TSTP Solution File: COM012+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COM012+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 : Fri Jul 15 01:32:30 EDT 2022
% Result : Theorem 0.15s 0.36s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 8
% Syntax : Number of formulae : 71 ( 19 unt; 1 def)
% Number of atoms : 252 ( 54 equ)
% Maximal formula atoms : 16 ( 3 avg)
% Number of connectives : 308 ( 127 ~; 151 |; 21 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 7 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 50 ( 0 sgn 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mTCTrans,axiom,
! [W0,W1,W2,W3] :
( ( aElement0(W0)
& aRewritingSystem0(W1)
& aElement0(W2)
& aElement0(W3) )
=> ( ( sdtmndtplgtdt0(W0,W1,W2)
& sdtmndtplgtdt0(W2,W1,W3) )
=> sdtmndtplgtdt0(W0,W1,W3) ) ) ).
fof(mTCRDef,definition,
! [W0,W1,W2] :
( ( aElement0(W0)
& aRewritingSystem0(W1)
& aElement0(W2) )
=> ( sdtmndtasgtdt0(W0,W1,W2)
<=> ( W0 = W2
| sdtmndtplgtdt0(W0,W1,W2) ) ) ) ).
fof(m__349,hypothesis,
( aElement0(xx)
& aRewritingSystem0(xR)
& aElement0(xy)
& aElement0(xz) ) ).
fof(m__,conjecture,
( ( sdtmndtasgtdt0(xx,xR,xy)
& sdtmndtasgtdt0(xy,xR,xz) )
=> sdtmndtasgtdt0(xx,xR,xz) ) ).
fof(subgoal_0,plain,
( ( sdtmndtasgtdt0(xx,xR,xy)
& sdtmndtasgtdt0(xy,xR,xz) )
=> sdtmndtasgtdt0(xx,xR,xz) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ( sdtmndtasgtdt0(xx,xR,xy)
& sdtmndtasgtdt0(xy,xR,xz) )
=> sdtmndtasgtdt0(xx,xR,xz) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( ~ sdtmndtasgtdt0(xx,xR,xz)
& sdtmndtasgtdt0(xx,xR,xy)
& sdtmndtasgtdt0(xy,xR,xz) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
sdtmndtasgtdt0(xy,xR,xz),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_3,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ( ~ sdtmndtasgtdt0(W0,W1,W2)
<=> ( W0 != W2
& ~ sdtmndtplgtdt0(W0,W1,W2) ) ) ),
inference(canonicalize,[],[mTCRDef]) ).
fof(normalize_0_4,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ( ~ sdtmndtasgtdt0(W0,W1,W2)
<=> ( W0 != W2
& ~ sdtmndtplgtdt0(W0,W1,W2) ) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [W0,W1,W2] :
( ( W0 != W2
| ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| sdtmndtasgtdt0(W0,W1,W2) )
& ( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| sdtmndtasgtdt0(W0,W1,W2) )
& ( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| W0 = W2
| sdtmndtplgtdt0(W0,W1,W2) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| sdtmndtasgtdt0(W0,W1,W2) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
sdtmndtasgtdt0(xx,xR,xy),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_8,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| W0 = W2
| sdtmndtplgtdt0(W0,W1,W2) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_9,plain,
( aElement0(xx)
& aElement0(xy)
& aElement0(xz)
& aRewritingSystem0(xR) ),
inference(canonicalize,[],[m__349]) ).
fof(normalize_0_10,plain,
aElement0(xx),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
aElement0(xy),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_12,plain,
aRewritingSystem0(xR),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_13,plain,
aElement0(xz),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_14,plain,
! [W0,W1,W2,W3] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aElement0(W3)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| ~ sdtmndtplgtdt0(W2,W1,W3)
| sdtmndtplgtdt0(W0,W1,W3) ),
inference(canonicalize,[],[mTCTrans]) ).
fof(normalize_0_15,plain,
! [W0,W1,W2,W3] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aElement0(W3)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| ~ sdtmndtplgtdt0(W2,W1,W3)
| sdtmndtplgtdt0(W0,W1,W3) ),
inference(specialize,[],[normalize_0_14]) ).
cnf(refute_0_0,plain,
sdtmndtasgtdt0(xy,xR,xz),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ sdtmndtasgtdt0(xx,xR,xz),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| sdtmndtasgtdt0(W0,W1,W2) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ aElement0(xx)
| ~ aElement0(xz)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtplgtdt0(xx,xR,xz)
| sdtmndtasgtdt0(xx,xR,xz) ),
inference(subst,[],[refute_0_2:[bind(W0,$fot(xx)),bind(W1,$fot(xR)),bind(W2,$fot(xz))]]) ).
