%------------------------------------------------------------------------------
% File : Metis---2.4
% Problem : GEO258+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : metis --show proof --show saturation %s
% Computer : n032.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 05:25:58 EDT 2022
% Result : Theorem 21.73s 21.97s
% Output : CNFRefutation 21.80s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 14
% Syntax : Number of formulae : 179 ( 39 unt; 0 def)
% Number of atoms : 413 ( 0 equ)
% Maximal formula atoms : 18 ( 2 avg)
% Number of connectives : 406 ( 172 ~; 189 |; 23 &)
% ( 15 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-4 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 299 ( 6 sgn 154 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a1_defns,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ) ).
fof(a4_defns,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ) ).
fof(a5_defns,axiom,
! [X,Y] :
( equally_directed_opposite_lines(X,Y)
<=> ~ unequally_directed_opposite_lines(X,Y) ) ).
fof(ax4_defns,axiom,
! [L,A,B] :
( before_on_line(L,A,B)
<=> ( distinct_points(A,B)
& incident_point_and_line(A,L)
& incident_point_and_line(B,L)
& equally_directed_lines(L,line_connecting(A,B)) ) ) ).
fof(a9_defns,axiom,
! [L,A,B,C] :
( between_on_line(L,A,B,C)
<=> ( ( before_on_line(L,A,B)
& before_on_line(L,B,C) )
| ( before_on_line(L,C,B)
& before_on_line(L,B,A) ) ) ) ).
fof(ax1_basics,axiom,
! [A] : ~ distinct_points(A,A) ).
fof(ax2_basics,axiom,
! [A,B,C] :
( distinct_points(A,B)
=> ( distinct_points(A,C)
| distinct_points(B,C) ) ) ).
fof(ax5_basics,axiom,
! [L] : equally_directed_lines(L,L) ).
fof(ax6_basics,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ) ) ).
fof(ax8_basics,axiom,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ) ).
fof(ax9_basics,axiom,
! [L,M] :
( ( unequally_directed_lines(L,M)
& unequally_directed_lines(L,reverse_line(M)) )
=> ( left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ) ) ).
fof(ax11_basics,axiom,
! [L,M] :
~ ( left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ) ).
fof(ax9_cons_objs,axiom,
! [A,B] :
( distinct_points(A,B)
=> equally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))) ) ).
fof(con,conjecture,
! [L,A,B,C] :
( between_on_line(L,A,B,C)
=> between_on_line(L,C,B,A) ) ).
fof(subgoal_0,plain,
! [L,A,B,C] :
( between_on_line(L,A,B,C)
=> between_on_line(L,C,B,A) ),
inference(strip,[],[con]) ).
fof(negate_0_0,plain,
~ ! [L,A,B,C] :
( between_on_line(L,A,B,C)
=> between_on_line(L,C,B,A) ),
inference(negate,[],[subgoal_0]) ).
fof(normalize_0_0,plain,
! [X,Y] :
( ~ equally_directed_lines(X,Y)
<=> unequally_directed_lines(X,Y) ),
inference(canonicalize,[],[a4_defns]) ).
fof(normalize_0_1,plain,
! [X,Y] :
( ~ equally_directed_lines(X,Y)
<=> unequally_directed_lines(X,Y) ),
inference(specialize,[],[normalize_0_0]) ).
fof(normalize_0_2,plain,
! [X,Y] :
( ( ~ equally_directed_lines(X,Y)
| ~ unequally_directed_lines(X,Y) )
& ( equally_directed_lines(X,Y)
| unequally_directed_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_1]) ).
fof(normalize_0_3,plain,
! [X,Y] :
( ~ equally_directed_lines(X,Y)
| ~ unequally_directed_lines(X,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_4,plain,
! [L,M,N] :
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(canonicalize,[],[ax6_basics]) ).
fof(normalize_0_5,plain,
! [L,M,N] :
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(specialize,[],[normalize_0_4]) ).
fof(normalize_0_6,plain,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax8_basics]) ).
fof(normalize_0_7,plain,
! [L,M] :
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(specialize,[],[normalize_0_6]) ).
fof(normalize_0_8,plain,
! [A,B] :
( ~ distinct_points(A,B)
| equally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))) ),
inference(canonicalize,[],[ax9_cons_objs]) ).
