TSTP Solution File: COM021+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COM021+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 01:32:34 EDT 2022
% Result : Theorem 261.39s 261.60s
% Output : CNFRefutation 261.39s
% Verified :
% SZS Type : Refutation
% Derivation depth : 38
% Number of leaves : 14
% Syntax : Number of formulae : 143 ( 39 unt; 3 def)
% Number of atoms : 531 ( 36 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 707 ( 319 ~; 332 |; 42 &)
% ( 9 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 9 con; 0-3 aty)
% Number of variables : 134 ( 1 sgn 77 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mTCDef,definition,
! [W0,W1,W2] :
( ( aElement0(W0)
& aRewritingSystem0(W1)
& aElement0(W2) )
=> ( sdtmndtplgtdt0(W0,W1,W2)
<=> ( aReductOfIn0(W2,W0,W1)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W0,W1)
& sdtmndtplgtdt0(W3,W1,W2) ) ) ) ) ).
fof(mTCRDef,definition,
! [W0,W1,W2] :
( ( aElement0(W0)
& aRewritingSystem0(W1)
& aElement0(W2) )
=> ( sdtmndtasgtdt0(W0,W1,W2)
<=> ( W0 = W2
| sdtmndtplgtdt0(W0,W1,W2) ) ) ) ).
fof(mTCRTrans,axiom,
! [W0,W1,W2,W3] :
( ( aElement0(W0)
& aRewritingSystem0(W1)
& aElement0(W2)
& aElement0(W3) )
=> ( ( sdtmndtasgtdt0(W0,W1,W2)
& sdtmndtasgtdt0(W2,W1,W3) )
=> sdtmndtasgtdt0(W0,W1,W3) ) ) ).
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__755,hypothesis,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& sdtmndtasgtdt0(xu,xR,xb) ) ).
fof(m__799,hypothesis,
( aElement0(xw)
& sdtmndtasgtdt0(xu,xR,xw)
& sdtmndtasgtdt0(xv,xR,xw) ) ).
fof(m__818,hypothesis,
aNormalFormOfIn0(xd,xw,xR) ).
fof(m__850,hypothesis,
( aElement0(xx)
& sdtmndtasgtdt0(xb,xR,xx)
& sdtmndtasgtdt0(xd,xR,xx) ) ).
fof(m__,conjecture,
sdtmndtasgtdt0(xb,xR,xd) ).
fof(subgoal_0,plain,
sdtmndtasgtdt0(xb,xR,xd),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( aElement0(xx)
& sdtmndtasgtdt0(xb,xR,xx)
& sdtmndtasgtdt0(xd,xR,xx) ),
inference(canonicalize,[],[m__850]) ).
fof(normalize_0_1,plain,
sdtmndtasgtdt0(xb,xR,xx),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
aNormalFormOfIn0(xd,xw,xR),
inference(canonicalize,[],[m__818]) ).
fof(normalize_0_3,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_4,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_3]) ).
fof(normalize_0_5,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_4]) ).
fof(normalize_0_6,plain,
! [W0,W1,W2,W3] :
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aReductOfIn0(W3,W2,W1)
| ~ aRewritingSystem0(W1) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| sdtmndtasgtdt0(W0,W1,W2) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_8,plain,
( aElement0(xw)
& sdtmndtasgtdt0(xu,xR,xw)
& sdtmndtasgtdt0(xv,xR,xw) ),
inference(canonicalize,[],[m__799]) ).
fof(normalize_0_9,plain,
aElement0(xw),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
aRewritingSystem0(xR),
inference(canonicalize,[],[m__656]) ).
fof(normalize_0_11,plain,
! [W0,W1,W2,W3] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aElement0(W3)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| ~ sdtmndtasgtdt0(W2,W1,W3)
| sdtmndtasgtdt0(W0,W1,W3) ),
inference(canonicalize,[],[mTCRTrans]) ).
