TSTP Solution File: COM022+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COM022+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n029.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 01:32:35 EDT 2022
% Result : Theorem 1.48s 1.66s
% Output : CNFRefutation 1.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 27
% Number of leaves : 10
% Syntax : Number of formulae : 102 ( 22 unt; 2 def)
% Number of atoms : 435 ( 66 equ)
% Maximal formula atoms : 36 ( 4 avg)
% Number of connectives : 534 ( 201 ~; 219 |; 99 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 88 ( 0 sgn 37 !; 26 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mTCRDef,definition,
! [W0,W1,W2] :
( ( aElement0(W0)
& aRewritingSystem0(W1)
& aElement0(W2) )
=> ( sdtmndtasgtdt0(W0,W1,W2)
<=> ( W0 = W2
| sdtmndtplgtdt0(W0,W1,W2) ) ) ) ).
fof(mNFRDef,definition,
! [W0,W1] :
( ( aElement0(W0)
& aRewritingSystem0(W1) )
=> ! [W2] :
( aNormalFormOfIn0(W2,W0,W1)
<=> ( aElement0(W2)
& sdtmndtasgtdt0(W0,W1,W2)
& ~ ? [W3] : aReductOfIn0(W3,W2,W1) ) ) ) ).
fof(m__656,hypothesis,
aRewritingSystem0(xR) ).
fof(m__731,hypothesis,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ) ).
fof(m__,conjecture,
( ( ( sdtmndtplgtdt0(xa,xR,xb)
& sdtmndtplgtdt0(xa,xR,xc) )
=> ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtasgtdt0(W0,xR,xb)
& ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xa,xR)
& sdtmndtasgtdt0(W1,xR,xc)
& ? [W2] :
( aElement0(W2)
& sdtmndtasgtdt0(W0,xR,W2)
& sdtmndtasgtdt0(W1,xR,W2)
& ? [W3] :
( aNormalFormOfIn0(W3,W2,xR)
& sdtmndtasgtdt0(xb,xR,W3)
& sdtmndtasgtdt0(xc,xR,W3) ) ) ) ) )
=> ( ( sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc) )
=> ? [W0] :
( aElement0(W0)
& sdtmndtasgtdt0(xb,xR,W0)
& sdtmndtasgtdt0(xc,xR,W0) ) ) ) ).
fof(subgoal_0,plain,
( ( ( ( sdtmndtplgtdt0(xa,xR,xb)
& sdtmndtplgtdt0(xa,xR,xc) )
=> ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtasgtdt0(W0,xR,xb)
& ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xa,xR)
& sdtmndtasgtdt0(W1,xR,xc)
& ? [W2] :
( aElement0(W2)
& sdtmndtasgtdt0(W0,xR,W2)
& sdtmndtasgtdt0(W1,xR,W2)
& ? [W3] :
( aNormalFormOfIn0(W3,W2,xR)
& sdtmndtasgtdt0(xb,xR,W3)
& sdtmndtasgtdt0(xc,xR,W3) ) ) ) ) )
& sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc) )
=> ? [W0] :
( aElement0(W0)
& sdtmndtasgtdt0(xb,xR,W0)
& sdtmndtasgtdt0(xc,xR,W0) ) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ( ( ( sdtmndtplgtdt0(xa,xR,xb)
& sdtmndtplgtdt0(xa,xR,xc) )
=> ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtasgtdt0(W0,xR,xb)
& ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xa,xR)
& sdtmndtasgtdt0(W1,xR,xc)
& ? [W2] :
( aElement0(W2)
& sdtmndtasgtdt0(W0,xR,W2)
& sdtmndtasgtdt0(W1,xR,W2)
& ? [W3] :
( aNormalFormOfIn0(W3,W2,xR)
& sdtmndtasgtdt0(xb,xR,W3)
& sdtmndtasgtdt0(xc,xR,W3) ) ) ) ) )
& sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc) )
=> ? [W0] :
( aElement0(W0)
& sdtmndtasgtdt0(xb,xR,W0)
& sdtmndtasgtdt0(xc,xR,W0) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
inference(canonicalize,[],[m__731]) ).
fof(normalize_0_1,plain,
aElement0(xc),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
aRewritingSystem0(xR),
inference(canonicalize,[],[m__656]) ).