fof(normalize_0_9,plain,
! [A,B] :
( ~ distinct_points(A,B)
| equally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))) ),
inference(specialize,[],[normalize_0_8]) ).
fof(normalize_0_10,plain,
! [A] : ~ distinct_points(A,A),
inference(canonicalize,[],[ax1_basics]) ).
fof(normalize_0_11,plain,
! [A] : ~ distinct_points(A,A),
inference(specialize,[],[normalize_0_10]) ).
fof(normalize_0_12,plain,
! [A,B,C] :
( ~ distinct_points(A,B)
| distinct_points(A,C)
| distinct_points(B,C) ),
inference(canonicalize,[],[ax2_basics]) ).
fof(normalize_0_13,plain,
! [A,B,C] :
( ~ distinct_points(A,B)
| distinct_points(A,C)
| distinct_points(B,C) ),
inference(specialize,[],[normalize_0_12]) ).
fof(normalize_0_14,plain,
! [A,B,L] :
( ~ before_on_line(L,A,B)
<=> ( ~ distinct_points(A,B)
| ~ equally_directed_lines(L,line_connecting(A,B))
| ~ incident_point_and_line(A,L)
| ~ incident_point_and_line(B,L) ) ),
inference(canonicalize,[],[ax4_defns]) ).
fof(normalize_0_15,plain,
! [A,B,L] :
( ~ before_on_line(L,A,B)
<=> ( ~ distinct_points(A,B)
| ~ equally_directed_lines(L,line_connecting(A,B))
| ~ incident_point_and_line(A,L)
| ~ incident_point_and_line(B,L) ) ),
inference(specialize,[],[normalize_0_14]) ).
fof(normalize_0_16,plain,
! [A,B,L] :
( ( ~ before_on_line(L,A,B)
| distinct_points(A,B) )
& ( ~ before_on_line(L,A,B)
| equally_directed_lines(L,line_connecting(A,B)) )
& ( ~ before_on_line(L,A,B)
| incident_point_and_line(A,L) )
& ( ~ before_on_line(L,A,B)
| incident_point_and_line(B,L) )
& ( ~ distinct_points(A,B)
| ~ equally_directed_lines(L,line_connecting(A,B))
| ~ incident_point_and_line(A,L)
| ~ incident_point_and_line(B,L)
| before_on_line(L,A,B) ) ),
inference(clausify,[],[normalize_0_15]) ).
fof(normalize_0_17,plain,
! [A,B,L] :
( ~ before_on_line(L,A,B)
| distinct_points(A,B) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_18,plain,
? [A,B,C,L] :
( ~ between_on_line(L,C,B,A)
& between_on_line(L,A,B,C) ),
inference(canonicalize,[],[negate_0_0]) ).
fof(normalize_0_19,plain,
( ~ between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A)
& between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(skolemize,[],[normalize_0_18]) ).
fof(normalize_0_20,plain,
between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_21,plain,
! [A,B,C,L] :
( ~ between_on_line(L,A,B,C)
<=> ( ( ~ before_on_line(L,A,B)
| ~ before_on_line(L,B,C) )
& ( ~ before_on_line(L,B,A)
| ~ before_on_line(L,C,B) ) ) ),
inference(canonicalize,[],[a9_defns]) ).
fof(normalize_0_22,plain,
! [A,B,C,L] :
( ~ between_on_line(L,A,B,C)
<=> ( ( ~ before_on_line(L,A,B)
| ~ before_on_line(L,B,C) )
& ( ~ before_on_line(L,B,A)
| ~ before_on_line(L,C,B) ) ) ),
inference(specialize,[],[normalize_0_21]) ).
fof(normalize_0_23,plain,
! [A,B,C,L] :
( ( ~ before_on_line(L,A,B)
| ~ before_on_line(L,B,C)
| between_on_line(L,A,B,C) )
& ( ~ before_on_line(L,B,A)
| ~ before_on_line(L,C,B)
| between_on_line(L,A,B,C) )
& ( ~ between_on_line(L,A,B,C)
| before_on_line(L,A,B)
| before_on_line(L,B,A) )
& ( ~ between_on_line(L,A,B,C)
| before_on_line(L,A,B)
| before_on_line(L,C,B) )
& ( ~ between_on_line(L,A,B,C)
| before_on_line(L,B,A)
| before_on_line(L,B,C) )
& ( ~ between_on_line(L,A,B,C)
| before_on_line(L,B,C)
| before_on_line(L,C,B) ) ),
inference(clausify,[],[normalize_0_22]) ).
