TSTP Solution File: GEO187+2 by Metis---2.4
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO187+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 05:25:04 EDT 2022
% Result : Theorem 13.32s 13.55s
% Output : CNFRefutation 13.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 9
% Syntax : Number of formulae : 172 ( 52 unt; 0 def)
% Number of atoms : 476 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 467 ( 163 ~; 248 |; 44 &)
% ( 0 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 8 con; 0-2 aty)
% Number of variables : 272 ( 0 sgn 137 !; 8 ?)
% 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,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)) ),
inference(strip,[],[con]) ).
fof(subgoal_1,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)) ),
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,X) ),
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,Y) ),
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,
? [U,V,X,Y] :
( ~ 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))
& distinct_points(U,V)
& distinct_points(X,Y) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_10,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))
& apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
& distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(skolemize,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(conjunct,[],[normalize_0_10]) ).
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(canonicalize,[],[ceq2]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_0_10]) ).
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(canonicalize,[],[ceq1]) ).
fof(normalize_0_16,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_18,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_20,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_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(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_23,plain,
~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(conjunct,[],[normalize_0_10]) ).
cnf(refute_0_0,plain,
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,X) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_2,plain,
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ),
inference(canonicalize,[],[normalize_0_4]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_4,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_4:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_6,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)))]]) ).
cnf(refute_0_8,plain,
distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_10,plain,
( ~ apart_point_and_line(X_34,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(X_34,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(X_34)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_11,plain,
apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_13,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(X_33,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_U,X_33) ),
inference(subst,[],[refute_0_12:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_14,plain,
( apart_point_and_line(X_33,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_U,X_33) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( apart_point_and_line(X_34,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_U,X_34) ),
inference(subst,[],[refute_0_14:[bind(X_33,$fot(X_34))]]) ).
cnf(refute_0_16,plain,
( apart_point_and_line(X_34,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z)
| distinct_points(skolemFOFtoCNF_U,X_34) ),
inference(resolve,[$cnf( apart_point_and_line(X_34,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_15,refute_0_10]) ).
cnf(refute_0_17,plain,
( apart_point_and_line(X_49,line_connecting(X_47,X_48))
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(X_47,X_48))
| distinct_points(skolemFOFtoCNF_U,X_49) ),
inference(subst,[],[refute_0_16:[bind(Z,$fot(line_connecting(X_47,X_48))),bind(X_34,$fot(X_49))]]) ).
cnf(refute_0_18,plain,
( ~ apart_point_and_line(X_49,line_connecting(X_47,X_48))
| ~ distinct_points(X_47,X_48)
| distinct_points(X_49,X_47) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(X_47)),bind(Y,$fot(X_48)),bind(Z,$fot(X_49))]]) ).
cnf(refute_0_19,plain,
( ~ distinct_points(X_47,X_48)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(X_47,X_48))
| distinct_points(X_49,X_47)
| distinct_points(skolemFOFtoCNF_U,X_49) ),
inference(resolve,[$cnf( apart_point_and_line(X_49,line_connecting(X_47,X_48)) )],[refute_0_17,refute_0_18]) ).
cnf(refute_0_20,plain,
( ~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_points(X_152,skolemFOFtoCNF_U)
| distinct_points(skolemFOFtoCNF_U,X_152) ),
inference(subst,[],[refute_0_19:[bind(X_47,$fot(skolemFOFtoCNF_U)),bind(X_48,$fot(skolemFOFtoCNF_V)),bind(X_49,$fot(X_152))]]) ).
cnf(refute_0_21,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_points(X_152,skolemFOFtoCNF_U)
| distinct_points(skolemFOFtoCNF_U,X_152) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V) )],[refute_0_8,refute_0_20]) ).
cnf(refute_0_22,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_U) ),
inference(subst,[],[refute_0_21:[bind(X_152,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_23,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_24,plain,
~ distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_U),
inference(subst,[],[refute_0_23:[bind(X,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_25,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_U) )],[refute_0_22,refute_0_24]) ).
cnf(refute_0_26,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_25,refute_0_7]) ).
cnf(refute_0_27,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_26:[bind(Z,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_28,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_27,refute_0_5]) ).
