TSTP Solution File: GEO177+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO177+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 05:24:55 EDT 2022
% Result : Theorem 25.05s 25.21s
% Output : CNFRefutation 25.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 36
% Number of leaves : 6
% Syntax : Number of formulae : 84 ( 18 unt; 0 def)
% Number of atoms : 282 ( 0 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 267 ( 69 ~; 169 |; 20 &)
% ( 0 <=>; 9 =>; 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 : 5 ( 5 usr; 4 con; 0-2 aty)
% Number of variables : 125 ( 0 sgn 63 !; 4 ?)
% 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(cu1,axiom,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_lines(U,V) )
=> ( apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ) ) ).
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(con,conjecture,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_points(U,V) )
=> ( ( apart_point_and_line(X,line_connecting(U,V))
| apart_point_and_line(Y,line_connecting(U,V)) )
=> ( apart_point_and_line(U,line_connecting(X,Y))
| apart_point_and_line(V,line_connecting(X,Y)) ) ) ) ).
fof(subgoal_0,plain,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_points(U,V)
& ( apart_point_and_line(X,line_connecting(U,V))
| apart_point_and_line(Y,line_connecting(U,V)) )
& ~ apart_point_and_line(U,line_connecting(X,Y)) )
=> apart_point_and_line(V,line_connecting(X,Y)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_points(U,V)
& ( apart_point_and_line(X,line_connecting(U,V))
| apart_point_and_line(Y,line_connecting(U,V)) )
& ~ apart_point_and_line(U,line_connecting(X,Y)) )
=> apart_point_and_line(V,line_connecting(X,Y)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [U,V,X,Y] :
( ~ apart_point_and_line(U,line_connecting(X,Y))
& ~ apart_point_and_line(V,line_connecting(X,Y))
& distinct_points(U,V)
& distinct_points(X,Y)
& ( apart_point_and_line(X,line_connecting(U,V))
| apart_point_and_line(Y,line_connecting(U,V)) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
& ~ apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
& distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& ( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[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)
& distinct_points(Z,Y) ) ),
inference(canonicalize,[],[con1]) ).
fof(normalize_0_4,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_3]) ).
fof(normalize_0_5,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_4]) ).
fof(normalize_0_6,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_5]) ).
fof(normalize_0_7,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_5]) ).
fof(normalize_0_8,plain,
distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_9,plain,
! [U,V,X,Y] :
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(canonicalize,[],[cu1]) ).
fof(normalize_0_10,plain,
! [U,V,X,Y] :
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(specialize,[],[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,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_14,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_15,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_17,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
~ apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_19,plain,
~ apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,X) ),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_2,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(skolemFOFtoCNF_X,X) ),
inference(subst,[],[refute_0_1:[bind(Z,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| ~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
| distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_1:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(skolemFOFtoCNF_V)),bind(Z,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_4,plain,
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| ~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
| distinct_points(skolemFOFtoCNF_V,skolemFOFtoCNF_V) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(skolemFOFtoCNF_V)),bind(Z,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_6,plain,
distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_8,plain,
( ~ distinct_lines(X_470,X_471)
| ~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
| apart_point_and_line(skolemFOFtoCNF_U,X_470)
| apart_point_and_line(skolemFOFtoCNF_U,X_471)
| apart_point_and_line(skolemFOFtoCNF_V,X_470)
| apart_point_and_line(skolemFOFtoCNF_V,X_471) ),
inference(subst,[],[refute_0_7:[bind(U,$fot(X_470)),bind(V,$fot(X_471)),bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_9,plain,
( ~ distinct_lines(X_470,X_471)
| apart_point_and_line(skolemFOFtoCNF_U,X_470)
| apart_point_and_line(skolemFOFtoCNF_U,X_471)
| apart_point_and_line(skolemFOFtoCNF_V,X_470)
| apart_point_and_line(skolemFOFtoCNF_V,X_471) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_6,refute_0_8]) ).
cnf(refute_0_10,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_1413)
| apart_point_and_line(skolemFOFtoCNF_U,X_1413)
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,X_1413)
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(subst,[],[refute_0_9:[bind(X_470,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(X_471,$fot(X_1413))]]) ).
cnf(refute_0_11,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_12,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_13,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_9:[bind(X_470,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(X_471,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_14,plain,
( ~ apart_point_and_line(X_132,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(X_132,Y) ),
inference(subst,[],[refute_0_4:[bind(Z,$fot(X_132))]]) ).
cnf(refute_0_15,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_16,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_17,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(X_18,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_points(skolemFOFtoCNF_Y,X_18) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(Z,$fot(X_18))]]) ).
cnf(refute_0_18,plain,
( apart_point_and_line(X_18,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_points(skolemFOFtoCNF_Y,X_18) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_15,refute_0_17]) ).
cnf(refute_0_19,plain,
( apart_point_and_line(X_21,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_points(skolemFOFtoCNF_Y,X_21) ),
inference(subst,[],[refute_0_18:[bind(X_18,$fot(X_21))]]) ).
cnf(refute_0_20,plain,
( ~ apart_point_and_line(X_21,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(X_21,X_23)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_23) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_21)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(Z,$fot(X_23))]]) ).