cnf(refute_0_4,plain,
sdtmndtasgtdt0(xx,xR,xy),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| W0 = W2
| sdtmndtplgtdt0(W0,W1,W2) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_6,plain,
( ~ aElement0(xx)
| ~ aElement0(xy)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(xx,xR,xy)
| xx = xy
| sdtmndtplgtdt0(xx,xR,xy) ),
inference(subst,[],[refute_0_5:[bind(W0,$fot(xx)),bind(W1,$fot(xR)),bind(W2,$fot(xy))]]) ).
cnf(refute_0_7,plain,
( ~ aElement0(xx)
| ~ aElement0(xy)
| ~ aRewritingSystem0(xR)
| xx = xy
| sdtmndtplgtdt0(xx,xR,xy) ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xx,xR,xy) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
aElement0(xx),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( ~ aElement0(xy)
| ~ aRewritingSystem0(xR)
| xx = xy
| sdtmndtplgtdt0(xx,xR,xy) ),
inference(resolve,[$cnf( aElement0(xx) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
aElement0(xy),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_11,plain,
( ~ aRewritingSystem0(xR)
| xx = xy
| sdtmndtplgtdt0(xx,xR,xy) ),
inference(resolve,[$cnf( aElement0(xy) )],[refute_0_10,refute_0_9]) ).
cnf(refute_0_12,plain,
aRewritingSystem0(xR),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_13,plain,
( xx = xy
| sdtmndtplgtdt0(xx,xR,xy) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
( ~ aElement0(xy)
| ~ aElement0(xz)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(xy,xR,xz)
| xy = xz
| sdtmndtplgtdt0(xy,xR,xz) ),
inference(subst,[],[refute_0_5:[bind(W0,$fot(xy)),bind(W1,$fot(xR)),bind(W2,$fot(xz))]]) ).
cnf(refute_0_15,plain,
( ~ aElement0(xy)
| ~ aElement0(xz)
| ~ aRewritingSystem0(xR)
| xy = xz
| sdtmndtplgtdt0(xy,xR,xz) ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xy,xR,xz) )],[refute_0_0,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ aElement0(xz)
| ~ aRewritingSystem0(xR)
| xy = xz
| sdtmndtplgtdt0(xy,xR,xz) ),
inference(resolve,[$cnf( aElement0(xy) )],[refute_0_10,refute_0_15]) ).
cnf(refute_0_17,plain,
aElement0(xz),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_18,plain,
( ~ aRewritingSystem0(xR)
| xy = xz
| sdtmndtplgtdt0(xy,xR,xz) ),
inference(resolve,[$cnf( aElement0(xz) )],[refute_0_17,refute_0_16]) ).
cnf(refute_0_19,plain,
( xy = xz
| sdtmndtplgtdt0(xy,xR,xz) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_12,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aElement0(W3)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| ~ sdtmndtplgtdt0(W2,W1,W3)
| sdtmndtplgtdt0(W0,W1,W3) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_21,plain,
( ~ aElement0(X_40)
| ~ aElement0(xy)
| ~ aElement0(xz)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtplgtdt0(X_40,xR,xy)
| ~ sdtmndtplgtdt0(xy,xR,xz)
| sdtmndtplgtdt0(X_40,xR,xz) ),
inference(subst,[],[refute_0_20:[bind(W0,$fot(X_40)),bind(W1,$fot(xR)),bind(W2,$fot(xy)),bind(W3,$fot(xz))]]) ).
cnf(refute_0_22,plain,
( ~ aElement0(X_40)
| ~ aElement0(xy)
| ~ aElement0(xz)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtplgtdt0(X_40,xR,xy)
| xy = xz
| sdtmndtplgtdt0(X_40,xR,xz) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xy,xR,xz) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( ~ aElement0(X_40)
| ~ aElement0(xz)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtplgtdt0(X_40,xR,xy)
| xy = xz
| sdtmndtplgtdt0(X_40,xR,xz) ),
inference(resolve,[$cnf( aElement0(xy) )],[refute_0_10,refute_0_22]) ).
cnf(refute_0_24,plain,
( ~ aElement0(X_40)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtplgtdt0(X_40,xR,xy)
| xy = xz
| sdtmndtplgtdt0(X_40,xR,xz) ),
inference(resolve,[$cnf( aElement0(xz) )],[refute_0_17,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ aElement0(X_40)
| ~ sdtmndtplgtdt0(X_40,xR,xy)
| xy = xz
| sdtmndtplgtdt0(X_40,xR,xz) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_12,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ aElement0(xx)
| ~ sdtmndtplgtdt0(xx,xR,xy)
| xy = xz
| sdtmndtplgtdt0(xx,xR,xz) ),
inference(subst,[],[refute_0_25:[bind(X_40,$fot(xx))]]) ).
cnf(refute_0_27,plain,
( ~ aElement0(xx)
| xx = xy
| xy = xz
| sdtmndtplgtdt0(xx,xR,xz) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xx,xR,xy) )],[refute_0_13,refute_0_26]) ).