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] :
( W0 != W2
| ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| sdtmndtasgtdt0(W0,W1,W2) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc)
& ( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtasgtdt0(W0,xR,xb)
& ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xa,xR)
& sdtmndtasgtdt0(W1,xR,xc)
& ? [W2] :
( aElement0(W2)
& sdtmndtasgtdt0(W0,xR,W2)
& sdtmndtasgtdt0(W1,xR,W2)
& ? [W3] :
( aNormalFormOfIn0(W3,W2,xR)
& sdtmndtasgtdt0(xb,xR,W3)
& sdtmndtasgtdt0(xc,xR,W3) ) ) ) ) )
& ! [W0] :
( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xb,xR,W0)
| ~ sdtmndtasgtdt0(xc,xR,W0) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_8,plain,
! [W0] :
( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xb,xR,W0)
| ~ sdtmndtasgtdt0(xc,xR,W0) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [W0] :
( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xb,xR,W0)
| ~ sdtmndtasgtdt0(xc,xR,W0) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
aElement0(xb),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_11,plain,
sdtmndtasgtdt0(xa,xR,xb),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_12,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_13,plain,
aElement0(xa),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_14,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtasgtdt0(W0,xR,xb)
& ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xa,xR)
& sdtmndtasgtdt0(W1,xR,xc)
& ? [W2] :
( aElement0(W2)
& sdtmndtasgtdt0(W0,xR,W2)
& sdtmndtasgtdt0(W1,xR,W2)
& ? [W3] :
( aNormalFormOfIn0(W3,W2,xR)
& sdtmndtasgtdt0(xb,xR,W3)
& sdtmndtasgtdt0(xc,xR,W3) ) ) ) ) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_15,plain,
( ( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| aElement0(skolemFOFtoCNF_W0) )
& ( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| aElement0(skolemFOFtoCNF_W1_3) )
& ( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| aElement0(skolemFOFtoCNF_W2_4) )
& ( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| aNormalFormOfIn0(skolemFOFtoCNF_W3_5,skolemFOFtoCNF_W2_4,xR) )
& ( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| aReductOfIn0(skolemFOFtoCNF_W0,xa,xR) )
& ( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| aReductOfIn0(skolemFOFtoCNF_W1_3,xa,xR) )
& ( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W2_4) )
& ( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,xb) )
& ( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| sdtmndtasgtdt0(skolemFOFtoCNF_W1_3,xR,skolemFOFtoCNF_W2_4) )
& ( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| sdtmndtasgtdt0(skolemFOFtoCNF_W1_3,xR,xc) )
& ( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| sdtmndtasgtdt0(xb,xR,skolemFOFtoCNF_W3_5) )
& ( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| sdtmndtasgtdt0(xc,xR,skolemFOFtoCNF_W3_5) ) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| aElement0(skolemFOFtoCNF_W2_4) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
sdtmndtasgtdt0(xa,xR,xc),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_18,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aRewritingSystem0(W1)
| ! [W2] :
( ~ aNormalFormOfIn0(W2,W0,W1)
<=> ( ~ aElement0(W2)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| ? [W3] : aReductOfIn0(W3,W2,W1) ) ) ),
inference(canonicalize,[],[mNFRDef]) ).
fof(normalize_0_19,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aRewritingSystem0(W1)
| ! [W2] :
( ~ aNormalFormOfIn0(W2,W0,W1)
<=> ( ~ aElement0(W2)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| ? [W3] : aReductOfIn0(W3,W2,W1) ) ) ),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [W0,W1,W2,W3] :
( ( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aReductOfIn0(W3,W2,W1)
| ~ aRewritingSystem0(W1) )
& ( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| aElement0(W2) )
& ( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| sdtmndtasgtdt0(W0,W1,W2) )
& ( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| aNormalFormOfIn0(W2,W0,W1)
| aReductOfIn0(skolemFOFtoCNF_W3_3(W1,W2),W2,W1) ) ),
inference(clausify,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| aElement0(W2) ),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| aNormalFormOfIn0(skolemFOFtoCNF_W3_5,skolemFOFtoCNF_W2_4,xR) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_23,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| sdtmndtasgtdt0(xb,xR,skolemFOFtoCNF_W3_5) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_24,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| sdtmndtasgtdt0(xc,xR,skolemFOFtoCNF_W3_5) ),
inference(conjunct,[],[normalize_0_15]) ).
cnf(refute_0_0,plain,
aElement0(xc),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
aRewritingSystem0(xR),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
( W0 != W2
| ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| sdtmndtasgtdt0(W0,W1,W2) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( W2 != W2
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| sdtmndtasgtdt0(W2,W1,W2) ),
inference(subst,[],[refute_0_2:[bind(W0,$fot(W2))]]) ).
