TSTP Solution File: COM022+4 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COM022+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n023.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Fri Jul 15 01:32:35 EDT 2022
% Result : Theorem 0.20s 0.49s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 12
% Syntax : Number of formulae : 96 ( 17 unt; 2 def)
% Number of atoms : 1032 ( 150 equ)
% Maximal formula atoms : 135 ( 10 avg)
% Number of connectives : 1197 ( 261 ~; 466 |; 459 &)
% ( 4 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 47 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 10 ( 7 usr; 2 prp; 0-3 aty)
% Number of functors : 19 ( 19 usr; 19 con; 0-0 aty)
% Number of variables : 150 ( 0 sgn 36 !; 96 ?)
% Comments :
%------------------------------------------------------------------------------
fof(m__731,hypothesis,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ) ).
fof(m__,conjecture,
( ( ( ( aReductOfIn0(xb,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xb) )
| sdtmndtplgtdt0(xa,xR,xb) )
& ( aReductOfIn0(xc,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xc) )
| sdtmndtplgtdt0(xa,xR,xc) ) )
=> ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& ( W0 = xb
| ( ( aReductOfIn0(xb,W0,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,xb) ) )
& sdtmndtplgtdt0(W0,xR,xb) ) )
& sdtmndtasgtdt0(W0,xR,xb)
& ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,xa,xR)
& ( W2 = xc
| ( ( aReductOfIn0(xc,W2,xR)
| ? [W5] :
( aElement0(W5)
& aReductOfIn0(W5,W2,xR)
& sdtmndtplgtdt0(W5,xR,xc) ) )
& sdtmndtplgtdt0(W2,xR,xc) ) )
& sdtmndtasgtdt0(W2,xR,xc)
& ? [W5] :
( aElement0(W5)
& ( W0 = W5
| ( ( aReductOfIn0(W5,W0,xR)
| ? [W6] :
( aElement0(W6)
& aReductOfIn0(W6,W0,xR)
& sdtmndtplgtdt0(W6,xR,W5) ) )
& sdtmndtplgtdt0(W0,xR,W5) ) )
& sdtmndtasgtdt0(W0,xR,W5)
& ( W2 = W5
| ( ( aReductOfIn0(W5,W2,xR)
| ? [W6] :
( aElement0(W6)
& aReductOfIn0(W6,W2,xR)
& sdtmndtplgtdt0(W6,xR,W5) ) )
& sdtmndtplgtdt0(W2,xR,W5) ) )
& sdtmndtasgtdt0(W2,xR,W5)
& ? [W6] :
( aElement0(W6)
& ( W5 = W6
| ( ( aReductOfIn0(W6,W5,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W5,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) )
& sdtmndtplgtdt0(W5,xR,W6) ) )
& sdtmndtasgtdt0(W5,xR,W6)
& ~ ? [W4] : aReductOfIn0(W4,W6,xR)
& aNormalFormOfIn0(W6,W5,xR)
& ( xb = W6
| ( ( aReductOfIn0(W6,xb,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,xb,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) )
& sdtmndtplgtdt0(xb,xR,W6) ) )
& sdtmndtasgtdt0(xb,xR,W6)
& ( xc = W6
| ( ( aReductOfIn0(W6,xc,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,xc,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) )
& sdtmndtplgtdt0(xc,xR,W6) ) )
& sdtmndtasgtdt0(xc,xR,W6) ) ) ) ) )
=> ( ( ( xa = xb
| ( ( aReductOfIn0(xb,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xb) ) )
& sdtmndtplgtdt0(xa,xR,xb) ) )
& sdtmndtasgtdt0(xa,xR,xb)
& ( xa = xc
| ( ( aReductOfIn0(xc,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xc) ) )
& sdtmndtplgtdt0(xa,xR,xc) ) )
& sdtmndtasgtdt0(xa,xR,xc) )
=> ? [W0] :
( aElement0(W0)
& ( xb = W0
| aReductOfIn0(W0,xb,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,xb,xR)
& sdtmndtplgtdt0(W2,xR,W0) )
| sdtmndtplgtdt0(xb,xR,W0)
| sdtmndtasgtdt0(xb,xR,W0) )
& ( xc = W0
| aReductOfIn0(W0,xc,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,xc,xR)
& sdtmndtplgtdt0(W2,xR,W0) )
| sdtmndtplgtdt0(xc,xR,W0)
| sdtmndtasgtdt0(xc,xR,W0) ) ) ) ) ).
fof(definition_0,definition,
( definitionFOFtoCNF_2
<=> ( ( ~ aReductOfIn0(xb,xa,xR)
& ~ sdtmndtplgtdt0(xa,xR,xb)
& ! [W0] :
( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR)
| ~ sdtmndtplgtdt0(W0,xR,xb) ) )
| ( ~ aReductOfIn0(xc,xa,xR)
& ~ sdtmndtplgtdt0(xa,xR,xc)
& ! [W0] :
( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR)
| ~ sdtmndtplgtdt0(W0,xR,xc) ) ) ) ) ).
fof(definition_1,definition,
! [W0] :
( definitionFOFtoCNF_3(W0)
<=> ( xb != W0
& ~ aReductOfIn0(W0,xb,xR)
& ~ sdtmndtasgtdt0(xb,xR,W0)
& ~ sdtmndtplgtdt0(xb,xR,W0) ) ) ).
