TSTP Solution File: GEO190+1 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO190+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n016.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 05:25:07 EDT 2022
% Result : Theorem 5.59s 5.80s
% Output : CNFRefutation 5.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 41
% Number of leaves : 10
% Syntax : Number of formulae : 120 ( 28 unt; 0 def)
% Number of atoms : 311 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 287 ( 96 ~; 163 |; 18 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 153 ( 0 sgn 75 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X) ).
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X) ).
fof(apart4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(X,Z)
| distinct_points(Y,Z) ) ) ).
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(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,Z] :
( ( distinct_points(X,Y)
& distinct_points(X,Z)
& distinct_points(Y,Z)
& ~ apart_point_and_line(Z,line_connecting(X,Y)) )
=> ~ apart_point_and_line(Z,line_connecting(Y,X)) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( distinct_points(X,Y)
& distinct_points(X,Z)
& distinct_points(Y,Z)
& ~ apart_point_and_line(Z,line_connecting(X,Y)) )
=> ~ apart_point_and_line(Z,line_connecting(Y,X)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( distinct_points(X,Y)
& distinct_points(X,Z)
& distinct_points(Y,Z)
& ~ apart_point_and_line(Z,line_connecting(X,Y)) )
=> ~ apart_point_and_line(Z,line_connecting(Y,X)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci2]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_5,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_7,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
? [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
& apart_point_and_line(Z,line_connecting(Y,X))
& distinct_points(X,Y)
& distinct_points(X,Z)
& distinct_points(Y,Z) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_9,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
& apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
& distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(skolemize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
distinct_points(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] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[ceq1]) ).
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(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[apart4]) ).
fof(normalize_0_16,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_18,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_19,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)),
inference(conjunct,[],[normalize_0_9]) ).
fof(normalize_0_21,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_22,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_21]) ).
fof(normalize_0_23,plain,
~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_0_9]) ).
cnf(refute_0_0,plain,
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_2,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_4,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_5,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_6,plain,
~ distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_5:[bind(X,$fot(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_7,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_8,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),Z) ),
inference(subst,[],[refute_0_7:[bind(X,$fot(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_9,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_10,plain,
( ~ apart_point_and_line(X_1000,line_connecting(X_1000,Y))
| ~ distinct_points(X_1000,Y) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_1000))]]) ).
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(X_985,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(X_985,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),Z) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_985)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_13,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_14,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_15,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_X,Z) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_16,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_17,plain,
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_18,plain,
( ~ distinct_points(skolemFOFtoCNF_Z,X_15)
| distinct_points(X_15,Z)
| distinct_points(skolemFOFtoCNF_Z,Z) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(X_15))]]) ).
cnf(refute_0_19,plain,
distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_20,plain,
( ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| distinct_points(skolemFOFtoCNF_Y,X_13)
| distinct_points(skolemFOFtoCNF_Z,X_13) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_Z)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_21,plain,
( distinct_points(skolemFOFtoCNF_Y,X_13)
| distinct_points(skolemFOFtoCNF_Z,X_13) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( distinct_points(skolemFOFtoCNF_Y,X_15)
| distinct_points(skolemFOFtoCNF_Z,X_15) ),
inference(subst,[],[refute_0_21:[bind(X_13,$fot(X_15))]]) ).
cnf(refute_0_23,plain,
( distinct_points(X_15,Z)
| distinct_points(skolemFOFtoCNF_Y,X_15)
| distinct_points(skolemFOFtoCNF_Z,Z) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,X_15) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_23:[bind(Z,$fot(skolemFOFtoCNF_Y)),bind(X_15,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_25,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_26,plain,
~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
inference(subst,[],[refute_0_25:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_27,plain,
distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_24,refute_0_26]) ).
cnf(refute_0_28,plain,
( ~ apart_point_and_line(X_47,line_connecting(X_47,Y))
| ~ distinct_points(X_47,Y) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(X_47))]]) ).
cnf(refute_0_29,plain,
apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_30,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(X_33,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| distinct_points(skolemFOFtoCNF_Z,X_33) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_31,plain,
( apart_point_and_line(X_33,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| distinct_points(skolemFOFtoCNF_Z,X_33) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( apart_point_and_line(X_37,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| distinct_points(skolemFOFtoCNF_Z,X_37) ),
inference(subst,[],[refute_0_31:[bind(X_33,$fot(X_37))]]) ).
