%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO210+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n014.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 05:25:25 EDT 2022
% Result : Theorem 0.20s 0.51s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 10
% Syntax : Number of formulae : 83 ( 23 unt; 0 def)
% Number of atoms : 198 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 188 ( 73 ~; 82 |; 20 &)
% ( 6 <=>; 7 =>; 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 : 130 ( 3 sgn 83 !; 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(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,L,M] :
( ( incident_point_and_line(A,L)
& orthogonal_lines(L,M) )
=> equal_lines(L,orthogonal_through_point(M,A)) ) ).
fof(subgoal_0,plain,
! [A,L,M] :
( ( incident_point_and_line(A,L)
& orthogonal_lines(L,M) )
=> equal_lines(L,orthogonal_through_point(M,A)) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [A,L,M] :
( ( incident_point_and_line(A,L)
& orthogonal_lines(L,M) )
=> equal_lines(L,orthogonal_through_point(M,A)) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
<=> unorthogonal_lines(X,Y) ),
inference(canonicalize,[],[a5]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
<=> unorthogonal_lines(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) )
& ( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(canonicalize,[],[ooc1]) ).
fof(normalize_0_5,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[p1]) ).
fof(normalize_0_7,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
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] :
( ~ equal_lines(L,orthogonal_through_point(M,A))
& incident_point_and_line(A,L)
& orthogonal_lines(L,M) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_11,plain,
( ~ equal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
& incident_point_and_line(skolemFOFtoCNF_A,skolemFOFtoCNF_L)
& orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(skolemize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
~ equal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_13,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
<=> equal_lines(X,Y) ),
inference(canonicalize,[],[ax2]) ).
fof(normalize_0_14,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
<=> equal_lines(X,Y) ),
inference(specialize,[],[normalize_0_13]) ).
fof(normalize_0_15,plain,
! [X,Y] :
( ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) )
& ( distinct_lines(X,Y)
| equal_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [X,Y] :
( distinct_lines(X,Y)
| equal_lines(X,Y) ),
inference(conjunct,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_18,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_17]) ).
fof(normalize_0_19,plain,
orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(conjunct,[],[normalize_0_11]) ).
fof(normalize_0_20,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[occu1]) ).
fof(normalize_0_21,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(canonicalize,[],[couo1]) ).
fof(normalize_0_23,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(specialize,[],[normalize_0_22]) ).
fof(normalize_0_24,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_25,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_24]) ).
fof(normalize_0_26,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_25]) ).
fof(normalize_0_27,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(conjunct,[],[normalize_0_26]) ).
cnf(refute_0_0,plain,
( ~ orthogonal_lines(X,Y)
| ~ unorthogonal_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| ~ unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_2,plain,
~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(canonicalize,[],[normalize_0_5]) ).
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)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
( ~ distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| convergent_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_4:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))),bind(Y,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_6,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_7,plain,
( ~ distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_82)
| distinct_lines(X_82,Z)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),Z) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))),bind(Y,$fot(X_82))]]) ).
cnf(refute_0_8,plain,
~ equal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)),
inference(canonicalize,[],[normalize_0_12]) ).
cnf(refute_0_9,plain,
( distinct_lines(X,Y)
| equal_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_16]) ).
cnf(refute_0_10,plain,
( distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| equal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_9:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_11,plain,
distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)),
inference(resolve,[$cnf( equal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)) )],[refute_0_10,refute_0_8]) ).
cnf(refute_0_12,plain,
( ~ distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_81)
| distinct_lines(skolemFOFtoCNF_L,X_81) ),
inference(subst,[],[refute_0_6:[bind(X,$fot(skolemFOFtoCNF_L)),bind(Y,$fot(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A))),bind(Z,$fot(X_81))]]) ).
cnf(refute_0_13,plain,
( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_81)
| distinct_lines(skolemFOFtoCNF_L,X_81) ),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A)) )],[refute_0_11,refute_0_12]) ).
cnf(refute_0_14,plain,
( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_82)
| distinct_lines(skolemFOFtoCNF_L,X_82) ),
inference(subst,[],[refute_0_13:[bind(X_81,$fot(X_82))]]) ).
cnf(refute_0_15,plain,
( distinct_lines(X_82,Z)
| distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),Z)
| distinct_lines(skolemFOFtoCNF_L,X_82) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_82) )],[refute_0_14,refute_0_7]) ).
cnf(refute_0_16,plain,
( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_15:[bind(Z,$fot(skolemFOFtoCNF_L)),bind(X_82,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_17,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_18]) ).