fof(normalize_0_12,plain,
! [W0,W1,W2,W3] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aElement0(W3)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| ~ sdtmndtasgtdt0(W2,W1,W3)
| sdtmndtasgtdt0(W0,W1,W3) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| aElement0(W2) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_14,plain,
( aElement0(xu)
& aReductOfIn0(xu,xa,xR)
& sdtmndtasgtdt0(xu,xR,xb) ),
inference(canonicalize,[],[m__755]) ).
fof(normalize_0_15,plain,
aReductOfIn0(xu,xa,xR),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ( ~ sdtmndtplgtdt0(W0,W1,W2)
<=> ( ~ aReductOfIn0(W2,W0,W1)
& ! [W3] :
( ~ aElement0(W3)
| ~ aReductOfIn0(W3,W0,W1)
| ~ sdtmndtplgtdt0(W3,W1,W2) ) ) ) ),
inference(canonicalize,[],[mTCDef]) ).
fof(normalize_0_17,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ( ~ sdtmndtplgtdt0(W0,W1,W2)
<=> ( ~ aReductOfIn0(W2,W0,W1)
& ! [W3] :
( ~ aElement0(W3)
| ~ aReductOfIn0(W3,W0,W1)
| ~ sdtmndtplgtdt0(W3,W1,W2) ) ) ) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [W0,W1,W2,W3] :
( ( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aReductOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| sdtmndtplgtdt0(W0,W1,W2) )
& ( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| aElement0(skolemFOFtoCNF_W3(W0,W1,W2))
| aReductOfIn0(W2,W0,W1) )
& ( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| aReductOfIn0(W2,W0,W1)
| aReductOfIn0(skolemFOFtoCNF_W3(W0,W1,W2),W0,W1) )
& ( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| aReductOfIn0(W2,W0,W1)
| sdtmndtplgtdt0(skolemFOFtoCNF_W3(W0,W1,W2),W1,W2) )
& ( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aElement0(W3)
| ~ aReductOfIn0(W3,W0,W1)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W3,W1,W2)
| sdtmndtplgtdt0(W0,W1,W2) ) ),
inference(clausify,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aReductOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| sdtmndtplgtdt0(W0,W1,W2) ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
inference(canonicalize,[],[m__731]) ).
fof(normalize_0_21,plain,
aElement0(xa),
inference(conjunct,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
aElement0(xu),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_23,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_24,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ( ~ sdtmndtasgtdt0(W0,W1,W2)
<=> ( W0 != W2
& ~ sdtmndtplgtdt0(W0,W1,W2) ) ) ),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,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_24]) ).
fof(normalize_0_26,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| sdtmndtasgtdt0(W0,W1,W2) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_28,plain,
! [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(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_29,plain,
sdtmndtasgtdt0(xd,xR,xx),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_30,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| W0 = W2
| sdtmndtplgtdt0(W0,W1,W2) ),
inference(conjunct,[],[normalize_0_25]) ).
fof(normalize_0_31,plain,
aElement0(xx),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_32,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| aReductOfIn0(W2,W0,W1)
| aReductOfIn0(skolemFOFtoCNF_W3(W0,W1,W2),W0,W1) ),
inference(conjunct,[],[normalize_0_18]) ).
fof(normalize_0_33,plain,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(canonicalize,[],[negate_0_0]) ).
cnf(refute_0_0,plain,
sdtmndtasgtdt0(xb,xR,xx),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
aNormalFormOfIn0(xd,xw,xR),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_2,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aReductOfIn0(W3,W2,W1)
| ~ aRewritingSystem0(W1) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(xd,W0,xR)
| ~ aReductOfIn0(skolemFOFtoCNF_W3_3(xR,xd),xd,xR)
| ~ aRewritingSystem0(xR) ),
inference(subst,[],[refute_0_2:[bind(W1,$fot(xR)),bind(W2,$fot(xd)),bind(W3,$fot(skolemFOFtoCNF_W3_3(xR,xd)))]]) ).
cnf(refute_0_4,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| sdtmndtasgtdt0(W0,W1,W2) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ aElement0(xw)
| ~ aNormalFormOfIn0(xd,xw,xR)
| ~ aRewritingSystem0(xR)
| sdtmndtasgtdt0(xw,xR,xd) ),
inference(subst,[],[refute_0_4:[bind(W0,$fot(xw)),bind(W1,$fot(xR)),bind(W2,$fot(xd))]]) ).