fof(subgoal_0,plain,
( ( ( ( ( aReductOfIn0(xb,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xb) )
| sdtmndtplgtdt0(xa,xR,xb) )
& ( aReductOfIn0(xc,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xc) )
| sdtmndtplgtdt0(xa,xR,xc) ) )
=> ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& ( W0 = xb
| ( ( aReductOfIn0(xb,W0,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,xb) ) )
& sdtmndtplgtdt0(W0,xR,xb) ) )
& sdtmndtasgtdt0(W0,xR,xb)
& ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,xa,xR)
& ( W2 = xc
| ( ( aReductOfIn0(xc,W2,xR)
| ? [W5] :
( aElement0(W5)
& aReductOfIn0(W5,W2,xR)
& sdtmndtplgtdt0(W5,xR,xc) ) )
& sdtmndtplgtdt0(W2,xR,xc) ) )
& sdtmndtasgtdt0(W2,xR,xc)
& ? [W5] :
( aElement0(W5)
& ( W0 = W5
| ( ( aReductOfIn0(W5,W0,xR)
| ? [W6] :
( aElement0(W6)
& aReductOfIn0(W6,W0,xR)
& sdtmndtplgtdt0(W6,xR,W5) ) )
& sdtmndtplgtdt0(W0,xR,W5) ) )
& sdtmndtasgtdt0(W0,xR,W5)
& ( W2 = W5
| ( ( aReductOfIn0(W5,W2,xR)
| ? [W6] :
( aElement0(W6)
& aReductOfIn0(W6,W2,xR)
& sdtmndtplgtdt0(W6,xR,W5) ) )
& sdtmndtplgtdt0(W2,xR,W5) ) )
& sdtmndtasgtdt0(W2,xR,W5)
& ? [W6] :
( aElement0(W6)
& ( W5 = W6
| ( ( aReductOfIn0(W6,W5,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W5,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) )
& sdtmndtplgtdt0(W5,xR,W6) ) )
& sdtmndtasgtdt0(W5,xR,W6)
& ~ ? [W4] : aReductOfIn0(W4,W6,xR)
& aNormalFormOfIn0(W6,W5,xR)
& ( xb = W6
| ( ( aReductOfIn0(W6,xb,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,xb,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) )
& sdtmndtplgtdt0(xb,xR,W6) ) )
& sdtmndtasgtdt0(xb,xR,W6)
& ( xc = W6
| ( ( aReductOfIn0(W6,xc,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,xc,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) )
& sdtmndtplgtdt0(xc,xR,W6) ) )
& sdtmndtasgtdt0(xc,xR,W6) ) ) ) ) )
& ( xa = xb
| ( ( aReductOfIn0(xb,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xb) ) )
& sdtmndtplgtdt0(xa,xR,xb) ) )
& sdtmndtasgtdt0(xa,xR,xb)
& ( xa = xc
| ( ( aReductOfIn0(xc,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xc) ) )
& sdtmndtplgtdt0(xa,xR,xc) ) )
& sdtmndtasgtdt0(xa,xR,xc) )
=> ? [W0] :
( aElement0(W0)
& ( xb = W0
| aReductOfIn0(W0,xb,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,xb,xR)
& sdtmndtplgtdt0(W2,xR,W0) )
| sdtmndtplgtdt0(xb,xR,W0)
| sdtmndtasgtdt0(xb,xR,W0) )
& ( xc = W0
| aReductOfIn0(W0,xc,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,xc,xR)
& sdtmndtplgtdt0(W2,xR,W0) )
| sdtmndtplgtdt0(xc,xR,W0)
| sdtmndtasgtdt0(xc,xR,W0) ) ) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ( ( ( ( ( aReductOfIn0(xb,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xb) )
| sdtmndtplgtdt0(xa,xR,xb) )
& ( aReductOfIn0(xc,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xc) )
| sdtmndtplgtdt0(xa,xR,xc) ) )
=> ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& ( W0 = xb
| ( ( aReductOfIn0(xb,W0,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,xb) ) )
& sdtmndtplgtdt0(W0,xR,xb) ) )
& sdtmndtasgtdt0(W0,xR,xb)
& ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,xa,xR)
& ( W2 = xc
| ( ( aReductOfIn0(xc,W2,xR)
| ? [W5] :
( aElement0(W5)
& aReductOfIn0(W5,W2,xR)
& sdtmndtplgtdt0(W5,xR,xc) ) )
& sdtmndtplgtdt0(W2,xR,xc) ) )
& sdtmndtasgtdt0(W2,xR,xc)
& ? [W5] :
( aElement0(W5)
& ( W0 = W5
| ( ( aReductOfIn0(W5,W0,xR)
| ? [W6] :
( aElement0(W6)
& aReductOfIn0(W6,W0,xR)
& sdtmndtplgtdt0(W6,xR,W5) ) )
& sdtmndtplgtdt0(W0,xR,W5) ) )
& sdtmndtasgtdt0(W0,xR,W5)
& ( W2 = W5
| ( ( aReductOfIn0(W5,W2,xR)
| ? [W6] :
( aElement0(W6)
& aReductOfIn0(W6,W2,xR)
& sdtmndtplgtdt0(W6,xR,W5) ) )
& sdtmndtplgtdt0(W2,xR,W5) ) )
& sdtmndtasgtdt0(W2,xR,W5)
& ? [W6] :
( aElement0(W6)
& ( W5 = W6
| ( ( aReductOfIn0(W6,W5,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W5,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) )
& sdtmndtplgtdt0(W5,xR,W6) ) )
& sdtmndtasgtdt0(W5,xR,W6)
& ~ ? [W4] : aReductOfIn0(W4,W6,xR)
& aNormalFormOfIn0(W6,W5,xR)
& ( xb = W6
| ( ( aReductOfIn0(W6,xb,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,xb,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) )
& sdtmndtplgtdt0(xb,xR,W6) ) )
& sdtmndtasgtdt0(xb,xR,W6)
& ( xc = W6
| ( ( aReductOfIn0(W6,xc,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,xc,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) )
& sdtmndtplgtdt0(xc,xR,W6) ) )
& sdtmndtasgtdt0(xc,xR,W6) ) ) ) ) )
& ( xa = xb
| ( ( aReductOfIn0(xb,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xb) ) )
& sdtmndtplgtdt0(xa,xR,xb) ) )
& sdtmndtasgtdt0(xa,xR,xb)
& ( xa = xc
| ( ( aReductOfIn0(xc,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xc) ) )
& sdtmndtplgtdt0(xa,xR,xc) ) )
& sdtmndtasgtdt0(xa,xR,xc) )
=> ? [W0] :
( aElement0(W0)
& ( xb = W0
| aReductOfIn0(W0,xb,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,xb,xR)
& sdtmndtplgtdt0(W2,xR,W0) )
| sdtmndtplgtdt0(xb,xR,W0)
| sdtmndtasgtdt0(xb,xR,W0) )
& ( xc = W0
| aReductOfIn0(W0,xc,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,xc,xR)
& sdtmndtplgtdt0(W2,xR,W0) )
| sdtmndtplgtdt0(xc,xR,W0)
| sdtmndtasgtdt0(xc,xR,W0) ) ) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( sdtmndtasgtdt0(xa,xR,xb)
& sdtmndtasgtdt0(xa,xR,xc)
& ( xa = xb
| ( sdtmndtplgtdt0(xa,xR,xb)
& ( aReductOfIn0(xb,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xb) ) ) ) )
& ( xa = xc
| ( sdtmndtplgtdt0(xa,xR,xc)
& ( aReductOfIn0(xc,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xc) ) ) ) )
