TSTP Solution File: GEO203+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO203+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n010.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 05:25:18 EDT 2022
% Result : Theorem 42.29s 42.54s
% Output : CNFRefutation 42.29s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 5
% Syntax : Number of formulae : 45 ( 11 unt; 0 def)
% Number of atoms : 121 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 123 ( 47 ~; 56 |; 13 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 56 ( 0 sgn 39 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ci1,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ) ).
fof(ci2,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ) ).
fof(ci3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ) ).
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(con,conjecture,
! [X,Y,Z] :
( ( convergent_lines(X,Y)
& convergent_lines(X,Z)
& distinct_points(intersection_point(X,Y),intersection_point(X,Z)) )
=> ~ distinct_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( convergent_lines(X,Y)
& convergent_lines(X,Z)
& distinct_points(intersection_point(X,Y),intersection_point(X,Z)) )
=> ~ distinct_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( convergent_lines(X,Y)
& convergent_lines(X,Z)
& distinct_points(intersection_point(X,Y),intersection_point(X,Z)) )
=> ~ distinct_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[ci3]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[ci2]) ).
fof(normalize_0_5,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [X,Y,Z] :
( convergent_lines(X,Y)
& convergent_lines(X,Z)
& distinct_lines(line_connecting(intersection_point(X,Y),intersection_point(X,Z)),X)
& distinct_points(intersection_point(X,Y),intersection_point(X,Z)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
& distinct_lines(line_connecting(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),skolemFOFtoCNF_X)
& distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
distinct_lines(line_connecting(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),skolemFOFtoCNF_X),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_10,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_11,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_10]) ).
fof(normalize_0_12,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_13,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_7]) ).
cnf(refute_0_0,plain,
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Y))]]) ).
cnf(refute_0_2,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_X)
| ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_3,plain,
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_4,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))
| ~ distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) ),
inference(subst,[],[refute_0_3:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))]]) ).
cnf(refute_0_5,plain,
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_6,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),line_connecting(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))
| ~ distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))]]) ).
cnf(refute_0_7,plain,
distinct_lines(line_connecting(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),skolemFOFtoCNF_X),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_8,plain,
distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,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_11]) ).
cnf(refute_0_10,plain,
( ~ distinct_lines(X_610,X_611)
| ~ distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_610)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_611)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_610)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_611) ),
inference(subst,[],[refute_0_9:[bind(U,$fot(X_610)),bind(V,$fot(X_611)),bind(X,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y))),bind(Y,$fot(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))]]) ).
cnf(refute_0_11,plain,
( ~ distinct_lines(X_610,X_611)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_610)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),X_611)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_610)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),X_611) ),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) )],[refute_0_8,refute_0_10]) ).
cnf(refute_0_12,plain,
( ~ distinct_lines(line_connecting(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),line_connecting(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_X) ),
inference(subst,[],[refute_0_11:[bind(X_610,$fot(line_connecting(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))),bind(X_611,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_13,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),line_connecting(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( distinct_lines(line_connecting(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)),skolemFOFtoCNF_X) )],[refute_0_7,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),line_connecting(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))) )],[refute_0_13,refute_0_6]) ).
cnf(refute_0_15,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)))
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) )],[refute_0_8,refute_0_14]) ).
cnf(refute_0_16,plain,
( ~ distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),line_connecting(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z))) )],[refute_0_15,refute_0_4]) ).
cnf(refute_0_17,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)) )],[refute_0_8,refute_0_16]) ).
cnf(refute_0_18,plain,
( ~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z)
| apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),skolemFOFtoCNF_X) )],[refute_0_17,refute_0_2]) ).
cnf(refute_0_19,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_20,plain,
apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Z) )],[refute_0_19,refute_0_18]) ).
cnf(refute_0_21,plain,
~ convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),skolemFOFtoCNF_X) )],[refute_0_20,refute_0_1]) ).
cnf(refute_0_22,plain,
convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_23,plain,
$false,
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_22,refute_0_21]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO203+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n010.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 06:03:53 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 42.29/42.54 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 42.29/42.54
% 42.29/42.54 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 42.29/42.54
%------------------------------------------------------------------------------