cnf(refute_0_33,plain,
( ~ apart_point_and_line(X_37,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(X_37,X_39)
| distinct_lines(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),X_39) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_37)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))),bind(Z,$fot(X_39))]]) ).
cnf(refute_0_34,plain,
( apart_point_and_line(X_37,X_39)
| distinct_lines(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),X_39)
| distinct_points(skolemFOFtoCNF_Z,X_37) ),
inference(resolve,[$cnf( apart_point_and_line(X_37,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) )],[refute_0_32,refute_0_33]) ).
cnf(refute_0_35,plain,
( apart_point_and_line(X_47,line_connecting(X_47,Y))
| distinct_lines(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),line_connecting(X_47,Y))
| distinct_points(skolemFOFtoCNF_Z,X_47) ),
inference(subst,[],[refute_0_34:[bind(X_37,$fot(X_47)),bind(X_39,$fot(line_connecting(X_47,Y)))]]) ).
cnf(refute_0_36,plain,
( ~ distinct_points(X_47,Y)
| distinct_lines(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),line_connecting(X_47,Y))
| distinct_points(skolemFOFtoCNF_Z,X_47) ),
inference(resolve,[$cnf( apart_point_and_line(X_47,line_connecting(X_47,Y)) )],[refute_0_35,refute_0_28]) ).
cnf(refute_0_37,plain,
( ~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| distinct_lines(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_36:[bind(Y,$fot(skolemFOFtoCNF_Y)),bind(X_47,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_38,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) )],[refute_0_27,refute_0_37]) ).
cnf(refute_0_39,plain,
~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z),
inference(subst,[],[refute_0_25:[bind(X,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_40,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,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_22]) ).
cnf(refute_0_42,plain,
( ~ distinct_lines(X_567,X_568)
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_X,X_567)
| apart_point_and_line(skolemFOFtoCNF_X,X_568)
| apart_point_and_line(skolemFOFtoCNF_Y,X_567)
| apart_point_and_line(skolemFOFtoCNF_Y,X_568) ),
inference(subst,[],[refute_0_41:[bind(U,$fot(X_567)),bind(V,$fot(X_568)),bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_43,plain,
( ~ distinct_lines(X_567,X_568)
| apart_point_and_line(skolemFOFtoCNF_X,X_567)
| apart_point_and_line(skolemFOFtoCNF_X,X_568)
| apart_point_and_line(skolemFOFtoCNF_Y,X_567)
| apart_point_and_line(skolemFOFtoCNF_Y,X_568) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_9,refute_0_42]) ).
cnf(refute_0_44,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_43:[bind(X_567,$fot(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))),bind(X_568,$fot(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_45,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_40,refute_0_44]) ).
cnf(refute_0_46,plain,
( ~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_45,refute_0_2]) ).
cnf(refute_0_47,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) )],[refute_0_27,refute_0_46]) ).
cnf(refute_0_48,plain,
( ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) )],[refute_0_47,refute_0_16]) ).
cnf(refute_0_49,plain,
( ~ distinct_points(skolemFOFtoCNF_Y,X_14)
| distinct_points(X_14,Z)
| distinct_points(skolemFOFtoCNF_Y,Z) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(X_14))]]) ).
cnf(refute_0_50,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_X,X_13)
| distinct_points(skolemFOFtoCNF_Y,X_13) ),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_13))]]) ).
cnf(refute_0_51,plain,
( distinct_points(skolemFOFtoCNF_X,X_13)
| distinct_points(skolemFOFtoCNF_Y,X_13) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_9,refute_0_50]) ).
cnf(refute_0_52,plain,
( distinct_points(skolemFOFtoCNF_X,X_14)
| distinct_points(skolemFOFtoCNF_Y,X_14) ),
inference(subst,[],[refute_0_51:[bind(X_13,$fot(X_14))]]) ).
cnf(refute_0_53,plain,
( distinct_points(X_14,Z)
| distinct_points(skolemFOFtoCNF_X,X_14)
| distinct_points(skolemFOFtoCNF_Y,Z) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,X_14) )],[refute_0_52,refute_0_49]) ).
cnf(refute_0_54,plain,
( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X)
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_53:[bind(Z,$fot(skolemFOFtoCNF_X)),bind(X_14,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_55,plain,
~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_0_25:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_56,plain,
distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_X),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_54,refute_0_55]) ).