fof(normalize_0_24,plain,
! [A,B,C,L] :
( ~ between_on_line(L,A,B,C)
| before_on_line(L,A,B)
| before_on_line(L,B,A) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_25,plain,
! [L,M] :
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax9_basics]) ).
fof(normalize_0_26,plain,
! [L,M] :
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(specialize,[],[normalize_0_25]) ).
fof(normalize_0_27,plain,
( ! [L,M] : ~ left_convergent_lines(L,M)
& ! [L,M] : ~ left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[ax11_basics]) ).
fof(normalize_0_28,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(conjunct,[],[normalize_0_27]) ).
fof(normalize_0_29,plain,
! [L,M] : ~ left_convergent_lines(L,M),
inference(specialize,[],[normalize_0_28]) ).
fof(normalize_0_30,plain,
! [L] : equally_directed_lines(L,L),
inference(canonicalize,[],[ax5_basics]) ).
fof(normalize_0_31,plain,
! [L] : equally_directed_lines(L,L),
inference(specialize,[],[normalize_0_30]) ).
fof(normalize_0_32,plain,
! [X,Y] :
( ~ equally_directed_opposite_lines(X,Y)
<=> unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[a5_defns]) ).
fof(normalize_0_33,plain,
! [X,Y] :
( ~ equally_directed_opposite_lines(X,Y)
<=> unequally_directed_opposite_lines(X,Y) ),
inference(specialize,[],[normalize_0_32]) ).
fof(normalize_0_34,plain,
! [X,Y] :
( ( ~ equally_directed_opposite_lines(X,Y)
| ~ unequally_directed_opposite_lines(X,Y) )
& ( equally_directed_opposite_lines(X,Y)
| unequally_directed_opposite_lines(X,Y) ) ),
inference(clausify,[],[normalize_0_33]) ).
fof(normalize_0_35,plain,
! [X,Y] :
( equally_directed_opposite_lines(X,Y)
| unequally_directed_opposite_lines(X,Y) ),
inference(conjunct,[],[normalize_0_34]) ).
fof(normalize_0_36,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
<=> ~ unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[a1_defns]) ).
fof(normalize_0_37,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
<=> ~ unequally_directed_opposite_lines(X,Y) ),
inference(specialize,[],[normalize_0_36]) ).
fof(normalize_0_38,plain,
! [X,Y] :
( ( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) )
& ( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ) ),
inference(clausify,[],[normalize_0_37]) ).
fof(normalize_0_39,plain,
! [X,Y] :
( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_40,plain,
! [X,Y] :
( ~ equally_directed_opposite_lines(X,Y)
| ~ unequally_directed_opposite_lines(X,Y) ),
inference(conjunct,[],[normalize_0_34]) ).
fof(normalize_0_41,plain,
! [X,Y] :
( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) ),
inference(conjunct,[],[normalize_0_38]) ).
fof(normalize_0_42,plain,
! [X,Y] :
( equally_directed_lines(X,Y)
| unequally_directed_lines(X,Y) ),
inference(conjunct,[],[normalize_0_2]) ).
fof(normalize_0_43,plain,
! [A,B,L] :
( ~ before_on_line(L,A,B)
| equally_directed_lines(L,line_connecting(A,B)) ),
inference(conjunct,[],[normalize_0_16]) ).
fof(normalize_0_44,plain,
! [A,B,C,L] :
( ~ before_on_line(L,A,B)
| ~ before_on_line(L,B,C)
| between_on_line(L,A,B,C) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_45,plain,
! [A,B,C,L] :
( ~ between_on_line(L,A,B,C)
| before_on_line(L,A,B)
| before_on_line(L,C,B) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_46,plain,
~ between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A),
inference(conjunct,[],[normalize_0_19]) ).
