%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COM013+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 01:32:31 EDT 2022
% Result : Theorem 0.20s 0.57s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 56
% Number of leaves : 11
% Syntax : Number of formulae : 157 ( 31 unt; 4 def)
% Number of atoms : 619 ( 43 equ)
% Maximal formula atoms : 30 ( 3 avg)
% Number of connectives : 844 ( 382 ~; 390 |; 42 &)
% ( 12 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 187 ( 6 sgn 107 !; 19 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mReduct,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aRewritingSystem0(W1) )
=> ! [W2] :
( aReductOfIn0(W2,W0,W1)
=> aElement0(W2) ) ) ).
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(mTermin,definition,
! [W0] :
( aRewritingSystem0(W0)
=> ( isTerminating0(W0)
<=> ! [W1,W2] :
( ( aElement0(W1)
& aElement0(W2) )
=> ( sdtmndtplgtdt0(W1,W0,W2)
=> iLess0(W2,W1) ) ) ) ) ).
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__587,hypothesis,
( aRewritingSystem0(xR)
& isTerminating0(xR) ) ).
fof(m__,conjecture,
! [W0] :
( aElement0(W0)
=> ( ! [W1] :
( aElement0(W1)
=> ( iLess0(W1,W0)
=> ? [W2] : aNormalFormOfIn0(W2,W1,xR) ) )
=> ? [W1] : aNormalFormOfIn0(W1,W0,xR) ) ) ).
fof(subgoal_0,plain,
! [W0] :
( ( aElement0(W0)
& ! [W1] :
( aElement0(W1)
=> ( iLess0(W1,W0)
=> ? [W2] : aNormalFormOfIn0(W2,W1,xR) ) ) )
=> ? [W1] : aNormalFormOfIn0(W1,W0,xR) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ! [W0] :
( ( aElement0(W0)
& ! [W1] :
( aElement0(W1)
=> ( iLess0(W1,W0)
=> ? [W2] : aNormalFormOfIn0(W2,W1,xR) ) ) )
=> ? [W1] : aNormalFormOfIn0(W1,W0,xR) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,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_1,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_0]) ).
fof(normalize_0_2,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_1]) ).
fof(normalize_0_3,plain,
! [W0,W1,W2,W3] :
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aReductOfIn0(W3,W2,W1)
| ~ aRewritingSystem0(W1) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,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_2]) ).
fof(normalize_0_5,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_6,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ( ~ sdtmndtasgtdt0(W0,W1,W2)
<=> ( W0 != W2
& ~ sdtmndtplgtdt0(W0,W1,W2) ) ) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,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_6]) ).
fof(normalize_0_8,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| sdtmndtasgtdt0(W0,W1,W2) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,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_10,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_9]) ).
fof(normalize_0_11,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_10]) ).
fof(normalize_0_12,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aReductOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| sdtmndtplgtdt0(W0,W1,W2) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
? [W0] :
( aElement0(W0)
& ! [W1] : ~ aNormalFormOfIn0(W1,W0,xR)
& ! [W1] :
( ~ aElement0(W1)
| ~ iLess0(W1,W0)
| ? [W2] : aNormalFormOfIn0(W2,W1,xR) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_14,plain,
( aElement0(skolemFOFtoCNF_W0)
& ! [W1] : ~ aNormalFormOfIn0(W1,skolemFOFtoCNF_W0,xR)
& ! [W1] :
( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| ? [W2] : aNormalFormOfIn0(W2,W1,xR) ) ),
inference(skolemize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
aElement0(skolemFOFtoCNF_W0),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
( aRewritingSystem0(xR)
& isTerminating0(xR) ),
inference(canonicalize,[],[m__587]) ).
