TSTP Solution File: GEO179+3 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO179+3 : TPTP v8.1.0. Released v4.0.0.
% 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 05:24:57 EDT 2022
% Result : Theorem 0.20s 0.39s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 10
% Syntax : Number of formulae : 86 ( 30 unt; 0 def)
% Number of atoms : 177 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 154 ( 63 ~; 62 |; 18 &)
% ( 0 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 6 con; 0-2 aty)
% Number of variables : 129 ( 4 sgn 81 !; 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(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(ceq2,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( distinct_lines(Y,Z)
| apart_point_and_line(X,Z) ) ) ).
fof(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ) ).
fof(cp1,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) ).
fof(cp2,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( distinct_points(X,Y)
& apart_point_and_line(Z,line_connecting(X,Y)) )
=> ( distinct_lines(line_connecting(X,Y),line_connecting(Z,X))
& distinct_lines(line_connecting(X,Y),line_connecting(Z,Y)) ) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( distinct_points(X,Y)
& apart_point_and_line(Z,line_connecting(X,Y)) )
=> distinct_lines(line_connecting(X,Y),line_connecting(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_lines(line_connecting(X,Y),line_connecting(Z,X)) )
=> distinct_lines(line_connecting(X,Y),line_connecting(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_lines(line_connecting(X,Y),line_connecting(Z,X)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[cp2]) ).
fof(normalize_0_1,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[cp1]) ).
fof(normalize_0_3,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_7,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [X,Y,Z] :
( ~ distinct_lines(line_connecting(X,Y),line_connecting(Z,X))
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(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_8]) ).
fof(normalize_0_10,plain,
apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_11,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_12,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_14,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_13]) ).
cnf(refute_0_0,plain,
~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ apart_point_and_line(skolemFOFtoCNF_Z,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_2,plain,
~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
~ convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_2:[bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_4,plain,
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ distinct_lines(X_78,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| convergent_lines(X_78,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_78)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_6,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_6:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_8,plain,
apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_9,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_10,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Z,X_55)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_55) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Z,$fot(X_55))]]) ).
cnf(refute_0_11,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,X_55)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_55) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,X_73)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_73) ),
inference(subst,[],[refute_0_11:[bind(X_55,$fot(X_73))]]) ).
cnf(refute_0_13,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_14,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_73)
| distinct_lines(X_73,X_74)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_74) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(X_73)),bind(Z,$fot(X_74))]]) ).
cnf(refute_0_15,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,X_73)
| distinct_lines(X_73,X_74)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_74) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_73) )],[refute_0_12,refute_0_14]) ).
cnf(refute_0_16,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,X_75)
| distinct_lines(X_75,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_15:[bind(X_73,$fot(X_75)),bind(X_74,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_17,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,X_75)
| distinct_lines(X_75,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_16,refute_0_7]) ).
cnf(refute_0_18,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,X_78)
| distinct_lines(X_78,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_17:[bind(X_75,$fot(X_78))]]) ).
cnf(refute_0_19,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,X_78)
| convergent_lines(X_78,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_lines(X_78,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_18,refute_0_5]) ).
cnf(refute_0_20,plain,
( apart_point_and_line(skolemFOFtoCNF_Z,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X))
| convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_19:[bind(X_78,$fot(parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X)))]]) ).
cnf(refute_0_21,plain,
apart_point_and_line(skolemFOFtoCNF_Z,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X)),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_20,refute_0_3]) ).
cnf(refute_0_22,plain,
apart_point_and_line(skolemFOFtoCNF_Z,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)),
inference(subst,[],[refute_0_21:[bind(X,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_Z)) )],[refute_0_22,refute_0_1]) ).
fof(negate_1_0,plain,
~ ! [X,Y,Z] :
( ( distinct_points(X,Y)
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_lines(line_connecting(X,Y),line_connecting(Z,X)) )
=> distinct_lines(line_connecting(X,Y),line_connecting(Z,Y)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci1]) ).
fof(normalize_1_1,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
? [X,Y,Z] :
( ~ distinct_lines(line_connecting(X,Y),line_connecting(Z,Y))
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_lines(line_connecting(X,Y),line_connecting(Z,X))
& distinct_points(X,Y) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_3,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1))
& apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
& distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_X_1))
& distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(skolemize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
~ distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)),
inference(conjunct,[],[normalize_1_3]) ).
fof(normalize_1_5,plain,
apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_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,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci2]) ).
fof(normalize_1_9,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_1_8]) ).
fof(normalize_1_10,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_11,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(specialize,[],[normalize_1_10]) ).
fof(normalize_1_12,plain,
distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(conjunct,[],[normalize_1_3]) ).
cnf(refute_1_0,plain,
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1))
| ~ distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_0:[bind(X,$fot(skolemFOFtoCNF_Z_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_2,plain,
~ distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_3,plain,
apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_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_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_Z_1,X_176)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_176) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(skolemFOFtoCNF_Z_1)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Z,$fot(X_176))]]) ).
cnf(refute_1_6,plain,
( apart_point_and_line(skolemFOFtoCNF_Z_1,X_176)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_176) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_3,refute_1_5]) ).
cnf(refute_1_7,plain,
( apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1))
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)) ),
inference(subst,[],[refute_1_6:[bind(X_176,$fot(line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_8,plain,
apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)) )],[refute_1_7,refute_1_2]) ).
cnf(refute_1_9,plain,
~ distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1)) )],[refute_1_8,refute_1_1]) ).
cnf(refute_1_10,plain,
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_1_9]) ).
cnf(refute_1_11,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_10:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_12,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_1_11]) ).
cnf(refute_1_13,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(X_159,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_Z_1,X_159) ),
inference(subst,[],[refute_1_12:[bind(X,$fot(skolemFOFtoCNF_Z_1)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Z,$fot(X_159))]]) ).
cnf(refute_1_14,plain,
( apart_point_and_line(X_159,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_Z_1,X_159) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_3,refute_1_13]) ).
cnf(refute_1_15,plain,
( apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_14:[bind(X_159,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_16,plain,
( ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_15,refute_1_11]) ).
cnf(refute_1_17,plain,
distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(canonicalize,[],[normalize_1_12]) ).
cnf(refute_1_18,plain,
distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_17,refute_1_16]) ).
cnf(refute_1_19,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z_1,skolemFOFtoCNF_Y_1) )],[refute_1_18,refute_1_9]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO179+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.12 % Command : metis --show proof --show saturation %s
% 0.14/0.33 % Computer : n015.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 600
% 0.14/0.33 % DateTime : Fri Jun 17 19:31:57 EDT 2022
% 0.14/0.34 % CPUTime :
% 0.14/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.39 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.39
% 0.20/0.39 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.40
%------------------------------------------------------------------------------