TSTP Solution File: COM018+4 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : COM018+4 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n018.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 01:32:33 EDT 2022
% Result : Theorem 0.19s 0.45s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 13 unt; 0 def)
% Number of atoms : 174 ( 12 equ)
% Maximal formula atoms : 30 ( 5 avg)
% Number of connectives : 192 ( 48 ~; 66 |; 73 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 54 ( 1 sgn 24 !; 24 ?)
% Comments :
%------------------------------------------------------------------------------
fof(mTermNF,axiom,
! [W0] :
( ( aRewritingSystem0(W0)
& isTerminating0(W0) )
=> ! [W1] :
( aElement0(W1)
=> ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ) ).
fof(m__656,hypothesis,
aRewritingSystem0(xR) ).
fof(m__656_01,hypothesis,
( ! [W0,W1,W2] :
( ( aElement0(W0)
& aElement0(W1)
& aElement0(W2)
& aReductOfIn0(W1,W0,xR)
& aReductOfIn0(W2,W0,xR) )
=> ? [W3] :
( aElement0(W3)
& ( W1 = W3
| ( ( aReductOfIn0(W3,W1,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W1,xR,W3) ) )
& sdtmndtasgtdt0(W1,xR,W3)
& ( W2 = W3
| ( ( aReductOfIn0(W3,W2,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) )
& sdtmndtplgtdt0(W2,xR,W3) ) )
& sdtmndtasgtdt0(W2,xR,W3) ) )
& isLocallyConfluent0(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__799,hypothesis,
( aElement0(xw)
& ( xu = xw
| ( ( aReductOfIn0(xw,xu,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xu,xR)
& sdtmndtplgtdt0(W0,xR,xw) ) )
& sdtmndtplgtdt0(xu,xR,xw) ) )
& sdtmndtasgtdt0(xu,xR,xw)
& ( xv = xw
| ( ( aReductOfIn0(xw,xv,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xv,xR)
& sdtmndtplgtdt0(W0,xR,xw) ) )
& sdtmndtplgtdt0(xv,xR,xw) ) )
& sdtmndtasgtdt0(xv,xR,xw) ) ).
fof(m__,conjecture,
? [W0] :
( ( aElement0(W0)
& ( xw = W0
| aReductOfIn0(W0,xw,xR)
| ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xw,xR)
& sdtmndtplgtdt0(W1,xR,W0) )
| sdtmndtplgtdt0(xw,xR,W0)
| sdtmndtasgtdt0(xw,xR,W0) )
& ~ ? [W1] : aReductOfIn0(W1,W0,xR) )
| aNormalFormOfIn0(W0,xw,xR) ) ).
fof(subgoal_0,plain,
? [W0] :
( ( aElement0(W0)
& ( xw = W0
| aReductOfIn0(W0,xw,xR)
| ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xw,xR)
& sdtmndtplgtdt0(W1,xR,W0) )
| sdtmndtplgtdt0(xw,xR,W0)
| sdtmndtasgtdt0(xw,xR,W0) )
& ~ ? [W1] : aReductOfIn0(W1,W0,xR) )
| aNormalFormOfIn0(W0,xw,xR) ),
inference(strip,[],[m__]) ).
fof(negate_0_0,plain,
~ ? [W0] :
( ( aElement0(W0)
& ( xw = W0
| aReductOfIn0(W0,xw,xR)
| ? [W1] :
( aElement0(W1)
& aReductOfIn0(W1,xw,xR)
& sdtmndtplgtdt0(W1,xR,W0) )
| sdtmndtplgtdt0(xw,xR,W0)
| sdtmndtasgtdt0(xw,xR,W0) )
& ~ ? [W1] : aReductOfIn0(W1,W0,xR) )
| aNormalFormOfIn0(W0,xw,xR) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
( aElement0(xw)
& sdtmndtasgtdt0(xu,xR,xw)
& sdtmndtasgtdt0(xv,xR,xw)
& ( xu = xw
| ( sdtmndtplgtdt0(xu,xR,xw)
& ( aReductOfIn0(xw,xu,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xu,xR)
& sdtmndtplgtdt0(W0,xR,xw) ) ) ) )
& ( xv = xw
| ( sdtmndtplgtdt0(xv,xR,xw)
& ( aReductOfIn0(xw,xv,xR)
| ? [W0] :
( aElement0(W0)
& aReductOfIn0(W0,xv,xR)
& sdtmndtplgtdt0(W0,xR,xw) ) ) ) ) ),
inference(canonicalize,[],[m__799]) ).