fof(normalize_0_17,plain,
aRewritingSystem0(xR),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
! [W0,W1,W2] :
( W0 != W2
| ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| sdtmndtasgtdt0(W0,W1,W2) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_19,plain,
! [W1] : ~ aNormalFormOfIn0(W1,skolemFOFtoCNF_W0,xR),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_20,plain,
! [W1] : ~ aNormalFormOfIn0(W1,skolemFOFtoCNF_W0,xR),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aRewritingSystem0(W1)
| ! [W2] :
( ~ aReductOfIn0(W2,W0,W1)
| aElement0(W2) ) ),
inference(canonicalize,[],[mReduct]) ).
fof(normalize_0_22,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aRewritingSystem0(W1)
| ! [W2] :
( ~ aReductOfIn0(W2,W0,W1)
| aElement0(W2) ) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aReductOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| aElement0(W2) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [W1] :
( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| ? [W2] : aNormalFormOfIn0(W2,W1,xR) ),
inference(conjunct,[],[normalize_0_14]) ).
fof(normalize_0_25,plain,
! [W1] :
( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| ? [W2] : aNormalFormOfIn0(W2,W1,xR) ),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [W1] :
( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(W1),W1,xR) ),
inference(clausify,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [W0] :
( ~ aRewritingSystem0(W0)
| ( ~ isTerminating0(W0)
<=> ? [W1,W2] :
( ~ iLess0(W2,W1)
& aElement0(W1)
& aElement0(W2)
& sdtmndtplgtdt0(W1,W0,W2) ) ) ),
inference(canonicalize,[],[mTermin]) ).
fof(normalize_0_28,plain,
! [W0] :
( ~ aRewritingSystem0(W0)
| ( ~ isTerminating0(W0)
<=> ? [W1,W2] :
( ~ iLess0(W2,W1)
& aElement0(W1)
& aElement0(W2)
& sdtmndtplgtdt0(W1,W0,W2) ) ) ),
inference(specialize,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [W0,W1,W2] :
( ( ~ aRewritingSystem0(W0)
| ~ iLess0(skolemFOFtoCNF_W2_2(W0),skolemFOFtoCNF_W1_2(W0))
| isTerminating0(W0) )
& ( ~ aRewritingSystem0(W0)
| aElement0(skolemFOFtoCNF_W1_2(W0))
| isTerminating0(W0) )
& ( ~ aRewritingSystem0(W0)
| aElement0(skolemFOFtoCNF_W2_2(W0))
| isTerminating0(W0) )
& ( ~ aRewritingSystem0(W0)
| isTerminating0(W0)
| sdtmndtplgtdt0(skolemFOFtoCNF_W1_2(W0),W0,skolemFOFtoCNF_W2_2(W0)) )
& ( ~ aElement0(W1)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ~ sdtmndtplgtdt0(W1,W0,W2)
| iLess0(W2,W1) ) ),
inference(clausify,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [W0,W1,W2] :
( ~ aElement0(W1)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ~ sdtmndtplgtdt0(W1,W0,W2)
| iLess0(W2,W1) ),
inference(conjunct,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
isTerminating0(xR),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_32,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| W0 = W2
| sdtmndtplgtdt0(W0,W1,W2) ),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_33,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| sdtmndtasgtdt0(W0,W1,W2) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_34,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| aElement0(W2) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_35,plain,
! [W0,W1,W2,W3] :
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aElement0(W3)
| ~ aReductOfIn0(W3,W0,W1)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W3,W1,W2)
| sdtmndtplgtdt0(W0,W1,W2) ),
inference(conjunct,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aReductOfIn0(W3,W2,W1)
| ~ aRewritingSystem0(W1) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),W0,xR)
| ~ aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR)
| ~ aRewritingSystem0(xR) ),
inference(subst,[],[refute_0_0:[bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))),bind(W3,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))))]]) ).
