TSTP Solution File: GEO221+3 by Metis---2.4
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%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO221+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n005.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 05:25:34 EDT 2022
% Result : Theorem 0.57s 0.75s
% Output : CNFRefutation 0.57s
% Verified :
% SZS Type : Refutation
% Derivation depth : 31
% Number of leaves : 12
% Syntax : Number of formulae : 123 ( 27 unt; 0 def)
% Number of atoms : 299 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 271 ( 95 ~; 147 |; 15 &)
% ( 6 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 207 ( 7 sgn 100 !; 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(ax6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| convergent_lines(Y,Z) ) ) ).
fof(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_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(couo1,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) )
=> ~ convergent_lines(M,N) ) ).
fof(ax2,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ) ).
fof(a5,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ) ).
fof(con,conjecture,
! [A,B,L] :
( incident_point_and_line(B,orthogonal_through_point(L,A))
=> equal_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B)) ) ).
fof(subgoal_0,plain,
! [A,B,L] :
( incident_point_and_line(B,orthogonal_through_point(L,A))
=> equal_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [A,B,L] :
( incident_point_and_line(B,orthogonal_through_point(L,A))
=> equal_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B)) ),
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)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
<=> unorthogonal_lines(X,Y) ),
inference(canonicalize,[],[a5]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
<=> unorthogonal_lines(X,Y) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [X,Y] :
( ( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) )
& ( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_7]) ).
fof(normalize_0_9,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[occu1]) ).
fof(normalize_0_11,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(canonicalize,[],[couo1]) ).
fof(normalize_0_13,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
? [A,B,L] :
( ~ equal_lines(orthogonal_through_point(L,A),orthogonal_through_point(L,B))
& incident_point_and_line(B,orthogonal_through_point(L,A)) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_17,plain,
( ~ equal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
& incident_point_and_line(skolemFOFtoCNF_B,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(skolemize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
~ equal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)),
inference(conjunct,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
<=> equal_lines(X,Y) ),
inference(canonicalize,[],[ax2]) ).
fof(normalize_0_20,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
<=> equal_lines(X,Y) ),
inference(specialize,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [X,Y] :
( ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) )
& ( distinct_lines(X,Y)
| equal_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X,Y] :
( distinct_lines(X,Y)
| equal_lines(X,Y) ),
inference(conjunct,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X,Y] :
( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) ),
inference(conjunct,[],[normalize_0_8]) ).
fof(normalize_0_24,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(M,N)
| unorthogonal_lines(L,N) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_25,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[ax6]) ).
fof(normalize_0_26,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_28,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_30,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_29]) ).
fof(normalize_0_31,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_32,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_31]) ).
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_B),skolemFOFtoCNF_L),
inference(subst,[],[refute_0_0:[bind(A,$fot(skolemFOFtoCNF_B)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_2,plain,
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| ~ unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),N) ),
inference(subst,[],[refute_0_2:[bind(L,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(M,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_4,plain,
( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_5,plain,
( ~ orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_510)
| ~ unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_510) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(Y,$fot(X_510))]]) ).
cnf(refute_0_6,plain,
( ~ orthogonal_lines(X_108,orthogonal_through_point(X_107,X_106))
| ~ unorthogonal_lines(X_108,orthogonal_through_point(X_107,X_106)) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(X_108)),bind(Y,$fot(orthogonal_through_point(X_107,X_106)))]]) ).
cnf(refute_0_7,plain,
~ unorthogonal_lines(orthogonal_through_point(X_14,A),X_14),
inference(subst,[],[refute_0_0:[bind(L,$fot(X_14))]]) ).
cnf(refute_0_8,plain,
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_9,plain,
( convergent_lines(orthogonal_through_point(X_14,A),X_14)
| unorthogonal_lines(orthogonal_through_point(X_14,A),X_14) ),
inference(subst,[],[refute_0_8:[bind(L,$fot(orthogonal_through_point(X_14,A))),bind(M,$fot(X_14))]]) ).
cnf(refute_0_10,plain,
convergent_lines(orthogonal_through_point(X_14,A),X_14),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(X_14,A),X_14) )],[refute_0_9,refute_0_7]) ).
cnf(refute_0_11,plain,
convergent_lines(orthogonal_through_point(X_101,A),X_101),
inference(subst,[],[refute_0_10:[bind(X_14,$fot(X_101))]]) ).
cnf(refute_0_12,plain,
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_13,plain,
( ~ convergent_lines(orthogonal_through_point(X_101,A),X_101)
| unorthogonal_lines(X_99,X_101)
| unorthogonal_lines(X_99,orthogonal_through_point(X_101,A)) ),
inference(subst,[],[refute_0_12:[bind(L,$fot(X_99)),bind(M,$fot(orthogonal_through_point(X_101,A))),bind(N,$fot(X_101))]]) ).