& ( ( ~ aReductOfIn0(xb,xa,xR)
& ~ sdtmndtplgtdt0(xa,xR,xb)
& ! [W0] :
( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR)
| ~ sdtmndtplgtdt0(W0,xR,xb) ) )
| ( ~ aReductOfIn0(xc,xa,xR)
& ~ sdtmndtplgtdt0(xa,xR,xc)
& ! [W0] :
( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR)
| ~ sdtmndtplgtdt0(W0,xR,xc) ) )
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtasgtdt0(W0,xR,xb)
& ( W0 = xb
| ( sdtmndtplgtdt0(W0,xR,xb)
& ( aReductOfIn0(xb,W0,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,xb) ) ) ) )
& ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,xa,xR)
& sdtmndtasgtdt0(W2,xR,xc)
& ( W2 = xc
| ( sdtmndtplgtdt0(W2,xR,xc)
& ( aReductOfIn0(xc,W2,xR)
| ? [W5] :
( aElement0(W5)
& aReductOfIn0(W5,W2,xR)
& sdtmndtplgtdt0(W5,xR,xc) ) ) ) )
& ? [W5] :
( aElement0(W5)
& sdtmndtasgtdt0(W0,xR,W5)
& sdtmndtasgtdt0(W2,xR,W5)
& ( W0 = W5
| ( sdtmndtplgtdt0(W0,xR,W5)
& ( aReductOfIn0(W5,W0,xR)
| ? [W6] :
( aElement0(W6)
& aReductOfIn0(W6,W0,xR)
& sdtmndtplgtdt0(W6,xR,W5) ) ) ) )
& ( W2 = W5
| ( sdtmndtplgtdt0(W2,xR,W5)
& ( aReductOfIn0(W5,W2,xR)
| ? [W6] :
( aElement0(W6)
& aReductOfIn0(W6,W2,xR)
& sdtmndtplgtdt0(W6,xR,W5) ) ) ) )
& ? [W6] :
( aElement0(W6)
& aNormalFormOfIn0(W6,W5,xR)
& sdtmndtasgtdt0(W5,xR,W6)
& sdtmndtasgtdt0(xb,xR,W6)
& sdtmndtasgtdt0(xc,xR,W6)
& ( W5 = W6
| ( sdtmndtplgtdt0(W5,xR,W6)
& ( aReductOfIn0(W6,W5,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W5,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) ) ) )
& ( xb = W6
| ( sdtmndtplgtdt0(xb,xR,W6)
& ( aReductOfIn0(W6,xb,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,xb,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) ) ) )
& ( xc = W6
| ( sdtmndtplgtdt0(xc,xR,W6)
& ( aReductOfIn0(W6,xc,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,xc,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) ) ) )
& ! [W4] : ~ aReductOfIn0(W4,W6,xR) ) ) ) ) )
& ! [W0] :
( ~ aElement0(W0)
| ( xb != W0
& ~ aReductOfIn0(W0,xb,xR)
& ~ sdtmndtasgtdt0(xb,xR,W0)
& ~ sdtmndtplgtdt0(xb,xR,W0)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,xb,xR)
| ~ sdtmndtplgtdt0(W2,xR,W0) ) )
| ( xc != W0
& ~ aReductOfIn0(W0,xc,xR)
& ~ sdtmndtasgtdt0(xc,xR,W0)
& ~ sdtmndtplgtdt0(xc,xR,W0)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,xc,xR)
| ~ sdtmndtplgtdt0(W2,xR,W0) ) ) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
! [W0] :
( ~ aElement0(W0)
| ( xb != W0
& ~ aReductOfIn0(W0,xb,xR)
& ~ sdtmndtasgtdt0(xb,xR,W0)
& ~ sdtmndtplgtdt0(xb,xR,W0)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,xb,xR)
| ~ sdtmndtplgtdt0(W2,xR,W0) ) )
| ( xc != W0
& ~ aReductOfIn0(W0,xc,xR)
& ~ sdtmndtasgtdt0(xc,xR,W0)
& ~ sdtmndtplgtdt0(xc,xR,W0)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,xc,xR)
| ~ sdtmndtplgtdt0(W2,xR,W0) ) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [W0] :
( ~ aElement0(W0)
| ( xb != W0
& ~ aReductOfIn0(W0,xb,xR)
& ~ sdtmndtasgtdt0(xb,xR,W0)
& ~ sdtmndtplgtdt0(xb,xR,W0)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,xb,xR)
| ~ sdtmndtplgtdt0(W2,xR,W0) ) )
| ( xc != W0
& ~ aReductOfIn0(W0,xc,xR)
& ~ sdtmndtasgtdt0(xc,xR,W0)
& ~ sdtmndtplgtdt0(xc,xR,W0)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,xc,xR)
| ~ sdtmndtplgtdt0(W2,xR,W0) ) ) ),
inference(specialize,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [W0] :
( ~ definitionFOFtoCNF_3(W0)
<=> ( xb = W0
| aReductOfIn0(W0,xb,xR)
| sdtmndtasgtdt0(xb,xR,W0)
| sdtmndtplgtdt0(xb,xR,W0) ) ),
inference(canonicalize,[],[definition_1]) ).
fof(normalize_0_4,plain,
! [W0] :
( ~ aElement0(W0)
| ( definitionFOFtoCNF_3(W0)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,xb,xR)
| ~ sdtmndtplgtdt0(W2,xR,W0) ) )
| ( xc != W0
& ~ aReductOfIn0(W0,xc,xR)
& ~ sdtmndtasgtdt0(xc,xR,W0)
& ~ sdtmndtplgtdt0(xc,xR,W0)
& ! [W2] :
( ~ aElement0(W2)
| ~ aReductOfIn0(W2,xc,xR)
| ~ sdtmndtplgtdt0(W2,xR,W0) ) ) ),
inference(simplify,[],[normalize_0_2,normalize_0_3]) ).
fof(normalize_0_5,plain,
! [W0,W2,W3] :
( ( xc != W0
| ~ aElement0(W0)
| definitionFOFtoCNF_3(W0) )
& ( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xc,xR)
| definitionFOFtoCNF_3(W0) )
& ( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xc,xR,W0)
| definitionFOFtoCNF_3(W0) )
& ( ~ aElement0(W0)
| ~ sdtmndtplgtdt0(xc,xR,W0)
| definitionFOFtoCNF_3(W0) )
& ( xc != W0
| ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aReductOfIn0(W2,xb,xR)
| ~ sdtmndtplgtdt0(W2,xR,W0) )
& ( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aReductOfIn0(W0,xc,xR)
| ~ aReductOfIn0(W2,xb,xR)
| ~ sdtmndtplgtdt0(W2,xR,W0) )
& ( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aReductOfIn0(W2,xb,xR)
| ~ sdtmndtasgtdt0(xc,xR,W0)
| ~ sdtmndtplgtdt0(W2,xR,W0) )
& ( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aReductOfIn0(W2,xb,xR)
| ~ sdtmndtplgtdt0(W2,xR,W0)
| ~ sdtmndtplgtdt0(xc,xR,W0) )
& ( ~ aElement0(W0)
| ~ aElement0(W3)
| ~ aReductOfIn0(W3,xc,xR)
| ~ sdtmndtplgtdt0(W3,xR,W0)
| definitionFOFtoCNF_3(W0) )
& ( ~ aElement0(W0)
| ~ aElement0(W2)
| ~ aElement0(W3)
| ~ aReductOfIn0(W2,xb,xR)
| ~ aReductOfIn0(W3,xc,xR)
| ~ sdtmndtplgtdt0(W2,xR,W0)
| ~ sdtmndtplgtdt0(W3,xR,W0) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W0] :
( xc != W0
| ~ aElement0(W0)
| definitionFOFtoCNF_3(W0) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( aElement0(xa)
& aElement0(xb)
& aElement0(xc) ),
inference(canonicalize,[],[m__731]) ).
