TSTP Solution File: GEO187+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO187+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n025.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 0.18s 0.43s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 104 ( 39 unt; 0 def)
% Number of atoms : 227 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 193 ( 70 ~; 72 |; 38 &)
% ( 5 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 8 con; 0-2 aty)
% Number of variables : 171 ( 8 sgn 103 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(X,Z)
| distinct_lines(Y,Z) ) ) ).
fof(ceq2,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( distinct_lines(Y,Z)
| apart_point_and_line(X,Z) ) ) ).
fof(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ) ).
fof(cp1,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y) ).
fof(cp2,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)) ).
fof(a4,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ) ).
fof(con,conjecture,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_points(U,V)
& incident_point_and_line(X,line_connecting(U,V))
& incident_point_and_line(Y,line_connecting(U,V)) )
=> ( incident_point_and_line(U,line_connecting(X,Y))
& incident_point_and_line(V,line_connecting(X,Y)) ) ) ).
fof(subgoal_0,plain,
! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_points(U,V)
& incident_point_and_line(X,line_connecting(U,V))
& incident_point_and_line(Y,line_connecting(U,V)) )
=> incident_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)
& incident_point_and_line(X,line_connecting(U,V))
& incident_point_and_line(Y,line_connecting(U,V))
& incident_point_and_line(U,line_connecting(X,Y)) )
=> incident_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)
& incident_point_and_line(X,line_connecting(U,V))
& incident_point_and_line(Y,line_connecting(U,V)) )
=> incident_point_and_line(U,line_connecting(X,Y)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[cp2]) ).
fof(normalize_0_1,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[cp1]) ).
fof(normalize_0_3,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_7,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
? [U,V,X,Y] :
( ~ incident_point_and_line(U,line_connecting(X,Y))
& distinct_points(U,V)
& distinct_points(X,Y)
& incident_point_and_line(X,line_connecting(U,V))
& incident_point_and_line(Y,line_connecting(U,V)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
( ~ incident_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
& distinct_points(skolemFOFtoCNF_U,skolemFOFtoCNF_V)
& distinct_points(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& incident_point_and_line(skolemFOFtoCNF_X,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V))
& incident_point_and_line(skolemFOFtoCNF_Y,line_connecting(skolemFOFtoCNF_U,skolemFOFtoCNF_V)) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
~ incident_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ apart_point_and_line(X,Y)
<=> incident_point_and_line(X,Y) ),
inference(canonicalize,[],[a4]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ apart_point_and_line(X,Y)
<=> incident_point_and_line(X,Y) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) )
& ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) ) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,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_18,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_17]) ).
cnf(refute_0_0,plain,
~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ apart_point_and_line(skolemFOFtoCNF_U,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_2,plain,
~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
~ convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_2:[bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_4,plain,
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ distinct_lines(X_166,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| convergent_lines(X_166,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_166)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_6,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(subst,[],[refute_0_6:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_8,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_100)
| distinct_lines(X_100,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(X_100))]]) ).
cnf(refute_0_10,plain,
~ incident_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_12,plain,
( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| incident_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)))]]) ).
cnf(refute_0_13,plain,
apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)),
inference(resolve,[$cnf( incident_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_12,refute_0_10]) ).
cnf(refute_0_14,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_15,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| apart_point_and_line(skolemFOFtoCNF_U,X_99)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_99) ),
inference(subst,[],[refute_0_14:[bind(X,$fot(skolemFOFtoCNF_U)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Z,$fot(X_99))]]) ).
cnf(refute_0_16,plain,
( apart_point_and_line(skolemFOFtoCNF_U,X_99)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_99) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_U,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_13,refute_0_15]) ).
cnf(refute_0_17,plain,
( apart_point_and_line(skolemFOFtoCNF_U,X_100)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_100) ),
inference(subst,[],[refute_0_16:[bind(X_99,$fot(X_100))]]) ).
cnf(refute_0_18,plain,
( apart_point_and_line(skolemFOFtoCNF_U,X_100)
| distinct_lines(X_100,Z)
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),Z) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_100) )],[refute_0_17,refute_0_9]) ).
cnf(refute_0_19,plain,
( apart_point_and_line(skolemFOFtoCNF_U,X_165)
| distinct_lines(X_165,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))
| distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_18:[bind(Z,$fot(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(X_100,$fot(X_165))]]) ).