cnf(refute_0_6,plain,
( ~ aElement0(xw)
| ~ aRewritingSystem0(xR)
| sdtmndtasgtdt0(xw,xR,xd) ),
inference(resolve,[$cnf( aNormalFormOfIn0(xd,xw,xR) )],[refute_0_1,refute_0_5]) ).
cnf(refute_0_7,plain,
aElement0(xw),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
( ~ aRewritingSystem0(xR)
| sdtmndtasgtdt0(xw,xR,xd) ),
inference(resolve,[$cnf( aElement0(xw) )],[refute_0_7,refute_0_6]) ).
cnf(refute_0_9,plain,
aRewritingSystem0(xR),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_10,plain,
sdtmndtasgtdt0(xw,xR,xd),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_8]) ).
cnf(refute_0_11,plain,
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aElement0(W3)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| ~ sdtmndtasgtdt0(W2,W1,W3)
| sdtmndtasgtdt0(W0,W1,W3) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_12,plain,
( ~ aElement0(X_471)
| ~ aElement0(xd)
| ~ aElement0(xw)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(X_471,xR,xw)
| ~ sdtmndtasgtdt0(xw,xR,xd)
| sdtmndtasgtdt0(X_471,xR,xd) ),
inference(subst,[],[refute_0_11:[bind(W0,$fot(X_471)),bind(W1,$fot(xR)),bind(W2,$fot(xw)),bind(W3,$fot(xd))]]) ).
cnf(refute_0_13,plain,
( ~ aElement0(X_471)
| ~ aElement0(xd)
| ~ aElement0(xw)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(X_471,xR,xw)
| sdtmndtasgtdt0(X_471,xR,xd) ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xw,xR,xd) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| aElement0(W2) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_15,plain,
( ~ aElement0(xw)
| ~ aNormalFormOfIn0(xd,xw,xR)
| ~ aRewritingSystem0(xR)
| aElement0(xd) ),
inference(subst,[],[refute_0_14:[bind(W0,$fot(xw)),bind(W1,$fot(xR)),bind(W2,$fot(xd))]]) ).
cnf(refute_0_16,plain,
( ~ aElement0(xw)
| ~ aRewritingSystem0(xR)
| aElement0(xd) ),
inference(resolve,[$cnf( aNormalFormOfIn0(xd,xw,xR) )],[refute_0_1,refute_0_15]) ).
cnf(refute_0_17,plain,
( ~ aRewritingSystem0(xR)
| aElement0(xd) ),
inference(resolve,[$cnf( aElement0(xw) )],[refute_0_7,refute_0_16]) ).
cnf(refute_0_18,plain,
aElement0(xd),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ aElement0(X_471)
| ~ aElement0(xw)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(X_471,xR,xw)
| sdtmndtasgtdt0(X_471,xR,xd) ),
inference(resolve,[$cnf( aElement0(xd) )],[refute_0_18,refute_0_13]) ).
cnf(refute_0_20,plain,
( ~ aElement0(X_471)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(X_471,xR,xw)
| sdtmndtasgtdt0(X_471,xR,xd) ),
inference(resolve,[$cnf( aElement0(xw) )],[refute_0_7,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ aElement0(X_471)
| ~ sdtmndtasgtdt0(X_471,xR,xw)
| sdtmndtasgtdt0(X_471,xR,xd) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_20]) ).
cnf(refute_0_22,plain,
( ~ aElement0(xa)
| ~ sdtmndtasgtdt0(xa,xR,xw)
| sdtmndtasgtdt0(xa,xR,xd) ),
inference(subst,[],[refute_0_21:[bind(X_471,$fot(xa))]]) ).
cnf(refute_0_23,plain,
aReductOfIn0(xu,xa,xR),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_24,plain,
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aReductOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| sdtmndtplgtdt0(W0,W1,W2) ),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_25,plain,
( ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aReductOfIn0(xu,xa,xR)
| ~ aRewritingSystem0(xR)
| sdtmndtplgtdt0(xa,xR,xu) ),
inference(subst,[],[refute_0_24:[bind(W0,$fot(xa)),bind(W1,$fot(xR)),bind(W2,$fot(xu))]]) ).