fof(normalize_0_8,plain,
aElement0(xc),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
( xa = xc
| ( sdtmndtplgtdt0(xa,xR,xc)
& ( aReductOfIn0(xc,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xc) ) ) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_10,plain,
( ( xa = xc
| sdtmndtplgtdt0(xa,xR,xc) )
& ( xa = xc
| aElement0(skolemFOFtoCNF_W0_1)
| aReductOfIn0(xc,xa,xR) )
& ( xa = xc
| aReductOfIn0(skolemFOFtoCNF_W0_1,xa,xR)
| aReductOfIn0(xc,xa,xR) )
& ( xa = xc
| aReductOfIn0(xc,xa,xR)
| sdtmndtplgtdt0(skolemFOFtoCNF_W0_1,xR,xc) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
( xa = xc
| sdtmndtplgtdt0(xa,xR,xc) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [W0] :
( ( xb != W0
| ~ definitionFOFtoCNF_3(W0) )
& ( ~ aReductOfIn0(W0,xb,xR)
| ~ definitionFOFtoCNF_3(W0) )
& ( ~ definitionFOFtoCNF_3(W0)
| ~ sdtmndtasgtdt0(xb,xR,W0) )
& ( ~ definitionFOFtoCNF_3(W0)
| ~ sdtmndtplgtdt0(xb,xR,W0) )
& ( xb = W0
| aReductOfIn0(W0,xb,xR)
| definitionFOFtoCNF_3(W0)
| sdtmndtasgtdt0(xb,xR,W0)
| sdtmndtplgtdt0(xb,xR,W0) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_13,plain,
! [W0] :
( ~ definitionFOFtoCNF_3(W0)
| ~ sdtmndtplgtdt0(xb,xR,W0) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
( xa = xb
| ( sdtmndtplgtdt0(xa,xR,xb)
& ( aReductOfIn0(xb,xa,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xb) ) ) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_15,plain,
( ( xa = xb
| sdtmndtplgtdt0(xa,xR,xb) )
& ( xa = xb
| aElement0(skolemFOFtoCNF_W0)
| aReductOfIn0(xb,xa,xR) )
& ( xa = xb
| aReductOfIn0(skolemFOFtoCNF_W0,xa,xR)
| aReductOfIn0(xb,xa,xR) )
& ( xa = xb
| aReductOfIn0(xb,xa,xR)
| sdtmndtplgtdt0(skolemFOFtoCNF_W0,xR,xb) ) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
( xa = xb
| sdtmndtplgtdt0(xa,xR,xb) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [W0] :
( ~ aElement0(W0)
| ~ sdtmndtplgtdt0(xc,xR,W0)
| definitionFOFtoCNF_3(W0) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_18,plain,
( ~ definitionFOFtoCNF_2
<=> ( ( aReductOfIn0(xb,xa,xR)
| sdtmndtplgtdt0(xa,xR,xb)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xb) ) )
& ( aReductOfIn0(xc,xa,xR)
| sdtmndtplgtdt0(xa,xR,xc)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtplgtdt0(W0,xR,xc) ) ) ) ),
inference(canonicalize,[],[definition_0]) ).
fof(normalize_0_19,plain,
! [W0,W1] :
( ( ~ aReductOfIn0(xb,xa,xR)
| ~ aReductOfIn0(xc,xa,xR)
| ~ definitionFOFtoCNF_2 )
& ( ~ aReductOfIn0(xb,xa,xR)
| ~ definitionFOFtoCNF_2
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( ~ aReductOfIn0(xc,xa,xR)
| ~ definitionFOFtoCNF_2
| ~ sdtmndtplgtdt0(xa,xR,xb) )
& ( ~ definitionFOFtoCNF_2
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( aElement0(skolemFOFtoCNF_W0_2)
| aReductOfIn0(xc,xa,xR)
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(xa,xR,xc) )
& ( aElement0(skolemFOFtoCNF_W0_3)
| aReductOfIn0(xb,xa,xR)
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(xa,xR,xb) )
& ( aReductOfIn0(skolemFOFtoCNF_W0_2,xa,xR)
| aReductOfIn0(xc,xa,xR)
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(xa,xR,xc) )
& ( aReductOfIn0(skolemFOFtoCNF_W0_3,xa,xR)
| aReductOfIn0(xb,xa,xR)
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(xa,xR,xb) )
& ( aReductOfIn0(xb,xa,xR)
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(skolemFOFtoCNF_W0_3,xR,xb)
| sdtmndtplgtdt0(xa,xR,xb) )
& ( aReductOfIn0(xc,xa,xR)
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(skolemFOFtoCNF_W0_2,xR,xc)
| sdtmndtplgtdt0(xa,xR,xc) )
& ( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR)
| ~ aReductOfIn0(xc,xa,xR)
| ~ definitionFOFtoCNF_2
| ~ sdtmndtplgtdt0(W0,xR,xb) )
& ( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR)
| ~ definitionFOFtoCNF_2
| ~ sdtmndtplgtdt0(W0,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) )
& ( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xa,xR)
| ~ aReductOfIn0(xb,xa,xR)
| ~ definitionFOFtoCNF_2
| ~ sdtmndtplgtdt0(W1,xR,xc) )
& ( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xa,xR)
| ~ definitionFOFtoCNF_2
| ~ sdtmndtplgtdt0(W1,xR,xc)
