TSTP Solution File: GEO183+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO183+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n015.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 05:25:01 EDT 2022
% Result : Theorem 0.19s 0.37s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 50 ( 18 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 117 ( 53 ~; 29 |; 27 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 71 ( 0 sgn 47 !; 10 ?)
% 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(ceq2,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( distinct_lines(Y,Z)
| apart_point_and_line(X,Z) ) ) ).
fof(con,conjecture,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& ~ distinct_lines(U,line_connecting(X,Y)) )
=> ( ~ apart_point_and_line(X,U)
& ~ apart_point_and_line(Y,U) ) ) ).
fof(subgoal_0,plain,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& ~ distinct_lines(U,line_connecting(X,Y)) )
=> ~ apart_point_and_line(X,U) ),
inference(strip,[],[con]) ).
fof(subgoal_1,plain,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& ~ distinct_lines(U,line_connecting(X,Y))
& ~ apart_point_and_line(X,U) )
=> ~ apart_point_and_line(Y,U) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& ~ distinct_lines(U,line_connecting(X,Y)) )
=> ~ apart_point_and_line(X,U) ),
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,
? [U,X,Y] :
( ~ distinct_lines(U,line_connecting(X,Y))
& apart_point_and_line(X,U)
& distinct_points(X,Y)
& ? [V] : convergent_lines(U,V) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_3,plain,
( ~ distinct_lines(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
& apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& ? [V] : convergent_lines(skolemFOFtoCNF_U,V) ),
inference(skolemize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
~ distinct_lines(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U),
inference(conjunct,[],[normalize_0_3]) ).
fof(normalize_0_6,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[ceq2]) ).
fof(normalize_0_7,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
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,
~ distinct_lines(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| apart_point_and_line(skolemFOFtoCNF_X,X_39)
| distinct_lines(skolemFOFtoCNF_U,X_39) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_U)),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_6,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_39)
| distinct_lines(skolemFOFtoCNF_U,X_39) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U) )],[refute_0_3,refute_0_5]) ).
cnf(refute_0_7,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_lines(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_6:[bind(X_39,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_8,plain,
apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_7,refute_0_2]) ).
cnf(refute_0_9,plain,
~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_8,refute_0_1]) ).
cnf(refute_0_10,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_11,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_10,refute_0_9]) ).
fof(negate_1_0,plain,
~ ! [X,Y,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& ~ distinct_lines(U,line_connecting(X,Y))
& ~ apart_point_and_line(X,U) )
=> ~ apart_point_and_line(Y,U) ),
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,
? [U,X,Y] :
( ~ apart_point_and_line(X,U)
& ~ distinct_lines(U,line_connecting(X,Y))
& apart_point_and_line(Y,U)
& distinct_points(X,Y)
& ? [V] : convergent_lines(U,V) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_3,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X_1,skolemFOFtoCNF_U_1)
& ~ distinct_lines(skolemFOFtoCNF_U_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
& apart_point_and_line(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_U_1)
& distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
& ? [V] : convergent_lines(skolemFOFtoCNF_U_1,V) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
~ distinct_lines(skolemFOFtoCNF_U_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
apart_point_and_line(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_U_1),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_6,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[ceq2]) ).
fof(normalize_1_7,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
distinct_points(skolemFOFtoCNF_X_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,
~ distinct_lines(skolemFOFtoCNF_U_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_3,plain,
apart_point_and_line(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_U_1),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_4,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_5,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_U_1)
| apart_point_and_line(skolemFOFtoCNF_Y_1,X_80)
| distinct_lines(skolemFOFtoCNF_U_1,X_80) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(skolemFOFtoCNF_Y_1)),bind(Y,$fot(skolemFOFtoCNF_U_1)),bind(Z,$fot(X_80))]]) ).
cnf(refute_1_6,plain,
( apart_point_and_line(skolemFOFtoCNF_Y_1,X_80)
| distinct_lines(skolemFOFtoCNF_U_1,X_80) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_U_1) )],[refute_1_3,refute_1_5]) ).
cnf(refute_1_7,plain,
( apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_lines(skolemFOFtoCNF_U_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(subst,[],[refute_1_6:[bind(X_80,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_8,plain,
apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_U_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_7,refute_1_2]) ).
cnf(refute_1_9,plain,
~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_8,refute_1_1]) ).
cnf(refute_1_10,plain,
distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_11,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_10,refute_1_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO183+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n015.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 : Sat Jun 18 11:04:43 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.37
% 0.19/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.37
%------------------------------------------------------------------------------