cnf(refute_0_2,plain,
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| aNormalFormOfIn0(W2,W0,W1)
| aReductOfIn0(skolemFOFtoCNF_W3_3(W1,W2),W2,W1) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| aNormalFormOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) ),
inference(subst,[],[refute_0_2:[bind(W0,$fot(skolemFOFtoCNF_W0)),bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_4,plain,
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W0,W1,W2)
| sdtmndtasgtdt0(W0,W1,W2) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aRewritingSystem0(xR)
| ~ sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) ),
inference(subst,[],[refute_0_4:[bind(W0,$fot(skolemFOFtoCNF_W0)),bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_6,plain,
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aReductOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| sdtmndtplgtdt0(W0,W1,W2) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_7,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR)
| ~ aRewritingSystem0(xR)
| sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) ),
inference(subst,[],[refute_0_6:[bind(W0,$fot(skolemFOFtoCNF_W0)),bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_8,plain,
aElement0(skolemFOFtoCNF_W0),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_9,plain,
aRewritingSystem0(xR),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_10,plain,
( W0 != W2
| ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| sdtmndtasgtdt0(W0,W1,W2) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_11,plain,
( W2 != W2
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| sdtmndtasgtdt0(W2,W1,W2) ),
inference(subst,[],[refute_0_10:[bind(W0,$fot(W2))]]) ).
cnf(refute_0_12,plain,
W2 = W2,
introduced(tautology,[refl,[$fot(W2)]]) ).
cnf(refute_0_13,plain,
( ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| sdtmndtasgtdt0(W2,W1,W2) ),
inference(resolve,[$cnf( $equal(W2,W2) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
( ~ aElement0(X_17)
| ~ aRewritingSystem0(xR)
| sdtmndtasgtdt0(X_17,xR,X_17) ),
inference(subst,[],[refute_0_13:[bind(W1,$fot(xR)),bind(W2,$fot(X_17))]]) ).
cnf(refute_0_15,plain,
( ~ aElement0(X_17)
| sdtmndtasgtdt0(X_17,xR,X_17) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W0) ),
inference(subst,[],[refute_0_15:[bind(X_17,$fot(skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_17,plain,
sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W0),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_8,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W0)
| aNormalFormOfIn0(skolemFOFtoCNF_W0,skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR) ),
inference(subst,[],[refute_0_2:[bind(W0,$fot(skolemFOFtoCNF_W0)),bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_19,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aRewritingSystem0(xR)
| aNormalFormOfIn0(skolemFOFtoCNF_W0,skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR) ),
inference(resolve,[$cnf( sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W0) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ aRewritingSystem0(xR)
| aNormalFormOfIn0(skolemFOFtoCNF_W0,skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_8,refute_0_19]) ).
cnf(refute_0_21,plain,
( aNormalFormOfIn0(skolemFOFtoCNF_W0,skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_20]) ).
cnf(refute_0_22,plain,
~ aNormalFormOfIn0(W1,skolemFOFtoCNF_W0,xR),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_23,plain,
~ aNormalFormOfIn0(skolemFOFtoCNF_W0,skolemFOFtoCNF_W0,xR),
inference(subst,[],[refute_0_22:[bind(W1,$fot(skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_24,plain,
aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR),
inference(resolve,[$cnf( aNormalFormOfIn0(skolemFOFtoCNF_W0,skolemFOFtoCNF_W0,xR) )],[refute_0_21,refute_0_23]) ).
cnf(refute_0_25,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aRewritingSystem0(xR)
| sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) ),
inference(resolve,[$cnf( aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR) )],[refute_0_24,refute_0_7]) ).
cnf(refute_0_26,plain,
( ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aRewritingSystem0(xR)
| sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_8,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ aElement0(W0)
| ~ aReductOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| aElement0(W2) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_28,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR)
| ~ aRewritingSystem0(xR)
| aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) ),
inference(subst,[],[refute_0_27:[bind(W0,$fot(skolemFOFtoCNF_W0)),bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_29,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aRewritingSystem0(xR)
| aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) ),
inference(resolve,[$cnf( aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR) )],[refute_0_24,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ aRewritingSystem0(xR)
| aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_8,refute_0_29]) ).
cnf(refute_0_31,plain,
aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ aRewritingSystem0(xR)
| sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) )],[refute_0_31,refute_0_26]) ).