cnf(refute_0_26,plain,
( ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aRewritingSystem0(xR)
| sdtmndtplgtdt0(xa,xR,xu) ),
inference(resolve,[$cnf( aReductOfIn0(xu,xa,xR) )],[refute_0_23,refute_0_25]) ).
cnf(refute_0_27,plain,
aElement0(xa),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_28,plain,
( ~ aElement0(xu)
| ~ aRewritingSystem0(xR)
| sdtmndtplgtdt0(xa,xR,xu) ),
inference(resolve,[$cnf( aElement0(xa) )],[refute_0_27,refute_0_26]) ).
cnf(refute_0_29,plain,
aElement0(xu),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_30,plain,
( ~ aRewritingSystem0(xR)
| sdtmndtplgtdt0(xa,xR,xu) ),
inference(resolve,[$cnf( aElement0(xu) )],[refute_0_29,refute_0_28]) ).
cnf(refute_0_31,plain,
sdtmndtplgtdt0(xa,xR,xu),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| sdtmndtasgtdt0(W0,W1,W2) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_33,plain,
( ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtplgtdt0(xa,xR,xu)
| sdtmndtasgtdt0(xa,xR,xu) ),
inference(subst,[],[refute_0_32:[bind(W0,$fot(xa)),bind(W1,$fot(xR)),bind(W2,$fot(xu))]]) ).
cnf(refute_0_34,plain,
( ~ aElement0(xa)
| ~ aElement0(xu)
| ~ aRewritingSystem0(xR)
| sdtmndtasgtdt0(xa,xR,xu) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xa,xR,xu) )],[refute_0_31,refute_0_33]) ).
cnf(refute_0_35,plain,
( ~ aElement0(xu)
| ~ aRewritingSystem0(xR)
| sdtmndtasgtdt0(xa,xR,xu) ),
inference(resolve,[$cnf( aElement0(xa) )],[refute_0_27,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ aRewritingSystem0(xR)
| sdtmndtasgtdt0(xa,xR,xu) ),
inference(resolve,[$cnf( aElement0(xu) )],[refute_0_29,refute_0_35]) ).
cnf(refute_0_37,plain,
sdtmndtasgtdt0(xa,xR,xu),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_36]) ).
cnf(refute_0_38,plain,
sdtmndtasgtdt0(xu,xR,xw),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_39,plain,
( ~ aElement0(X_471)
| ~ aElement0(xu)
| ~ aElement0(xw)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(X_471,xR,xu)
| ~ sdtmndtasgtdt0(xu,xR,xw)
| sdtmndtasgtdt0(X_471,xR,xw) ),
inference(subst,[],[refute_0_11:[bind(W0,$fot(X_471)),bind(W1,$fot(xR)),bind(W2,$fot(xu)),bind(W3,$fot(xw))]]) ).
cnf(refute_0_40,plain,
( ~ aElement0(X_471)
| ~ aElement0(xu)
| ~ aElement0(xw)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(X_471,xR,xu)
| sdtmndtasgtdt0(X_471,xR,xw) ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xu,xR,xw) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ aElement0(X_471)
| ~ aElement0(xw)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(X_471,xR,xu)
| sdtmndtasgtdt0(X_471,xR,xw) ),
inference(resolve,[$cnf( aElement0(xu) )],[refute_0_29,refute_0_40]) ).
cnf(refute_0_42,plain,
( ~ aElement0(X_471)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(X_471,xR,xu)
| sdtmndtasgtdt0(X_471,xR,xw) ),
inference(resolve,[$cnf( aElement0(xw) )],[refute_0_7,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ aElement0(X_471)
| ~ sdtmndtasgtdt0(X_471,xR,xu)
| sdtmndtasgtdt0(X_471,xR,xw) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ aElement0(xa)
| ~ sdtmndtasgtdt0(xa,xR,xu)
| sdtmndtasgtdt0(xa,xR,xw) ),
inference(subst,[],[refute_0_43:[bind(X_471,$fot(xa))]]) ).
