%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO223+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n021.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 05:25:36 EDT 2022
% Result : Theorem 0.17s 0.40s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 13
% Syntax : Number of formulae : 118 ( 45 unt; 0 def)
% Number of atoms : 283 ( 0 equ)
% Maximal formula atoms : 16 ( 2 avg)
% Number of connectives : 267 ( 102 ~; 136 |; 20 &)
% ( 3 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 215 ( 20 sgn 103 !; 2 ?)
% 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(cp1,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,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(cotno1,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(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(con,conjecture,
! [A,L] : equal_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)) ).
fof(subgoal_0,plain,
! [A,L] : equal_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [A,L] : equal_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X] : ~ convergent_lines(X,X),
inference(canonicalize,[],[apart3]) ).
fof(normalize_0_1,plain,
! [X] : ~ convergent_lines(X,X),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| ( convergent_lines(L,M)
& unorthogonal_lines(L,M) )
| ( convergent_lines(L,N)
& unorthogonal_lines(L,N) ) ),
inference(canonicalize,[],[cotno1]) ).
fof(normalize_0_3,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| ( convergent_lines(L,M)
& unorthogonal_lines(L,M) )
| ( convergent_lines(L,N)
& unorthogonal_lines(L,N) ) ),
inference(specialize,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [L,M,N] :
( ( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,M)
| convergent_lines(L,N) )
& ( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,M)
| unorthogonal_lines(L,N) )
& ( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,N)
| unorthogonal_lines(L,M) )
& ( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ) ),
inference(clausify,[],[normalize_0_3]) ).
fof(normalize_0_5,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(conjunct,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(canonicalize,[],[ooc1]) ).
fof(normalize_0_7,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(canonicalize,[],[couo1]) ).
fof(normalize_0_9,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[cp1]) ).
fof(normalize_0_11,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[ax6]) ).
fof(normalize_0_13,plain,
! [X,Y,Z] :
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
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,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[apart5]) ).
fof(normalize_0_17,plain,
! [X,Y,Z] :
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(specialize,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
? [A,L] : ~ equal_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_19,plain,
~ equal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(skolemize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
<=> equal_lines(X,Y) ),
inference(canonicalize,[],[ax2]) ).
fof(normalize_0_21,plain,
! [X,Y] :
( ~ distinct_lines(X,Y)
<=> equal_lines(X,Y) ),
inference(specialize,[],[normalize_0_20]) ).
fof(normalize_0_22,plain,
! [X,Y] :
( ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) )
& ( distinct_lines(X,Y)
| equal_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [X,Y] :
( distinct_lines(X,Y)
| equal_lines(X,Y) ),
inference(conjunct,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [X] : ~ distinct_lines(X,X),
inference(canonicalize,[],[apart2]) ).
fof(normalize_0_25,plain,
! [X] : ~ distinct_lines(X,X),
inference(specialize,[],[normalize_0_24]) ).
fof(normalize_0_26,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[occu1]) ).
fof(normalize_0_27,plain,
! [L,M] :
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(specialize,[],[normalize_0_26]) ).
fof(normalize_0_28,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_29,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_28]) ).
fof(normalize_0_30,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_29]) ).
fof(normalize_0_31,plain,
! [L,M,N] :
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(conjunct,[],[normalize_0_30]) ).
cnf(refute_0_0,plain,
~ convergent_lines(X,X),
inference(canonicalize,[],[normalize_0_1]) ).
cnf(refute_0_1,plain,
~ convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_0:[bind(X,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_2,plain,
( ~ convergent_lines(M,N)
| ~ unorthogonal_lines(M,N)
| convergent_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_3,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| ~ unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(L,skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_2:[bind(M,$fot(skolemFOFtoCNF_L)),bind(N,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_4,plain,
~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_5,plain,
~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A)),bind(L,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_6,plain,
~ unorthogonal_lines(orthogonal_through_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_4:[bind(L,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_7,plain,
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,M)
| unorthogonal_lines(L,N) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_8,plain,
( ~ convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(X_160,X_159))
| unorthogonal_lines(L,parallel_through_point(X_160,X_159))
| unorthogonal_lines(L,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_7:[bind(M,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(N,$fot(parallel_through_point(X_160,X_159)))]]) ).
