%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COM013+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 0.12s 0.37s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 8
% Syntax : Number of formulae : 94 ( 19 unt; 1 def)
% Number of atoms : 486 ( 43 equ)
% Maximal formula atoms : 31 ( 5 avg)
% Number of connectives : 652 ( 260 ~; 256 |; 118 &)
% ( 3 <=>; 15 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 143 ( 5 sgn 80 !; 35 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mReduct,axiom,
! [W0,W1] :
( ( aElement0(W0)
& aRewritingSystem0(W1) )
=> ! [W2] :
( aReductOfIn0(W2,W0,W1)
=> aElement0(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__587,hypothesis,
( aRewritingSystem0(xR)
& ! [W0,W1] :
( ( aElement0(W0)
& aElement0(W1) )
=> ( ( aReductOfIn0(W1,W0,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,W1) )
| sdtmndtplgtdt0(W0,xR,W1) )
=> iLess0(W1,W0) ) )
& isTerminating0(xR) ) ).
fof(m__,conjecture,
! [W0] :
( aElement0(W0)
=> ( ! [W1] :
( aElement0(W1)
=> ( iLess0(W1,W0)
=> ? [W2] :
( aElement0(W2)
& ( W1 = W2
| ( ( aReductOfIn0(W2,W1,xR)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W1,xR)
& sdtmndtplgtdt0(W3,xR,W2) ) )
& sdtmndtplgtdt0(W1,xR,W2) ) )
& sdtmndtasgtdt0(W1,xR,W2)
& ~ ? [W3] : aReductOfIn0(W3,W2,xR)
& aNormalFormOfIn0(W2,W1,xR) ) ) )
=> ? [W1] :
( ( aElement0(W1)
& ( W0 = W1
| aReductOfIn0(W1,W0,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,W1) )
| sdtmndtplgtdt0(W0,xR,W1)
| sdtmndtasgtdt0(W0,xR,W1) )
& ~ ? [W2] : aReductOfIn0(W2,W1,xR) )
| aNormalFormOfIn0(W1,W0,xR) ) ) ) ).
fof(subgoal_0,plain,
! [W0] :
( ( aElement0(W0)
& ! [W1] :
( aElement0(W1)
=> ( iLess0(W1,W0)
=> ? [W2] :
( aElement0(W2)
& ( W1 = W2
| ( ( aReductOfIn0(W2,W1,xR)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W1,xR)
& sdtmndtplgtdt0(W3,xR,W2) ) )
& sdtmndtplgtdt0(W1,xR,W2) ) )
& sdtmndtasgtdt0(W1,xR,W2)
& ~ ? [W3] : aReductOfIn0(W3,W2,xR)
& aNormalFormOfIn0(W2,W1,xR) ) ) ) )
=> ? [W1] :
( ( aElement0(W1)
& ( W0 = W1
| aReductOfIn0(W1,W0,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,W1) )
| sdtmndtplgtdt0(W0,xR,W1)
| sdtmndtasgtdt0(W0,xR,W1) )
& ~ ? [W2] : aReductOfIn0(W2,W1,xR) )
| aNormalFormOfIn0(W1,W0,xR) ) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ! [W0] :
( ( aElement0(W0)
& ! [W1] :
( aElement0(W1)
=> ( iLess0(W1,W0)
=> ? [W2] :
( aElement0(W2)
& ( W1 = W2
| ( ( aReductOfIn0(W2,W1,xR)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W1,xR)
& sdtmndtplgtdt0(W3,xR,W2) ) )
& sdtmndtplgtdt0(W1,xR,W2) ) )
& sdtmndtasgtdt0(W1,xR,W2)
& ~ ? [W3] : aReductOfIn0(W3,W2,xR)
& aNormalFormOfIn0(W2,W1,xR) ) ) ) )
=> ? [W1] :
( ( aElement0(W1)
& ( W0 = W1
| aReductOfIn0(W1,W0,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,W1) )
| sdtmndtplgtdt0(W0,xR,W1)
| sdtmndtasgtdt0(W0,xR,W1) )
& ~ ? [W2] : aReductOfIn0(W2,W1,xR) )
| aNormalFormOfIn0(W1,W0,xR) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [W0] :
( aElement0(W0)
& ! [W1] : ~ aNormalFormOfIn0(W1,W0,xR)
& ! [W1] :
( ~ aElement0(W1)
| ~ iLess0(W1,W0)
| ? [W2] :
( aElement0(W2)
& aNormalFormOfIn0(W2,W1,xR)
& sdtmndtasgtdt0(W1,xR,W2)
& ( W1 = W2
| ( sdtmndtplgtdt0(W1,xR,W2)
& ( aReductOfIn0(W2,W1,xR)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W1,xR)
& sdtmndtplgtdt0(W3,xR,W2) ) ) ) )