cnf(refute_0_45,plain,
( ~ aElement0(xa)
| sdtmndtasgtdt0(xa,xR,xw) ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xa,xR,xu) )],[refute_0_37,refute_0_44]) ).
cnf(refute_0_46,plain,
sdtmndtasgtdt0(xa,xR,xw),
inference(resolve,[$cnf( aElement0(xa) )],[refute_0_27,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ aElement0(xa)
| sdtmndtasgtdt0(xa,xR,xd) ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xa,xR,xw) )],[refute_0_46,refute_0_22]) ).
cnf(refute_0_48,plain,
sdtmndtasgtdt0(xa,xR,xd),
inference(resolve,[$cnf( aElement0(xa) )],[refute_0_27,refute_0_47]) ).
cnf(refute_0_49,plain,
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| aNormalFormOfIn0(W2,W0,W1)
| aReductOfIn0(skolemFOFtoCNF_W3_3(W1,W2),W2,W1) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_50,plain,
( ~ aElement0(xa)
| ~ aElement0(xd)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(xa,xR,xd)
| aNormalFormOfIn0(xd,xa,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,xd),xd,xR) ),
inference(subst,[],[refute_0_49:[bind(W0,$fot(xa)),bind(W1,$fot(xR)),bind(W2,$fot(xd))]]) ).
cnf(refute_0_51,plain,
( ~ aElement0(xa)
| ~ aElement0(xd)
| ~ aRewritingSystem0(xR)
| aNormalFormOfIn0(xd,xa,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,xd),xd,xR) ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xa,xR,xd) )],[refute_0_48,refute_0_50]) ).
cnf(refute_0_52,plain,
( ~ aElement0(xd)
| ~ aRewritingSystem0(xR)
| aNormalFormOfIn0(xd,xa,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,xd),xd,xR) ),
inference(resolve,[$cnf( aElement0(xa) )],[refute_0_27,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ aRewritingSystem0(xR)
| aNormalFormOfIn0(xd,xa,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,xd),xd,xR) ),
inference(resolve,[$cnf( aElement0(xd) )],[refute_0_18,refute_0_52]) ).
cnf(refute_0_54,plain,
( aNormalFormOfIn0(xd,xa,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,xd),xd,xR) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_53]) ).
cnf(refute_0_55,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(xd,W0,xR)
| ~ aRewritingSystem0(xR)
| aNormalFormOfIn0(xd,xa,xR) ),
inference(resolve,[$cnf( aReductOfIn0(skolemFOFtoCNF_W3_3(xR,xd),xd,xR) )],[refute_0_54,refute_0_3]) ).
cnf(refute_0_56,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(xd,W0,xR)
| aNormalFormOfIn0(xd,xa,xR) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_55]) ).
cnf(refute_0_57,plain,
( ~ aElement0(xw)
| ~ aNormalFormOfIn0(xd,xw,xR)
| aNormalFormOfIn0(xd,xa,xR) ),
inference(subst,[],[refute_0_56:[bind(W0,$fot(xw))]]) ).
cnf(refute_0_58,plain,
( ~ aElement0(xw)
| aNormalFormOfIn0(xd,xa,xR) ),
inference(resolve,[$cnf( aNormalFormOfIn0(xd,xw,xR) )],[refute_0_1,refute_0_57]) ).
cnf(refute_0_59,plain,
aNormalFormOfIn0(xd,xa,xR),
inference(resolve,[$cnf( aElement0(xw) )],[refute_0_7,refute_0_58]) ).
cnf(refute_0_60,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(xd,W0,xR)
| ~ aReductOfIn0(xx,xd,xR)
| ~ aRewritingSystem0(xR) ),
inference(subst,[],[refute_0_2:[bind(W1,$fot(xR)),bind(W2,$fot(xd)),bind(W3,$fot(xx))]]) ).