cnf(refute_0_20,plain,
( apart_point_and_line(skolemFOFtoCNF_U,X_165)
| distinct_lines(X_165,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_19,refute_0_7]) ).
cnf(refute_0_21,plain,
( apart_point_and_line(skolemFOFtoCNF_U,X_166)
| distinct_lines(X_166,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_20:[bind(X_165,$fot(X_166))]]) ).
cnf(refute_0_22,plain,
( apart_point_and_line(skolemFOFtoCNF_U,X_166)
| convergent_lines(X_166,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(resolve,[$cnf( distinct_lines(X_166,line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_21,refute_0_5]) ).
cnf(refute_0_23,plain,
( apart_point_and_line(skolemFOFtoCNF_U,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X))
| convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) ),
inference(subst,[],[refute_0_22:[bind(X_166,$fot(parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X)))]]) ).
cnf(refute_0_24,plain,
apart_point_and_line(skolemFOFtoCNF_U,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X)),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X),line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)) )],[refute_0_23,refute_0_3]) ).
cnf(refute_0_25,plain,
apart_point_and_line(skolemFOFtoCNF_U,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)),
inference(subst,[],[refute_0_24:[bind(X,$fot(skolemFOFtoCNF_U))]]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_U,parallel_through_point(line_connecting(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_U)) )],[refute_0_25,refute_0_1]) ).
fof(negate_1_0,plain,
~ ! [X,Y,U,V] :
( ( distinct_points(X,Y)
& distinct_points(U,V)
& incident_point_and_line(X,line_connecting(U,V))
& incident_point_and_line(Y,line_connecting(U,V))
& incident_point_and_line(U,line_connecting(X,Y)) )
=> incident_point_and_line(V,line_connecting(X,Y)) ),
inference(negate,[],[subgoal_1]) ).
fof(normalize_1_0,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[cp2]) ).
fof(normalize_1_1,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(specialize,[],[normalize_1_0]) ).
fof(normalize_1_2,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[cp1]) ).
fof(normalize_1_3,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(specialize,[],[normalize_1_2]) ).
fof(normalize_1_4,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_1_5,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(specialize,[],[normalize_1_4]) ).
fof(normalize_1_6,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_1_7,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_1_6]) ).
fof(normalize_1_8,plain,
? [U,V,X,Y] :
( ~ incident_point_and_line(V,line_connecting(X,Y))
& distinct_points(U,V)
& distinct_points(X,Y)
& incident_point_and_line(U,line_connecting(X,Y))
& incident_point_and_line(X,line_connecting(U,V))
& incident_point_and_line(Y,line_connecting(U,V)) ),
inference(canonicalize,[],[negate_1_0]) ).
fof(normalize_1_9,plain,
( ~ incident_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)
& incident_point_and_line(skolemFOFtoCNF_U_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
& incident_point_and_line(skolemFOFtoCNF_X_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1))
& incident_point_and_line(skolemFOFtoCNF_Y_1,line_connecting(skolemFOFtoCNF_U_1,skolemFOFtoCNF_V_1)) ),
inference(skolemize,[],[normalize_1_8]) ).
fof(normalize_1_10,plain,
~ incident_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(conjunct,[],[normalize_1_9]) ).
fof(normalize_1_11,plain,
! [X,Y] :
( ~ apart_point_and_line(X,Y)
<=> incident_point_and_line(X,Y) ),
inference(canonicalize,[],[a4]) ).
fof(normalize_1_12,plain,
! [X,Y] :
( ~ apart_point_and_line(X,Y)
<=> incident_point_and_line(X,Y) ),
inference(specialize,[],[normalize_1_11]) ).
fof(normalize_1_13,plain,
! [X,Y] :
( ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) )
& ( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) ) ),
inference(clausify,[],[normalize_1_12]) ).
fof(normalize_1_14,plain,
! [X,Y] :
( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) ),
inference(conjunct,[],[normalize_1_13]) ).
fof(normalize_1_15,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_16,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_1_15]) ).
fof(normalize_1_17,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_1_18,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_1_17]) ).
cnf(refute_1_0,plain,
~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[normalize_1_1]) ).
cnf(refute_1_1,plain,
~ apart_point_and_line(skolemFOFtoCNF_V_1,parallel_through_point(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_V_1)),
inference(subst,[],[refute_1_0:[bind(X,$fot(skolemFOFtoCNF_V_1)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_2,plain,
~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[normalize_1_3]) ).
