TSTP Solution File: GEO221+1 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO221+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n026.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 05:25:33 EDT 2022
% Result : Theorem 0.82s 1.02s
% Output : CNFRefutation 0.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 32 ( 17 unt; 0 def)
% Number of atoms : 67 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 61 ( 26 ~; 29 |; 2 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 51 ( 2 sgn 33 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ooc1,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L) ).
fof(ooc2,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)) ).
fof(ouo1,axiom,
! [A,L,M,N] :
( distinct_lines(L,M)
=> ( apart_point_and_line(A,L)
| apart_point_and_line(A,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ) ) ).
fof(con,conjecture,
! [A,B,L] :
( ~ apart_point_and_line(B,orthogonal_through_point(L,A))
=> ~ distinct_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B)) ) ).
fof(subgoal_0,plain,
! [A,B,L] :
( ~ apart_point_and_line(B,orthogonal_through_point(L,A))
=> ~ distinct_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [A,B,L] :
( ~ apart_point_and_line(B,orthogonal_through_point(L,A))
=> ~ distinct_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(canonicalize,[],[ooc2]) ).
fof(normalize_0_1,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(canonicalize,[],[ooc1]) ).
fof(normalize_0_3,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
? [A,B,L] :
( ~ apart_point_and_line(B,orthogonal_through_point(L,A))
& distinct_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_5,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_B,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
& distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) ),
inference(skolemize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)),
inference(conjunct,[],[normalize_0_5]) ).
fof(normalize_0_7,plain,
! [A,L,M,N] :
( ~ distinct_lines(L,M)
| apart_point_and_line(A,L)
| apart_point_and_line(A,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[ouo1]) ).
fof(normalize_0_8,plain,
! [A,L,M,N] :
( ~ distinct_lines(L,M)
| apart_point_and_line(A,L)
| apart_point_and_line(A,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(specialize,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
~ apart_point_and_line(skolemFOFtoCNF_B,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(conjunct,[],[normalize_0_5]) ).
cnf(refute_0_0,plain,
~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ apart_point_and_line(skolemFOFtoCNF_B,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_B)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_2,plain,
~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_3,plain,
~ unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),skolemFOFtoCNF_L),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_B)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_4,plain,
distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)),
inference(canonicalize,[],[normalize_0_6]) ).
cnf(refute_0_5,plain,
( ~ distinct_lines(L,M)
| apart_point_and_line(A,L)
| apart_point_and_line(A,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_6,plain,
( ~ distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| apart_point_and_line(X_349,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| apart_point_and_line(X_349,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_352)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),X_352) ),
inference(subst,[],[refute_0_5:[bind(A,$fot(X_349)),bind(L,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(M,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))),bind(N,$fot(X_352))]]) ).
cnf(refute_0_7,plain,
( apart_point_and_line(X_349,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| apart_point_and_line(X_349,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_352)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),X_352) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( apart_point_and_line(X_701,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| apart_point_and_line(X_701,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_7:[bind(X_349,$fot(X_701)),bind(X_352,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_9,plain,
( apart_point_and_line(X_701,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| apart_point_and_line(X_701,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),skolemFOFtoCNF_L) )],[refute_0_8,refute_0_3]) ).
cnf(refute_0_10,plain,
~ unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_11,plain,
( apart_point_and_line(X_701,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| apart_point_and_line(X_701,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_9,refute_0_10]) ).
cnf(refute_0_12,plain,
( apart_point_and_line(skolemFOFtoCNF_B,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| apart_point_and_line(skolemFOFtoCNF_B,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_11:[bind(X_701,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_13,plain,
apart_point_and_line(skolemFOFtoCNF_B,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_B,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) )],[refute_0_12,refute_0_1]) ).
cnf(refute_0_14,plain,
~ apart_point_and_line(skolemFOFtoCNF_B,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_15,plain,
$false,
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_B,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_13,refute_0_14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : GEO221+1 : TPTP v8.1.0. Released v3.3.0.
% 0.06/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n026.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 : Fri Jun 17 16:24:24 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.82/1.02 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.82/1.02
% 0.82/1.02 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.82/1.03
%------------------------------------------------------------------------------