& ! [W3] : ~ aReductOfIn0(W3,W2,xR) ) )
& ! [W1] :
( ~ aElement0(W1)
| ( W0 != W1
& ~ aReductOfIn0(W1,W0,xR)
& ~ sdtmndtasgtdt0(W0,xR,W1)
& ~ sdtmndtplgtdt0(W0,xR,W1)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,W0,xR)
| ~ sdtmndtplgtdt0(W2,xR,W1) ) )
| ? [W2] : aReductOfIn0(W2,W1,xR) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( aElement0(skolemFOFtoCNF_W0)
& ! [W1] : ~ aNormalFormOfIn0(W1,skolemFOFtoCNF_W0,xR)
& ! [W1] :
( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| ? [W2] :
( aElement0(W2)
& aNormalFormOfIn0(W2,W1,xR)
& sdtmndtasgtdt0(W1,xR,W2)
& ( W1 = W2
| ( sdtmndtplgtdt0(W1,xR,W2)
& ( aReductOfIn0(W2,W1,xR)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W1,xR)
& sdtmndtplgtdt0(W3,xR,W2) ) ) ) )
& ! [W3] : ~ aReductOfIn0(W3,W2,xR) ) )
& ! [W1] :
( ~ aElement0(W1)
| ( skolemFOFtoCNF_W0 != W1
& ~ aReductOfIn0(W1,skolemFOFtoCNF_W0,xR)
& ~ sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,W1)
& ~ sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,W1)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,skolemFOFtoCNF_W0,xR)
| ~ sdtmndtplgtdt0(W2,xR,W1) ) )
| ? [W2] : aReductOfIn0(W2,W1,xR) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [W1] :
( ~ aElement0(W1)
| ( skolemFOFtoCNF_W0 != W1
& ~ aReductOfIn0(W1,skolemFOFtoCNF_W0,xR)
& ~ sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,W1)
& ~ sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,W1)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,skolemFOFtoCNF_W0,xR)
| ~ sdtmndtplgtdt0(W2,xR,W1) ) )
| ? [W2] : aReductOfIn0(W2,W1,xR) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [W1] :
( ~ aElement0(W1)
| ( skolemFOFtoCNF_W0 != W1
& ~ aReductOfIn0(W1,skolemFOFtoCNF_W0,xR)
& ~ sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,W1)
& ~ sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,W1)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,skolemFOFtoCNF_W0,xR)
| ~ sdtmndtplgtdt0(W2,xR,W1) ) )
| ? [W2] : aReductOfIn0(W2,W1,xR) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [W1,W2] :
( ( skolemFOFtoCNF_W0 != W1
| ~ aElement0(W1)
| aReductOfIn0(skolemFOFtoCNF_W2_4(W1),W1,xR) )
& ( ~ aElement0(W1)
| ~ aReductOfIn0(W1,skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W2_4(W1),W1,xR) )
& ( ~ aElement0(W1)
| ~ sdtmndtasgtdt0(skolemFOFtoCNF_W0,xR,W1)
| aReductOfIn0(skolemFOFtoCNF_W2_4(W1),W1,xR) )
& ( ~ aElement0(W1)
| ~ sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,W1)
| aReductOfIn0(skolemFOFtoCNF_W2_4(W1),W1,xR) )
& ( ~ aElement0(W1)
| ~ aElement0(W2)
| ~ aReductOfIn0(W2,skolemFOFtoCNF_W0,xR)
| ~ sdtmndtplgtdt0(W2,xR,W1)
| aReductOfIn0(skolemFOFtoCNF_W2_4(W1),W1,xR) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [W1] :
( skolemFOFtoCNF_W0 != W1
| ~ aElement0(W1)
| aReductOfIn0(skolemFOFtoCNF_W2_4(W1),W1,xR) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
aElement0(skolemFOFtoCNF_W0),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_7,plain,
! [W1] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W2_4(W1),W1,xR) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_8,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aRewritingSystem0(W1)
| ! [W2] :
( ~ aReductOfIn0(W2,W0,W1)
| aElement0(W2) ) ),
inference(canonicalize,[],[mReduct]) ).