cnf(refute_0_18,plain,
~ distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L),
inference(subst,[],[refute_0_17:[bind(X,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_19,plain,
distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(resolve,[$cnf( distinct_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_L) )],[refute_0_16,refute_0_18]) ).
cnf(refute_0_20,plain,
convergent_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_19,refute_0_5]) ).
cnf(refute_0_21,plain,
~ unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,A),skolemFOFtoCNF_M),
inference(subst,[],[refute_0_2:[bind(L,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_22,plain,
orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_23,plain,
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[normalize_0_21]) ).
cnf(refute_0_24,plain,
( convergent_lines(X_39,X_40)
| unorthogonal_lines(X_39,X_40) ),
inference(subst,[],[refute_0_23:[bind(L,$fot(X_39)),bind(M,$fot(X_40))]]) ).
cnf(refute_0_25,plain,
( ~ orthogonal_lines(X_39,X_40)
| ~ unorthogonal_lines(X_39,X_40) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(X_39)),bind(Y,$fot(X_40))]]) ).
cnf(refute_0_26,plain,
( ~ orthogonal_lines(X_39,X_40)
| convergent_lines(X_39,X_40) ),
inference(resolve,[$cnf( unorthogonal_lines(X_39,X_40) )],[refute_0_24,refute_0_25]) ).
cnf(refute_0_27,plain,
( ~ orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_26:[bind(X_39,$fot(skolemFOFtoCNF_L)),bind(X_40,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_28,plain,
convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(resolve,[$cnf( orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_22,refute_0_27]) ).
cnf(refute_0_29,plain,
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_30,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M)
| unorthogonal_lines(X_53,skolemFOFtoCNF_L)
| unorthogonal_lines(X_53,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_29:[bind(L,$fot(X_53)),bind(M,$fot(skolemFOFtoCNF_L)),bind(N,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_31,plain,
( unorthogonal_lines(X_53,skolemFOFtoCNF_L)
| unorthogonal_lines(X_53,skolemFOFtoCNF_M) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_28,refute_0_30]) ).
cnf(refute_0_32,plain,
( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,A),skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,A),skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_31:[bind(X_53,$fot(orthogonal_through_point(skolemFOFtoCNF_M,A)))]]) ).
cnf(refute_0_33,plain,
unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,A),skolemFOFtoCNF_L),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,A),skolemFOFtoCNF_M) )],[refute_0_32,refute_0_21]) ).
cnf(refute_0_34,plain,
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_35,plain,
( ~ convergent_lines(orthogonal_through_point(skolemFOFtoCNF_M,A),skolemFOFtoCNF_L)
| ~ unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,A),skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,A),X_340)
| unorthogonal_lines(skolemFOFtoCNF_L,X_340) ),
inference(subst,[],[refute_0_34:[bind(L,$fot(orthogonal_through_point(skolemFOFtoCNF_M,A))),bind(M,$fot(skolemFOFtoCNF_L)),bind(N,$fot(X_340))]]) ).
cnf(refute_0_36,plain,
( ~ convergent_lines(orthogonal_through_point(skolemFOFtoCNF_M,A),skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,A),X_340)
| unorthogonal_lines(skolemFOFtoCNF_L,X_340) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,A),skolemFOFtoCNF_L) )],[refute_0_33,refute_0_35]) ).
cnf(refute_0_37,plain,
( ~ convergent_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_342)
| unorthogonal_lines(skolemFOFtoCNF_L,X_342) ),
inference(subst,[],[refute_0_36:[bind(A,$fot(skolemFOFtoCNF_A)),bind(X_340,$fot(X_342))]]) ).
cnf(refute_0_38,plain,
( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),X_342)
| unorthogonal_lines(skolemFOFtoCNF_L,X_342) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_20,refute_0_37]) ).
cnf(refute_0_39,plain,
( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_M)
| unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) ),
inference(subst,[],[refute_0_38:[bind(X_342,$fot(skolemFOFtoCNF_M))]]) ).
cnf(refute_0_40,plain,
unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_M,skolemFOFtoCNF_A),skolemFOFtoCNF_M) )],[refute_0_39,refute_0_3]) ).
cnf(refute_0_41,plain,
~ orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_40,refute_0_1]) ).
cnf(refute_0_42,plain,
$false,
inference(resolve,[$cnf( orthogonal_lines(skolemFOFtoCNF_L,skolemFOFtoCNF_M) )],[refute_0_22,refute_0_41]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : GEO210+3 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : metis --show proof --show saturation %s
% 0.12/0.34 % Computer : n014.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 18:12:34 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.20/0.51 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.51
% 0.20/0.51 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.20/0.51
%------------------------------------------------------------------------------