| ~ sdtmndtplgtdt0(xa,xR,xb) )
& ( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aReductOfIn0(W0,xa,xR)
| ~ aReductOfIn0(W1,xa,xR)
| ~ definitionFOFtoCNF_2
| ~ sdtmndtplgtdt0(W0,xR,xb)
| ~ sdtmndtplgtdt0(W1,xR,xc) ) ),
inference(clausify,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
( ~ definitionFOFtoCNF_2
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) ),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
( ( ~ aReductOfIn0(xb,xa,xR)
& ~ sdtmndtplgtdt0(xa,xR,xb)
& ! [W0] :
( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR)
| ~ sdtmndtplgtdt0(W0,xR,xb) ) )
| ( ~ aReductOfIn0(xc,xa,xR)
& ~ sdtmndtplgtdt0(xa,xR,xc)
& ! [W0] :
( ~ aElement0(W0)
| ~ aReductOfIn0(W0,xa,xR)
| ~ sdtmndtplgtdt0(W0,xR,xc) ) )
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtasgtdt0(W0,xR,xb)
& ( W0 = xb
| ( sdtmndtplgtdt0(W0,xR,xb)
& ( aReductOfIn0(xb,W0,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,xb) ) ) ) )
& ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,xa,xR)
& sdtmndtasgtdt0(W2,xR,xc)
& ( W2 = xc
| ( sdtmndtplgtdt0(W2,xR,xc)
& ( aReductOfIn0(xc,W2,xR)
| ? [W5] :
( aElement0(W5)
& aReductOfIn0(W5,W2,xR)
& sdtmndtplgtdt0(W5,xR,xc) ) ) ) )
& ? [W5] :
( aElement0(W5)
& sdtmndtasgtdt0(W0,xR,W5)
& sdtmndtasgtdt0(W2,xR,W5)
& ( W0 = W5
| ( sdtmndtplgtdt0(W0,xR,W5)
& ( aReductOfIn0(W5,W0,xR)
| ? [W6] :
( aElement0(W6)
& aReductOfIn0(W6,W0,xR)
& sdtmndtplgtdt0(W6,xR,W5) ) ) ) )
& ( W2 = W5
| ( sdtmndtplgtdt0(W2,xR,W5)
& ( aReductOfIn0(W5,W2,xR)
| ? [W6] :
( aElement0(W6)
& aReductOfIn0(W6,W2,xR)
& sdtmndtplgtdt0(W6,xR,W5) ) ) ) )
& ? [W6] :
( aElement0(W6)
& aNormalFormOfIn0(W6,W5,xR)
& sdtmndtasgtdt0(W5,xR,W6)
& sdtmndtasgtdt0(xb,xR,W6)
& sdtmndtasgtdt0(xc,xR,W6)
& ( W5 = W6
| ( sdtmndtplgtdt0(W5,xR,W6)
& ( aReductOfIn0(W6,W5,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W5,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) ) ) )
& ( xb = W6
| ( sdtmndtplgtdt0(xb,xR,W6)
& ( aReductOfIn0(W6,xb,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,xb,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) ) ) )
& ( xc = W6
| ( sdtmndtplgtdt0(xc,xR,W6)
& ( aReductOfIn0(W6,xc,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,xc,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) ) ) )
& ! [W4] : ~ aReductOfIn0(W4,W6,xR) ) ) ) ) ),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_22,plain,
( definitionFOFtoCNF_2
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xa,xR)
& sdtmndtasgtdt0(W0,xR,xb)
& ( W0 = xb
| ( sdtmndtplgtdt0(W0,xR,xb)
& ( aReductOfIn0(xb,W0,xR)
| ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,W0,xR)
& sdtmndtplgtdt0(W2,xR,xb) ) ) ) )
& ? [W2] :
( aElement0(W2)
& aReductOfIn0(W2,xa,xR)
& sdtmndtasgtdt0(W2,xR,xc)
& ( W2 = xc
| ( sdtmndtplgtdt0(W2,xR,xc)
& ( aReductOfIn0(xc,W2,xR)
| ? [W5] :
( aElement0(W5)
& aReductOfIn0(W5,W2,xR)
& sdtmndtplgtdt0(W5,xR,xc) ) ) ) )
& ? [W5] :
( aElement0(W5)
& sdtmndtasgtdt0(W0,xR,W5)
& sdtmndtasgtdt0(W2,xR,W5)
& ( W0 = W5
| ( sdtmndtplgtdt0(W0,xR,W5)
& ( aReductOfIn0(W5,W0,xR)
| ? [W6] :
( aElement0(W6)
& aReductOfIn0(W6,W0,xR)
& sdtmndtplgtdt0(W6,xR,W5) ) ) ) )
& ( W2 = W5
| ( sdtmndtplgtdt0(W2,xR,W5)
& ( aReductOfIn0(W5,W2,xR)
| ? [W6] :
( aElement0(W6)
& aReductOfIn0(W6,W2,xR)
& sdtmndtplgtdt0(W6,xR,W5) ) ) ) )
& ? [W6] :
( aElement0(W6)
& aNormalFormOfIn0(W6,W5,xR)
& sdtmndtasgtdt0(W5,xR,W6)
& sdtmndtasgtdt0(xb,xR,W6)
& sdtmndtasgtdt0(xc,xR,W6)
& ( W5 = W6
| ( sdtmndtplgtdt0(W5,xR,W6)
& ( aReductOfIn0(W6,W5,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W5,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) ) ) )
& ( xb = W6
| ( sdtmndtplgtdt0(xb,xR,W6)
& ( aReductOfIn0(W6,xb,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,xb,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) ) ) )
& ( xc = W6
| ( sdtmndtplgtdt0(xc,xR,W6)
& ( aReductOfIn0(W6,xc,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,xc,xR)
& sdtmndtplgtdt0(W4,xR,W6) ) ) ) )
& ! [W4] : ~ aReductOfIn0(W4,W6,xR) ) ) ) ) ),
inference(simplify,[],[normalize_0_21,normalize_0_18]) ).