cnf(refute_0_33,plain,
sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aRewritingSystem0(xR)
| sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) )],[refute_0_33,refute_0_5]) ).
cnf(refute_0_35,plain,
( ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aRewritingSystem0(xR)
| sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_8,refute_0_34]) ).
cnf(refute_0_36,plain,
( ~ aRewritingSystem0(xR)
| sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) )],[refute_0_31,refute_0_35]) ).
cnf(refute_0_37,plain,
sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_36]) ).
cnf(refute_0_38,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aRewritingSystem0(xR)
| aNormalFormOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) ),
inference(resolve,[$cnf( sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) )],[refute_0_37,refute_0_3]) ).
cnf(refute_0_39,plain,
( ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aRewritingSystem0(xR)
| aNormalFormOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_8,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ aRewritingSystem0(xR)
| aNormalFormOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) )],[refute_0_31,refute_0_39]) ).
cnf(refute_0_41,plain,
( aNormalFormOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_40]) ).
cnf(refute_0_42,plain,
~ aNormalFormOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR),
inference(subst,[],[refute_0_22:[bind(W1,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_43,plain,
aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR),
inference(resolve,[$cnf( aNormalFormOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR) )],[refute_0_41,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),W0,xR)
| ~ aRewritingSystem0(xR) ),
inference(resolve,[$cnf( aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) )],[refute_0_43,refute_0_1]) ).
cnf(refute_0_45,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),W0,xR) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aNormalFormOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) ),
inference(subst,[],[refute_0_45:[bind(W0,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_47,plain,
( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(W1),W1,xR) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_48,plain,
( ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ iLess0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0)
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) ),
inference(subst,[],[refute_0_47:[bind(W1,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_49,plain,
( ~ aElement0(W1)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ~ sdtmndtplgtdt0(W1,W0,W2)
| iLess0(W2,W1) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_50,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aRewritingSystem0(xR)
| ~ isTerminating0(xR)
| ~ sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| iLess0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0) ),
inference(subst,[],[refute_0_49:[bind(W0,$fot(xR)),bind(W1,$fot(skolemFOFtoCNF_W0)),bind(W2,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_51,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aRewritingSystem0(xR)
| ~ isTerminating0(xR)
| iLess0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) )],[refute_0_33,refute_0_50]) ).
cnf(refute_0_52,plain,
( ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aRewritingSystem0(xR)
| ~ isTerminating0(xR)
| iLess0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_8,refute_0_51]) ).
cnf(refute_0_53,plain,
( ~ aRewritingSystem0(xR)
| ~ isTerminating0(xR)
| iLess0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) )],[refute_0_31,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ isTerminating0(xR)
| iLess0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_53]) ).
cnf(refute_0_55,plain,
isTerminating0(xR),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_56,plain,
iLess0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0),
inference(resolve,[$cnf( isTerminating0(xR) )],[refute_0_55,refute_0_54]) ).
cnf(refute_0_57,plain,
( ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) ),
inference(resolve,[$cnf( iLess0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0) )],[refute_0_56,refute_0_48]) ).
cnf(refute_0_58,plain,
aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) )],[refute_0_31,refute_0_57]) ).
cnf(refute_0_59,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),xR) ),
inference(subst,[],[refute_0_2:[bind(W0,$fot(skolemFOFtoCNF_W0)),bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))))]]) ).
cnf(refute_0_60,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))
| ~ aRewritingSystem0(xR)
| ~ sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))
| sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(subst,[],[refute_0_4:[bind(W0,$fot(skolemFOFtoCNF_W0)),bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))))]]) ).
cnf(refute_0_61,plain,
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtasgtdt0(W0,W1,W2)
| W0 = W2
| sdtmndtplgtdt0(W0,W1,W2) ),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_62,plain,
( ~ aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))
| ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aRewritingSystem0(xR)
| ~ sdtmndtasgtdt0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))
| skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtplgtdt0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(subst,[],[refute_0_61:[bind(W0,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))),bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))))]]) ).
