%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO210+2 : 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 05:25:24 EDT 2022
% Result : Theorem 1.05s 1.23s
% Output : CNFRefutation 1.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 24 unt; 0 def)
% Number of atoms : 106 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 99 ( 42 ~; 45 |; 7 &)
% ( 0 <=>; 5 =>; 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 : 74 ( 2 sgn 45 !; 3 ?)
% 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(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,L,M] :
( ( ~ apart_point_and_line(A,L)
& ~ unorthogonal_lines(L,M) )
=> ~ distinct_lines(L,orthogonal_through_point(M,A)) ) ).
fof(subgoal_0,plain,
! [A,L,M] :
( ( ~ apart_point_and_line(A,L)
& ~ unorthogonal_lines(L,M) )
=> ~ distinct_lines(L,orthogonal_through_point(M,A)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [A,L,M] :
( ( ~ apart_point_and_line(A,L)
& ~ unorthogonal_lines(L,M) )
=> ~ distinct_lines(L,orthogonal_through_point(M,A)) ),
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,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_5,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [A,L,M] :
( ~ apart_point_and_line(A,L)
& ~ unorthogonal_lines(L,M)
& distinct_lines(L,orthogonal_through_point(M,A)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
( ~ apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_L)
& ~ unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
& distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)) ),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_10,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_9]) ).
fof(normalize_0_11,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_12,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_11]) ).
fof(normalize_0_13,plain,
~ unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(conjunct,[],[normalize_0_7]) ).
fof(normalize_0_14,plain,
~ apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_L),
inference(conjunct,[],[normalize_0_7]) ).
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_A,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A)),bind(L,$fot(skolemFOFtoCNF_M))]]) ).
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_M,skolemFOFtoCNF_A),skolemFOFtoCNF_M),
inference(subst,[],[refute_0_2:[bind(A,$fot(skolemFOFtoCNF_A)),bind(L,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_4,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_5,plain,
( ~ distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_26)
| distinct_lines(X_26,Z)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),Z) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))),bind(Y,$fot(X_26))]]) ).
cnf(refute_0_6,plain,
distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)),
inference(canonicalize,[],[normalize_0_8]) ).
cnf(refute_0_7,plain,
( ~ distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_24)
| distinct_lines(skolemFOFtoCNF_L,X_24) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))),bind(Z,$fot(X_24))]]) ).
cnf(refute_0_8,plain,
( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_24)
| distinct_lines(skolemFOFtoCNF_L,X_24) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)) )],[refute_0_6,refute_0_7]) ).
cnf(refute_0_9,plain,
( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_26)
| distinct_lines(skolemFOFtoCNF_L,X_26) ),
inference(subst,[],[refute_0_8:[bind(X_24,$fot(X_26))]]) ).
cnf(refute_0_10,plain,
( distinct_lines(X_26,Z)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),Z)
| distinct_lines(skolemFOFtoCNF_L,X_26) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_26) )],[refute_0_9,refute_0_5]) ).
cnf(refute_0_11,plain,
( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_10:[bind(Z,$fot(skolemFOFtoCNF_L)),bind(X_26,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_12,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_10]) ).
cnf(refute_0_13,plain,
~ distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
inference(subst,[],[refute_0_12:[bind(X,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_14,plain,
distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,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_12]) ).
cnf(refute_0_16,plain,
( ~ distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| apart_point_and_line(X_529,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| apart_point_and_line(X_529,skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_532)
| unorthogonal_lines(skolemFOFtoCNF_L,X_532) ),
inference(subst,[],[refute_0_15:[bind(A,$fot(X_529)),bind(L,$fot(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))),bind(M,$fot(skolemFOFtoCNF_L)),bind(N,$fot(X_532))]]) ).
cnf(refute_0_17,plain,
( apart_point_and_line(X_529,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| apart_point_and_line(X_529,skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_532)
| unorthogonal_lines(skolemFOFtoCNF_L,X_532) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_14,refute_0_16]) ).
cnf(refute_0_18,plain,
( apart_point_and_line(X_1061,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| apart_point_and_line(X_1061,skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_M)
| unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_17:[bind(X_529,$fot(X_1061)),bind(X_532,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_19,plain,
( apart_point_and_line(X_1061,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| apart_point_and_line(X_1061,skolemFOFtoCNF_L)
| unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_M) )],[refute_0_18,refute_0_3]) ).
cnf(refute_0_20,plain,
~ unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_21,plain,
( apart_point_and_line(X_1061,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| apart_point_and_line(X_1061,skolemFOFtoCNF_L) ),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_19,refute_0_20]) ).
cnf(refute_0_22,plain,
( apart_point_and_line(skolemFOFtoCNF_A,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_21:[bind(X_1061,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_23,plain,
apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_L),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_A,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)) )],[refute_0_22,refute_0_1]) ).
cnf(refute_0_24,plain,
~ apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_L),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_25,plain,
$false,
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_L) )],[refute_0_23,refute_0_24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO210+2 : TPTP v8.1.0. Released v3.3.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.11/0.33 % Computer : n013.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 600
% 0.11/0.33 % DateTime : Sat Jun 18 04:43:29 EDT 2022
% 0.11/0.33 % CPUTime :
% 0.11/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.05/1.23 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 1.05/1.23
% 1.05/1.23 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 1.05/1.23
%------------------------------------------------------------------------------