fof(normalize_0_9,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aRewritingSystem0(W1)
| ! [W2] :
( ~ aReductOfIn0(W2,W0,W1)
| aElement0(W2) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aReductOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| aElement0(W2) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
( aRewritingSystem0(xR)
& isTerminating0(xR)
& ! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| iLess0(W1,W0)
| ( ~ aReductOfIn0(W1,W0,xR)
& ~ sdtmndtplgtdt0(W0,xR,W1)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,W0,xR)
| ~ sdtmndtplgtdt0(W2,xR,W1) ) ) ) ),
inference(canonicalize,[],[m__587]) ).
fof(normalize_0_12,plain,
aRewritingSystem0(xR),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,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_14,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_13]) ).
fof(normalize_0_15,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_14]) ).
fof(normalize_0_16,plain,
! [W0,W1,W2,W3] :
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aReductOfIn0(W3,W2,W1)
| ~ aRewritingSystem0(W1) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [W1] :
( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| ? [W2] :
( aElement0(W2)
& aNormalFormOfIn0(W2,W1,xR)
& sdtmndtasgtdt0(W1,xR,W2)
& ( W1 = W2
| ( sdtmndtplgtdt0(W1,xR,W2)
& ( aReductOfIn0(W2,W1,xR)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W1,xR)
& sdtmndtplgtdt0(W3,xR,W2) ) ) ) )
& ! [W3] : ~ aReductOfIn0(W3,W2,xR) ) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_18,plain,
! [W1] :
( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| ? [W2] :
( aElement0(W2)
& aNormalFormOfIn0(W2,W1,xR)
& sdtmndtasgtdt0(W1,xR,W2)
& ( W1 = W2
| ( sdtmndtplgtdt0(W1,xR,W2)
& ( aReductOfIn0(W2,W1,xR)
| ? [W3] :
( aElement0(W3)
& aReductOfIn0(W3,W1,xR)
& sdtmndtplgtdt0(W3,xR,W2) ) ) ) )
& ! [W3] : ~ aReductOfIn0(W3,W2,xR) ) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [W1,W3] :
( ( ~ aElement0(W1)
| ~ aReductOfIn0(W3,skolemFOFtoCNF_W2_3(W1),xR)
| ~ iLess0(W1,skolemFOFtoCNF_W0) )
& ( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| aElement0(skolemFOFtoCNF_W2_3(W1)) )
& ( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(W1),W1,xR) )
& ( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| sdtmndtasgtdt0(W1,xR,skolemFOFtoCNF_W2_3(W1)) )
& ( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| W1 = skolemFOFtoCNF_W2_3(W1)
| sdtmndtplgtdt0(W1,xR,skolemFOFtoCNF_W2_3(W1)) )
& ( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| W1 = skolemFOFtoCNF_W2_3(W1)
| aElement0(skolemFOFtoCNF_W3_4(W1))
| aReductOfIn0(skolemFOFtoCNF_W2_3(W1),W1,xR) )
& ( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| W1 = skolemFOFtoCNF_W2_3(W1)
| aReductOfIn0(skolemFOFtoCNF_W2_3(W1),W1,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_4(W1),W1,xR) )
& ( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| W1 = skolemFOFtoCNF_W2_3(W1)
| aReductOfIn0(skolemFOFtoCNF_W2_3(W1),W1,xR)
| sdtmndtplgtdt0(skolemFOFtoCNF_W3_4(W1),xR,skolemFOFtoCNF_W2_3(W1)) ) ),
inference(clausify,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [W1] :
( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(W1),W1,xR) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| iLess0(W1,W0)
| ( ~ aReductOfIn0(W1,W0,xR)
& ~ sdtmndtplgtdt0(W0,xR,W1)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,W0,xR)
| ~ sdtmndtplgtdt0(W2,xR,W1) ) ) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_22,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| iLess0(W1,W0)
| ( ~ aReductOfIn0(W1,W0,xR)
& ~ sdtmndtplgtdt0(W0,xR,W1)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,W0,xR)
| ~ sdtmndtplgtdt0(W2,xR,W1) ) ) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [W0,W1,W2] :
( ( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| iLess0(W1,W0) )
& ( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ sdtmndtplgtdt0(W0,xR,W1)
| iLess0(W1,W0) )
& ( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aElement0(W2)
| ~ aReductOfIn0(W2,W0,xR)
| ~ sdtmndtplgtdt0(W2,xR,W1)
| iLess0(W1,W0) ) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [W0,W1] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| iLess0(W1,W0) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [W1] :
( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| W1 = skolemFOFtoCNF_W2_3(W1)
| sdtmndtplgtdt0(W1,xR,skolemFOFtoCNF_W2_3(W1)) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_26,plain,
! [W1,W2] :
( ~ aElement0(W1)
| ~ aElement0(W2)
| ~ aReductOfIn0(W2,skolemFOFtoCNF_W0,xR)
| ~ sdtmndtplgtdt0(W2,xR,W1)
| aReductOfIn0(skolemFOFtoCNF_W2_4(W1),W1,xR) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_27,plain,
! [W1] :
( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| aElement0(skolemFOFtoCNF_W2_3(W1)) ),
inference(conjunct,[],[normalize_0_19]) ).