cnf(refute_0_61,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(xd,W0,xR)
| ~ aReductOfIn0(skolemFOFtoCNF_W3(xd,xR,xx),xd,xR)
| ~ aRewritingSystem0(xR) ),
inference(subst,[],[refute_0_2:[bind(W1,$fot(xR)),bind(W2,$fot(xd)),bind(W3,$fot(skolemFOFtoCNF_W3(xd,xR,xx)))]]) ).
cnf(refute_0_62,plain,
sdtmndtasgtdt0(xd,xR,xx),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_63,plain,
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| W0 = W2
| sdtmndtplgtdt0(W0,W1,W2) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_64,plain,
( ~ aElement0(xd)
| ~ aElement0(xx)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(xd,xR,xx)
| xd = xx
| sdtmndtplgtdt0(xd,xR,xx) ),
inference(subst,[],[refute_0_63:[bind(W0,$fot(xd)),bind(W1,$fot(xR)),bind(W2,$fot(xx))]]) ).
cnf(refute_0_65,plain,
( ~ aElement0(xd)
| ~ aElement0(xx)
| ~ aRewritingSystem0(xR)
| xd = xx
| sdtmndtplgtdt0(xd,xR,xx) ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xd,xR,xx) )],[refute_0_62,refute_0_64]) ).
cnf(refute_0_66,plain,
( ~ aElement0(xx)
| ~ aRewritingSystem0(xR)
| xd = xx
| sdtmndtplgtdt0(xd,xR,xx) ),
inference(resolve,[$cnf( aElement0(xd) )],[refute_0_18,refute_0_65]) ).
cnf(refute_0_67,plain,
aElement0(xx),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_68,plain,
( ~ aRewritingSystem0(xR)
| xd = xx
| sdtmndtplgtdt0(xd,xR,xx) ),
inference(resolve,[$cnf( aElement0(xx) )],[refute_0_67,refute_0_66]) ).
cnf(refute_0_69,plain,
( xd = xx
| sdtmndtplgtdt0(xd,xR,xx) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_68]) ).
cnf(refute_0_70,plain,
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| aReductOfIn0(W2,W0,W1)
| aReductOfIn0(skolemFOFtoCNF_W3(W0,W1,W2),W0,W1) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_71,plain,
( ~ aElement0(xd)
| ~ aElement0(xx)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtplgtdt0(xd,xR,xx)
| aReductOfIn0(skolemFOFtoCNF_W3(xd,xR,xx),xd,xR)
| aReductOfIn0(xx,xd,xR) ),
inference(subst,[],[refute_0_70:[bind(W0,$fot(xd)),bind(W1,$fot(xR)),bind(W2,$fot(xx))]]) ).
cnf(refute_0_72,plain,
( ~ aElement0(xd)
| ~ aElement0(xx)
| ~ aRewritingSystem0(xR)
| xd = xx
| aReductOfIn0(skolemFOFtoCNF_W3(xd,xR,xx),xd,xR)
| aReductOfIn0(xx,xd,xR) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xd,xR,xx) )],[refute_0_69,refute_0_71]) ).
cnf(refute_0_73,plain,
( ~ aElement0(xx)
| ~ aRewritingSystem0(xR)
| xd = xx
| aReductOfIn0(skolemFOFtoCNF_W3(xd,xR,xx),xd,xR)
| aReductOfIn0(xx,xd,xR) ),
inference(resolve,[$cnf( aElement0(xd) )],[refute_0_18,refute_0_72]) ).
cnf(refute_0_74,plain,
( ~ aRewritingSystem0(xR)
| xd = xx
| aReductOfIn0(skolemFOFtoCNF_W3(xd,xR,xx),xd,xR)
| aReductOfIn0(xx,xd,xR) ),
inference(resolve,[$cnf( aElement0(xx) )],[refute_0_67,refute_0_73]) ).
cnf(refute_0_75,plain,
( xd = xx
| aReductOfIn0(skolemFOFtoCNF_W3(xd,xR,xx),xd,xR)
| aReductOfIn0(xx,xd,xR) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_74]) ).
