TSTP Solution File: GEO185+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO185+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n024.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 05:25:03 EDT 2022
% Result : Theorem 0.12s 0.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 66 ( 27 unt; 0 def)
% Number of atoms : 161 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 173 ( 78 ~; 54 |; 33 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 97 ( 0 sgn 67 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X) ).
fof(con2,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,X)
| apart_point_and_line(Z,Y) )
=> distinct_points(Z,intersection_point(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,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& ~ distinct_points(X,intersection_point(U,V)) )
=> ( ~ apart_point_and_line(X,U)
& ~ apart_point_and_line(X,V) ) ) ).
fof(subgoal_0,plain,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& ~ distinct_points(X,intersection_point(U,V)) )
=> ~ 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_points(X,intersection_point(U,V))
& ~ apart_point_and_line(X,U) )
=> ~ apart_point_and_line(X,V) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& ~ distinct_points(X,intersection_point(U,V)) )
=> ~ apart_point_and_line(X,U) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U,V,X,Y] :
( ~ distinct_points(X,intersection_point(U,V))
& apart_point_and_line(X,U)
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
& apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
& convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,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_5,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_7,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,X)
& ~ apart_point_and_line(Z,Y) ) ),
inference(canonicalize,[],[con2]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,X)
& ~ apart_point_and_line(Z,Y) ) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) )
& ( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ) ),
inference(clausify,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_12,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
~ distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| apart_point_and_line(X_28,skolemFOFtoCNF_U)
| distinct_points(skolemFOFtoCNF_X,X_28) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_U)),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_4,plain,
( apart_point_and_line(X_28,skolemFOFtoCNF_U)
| distinct_points(skolemFOFtoCNF_X,X_28) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U) )],[refute_0_1,refute_0_3]) ).
cnf(refute_0_5,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_4:[bind(X_28,$fot(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_6,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_5,refute_0_0]) ).
cnf(refute_0_7,plain,
convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_8,plain,
( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( ~ apart_point_and_line(X_63,skolemFOFtoCNF_U)
| ~ convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
| distinct_points(X_63,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(skolemFOFtoCNF_V)),bind(Z,$fot(X_63))]]) ).
cnf(refute_0_10,plain,
( ~ apart_point_and_line(X_63,skolemFOFtoCNF_U)
| distinct_points(X_63,intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_7,refute_0_9]) ).
cnf(refute_0_11,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U)
| distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_10:[bind(X_63,$fot(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_12,plain,
distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),skolemFOFtoCNF_U) )],[refute_0_6,refute_0_11]) ).
cnf(refute_0_13,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_14,plain,
~ distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(subst,[],[refute_0_13:[bind(X,$fot(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V),intersection_point(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_12,refute_0_14]) ).
fof(negate_1_0,plain,
~ ! [X,Y,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& ~ distinct_points(X,intersection_point(U,V))
& ~ apart_point_and_line(X,U) )
=> ~ apart_point_and_line(X,V) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
? [U,V,X,Y] :
( ~ apart_point_and_line(X,U)
& ~ distinct_points(X,intersection_point(U,V))
& apart_point_and_line(X,V)
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X_1,skolemFOFtoCNF_U_1)
& ~ distinct_points(skolemFOFtoCNF_X_1,intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
& apart_point_and_line(skolemFOFtoCNF_X_1,skolemFOFtoCNF_V_1)
& convergent_lines(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)
& distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(skolemize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
~ distinct_points(skolemFOFtoCNF_X_1,intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_3,plain,
apart_point_and_line(skolemFOFtoCNF_X_1,skolemFOFtoCNF_V_1),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_4,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_5,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
convergent_lines(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),
inference(conjunct,[],[normalize_1_1]) ).
fof(normalize_1_7,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,X)
& ~ apart_point_and_line(Z,Y) ) ),
inference(canonicalize,[],[con2]) ).
fof(normalize_1_8,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,X)
& ~ apart_point_and_line(Z,Y) ) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) )
& ( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ) ),
inference(clausify,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_1_12,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_1_11]) ).
cnf(refute_1_0,plain,
~ distinct_points(skolemFOFtoCNF_X_1,intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)),
inference(canonicalize,[],[normalize_1_2]) ).
cnf(refute_1_1,plain,
apart_point_and_line(skolemFOFtoCNF_X_1,skolemFOFtoCNF_V_1),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_2,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_3,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X_1,skolemFOFtoCNF_V_1)
| apart_point_and_line(X_101,skolemFOFtoCNF_V_1)
| distinct_points(skolemFOFtoCNF_X_1,X_101) ),
inference(subst,[],[refute_1_2:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_V_1)),bind(Z,$fot(X_101))]]) ).
cnf(refute_1_4,plain,
( apart_point_and_line(X_101,skolemFOFtoCNF_V_1)
| distinct_points(skolemFOFtoCNF_X_1,X_101) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X_1,skolemFOFtoCNF_V_1) )],[refute_1_1,refute_1_3]) ).
cnf(refute_1_5,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),skolemFOFtoCNF_V_1)
| distinct_points(skolemFOFtoCNF_X_1,intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)) ),
inference(subst,[],[refute_1_4:[bind(X_101,$fot(intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)))]]) ).
cnf(refute_1_6,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),skolemFOFtoCNF_V_1),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)) )],[refute_1_5,refute_1_0]) ).
cnf(refute_1_7,plain,
convergent_lines(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_8,plain,
( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_9,plain,
( ~ apart_point_and_line(X_140,skolemFOFtoCNF_V_1)
| ~ convergent_lines(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)
| distinct_points(X_140,intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)) ),
inference(subst,[],[refute_1_8:[bind(X,$fot(skolemFOFtoCNF_U_1)),bind(Y,$fot(skolemFOFtoCNF_V_1)),bind(Z,$fot(X_140))]]) ).
cnf(refute_1_10,plain,
( ~ apart_point_and_line(X_140,skolemFOFtoCNF_V_1)
| distinct_points(X_140,intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1) )],[refute_1_7,refute_1_9]) ).
cnf(refute_1_11,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),skolemFOFtoCNF_V_1)
| distinct_points(intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)) ),
inference(subst,[],[refute_1_10:[bind(X_140,$fot(intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)))]]) ).
cnf(refute_1_12,plain,
distinct_points(intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),skolemFOFtoCNF_V_1) )],[refute_1_6,refute_1_11]) ).
cnf(refute_1_13,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_14,plain,
~ distinct_points(intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)),
inference(subst,[],[refute_1_13:[bind(X,$fot(intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)))]]) ).
cnf(refute_1_15,plain,
$false,
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),intersection_point(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)) )],[refute_1_12,refute_1_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO185+2 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n024.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 600
% 0.12/0.34 % DateTime : Sat Jun 18 18:10:47 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.40
% 0.12/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.41
%------------------------------------------------------------------------------