cnf(refute_0_4,plain,
W2 = W2,
introduced(tautology,[refl,[$fot(W2)]]) ).
cnf(refute_0_5,plain,
( ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| sdtmndtasgtdt0(W2,W1,W2) ),
inference(resolve,[$cnf( $equal(W2,W2) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ aElement0(X_10)
| ~ aRewritingSystem0(xR)
| sdtmndtasgtdt0(X_10,xR,X_10) ),
inference(subst,[],[refute_0_5:[bind(W1,$fot(xR)),bind(W2,$fot(X_10))]]) ).
cnf(refute_0_7,plain,
( ~ aElement0(X_10)
| sdtmndtasgtdt0(X_10,xR,X_10) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_1,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ aElement0(xc)
| sdtmndtasgtdt0(xc,xR,xc) ),
inference(subst,[],[refute_0_7:[bind(X_10,$fot(xc))]]) ).
cnf(refute_0_9,plain,
sdtmndtasgtdt0(xc,xR,xc),
inference(resolve,[$cnf( aElement0(xc) )],[refute_0_0,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xb,xR,W0)
| ~ sdtmndtasgtdt0(xc,xR,W0) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_11,plain,
( ~ aElement0(xc)
| ~ sdtmndtasgtdt0(xb,xR,xc)
| ~ sdtmndtasgtdt0(xc,xR,xc) ),
inference(subst,[],[refute_0_10:[bind(W0,$fot(xc))]]) ).
cnf(refute_0_12,plain,
( ~ aElement0(xc)
| ~ sdtmndtasgtdt0(xb,xR,xc) ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xc,xR,xc) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
~ sdtmndtasgtdt0(xb,xR,xc),
inference(resolve,[$cnf( aElement0(xc) )],[refute_0_0,refute_0_12]) ).
cnf(refute_0_14,plain,
aElement0(xb),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_15,plain,
( ~ aElement0(xb)
| sdtmndtasgtdt0(xb,xR,xb) ),
inference(subst,[],[refute_0_7:[bind(X_10,$fot(xb))]]) ).
cnf(refute_0_16,plain,
sdtmndtasgtdt0(xb,xR,xb),
inference(resolve,[$cnf( aElement0(xb) )],[refute_0_14,refute_0_15]) ).
cnf(refute_0_17,plain,
sdtmndtasgtdt0(xa,xR,xb),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_18,plain,
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| W0 = W2
| sdtmndtplgtdt0(W0,W1,W2) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_19,plain,
( ~ aElement0(xa)
| ~ aElement0(xb)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(xa,xR,xb)
| xa = xb
| sdtmndtplgtdt0(xa,xR,xb) ),
inference(subst,[],[refute_0_18:[bind(W0,$fot(xa)),bind(W1,$fot(xR)),bind(W2,$fot(xb))]]) ).
cnf(refute_0_20,plain,
( ~ aElement0(xa)
| ~ aElement0(xb)
| ~ aRewritingSystem0(xR)
| xa = xb
| sdtmndtplgtdt0(xa,xR,xb) ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xa,xR,xb) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
aElement0(xa),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_22,plain,
( ~ aElement0(xb)
| ~ aRewritingSystem0(xR)
| xa = xb
| sdtmndtplgtdt0(xa,xR,xb) ),
inference(resolve,[$cnf( aElement0(xa) )],[refute_0_21,refute_0_20]) ).
cnf(refute_0_23,plain,
( ~ aRewritingSystem0(xR)
| xa = xb
| sdtmndtplgtdt0(xa,xR,xb) ),
inference(resolve,[$cnf( aElement0(xb) )],[refute_0_14,refute_0_22]) ).
cnf(refute_0_24,plain,
( xa = xb
| sdtmndtplgtdt0(xa,xR,xb) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_1,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| aElement0(skolemFOFtoCNF_W2_4) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_26,plain,
sdtmndtasgtdt0(xa,xR,xc),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_27,plain,
( ~ aElement0(xa)
| ~ aElement0(xc)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(xa,xR,xc)
| xa = xc
| sdtmndtplgtdt0(xa,xR,xc) ),
inference(subst,[],[refute_0_18:[bind(W0,$fot(xa)),bind(W1,$fot(xR)),bind(W2,$fot(xc))]]) ).