cnf(refute_0_76,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(xd,W0,xR)
| ~ aRewritingSystem0(xR)
| xd = xx
| aReductOfIn0(xx,xd,xR) ),
inference(resolve,[$cnf( aReductOfIn0(skolemFOFtoCNF_W3(xd,xR,xx),xd,xR) )],[refute_0_75,refute_0_61]) ).
cnf(refute_0_77,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(xd,W0,xR)
| xd = xx
| aReductOfIn0(xx,xd,xR) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_76]) ).
cnf(refute_0_78,plain,
( ~ aElement0(xa)
| ~ aNormalFormOfIn0(xd,xa,xR)
| xd = xx
| aReductOfIn0(xx,xd,xR) ),
inference(subst,[],[refute_0_77:[bind(W0,$fot(xa))]]) ).
cnf(refute_0_79,plain,
( ~ aElement0(xa)
| xd = xx
| aReductOfIn0(xx,xd,xR) ),
inference(resolve,[$cnf( aNormalFormOfIn0(xd,xa,xR) )],[refute_0_59,refute_0_78]) ).
cnf(refute_0_80,plain,
( xd = xx
| aReductOfIn0(xx,xd,xR) ),
inference(resolve,[$cnf( aElement0(xa) )],[refute_0_27,refute_0_79]) ).
cnf(refute_0_81,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(xd,W0,xR)
| ~ aRewritingSystem0(xR)
| xd = xx ),
inference(resolve,[$cnf( aReductOfIn0(xx,xd,xR) )],[refute_0_80,refute_0_60]) ).
cnf(refute_0_82,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(xd,W0,xR)
| xd = xx ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_81]) ).
cnf(refute_0_83,plain,
( ~ aElement0(xa)
| ~ aNormalFormOfIn0(xd,xa,xR)
| xd = xx ),
inference(subst,[],[refute_0_82:[bind(W0,$fot(xa))]]) ).
cnf(refute_0_84,plain,
( ~ aElement0(xa)
| xd = xx ),
inference(resolve,[$cnf( aNormalFormOfIn0(xd,xa,xR) )],[refute_0_59,refute_0_83]) ).
cnf(refute_0_85,plain,
xd = xx,
inference(resolve,[$cnf( aElement0(xa) )],[refute_0_27,refute_0_84]) ).
cnf(refute_0_86,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_87,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_88,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_86,refute_0_87]) ).
cnf(refute_0_89,plain,
( xd != xx
| xx = xd ),
inference(subst,[],[refute_0_88:[bind(X,$fot(xd)),bind(Y,$fot(xx))]]) ).
cnf(refute_0_90,plain,
xx = xd,
inference(resolve,[$cnf( $equal(xd,xx) )],[refute_0_85,refute_0_89]) ).
cnf(refute_0_91,plain,
( xx != xd
| ~ sdtmndtasgtdt0(xb,xR,xx)
| sdtmndtasgtdt0(xb,xR,xd) ),
introduced(tautology,[equality,[$cnf( sdtmndtasgtdt0(xb,xR,xx) ),[2],$fot(xd)]]) ).
cnf(refute_0_92,plain,
( ~ sdtmndtasgtdt0(xb,xR,xx)
| sdtmndtasgtdt0(xb,xR,xd) ),
inference(resolve,[$cnf( $equal(xx,xd) )],[refute_0_90,refute_0_91]) ).
cnf(refute_0_93,plain,
sdtmndtasgtdt0(xb,xR,xd),
inference(resolve,[$cnf( sdtmndtasgtdt0(xb,xR,xx) )],[refute_0_0,refute_0_92]) ).
cnf(refute_0_94,plain,
~ sdtmndtasgtdt0(xb,xR,xd),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_95,plain,
$false,
inference(resolve,[$cnf( sdtmndtasgtdt0(xb,xR,xd) )],[refute_0_93,refute_0_94]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : COM021+1 : TPTP v8.1.0. Released v4.0.0.
% 0.12/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n012.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 18:29:24 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 261.39/261.60 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 261.39/261.60
% 261.39/261.60 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 261.39/261.61
%------------------------------------------------------------------------------