cnf(refute_0_14,plain,
( unorthogonal_lines(X_99,X_101)
| unorthogonal_lines(X_99,orthogonal_through_point(X_101,A)) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_101,A),X_101) )],[refute_0_11,refute_0_13]) ).
cnf(refute_0_15,plain,
( unorthogonal_lines(X_108,X_107)
| unorthogonal_lines(X_108,orthogonal_through_point(X_107,X_106)) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(X_106)),bind(X_101,$fot(X_107)),bind(X_99,$fot(X_108))]]) ).
cnf(refute_0_16,plain,
( ~ orthogonal_lines(X_108,orthogonal_through_point(X_107,X_106))
| unorthogonal_lines(X_108,X_107) ),
inference(resolve,[$cnf( unorthogonal_lines(X_108,orthogonal_through_point(X_107,X_106)) )],[refute_0_15,refute_0_6]) ).
cnf(refute_0_17,plain,
( ~ orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_16:[bind(X_106,$fot(skolemFOFtoCNF_B)),bind(X_107,$fot(skolemFOFtoCNF_L)),bind(X_108,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_18,plain,
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_19,plain,
( ~ distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(Y,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_20,plain,
~ equal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_21,plain,
( distinct_lines(X,Y)
| equal_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_22]) ).
cnf(refute_0_22,plain,
( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| equal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_21:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(Y,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_23,plain,
distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)),
inference(resolve,[$cnf( equal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) )],[refute_0_22,refute_0_20]) ).
cnf(refute_0_24,plain,
convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) )],[refute_0_23,refute_0_19]) ).
cnf(refute_0_25,plain,
( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_26,plain,
( orthogonal_lines(X_204,X_205)
| unorthogonal_lines(X_204,X_205) ),
inference(subst,[],[refute_0_25:[bind(X,$fot(X_204)),bind(Y,$fot(X_205))]]) ).
cnf(refute_0_27,plain,
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| convergent_lines(M,N)
| unorthogonal_lines(L,N) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_28,plain,
( ~ convergent_lines(X_204,X_205)
| ~ unorthogonal_lines(X_204,X_205)
| convergent_lines(X_205,X_206)
| unorthogonal_lines(X_204,X_206) ),
inference(subst,[],[refute_0_27:[bind(L,$fot(X_204)),bind(M,$fot(X_205)),bind(N,$fot(X_206))]]) ).
cnf(refute_0_29,plain,
( ~ convergent_lines(X_204,X_205)
| convergent_lines(X_205,X_206)
| orthogonal_lines(X_204,X_205)
| unorthogonal_lines(X_204,X_206) ),
inference(resolve,[$cnf( unorthogonal_lines(X_204,X_205) )],[refute_0_26,refute_0_28]) ).
cnf(refute_0_30,plain,
( ~ convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),X_499)
| orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_499) ),
inference(subst,[],[refute_0_29:[bind(X_204,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(X_205,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))),bind(X_206,$fot(X_499))]]) ).
cnf(refute_0_31,plain,
( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),X_499)
| orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_499) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) )],[refute_0_24,refute_0_30]) ).
cnf(refute_0_32,plain,
( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),X_509)
| orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_509) ),
inference(subst,[],[refute_0_31:[bind(X_499,$fot(X_509))]]) ).
cnf(refute_0_33,plain,
( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),X_509)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_509)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) ),
inference(resolve,[$cnf( orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) )],[refute_0_32,refute_0_17]) ).
cnf(refute_0_34,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_35,plain,
( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),X_509)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_509) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_33,refute_0_34]) ).
cnf(refute_0_36,plain,
( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),X_510)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_510) ),
inference(subst,[],[refute_0_35:[bind(X_509,$fot(X_510))]]) ).
cnf(refute_0_37,plain,
( ~ orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_510)
| convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),X_510) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_510) )],[refute_0_36,refute_0_5]) ).
cnf(refute_0_38,plain,
( ~ orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_515)
| convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),X_515) ),
inference(subst,[],[refute_0_37:[bind(X_510,$fot(X_515))]]) ).
cnf(refute_0_39,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_40,plain,
( ~ convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_125)
| convergent_lines(X_125,Z)
| convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),Z) ),
inference(subst,[],[refute_0_39:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(Y,$fot(X_125))]]) ).
cnf(refute_0_41,plain,
( ~ distinct_lines(X_122,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| convergent_lines(X_122,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(X_122)),bind(Y,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_42,plain,
( ~ distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_120)
| convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_120) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(Y,$fot(X_120))]]) ).
cnf(refute_0_43,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_28]) ).
cnf(refute_0_44,plain,
~ distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)),
inference(subst,[],[refute_0_43:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_45,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_30]) ).
cnf(refute_0_46,plain,
( ~ distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),X_63)
| distinct_lines(X_63,Z)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),Z) ),
inference(subst,[],[refute_0_45:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))),bind(Y,$fot(X_63))]]) ).