cnf(refute_0_9,plain,
~ convergent_lines(parallel_through_point(Y,X),Y),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_10,plain,
~ convergent_lines(parallel_through_point(X_116,X),X_116),
inference(subst,[],[refute_0_9:[bind(Y,$fot(X_116))]]) ).
cnf(refute_0_11,plain,
( ~ convergent_lines(X,Y)
| convergent_lines(X,Z)
| convergent_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_12,plain,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_67)
| convergent_lines(X_67,Z)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Y,$fot(X_67))]]) ).
cnf(refute_0_13,plain,
( ~ distinct_lines(X,Y)
| convergent_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_15]) ).
cnf(refute_0_14,plain,
( ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_13:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Y,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_15,plain,
( ~ distinct_lines(X,Y)
| distinct_lines(X,Z)
| distinct_lines(Y,Z) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_16,plain,
( ~ distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_62)
| distinct_lines(X_62,Z)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Y,$fot(X_62))]]) ).
cnf(refute_0_17,plain,
~ equal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(canonicalize,[],[normalize_0_19]) ).
cnf(refute_0_18,plain,
( distinct_lines(X,Y)
| equal_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_23]) ).
cnf(refute_0_19,plain,
( distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))
| equal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_18:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(Y,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_20,plain,
distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)),
inference(resolve,[$cnf( equal_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A)) )],[refute_0_19,refute_0_17]) ).
cnf(refute_0_21,plain,
( ~ distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),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_61)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_61) ),
inference(subst,[],[refute_0_15:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(Y,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Z,$fot(X_61))]]) ).
cnf(refute_0_22,plain,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_61)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_61) ),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),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_62)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_62) ),
inference(subst,[],[refute_0_22:[bind(X_61,$fot(X_62))]]) ).
cnf(refute_0_24,plain,
( distinct_lines(X_62,Z)
| distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z)
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_62) ),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_62) )],[refute_0_23,refute_0_16]) ).
cnf(refute_0_25,plain,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_24:[bind(Z,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(X_62,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_26,plain,
~ distinct_lines(X,X),
inference(canonicalize,[],[normalize_0_25]) ).
cnf(refute_0_27,plain,
~ distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_26:[bind(X,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_28,plain,
distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(resolve,[$cnf( distinct_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_25,refute_0_27]) ).
cnf(refute_0_29,plain,
convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(resolve,[$cnf( distinct_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_28,refute_0_14]) ).
cnf(refute_0_30,plain,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_66)
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_66) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A))),bind(Y,$fot(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))),bind(Z,$fot(X_66))]]) ).
cnf(refute_0_31,plain,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_66)
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_66) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_29,refute_0_30]) ).
cnf(refute_0_32,plain,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_67)
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_67) ),
inference(subst,[],[refute_0_31:[bind(X_66,$fot(X_67))]]) ).
cnf(refute_0_33,plain,
( convergent_lines(X_67,Z)
| convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),Z)
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),X_67) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_67) )],[refute_0_32,refute_0_12]) ).
cnf(refute_0_34,plain,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_116)
| convergent_lines(parallel_through_point(X_116,X),X_116)
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(X_116,X)) ),
inference(subst,[],[refute_0_33:[bind(Z,$fot(X_116)),bind(X_67,$fot(parallel_through_point(X_116,X)))]]) ).
cnf(refute_0_35,plain,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_116)
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(X_116,X)) ),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(X_116,X),X_116) )],[refute_0_34,refute_0_10]) ).
cnf(refute_0_36,plain,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_160)
| convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(X_160,X_159)) ),
inference(subst,[],[refute_0_35:[bind(X,$fot(X_159)),bind(X_116,$fot(X_160))]]) ).
cnf(refute_0_37,plain,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_160)
| unorthogonal_lines(L,parallel_through_point(X_160,X_159))
| unorthogonal_lines(L,parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(resolve,[$cnf( convergent_lines(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),parallel_through_point(X_160,X_159)) )],[refute_0_36,refute_0_8]) ).