cnf(refute_0_0,plain,
( skolemFOFtoCNF_W0 != W1
| ~ aElement0(W1)
| aReductOfIn0(skolemFOFtoCNF_W2_4(W1),W1,xR) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_1,plain,
( skolemFOFtoCNF_W0 != skolemFOFtoCNF_W0
| ~ aElement0(skolemFOFtoCNF_W0)
| aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR) ),
inference(subst,[],[refute_0_0:[bind(W1,$fot(skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_2,plain,
skolemFOFtoCNF_W0 = skolemFOFtoCNF_W0,
introduced(tautology,[refl,[$fot(skolemFOFtoCNF_W0)]]) ).
cnf(refute_0_3,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W0,skolemFOFtoCNF_W0) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
aElement0(skolemFOFtoCNF_W0),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W2_4(W1),W1,xR) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
( ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| ~ aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR)
| aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR) ),
inference(subst,[],[refute_0_6:[bind(W1,$fot(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_8,plain,
( ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR) ),
inference(resolve,[$cnf( aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR) )],[refute_0_5,refute_0_7]) ).
cnf(refute_0_9,plain,
( ~ aElement0(W0)
| ~ aReductOfIn0(W2,W0,W1)
| ~ aRewritingSystem0(W1)
| aElement0(W2) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_10,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR)
| ~ aRewritingSystem0(xR)
| aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)) ),
inference(subst,[],[refute_0_9:[bind(W0,$fot(skolemFOFtoCNF_W0)),bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_11,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aRewritingSystem0(xR)
| aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)) ),
inference(resolve,[$cnf( aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR) )],[refute_0_5,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ aRewritingSystem0(xR)
| aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_4,refute_0_11]) ).
cnf(refute_0_13,plain,
aRewritingSystem0(xR),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_14,plain,
aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)) )],[refute_0_14,refute_0_8]) ).
cnf(refute_0_16,plain,
( ~ aElement0(W0)
| ~ aNormalFormOfIn0(W2,W0,W1)
| ~ aReductOfIn0(W3,W2,W1)
| ~ aRewritingSystem0(W1) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_17,plain,
( ~ aElement0(X_56)
| ~ aNormalFormOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),X_56,xR)
| ~ aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR)
| ~ aRewritingSystem0(xR) ),
inference(subst,[],[refute_0_16:[bind(W0,$fot(X_56)),bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))),bind(W3,$fot(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))))]]) ).
cnf(refute_0_18,plain,
( ~ aElement0(X_56)
| ~ aNormalFormOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),X_56,xR)
| ~ aRewritingSystem0(xR) ),
inference(resolve,[$cnf( aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
( ~ aElement0(X_56)
| ~ aNormalFormOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),X_56,xR) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_13,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| ~ aNormalFormOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR) ),
inference(subst,[],[refute_0_19:[bind(X_56,$fot(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_21,plain,
( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(W1),W1,xR) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_22,plain,
( ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| ~ iLess0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0)
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR) ),
inference(subst,[],[refute_0_21:[bind(W1,$fot(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_23,plain,
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W1,W0,xR)
| iLess0(W1,W0) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_24,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| ~ aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR)
| iLess0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0) ),
inference(subst,[],[refute_0_23:[bind(W0,$fot(skolemFOFtoCNF_W0)),bind(W1,$fot(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_25,plain,
( ~ aElement0(skolemFOFtoCNF_W0)
| ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| iLess0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0) ),
inference(resolve,[$cnf( aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR) )],[refute_0_5,refute_0_24]) ).
cnf(refute_0_26,plain,
( ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| iLess0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W0) )],[refute_0_4,refute_0_25]) ).
cnf(refute_0_27,plain,
iLess0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)) )],[refute_0_14,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR) ),
inference(resolve,[$cnf( iLess0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0) )],[refute_0_27,refute_0_22]) ).
cnf(refute_0_29,plain,
aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)) )],[refute_0_14,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| W1 = skolemFOFtoCNF_W2_3(W1)
| sdtmndtplgtdt0(W1,xR,skolemFOFtoCNF_W2_3(W1)) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_31,plain,
( ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| ~ iLess0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0)
| skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| sdtmndtplgtdt0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))) ),
inference(subst,[],[refute_0_30:[bind(W1,$fot(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_32,plain,
( ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| sdtmndtplgtdt0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( iLess0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0) )],[refute_0_27,refute_0_31]) ).