cnf(refute_0_63,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| sdtmndtasgtdt0(W0,W1,W2) ),
inference(canonicalize,[],[normalize_0_33]) ).
cnf(refute_0_64,plain,
( ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR)
| ~ aRewritingSystem0(xR)
| sdtmndtasgtdt0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(subst,[],[refute_0_63:[bind(W0,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))),bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))))]]) ).
cnf(refute_0_65,plain,
( ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aRewritingSystem0(xR)
| sdtmndtasgtdt0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) )],[refute_0_58,refute_0_64]) ).
cnf(refute_0_66,plain,
( ~ aRewritingSystem0(xR)
| sdtmndtasgtdt0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) )],[refute_0_31,refute_0_65]) ).
cnf(refute_0_67,plain,
sdtmndtasgtdt0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))
| ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aRewritingSystem0(xR)
| skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtplgtdt0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( sdtmndtasgtdt0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) )],[refute_0_67,refute_0_62]) ).
cnf(refute_0_69,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| aElement0(W2) ),
inference(canonicalize,[],[normalize_0_34]) ).
cnf(refute_0_70,plain,
( ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR)
| ~ aRewritingSystem0(xR)
| aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(subst,[],[refute_0_69:[bind(W0,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))),bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))))]]) ).
cnf(refute_0_71,plain,
( ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aRewritingSystem0(xR)
| aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) )],[refute_0_58,refute_0_70]) ).
cnf(refute_0_72,plain,
( ~ aRewritingSystem0(xR)
| aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) )],[refute_0_31,refute_0_71]) ).
cnf(refute_0_73,plain,
aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_72]) ).
cnf(refute_0_74,plain,
( ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aRewritingSystem0(xR)
| skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtplgtdt0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) )],[refute_0_73,refute_0_68]) ).
cnf(refute_0_75,plain,
( ~ aRewritingSystem0(xR)
| skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtplgtdt0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) )],[refute_0_31,refute_0_74]) ).
cnf(refute_0_76,plain,
( skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtplgtdt0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_75]) ).
cnf(refute_0_77,plain,
( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aElement0(W3)
| ~ aReductOfIn0(W3,W0,W1)
| ~ aRewritingSystem0(W1)
| ~ sdtmndtplgtdt0(W3,W1,W2)
| sdtmndtplgtdt0(W0,W1,W2) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_78,plain,
( ~ aElement0(X_121)
| ~ aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))
| ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),X_121,xR)
| ~ aRewritingSystem0(xR)
| ~ sdtmndtplgtdt0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))
| sdtmndtplgtdt0(X_121,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(subst,[],[refute_0_77:[bind(W0,$fot(X_121)),bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))),bind(W3,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_79,plain,
( ~ aElement0(X_121)
| ~ aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))
| ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),X_121,xR)
| ~ aRewritingSystem0(xR)
| skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtplgtdt0(X_121,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) )],[refute_0_76,refute_0_78]) ).
cnf(refute_0_80,plain,
( ~ aElement0(X_121)
| ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),X_121,xR)
| ~ aRewritingSystem0(xR)
| skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtplgtdt0(X_121,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) )],[refute_0_73,refute_0_79]) ).
cnf(refute_0_81,plain,
( ~ aElement0(X_121)
| ~ aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),X_121,xR)
| ~ aRewritingSystem0(xR)
| skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtplgtdt0(X_121,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) )],[refute_0_31,refute_0_80]) ).
cnf(refute_0_82,plain,
( ~ aElement0(X_121)
| ~ aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),X_121,xR)
| skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtplgtdt0(X_121,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_81]) ).
cnf(refute_0_83,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR)
| skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(subst,[],[refute_0_82:[bind(X_121,$fot(skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_84,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR) )],[refute_0_24,refute_0_83]) ).