cnf(refute_0_47,plain,
( ~ distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_62)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),X_62) ),
inference(subst,[],[refute_0_45:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(Y,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))),bind(Z,$fot(X_62))]]) ).
cnf(refute_0_48,plain,
( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_62)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),X_62) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) )],[refute_0_23,refute_0_47]) ).
cnf(refute_0_49,plain,
( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_63)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),X_63) ),
inference(subst,[],[refute_0_48:[bind(X_62,$fot(X_63))]]) ).
cnf(refute_0_50,plain,
( distinct_lines(X_63,Z)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_63)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),Z) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),X_63) )],[refute_0_49,refute_0_46]) ).
cnf(refute_0_51,plain,
( distinct_lines(X_119,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_119)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_50:[bind(Z,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))),bind(X_63,$fot(X_119))]]) ).
cnf(refute_0_52,plain,
( distinct_lines(X_119,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_119) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) )],[refute_0_51,refute_0_44]) ).
cnf(refute_0_53,plain,
( distinct_lines(X_120,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_120) ),
inference(subst,[],[refute_0_52:[bind(X_119,$fot(X_120))]]) ).
cnf(refute_0_54,plain,
( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_120)
| distinct_lines(X_120,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_120) )],[refute_0_53,refute_0_42]) ).
cnf(refute_0_55,plain,
( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_122)
| distinct_lines(X_122,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_54:[bind(X_120,$fot(X_122))]]) ).
cnf(refute_0_56,plain,
( convergent_lines(X_122,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_122) ),
inference(resolve,[$cnf( distinct_lines(X_122,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) )],[refute_0_55,refute_0_41]) ).
cnf(refute_0_57,plain,
( convergent_lines(X_125,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_125) ),
inference(subst,[],[refute_0_56:[bind(X_122,$fot(X_125))]]) ).
cnf(refute_0_58,plain,
( convergent_lines(X_125,Z)
| convergent_lines(X_125,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),Z) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_125) )],[refute_0_57,refute_0_40]) ).
cnf(refute_0_59,plain,
( convergent_lines(X_125,X_498)
| convergent_lines(X_125,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_498) ),
inference(subst,[],[refute_0_58:[bind(Z,$fot(X_498))]]) ).
cnf(refute_0_60,plain,
( ~ convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_498)
| convergent_lines(X_498,X_499)
| orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_498)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_499) ),
inference(subst,[],[refute_0_29:[bind(X_204,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(X_205,$fot(X_498)),bind(X_206,$fot(X_499))]]) ).
cnf(refute_0_61,plain,
( convergent_lines(X_125,X_498)
| convergent_lines(X_125,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| convergent_lines(X_498,X_499)
| orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_498)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_499) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_498) )],[refute_0_59,refute_0_60]) ).
cnf(refute_0_62,plain,
( convergent_lines(X_498,X_498)
| convergent_lines(X_498,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_498)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_61:[bind(X_125,$fot(X_498)),bind(X_499,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_63,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_32]) ).
cnf(refute_0_64,plain,
~ convergent_lines(X_498,X_498),
inference(subst,[],[refute_0_63:[bind(X,$fot(X_498))]]) ).
cnf(refute_0_65,plain,
( convergent_lines(X_498,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_498)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( convergent_lines(X_498,X_498) )],[refute_0_62,refute_0_64]) ).
cnf(refute_0_66,plain,
( convergent_lines(X_515,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_515)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_65:[bind(X_498,$fot(X_515))]]) ).
cnf(refute_0_67,plain,
( convergent_lines(X_515,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),X_515)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) ),
inference(resolve,[$cnf( orthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_515) )],[refute_0_66,refute_0_38]) ).
cnf(refute_0_68,plain,
( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_67:[bind(X_515,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_69,plain,
~ convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)),
inference(subst,[],[refute_0_63:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_70,plain,
unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) )],[refute_0_68,refute_0_69]) ).
cnf(refute_0_71,plain,
( ~ convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B))
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),N) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) )],[refute_0_70,refute_0_3]) ).
cnf(refute_0_72,plain,
( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),N)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),N) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B)) )],[refute_0_24,refute_0_71]) ).
cnf(refute_0_73,plain,
( 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_72:[bind(N,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_74,plain,
unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_B),skolemFOFtoCNF_L) )],[refute_0_73,refute_0_1]) ).
cnf(refute_0_75,plain,
$false,
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_74,refute_0_34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO221+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.13/0.34 % Computer : n005.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 600
% 0.13/0.34 % DateTime : Sat Jun 18 18:37:38 EDT 2022
% 0.13/0.34 % CPUTime :
% 0.13/0.34 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.57/0.75 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.57/0.75
% 0.57/0.75 % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 0.57/0.75
%------------------------------------------------------------------------------