on:random_seed=927656747:i=109:sd=1:ins=1:gsp=on:ss=axioms_2999 on theBenchmark for (2999ds/109Mi)
% 2.53/1.30 % (885655)lrs+10_1_ncem=casc2026/models/loop8.pt:sil=128000:tgt=full:npcc=on:drc=off:sp=weighted_frequency:spb=goal:fd=preordered:foolp=on:random_seed=124365309:i=141193_2999 on theBenchmark for (2999ds/141193Mi)
% 2.53/1.30 % (885656)lrs+11_1_ncem=casc2026/models/loop8.pt:sil=128000:npcc=on:lma=off:spb=units:urr=ec_only:bce=on:s2agt=64:updr=off:random_seed=295948027:i=134677:sd=20:aac=none:nm=16:ss=included:sgt=10_2999 on theBenchmark for (2999ds/134677Mi)
% 2.53/1.30 % (885657)lrs+1010_1_anc=all:sfv=off:to=kbo:ncem=casc2026/models/loop7.pt:sil=128000:npcc=on:prc=on:sos=all:bsr=unit_only:sac=on:random_seed=2718997864:i=141695:sd=1:nm=32:gsp=on:ss=included_2999 on theBenchmark for (2999ds/141695Mi)
% 2.53/1.30 % (885658)Instruction limit reached!
% 2.53/1.30 % (885658)------------------------------
% 2.53/1.30 % (885658)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.30 % (885658)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.30 % (885658)CaDiCaL version: 2.1.3
% 2.53/1.30 % (885658)Termination reason: Instruction limit
% 2.53/1.30 % (885658)Termination phase: Saturation
% 2.53/1.30 % (885658)Time elapsed: 0.039 s
% 2.53/1.30 % (885658)Peak memory usage: 90 MB
% 2.53/1.30 % (885658)Instructions burned: 111 (million)
% 2.53/1.30 % (885661)dis-21_1_sil=8000:lcm=predicate:random_seed=135001045:st=5:avsq=on:i=129:avsqr=1,16:sd=3:aac=none:ep=RS:fsr=off:ss=included_2999 on theBenchmark for (2999ds/129Mi)
% 2.53/1.30 % (885659)dis-1010_2:3_sil=16000:sp=reverse_frequency:random_seed=3850857336:i=119:av=off:ss=axioms_2999 on theBenchmark for (2999ds/119Mi)
% 2.53/1.30 % (885660)dis-1011_1_sil=16000:fde=unused:s2agt=70:random_seed=1131102289:s2a=on:i=139:gtg=position_2999 on theBenchmark for (2999ds/139Mi)
% 2.53/1.30 % (885661)First to succeed.
% 2.53/1.30 % (885661)Solution written to "/export/starexec/sandbox/tmp/vampire-proof-885632"
% 2.53/1.30 % (885659)Instruction limit reached!
% 2.53/1.30 % (885659)------------------------------
% 2.53/1.30 % (885659)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.30 % (885659)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.30 % (885659)CaDiCaL version: 2.1.3
% 2.53/1.30 % (885659)Termination reason: Instruction limit
% 2.53/1.30 % (885659)Termination phase: Saturation
% 2.53/1.30 % (885659)Time elapsed: 0.067 s
% 2.53/1.30 % (885659)Peak memory usage: 88 MB
% 2.53/1.30 % (885659)Instructions burned: 120 (million)
% 2.53/1.30 % (885660)Instruction limit reached!
% 2.53/1.30 % (885660)------------------------------
% 2.53/1.30 % (885660)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.30 % (885660)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.30 % (885660)CaDiCaL version: 2.1.3
% 2.53/1.30 % (885660)Termination reason: Instruction limit
% 2.53/1.30 % (885660)Termination phase: Saturation
% 2.53/1.30 % (885660)Time elapsed: 0.084 s
% 2.53/1.30 % (885660)Peak memory usage: 90 MB
% 2.53/1.30 % (885660)Instructions burned: 139 (million)
% 2.53/1.30 % (885666)lrs+10_1_sil=8000:sp=occurrence:random_seed=3085953958:i=285:sd=3:ss=axioms:sgt=8_2998 on theBenchmark for (2998ds/285Mi)
% 2.53/1.30 % (885666)Instruction limit reached!
% 2.53/1.30 % (885666)------------------------------
% 2.53/1.30 % (885666)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 2.53/1.30 % (885666)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 2.53/1.30 % (885666)CaDiCaL version: 2.1.3
% 2.53/1.30 % (885666)Termination reason: Instruction limit
% 2.53/1.30 % (885666)Termination phase: Saturation
% 2.53/1.30 % (885666)Time elapsed: 0.088 s
% 2.53/1.30 % (885666)Peak memory usage: 93 MB
% 2.53/1.30 % (885666)Instructions burned: 286 (million)
% 2.53/1.30 % (885670)lrs+10_1_sil=32000:urr=on:br=off:random_seed=4286775197:i=157:sd=1:gtg=position:ss=axioms:sgt=8_2997 on theBenchmark for (2997ds/157Mi)
% 2.53/1.30 % (885671)lrs+1011_1_sil=32000:sp=occurrence:random_seed=4012698916:i=325:sd=1:ss=axioms:sgt=32_2997 on theBenchmark for (2997ds/325Mi)
% 2.53/1.30 % (885661)Refutation found. Thanks to Tanya!
% 2.53/1.30 % SZS status Theorem for theBenchmark
% 2.53/1.30 % SZS output start Proof for theBenchmark
% See solution above
% 3.67/1.49 % (885661)------------------------------
% 3.67/1.49 % (885661)Version: Vampire 5.0.1 (Release build, commit ea8961452 on 2026-07-16 15:14:34 +0200)
% 3.67/1.49 % (885661)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 3.67/1.49 % (885661)CaDiCaL version: 2.1.3
% 3.67/1.49 % (885661)Termination reason: Refutation
% 3.67/1.49 % (885661)Time elapsed: 0.008 s
% 3.67/1.49 % (885661)Peak memory usage: 89 MB
% 3.67/1.49 % (885661)Instructions burned: 9 (million)
% 3.67/1.49 % (885661)------------------------------
% 3.67/1.49 % (885661)------------------------------
% 3.67/1.49 % (885632)Success in time 0.439 s
% 3.67/1.49 % Vampire exiting
%------------------------------------------------------------------------------