cnf(refute_0_85,plain,
( skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_8,refute_0_84]) ).
cnf(refute_0_86,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))
| ~ aRewritingSystem0(xR)
| skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) )],[refute_0_85,refute_0_60]) ).
cnf(refute_0_87,plain,
( ~ aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))
| ~ aRewritingSystem0(xR)
| skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_8,refute_0_86]) ).
cnf(refute_0_88,plain,
( ~ aRewritingSystem0(xR)
| skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) )],[refute_0_73,refute_0_87]) ).
cnf(refute_0_89,plain,
( skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_88]) ).
cnf(refute_0_90,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))
| ~ aRewritingSystem0(xR)
| skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),xR) ),
inference(resolve,[$cnf( sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) )],[refute_0_89,refute_0_59]) ).
cnf(refute_0_91,plain,
( ~ aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))
| ~ aRewritingSystem0(xR)
| skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),xR) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_8,refute_0_90]) ).
cnf(refute_0_92,plain,
( ~ aRewritingSystem0(xR)
| skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),xR) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) )],[refute_0_73,refute_0_91]) ).
cnf(refute_0_93,plain,
( skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),xR) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_92]) ).
cnf(refute_0_94,plain,
~ aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W0,xR),
inference(subst,[],[refute_0_22:[bind(W1,$fot(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))))]]) ).
cnf(refute_0_95,plain,
( skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),xR) ),
inference(resolve,[$cnf( aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W0,xR) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
( ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR)
| ~ aReductOfIn0(W3,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),xR)
| ~ aRewritingSystem0(xR) ),
inference(subst,[],[refute_0_0:[bind(W0,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))),bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))))]]) ).
cnf(refute_0_97,plain,
( ~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| ~ aReductOfIn0(W3,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),xR)
| ~ aRewritingSystem0(xR) ),
inference(resolve,[$cnf( aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) )],[refute_0_58,refute_0_96]) ).
cnf(refute_0_98,plain,
( ~ aReductOfIn0(W3,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),xR)
| ~ aRewritingSystem0(xR) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) )],[refute_0_31,refute_0_97]) ).
cnf(refute_0_99,plain,
~ aReductOfIn0(W3,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),xR),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_9,refute_0_98]) ).
cnf(refute_0_100,plain,
~ aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),xR),
inference(subst,[],[refute_0_99:[bind(W3,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)))))]]) ).
cnf(refute_0_101,plain,
skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),
inference(resolve,[$cnf( aReductOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),xR) )],[refute_0_95,refute_0_100]) ).
cnf(refute_0_102,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_103,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_104,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_102,refute_0_103]) ).
cnf(refute_0_105,plain,
( skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) != skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))
| skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) = skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0) ),
inference(subst,[],[refute_0_104:[bind(X,$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))),bind(Y,$fot(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))))]]) ).
cnf(refute_0_106,plain,
skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) = skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))) )],[refute_0_101,refute_0_105]) ).
cnf(refute_0_107,plain,
( skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) != skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)
| ~ aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR)
| aNormalFormOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) ),
introduced(tautology,[equality,[$cnf( aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) ),[0],$fot(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_108,plain,
( ~ aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR)
| aNormalFormOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) )],[refute_0_106,refute_0_107]) ).
cnf(refute_0_109,plain,
aNormalFormOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR),
inference(resolve,[$cnf( aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) )],[refute_0_58,refute_0_108]) ).
cnf(refute_0_110,plain,
~ aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)),
inference(resolve,[$cnf( aNormalFormOfIn0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0),xR) )],[refute_0_109,refute_0_46]) ).
cnf(refute_0_111,plain,
$false,
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W3_3(xR,skolemFOFtoCNF_W0)) )],[refute_0_31,refute_0_110]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COM013+1 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n021.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Thu Jun 16 17:01:00 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.57 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.57
% 0.20/0.57 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.59
%------------------------------------------------------------------------------