fof(normalize_0_1,plain,
aElement0(xw),
inference(conjunct,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
( isLocallyConfluent0(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) ) ) )
& ! [W0,W1,W2] :
( ~ aElement0(W0)
| ~ aElement0(W1)
| ~ aElement0(W2)
| ~ aReductOfIn0(W1,W0,xR)
| ~ aReductOfIn0(W2,W0,xR)
| ? [W3] :
( aElement0(W3)
& sdtmndtasgtdt0(W1,xR,W3)
& sdtmndtasgtdt0(W2,xR,W3)
& ( W1 = W3
| ( sdtmndtplgtdt0(W1,xR,W3)
& ( aReductOfIn0(W3,W1,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W1,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) ) ) )
& ( W2 = W3
| ( sdtmndtplgtdt0(W2,xR,W3)
& ( aReductOfIn0(W3,W2,xR)
| ? [W4] :
( aElement0(W4)
& aReductOfIn0(W4,W2,xR)
& sdtmndtplgtdt0(W4,xR,W3) ) ) ) ) ) ) ),
inference(canonicalize,[],[m__656_01]) ).
fof(normalize_0_3,plain,
isTerminating0(xR),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [W0] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1] :
( ~ aElement0(W1)
| ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ),
inference(canonicalize,[],[mTermNF]) ).
fof(normalize_0_5,plain,
! [W0] :
( ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| ! [W1] :
( ~ aElement0(W1)
| ? [W2] : aNormalFormOfIn0(W2,W1,W0) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [W0,W1] :
( ~ aElement0(W1)
| ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(W0,W1),W1,W0) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
aRewritingSystem0(xR),
inference(canonicalize,[],[m__656]) ).
fof(normalize_0_8,plain,
( ! [W0] : ~ aNormalFormOfIn0(W0,xw,xR)
& ! [W0] :
( ~ aElement0(W0)
| ( xw != W0
& ~ aReductOfIn0(W0,xw,xR)
& ~ sdtmndtasgtdt0(xw,xR,W0)
& ~ sdtmndtplgtdt0(xw,xR,W0)
& ! [W1] :
( ~ aElement0(W1)
| ~ aReductOfIn0(W1,xw,xR)
| ~ sdtmndtplgtdt0(W1,xR,W0) ) )
| ? [W1] : aReductOfIn0(W1,W0,xR) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
! [W0] : ~ aNormalFormOfIn0(W0,xw,xR),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [W0] : ~ aNormalFormOfIn0(W0,xw,xR),
inference(specialize,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
aElement0(xw),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
isTerminating0(xR),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ aElement0(W1)
| ~ aRewritingSystem0(W0)
| ~ isTerminating0(W0)
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(W0,W1),W1,W0) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ aElement0(X_52)
| ~ aRewritingSystem0(xR)
| ~ isTerminating0(xR)
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(xR,X_52),X_52,xR) ),
inference(subst,[],[refute_0_2:[bind(W0,$fot(xR)),bind(W1,$fot(X_52))]]) ).
cnf(refute_0_4,plain,
( ~ aElement0(X_52)
| ~ aRewritingSystem0(xR)
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(xR,X_52),X_52,xR) ),
inference(resolve,[$cnf( isTerminating0(xR) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
aRewritingSystem0(xR),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_6,plain,
( ~ aElement0(X_52)
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(xR,X_52),X_52,xR) ),
inference(resolve,[$cnf( aRewritingSystem0(xR) )],[refute_0_5,refute_0_4]) ).
cnf(refute_0_7,plain,
( ~ aElement0(xw)
| aNormalFormOfIn0(skolemFOFtoCNF_W2_3(xR,xw),xw,xR) ),
inference(subst,[],[refute_0_6:[bind(X_52,$fot(xw))]]) ).
cnf(refute_0_8,plain,
aNormalFormOfIn0(skolemFOFtoCNF_W2_3(xR,xw),xw,xR),
inference(resolve,[$cnf( aElement0(xw) )],[refute_0_0,refute_0_7]) ).
cnf(refute_0_9,plain,
~ aNormalFormOfIn0(W0,xw,xR),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_10,plain,
~ aNormalFormOfIn0(skolemFOFtoCNF_W2_3(xR,xw),xw,xR),
inference(subst,[],[refute_0_9:[bind(W0,$fot(skolemFOFtoCNF_W2_3(xR,xw)))]]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( aNormalFormOfIn0(skolemFOFtoCNF_W2_3(xR,xw),xw,xR) )],[refute_0_8,refute_0_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : COM018+4 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n018.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 17:45:01 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.45 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.45
% 0.19/0.45 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.46
%------------------------------------------------------------------------------