TSTP Solution File: GEO206+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO206+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n013.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 05:25:20 EDT 2022
% Result : Theorem 0.13s 0.40s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 7
% Syntax : Number of formulae : 53 ( 24 unt; 0 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 107 ( 45 ~; 49 |; 7 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 83 ( 4 sgn 51 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X) ).
fof(ax6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_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(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(cup1,axiom,
! [X,Y,Z] :
( distinct_lines(Y,Z)
=> ( apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| convergent_lines(Y,Z) ) ) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( ~ apart_point_and_line(X,Y)
& ~ convergent_lines(Y,Z) )
=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ) ).
fof(subgoal_0,plain,
! [X,Y,Z] :
( ( ~ apart_point_and_line(X,Y)
& ~ convergent_lines(Y,Z) )
=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [X,Y,Z] :
( ( ~ apart_point_and_line(X,Y)
& ~ convergent_lines(Y,Z) )
=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[cp1]) ).
fof(normalize_0_1,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[ax6]) ).
fof(normalize_0_3,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_5,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[cp2]) ).
fof(normalize_0_7,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,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_9,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
? [X,Y,Z] :
( ~ apart_point_and_line(X,Y)
& ~ convergent_lines(Y,Z)
& distinct_lines(Y,parallel_through_point(Z,X)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
& ~ convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z)
& distinct_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
distinct_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ distinct_lines(Y,Z)
| apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[cup1]) ).
fof(normalize_0_14,plain,
! [X,Y,Z] :
( ~ distinct_lines(Y,Z)
| apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_16,plain,
~ convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(conjunct,[],[normalize_0_11]) ).
cnf(refute_0_0,plain,
~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ convergent_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),skolemFOFtoCNF_Z),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_X)),bind(Y,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_2,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
( ~ convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
| convergent_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),Z)
| convergent_lines(skolemFOFtoCNF_Y,Z) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_Y)),bind(Y,$fot(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_4,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
~ distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)),
inference(subst,[],[refute_0_4:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_6,plain,
~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
~ apart_point_and_line(X_71,parallel_through_point(Y,X_71)),
inference(subst,[],[refute_0_6:[bind(X,$fot(X_71))]]) ).
cnf(refute_0_8,plain,
( ~ apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,plain,
( ~ apart_point_and_line(X_44,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
| apart_point_and_line(X_44,Z)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),Z) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(X_44)),bind(Y,$fot(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_10,plain,
distinct_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_11,plain,
( ~ distinct_lines(Y,Z)
| apart_point_and_line(X,Y)
| apart_point_and_line(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
( ~ distinct_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
| apart_point_and_line(X_41,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
| apart_point_and_line(X_41,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(X_41)),bind(Y,$fot(skolemFOFtoCNF_Y)),bind(Z,$fot(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)))]]) ).
cnf(refute_0_13,plain,
( apart_point_and_line(X_41,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
| apart_point_and_line(X_41,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) )],[refute_0_10,refute_0_12]) ).
cnf(refute_0_14,plain,
( apart_point_and_line(X_44,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
| apart_point_and_line(X_44,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_13:[bind(X_41,$fot(X_44))]]) ).
cnf(refute_0_15,plain,
( apart_point_and_line(X_44,Z)
| apart_point_and_line(X_44,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
| distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),Z) ),
inference(resolve,[$cnf( apart_point_and_line(X_44,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) )],[refute_0_14,refute_0_9]) ).
cnf(refute_0_16,plain,
( apart_point_and_line(X_71,parallel_through_point(Y,X_71))
| apart_point_and_line(X_71,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
| distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),parallel_through_point(Y,X_71)) ),
inference(subst,[],[refute_0_15:[bind(Z,$fot(parallel_through_point(Y,X_71))),bind(X_44,$fot(X_71))]]) ).
cnf(refute_0_17,plain,
( apart_point_and_line(X_71,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
| distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),parallel_through_point(Y,X_71)) ),
inference(resolve,[$cnf( apart_point_and_line(X_71,parallel_through_point(Y,X_71)) )],[refute_0_16,refute_0_7]) ).
cnf(refute_0_18,plain,
( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X))
| distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) ),
inference(subst,[],[refute_0_17:[bind(Y,$fot(skolemFOFtoCNF_Z)),bind(X_71,$fot(skolemFOFtoCNF_X))]]) ).
cnf(refute_0_19,plain,
( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y)
| convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) )],[refute_0_18,refute_0_5]) ).
cnf(refute_0_20,plain,
~ apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_21,plain,
convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_X,skolemFOFtoCNF_Y) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( convergent_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),Z)
| convergent_lines(skolemFOFtoCNF_Y,Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Y,parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X)) )],[refute_0_21,refute_0_3]) ).
cnf(refute_0_23,plain,
( convergent_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),skolemFOFtoCNF_Z)
| convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) ),
inference(subst,[],[refute_0_22:[bind(Z,$fot(skolemFOFtoCNF_Z))]]) ).
cnf(refute_0_24,plain,
convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_Z,skolemFOFtoCNF_X),skolemFOFtoCNF_Z) )],[refute_0_23,refute_0_1]) ).
cnf(refute_0_25,plain,
~ convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_26,plain,
$false,
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_Y,skolemFOFtoCNF_Z) )],[refute_0_24,refute_0_25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GEO206+1 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.14 % Command : metis --show proof --show saturation %s
% 0.13/0.35 % Computer : n013.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 600
% 0.13/0.35 % DateTime : Sat Jun 18 02:05:59 EDT 2022
% 0.13/0.36 % CPUTime :
% 0.13/0.36 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.13/0.40 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/0.40
% 0.13/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.20/0.41
%------------------------------------------------------------------------------