cnf(refute_0_33,plain,
( skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| sdtmndtplgtdt0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)) )],[refute_0_14,refute_0_32]) ).
cnf(refute_0_34,plain,
( ~ aElement0(W1)
| ~ aElement0(W2)
| ~ aReductOfIn0(W2,skolemFOFtoCNF_W0,xR)
| ~ sdtmndtplgtdt0(W2,xR,W1)
| aReductOfIn0(skolemFOFtoCNF_W2_4(W1),W1,xR) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_35,plain,
( ~ aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)))
| ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| ~ aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR)
| ~ sdtmndtplgtdt0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)))
| aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),xR) ),
inference(subst,[],[refute_0_34:[bind(W1,$fot(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)))),bind(W2,$fot(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_36,plain,
( ~ aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)))
| ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| ~ aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR)
| skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),xR) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))) )],[refute_0_33,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ aElement0(W1)
| ~ iLess0(W1,skolemFOFtoCNF_W0)
| aElement0(skolemFOFtoCNF_W2_3(W1)) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_38,plain,
( ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| ~ iLess0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0)
| aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))) ),
inference(subst,[],[refute_0_37:[bind(W1,$fot(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)))]]) ).
cnf(refute_0_39,plain,
( ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))) ),
inference(resolve,[$cnf( iLess0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0) )],[refute_0_27,refute_0_38]) ).
cnf(refute_0_40,plain,
aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)) )],[refute_0_14,refute_0_39]) ).
cnf(refute_0_41,plain,
( ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| ~ aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR)
| skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),xR) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))) )],[refute_0_40,refute_0_36]) ).
cnf(refute_0_42,plain,
( ~ aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR)
| skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),xR) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)) )],[refute_0_14,refute_0_41]) ).
cnf(refute_0_43,plain,
( skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),xR) ),
inference(resolve,[$cnf( aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W0,xR) )],[refute_0_5,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| ~ aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR)
| ~ aReductOfIn0(X_59,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),xR)
| ~ aRewritingSystem0(xR) ),
inference(subst,[],[refute_0_16:[bind(W0,$fot(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))),bind(W1,$fot(xR)),bind(W2,$fot(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)))),bind(W3,$fot(X_59))]]) ).
cnf(refute_0_45,plain,
( ~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| ~ aReductOfIn0(X_59,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),xR)
| ~ aRewritingSystem0(xR) ),
inference(resolve,[$cnf( aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR) )],[refute_0_29,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ aReductOfIn0(X_59,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),xR)
| ~ aRewritingSystem0(xR) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)) )],[refute_0_14,refute_0_45]) ).
cnf(refute_0_47,plain,
~ aReductOfIn0(X_59,skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),xR),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_13,refute_0_46]) ).
cnf(refute_0_48,plain,
~ aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),xR),
inference(subst,[],[refute_0_47:[bind(X_59,$fot(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)))))]]) ).
cnf(refute_0_49,plain,
skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0) = skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),
inference(resolve,[$cnf( aReductOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),xR) )],[refute_0_43,refute_0_48]) ).
cnf(refute_0_50,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_51,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_52,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_50,refute_0_51]) ).
cnf(refute_0_53,plain,
( skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0) != skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))
| skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)) = skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0) ),
inference(subst,[],[refute_0_52:[bind(X,$fot(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))),bind(Y,$fot(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))))]]) ).
cnf(refute_0_54,plain,
skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)) = skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))) )],[refute_0_49,refute_0_53]) ).
cnf(refute_0_55,plain,
( skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)) != skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)
| ~ aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR)
| aNormalFormOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR) ),
introduced(tautology,[equality,[$cnf( aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR) ),[0],$fot(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0))]]) ).
cnf(refute_0_56,plain,
( ~ aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR)
| aNormalFormOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR) ),
inference(resolve,[$cnf( $equal(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
aNormalFormOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR),
inference(resolve,[$cnf( aNormalFormOfIn0(skolemFOFtoCNF_W2_3(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR) )],[refute_0_29,refute_0_56]) ).
cnf(refute_0_58,plain,
~ aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)),
inference(resolve,[$cnf( aNormalFormOfIn0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0),xR) )],[refute_0_57,refute_0_20]) ).
cnf(refute_0_59,plain,
$false,
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W2_4(skolemFOFtoCNF_W0)) )],[refute_0_14,refute_0_58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : COM013+4 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n005.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 17:07:23 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.33 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.18/0.39
%------------------------------------------------------------------------------