TSTP Solution File: NUM427+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : NUM427+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 12:26:35 EDT 2022
% Result : Theorem 0.18s 0.36s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 32 ( 11 unt; 0 def)
% Number of atoms : 63 ( 29 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 62 ( 31 ~; 19 |; 9 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of predicates : 6 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 19 ( 0 sgn 6 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mIntNeg,axiom,
! [W0] :
( aInteger0(W0)
=> aInteger0(smndt0(W0)) ) ).
fof(m__747,hypothesis,
( aInteger0(xn)
& sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb)) ) ).
fof(m__767,hypothesis,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)) ).
fof(m__,conjecture,
( ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) )
| aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
| sdteqdtlpzmzozddtrp0(xb,xa,xq) ) ).
fof(subgoal_0,plain,
( ( ~ ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) )
& ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) )
=> sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ( ~ ? [W0] :
( aInteger0(W0)
& sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) )
& ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa))) )
=> sdteqdtlpzmzozddtrp0(xb,xa,xq) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( sdtasdt0(xq,xn) = sdtpldt0(xa,smndt0(xb))
& aInteger0(xn) ),
inference(canonicalize,[],[m__747]) ).
fof(normalize_0_1,plain,
aInteger0(xn),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [W0] :
( ~ aInteger0(W0)
| aInteger0(smndt0(W0)) ),
inference(canonicalize,[],[mIntNeg]) ).
fof(normalize_0_3,plain,
! [W0] :
( ~ aInteger0(W0)
| aInteger0(smndt0(W0)) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
( ~ aDivisorOf0(xq,sdtpldt0(xb,smndt0(xa)))
& ~ sdteqdtlpzmzozddtrp0(xb,xa,xq)
& ! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(W0) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(W0) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W0] :
( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(W0) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(canonicalize,[],[m__767]) ).
cnf(refute_0_0,plain,
aInteger0(xn),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ aInteger0(W0)
| aInteger0(smndt0(W0)) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ aInteger0(xn)
| aInteger0(smndt0(xn)) ),
inference(subst,[],[refute_0_1:[bind(W0,$fot(xn))]]) ).
cnf(refute_0_3,plain,
aInteger0(smndt0(xn)),
inference(resolve,[$cnf( aInteger0(xn) )],[refute_0_0,refute_0_2]) ).
cnf(refute_0_4,plain,
( sdtasdt0(xq,W0) != sdtpldt0(xb,smndt0(xa))
| ~ aInteger0(W0) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
sdtasdt0(xq,smndt0(xn)) = sdtpldt0(xb,smndt0(xa)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_7,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_8,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( sdtasdt0(xq,smndt0(xn)) != sdtpldt0(xb,smndt0(xa))
| sdtpldt0(xb,smndt0(xa)) = sdtasdt0(xq,smndt0(xn)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(sdtasdt0(xq,smndt0(xn)))),bind(Y,$fot(sdtpldt0(xb,smndt0(xa))))]]) ).
cnf(refute_0_10,plain,
sdtpldt0(xb,smndt0(xa)) = sdtasdt0(xq,smndt0(xn)),
inference(resolve,[$cnf( $equal(sdtasdt0(xq,smndt0(xn)),sdtpldt0(xb,smndt0(xa))) )],[refute_0_5,refute_0_9]) ).
cnf(refute_0_11,plain,
( sdtasdt0(xq,W0) != sdtasdt0(xq,smndt0(xn))
| sdtpldt0(xb,smndt0(xa)) != sdtasdt0(xq,smndt0(xn))
| sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ),
introduced(tautology,[equality,[$cnf( ~ $equal(sdtasdt0(xq,W0),sdtpldt0(xb,smndt0(xa))) ),[1],$fot(sdtasdt0(xq,smndt0(xn)))]]) ).
cnf(refute_0_12,plain,
( sdtasdt0(xq,W0) != sdtasdt0(xq,smndt0(xn))
| sdtasdt0(xq,W0) = sdtpldt0(xb,smndt0(xa)) ),
inference(resolve,[$cnf( $equal(sdtpldt0(xb,smndt0(xa)),sdtasdt0(xq,smndt0(xn))) )],[refute_0_10,refute_0_11]) ).
cnf(refute_0_13,plain,
( sdtasdt0(xq,W0) != sdtasdt0(xq,smndt0(xn))
| ~ aInteger0(W0) ),
inference(resolve,[$cnf( $equal(sdtasdt0(xq,W0),sdtpldt0(xb,smndt0(xa))) )],[refute_0_12,refute_0_4]) ).
cnf(refute_0_14,plain,
( sdtasdt0(xq,smndt0(xn)) != sdtasdt0(xq,smndt0(xn))
| ~ aInteger0(smndt0(xn)) ),
inference(subst,[],[refute_0_13:[bind(W0,$fot(smndt0(xn)))]]) ).
cnf(refute_0_15,plain,
sdtasdt0(xq,smndt0(xn)) = sdtasdt0(xq,smndt0(xn)),
introduced(tautology,[refl,[$fot(sdtasdt0(xq,smndt0(xn)))]]) ).
cnf(refute_0_16,plain,
~ aInteger0(smndt0(xn)),
inference(resolve,[$cnf( $equal(sdtasdt0(xq,smndt0(xn)),sdtasdt0(xq,smndt0(xn))) )],[refute_0_15,refute_0_14]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( aInteger0(smndt0(xn)) )],[refute_0_3,refute_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : NUM427+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n026.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Thu Jul 7 12:31:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.18/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.18/0.36
% 0.18/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.36
%------------------------------------------------------------------------------