cnf(refute_0_21,plain,
( apart_point_and_line(X_21,X_23)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_23)
| distinct_points(skolemFOFtoCNF_Y,X_21) ),
inference(resolve,[$cnf( apart_point_and_line(X_21,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( apart_point_and_line(X_132,line_connecting(X,Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(X,Y))
| distinct_points(skolemFOFtoCNF_Y,X_132) ),
inference(subst,[],[refute_0_21:[bind(X_21,$fot(X_132)),bind(X_23,$fot(line_connecting(X,Y)))]]) ).
cnf(refute_0_23,plain,
( ~ distinct_points(X,Y)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(X,Y))
| distinct_points(X_132,Y)
| distinct_points(skolemFOFtoCNF_Y,X_132) ),
inference(resolve,[$cnf( apart_point_and_line(X_132,line_connecting(X,Y)) )],[refute_0_22,refute_0_14]) ).
cnf(refute_0_24,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_1371,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Y,X_1371) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(X_132,$fot(X_1371))]]) ).
cnf(refute_0_25,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(X_1371,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Y,X_1371) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_0,refute_0_24]) ).
cnf(refute_0_26,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_25:[bind(X_1371,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_27,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_28,plain,
~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
inference(subst,[],[refute_0_27:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_29,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_26,refute_0_28]) ).
cnf(refute_0_30,plain,
( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_29,refute_0_13]) ).
cnf(refute_0_31,plain,
~ apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_32,plain,
( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_30,refute_0_31]) ).
cnf(refute_0_33,plain,
~ apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_34,plain,
( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_34,refute_0_12]) ).
cnf(refute_0_36,plain,
( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,X_1413)
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_1413) ),
inference(subst,[],[refute_0_35:[bind(Z,$fot(X_1413))]]) ).
cnf(refute_0_37,plain,
( apart_point_and_line(skolemFOFtoCNF_U,X_1413)
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,X_1413)
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,X_1413) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),X_1413) )],[refute_0_36,refute_0_10]) ).
cnf(refute_0_38,plain,
( apart_point_and_line(skolemFOFtoCNF_U,X_1530)
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,X_1530)
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,X_1530) ),
inference(subst,[],[refute_0_37:[bind(X_1413,$fot(X_1530))]]) ).
cnf(refute_0_39,plain,
( ~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
| apart_point_and_line(skolemFOFtoCNF_U,X_1530)
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,X_1530)
| apart_point_and_line(skolemFOFtoCNF_X,X_1530)
| distinct_points(skolemFOFtoCNF_V,skolemFOFtoCNF_V) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_38,refute_0_5]) ).
cnf(refute_0_40,plain,
( apart_point_and_line(skolemFOFtoCNF_U,X_1530)
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,X_1530)
| apart_point_and_line(skolemFOFtoCNF_X,X_1530)
| distinct_points(skolemFOFtoCNF_V,skolemFOFtoCNF_V) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_6,refute_0_39]) ).
cnf(refute_0_41,plain,
~ distinct_points(skolemFOFtoCNF_V,skolemFOFtoCNF_V),
inference(subst,[],[refute_0_27:[bind(X,$fot(skolemFOFtoCNF_V))]]) ).
cnf(refute_0_42,plain,
( apart_point_and_line(skolemFOFtoCNF_U,X_1530)
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,X_1530)
| apart_point_and_line(skolemFOFtoCNF_X,X_1530) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_V,skolemFOFtoCNF_V) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( apart_point_and_line(skolemFOFtoCNF_U,X_1531)
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_V,X_1531)
| apart_point_and_line(skolemFOFtoCNF_X,X_1531) ),
inference(subst,[],[refute_0_42:[bind(X_1530,$fot(X_1531))]]) ).
cnf(refute_0_44,plain,
( ~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
| apart_point_and_line(skolemFOFtoCNF_U,X_1531)
| apart_point_and_line(skolemFOFtoCNF_V,X_1531)
| apart_point_and_line(skolemFOFtoCNF_X,X_1531)
| distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_43,refute_0_3]) ).
cnf(refute_0_45,plain,
( apart_point_and_line(skolemFOFtoCNF_U,X_1531)
| apart_point_and_line(skolemFOFtoCNF_V,X_1531)
| apart_point_and_line(skolemFOFtoCNF_X,X_1531)
| distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_6,refute_0_44]) ).
cnf(refute_0_46,plain,
~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_U),
inference(subst,[],[refute_0_27:[bind(X,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_47,plain,
( apart_point_and_line(skolemFOFtoCNF_U,X_1531)
| apart_point_and_line(skolemFOFtoCNF_V,X_1531)
| apart_point_and_line(skolemFOFtoCNF_X,X_1531) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_U) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(X,Y))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(X,Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(X,Y)) ),
inference(subst,[],[refute_0_47:[bind(X_1531,$fot(line_connecting(X,Y)))]]) ).
cnf(refute_0_49,plain,
( ~ distinct_points(X,Y)
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(X,Y))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(X,Y))
| distinct_points(skolemFOFtoCNF_X,X) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(X,Y)) )],[refute_0_48,refute_0_2]) ).
cnf(refute_0_50,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_49:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_51,plain,
( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_0,refute_0_50]) ).
cnf(refute_0_52,plain,
( apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_51,refute_0_31]) ).
cnf(refute_0_53,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_V,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_52,refute_0_33]) ).
cnf(refute_0_54,plain,
~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_0_27:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_55,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_53,refute_0_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO177+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n010.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 17:34:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 25.05/25.21 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 25.05/25.21
% 25.05/25.21 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 25.05/25.22
%------------------------------------------------------------------------------