cnf(refute_0_38,plain,
( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_37:[bind(L,$fot(orthogonal_through_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),A))),bind(X_159,$fot(skolemFOFtoCNF_A)),bind(X_160,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_39,plain,
convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),A),parallel_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_38,refute_0_6]) ).
cnf(refute_0_40,plain,
~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X_97,X_95),A),orthogonal_through_point(X_97,X_95)),
inference(subst,[],[refute_0_4:[bind(L,$fot(orthogonal_through_point(X_97,X_95)))]]) ).
cnf(refute_0_41,plain,
~ unorthogonal_lines(orthogonal_through_point(X_16,A),X_16),
inference(subst,[],[refute_0_4:[bind(L,$fot(X_16))]]) ).
cnf(refute_0_42,plain,
( convergent_lines(L,M)
| unorthogonal_lines(L,M) ),
inference(canonicalize,[],[normalize_0_27]) ).
cnf(refute_0_43,plain,
( convergent_lines(orthogonal_through_point(X_16,A),X_16)
| unorthogonal_lines(orthogonal_through_point(X_16,A),X_16) ),
inference(subst,[],[refute_0_42:[bind(L,$fot(orthogonal_through_point(X_16,A))),bind(M,$fot(X_16))]]) ).
cnf(refute_0_44,plain,
convergent_lines(orthogonal_through_point(X_16,A),X_16),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(X_16,A),X_16) )],[refute_0_43,refute_0_41]) ).
cnf(refute_0_45,plain,
convergent_lines(orthogonal_through_point(X_90,A),X_90),
inference(subst,[],[refute_0_44:[bind(X_16,$fot(X_90))]]) ).
cnf(refute_0_46,plain,
( ~ convergent_lines(orthogonal_through_point(X_90,A),X_90)
| unorthogonal_lines(X_88,X_90)
| unorthogonal_lines(X_88,orthogonal_through_point(X_90,A)) ),
inference(subst,[],[refute_0_7:[bind(L,$fot(X_88)),bind(M,$fot(orthogonal_through_point(X_90,A))),bind(N,$fot(X_90))]]) ).
cnf(refute_0_47,plain,
( unorthogonal_lines(X_88,X_90)
| unorthogonal_lines(X_88,orthogonal_through_point(X_90,A)) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_90,A),X_90) )],[refute_0_45,refute_0_46]) ).
cnf(refute_0_48,plain,
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X_97,X_95),A),X_97)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X_97,X_95),A),orthogonal_through_point(X_97,X_95)) ),
inference(subst,[],[refute_0_47:[bind(A,$fot(X_95)),bind(X_88,$fot(orthogonal_through_point(orthogonal_through_point(X_97,X_95),A))),bind(X_90,$fot(X_97))]]) ).
cnf(refute_0_49,plain,
unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X_97,X_95),A),X_97),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X_97,X_95),A),orthogonal_through_point(X_97,X_95)) )],[refute_0_48,refute_0_40]) ).
cnf(refute_0_50,plain,
unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X_208,X_95),A),X_208),
inference(subst,[],[refute_0_49:[bind(X_97,$fot(X_208))]]) ).
cnf(refute_0_51,plain,
( ~ convergent_lines(L,M)
| ~ unorthogonal_lines(L,M)
| unorthogonal_lines(L,N)
| unorthogonal_lines(M,N) ),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_52,plain,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(X_208,X_95),A),X_208)
| ~ unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X_208,X_95),A),X_208)
| unorthogonal_lines(X_208,X_209)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X_208,X_95),A),X_209) ),
inference(subst,[],[refute_0_51:[bind(L,$fot(orthogonal_through_point(orthogonal_through_point(X_208,X_95),A))),bind(M,$fot(X_208)),bind(N,$fot(X_209))]]) ).
cnf(refute_0_53,plain,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(X_208,X_95),A),X_208)
| unorthogonal_lines(X_208,X_209)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X_208,X_95),A),X_209) ),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(X_208,X_95),A),X_208) )],[refute_0_50,refute_0_52]) ).
