TSTP Solution File: GEO188+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO188+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 05:25:05 EDT 2022
% Result : Theorem 4.17s 4.36s
% Output : CNFRefutation 4.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 40
% Number of leaves : 9
% Syntax : Number of formulae : 115 ( 27 unt; 0 def)
% Number of atoms : 322 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 294 ( 87 ~; 175 |; 22 &)
% ( 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 : 184 ( 0 sgn 81 !; 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(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,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(X,line_connecting(Z,Y)) ) ).
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(X,line_connecting(Z,Y)) ),
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(X,line_connecting(Z,Y)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| ( distinct_points(Z,X)
& distinct_points(Z,Y) ) ),
inference(canonicalize,[],[con1]) ).
fof(normalize_0_1,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| ( distinct_points(Z,X)
& distinct_points(Z,Y) ) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,X) )
& ( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
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) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_5,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_6,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_10,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[apart4]) ).
fof(normalize_0_12,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(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] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
& apart_point_and_line(X,line_connecting(Z,Y))
& distinct_points(X,Y)
& distinct_points(X,Z)
& distinct_points(Y,Z) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_16,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
& apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
& distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(skolemize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_19,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_20,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_19]) ).
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_16]) ).
fof(normalize_0_24,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_16]) ).
cnf(refute_0_0,plain,
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_2,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,X) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_4,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_5,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_6,plain,
~ distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_5:[bind(X,$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_8]) ).
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(X,X),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_10,plain,
~ distinct_points(X_98,X_98),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_98))]]) ).
cnf(refute_0_11,plain,
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_12,plain,
( ~ distinct_points(X_60,X_61)
| distinct_points(X_60,Z)
| distinct_points(X_61,Z) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_60)),bind(Y,$fot(X_61))]]) ).
cnf(refute_0_13,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_14,plain,
( ~ apart_point_and_line(X_23,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(X_23,Z) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_23)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_15,plain,
( ~ distinct_points(X_22,X_21)
| distinct_points(X_21,Z)
| distinct_points(X_22,Z) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_22)),bind(Y,$fot(X_21))]]) ).
cnf(refute_0_16,plain,
( ~ apart_point_and_line(X_20,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(X_20,Z) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_20)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_17,plain,
apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_18,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(X_19,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_X,X_19) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))),bind(Z,$fot(X_19))]]) ).
cnf(refute_0_19,plain,
( apart_point_and_line(X_19,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_X,X_19) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( apart_point_and_line(X_20,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_X,X_20) ),
inference(subst,[],[refute_0_19:[bind(X_19,$fot(X_20))]]) ).
cnf(refute_0_21,plain,
( apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(X_20,Z)
| distinct_points(skolemFOFtoCNF_X,X_20) ),
inference(resolve,[$cnf( apart_point_and_line(X_20,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_20,refute_0_16]) ).
cnf(refute_0_22,plain,
( apart_point_and_line(X_21,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(X_22,X_21)
| distinct_points(skolemFOFtoCNF_X,X_22) ),
inference(subst,[],[refute_0_21:[bind(Z,$fot(X_21)),bind(X_20,$fot(X_22))]]) ).
cnf(refute_0_23,plain,
( apart_point_and_line(X_21,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(X_21,Z)
| distinct_points(X_22,Z)
| distinct_points(skolemFOFtoCNF_X,X_22) ),
inference(resolve,[$cnf( distinct_points(X_22,X_21) )],[refute_0_22,refute_0_15]) ).
cnf(refute_0_24,plain,
( apart_point_and_line(X_21,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(X_21,skolemFOFtoCNF_X)
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_23:[bind(Z,$fot(skolemFOFtoCNF_X)),bind(X_22,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_25,plain,
~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_26,plain,
( apart_point_and_line(X_21,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(X_21,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( apart_point_and_line(X_23,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(X_23,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_26:[bind(X_21,$fot(X_23))]]) ).
cnf(refute_0_28,plain,
( apart_point_and_line(Z,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(X_23,Z)
| distinct_points(X_23,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(X_23,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_27,refute_0_14]) ).
