TSTP Solution File: GEO178+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO178+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n008.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 05:24:56 EDT 2022
% Result : Theorem 0.21s 0.41s
% Output : CNFRefutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 50 ( 16 unt; 0 def)
% Number of atoms : 107 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 95 ( 38 ~; 31 |; 18 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 62 ( 0 sgn 42 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ci1,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) ).
fof(ci2,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) ).
fof(ceq1,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( distinct_points(X,Z)
| apart_point_and_line(Z,Y) ) ) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( distinct_points(X,Y)
& apart_point_and_line(Z,line_connecting(X,Y)) )
=> ( distinct_points(Z,X)
& distinct_points(Z,Y) ) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( distinct_points(X,Y)
& apart_point_and_line(Z,line_connecting(X,Y)) )
=> distinct_points(Z,X) ),
inference(strip,[],[con]) ).
fof(subgoal_1,plain,
! [X,Y,Z] :
( ( distinct_points(X,Y)
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(Z,X) )
=> distinct_points(Z,Y) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( distinct_points(X,Y)
& apart_point_and_line(Z,line_connecting(X,Y)) )
=> distinct_points(Z,X) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci1]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
? [X,Y,Z] :
( ~ distinct_points(Z,X)
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( ~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)
& apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[ceq1]) ).
fof(normalize_0_6,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_8,plain,
~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_3]) ).
cnf(refute_0_0,plain,
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_2,plain,
apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_4,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(X_78,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,X_78) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Z,$fot(X_78))]]) ).
cnf(refute_0_5,plain,
( apart_point_and_line(X_78,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,X_78) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_2,refute_0_4]) ).
cnf(refute_0_6,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_5:[bind(X_78,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_7,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_6,refute_0_1]) ).
cnf(refute_0_8,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_9,plain,
distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_8,refute_0_7]) ).
cnf(refute_0_10,plain,
~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_X) )],[refute_0_9,refute_0_10]) ).
fof(negate_1_0,plain,
~ ! [X,Y,Z] :
( ( distinct_points(X,Y)
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(Z,X) )
=> distinct_points(Z,Y) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci2]) ).
fof(normalize_1_1,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [X,Y,Z] :
( ~ distinct_points(Z,Y)
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y)
& distinct_points(Z,X) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_3,plain,
( ~ distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)
& apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
& distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
& distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_X_1) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[ceq1]) ).
fof(normalize_1_6,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_8,plain,
~ distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1),
inference(conjunct,[],[normalize_1_3]) ).
cnf(refute_1_0,plain,
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_0:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_2,plain,
apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_3,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_4,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(X_156,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_Z_1,X_156) ),
inference(subst,[],[refute_1_3:[bind(X,$fot(skolemFOFtoCNF_Z_1)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Z,$fot(X_156))]]) ).
cnf(refute_1_5,plain,
( apart_point_and_line(X_156,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_Z_1,X_156) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_2,refute_1_4]) ).
cnf(refute_1_6,plain,
( apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_5:[bind(X_156,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_7,plain,
( ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_6,refute_1_1]) ).
cnf(refute_1_8,plain,
distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_9,plain,
distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_8,refute_1_7]) ).
cnf(refute_1_10,plain,
~ distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_11,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) )],[refute_1_9,refute_1_10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : GEO178+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.14 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n008.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 600
% 0.14/0.36 % DateTime : Fri Jun 17 18:52:52 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.21/0.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.21/0.41
% 0.21/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.21/0.41
%------------------------------------------------------------------------------