cnf(refute_0_29,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_30,plain,
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_31,plain,
( ~ distinct_lines(X_656,X_657)
| ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_X,X_656)
| apart_point_and_line(skolemFOFtoCNF_X,X_657)
| apart_point_and_line(skolemFOFtoCNF_Y,X_656)
| apart_point_and_line(skolemFOFtoCNF_Y,X_657) ),
inference(subst,[],[refute_0_30:[bind(U,$fot(X_656)),bind(V,$fot(X_657)),bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_32,plain,
( ~ distinct_lines(X_656,X_657)
| apart_point_and_line(skolemFOFtoCNF_X,X_656)
| apart_point_and_line(skolemFOFtoCNF_X,X_657)
| apart_point_and_line(skolemFOFtoCNF_Y,X_656)
| apart_point_and_line(skolemFOFtoCNF_Y,X_657) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_29,refute_0_31]) ).
cnf(refute_0_33,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_32:[bind(X_656,$fot(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))),bind(X_657,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_34,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_28,refute_0_33]) ).
cnf(refute_0_35,plain,
~ apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_36,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_34,refute_0_35]) ).
cnf(refute_0_37,plain,
~ apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_38,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) )],[refute_0_36,refute_0_37]) ).
cnf(refute_0_39,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_38,refute_0_3]) ).
cnf(refute_0_40,plain,
( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_29,refute_0_39]) ).
cnf(refute_0_41,plain,
~ distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
inference(subst,[],[refute_0_23:[bind(X,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_42,plain,
apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_40,refute_0_41]) ).
cnf(refute_0_43,plain,
( ~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_42,refute_0_1]) ).
cnf(refute_0_44,plain,
distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_29,refute_0_43]) ).
cnf(refute_0_45,plain,
~ distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X),
inference(subst,[],[refute_0_23:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_46,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_X) )],[refute_0_44,refute_0_45]) ).
fof(negate_1_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_1]) ).
fof(normalize_1_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_1_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_1_0]) ).
fof(normalize_1_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_1_1]) ).
fof(normalize_1_3,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,X) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ),
inference(conjunct,[],[normalize_1_2]) ).
fof(normalize_1_5,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_1_6,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_1_5]) ).
fof(normalize_1_7,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_1_8,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_1_7]) ).
fof(normalize_1_9,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[apart4]) ).
fof(normalize_1_10,plain,
! [X,Y,Z] :
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(specialize,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
? [U,V,X,Y] :
( ~ apart_point_and_line(U,line_connecting(X,Y))
& ~ apart_point_and_line(X,line_connecting(U,V))
& ~ apart_point_and_line(Y,line_connecting(U,V))
& apart_point_and_line(V,line_connecting(X,Y))
& distinct_points(U,V)
& distinct_points(X,Y) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_12,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_U_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
& ~ apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
& ~ apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
& apart_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
& distinct_points(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)
& distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) ),
inference(skolemize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
distinct_points(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),
inference(conjunct,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_1_15,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_1_14]) ).
fof(normalize_1_16,plain,
apart_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(conjunct,[],[normalize_1_12]) ).
fof(normalize_1_17,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_18,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(specialize,[],[normalize_1_17]) ).
fof(normalize_1_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_1_20,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_1_19]) ).
fof(normalize_1_21,plain,
distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(conjunct,[],[normalize_1_12]) ).
fof(normalize_1_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(canonicalize,[],[cu1]) ).
fof(normalize_1_23,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_1_22]) ).
fof(normalize_1_24,plain,
~ apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)),
inference(conjunct,[],[normalize_1_12]) ).
fof(normalize_1_25,plain,
~ apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)),
inference(conjunct,[],[normalize_1_12]) ).
cnf(refute_1_0,plain,
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,X) ),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X_1) ),
inference(subst,[],[refute_1_0:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1)),bind(Z,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_1_2,plain,
( ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y)
| distinct_points(Z,Y) ),
inference(canonicalize,[],[normalize_1_4]) ).
cnf(refute_1_3,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| distinct_points(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Y_1) ),
inference(subst,[],[refute_1_2:[bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1)),bind(Z,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_4,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_1_6]) ).
cnf(refute_1_5,plain,
~ distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(subst,[],[refute_1_4:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_6,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_1_8]) ).
cnf(refute_1_7,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
| distinct_lines(line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),Z) ),
inference(subst,[],[refute_1_6:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Y,$fot(line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)))]]) ).
cnf(refute_1_8,plain,
( ~ distinct_points(X,Y)
| distinct_points(X,Z)
| distinct_points(Y,Z) ),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_9,plain,
( ~ distinct_points(X_1118,X_1117)
| distinct_points(X_1117,Z)
| distinct_points(X_1118,Z) ),
inference(subst,[],[refute_1_8:[bind(X,$fot(X_1118)),bind(Y,$fot(X_1117))]]) ).