fof(normalize_0_47,plain,
! [A,B,C,L] :
( ~ before_on_line(L,B,A)
| ~ before_on_line(L,C,B)
| between_on_line(L,A,B,C) ),
inference(conjunct,[],[normalize_0_23]) ).
fof(normalize_0_48,plain,
! [A,B,C,L] :
( ~ between_on_line(L,A,B,C)
| before_on_line(L,B,A)
| before_on_line(L,B,C) ),
inference(conjunct,[],[normalize_0_23]) ).
cnf(refute_0_0,plain,
( ~ equally_directed_lines(X,Y)
| ~ unequally_directed_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_3]) ).
cnf(refute_0_1,plain,
( ~ equally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_L)
| ~ unequally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B))),bind(Y,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_2,plain,
( ~ equally_directed_lines(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A),X_10651)
| ~ unequally_directed_lines(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A),X_10651) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A))),bind(Y,$fot(X_10651))]]) ).
cnf(refute_0_3,plain,
( ~ unequally_directed_lines(L,M)
| unequally_directed_lines(L,N)
| unequally_directed_lines(M,N) ),
inference(canonicalize,[],[normalize_0_5]) ).
cnf(refute_0_4,plain,
( ~ unequally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A))
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),N)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A),N) ),
inference(subst,[],[refute_0_3:[bind(L,$fot(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B))),bind(M,$fot(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_5,plain,
( ~ equally_directed_lines(X_47,reverse_line(X_48))
| ~ unequally_directed_lines(X_47,reverse_line(X_48)) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(X_47)),bind(Y,$fot(reverse_line(X_48)))]]) ).
cnf(refute_0_6,plain,
( unequally_directed_lines(L,M)
| unequally_directed_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_0_7]) ).
cnf(refute_0_7,plain,
( unequally_directed_lines(X_47,X_48)
| unequally_directed_lines(X_47,reverse_line(X_48)) ),
inference(subst,[],[refute_0_6:[bind(L,$fot(X_47)),bind(M,$fot(X_48))]]) ).
cnf(refute_0_8,plain,
( ~ equally_directed_lines(X_47,reverse_line(X_48))
| unequally_directed_lines(X_47,X_48) ),
inference(resolve,[$cnf( unequally_directed_lines(X_47,reverse_line(X_48)) )],[refute_0_7,refute_0_5]) ).
cnf(refute_0_9,plain,
( ~ equally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),reverse_line(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A)))
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_8:[bind(X_47,$fot(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B))),bind(X_48,$fot(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_10,plain,
( ~ distinct_points(A,B)
| equally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))) ),
inference(canonicalize,[],[normalize_0_9]) ).
cnf(refute_0_11,plain,
( ~ distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| equally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),reverse_line(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A))) ),
inference(subst,[],[refute_0_10:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_12,plain,
~ distinct_points(A,A),
inference(canonicalize,[],[normalize_0_11]) ).
cnf(refute_0_13,plain,
~ distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_B),
inference(subst,[],[refute_0_12:[bind(A,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_14,plain,
( ~ distinct_points(A,B)
| distinct_points(A,C)
| distinct_points(B,C) ),
inference(canonicalize,[],[normalize_0_13]) ).
cnf(refute_0_15,plain,
( ~ distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| distinct_points(skolemFOFtoCNF_A,C)
| distinct_points(skolemFOFtoCNF_B,C) ),
inference(subst,[],[refute_0_14:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_16,plain,
( ~ before_on_line(L,A,B)
| distinct_points(A,B) ),
inference(canonicalize,[],[normalize_0_17]) ).
cnf(refute_0_17,plain,
( ~ before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_18,plain,
( ~ before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_16:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_A)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_19,plain,
between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C),
inference(canonicalize,[],[normalize_0_20]) ).
cnf(refute_0_20,plain,
( ~ between_on_line(L,A,B,C)
| before_on_line(L,A,B)
| before_on_line(L,B,A) ),
inference(canonicalize,[],[normalize_0_24]) ).
cnf(refute_0_21,plain,
( ~ between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_20:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_22,plain,
( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_19,refute_0_21]) ).
cnf(refute_0_23,plain,
( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_22,refute_0_18]) ).
cnf(refute_0_24,plain,
( distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_23,refute_0_17]) ).