cnf(refute_0_57,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_X) )],[refute_0_56,refute_0_48]) ).
cnf(refute_0_58,plain,
( apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| distinct_points(skolemFOFtoCNF_X,Z) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_57,refute_0_15]) ).
cnf(refute_0_59,plain,
( apart_point_and_line(X_984,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X))
| distinct_points(skolemFOFtoCNF_X,X_984) ),
inference(subst,[],[refute_0_58:[bind(Z,$fot(X_984))]]) ).
cnf(refute_0_60,plain,
( ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)
| apart_point_and_line(X_984,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_X,X_984) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) )],[refute_0_59,refute_0_13]) ).
cnf(refute_0_61,plain,
( apart_point_and_line(X_984,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_X,X_984) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_X) )],[refute_0_56,refute_0_60]) ).
cnf(refute_0_62,plain,
( apart_point_and_line(X_985,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_X,X_985) ),
inference(subst,[],[refute_0_61:[bind(X_984,$fot(X_985))]]) ).
cnf(refute_0_63,plain,
( apart_point_and_line(X_985,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),Z)
| distinct_points(skolemFOFtoCNF_X,X_985) ),
inference(resolve,[$cnf( apart_point_and_line(X_985,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_62,refute_0_12]) ).
cnf(refute_0_64,plain,
( apart_point_and_line(X_1000,line_connecting(X_1000,Y))
| distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(X_1000,Y))
| distinct_points(skolemFOFtoCNF_X,X_1000) ),
inference(subst,[],[refute_0_63:[bind(Z,$fot(line_connecting(X_1000,Y))),bind(X_985,$fot(X_1000))]]) ).
cnf(refute_0_65,plain,
( ~ distinct_points(X_1000,Y)
| distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(X_1000,Y))
| distinct_points(skolemFOFtoCNF_X,X_1000) ),
inference(resolve,[$cnf( apart_point_and_line(X_1000,line_connecting(X_1000,Y)) )],[refute_0_64,refute_0_10]) ).
cnf(refute_0_66,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_65:[bind(Y,$fot(skolemFOFtoCNF_Y)),bind(X_1000,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_67,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_9,refute_0_66]) ).
cnf(refute_0_68,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_67,refute_0_55]) ).
cnf(refute_0_69,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),Z) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_68,refute_0_8]) ).
cnf(refute_0_70,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_69:[bind(Z,$fot(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_71,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_70,refute_0_6]) ).
cnf(refute_0_72,plain,
( ~ distinct_lines(X_567,X_568)
| ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| apart_point_and_line(skolemFOFtoCNF_Y,X_567)
| apart_point_and_line(skolemFOFtoCNF_Y,X_568)
| apart_point_and_line(skolemFOFtoCNF_Z,X_567)
| apart_point_and_line(skolemFOFtoCNF_Z,X_568) ),
inference(subst,[],[refute_0_41:[bind(U,$fot(X_567)),bind(V,$fot(X_568)),bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_73,plain,
( ~ distinct_lines(X_567,X_568)
| apart_point_and_line(skolemFOFtoCNF_Y,X_567)
| apart_point_and_line(skolemFOFtoCNF_Y,X_568)
| apart_point_and_line(skolemFOFtoCNF_Z,X_567)
| apart_point_and_line(skolemFOFtoCNF_Z,X_568) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_19,refute_0_72]) ).
cnf(refute_0_74,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_73:[bind(X_567,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(X_568,$fot(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_75,plain,
( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_71,refute_0_74]) ).
cnf(refute_0_76,plain,
~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_77,plain,
( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_75,refute_0_76]) ).
cnf(refute_0_78,plain,
( ~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_77,refute_0_4]) ).
cnf(refute_0_79,plain,
( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) )],[refute_0_27,refute_0_78]) ).
cnf(refute_0_80,plain,
( ~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_79,refute_0_2]) ).
cnf(refute_0_81,plain,
apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) )],[refute_0_27,refute_0_80]) ).
cnf(refute_0_82,plain,
~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_81,refute_0_1]) ).
cnf(refute_0_83,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_9,refute_0_82]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO190+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.14/0.35 % Computer : n016.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Sat Jun 18 03:49:51 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 5.59/5.80 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 5.59/5.80
% 5.59/5.80 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 5.59/5.81
%------------------------------------------------------------------------------