TSTP Solution File: GEO209+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO209+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 05:25:23 EDT 2022
% Result : Theorem 0.17s 0.36s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 3
% Syntax : Number of formulae : 34 ( 12 unt; 0 def)
% Number of atoms : 98 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 104 ( 40 ~; 37 |; 22 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 4 con; 0-0 aty)
% Number of variables : 49 ( 0 sgn 30 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ) ).
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,
! [A,L,M,N] :
( ( apart_point_and_line(A,L)
& ~ apart_point_and_line(A,M)
& ~ apart_point_and_line(A,N)
& ~ convergent_lines(M,L)
& ~ convergent_lines(N,L) )
=> ~ distinct_lines(M,N) ) ).
fof(subgoal_0,plain,
! [A,L,M,N] :
( ( apart_point_and_line(A,L)
& ~ apart_point_and_line(A,M)
& ~ apart_point_and_line(A,N)
& ~ convergent_lines(M,L)
& ~ convergent_lines(N,L) )
=> ~ distinct_lines(M,N) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [A,L,M,N] :
( ( apart_point_and_line(A,L)
& ~ apart_point_and_line(A,M)
& ~ apart_point_and_line(A,N)
& ~ convergent_lines(M,L)
& ~ convergent_lines(N,L) )
=> ~ distinct_lines(M,N) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
? [A,L,M,N] :
( ~ apart_point_and_line(A,M)
& ~ apart_point_and_line(A,N)
& ~ convergent_lines(M,L)
& ~ convergent_lines(N,L)
& apart_point_and_line(A,L)
& distinct_lines(M,N) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_1,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_M)
& ~ apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_N)
& ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
& ~ convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L)
& apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_L)
& distinct_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) ),
inference(skolemize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
~ apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_N),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
~ convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_4,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[ax6]) ).
fof(normalize_0_5,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
distinct_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_7,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_8,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_7]) ).
fof(normalize_0_9,plain,
~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(conjunct,[],[normalize_0_1]) ).
fof(normalize_0_10,plain,
~ apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_M),
inference(conjunct,[],[normalize_0_1]) ).
cnf(refute_0_0,plain,
~ apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_N),
inference(canonicalize,[],[normalize_0_2]) ).
cnf(refute_0_1,plain,
~ convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_2,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_M,Z)
| convergent_lines(skolemFOFtoCNF_N,Z) ),
inference(subst,[],[refute_0_2:[bind(X,$fot(skolemFOFtoCNF_M)),bind(Y,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_4,plain,
distinct_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,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_8]) ).
cnf(refute_0_6,plain,
( ~ distinct_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N)
| apart_point_and_line(X_53,skolemFOFtoCNF_M)
| apart_point_and_line(X_53,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(X_53)),bind(Y,$fot(skolemFOFtoCNF_M)),bind(Z,$fot(skolemFOFtoCNF_N))]]) ).
cnf(refute_0_7,plain,
( apart_point_and_line(X_53,skolemFOFtoCNF_M)
| apart_point_and_line(X_53,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( apart_point_and_line(X_56,skolemFOFtoCNF_M)
| apart_point_and_line(X_56,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_7:[bind(X_53,$fot(X_56))]]) ).
cnf(refute_0_9,plain,
( apart_point_and_line(X_56,skolemFOFtoCNF_M)
| apart_point_and_line(X_56,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_M,Z)
| convergent_lines(skolemFOFtoCNF_N,Z) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_N) )],[refute_0_8,refute_0_3]) ).
cnf(refute_0_10,plain,
( apart_point_and_line(X_63,skolemFOFtoCNF_M)
| apart_point_and_line(X_63,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L)
| convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_9:[bind(Z,$fot(skolemFOFtoCNF_L)),bind(X_56,$fot(X_63))]]) ).
cnf(refute_0_11,plain,
( apart_point_and_line(X_63,skolemFOFtoCNF_M)
| apart_point_and_line(X_63,skolemFOFtoCNF_N)
| convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_N,skolemFOFtoCNF_L) )],[refute_0_10,refute_0_1]) ).
cnf(refute_0_12,plain,
~ convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_13,plain,
( apart_point_and_line(X_63,skolemFOFtoCNF_M)
| apart_point_and_line(X_63,skolemFOFtoCNF_N) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_M,skolemFOFtoCNF_L) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_M)
| apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_N) ),
inference(subst,[],[refute_0_13:[bind(X_63,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_15,plain,
apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_M),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_N) )],[refute_0_14,refute_0_0]) ).
cnf(refute_0_16,plain,
~ apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_M),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_17,plain,
$false,
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_M) )],[refute_0_15,refute_0_16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11 % Problem : GEO209+1 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.11 % Command : metis --show proof --show saturation %s
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sat Jun 18 18:23:04 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.17/0.36 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.36
% 0.17/0.36 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.17/0.36
%------------------------------------------------------------------------------