TSTP Solution File: GEO222+2 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO222+2 : TPTP v8.1.0. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n012.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 05:25:35 EDT 2022
% Result : Theorem 0.48s 0.68s
% Output : CNFRefutation 0.53s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 12
% Syntax : Number of formulae : 102 ( 38 unt; 0 def)
% Number of atoms : 250 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 237 ( 89 ~; 128 |; 13 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 169 ( 6 sgn 96 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X) ).
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(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ) ).
fof(con2,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,X)
| apart_point_and_line(Z,Y) )
=> distinct_points(Z,intersection_point(X,Y)) ) ) ).
fof(ceq3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ) ).
fof(occu1,axiom,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ) ).
fof(oac1,axiom,
! [L,M,N] :
( ( convergent_lines(L,M)
& unorthogonal_lines(L,M) )
=> ( ( convergent_lines(L,N)
& unorthogonal_lines(L,N) )
| ( convergent_lines(M,N)
& unorthogonal_lines(M,N) ) ) ) ).
fof(ooc1,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L) ).
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] : ~ convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)) ).
fof(subgoal_0,plain,
! [A,L] : ~ convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [A,L] : ~ convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(canonicalize,[],[ooc1]) ).
fof(normalize_0_1,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| ( convergent_lines(L,N)
& unorthogonal_lines(L,N) )
| ( convergent_lines(M,N)
& unorthogonal_lines(M,N) ) ),
inference(canonicalize,[],[oac1]) ).
fof(normalize_0_3,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| ( convergent_lines(L,N)
& unorthogonal_lines(L,N) )
| ( convergent_lines(M,N)
& unorthogonal_lines(M,N) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [L,M,N] :
( ( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| convergent_lines(M,N) )
& ( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| unorthogonal_lines(M,N) )
& ( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(M,N)
| unorthogonal_lines(L,N) )
& ( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
? [A,L] : convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_7,plain,
convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(skolemize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,X)
& ~ apart_point_and_line(Z,Y) ) ),
inference(canonicalize,[],[con2]) ).
fof(normalize_0_9,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,X)
& ~ apart_point_and_line(Z,Y) ) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) )
& ( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ) ),
inference(clausify,[],[normalize_0_9]) ).
fof(normalize_0_11,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X] : ~ distinct_points(X,X),
inference(canonicalize,[],[apart1]) ).
fof(normalize_0_13,plain,
! [X] : ~ distinct_points(X,X),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y,Z] :
( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(conjunct,[],[normalize_0_10]) ).
fof(normalize_0_15,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_16,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| distinct_lines(X,Y) ),
inference(canonicalize,[],[ceq3]) ).
fof(normalize_0_18,plain,
! [X,Y] :
( ~ convergent_lines(X,Y)
| distinct_lines(X,Y) ),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_20,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,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_22,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_21]) ).
fof(normalize_0_23,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_24,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[occu1]) ).
fof(normalize_0_26,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[apart6]) ).
fof(normalize_0_28,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_27]) ).
cnf(refute_0_0,plain,
~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_2,plain,
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| ~ unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(skolemFOFtoCNF_L,N)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N) ),
inference(subst,[],[refute_0_2:[bind(L,$fot(skolemFOFtoCNF_L)),bind(M,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_4,plain,
convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ apart_point_and_line(Z,X)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_6,plain,
( ~ apart_point_and_line(X_58,skolemFOFtoCNF_L)
| ~ convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| distinct_points(X_58,intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))) ),
inference(subst,[],[refute_0_5:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Z,$fot(X_58))]]) ).
cnf(refute_0_7,plain,
( ~ apart_point_and_line(X_58,skolemFOFtoCNF_L)
| distinct_points(X_58,intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_4,refute_0_6]) ).
cnf(refute_0_8,plain,
( ~ apart_point_and_line(intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),skolemFOFtoCNF_L)
| distinct_points(intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))) ),
inference(subst,[],[refute_0_7:[bind(X_58,$fot(intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))))]]) ).
