TSTP Solution File: GEO224+3 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO224+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n019.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 05:25:37 EDT 2022
% Result : Theorem 1.93s 2.10s
% Output : CNFRefutation 1.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 22
% Number of leaves : 8
% Syntax : Number of formulae : 62 ( 21 unt; 0 def)
% Number of atoms : 127 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 112 ( 47 ~; 45 |; 11 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 98 ( 4 sgn 59 !; 5 ?)
% 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] :
( ( point(X)
& line(Y) )
=> ? [Z] :
( point(Z)
& incident_point_and_line(Z,Y) ) ) ).
fof(subgoal_0,plain,
! [X,Y] :
( ( point(X)
& line(Y) )
=> ? [Z] :
( point(Z)
& incident_point_and_line(Z,Y) ) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y] :
( ( point(X)
& line(Y) )
=> ? [Z] :
( point(Z)
& incident_point_and_line(Z,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,
? [X,Y] :
( line(Y)
& point(X)
& ! [Z] :
( ~ incident_point_and_line(Z,Y)
| ~ point(Z) ) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
( line(skolemFOFtoCNF_Y)
& point(skolemFOFtoCNF_X)
& ! [Z] :
( ~ incident_point_and_line(Z,skolemFOFtoCNF_Y)
| ~ point(Z) ) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
point(skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [Z] :
( ~ incident_point_and_line(Z,skolemFOFtoCNF_Y)
| ~ point(Z) ),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_14,plain,
! [Z] :
( ~ incident_point_and_line(Z,skolemFOFtoCNF_Y)
| ~ point(Z) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ apart_point_and_line(X,Y)
<=> incident_point_and_line(X,Y) ),
inference(canonicalize,[],[a4]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( ~ apart_point_and_line(X,Y)
<=> incident_point_and_line(X,Y) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,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_16]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) ),
inference(conjunct,[],[normalize_0_17]) ).
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]) ).
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_X,parallel_through_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(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(skolemFOFtoCNF_Y,X),skolemFOFtoCNF_Y),
inference(subst,[],[refute_0_2:[bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_4,plain,
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ distinct_lines(X_127,skolemFOFtoCNF_Y)
| convergent_lines(X_127,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_127)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_6,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
~ distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y),
inference(subst,[],[refute_0_6:[bind(X,$fot(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(skolemFOFtoCNF_Y,X_123)
| distinct_lines(X_123,Z)
| distinct_lines(skolemFOFtoCNF_Y,Z) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(X_123))]]) ).
cnf(refute_0_10,plain,
point(skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
( ~ incident_point_and_line(Z,skolemFOFtoCNF_Y)
| ~ point(Z) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
( ~ incident_point_and_line(X_34,skolemFOFtoCNF_Y)
| ~ point(X_34) ),
inference(subst,[],[refute_0_11:[bind(Z,$fot(X_34))]]) ).
cnf(refute_0_13,plain,
( apart_point_and_line(X,Y)
| incident_point_and_line(X,Y) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_14,plain,
( apart_point_and_line(X_34,skolemFOFtoCNF_Y)
| incident_point_and_line(X_34,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(X_34)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_15,plain,
( ~ point(X_34)
| apart_point_and_line(X_34,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( incident_point_and_line(X_34,skolemFOFtoCNF_Y) )],[refute_0_14,refute_0_12]) ).
cnf(refute_0_16,plain,
( ~ point(skolemFOFtoCNF_X)
| apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_15:[bind(X_34,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_17,plain,
apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( point(skolemFOFtoCNF_X) )],[refute_0_10,refute_0_16]) ).
cnf(refute_0_18,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_19,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| apart_point_and_line(skolemFOFtoCNF_X,X_122)
| distinct_lines(skolemFOFtoCNF_Y,X_122) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(X_122))]]) ).
cnf(refute_0_20,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_122)
| distinct_lines(skolemFOFtoCNF_Y,X_122) ),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_17,refute_0_19]) ).
cnf(refute_0_21,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_123)
| distinct_lines(skolemFOFtoCNF_Y,X_123) ),
inference(subst,[],[refute_0_20:[bind(X_122,$fot(X_123))]]) ).
cnf(refute_0_22,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_123)
| distinct_lines(X_123,Z)
| distinct_lines(skolemFOFtoCNF_Y,Z) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Y,X_123) )],[refute_0_21,refute_0_9]) ).
cnf(refute_0_23,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_126)
| distinct_lines(X_126,skolemFOFtoCNF_Y)
| distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_22:[bind(Z,$fot(skolemFOFtoCNF_Y)),bind(X_123,$fot(X_126))]]) ).
cnf(refute_0_24,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_126)
| distinct_lines(X_126,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Y) )],[refute_0_23,refute_0_7]) ).
cnf(refute_0_25,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_127)
| distinct_lines(X_127,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_24:[bind(X_126,$fot(X_127))]]) ).
cnf(refute_0_26,plain,
( apart_point_and_line(skolemFOFtoCNF_X,X_127)
| convergent_lines(X_127,skolemFOFtoCNF_Y) ),
inference(resolve,[$cnf( distinct_lines(X_127,skolemFOFtoCNF_Y) )],[refute_0_25,refute_0_5]) ).
cnf(refute_0_27,plain,
( apart_point_and_line(skolemFOFtoCNF_X,parallel_through_point(skolemFOFtoCNF_Y,X))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_Y,X),skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_26:[bind(X_127,$fot(parallel_through_point(skolemFOFtoCNF_Y,X)))]]) ).
cnf(refute_0_28,plain,
apart_point_and_line(skolemFOFtoCNF_X,parallel_through_point(skolemFOFtoCNF_Y,X)),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_Y,X),skolemFOFtoCNF_Y) )],[refute_0_27,refute_0_3]) ).
cnf(refute_0_29,plain,
apart_point_and_line(skolemFOFtoCNF_X,parallel_through_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)),
inference(subst,[],[refute_0_28:[bind(X,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_30,plain,
$false,
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,parallel_through_point(skolemFOFtoCNF_Y,skolemFOFtoCNF_X)) )],[refute_0_29,refute_0_1]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : GEO224+3 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n019.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 : Fri Jun 17 15:28:54 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.93/2.10 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.93/2.10
% 1.93/2.10 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.93/2.11
%------------------------------------------------------------------------------