TSTP Solution File: NUM423+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM423+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %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 : 600s
% DateTime : Mon Jul 18 12:26:33 EDT 2022
% Result : Theorem 2.92s 3.08s
% Output : CNFRefutation 2.92s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 42 ( 12 unt; 0 def)
% Number of atoms : 94 ( 47 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 96 ( 44 ~; 29 |; 19 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 22 ( 0 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mIntZero,axiom,
aInteger0(sz00) ).
fof(mAddNeg,axiom,
! [W0] :
( aInteger0(W0)
=> ( sdtpldt0(W0,smndt0(W0)) = sz00
& sz00 = sdtpldt0(smndt0(W0),W0) ) ) ).
fof(mMulZero,axiom,
! [W0] :
( aInteger0(W0)
=> ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ) ).
fof(m__671,hypothesis,
( aInteger0(xa)
& aInteger0(xq)
& xq != sz00 ) ).
fof(m__,conjecture,
( ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xa,xa,xq) ) ).
fof(subgoal_0,plain,
( ( ~ ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) )
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) )
=> sdteqdtlpzmzozddtrp0(xa,xa,xq) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ( ~ ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) )
& ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa))) )
=> sdteqdtlpzmzozddtrp0(xa,xa,xq) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xa,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(xa,xa,xq)
& ! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa))
| ~ aInteger0(W0) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa))
| ~ aInteger0(W0) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa))
| ~ aInteger0(W0) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
( xq != sz00
& aInteger0(xa)
& aInteger0(xq) ),
inference(canonicalize,[],[m__671]) ).
fof(normalize_0_4,plain,
aInteger0(xa),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [W0] :
( ~ aInteger0(W0)
| ( sdtpldt0(W0,smndt0(W0)) = sz00
& sz00 = sdtpldt0(smndt0(W0),W0) ) ),
inference(canonicalize,[],[mAddNeg]) ).
fof(normalize_0_6,plain,
! [W0] :
( ~ aInteger0(W0)
| ( sdtpldt0(W0,smndt0(W0)) = sz00
& sz00 = sdtpldt0(smndt0(W0),W0) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [W0] :
( ( ~ aInteger0(W0)
| sdtpldt0(W0,smndt0(W0)) = sz00 )
& ( ~ aInteger0(W0)
| sz00 = sdtpldt0(smndt0(W0),W0) ) ),
inference(clausify,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [W0] :
( ~ aInteger0(W0)
| sdtpldt0(W0,smndt0(W0)) = sz00 ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
aInteger0(xq),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_10,plain,
! [W0] :
( ~ aInteger0(W0)
| ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ),
inference(canonicalize,[],[mMulZero]) ).
fof(normalize_0_11,plain,
! [W0] :
( ~ aInteger0(W0)
| ( sdtasdt0(W0,sz00) = sz00
& sz00 = sdtasdt0(sz00,W0) ) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [W0] :
( ( ~ aInteger0(W0)
| sdtasdt0(W0,sz00) = sz00 )
& ( ~ aInteger0(W0)
| sz00 = sdtasdt0(sz00,W0) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [W0] :
( ~ aInteger0(W0)
| sdtasdt0(W0,sz00) = sz00 ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
aInteger0(sz00),
inference(canonicalize,[],[mIntZero]) ).
cnf(refute_0_0,plain,
( sdtasdt0(xq,W0) != sdtpldt0(xa,smndt0(xa))
| ~ aInteger0(W0) ),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
aInteger0(xa),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_2,plain,
( ~ aInteger0(W0)
| sdtpldt0(W0,smndt0(W0)) = sz00 ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_3,plain,
( ~ aInteger0(xa)
| sdtpldt0(xa,smndt0(xa)) = sz00 ),
inference(subst,[],[refute_0_2:[bind(W0,$fot(xa))]]) ).
cnf(refute_0_4,plain,
sdtpldt0(xa,smndt0(xa)) = sz00,
inference(resolve,[$cnf( aInteger0(xa) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( sdtasdt0(xq,W0) != sz00
| sdtpldt0(xa,smndt0(xa)) != sz00
| sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(sdtasdt0(xq,W0),sdtpldt0(xa,smndt0(xa))) ),[1],$fot(sz00)]]) ).
cnf(refute_0_6,plain,
( sdtasdt0(xq,W0) != sz00
| sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xa)) ),
inference(resolve,[$cnf( $equal(sdtpldt0(xa,smndt0(xa)),sz00) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
( sdtasdt0(xq,W0) != sz00
| ~ aInteger0(W0) ),
inference(resolve,[$cnf( $equal(sdtasdt0(xq,W0),sdtpldt0(xa,smndt0(xa))) )],[refute_0_6,refute_0_0]) ).
cnf(refute_0_8,plain,
( sdtasdt0(xq,sz00) != sz00
| ~ aInteger0(sz00) ),
inference(subst,[],[refute_0_7:[bind(W0,$fot(sz00))]]) ).
cnf(refute_0_9,plain,
aInteger0(xq),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_10,plain,
( ~ aInteger0(W0)
| sdtasdt0(W0,sz00) = sz00 ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_11,plain,
( ~ aInteger0(xq)
| sdtasdt0(xq,sz00) = sz00 ),
inference(subst,[],[refute_0_10:[bind(W0,$fot(xq))]]) ).
cnf(refute_0_12,plain,
sdtasdt0(xq,sz00) = sz00,
inference(resolve,[$cnf( aInteger0(xq) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( sdtasdt0(xq,sz00) != sz00
| sz00 != sz00
| sdtasdt0(xq,sz00) = sz00 ),
introduced(tautology,[equality,[$cnf( ~ $equal(sdtasdt0(xq,sz00),sz00) ),[0],$fot(sz00)]]) ).
cnf(refute_0_14,plain,
( sz00 != sz00
| sdtasdt0(xq,sz00) = sz00 ),
inference(resolve,[$cnf( $equal(sdtasdt0(xq,sz00),sz00) )],[refute_0_12,refute_0_13]) ).
cnf(refute_0_15,plain,
( sz00 != sz00
| ~ aInteger0(sz00) ),
inference(resolve,[$cnf( $equal(sdtasdt0(xq,sz00),sz00) )],[refute_0_14,refute_0_8]) ).
cnf(refute_0_16,plain,
sz00 = sz00,
introduced(tautology,[refl,[$fot(sz00)]]) ).
cnf(refute_0_17,plain,
~ aInteger0(sz00),
inference(resolve,[$cnf( $equal(sz00,sz00) )],[refute_0_16,refute_0_15]) ).
cnf(refute_0_18,plain,
aInteger0(sz00),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_19,plain,
$false,
inference(resolve,[$cnf( aInteger0(sz00) )],[refute_0_18,refute_0_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : NUM423+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n015.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Tue Jul 5 18:46:33 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 2.92/3.08 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 2.92/3.08
% 2.92/3.08 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 2.92/3.08
%------------------------------------------------------------------------------