cnf(refute_0_9,plain,
~ distinct_points(X,X),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_10,plain,
~ distinct_points(intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),
inference(subst,[],[refute_0_9:[bind(X,$fot(intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))))]]) ).
cnf(refute_0_11,plain,
( ~ apart_point_and_line(Z,Y)
| ~ convergent_lines(X,Y)
| distinct_points(Z,intersection_point(X,Y)) ),
inference(canonicalize,[],[normalize_0_14]) ).
cnf(refute_0_12,plain,
( ~ apart_point_and_line(X_66,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| ~ convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| distinct_points(X_66,intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Z,$fot(X_66))]]) ).
cnf(refute_0_13,plain,
( ~ apart_point_and_line(X_66,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| distinct_points(X_66,intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_4,refute_0_12]) ).
cnf(refute_0_14,plain,
( ~ apart_point_and_line(X_642,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| distinct_points(X_642,intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))) ),
inference(subst,[],[refute_0_13:[bind(X_66,$fot(X_642))]]) ).
cnf(refute_0_15,plain,
~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_A)),bind(L,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_16,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_17,plain,
( ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_22)
| distinct_lines(X_22,Z)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Y,$fot(X_22))]]) ).
cnf(refute_0_18,plain,
( ~ convergent_lines(X,Y)
| distinct_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_19,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_20,plain,
distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_4,refute_0_19]) ).
cnf(refute_0_21,plain,
( ~ distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_21)
| distinct_lines(skolemFOFtoCNF_L,X_21) ),
inference(subst,[],[refute_0_16:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Z,$fot(X_21))]]) ).
cnf(refute_0_22,plain,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_21)
| distinct_lines(skolemFOFtoCNF_L,X_21) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_20,refute_0_21]) ).
cnf(refute_0_23,plain,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_22)
| distinct_lines(skolemFOFtoCNF_L,X_22) ),
inference(subst,[],[refute_0_22:[bind(X_21,$fot(X_22))]]) ).
cnf(refute_0_24,plain,
( distinct_lines(X_22,Z)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z)
| distinct_lines(skolemFOFtoCNF_L,X_22) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_22) )],[refute_0_23,refute_0_17]) ).
cnf(refute_0_25,plain,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_24:[bind(Z,$fot(skolemFOFtoCNF_L)),bind(X_22,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_26,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_27,plain,
~ distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
inference(subst,[],[refute_0_26:[bind(X,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_28,plain,
distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) )],[refute_0_25,refute_0_27]) ).
cnf(refute_0_29,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_22]) ).
cnf(refute_0_30,plain,
( ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| apart_point_and_line(X_298,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_298,skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_301)
| unorthogonal_lines(skolemFOFtoCNF_L,X_301) ),
inference(subst,[],[refute_0_29:[bind(A,$fot(X_298)),bind(L,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(M,$fot(skolemFOFtoCNF_L)),bind(N,$fot(X_301))]]) ).
cnf(refute_0_31,plain,
( apart_point_and_line(X_298,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_298,skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_301)
| unorthogonal_lines(skolemFOFtoCNF_L,X_301) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
( apart_point_and_line(X_640,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_640,skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_31:[bind(X_298,$fot(X_640)),bind(X_301,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_33,plain,
( apart_point_and_line(X_640,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_640,skolemFOFtoCNF_L)
| unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_32,refute_0_15]) ).
cnf(refute_0_34,plain,
( apart_point_and_line(X_642,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| apart_point_and_line(X_642,skolemFOFtoCNF_L)
| unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_33:[bind(X_640,$fot(X_642))]]) ).
cnf(refute_0_35,plain,
( apart_point_and_line(X_642,skolemFOFtoCNF_L)
| distinct_points(X_642,intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))
| unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( apart_point_and_line(X_642,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_34,refute_0_14]) ).
cnf(refute_0_36,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),skolemFOFtoCNF_L)
| distinct_points(intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))
| unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_35:[bind(X_642,$fot(intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))))]]) ).
cnf(refute_0_37,plain,
( apart_point_and_line(intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),skolemFOFtoCNF_L)
| unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))) )],[refute_0_36,refute_0_10]) ).