fof(normalize_0_23,plain,
! [W4] :
( ( ~ aReductOfIn0(W4,skolemFOFtoCNF_W3_6,xR)
| definitionFOFtoCNF_2 )
& ( aElement0(skolemFOFtoCNF_W0_4)
| definitionFOFtoCNF_2 )
& ( aElement0(skolemFOFtoCNF_W1_3)
| definitionFOFtoCNF_2 )
& ( aElement0(skolemFOFtoCNF_W2_4)
| definitionFOFtoCNF_2 )
& ( aElement0(skolemFOFtoCNF_W3_6)
| definitionFOFtoCNF_2 )
& ( aNormalFormOfIn0(skolemFOFtoCNF_W3_6,skolemFOFtoCNF_W2_4,xR)
| definitionFOFtoCNF_2 )
& ( aReductOfIn0(skolemFOFtoCNF_W0_4,xa,xR)
| definitionFOFtoCNF_2 )
& ( aReductOfIn0(skolemFOFtoCNF_W1_3,xa,xR)
| definitionFOFtoCNF_2 )
& ( definitionFOFtoCNF_2
| sdtmndtasgtdt0(skolemFOFtoCNF_W0_4,xR,skolemFOFtoCNF_W2_4) )
& ( definitionFOFtoCNF_2
| sdtmndtasgtdt0(skolemFOFtoCNF_W0_4,xR,xb) )
& ( definitionFOFtoCNF_2
| sdtmndtasgtdt0(skolemFOFtoCNF_W1_3,xR,skolemFOFtoCNF_W2_4) )
& ( definitionFOFtoCNF_2
| sdtmndtasgtdt0(skolemFOFtoCNF_W1_3,xR,xc) )
& ( definitionFOFtoCNF_2
| sdtmndtasgtdt0(skolemFOFtoCNF_W2_4,xR,skolemFOFtoCNF_W3_6) )
& ( definitionFOFtoCNF_2
| sdtmndtasgtdt0(xb,xR,skolemFOFtoCNF_W3_6) )
& ( definitionFOFtoCNF_2
| sdtmndtasgtdt0(xc,xR,skolemFOFtoCNF_W3_6) )
& ( skolemFOFtoCNF_W0_4 = skolemFOFtoCNF_W2_4
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(skolemFOFtoCNF_W0_4,xR,skolemFOFtoCNF_W2_4) )
& ( skolemFOFtoCNF_W0_4 = xb
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(skolemFOFtoCNF_W0_4,xR,xb) )
& ( skolemFOFtoCNF_W1_3 = skolemFOFtoCNF_W2_4
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(skolemFOFtoCNF_W1_3,xR,skolemFOFtoCNF_W2_4) )
& ( skolemFOFtoCNF_W1_3 = xc
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(skolemFOFtoCNF_W1_3,xR,xc) )
& ( skolemFOFtoCNF_W2_4 = skolemFOFtoCNF_W3_6
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(skolemFOFtoCNF_W2_4,xR,skolemFOFtoCNF_W3_6) )
& ( xb = skolemFOFtoCNF_W3_6
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(xb,xR,skolemFOFtoCNF_W3_6) )
& ( xc = skolemFOFtoCNF_W3_6
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(xc,xR,skolemFOFtoCNF_W3_6) )
& ( skolemFOFtoCNF_W0_4 = skolemFOFtoCNF_W2_4
| aElement0(skolemFOFtoCNF_W3_8)
| aReductOfIn0(skolemFOFtoCNF_W2_4,skolemFOFtoCNF_W0_4,xR)
| definitionFOFtoCNF_2 )
& ( skolemFOFtoCNF_W0_4 = skolemFOFtoCNF_W2_4
| aReductOfIn0(skolemFOFtoCNF_W2_4,skolemFOFtoCNF_W0_4,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_8,skolemFOFtoCNF_W0_4,xR)
| definitionFOFtoCNF_2 )
& ( skolemFOFtoCNF_W0_4 = skolemFOFtoCNF_W2_4
| aReductOfIn0(skolemFOFtoCNF_W2_4,skolemFOFtoCNF_W0_4,xR)
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(skolemFOFtoCNF_W3_8,xR,skolemFOFtoCNF_W2_4) )
& ( skolemFOFtoCNF_W0_4 = xb
| aElement0(skolemFOFtoCNF_W1_4)
| aReductOfIn0(xb,skolemFOFtoCNF_W0_4,xR)
| definitionFOFtoCNF_2 )
& ( skolemFOFtoCNF_W0_4 = xb
| aReductOfIn0(skolemFOFtoCNF_W1_4,skolemFOFtoCNF_W0_4,xR)
| aReductOfIn0(xb,skolemFOFtoCNF_W0_4,xR)
| definitionFOFtoCNF_2 )
& ( skolemFOFtoCNF_W0_4 = xb
| aReductOfIn0(xb,skolemFOFtoCNF_W0_4,xR)
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(skolemFOFtoCNF_W1_4,xR,xb) )
& ( skolemFOFtoCNF_W1_3 = skolemFOFtoCNF_W2_4
| aElement0(skolemFOFtoCNF_W3_7)
| aReductOfIn0(skolemFOFtoCNF_W2_4,skolemFOFtoCNF_W1_3,xR)
| definitionFOFtoCNF_2 )
& ( skolemFOFtoCNF_W1_3 = skolemFOFtoCNF_W2_4
| aReductOfIn0(skolemFOFtoCNF_W2_4,skolemFOFtoCNF_W1_3,xR)
| aReductOfIn0(skolemFOFtoCNF_W3_7,skolemFOFtoCNF_W1_3,xR)
| definitionFOFtoCNF_2 )
& ( skolemFOFtoCNF_W1_3 = skolemFOFtoCNF_W2_4
| aReductOfIn0(skolemFOFtoCNF_W2_4,skolemFOFtoCNF_W1_3,xR)
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(skolemFOFtoCNF_W3_7,xR,skolemFOFtoCNF_W2_4) )
& ( skolemFOFtoCNF_W1_3 = xc
| aElement0(skolemFOFtoCNF_W2_5)
| aReductOfIn0(xc,skolemFOFtoCNF_W1_3,xR)
| definitionFOFtoCNF_2 )
& ( skolemFOFtoCNF_W1_3 = xc
| aReductOfIn0(skolemFOFtoCNF_W2_5,skolemFOFtoCNF_W1_3,xR)
| aReductOfIn0(xc,skolemFOFtoCNF_W1_3,xR)
| definitionFOFtoCNF_2 )
& ( skolemFOFtoCNF_W1_3 = xc
| aReductOfIn0(xc,skolemFOFtoCNF_W1_3,xR)
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(skolemFOFtoCNF_W2_5,xR,xc) )
& ( skolemFOFtoCNF_W2_4 = skolemFOFtoCNF_W3_6
| aElement0(skolemFOFtoCNF_W4_8)
| aReductOfIn0(skolemFOFtoCNF_W3_6,skolemFOFtoCNF_W2_4,xR)
| definitionFOFtoCNF_2 )
& ( skolemFOFtoCNF_W2_4 = skolemFOFtoCNF_W3_6
| aReductOfIn0(skolemFOFtoCNF_W3_6,skolemFOFtoCNF_W2_4,xR)
| aReductOfIn0(skolemFOFtoCNF_W4_8,skolemFOFtoCNF_W2_4,xR)
| definitionFOFtoCNF_2 )
& ( skolemFOFtoCNF_W2_4 = skolemFOFtoCNF_W3_6
| aReductOfIn0(skolemFOFtoCNF_W3_6,skolemFOFtoCNF_W2_4,xR)
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(skolemFOFtoCNF_W4_8,xR,skolemFOFtoCNF_W3_6) )
& ( xb = skolemFOFtoCNF_W3_6
| aElement0(skolemFOFtoCNF_W4_7)
| aReductOfIn0(skolemFOFtoCNF_W3_6,xb,xR)
| definitionFOFtoCNF_2 )
& ( xb = skolemFOFtoCNF_W3_6
| aReductOfIn0(skolemFOFtoCNF_W3_6,xb,xR)
| aReductOfIn0(skolemFOFtoCNF_W4_7,xb,xR)
| definitionFOFtoCNF_2 )
& ( xb = skolemFOFtoCNF_W3_6
| aReductOfIn0(skolemFOFtoCNF_W3_6,xb,xR)
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(skolemFOFtoCNF_W4_7,xR,skolemFOFtoCNF_W3_6) )
& ( xc = skolemFOFtoCNF_W3_6
| aElement0(skolemFOFtoCNF_W4_6)
| aReductOfIn0(skolemFOFtoCNF_W3_6,xc,xR)
| definitionFOFtoCNF_2 )
& ( xc = skolemFOFtoCNF_W3_6
| aReductOfIn0(skolemFOFtoCNF_W3_6,xc,xR)
| aReductOfIn0(skolemFOFtoCNF_W4_6,xc,xR)
| definitionFOFtoCNF_2 )
& ( xc = skolemFOFtoCNF_W3_6
| aReductOfIn0(skolemFOFtoCNF_W3_6,xc,xR)
| definitionFOFtoCNF_2
| sdtmndtplgtdt0(skolemFOFtoCNF_W4_6,xR,skolemFOFtoCNF_W3_6) ) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
( definitionFOFtoCNF_2
| sdtmndtasgtdt0(xb,xR,skolemFOFtoCNF_W3_6) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [W0] :
( ~ definitionFOFtoCNF_3(W0)
| ~ sdtmndtasgtdt0(xb,xR,W0) ),
inference(conjunct,[],[normalize_0_12]) ).