cnf(refute_1_3,plain,
~ convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(subst,[],[refute_1_2:[bind(Y,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_4,plain,
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_1_5]) ).
cnf(refute_1_5,plain,
( ~ distinct_lines(X_244,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| convergent_lines(X_244,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(subst,[],[refute_1_4:[bind(X,$fot(X_244)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_6,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_1_7]) ).
cnf(refute_1_7,plain,
~ distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(subst,[],[refute_1_6:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_8,plain,
~ incident_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(canonicalize,[],[normalize_1_10]) ).
cnf(refute_1_9,plain,
( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) ),
inference(canonicalize,[],[normalize_1_14]) ).
cnf(refute_1_10,plain,
( apart_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| incident_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(subst,[],[refute_1_9:[bind(X,$fot(skolemFOFtoCNF_V_1)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_11,plain,
apart_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)),
inference(resolve,[$cnf( incident_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_10,refute_1_8]) ).
cnf(refute_1_12,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_1_16]) ).
cnf(refute_1_13,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))
| apart_point_and_line(skolemFOFtoCNF_V_1,X_224)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_224) ),
inference(subst,[],[refute_1_12:[bind(X,$fot(skolemFOFtoCNF_V_1)),bind(Y,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Z,$fot(X_224))]]) ).
cnf(refute_1_14,plain,
( apart_point_and_line(skolemFOFtoCNF_V_1,X_224)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_224) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_V_1,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_11,refute_1_13]) ).
cnf(refute_1_15,plain,
( apart_point_and_line(skolemFOFtoCNF_V_1,X_240)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_240) ),
inference(subst,[],[refute_1_14:[bind(X_224,$fot(X_240))]]) ).
cnf(refute_1_16,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_1_18]) ).
cnf(refute_1_17,plain,
( ~ distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_240)
| distinct_lines(X_240,X_241)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_241) ),
inference(subst,[],[refute_1_16:[bind(X,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1))),bind(Y,$fot(X_240)),bind(Z,$fot(X_241))]]) ).
cnf(refute_1_18,plain,
( apart_point_and_line(skolemFOFtoCNF_V_1,X_240)
| distinct_lines(X_240,X_241)
| distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_241) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X_240) )],[refute_1_15,refute_1_17]) ).
cnf(refute_1_19,plain,
( apart_point_and_line(skolemFOFtoCNF_V_1,X_242)
| distinct_lines(X_242,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_18:[bind(X_240,$fot(X_242)),bind(X_241,$fot(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)))]]) ).
cnf(refute_1_20,plain,
( apart_point_and_line(skolemFOFtoCNF_V_1,X_242)
| distinct_lines(X_242,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_19,refute_1_7]) ).
cnf(refute_1_21,plain,
( apart_point_and_line(skolemFOFtoCNF_V_1,X_244)
| distinct_lines(X_244,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(subst,[],[refute_1_20:[bind(X_242,$fot(X_244))]]) ).
cnf(refute_1_22,plain,
( apart_point_and_line(skolemFOFtoCNF_V_1,X_244)
| convergent_lines(X_244,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(resolve,[$cnf( distinct_lines(X_244,line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_21,refute_1_5]) ).
cnf(refute_1_23,plain,
( apart_point_and_line(skolemFOFtoCNF_V_1,parallel_through_point(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X))
| convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) ),
inference(subst,[],[refute_1_22:[bind(X_244,$fot(parallel_through_point(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X)))]]) ).
cnf(refute_1_24,plain,
apart_point_and_line(skolemFOFtoCNF_V_1,parallel_through_point(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X)),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),X),line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1)) )],[refute_1_23,refute_1_3]) ).
cnf(refute_1_25,plain,
apart_point_and_line(skolemFOFtoCNF_V_1,parallel_through_point(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_V_1)),
inference(subst,[],[refute_1_24:[bind(X,$fot(skolemFOFtoCNF_V_1))]]) ).
cnf(refute_1_26,plain,
$false,
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_V_1,parallel_through_point(line_connecting(skolemFOFtoCNF_X_1,skolemFOFtoCNF_Y_1),skolemFOFtoCNF_V_1)) )],[refute_1_25,refute_1_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO187+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n025.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 600
% 0.12/0.33 % DateTime : Sat Jun 18 05:17:43 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.18/0.43 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43
% 0.18/0.43 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.18/0.44
%------------------------------------------------------------------------------