TSTP Solution File: GEO174+2 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO174+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n003.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 05:24:52 EDT 2022
% Result : Theorem 0.12s 0.37s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 4
% Syntax : Number of formulae : 45 ( 14 unt; 0 def)
% Number of atoms : 116 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 109 ( 38 ~; 49 |; 16 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 42 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X) ).
fof(con1,axiom,
! [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(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)
& ( apart_point_and_line(X,U)
| apart_point_and_line(Y,U) ) )
=> distinct_lines(U,line_connecting(X,Y)) ) ).
fof(subgoal_0,plain,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& ( apart_point_and_line(X,U)
| apart_point_and_line(Y,U) ) )
=> distinct_lines(U,line_connecting(X,Y)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,U,V] :
( ( distinct_points(X,Y)
& convergent_lines(U,V)
& ( apart_point_and_line(X,U)
| apart_point_and_line(Y,U) ) )
=> distinct_lines(U,line_connecting(X,Y)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| ( distinct_points(Z,X)
& distinct_points(Z,Y) ) ),
inference(canonicalize,[],[con1]) ).
fof(normalize_0_1,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| ( distinct_points(Z,X)
& distinct_points(Z,Y) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,X) )
& ( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,X) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [U,X,Y] :
( ~ distinct_lines(U,line_connecting(X,Y))
& distinct_points(X,Y)
& ( apart_point_and_line(X,U)
| apart_point_and_line(Y,U) )
& ? [V] : convergent_lines(U,V) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ distinct_lines(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& ( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U) )
& ? [V] : convergent_lines(skolemFOFtoCNF_U,V) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
~ distinct_lines(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_0_5]) ).
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(canonicalize,[],[ceq2]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U) ),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_10,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_11,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_12,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_13,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_0_12]) ).
cnf(refute_0_0,plain,
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,X) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_2,plain,
~ distinct_lines(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_4,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| apart_point_and_line(skolemFOFtoCNF_X,Z)
| distinct_lines(skolemFOFtoCNF_U,Z) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_5,plain,
( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_6,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U)
| apart_point_and_line(skolemFOFtoCNF_Y,X_35)
| distinct_lines(skolemFOFtoCNF_U,X_35) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_U)),bind(Z,$fot(X_35))]]) ).
cnf(refute_0_7,plain,
( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| apart_point_and_line(skolemFOFtoCNF_Y,X_35)
| distinct_lines(skolemFOFtoCNF_U,X_35) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,skolemFOFtoCNF_U) )],[refute_0_5,refute_0_6]) ).
cnf(refute_0_8,plain,
( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_lines(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_7:[bind(X_35,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_9,plain,
( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_8,refute_0_2]) ).
cnf(refute_0_10,plain,
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_11,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_10:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_12,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_9,refute_0_11]) ).
cnf(refute_0_13,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_14,plain,
( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U)
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_13,refute_0_12]) ).
cnf(refute_0_15,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_16,plain,
~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
inference(subst,[],[refute_0_15:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_17,plain,
apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
( apart_point_and_line(skolemFOFtoCNF_X,Z)
| distinct_lines(skolemFOFtoCNF_U,Z) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_U) )],[refute_0_17,refute_0_4]) ).
cnf(refute_0_19,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_lines(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_18:[bind(Z,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_20,plain,
apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_19,refute_0_2]) ).
cnf(refute_0_21,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_20,refute_0_1]) ).
cnf(refute_0_22,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_13,refute_0_21]) ).
cnf(refute_0_23,plain,
~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_0_15:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_24,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_22,refute_0_23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO174+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 13:28:58 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.12/0.37 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.12/0.37
% 0.12/0.37 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.12/0.38
%------------------------------------------------------------------------------