cnf(refute_0_28,plain,
( ~ aElement0(xa)
| ~ aElement0(xc)
| ~ aRewritingSystem0(xR)
| xa = xc
| sdtmndtplgtdt0(xa,xR,xc) ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xa,xR,xc) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ aElement0(xc)
| ~ aRewritingSystem0(xR)
| xa = xc
| sdtmndtplgtdt0(xa,xR,xc) ),
inference(resolve,[$cnf( aElement0(xa) )],[refute_0_21,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ aRewritingSystem0(xR)
| xa = xc
| sdtmndtplgtdt0(xa,xR,xc) ),
inference(resolve,[$cnf( aElement0(xc) )],[refute_0_0,refute_0_29]) ).
cnf(refute_0_31,plain,
( xa = xc
| sdtmndtplgtdt0(xa,xR,xc) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_1,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| xa = xc
| aElement0(skolemFOFtoCNF_W2_4) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xa,xR,xc) )],[refute_0_31,refute_0_25]) ).
cnf(refute_0_33,plain,
( xa = xb
| xa = xc
| aElement0(skolemFOFtoCNF_W2_4) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xa,xR,xb) )],[refute_0_24,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| aElement0(W2) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_35,plain,
( ~ aElement0(skolemFOFtoCNF_W2_4)
| ~ aNormalFormOfIn0(skolemFOFtoCNF_W3_5,skolemFOFtoCNF_W2_4,xR)
| ~ aRewritingSystem0(xR)
| aElement0(skolemFOFtoCNF_W3_5) ),
inference(subst,[],[refute_0_34:[bind(W0,$fot(skolemFOFtoCNF_W2_4)),bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W3_5))]]) ).
cnf(refute_0_36,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| aNormalFormOfIn0(skolemFOFtoCNF_W3_5,skolemFOFtoCNF_W2_4,xR) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_37,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| xa = xc
| aNormalFormOfIn0(skolemFOFtoCNF_W3_5,skolemFOFtoCNF_W2_4,xR) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xa,xR,xc) )],[refute_0_31,refute_0_36]) ).
cnf(refute_0_38,plain,
( xa = xb
| xa = xc
| aNormalFormOfIn0(skolemFOFtoCNF_W3_5,skolemFOFtoCNF_W2_4,xR) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xa,xR,xb) )],[refute_0_24,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ aElement0(skolemFOFtoCNF_W2_4)
| ~ aRewritingSystem0(xR)
| xa = xb
| xa = xc
| aElement0(skolemFOFtoCNF_W3_5) ),
inference(resolve,[$cnf( aNormalFormOfIn0(skolemFOFtoCNF_W3_5,skolemFOFtoCNF_W2_4,xR) )],[refute_0_38,refute_0_35]) ).
cnf(refute_0_40,plain,
( ~ aElement0(skolemFOFtoCNF_W2_4)
| xa = xb
| xa = xc
| aElement0(skolemFOFtoCNF_W3_5) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_1,refute_0_39]) ).
cnf(refute_0_41,plain,
( xa = xb
| xa = xc
| aElement0(skolemFOFtoCNF_W3_5) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W2_4) )],[refute_0_33,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| sdtmndtasgtdt0(xb,xR,skolemFOFtoCNF_W3_5) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_43,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| xa = xc
| sdtmndtasgtdt0(xb,xR,skolemFOFtoCNF_W3_5) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xa,xR,xc) )],[refute_0_31,refute_0_42]) ).
cnf(refute_0_44,plain,
( xa = xb
| xa = xc
| sdtmndtasgtdt0(xb,xR,skolemFOFtoCNF_W3_5) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xa,xR,xb) )],[refute_0_24,refute_0_43]) ).
cnf(refute_0_45,plain,
( ~ aElement0(skolemFOFtoCNF_W3_5)
| ~ sdtmndtasgtdt0(xb,xR,skolemFOFtoCNF_W3_5)
| ~ sdtmndtasgtdt0(xc,xR,skolemFOFtoCNF_W3_5) ),
inference(subst,[],[refute_0_10:[bind(W0,$fot(skolemFOFtoCNF_W3_5))]]) ).
cnf(refute_0_46,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc)
| sdtmndtasgtdt0(xc,xR,skolemFOFtoCNF_W3_5) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_47,plain,
( ~ sdtmndtplgtdt0(xa,xR,xb)
| xa = xc
| sdtmndtasgtdt0(xc,xR,skolemFOFtoCNF_W3_5) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xa,xR,xc) )],[refute_0_31,refute_0_46]) ).