fof(normalize_0_26,plain,
( aElement0(skolemFOFtoCNF_W3_6)
| definitionFOFtoCNF_2 ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_27,plain,
( definitionFOFtoCNF_2
| sdtmndtasgtdt0(xc,xR,skolemFOFtoCNF_W3_6) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_28,plain,
! [W0] :
( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xc,xR,W0)
| definitionFOFtoCNF_3(W0) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_29,plain,
aElement0(xb),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_30,plain,
! [W0] :
( xb != W0
| ~ definitionFOFtoCNF_3(W0) ),
inference(conjunct,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
( xc != W0
| ~ aElement0(W0)
| definitionFOFtoCNF_3(W0) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_1,plain,
( xc != xc
| ~ aElement0(xc)
| definitionFOFtoCNF_3(xc) ),
inference(subst,[],[refute_0_0:[bind(W0,$fot(xc))]]) ).
cnf(refute_0_2,plain,
xc = xc,
introduced(tautology,[refl,[$fot(xc)]]) ).
cnf(refute_0_3,plain,
( ~ aElement0(xc)
| definitionFOFtoCNF_3(xc) ),
inference(resolve,[$cnf( $equal(xc,xc) )],[refute_0_2,refute_0_1]) ).
cnf(refute_0_4,plain,
aElement0(xc),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_5,plain,
definitionFOFtoCNF_3(xc),
inference(resolve,[$cnf( aElement0(xc) )],[refute_0_4,refute_0_3]) ).
cnf(refute_0_6,plain,
( xa = xc
| sdtmndtplgtdt0(xa,xR,xc) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_7,plain,
( ~ definitionFOFtoCNF_3(W0)
| ~ sdtmndtplgtdt0(xb,xR,W0) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_8,plain,
( xa = xb
| sdtmndtplgtdt0(xa,xR,xb) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_9,plain,
( ~ aElement0(W0)
| ~ sdtmndtplgtdt0(xc,xR,W0)
| definitionFOFtoCNF_3(W0) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_10,plain,
( ~ aElement0(X_23)
| ~ sdtmndtplgtdt0(xc,xR,X_23)
| definitionFOFtoCNF_3(X_23) ),
inference(subst,[],[refute_0_9:[bind(W0,$fot(X_23))]]) ).
cnf(refute_0_11,plain,
( ~ definitionFOFtoCNF_2
| ~ sdtmndtplgtdt0(xa,xR,xb)
| ~ sdtmndtplgtdt0(xa,xR,xc) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_12,plain,
( ~ definitionFOFtoCNF_2
| ~ sdtmndtplgtdt0(xa,xR,xb)
| xa = xc ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xa,xR,xc) )],[refute_0_6,refute_0_11]) ).
cnf(refute_0_13,plain,
( ~ definitionFOFtoCNF_2
| xa = xb
| xa = xc ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xa,xR,xb) )],[refute_0_8,refute_0_12]) ).
cnf(refute_0_14,plain,
( definitionFOFtoCNF_2
| sdtmndtasgtdt0(xb,xR,skolemFOFtoCNF_W3_6) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_15,plain,
( ~ definitionFOFtoCNF_3(W0)
| ~ sdtmndtasgtdt0(xb,xR,W0) ),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_16,plain,
( ~ definitionFOFtoCNF_3(skolemFOFtoCNF_W3_6)
| ~ sdtmndtasgtdt0(xb,xR,skolemFOFtoCNF_W3_6) ),
inference(subst,[],[refute_0_15:[bind(W0,$fot(skolemFOFtoCNF_W3_6))]]) ).
cnf(refute_0_17,plain,
( ~ definitionFOFtoCNF_3(skolemFOFtoCNF_W3_6)
| definitionFOFtoCNF_2 ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xb,xR,skolemFOFtoCNF_W3_6) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
( aElement0(skolemFOFtoCNF_W3_6)
| definitionFOFtoCNF_2 ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_19,plain,
( definitionFOFtoCNF_2
| sdtmndtasgtdt0(xc,xR,skolemFOFtoCNF_W3_6) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_20,plain,
( ~ aElement0(W0)
| ~ sdtmndtasgtdt0(xc,xR,W0)
| definitionFOFtoCNF_3(W0) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_21,plain,
( ~ aElement0(skolemFOFtoCNF_W3_6)
| ~ sdtmndtasgtdt0(xc,xR,skolemFOFtoCNF_W3_6)
| definitionFOFtoCNF_3(skolemFOFtoCNF_W3_6) ),
inference(subst,[],[refute_0_20:[bind(W0,$fot(skolemFOFtoCNF_W3_6))]]) ).
cnf(refute_0_22,plain,
( ~ aElement0(skolemFOFtoCNF_W3_6)
| definitionFOFtoCNF_2
| definitionFOFtoCNF_3(skolemFOFtoCNF_W3_6) ),
inference(resolve,[$cnf( sdtmndtasgtdt0(xc,xR,skolemFOFtoCNF_W3_6) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( definitionFOFtoCNF_2
| definitionFOFtoCNF_3(skolemFOFtoCNF_W3_6) ),
inference(resolve,[$cnf( aElement0(skolemFOFtoCNF_W3_6) )],[refute_0_18,refute_0_22]) ).
cnf(refute_0_24,plain,
definitionFOFtoCNF_2,
inference(resolve,[$cnf( definitionFOFtoCNF_3(skolemFOFtoCNF_W3_6) )],[refute_0_23,refute_0_17]) ).
cnf(refute_0_25,plain,
( xa = xb
| xa = xc ),
inference(resolve,[$cnf( definitionFOFtoCNF_2 )],[refute_0_24,refute_0_13]) ).
cnf(refute_0_26,plain,
X = X,
introduced(tautology,[refl,[$fot(X)]]) ).
cnf(refute_0_27,plain,
( X != X
| X != Y
| Y = X ),
introduced(tautology,[equality,[$cnf( $equal(X,X) ),[0],$fot(Y)]]) ).