cnf(refute_1_10,plain,
( ~ distinct_points(X_953,X_952)
| distinct_points(X_952,Z)
| distinct_points(X_953,Z) ),
inference(subst,[],[refute_1_8:[bind(X,$fot(X_953)),bind(Y,$fot(X_952))]]) ).
cnf(refute_1_11,plain,
( ~ distinct_points(skolemFOFtoCNF_V_1,X_914)
| distinct_points(X_914,Z)
| distinct_points(skolemFOFtoCNF_V_1,Z) ),
inference(subst,[],[refute_1_8:[bind(X,$fot(skolemFOFtoCNF_V_1)),bind(Y,$fot(X_914))]]) ).
cnf(refute_1_12,plain,
distinct_points(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),
inference(canonicalize,[],[normalize_1_13]) ).
cnf(refute_1_13,plain,
( ~ distinct_points(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)
| distinct_points(skolemFOFtoCNF_U_1,X_912)
| distinct_points(skolemFOFtoCNF_V_1,X_912) ),
inference(subst,[],[refute_1_8:[bind(X,$fot(skolemFOFtoCNF_U_1)),bind(Y,$fot(skolemFOFtoCNF_V_1)),bind(Z,$fot(X_912))]]) ).
cnf(refute_1_14,plain,
( distinct_points(skolemFOFtoCNF_U_1,X_912)
| distinct_points(skolemFOFtoCNF_V_1,X_912) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1) )],[refute_1_12,refute_1_13]) ).
cnf(refute_1_15,plain,
( distinct_points(skolemFOFtoCNF_U_1,X_914)
| distinct_points(skolemFOFtoCNF_V_1,X_914) ),
inference(subst,[],[refute_1_14:[bind(X_912,$fot(X_914))]]) ).
cnf(refute_1_16,plain,
( distinct_points(X_914,Z)
| distinct_points(skolemFOFtoCNF_U_1,X_914)
| distinct_points(skolemFOFtoCNF_V_1,Z) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_V_1,X_914) )],[refute_1_15,refute_1_11]) ).
cnf(refute_1_17,plain,
( distinct_points(X_953,X_952)
| distinct_points(skolemFOFtoCNF_U_1,X_953)
| distinct_points(skolemFOFtoCNF_V_1,X_952) ),
inference(subst,[],[refute_1_16:[bind(Z,$fot(X_952)),bind(X_914,$fot(X_953))]]) ).
cnf(refute_1_18,plain,
( distinct_points(X_952,Z)
| distinct_points(X_953,Z)
| distinct_points(skolemFOFtoCNF_U_1,X_953)
| distinct_points(skolemFOFtoCNF_V_1,X_952) ),
inference(resolve,[$cnf( distinct_points(X_953,X_952) )],[refute_1_17,refute_1_10]) ).
cnf(refute_1_19,plain,
( distinct_points(X_1118,X_1117)
| distinct_points(X_1119,X_1117)
| distinct_points(skolemFOFtoCNF_U_1,X_1119)
| distinct_points(skolemFOFtoCNF_V_1,X_1118) ),
inference(subst,[],[refute_1_18:[bind(Z,$fot(X_1117)),bind(X_952,$fot(X_1118)),bind(X_953,$fot(X_1119))]]) ).
cnf(refute_1_20,plain,
( distinct_points(X_1117,Z)
| distinct_points(X_1118,Z)
| distinct_points(X_1119,X_1117)
| distinct_points(skolemFOFtoCNF_U_1,X_1119)
| distinct_points(skolemFOFtoCNF_V_1,X_1118) ),
inference(resolve,[$cnf( distinct_points(X_1118,X_1117) )],[refute_1_19,refute_1_9]) ).
cnf(refute_1_21,plain,
( distinct_points(X_1117,skolemFOFtoCNF_V_1)
| distinct_points(X_1119,X_1117)
| distinct_points(skolemFOFtoCNF_U_1,X_1119)
| distinct_points(skolemFOFtoCNF_V_1,skolemFOFtoCNF_V_1) ),
inference(subst,[],[refute_1_20:[bind(Z,$fot(skolemFOFtoCNF_V_1)),bind(X_1118,$fot(skolemFOFtoCNF_V_1))]]) ).
cnf(refute_1_22,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_1_15]) ).