cnf(refute_0_29,plain,
( apart_point_and_line(X_59,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(X_23,X_59)
| distinct_points(X_23,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_28:[bind(Z,$fot(X_59))]]) ).
cnf(refute_0_30,plain,
( ~ apart_point_and_line(X_59,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| distinct_points(X_59,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_59))]]) ).
cnf(refute_0_31,plain,
( ~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| distinct_points(X_23,X_59)
| distinct_points(X_23,skolemFOFtoCNF_X)
| distinct_points(X_59,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( apart_point_and_line(X_59,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( ~ distinct_points(skolemFOFtoCNF_Z,X_10)
| distinct_points(X_10,Z)
| distinct_points(skolemFOFtoCNF_Z,Z) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(skolemFOFtoCNF_Z)),bind(Y,$fot(X_10))]]) ).
cnf(refute_0_33,plain,
distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_34,plain,
( ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| distinct_points(skolemFOFtoCNF_Y,X_7)
| distinct_points(skolemFOFtoCNF_Z,X_7) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_Z)),bind(Z,$fot(X_7))]]) ).
cnf(refute_0_35,plain,
( distinct_points(skolemFOFtoCNF_Y,X_7)
| distinct_points(skolemFOFtoCNF_Z,X_7) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( distinct_points(skolemFOFtoCNF_Y,X_10)
| distinct_points(skolemFOFtoCNF_Z,X_10) ),
inference(subst,[],[refute_0_35:[bind(X_7,$fot(X_10))]]) ).
cnf(refute_0_37,plain,
( distinct_points(X_10,Z)
| distinct_points(skolemFOFtoCNF_Y,X_10)
| distinct_points(skolemFOFtoCNF_Z,Z) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,X_10) )],[refute_0_36,refute_0_32]) ).
cnf(refute_0_38,plain,
( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_37:[bind(Z,$fot(skolemFOFtoCNF_Y)),bind(X_10,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_39,plain,
~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_40,plain,
distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_38,refute_0_39]) ).
cnf(refute_0_41,plain,
( distinct_points(X_23,X_59)
| distinct_points(X_23,skolemFOFtoCNF_X)
| distinct_points(X_59,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) )],[refute_0_40,refute_0_31]) ).
cnf(refute_0_42,plain,
( distinct_points(X_60,X_61)
| distinct_points(X_60,skolemFOFtoCNF_X)
| distinct_points(X_61,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_41:[bind(X_23,$fot(X_60)),bind(X_59,$fot(X_61))]]) ).
cnf(refute_0_43,plain,
( distinct_points(X_60,Z)
| distinct_points(X_60,skolemFOFtoCNF_X)
| distinct_points(X_61,Z)
| distinct_points(X_61,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( distinct_points(X_60,X_61) )],[refute_0_42,refute_0_12]) ).
cnf(refute_0_44,plain,
( distinct_points(X_100,X_98)
| distinct_points(X_100,skolemFOFtoCNF_Y)
| distinct_points(X_98,X_98)
| distinct_points(X_98,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_43:[bind(Z,$fot(X_98)),bind(X_60,$fot(X_98)),bind(X_61,$fot(X_100))]]) ).
cnf(refute_0_45,plain,
( distinct_points(X_100,X_98)
| distinct_points(X_100,skolemFOFtoCNF_Y)
| distinct_points(X_98,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( distinct_points(X_98,X_98) )],[refute_0_44,refute_0_10]) ).
cnf(refute_0_46,plain,
( distinct_points(X_402,X_98)
| distinct_points(X_402,skolemFOFtoCNF_Y)
| distinct_points(X_98,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_45:[bind(X_100,$fot(X_402))]]) ).
cnf(refute_0_47,plain,
( ~ apart_point_and_line(X_74,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(X_74,X) ),
inference(subst,[],[refute_0_3:[bind(Z,$fot(X_74))]]) ).
cnf(refute_0_48,plain,
( apart_point_and_line(X_24,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(X_24,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_26:[bind(X_21,$fot(X_24))]]) ).
cnf(refute_0_49,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_50,plain,
( ~ apart_point_and_line(X_24,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(X_24,X_26)
| distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),X_26) ),
inference(subst,[],[refute_0_49:[bind(X,$fot(X_24)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))),bind(Z,$fot(X_26))]]) ).