cnf(refute_0_54,plain,
( ~ convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_233)
| unorthogonal_lines(skolemFOFtoCNF_L,X_233) ),
inference(subst,[],[refute_0_53:[bind(A,$fot(skolemFOFtoCNF_A)),bind(X_208,$fot(skolemFOFtoCNF_L)),bind(X_209,$fot(X_233)),bind(X_95,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_55,plain,
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),X_233)
| unorthogonal_lines(skolemFOFtoCNF_L,X_233) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_39,refute_0_54]) ).
cnf(refute_0_56,plain,
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_55:[bind(X_233,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_57,plain,
unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_56,refute_0_5]) ).
cnf(refute_0_58,plain,
( ~ convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| convergent_lines(L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(L,skolemFOFtoCNF_L) ),
inference(resolve,[$cnf( unorthogonal_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_57,refute_0_3]) ).
cnf(refute_0_59,plain,
~ convergent_lines(orthogonal_through_point(X_69,X_68),orthogonal_through_point(X_69,X_68)),
inference(subst,[],[refute_0_0:[bind(X,$fot(orthogonal_through_point(X_69,X_68)))]]) ).
cnf(refute_0_60,plain,
convergent_lines(orthogonal_through_point(X_65,A),X_65),
inference(subst,[],[refute_0_44:[bind(X_16,$fot(X_65))]]) ).
cnf(refute_0_61,plain,
( ~ convergent_lines(orthogonal_through_point(X_65,A),X_65)
| convergent_lines(X_65,X_66)
| convergent_lines(orthogonal_through_point(X_65,A),X_66) ),
inference(subst,[],[refute_0_11:[bind(X,$fot(orthogonal_through_point(X_65,A))),bind(Y,$fot(X_65)),bind(Z,$fot(X_66))]]) ).
cnf(refute_0_62,plain,
( convergent_lines(X_65,X_66)
| convergent_lines(orthogonal_through_point(X_65,A),X_66) ),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_65,A),X_65) )],[refute_0_60,refute_0_61]) ).
cnf(refute_0_63,plain,
( convergent_lines(X_69,orthogonal_through_point(X_69,X_68))
| convergent_lines(orthogonal_through_point(X_69,X_68),orthogonal_through_point(X_69,X_68)) ),
inference(subst,[],[refute_0_62:[bind(A,$fot(X_68)),bind(X_65,$fot(X_69)),bind(X_66,$fot(orthogonal_through_point(X_69,X_68)))]]) ).
cnf(refute_0_64,plain,
convergent_lines(X_69,orthogonal_through_point(X_69,X_68)),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(X_69,X_68),orthogonal_through_point(X_69,X_68)) )],[refute_0_63,refute_0_59]) ).
cnf(refute_0_65,plain,
convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)),
inference(subst,[],[refute_0_64:[bind(X_68,$fot(skolemFOFtoCNF_A)),bind(X_69,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_66,plain,
( convergent_lines(L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(L,skolemFOFtoCNF_L) ),
inference(resolve,[$cnf( convergent_lines(skolemFOFtoCNF_L,orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_65,refute_0_58]) ).
cnf(refute_0_67,plain,
( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A))
| unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_66:[bind(L,$fot(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_68,plain,
unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(resolve,[$cnf( convergent_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A)) )],[refute_0_67,refute_0_1]) ).
cnf(refute_0_69,plain,
~ unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(subst,[],[refute_0_4:[bind(A,$fot(skolemFOFtoCNF_A)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_70,plain,
$false,
inference(resolve,[$cnf( unorthogonal_lines(orthogonal_through_point(skolemFOFtoCNF_L,skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_68,refute_0_69]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.11 % Problem : GEO223+3 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.11 % Command : metis --show proof --show saturation %s
% 0.11/0.32 % Computer : n021.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 600
% 0.11/0.32 % DateTime : Sat Jun 18 18:28:32 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 0.17/0.40 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.40
% 0.17/0.40 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 0.17/0.40
%------------------------------------------------------------------------------