cnf(refute_1_23,plain,
~ distinct_points(skolemFOFtoCNF_V_1,skolemFOFtoCNF_V_1),
inference(subst,[],[refute_1_22:[bind(X,$fot(skolemFOFtoCNF_V_1))]]) ).
cnf(refute_1_24,plain,
( distinct_points(X_1117,skolemFOFtoCNF_V_1)
| distinct_points(X_1119,X_1117)
| distinct_points(skolemFOFtoCNF_U_1,X_1119) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_V_1,skolemFOFtoCNF_V_1) )],[refute_1_21,refute_1_23]) ).
cnf(refute_1_25,plain,
( distinct_points(X_1117,skolemFOFtoCNF_V_1)
| distinct_points(X_1237,X_1117)
| distinct_points(skolemFOFtoCNF_U_1,X_1237) ),
inference(subst,[],[refute_1_24:[bind(X_1119,$fot(X_1237))]]) ).
cnf(refute_1_26,plain,
apart_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_27,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(Z,Y)
| distinct_points(X,Z) ),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_28,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(X_923,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_V_1,X_923) ),
inference(subst,[],[refute_1_27:[bind(X,$fot(skolemFOFtoCNF_V_1)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Z,$fot(X_923))]]) ).
cnf(refute_1_29,plain,
( apart_point_and_line(X_923,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_V_1,X_923) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_26,refute_1_28]) ).
cnf(refute_1_30,plain,
( apart_point_and_line(X_929,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_V_1,X_929) ),
inference(subst,[],[refute_1_29:[bind(X_923,$fot(X_929))]]) ).
cnf(refute_1_31,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_1_20]) ).
cnf(refute_1_32,plain,
( ~ apart_point_and_line(X_929,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(X_929,X_931)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_931) ),
inference(subst,[],[refute_1_31:[bind(X,$fot(X_929)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Z,$fot(X_931))]]) ).
cnf(refute_1_33,plain,
( apart_point_and_line(X_929,X_931)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_931)
| distinct_points(skolemFOFtoCNF_V_1,X_929) ),
inference(resolve,[$cnf( apart_point_and_line(X_929,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_30,refute_1_32]) ).
cnf(refute_1_34,plain,
( apart_point_and_line(X_939,line_connecting(X_937,X_938))
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(X_937,X_938))
| distinct_points(skolemFOFtoCNF_V_1,X_939) ),
inference(subst,[],[refute_1_33:[bind(X_929,$fot(X_939)),bind(X_931,$fot(line_connecting(X_937,X_938)))]]) ).
cnf(refute_1_35,plain,
( ~ apart_point_and_line(X_939,line_connecting(X_937,X_938))
| ~ distinct_points(X_937,X_938)
| distinct_points(X_939,X_938) ),
inference(subst,[],[refute_1_2:[bind(X,$fot(X_937)),bind(Y,$fot(X_938)),bind(Z,$fot(X_939))]]) ).
cnf(refute_1_36,plain,
( ~ distinct_points(X_937,X_938)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(X_937,X_938))
| distinct_points(X_939,X_938)
| distinct_points(skolemFOFtoCNF_V_1,X_939) ),
inference(resolve,[$cnf( apart_point_and_line(X_939,line_connecting(X_937,X_938)) )],[refute_1_34,refute_1_35]) ).
cnf(refute_1_37,plain,
( ~ distinct_points(skolemFOFtoCNF_U_1,X_1237)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_U_1,X_1237))
| distinct_points(X_1238,X_1237)
| distinct_points(skolemFOFtoCNF_V_1,X_1238) ),
inference(subst,[],[refute_1_36:[bind(X_937,$fot(skolemFOFtoCNF_U_1)),bind(X_938,$fot(X_1237)),bind(X_939,$fot(X_1238))]]) ).
cnf(refute_1_38,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_U_1,X_1237))
| distinct_points(X_1117,skolemFOFtoCNF_V_1)
| distinct_points(X_1237,X_1117)
| distinct_points(X_1238,X_1237)
| distinct_points(skolemFOFtoCNF_V_1,X_1238) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_U_1,X_1237) )],[refute_1_25,refute_1_37]) ).
cnf(refute_1_39,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
| distinct_points(skolemFOFtoCNF_V_1,skolemFOFtoCNF_V_1) ),
inference(subst,[],[refute_1_38:[bind(X_1117,$fot(skolemFOFtoCNF_V_1)),bind(X_1237,$fot(skolemFOFtoCNF_V_1)),bind(X_1238,$fot(skolemFOFtoCNF_V_1))]]) ).
