TSTP Solution File: GEO237+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO237+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 05:25:45 EDT 2022
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 73 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 80 ( 38 ~; 16 |; 16 &)
% ( 6 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 62 ( 10 sgn 42 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a2_defns,axiom,
! [X,Y] :
( right_apart_point(X,Y)
<=> left_apart_point(X,reverse_line(Y)) ) ).
fof(a6_defns,axiom,
! [A,L] :
( apart_point_and_line(A,L)
<=> ( left_apart_point(A,L)
| right_apart_point(A,L) ) ) ).
fof(ax10_basics,axiom,
! [A,L] :
~ ( left_apart_point(A,L)
| left_apart_point(A,reverse_line(L)) ) ).
fof(con,conjecture,
! [A,B,C,L] :
( apart_point_and_line(C,L)
=> ( divides_points(L,A,B)
=> ( divides_points(L,A,C)
| divides_points(L,B,C) ) ) ) ).
fof(subgoal_0,plain,
! [A,B,C,L] :
( ( apart_point_and_line(C,L)
& divides_points(L,A,B)
& ~ divides_points(L,A,C) )
=> divides_points(L,B,C) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [A,B,C,L] :
( ( apart_point_and_line(C,L)
& divides_points(L,A,B)
& ~ divides_points(L,A,C) )
=> divides_points(L,B,C) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,B,C,L] :
( ~ divides_points(L,A,C)
& ~ divides_points(L,B,C)
& apart_point_and_line(C,L)
& divides_points(L,A,B) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ divides_points(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_C)
& ~ divides_points(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
& apart_point_and_line(skolemFOFtoCNF_C,skolemFOFtoCNF_L)
& divides_points(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
apart_point_and_line(skolemFOFtoCNF_C,skolemFOFtoCNF_L),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [A,L] :
( ~ apart_point_and_line(A,L)
<=> ( ~ left_apart_point(A,L)
& ~ right_apart_point(A,L) ) ),
inference(canonicalize,[],[a6_defns]) ).
fof(normalize_0_4,plain,
! [A,L] :
( ~ apart_point_and_line(A,L)
<=> ( ~ left_apart_point(A,L)
& ~ right_apart_point(A,L) ) ),
inference(specialize,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [A,L] :
( ( ~ left_apart_point(A,L)
| apart_point_and_line(A,L) )
& ( ~ right_apart_point(A,L)
| apart_point_and_line(A,L) )
& ( ~ apart_point_and_line(A,L)
| left_apart_point(A,L)
| right_apart_point(A,L) ) ),
inference(clausify,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,L] :
( ~ apart_point_and_line(A,L)
| left_apart_point(A,L)
| right_apart_point(A,L) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
( ! [A,L] : ~ left_apart_point(A,L)
& ! [A,L] : ~ left_apart_point(A,reverse_line(L)) ),
inference(canonicalize,[],[ax10_basics]) ).
fof(normalize_0_8,plain,
! [A,L] : ~ left_apart_point(A,L),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [A,L] : ~ left_apart_point(A,L),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] :
( ~ left_apart_point(X,reverse_line(Y))
<=> ~ right_apart_point(X,Y) ),
inference(canonicalize,[],[a2_defns]) ).
fof(normalize_0_11,plain,
! [X,Y] :
( ~ left_apart_point(X,reverse_line(Y))
<=> ~ right_apart_point(X,Y) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y] :
( ( ~ left_apart_point(X,reverse_line(Y))
| right_apart_point(X,Y) )
& ( ~ right_apart_point(X,Y)
| left_apart_point(X,reverse_line(Y)) ) ),
inference(clausify,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ right_apart_point(X,Y)
| left_apart_point(X,reverse_line(Y)) ),
inference(conjunct,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
apart_point_and_line(skolemFOFtoCNF_C,skolemFOFtoCNF_L),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ apart_point_and_line(A,L)
| left_apart_point(A,L)
| right_apart_point(A,L) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
~ left_apart_point(A,L),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(A,L)
| right_apart_point(A,L) ),
inference(resolve,[$cnf( left_apart_point(A,L) )],[refute_0_1,refute_0_2]) ).
cnf(refute_0_4,plain,
( ~ right_apart_point(X,Y)
| left_apart_point(X,reverse_line(Y)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_5,plain,
~ left_apart_point(X,reverse_line(Y)),
inference(subst,[],[refute_0_2:[bind(A,$fot(X)),bind(L,$fot(reverse_line(Y)))]]) ).
cnf(refute_0_6,plain,
~ right_apart_point(X,Y),
inference(resolve,[$cnf( left_apart_point(X,reverse_line(Y)) )],[refute_0_4,refute_0_5]) ).
cnf(refute_0_7,plain,
~ right_apart_point(A,L),
inference(subst,[],[refute_0_6:[bind(X,$fot(A)),bind(Y,$fot(L))]]) ).
cnf(refute_0_8,plain,
~ apart_point_and_line(A,L),
inference(resolve,[$cnf( right_apart_point(A,L) )],[refute_0_3,refute_0_7]) ).
cnf(refute_0_9,plain,
~ apart_point_and_line(skolemFOFtoCNF_C,skolemFOFtoCNF_L),
inference(subst,[],[refute_0_8:[bind(A,$fot(skolemFOFtoCNF_C)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_10,plain,
$false,
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_C,skolemFOFtoCNF_L) )],[refute_0_0,refute_0_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO237+3 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % 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 : Sat Jun 18 14:06:58 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.36
% 0.13/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.13/0.37
%------------------------------------------------------------------------------