TSTP Solution File: GEO210+1 by Metis---2.4
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- Process Solution
%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO210+1 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n017.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 1.07s 1.26s
% Output : CNFRefutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 8
% Syntax : Number of formulae : 67 ( 28 unt; 0 def)
% Number of atoms : 173 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 158 ( 52 ~; 93 |; 7 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 120 ( 2 sgn 57 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X) ).
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(X,Z)
| distinct_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(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,
! [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_5,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_4]) ).
fof(normalize_0_6,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_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(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,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_11,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_10]) ).
fof(normalize_0_12,plain,
distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_14,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_16,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
~ unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_18,plain,
~ apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_L),
inference(conjunct,[],[normalize_0_11]) ).
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(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_5]) ).
cnf(refute_0_5,plain,
( ~ distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_652)
| apart_point_and_line(A,X_652)
| apart_point_and_line(A,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| unorthogonal_lines(X_652,N)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),N) ),
inference(subst,[],[refute_0_4:[bind(L,$fot(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))),bind(M,$fot(X_652))]]) ).
cnf(refute_0_6,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_7]) ).
cnf(refute_0_7,plain,
( ~ distinct_lines(X_400,X_399)
| apart_point_and_line(X,X_399)
| apart_point_and_line(X,X_400)
| convergent_lines(X_400,X_399) ),
inference(subst,[],[refute_0_6:[bind(Y,$fot(X_400)),bind(Z,$fot(X_399))]]) ).
cnf(refute_0_8,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_9,plain,
( ~ distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_96)
| distinct_lines(X_96,Z)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),Z) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))),bind(Y,$fot(X_96))]]) ).
cnf(refute_0_10,plain,
( ~ distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_29)
| distinct_lines(X_29,Z)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),Z) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))),bind(Y,$fot(X_29))]]) ).
cnf(refute_0_11,plain,
distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_12,plain,
( ~ distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_28)
| distinct_lines(skolemFOFtoCNF_L,X_28) ),
inference(subst,[],[refute_0_8:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))),bind(Z,$fot(X_28))]]) ).
cnf(refute_0_13,plain,
( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_28)
| distinct_lines(skolemFOFtoCNF_L,X_28) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_29)
| distinct_lines(skolemFOFtoCNF_L,X_29) ),
inference(subst,[],[refute_0_13:[bind(X_28,$fot(X_29))]]) ).
cnf(refute_0_15,plain,
( distinct_lines(X_29,Z)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),Z)
| distinct_lines(skolemFOFtoCNF_L,X_29) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_29) )],[refute_0_14,refute_0_10]) ).
cnf(refute_0_16,plain,
( distinct_lines(X_97,X_96)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_96)
| distinct_lines(skolemFOFtoCNF_L,X_97) ),
inference(subst,[],[refute_0_15:[bind(Z,$fot(X_96)),bind(X_29,$fot(X_97))]]) ).
cnf(refute_0_17,plain,
( distinct_lines(X_96,Z)
| distinct_lines(X_97,X_96)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),Z)
| distinct_lines(skolemFOFtoCNF_L,X_97) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_96) )],[refute_0_16,refute_0_9]) ).
cnf(refute_0_18,plain,
( distinct_lines(X_400,X_399)
| distinct_lines(X_401,X_400)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_399)
| distinct_lines(skolemFOFtoCNF_L,X_401) ),
inference(subst,[],[refute_0_17:[bind(Z,$fot(X_399)),bind(X_96,$fot(X_400)),bind(X_97,$fot(X_401))]]) ).
cnf(refute_0_19,plain,
( apart_point_and_line(X,X_399)
| apart_point_and_line(X,X_400)
| convergent_lines(X_400,X_399)
| distinct_lines(X_401,X_400)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_399)
| distinct_lines(skolemFOFtoCNF_L,X_401) ),
inference(resolve,[$cnf( distinct_lines(X_400,X_399) )],[refute_0_18,refute_0_7]) ).
cnf(refute_0_20,plain,
( apart_point_and_line(X,X_399)
| apart_point_and_line(X,skolemFOFtoCNF_L)
| convergent_lines(skolemFOFtoCNF_L,X_399)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_399)
| distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_19:[bind(X_400,$fot(skolemFOFtoCNF_L)),bind(X_401,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_21,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_22,plain,
~ distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
inference(subst,[],[refute_0_21:[bind(X,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_23,plain,
( apart_point_and_line(X,X_399)
| apart_point_and_line(X,skolemFOFtoCNF_L)
| convergent_lines(skolemFOFtoCNF_L,X_399)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_399) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) )],[refute_0_20,refute_0_22]) ).
cnf(refute_0_24,plain,
( apart_point_and_line(X_651,X_652)
| apart_point_and_line(X_651,skolemFOFtoCNF_L)
| convergent_lines(skolemFOFtoCNF_L,X_652)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_652) ),
inference(subst,[],[refute_0_23:[bind(X,$fot(X_651)),bind(X_399,$fot(X_652))]]) ).
cnf(refute_0_25,plain,
( apart_point_and_line(A,X_652)
| apart_point_and_line(A,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| apart_point_and_line(X_651,X_652)
| apart_point_and_line(X_651,skolemFOFtoCNF_L)
| convergent_lines(skolemFOFtoCNF_L,X_652)
| unorthogonal_lines(X_652,N)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),N) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_652) )],[refute_0_24,refute_0_5]) ).
cnf(refute_0_26,plain,
( apart_point_and_line(X_651,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| apart_point_and_line(X_651,skolemFOFtoCNF_L)
| convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),N)
| unorthogonal_lines(skolemFOFtoCNF_L,N) ),
inference(subst,[],[refute_0_25:[bind(A,$fot(X_651)),bind(X_652,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_27,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_28,plain,
~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
inference(subst,[],[refute_0_27:[bind(X,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_29,plain,
( apart_point_and_line(X_651,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| apart_point_and_line(X_651,skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),N)
| unorthogonal_lines(skolemFOFtoCNF_L,N) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) )],[refute_0_26,refute_0_28]) ).
cnf(refute_0_30,plain,
( apart_point_and_line(X_1016,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| apart_point_and_line(X_1016,skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_M)
| unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_29:[bind(N,$fot(skolemFOFtoCNF_M)),bind(X_651,$fot(X_1016))]]) ).
cnf(refute_0_31,plain,
( apart_point_and_line(X_1016,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| apart_point_and_line(X_1016,skolemFOFtoCNF_L)
| unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_M) )],[refute_0_30,refute_0_3]) ).
cnf(refute_0_32,plain,
~ unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_33,plain,
( apart_point_and_line(X_1016,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| apart_point_and_line(X_1016,skolemFOFtoCNF_L) ),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_31,refute_0_32]) ).
cnf(refute_0_34,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_33:[bind(X_1016,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_35,plain,
apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_L),
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_A,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)) )],[refute_0_34,refute_0_1]) ).
cnf(refute_0_36,plain,
~ apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_L),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_37,plain,
$false,
inference(resolve,[$cnf( apart_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_L) )],[refute_0_35,refute_0_36]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : GEO210+1 : TPTP v8.1.0. Released v3.3.0.
% 0.11/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.33 % Computer : n017.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % 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 05:15:42 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 1.07/1.26 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 1.07/1.26
% 1.07/1.26 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 1.07/1.27
%------------------------------------------------------------------------------