TSTP Solution File: NUM430+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM430+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 12:26:37 EDT 2022
% Result : Theorem 0.20s 0.37s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 26 ( 9 unt; 0 def)
% Number of atoms : 57 ( 31 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 50 ( 19 ~; 12 |; 19 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 2 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__853,hypothesis,
( ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb)) )
& aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) )
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& sdteqdtlpzmzozddtrp0(xb,xc,xq) ) ).
fof(m__,conjecture,
? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ) ).
fof(subgoal_0,plain,
? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xc))
| ~ aInteger0(W0) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xc))
| ~ aInteger0(W0) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( aDivisorOf0(xq,sdtpldt0(xa,smndt0(xb)))
& aDivisorOf0(xq,sdtpldt0(xb,smndt0(xc)))
& sdteqdtlpzmzozddtrp0(xa,xb,xq)
& sdteqdtlpzmzozddtrp0(xb,xc,xq)
& ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xa,smndt0(xb))
& aInteger0(W0) )
& ? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc))
& aInteger0(W0) ) ),
inference(canonicalize,[],[m__853]) ).
fof(normalize_0_3,plain,
? [W0] :
( sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc))
& aInteger0(W0) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
( sdtasdt0(xq,skolemFOFtoCNF_W0_1) = sdtpldt0(xb,smndt0(xc))
& aInteger0(skolemFOFtoCNF_W0_1) ),
inference(skolemize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
sdtasdt0(xq,skolemFOFtoCNF_W0_1) = sdtpldt0(xb,smndt0(xc)),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
aInteger0(skolemFOFtoCNF_W0_1),
inference(conjunct,[],[normalize_0_4]) ).
cnf(refute_0_0,plain,
( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xc))
| ~ aInteger0(W0) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
sdtasdt0(xq,skolemFOFtoCNF_W0_1) = sdtpldt0(xb,smndt0(xc)),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_2,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_3,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_4,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_2,refute_0_3]) ).
cnf(refute_0_5,plain,
( sdtasdt0(xq,skolemFOFtoCNF_W0_1) != sdtpldt0(xb,smndt0(xc))
| sdtpldt0(xb,smndt0(xc)) = sdtasdt0(xq,skolemFOFtoCNF_W0_1) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(sdtasdt0(xq,skolemFOFtoCNF_W0_1))),bind(Y,$fot(sdtpldt0(xb,smndt0(xc))))]]) ).
cnf(refute_0_6,plain,
sdtpldt0(xb,smndt0(xc)) = sdtasdt0(xq,skolemFOFtoCNF_W0_1),
inference(resolve,[$cnf( $equal(sdtasdt0(xq,skolemFOFtoCNF_W0_1),sdtpldt0(xb,smndt0(xc))) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
( sdtasdt0(xq,W0) != sdtasdt0(xq,skolemFOFtoCNF_W0_1)
| sdtpldt0(xb,smndt0(xc)) != sdtasdt0(xq,skolemFOFtoCNF_W0_1)
| sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(sdtasdt0(xq,W0),sdtpldt0(xb,smndt0(xc))) ),[1],$fot(sdtasdt0(xq,skolemFOFtoCNF_W0_1))]]) ).
cnf(refute_0_8,plain,
( sdtasdt0(xq,W0) != sdtasdt0(xq,skolemFOFtoCNF_W0_1)
| sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xc)) ),
inference(resolve,[$cnf( $equal(sdtpldt0(xb,smndt0(xc)),sdtasdt0(xq,skolemFOFtoCNF_W0_1)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( sdtasdt0(xq,W0) != sdtasdt0(xq,skolemFOFtoCNF_W0_1)
| ~ aInteger0(W0) ),
inference(resolve,[$cnf( $equal(sdtasdt0(xq,W0),sdtpldt0(xb,smndt0(xc))) )],[refute_0_8,refute_0_0]) ).
cnf(refute_0_10,plain,
( sdtasdt0(xq,skolemFOFtoCNF_W0_1) != sdtasdt0(xq,skolemFOFtoCNF_W0_1)
| ~ aInteger0(skolemFOFtoCNF_W0_1) ),
inference(subst,[],[refute_0_9:[bind(W0,$fot(skolemFOFtoCNF_W0_1))]]) ).
cnf(refute_0_11,plain,
sdtasdt0(xq,skolemFOFtoCNF_W0_1) = sdtasdt0(xq,skolemFOFtoCNF_W0_1),
introduced(tautology,[refl,[$fot(sdtasdt0(xq,skolemFOFtoCNF_W0_1))]]) ).
cnf(refute_0_12,plain,
~ aInteger0(skolemFOFtoCNF_W0_1),
inference(resolve,[$cnf( $equal(sdtasdt0(xq,skolemFOFtoCNF_W0_1),sdtasdt0(xq,skolemFOFtoCNF_W0_1)) )],[refute_0_11,refute_0_10]) ).
cnf(refute_0_13,plain,
aInteger0(skolemFOFtoCNF_W0_1),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_14,plain,
$false,
inference(resolve,[$cnf( aInteger0(skolemFOFtoCNF_W0_1) )],[refute_0_13,refute_0_12]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM430+3 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n003.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.20/0.34 % CPULimit : 300
% 0.20/0.34 % WCLimit : 600
% 0.20/0.34 % DateTime : Tue Jul 5 22:23:26 EDT 2022
% 0.20/0.34 % CPUTime :
% 0.20/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.37
% 0.20/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.38
%------------------------------------------------------------------------------