cnf(refute_0_28,plain,
( xx = xy
| xy = xz
| sdtmndtplgtdt0(xx,xR,xz) ),
inference(resolve,[$cnf( aElement0(xx) )],[refute_0_8,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ aElement0(xx)
| ~ aElement0(xz)
| ~ aRewritingSystem0(xR)
| xx = xy
| xy = xz
| sdtmndtasgtdt0(xx,xR,xz) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xx,xR,xz) )],[refute_0_28,refute_0_3]) ).
cnf(refute_0_30,plain,
( ~ aElement0(xz)
| ~ aRewritingSystem0(xR)
| xx = xy
| xy = xz
| sdtmndtasgtdt0(xx,xR,xz) ),
inference(resolve,[$cnf( aElement0(xx) )],[refute_0_8,refute_0_29]) ).
cnf(refute_0_31,plain,
( ~ aRewritingSystem0(xR)
| xx = xy
| xy = xz
| sdtmndtasgtdt0(xx,xR,xz) ),
inference(resolve,[$cnf( aElement0(xz) )],[refute_0_17,refute_0_30]) ).
cnf(refute_0_32,plain,
( xx = xy
| xy = xz
| sdtmndtasgtdt0(xx,xR,xz) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_12,refute_0_31]) ).
cnf(refute_0_33,plain,
( xx = xy
| xy = xz ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xx,xR,xz) )],[refute_0_32,refute_0_1]) ).
cnf(refute_0_34,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_35,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_36,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
( xy != xz
| xz = xy ),
inference(subst,[],[refute_0_36:[bind(X,$fot(xy)),bind(Y,$fot(xz))]]) ).
cnf(refute_0_38,plain,
( xx = xy
| xz = xy ),
inference(resolve,[$cnf( $equal(xy,xz) )],[refute_0_33,refute_0_37]) ).
cnf(refute_0_39,plain,
( xz != xy
| ~ sdtmndtasgtdt0(xx,xR,xy)
| sdtmndtasgtdt0(xx,xR,xz) ),
introduced(tautology,[equality,[$cnf( ~ sdtmndtasgtdt0(xx,xR,xz) ),[2],$fot(xy)]]) ).
cnf(refute_0_40,plain,
( ~ sdtmndtasgtdt0(xx,xR,xy)
| xx = xy
| sdtmndtasgtdt0(xx,xR,xz) ),
inference(resolve,[$cnf( $equal(xz,xy) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ sdtmndtasgtdt0(xx,xR,xy)
| xx = xy ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xx,xR,xz) )],[refute_0_40,refute_0_1]) ).
cnf(refute_0_42,plain,
xx = xy,
inference(resolve,[$cnf( sdtmndtasgtdt0(xx,xR,xy) )],[refute_0_4,refute_0_41]) ).
cnf(refute_0_43,plain,
( xx != xy
| xy = xx ),
inference(subst,[],[refute_0_36:[bind(X,$fot(xx)),bind(Y,$fot(xy))]]) ).
cnf(refute_0_44,plain,
xy = xx,
inference(resolve,[$cnf( $equal(xx,xy) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( xy != xx
| ~ sdtmndtasgtdt0(xy,xR,xz)
| sdtmndtasgtdt0(xx,xR,xz) ),
introduced(tautology,[equality,[$cnf( sdtmndtasgtdt0(xy,xR,xz) ),[0],$fot(xx)]]) ).
cnf(refute_0_46,plain,
( ~ sdtmndtasgtdt0(xy,xR,xz)
| sdtmndtasgtdt0(xx,xR,xz) ),
inference(resolve,[$cnf( $equal(xy,xx) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
sdtmndtasgtdt0(xx,xR,xz),
inference(resolve,[$cnf( sdtmndtasgtdt0(xy,xR,xz) )],[refute_0_0,refute_0_46]) ).
cnf(refute_0_48,plain,
$false,
inference(resolve,[$cnf( sdtmndtasgtdt0(xx,xR,xz) )],[refute_0_47,refute_0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : COM012+1 : TPTP v8.1.0. Released v4.0.0.
% 0.09/0.10 % Command : metis --show proof --show saturation %s
% 0.10/0.30 % Computer : n032.cluster.edu
% 0.10/0.30 % Model : x86_64 x86_64
% 0.10/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30 % Memory : 8042.1875MB
% 0.10/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30 % CPULimit : 300
% 0.10/0.30 % WCLimit : 600
% 0.10/0.30 % DateTime : Thu Jun 16 19:40:00 EDT 2022
% 0.10/0.30 % CPUTime :
% 0.10/0.30 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.15/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.15/0.36
% 0.15/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.15/0.36
%------------------------------------------------------------------------------