cnf(refute_0_28,plain,
( X != Y
| Y = X ),
inference(resolve,[$cnf( $equal(X,X) )],[refute_0_26,refute_0_27]) ).
cnf(refute_0_29,plain,
( xa != xc
| xc = xa ),
inference(subst,[],[refute_0_28:[bind(X,$fot(xa)),bind(Y,$fot(xc))]]) ).
cnf(refute_0_30,plain,
( xa = xb
| xc = xa ),
inference(resolve,[$cnf( $equal(xa,xc) )],[refute_0_25,refute_0_29]) ).
cnf(refute_0_31,plain,
( xc != xa
| ~ sdtmndtplgtdt0(xa,xR,X_23)
| sdtmndtplgtdt0(xc,xR,X_23) ),
introduced(tautology,[equality,[$cnf( ~ sdtmndtplgtdt0(xc,xR,X_23) ),[0],$fot(xa)]]) ).
cnf(refute_0_32,plain,
( ~ sdtmndtplgtdt0(xa,xR,X_23)
| xa = xb
| sdtmndtplgtdt0(xc,xR,X_23) ),
inference(resolve,[$cnf( $equal(xc,xa) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ aElement0(X_23)
| ~ sdtmndtplgtdt0(xa,xR,X_23)
| xa = xb
| definitionFOFtoCNF_3(X_23) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xc,xR,X_23) )],[refute_0_32,refute_0_10]) ).
cnf(refute_0_34,plain,
( ~ aElement0(xb)
| ~ sdtmndtplgtdt0(xa,xR,xb)
| xa = xb
| definitionFOFtoCNF_3(xb) ),
inference(subst,[],[refute_0_33:[bind(X_23,$fot(xb))]]) ).
cnf(refute_0_35,plain,
( ~ aElement0(xb)
| xa = xb
| definitionFOFtoCNF_3(xb) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xa,xR,xb) )],[refute_0_8,refute_0_34]) ).
cnf(refute_0_36,plain,
aElement0(xb),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_37,plain,
( xa = xb
| definitionFOFtoCNF_3(xb) ),
inference(resolve,[$cnf( aElement0(xb) )],[refute_0_36,refute_0_35]) ).
cnf(refute_0_38,plain,
( xb != W0
| ~ definitionFOFtoCNF_3(W0) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_39,plain,
( xb != xb
| ~ definitionFOFtoCNF_3(xb) ),
inference(subst,[],[refute_0_38:[bind(W0,$fot(xb))]]) ).
cnf(refute_0_40,plain,
xb = xb,
introduced(tautology,[refl,[$fot(xb)]]) ).
cnf(refute_0_41,plain,
~ definitionFOFtoCNF_3(xb),
inference(resolve,[$cnf( $equal(xb,xb) )],[refute_0_40,refute_0_39]) ).
cnf(refute_0_42,plain,
xa = xb,
inference(resolve,[$cnf( definitionFOFtoCNF_3(xb) )],[refute_0_37,refute_0_41]) ).
cnf(refute_0_43,plain,
( xa != xb
| xb = xa ),
inference(subst,[],[refute_0_28:[bind(X,$fot(xa)),bind(Y,$fot(xb))]]) ).
cnf(refute_0_44,plain,
xb = xa,
inference(resolve,[$cnf( $equal(xa,xb) )],[refute_0_42,refute_0_43]) ).
cnf(refute_0_45,plain,
( xb != xa
| ~ sdtmndtplgtdt0(xa,xR,W0)
| sdtmndtplgtdt0(xb,xR,W0) ),
introduced(tautology,[equality,[$cnf( ~ sdtmndtplgtdt0(xb,xR,W0) ),[0],$fot(xa)]]) ).
cnf(refute_0_46,plain,
( ~ sdtmndtplgtdt0(xa,xR,W0)
| sdtmndtplgtdt0(xb,xR,W0) ),
inference(resolve,[$cnf( $equal(xb,xa) )],[refute_0_44,refute_0_45]) ).
cnf(refute_0_47,plain,
( ~ definitionFOFtoCNF_3(W0)
| ~ sdtmndtplgtdt0(xa,xR,W0) ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xb,xR,W0) )],[refute_0_46,refute_0_7]) ).
cnf(refute_0_48,plain,
( ~ definitionFOFtoCNF_3(xc)
| ~ sdtmndtplgtdt0(xa,xR,xc) ),
inference(subst,[],[refute_0_47:[bind(W0,$fot(xc))]]) ).
cnf(refute_0_49,plain,
( ~ definitionFOFtoCNF_3(xc)
| xa = xc ),
inference(resolve,[$cnf( sdtmndtplgtdt0(xa,xR,xc) )],[refute_0_6,refute_0_48]) ).
cnf(refute_0_50,plain,
xa = xc,
inference(resolve,[$cnf( definitionFOFtoCNF_3(xc) )],[refute_0_5,refute_0_49]) ).
cnf(refute_0_51,plain,
xc = xa,
inference(resolve,[$cnf( $equal(xa,xc) )],[refute_0_50,refute_0_29]) ).
cnf(refute_0_52,plain,
( xc != xa
| ~ definitionFOFtoCNF_3(xc)
| definitionFOFtoCNF_3(xa) ),
introduced(tautology,[equality,[$cnf( definitionFOFtoCNF_3(xc) ),[0],$fot(xa)]]) ).
cnf(refute_0_53,plain,
( ~ definitionFOFtoCNF_3(xc)
| definitionFOFtoCNF_3(xa) ),
inference(resolve,[$cnf( $equal(xc,xa) )],[refute_0_51,refute_0_52]) ).
cnf(refute_0_54,plain,
definitionFOFtoCNF_3(xa),
inference(resolve,[$cnf( definitionFOFtoCNF_3(xc) )],[refute_0_5,refute_0_53]) ).
cnf(refute_0_55,plain,
( xb != xa
| ~ definitionFOFtoCNF_3(xa)
| definitionFOFtoCNF_3(xb) ),
introduced(tautology,[equality,[$cnf( ~ definitionFOFtoCNF_3(xb) ),[0],$fot(xa)]]) ).
cnf(refute_0_56,plain,
( ~ definitionFOFtoCNF_3(xa)
| definitionFOFtoCNF_3(xb) ),
inference(resolve,[$cnf( $equal(xb,xa) )],[refute_0_44,refute_0_55]) ).
cnf(refute_0_57,plain,
~ definitionFOFtoCNF_3(xa),
inference(resolve,[$cnf( definitionFOFtoCNF_3(xb) )],[refute_0_56,refute_0_41]) ).
cnf(refute_0_58,plain,
$false,
inference(resolve,[$cnf( definitionFOFtoCNF_3(xa) )],[refute_0_54,refute_0_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : COM022+4 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n023.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Thu Jun 16 20:25:35 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.49 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.49
% 0.20/0.49 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.51
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