cnf(refute_1_40,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_V_1,skolemFOFtoCNF_V_1) )],[refute_1_39,refute_1_23]) ).
cnf(refute_1_41,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),Z) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)) )],[refute_1_40,refute_1_7]) ).
cnf(refute_1_42,plain,
( distinct_lines(line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(subst,[],[refute_1_41:[bind(Z,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_43,plain,
distinct_lines(line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_42,refute_1_5]) ).
cnf(refute_1_44,plain,
distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),
inference(canonicalize,[],[normalize_1_21]) ).
cnf(refute_1_45,plain,
( ~ distinct_lines(U,V)
| ~ distinct_points(X,Y)
| apart_point_and_line(X,U)
| apart_point_and_line(X,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(Y,V) ),
inference(canonicalize,[],[normalize_1_23]) ).
cnf(refute_1_46,plain,
( ~ distinct_lines(X_1932,X_1933)
| ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| apart_point_and_line(skolemFOFtoCNF_X_1,X_1932)
| apart_point_and_line(skolemFOFtoCNF_X_1,X_1933)
| apart_point_and_line(skolemFOFtoCNF_Y_1,X_1932)
| apart_point_and_line(skolemFOFtoCNF_Y_1,X_1933) ),
inference(subst,[],[refute_1_45:[bind(U,$fot(X_1932)),bind(V,$fot(X_1933)),bind(X,$fot(skolemFOFtoCNF_X_1)),bind(Y,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_47,plain,
( ~ distinct_lines(X_1932,X_1933)
| apart_point_and_line(skolemFOFtoCNF_X_1,X_1932)
| apart_point_and_line(skolemFOFtoCNF_X_1,X_1933)
| apart_point_and_line(skolemFOFtoCNF_Y_1,X_1932)
| apart_point_and_line(skolemFOFtoCNF_Y_1,X_1933) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_44,refute_1_46]) ).
cnf(refute_1_48,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
| apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(subst,[],[refute_1_47:[bind(X_1932,$fot(line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))),bind(X_1933,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_49,plain,
( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
| apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_43,refute_1_48]) ).
cnf(refute_1_50,plain,
~ apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)),
inference(canonicalize,[],[normalize_1_24]) ).
cnf(refute_1_51,plain,
( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
| apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)) )],[refute_1_49,refute_1_50]) ).
cnf(refute_1_52,plain,
~ apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)),
inference(canonicalize,[],[normalize_1_25]) ).
cnf(refute_1_53,plain,
( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)) )],[refute_1_51,refute_1_52]) ).
cnf(refute_1_54,plain,
( ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Y_1) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_53,refute_1_3]) ).
cnf(refute_1_55,plain,
( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| distinct_points(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Y_1) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_44,refute_1_54]) ).
cnf(refute_1_56,plain,
~ distinct_points(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Y_1),
inference(subst,[],[refute_1_22:[bind(X,$fot(skolemFOFtoCNF_Y_1))]]) ).
cnf(refute_1_57,plain,
apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_Y_1,skolemFOFtoCNF_Y_1) )],[refute_1_55,refute_1_56]) ).
cnf(refute_1_58,plain,
( ~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)
| distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X_1) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_57,refute_1_1]) ).
cnf(refute_1_59,plain,
distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X_1),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1) )],[refute_1_44,refute_1_58]) ).
cnf(refute_1_60,plain,
~ distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X_1),
inference(subst,[],[refute_1_22:[bind(X,$fot(skolemFOFtoCNF_X_1))]]) ).
cnf(refute_1_61,plain,
$false,
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_X_1,skolemFOFtoCNF_X_1) )],[refute_1_59,refute_1_60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09 % Problem : GEO187+2 : TPTP v8.1.0. Released v3.3.0.
% 0.09/0.09 % Command : metis --show proof --show saturation %s
% 0.09/0.28 % Computer : n032.cluster.edu
% 0.09/0.28 % Model : x86_64 x86_64
% 0.09/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.28 % Memory : 8042.1875MB
% 0.09/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.28 % CPULimit : 300
% 0.09/0.28 % WCLimit : 600
% 0.09/0.28 % DateTime : Sat Jun 18 16:51:32 EDT 2022
% 0.09/0.28 % CPUTime :
% 0.09/0.28 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 13.32/13.55 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 13.32/13.55
% 13.32/13.55 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 13.32/13.56
%------------------------------------------------------------------------------