cnf(refute_0_51,plain,
( apart_point_and_line(X_24,X_26)
| distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),X_26)
| distinct_points(X_24,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(X_24,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_48,refute_0_50]) ).
cnf(refute_0_52,plain,
( apart_point_and_line(X_74,line_connecting(X,Y))
| distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(X,Y))
| distinct_points(X_74,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_51:[bind(X_24,$fot(X_74)),bind(X_26,$fot(line_connecting(X,Y)))]]) ).
cnf(refute_0_53,plain,
( ~ distinct_points(X,Y)
| distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(X,Y))
| distinct_points(X_74,X)
| distinct_points(X_74,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(X_74,line_connecting(X,Y)) )],[refute_0_52,refute_0_47]) ).
cnf(refute_0_54,plain,
( ~ distinct_points(X_402,skolemFOFtoCNF_Y)
| distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(X_402,skolemFOFtoCNF_Y))
| distinct_points(X_404,X_402)
| distinct_points(X_404,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_53:[bind(X,$fot(X_402)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(X_74,$fot(X_404))]]) ).
cnf(refute_0_55,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(X_402,skolemFOFtoCNF_Y))
| distinct_points(X_402,X_98)
| distinct_points(X_404,X_402)
| distinct_points(X_404,skolemFOFtoCNF_X)
| distinct_points(X_98,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( distinct_points(X_402,skolemFOFtoCNF_Y) )],[refute_0_46,refute_0_54]) ).
cnf(refute_0_56,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_55:[bind(X_402,$fot(skolemFOFtoCNF_X)),bind(X_404,$fot(skolemFOFtoCNF_X)),bind(X_98,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_57,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_56,refute_0_25]) ).
cnf(refute_0_58,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),Z) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_57,refute_0_8]) ).
cnf(refute_0_59,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_58:[bind(Z,$fot(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_60,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_59,refute_0_6]) ).
cnf(refute_0_61,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_62,plain,
( ~ distinct_lines(X_390,X_391)
| ~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
| apart_point_and_line(skolemFOFtoCNF_Y,X_390)
| apart_point_and_line(skolemFOFtoCNF_Y,X_391)
| apart_point_and_line(skolemFOFtoCNF_Z,X_390)
| apart_point_and_line(skolemFOFtoCNF_Z,X_391) ),
inference(subst,[],[refute_0_61:[bind(U,$fot(X_390)),bind(V,$fot(X_391)),bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_63,plain,
( ~ distinct_lines(X_390,X_391)
| apart_point_and_line(skolemFOFtoCNF_Y,X_390)
| apart_point_and_line(skolemFOFtoCNF_Y,X_391)
| apart_point_and_line(skolemFOFtoCNF_Z,X_390)
| apart_point_and_line(skolemFOFtoCNF_Z,X_391) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_33,refute_0_62]) ).
cnf(refute_0_64,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_63:[bind(X_390,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(X_391,$fot(line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_65,plain,
( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_60,refute_0_64]) ).
cnf(refute_0_66,plain,
~ apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_67,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,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( ~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Z,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_67,refute_0_4]) ).
cnf(refute_0_69,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))
| distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) )],[refute_0_40,refute_0_68]) ).
cnf(refute_0_70,plain,
~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_71,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,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Z) )],[refute_0_69,refute_0_70]) ).
cnf(refute_0_72,plain,
( ~ distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y)) )],[refute_0_71,refute_0_2]) ).
cnf(refute_0_73,plain,
( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Z,skolemFOFtoCNF_Y) )],[refute_0_40,refute_0_72]) ).
cnf(refute_0_74,plain,
apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_73,refute_0_39]) ).
cnf(refute_0_75,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_74,refute_0_1]) ).
cnf(refute_0_76,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_77,plain,
distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_76,refute_0_75]) ).
cnf(refute_0_78,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_77,refute_0_39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO188+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n012.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 14:03:08 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 4.17/4.36 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 4.17/4.36
% 4.17/4.36 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 4.17/4.36
%------------------------------------------------------------------------------