cnf(refute_0_48,plain,
( xa = xb
| xa = xc
| sdtmndtasgtdt0(xc,xR,skolemFOFtoCNF_W3_5) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xa,xR,xb) )],[refute_0_24,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ aElement0(skolemFOFtoCNF_W3_5)
| ~ sdtmndtasgtdt0(xb,xR,skolemFOFtoCNF_W3_5)
| xa = xb
| xa = xc ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xc,xR,skolemFOFtoCNF_W3_5) )],[refute_0_48,refute_0_45]) ).
cnf(refute_0_50,plain,
( ~ aElement0(skolemFOFtoCNF_W3_5)
| xa = xb
| xa = xc ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xb,xR,skolemFOFtoCNF_W3_5) )],[refute_0_44,refute_0_49]) ).
cnf(refute_0_51,plain,
( xa = xb
| xa = xc ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W3_5) )],[refute_0_41,refute_0_50]) ).
cnf(refute_0_52,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_53,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_54,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_52,refute_0_53]) ).
cnf(refute_0_55,plain,
( xa != xc
| xc = xa ),
inference(subst,[],[refute_0_54:[bind(X,$fot(xa)),bind(Y,$fot(xc))]]) ).
cnf(refute_0_56,plain,
( xa = xb
| xc = xa ),
inference(resolve,[$cnf( $equal(xa,xc) )],[refute_0_51,refute_0_55]) ).
cnf(refute_0_57,plain,
( xc != xa
| ~ sdtmndtasgtdt0(xa,xR,W0)
| sdtmndtasgtdt0(xc,xR,W0) ),
introduced(tautology,[equality,[$cnf( ~ sdtmndtasgtdt0(xc,xR,W0) ),[0],$fot(xa)]]) ).
cnf(refute_0_58,plain,
( ~ sdtmndtasgtdt0(xa,xR,W0)
| xa = xb
| sdtmndtasgtdt0(xc,xR,W0) ),
inference(resolve,[$cnf( $equal(xc,xa) )],[refute_0_56,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xa,xR,W0)
| ~ sdtmndtasgtdt0(xb,xR,W0)
| xa = xb ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xc,xR,W0) )],[refute_0_58,refute_0_10]) ).
cnf(refute_0_60,plain,
( ~ aElement0(xb)
| ~ sdtmndtasgtdt0(xa,xR,xb)
| ~ sdtmndtasgtdt0(xb,xR,xb)
| xa = xb ),
inference(subst,[],[refute_0_59:[bind(W0,$fot(xb))]]) ).
cnf(refute_0_61,plain,
( ~ aElement0(xb)
| ~ sdtmndtasgtdt0(xa,xR,xb)
| xa = xb ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xb,xR,xb) )],[refute_0_16,refute_0_60]) ).
cnf(refute_0_62,plain,
( ~ sdtmndtasgtdt0(xa,xR,xb)
| xa = xb ),
inference(resolve,[$cnf( aElement0(xb) )],[refute_0_14,refute_0_61]) ).
cnf(refute_0_63,plain,
xa = xb,
inference(resolve,[$cnf( sdtmndtasgtdt0(xa,xR,xb) )],[refute_0_17,refute_0_62]) ).
cnf(refute_0_64,plain,
( xa != xb
| xb = xa ),
inference(subst,[],[refute_0_54:[bind(X,$fot(xa)),bind(Y,$fot(xb))]]) ).
cnf(refute_0_65,plain,
xb = xa,
inference(resolve,[$cnf( $equal(xa,xb) )],[refute_0_63,refute_0_64]) ).
cnf(refute_0_66,plain,
( xb != xa
| ~ sdtmndtasgtdt0(xa,xR,xc)
| sdtmndtasgtdt0(xb,xR,xc) ),
introduced(tautology,[equality,[$cnf( ~ sdtmndtasgtdt0(xb,xR,xc) ),[0],$fot(xa)]]) ).
cnf(refute_0_67,plain,
( ~ sdtmndtasgtdt0(xa,xR,xc)
| sdtmndtasgtdt0(xb,xR,xc) ),
inference(resolve,[$cnf( $equal(xb,xa) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
~ sdtmndtasgtdt0(xa,xR,xc),
inference(resolve,[$cnf( sdtmndtasgtdt0(xb,xR,xc) )],[refute_0_67,refute_0_13]) ).
cnf(refute_0_69,plain,
$false,
inference(resolve,[$cnf( sdtmndtasgtdt0(xa,xR,xc) )],[refute_0_26,refute_0_68]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COM022+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n029.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 Jun 16 20:06:27 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.48/1.66 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.48/1.66
% 1.48/1.66 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.48/1.66
%------------------------------------------------------------------------------