TSTP Solution File: GEO262+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO262+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 05:26:00 EDT 2022
% Result : Theorem 0.20s 0.37s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 25 ( 9 unt; 0 def)
% Number of atoms : 76 ( 0 equ)
% Maximal formula atoms : 7 ( 3 avg)
% Number of connectives : 85 ( 34 ~; 14 |; 30 &)
% ( 3 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-4 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 58 ( 6 sgn 42 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(con_def,axiom,
! [L,M] :
( convergent_lines(L,M)
<=> ( unequally_directed_lines(L,M)
& unequally_directed_lines(L,reverse_line(M)) ) ) ).
fof(oag9,axiom,
! [L,M] :
( ( unequally_directed_lines(L,M)
& unequally_directed_lines(L,reverse_line(M)) )
=> ( left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ) ) ).
fof(oag11,axiom,
! [L,M] :
~ ( left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ) ).
fof(con,conjecture,
! [L,M,N,A,B,C] :
( ( between_on_line(L,A,B,C)
& convergent_lines(L,M)
& ~ apart_point_and_line(B,M)
& convergent_lines(L,N)
& convergent_lines(M,N)
& ~ apart_point_and_line(B,N) )
=> between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C))) ) ).
fof(subgoal_0,plain,
! [L,M,N,A,B,C] :
( ( between_on_line(L,A,B,C)
& convergent_lines(L,M)
& ~ apart_point_and_line(B,M)
& convergent_lines(L,N)
& convergent_lines(M,N)
& ~ apart_point_and_line(B,N) )
=> between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C))) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [L,M,N,A,B,C] :
( ( between_on_line(L,A,B,C)
& convergent_lines(L,M)
& ~ apart_point_and_line(B,M)
& convergent_lines(L,N)
& convergent_lines(M,N)
& ~ apart_point_and_line(B,N) )
=> between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C))) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,L,M,N] :
( ~ apart_point_and_line(B,M)
& ~ apart_point_and_line(B,N)
& ~ between_on_line(M,intersection_point(M,parallel_through_point(N,A)),B,intersection_point(M,parallel_through_point(N,C)))
& between_on_line(L,A,B,C)
& convergent_lines(L,M)
& convergent_lines(L,N)
& convergent_lines(M,N) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_B,skolemFOFtoCNF_M)
& ~ apart_point_and_line(skolemFOFtoCNF_B,skolemFOFtoCNF_N)
& ~ between_on_line(skolemFOFtoCNF_M,intersection_point(skolemFOFtoCNF_M,parallel_through_point(skolemFOFtoCNF_N,skolemFOFtoCNF_A)),skolemFOFtoCNF_B,intersection_point(skolemFOFtoCNF_M,parallel_through_point(skolemFOFtoCNF_N,skolemFOFtoCNF_C)))
& between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
& convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_N)
& convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [L,M] :
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[oag9]) ).
fof(normalize_0_4,plain,
! [L,M] :
( ~ convergent_lines(L,M)
<=> ( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M)) ) ),
inference(canonicalize,[],[con_def]) ).
fof(normalize_0_5,plain,
! [L,M] :
( ~ convergent_lines(L,M)
<=> ( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M)) ) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [L,M] :
( ~ convergent_lines(L,M)
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(simplify,[],[normalize_0_3,normalize_0_5]) ).
fof(normalize_0_7,plain,
! [L,M] :
( ~ convergent_lines(L,M)
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
( ! [L,M] : ~ left_convergent_lines(L,M)
& ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[oag11]) ).
fof(normalize_0_9,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(specialize,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ convergent_lines(L,M)
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_2,plain,
~ left_convergent_lines(L,M),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_3,plain,
( ~ convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,M) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
~ left_convergent_lines(L,reverse_line(M)),
inference(subst,[],[refute_0_2:[bind(M,$fot(reverse_line(M)))]]) ).
cnf(refute_0_5,plain,
~ convergent_lines(L,M),
inference(resolve,[$cnf( left_convergent_lines(L,reverse_line(M)) )],[refute_0_3,refute_0_4]) ).
cnf(refute_0_6,plain,
~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(subst,[],[refute_0_5:[bind(L,$fot(skolemFOFtoCNF_L)),bind(M,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_7,plain,
$false,
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_0,refute_0_6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.13 % Problem : GEO262+1 : TPTP v8.1.0. Bugfixed v6.4.0.
% 0.13/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.20/0.35 % WCLimit : 600
% 0.20/0.35 % DateTime : Sat Jun 18 12:34:59 EDT 2022
% 0.20/0.35 % CPUTime :
% 0.20/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.37 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.37
% 0.20/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.37
%------------------------------------------------------------------------------