cnf(refute_0_38,plain,
( distinct_points(intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))
| unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( apart_point_and_line(intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),skolemFOFtoCNF_L) )],[refute_0_37,refute_0_8]) ).
cnf(refute_0_39,plain,
unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(resolve,[$cnf( distinct_points(intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),intersection_point(skolemFOFtoCNF_L,orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))) )],[refute_0_38,refute_0_10]) ).
cnf(refute_0_40,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(skolemFOFtoCNF_L,N)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N) ),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_39,refute_0_3]) ).
cnf(refute_0_41,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_42,plain,
~ convergent_lines(orthogonal_through_point(X_37,X_36),orthogonal_through_point(X_37,X_36)),
inference(subst,[],[refute_0_41:[bind(X,$fot(orthogonal_through_point(X_37,X_36)))]]) ).
cnf(refute_0_43,plain,
~ unorthogonal_lines(orthogonal_through_point(X_14,A),X_14),
inference(subst,[],[refute_0_0:[bind(L,$fot(X_14))]]) ).
cnf(refute_0_44,plain,
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_45,plain,
( convergent_lines(orthogonal_through_point(X_14,A),X_14)
| unorthogonal_lines(orthogonal_through_point(X_14,A),X_14) ),
inference(subst,[],[refute_0_44:[bind(L,$fot(orthogonal_through_point(X_14,A))),bind(M,$fot(X_14))]]) ).
cnf(refute_0_46,plain,
convergent_lines(orthogonal_through_point(X_14,A),X_14),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(X_14,A),X_14) )],[refute_0_45,refute_0_43]) ).
cnf(refute_0_47,plain,
convergent_lines(orthogonal_through_point(X_32,A),X_32),
inference(subst,[],[refute_0_46:[bind(X_14,$fot(X_32))]]) ).
cnf(refute_0_48,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_49,plain,
( ~ convergent_lines(orthogonal_through_point(X_32,A),X_32)
| convergent_lines(X_32,X_33)
| convergent_lines(orthogonal_through_point(X_32,A),X_33) ),
inference(subst,[],[refute_0_48:[bind(X,$fot(orthogonal_through_point(X_32,A))),bind(Y,$fot(X_32)),bind(Z,$fot(X_33))]]) ).
cnf(refute_0_50,plain,
( convergent_lines(X_32,X_33)
| convergent_lines(orthogonal_through_point(X_32,A),X_33) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_32,A),X_32) )],[refute_0_47,refute_0_49]) ).
cnf(refute_0_51,plain,
( convergent_lines(X_37,orthogonal_through_point(X_37,X_36))
| convergent_lines(orthogonal_through_point(X_37,X_36),orthogonal_through_point(X_37,X_36)) ),
inference(subst,[],[refute_0_50:[bind(A,$fot(X_36)),bind(X_32,$fot(X_37)),bind(X_33,$fot(orthogonal_through_point(X_37,X_36)))]]) ).
cnf(refute_0_52,plain,
convergent_lines(X_37,orthogonal_through_point(X_37,X_36)),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_37,X_36),orthogonal_through_point(X_37,X_36)) )],[refute_0_51,refute_0_42]) ).
cnf(refute_0_53,plain,
convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_52:[bind(X_36,$fot(skolemFOFtoCNF_A)),bind(X_37,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_54,plain,
( convergent_lines(skolemFOFtoCNF_L,N)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_53,refute_0_40]) ).
cnf(refute_0_55,plain,
( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_54:[bind(N,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_56,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_55,refute_0_1]) ).
cnf(refute_0_57,plain,
~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
inference(subst,[],[refute_0_41:[bind(X,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_58,plain,
$false,
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) )],[refute_0_56,refute_0_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO222+2 : TPTP v8.1.0. Released v3.3.0.
% 0.07/0.12 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n012.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 : Sat Jun 18 07:14:23 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.48/0.68 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.48/0.68
% 0.48/0.68 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.53/0.69
%------------------------------------------------------------------------------