TSTP Solution File: GEO220+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO220+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 05:25:33 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 4
% Syntax : Number of formulae : 39 ( 10 unt; 0 def)
% Number of atoms : 82 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 76 ( 33 ~; 23 |; 10 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 53 ( 0 sgn 38 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(couo1,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) )
=> ~ convergent_lines(M,N) ) ).
fof(a3,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ) ).
fof(a5,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ) ).
fof(con,conjecture,
! [L,M,N] :
( ( orthogonal_lines(L,M)
& orthogonal_lines(L,N) )
=> parallel_lines(M,N) ) ).
fof(subgoal_0,plain,
! [L,M,N] :
( ( orthogonal_lines(L,M)
& orthogonal_lines(L,N) )
=> parallel_lines(M,N) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [L,M,N] :
( ( orthogonal_lines(L,M)
& orthogonal_lines(L,N) )
=> parallel_lines(M,N) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
<=> unorthogonal_lines(X,Y) ),
inference(canonicalize,[],[a5]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
<=> unorthogonal_lines(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) )
& ( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [L,M,N] :
( ~ parallel_lines(M,N)
& orthogonal_lines(L,M)
& orthogonal_lines(L,N) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
& orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
& orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
~ parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
<=> parallel_lines(X,Y) ),
inference(canonicalize,[],[a3]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
<=> parallel_lines(X,Y) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) )
& ( convergent_lines(X,Y)
| parallel_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( convergent_lines(X,Y)
| parallel_lines(X,Y) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(canonicalize,[],[couo1]) ).
fof(normalize_0_13,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| ~ unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_2,plain,
orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ orthogonal_lines(X_113,skolemFOFtoCNF_N)
| ~ unorthogonal_lines(X_113,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(X_113)),bind(Y,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_4,plain,
~ parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( convergent_lines(X,Y)
| parallel_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_6,plain,
( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_7,plain,
convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(resolve,[$cnf( parallel_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_6,refute_0_4]) ).
cnf(refute_0_8,plain,
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_9,plain,
( ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| unorthogonal_lines(X_104,skolemFOFtoCNF_M)
| unorthogonal_lines(X_104,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_8:[bind(L,$fot(X_104)),bind(M,$fot(skolemFOFtoCNF_M)),bind(N,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_10,plain,
( unorthogonal_lines(X_104,skolemFOFtoCNF_M)
| unorthogonal_lines(X_104,skolemFOFtoCNF_N) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( unorthogonal_lines(X_113,skolemFOFtoCNF_M)
| unorthogonal_lines(X_113,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_10:[bind(X_104,$fot(X_113))]]) ).
cnf(refute_0_12,plain,
( ~ orthogonal_lines(X_113,skolemFOFtoCNF_N)
| unorthogonal_lines(X_113,skolemFOFtoCNF_M) ),
inference(resolve,[$cnf( unorthogonal_lines(X_113,skolemFOFtoCNF_N) )],[refute_0_11,refute_0_3]) ).
cnf(refute_0_13,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
| unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_12:[bind(X_113,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_14,plain,
unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(resolve,[$cnf( orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N) )],[refute_0_2,refute_0_13]) ).
cnf(refute_0_15,plain,
~ orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_14,refute_0_1]) ).
cnf(refute_0_16,plain,
orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_16,refute_0_15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO220+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n016.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 : Fri Jun 17 20:18:51 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.20/0.39
% 0.20/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.39
%------------------------------------------------------------------------------