TSTP Solution File: GEO214+2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO214+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n022.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 : Sat Jul 16 05:25:28 EDT 2022
% Result : Theorem 0.17s 0.41s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 14 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 99 ( 34 ~; 48 |; 12 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 55 ( 0 sgn 39 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X) ).
fof(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ) ).
fof(occu1,axiom,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ) ).
fof(oac1,axiom,
! [L,M,N] :
( ( convergent_lines(L,M)
& unorthogonal_lines(L,M) )
=> ( ( convergent_lines(L,N)
& unorthogonal_lines(L,N) )
| ( convergent_lines(M,N)
& unorthogonal_lines(M,N) ) ) ) ).
fof(con,conjecture,
! [L,M] :
( unorthogonal_lines(L,M)
=> unorthogonal_lines(M,L) ) ).
fof(subgoal_0,plain,
! [L,M] :
( unorthogonal_lines(L,M)
=> unorthogonal_lines(M,L) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [L,M] :
( unorthogonal_lines(L,M)
=> unorthogonal_lines(M,L) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [L,M] :
( ~ unorthogonal_lines(M,L)
& unorthogonal_lines(L,M) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
& unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| ( convergent_lines(L,N)
& unorthogonal_lines(L,N) )
| ( convergent_lines(M,N)
& unorthogonal_lines(M,N) ) ),
inference(canonicalize,[],[oac1]) ).
fof(normalize_0_5,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| ( convergent_lines(L,N)
& unorthogonal_lines(L,N) )
| ( convergent_lines(M,N)
& unorthogonal_lines(M,N) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [L,M,N] :
( ( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| convergent_lines(M,N) )
& ( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| unorthogonal_lines(M,N) )
& ( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(M,N)
| unorthogonal_lines(L,N) )
& ( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ) ),
inference(clausify,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(conjunct,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_9,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[occu1]) ).
fof(normalize_0_11,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[apart6]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
~ unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_3,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| ~ unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_L,X_250)
| unorthogonal_lines(skolemFOFtoCNF_M,X_250) ),
inference(subst,[],[refute_0_2:[bind(L,$fot(skolemFOFtoCNF_L)),bind(M,$fot(skolemFOFtoCNF_M)),bind(N,$fot(X_250))]]) ).
cnf(refute_0_4,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_L,X_250)
| unorthogonal_lines(skolemFOFtoCNF_M,X_250) ),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M),
inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_7,plain,
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_8,plain,
( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_7:[bind(L,$fot(skolemFOFtoCNF_M)),bind(M,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_9,plain,
convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) )],[refute_0_8,refute_0_0]) ).
cnf(refute_0_10,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_11,plain,
( ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| convergent_lines(skolemFOFtoCNF_L,X_21)
| convergent_lines(skolemFOFtoCNF_M,X_21) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(skolemFOFtoCNF_L)),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_12,plain,
( convergent_lines(skolemFOFtoCNF_L,X_21)
| convergent_lines(skolemFOFtoCNF_M,X_21) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_12:[bind(X_21,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_14,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_M) )],[refute_0_13,refute_0_6]) ).
cnf(refute_0_15,plain,
( convergent_lines(skolemFOFtoCNF_L,X_250)
| unorthogonal_lines(skolemFOFtoCNF_M,X_250) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_14,refute_0_4]) ).
cnf(refute_0_16,plain,
( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L)
| unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_15:[bind(X_250,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_17,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) )],[refute_0_16,refute_0_0]) ).
cnf(refute_0_18,plain,
~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_19,plain,
$false,
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) )],[refute_0_17,refute_0_18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO214+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.11/0.31 % Computer : n022.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 600
% 0.11/0.31 % DateTime : Fri Jun 17 18:19:17 EDT 2022
% 0.11/0.31 % CPUTime :
% 0.17/0.31 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.17/0.41 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.41
% 0.17/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.17/0.42
%------------------------------------------------------------------------------