TSTP Solution File: GEO192+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO192+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 05:25:09 EDT 2022
% Result : Theorem 0.19s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 6
% Syntax : Number of formulae : 74 ( 27 unt; 0 def)
% Number of atoms : 153 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 134 ( 55 ~; 52 |; 17 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-2 aty)
% Number of variables : 94 ( 0 sgn 62 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(X,Z)
| distinct_lines(Y,Z) ) ) ).
fof(ci3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ) ).
fof(ci4,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),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,Z] :
( convergent_lines(X,Y)
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> ( distinct_lines(X,Z)
& distinct_lines(Y,Z) ) ) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( convergent_lines(X,Y)
& apart_point_and_line(intersection_point(X,Y),Z) )
=> distinct_lines(X,Z) ),
inference(strip,[],[con]) ).
fof(subgoal_1,plain,
! [X,Y,Z] :
( ( convergent_lines(X,Y)
& apart_point_and_line(intersection_point(X,Y),Z)
& distinct_lines(X,Z) )
=> distinct_lines(Y,Z) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( convergent_lines(X,Y)
& apart_point_and_line(intersection_point(X,Y),Z) )
=> distinct_lines(X,Z) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_1,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[ci3]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [X,Y,Z] :
( ~ distinct_lines(X,Z)
& apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Y) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
( ~ distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
& apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)
& convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,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_10,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_12,plain,
~ distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_2,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)
| distinct_lines(skolemFOFtoCNF_X,Z)
| distinct_lines(skolemFOFtoCNF_Z,Z) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_4,plain,
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_6,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_77)
| distinct_lines(skolemFOFtoCNF_Z,X_77) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(skolemFOFtoCNF_Z)),bind(Z,$fot(X_77))]]) ).
cnf(refute_0_9,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_77)
| distinct_lines(skolemFOFtoCNF_Z,X_77) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_9:[bind(X_77,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_11,plain,
( ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X) )],[refute_0_10,refute_0_5]) ).
cnf(refute_0_12,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_13,plain,
distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_12,refute_0_11]) ).
cnf(refute_0_14,plain,
( distinct_lines(skolemFOFtoCNF_X,Z)
| distinct_lines(skolemFOFtoCNF_Z,Z) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_X) )],[refute_0_13,refute_0_3]) ).
cnf(refute_0_15,plain,
( distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
| distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_14:[bind(Z,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_16,plain,
distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_15,refute_0_1]) ).
cnf(refute_0_17,plain,
~ distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_18,plain,
$false,
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) )],[refute_0_16,refute_0_17]) ).
fof(negate_1_0,plain,
~ ! [X,Y,Z] :
( ( convergent_lines(X,Y)
& apart_point_and_line(intersection_point(X,Y),Z)
& distinct_lines(X,Z) )
=> distinct_lines(Y,Z) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_1_1,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_1_3,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[ci4]) ).
fof(normalize_1_5,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
? [X,Y,Z] :
( ~ distinct_lines(Y,Z)
& apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Y)
& distinct_lines(X,Z) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_7,plain,
( ~ distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1)
& apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Z_1)
& convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
& distinct_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Z_1) ),
inference(skolemize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Z_1),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_9,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_10,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(conjunct,[],[normalize_1_7]) ).
fof(normalize_1_12,plain,
~ distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1),
inference(conjunct,[],[normalize_1_7]) ).
cnf(refute_1_0,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
~ distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Z_1),
inference(subst,[],[refute_1_0:[bind(X,$fot(skolemFOFtoCNF_Z_1))]]) ).
cnf(refute_1_2,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_3,plain,
( ~ distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)
| distinct_lines(skolemFOFtoCNF_Y_1,Z)
| distinct_lines(skolemFOFtoCNF_Z_1,Z) ),
inference(subst,[],[refute_1_2:[bind(X,$fot(skolemFOFtoCNF_Z_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_4,plain,
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_5,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Y_1)
| ~ convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_6,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Z_1),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_7,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_8,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Z_1)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_213)
| distinct_lines(skolemFOFtoCNF_Z_1,X_213) ),
inference(subst,[],[refute_1_7:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Y,$fot(skolemFOFtoCNF_Z_1)),bind(Z,$fot(X_213))]]) ).
cnf(refute_1_9,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_213)
| distinct_lines(skolemFOFtoCNF_Z_1,X_213) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Z_1) )],[refute_1_6,refute_1_8]) ).
cnf(refute_1_10,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Y_1)
| distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_9:[bind(X_213,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_11,plain,
( ~ convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_Y_1) )],[refute_1_10,refute_1_5]) ).
cnf(refute_1_12,plain,
convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_13,plain,
distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_12,refute_1_11]) ).
cnf(refute_1_14,plain,
( distinct_lines(skolemFOFtoCNF_Y_1,Z)
| distinct_lines(skolemFOFtoCNF_Z_1,Z) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) )],[refute_1_13,refute_1_3]) ).
cnf(refute_1_15,plain,
( distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1)
| distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Z_1) ),
inference(subst,[],[refute_1_14:[bind(Z,$fot(skolemFOFtoCNF_Z_1))]]) ).
cnf(refute_1_16,plain,
distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Z_1) )],[refute_1_15,refute_1_1]) ).
cnf(refute_1_17,plain,
~ distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_18,plain,
$false,
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Z_1) )],[refute_1_16,refute_1_17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : GEO192+3 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n013.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 18:14:14 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.19/0.41 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.19/0.41
% 0.19/0.41 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.19/0.42
%------------------------------------------------------------------------------