cnf(refute_0_25,plain,
( distinct_points(skolemFOFtoCNF_A,C)
| distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| distinct_points(skolemFOFtoCNF_B,C) ),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_24,refute_0_15]) ).
cnf(refute_0_26,plain,
( distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_25:[bind(C,$fot(skolemFOFtoCNF_B))]]) ).
cnf(refute_0_27,plain,
distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_B,skolemFOFtoCNF_B) )],[refute_0_26,refute_0_13]) ).
cnf(refute_0_28,plain,
equally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),reverse_line(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A))),
inference(resolve,[$cnf( distinct_points(skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_27,refute_0_11]) ).
cnf(refute_0_29,plain,
unequally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A)),
inference(resolve,[$cnf( equally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),reverse_line(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A))) )],[refute_0_28,refute_0_9]) ).
cnf(refute_0_30,plain,
( unequally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),N)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A),N) ),
inference(resolve,[$cnf( unequally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) )],[refute_0_29,refute_0_4]) ).
cnf(refute_0_31,plain,
( unequally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),X_10651)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A),X_10651) ),
inference(subst,[],[refute_0_30:[bind(N,$fot(X_10651))]]) ).
cnf(refute_0_32,plain,
( ~ equally_directed_lines(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A),X_10651)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),X_10651) ),
inference(resolve,[$cnf( unequally_directed_lines(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A),X_10651) )],[refute_0_31,refute_0_2]) ).
cnf(refute_0_33,plain,
( ~ equally_directed_lines(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A),skolemFOFtoCNF_L)
| unequally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_32:[bind(X_10651,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_34,plain,
( ~ equally_directed_lines(X_7907,X_7908)
| ~ unequally_directed_lines(X_7907,X_7908) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(X_7907)),bind(Y,$fot(X_7908))]]) ).
cnf(refute_0_35,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| left_convergent_lines(L,reverse_line(M)) ),
inference(canonicalize,[],[normalize_0_26]) ).
cnf(refute_0_36,plain,
~ left_convergent_lines(L,M),
inference(canonicalize,[],[normalize_0_29]) ).
cnf(refute_0_37,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| left_convergent_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,M) )],[refute_0_35,refute_0_36]) ).
cnf(refute_0_38,plain,
~ left_convergent_lines(L,reverse_line(M)),
inference(subst,[],[refute_0_36:[bind(M,$fot(reverse_line(M)))]]) ).
cnf(refute_0_39,plain,
( ~ unequally_directed_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M)) ),
inference(resolve,[$cnf( left_convergent_lines(L,reverse_line(M)) )],[refute_0_37,refute_0_38]) ).
cnf(refute_0_40,plain,
( ~ unequally_directed_lines(X_247,X_247)
| ~ unequally_directed_lines(X_247,reverse_line(X_247)) ),
inference(subst,[],[refute_0_39:[bind(L,$fot(X_247)),bind(M,$fot(X_247))]]) ).
cnf(refute_0_41,plain,
equally_directed_lines(L,L),
inference(canonicalize,[],[normalize_0_31]) ).
cnf(refute_0_42,plain,
equally_directed_lines(reverse_line(X_245),reverse_line(X_245)),
inference(subst,[],[refute_0_41:[bind(L,$fot(reverse_line(X_245)))]]) ).
cnf(refute_0_43,plain,
( ~ equally_directed_lines(reverse_line(X_243),X_244)
| ~ unequally_directed_lines(reverse_line(X_243),X_244) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(reverse_line(X_243))),bind(Y,$fot(X_244))]]) ).
cnf(refute_0_44,plain,
equally_directed_lines(reverse_line(X_43),reverse_line(X_43)),
inference(subst,[],[refute_0_41:[bind(L,$fot(reverse_line(X_43)))]]) ).
cnf(refute_0_45,plain,
( ~ equally_directed_lines(X_40,reverse_line(X_41))
| ~ unequally_directed_lines(X_40,reverse_line(X_41)) ),
inference(subst,[],[refute_0_0:[bind(X,$fot(X_40)),bind(Y,$fot(reverse_line(X_41)))]]) ).
cnf(refute_0_46,plain,
( equally_directed_opposite_lines(X,Y)
| unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_35]) ).
cnf(refute_0_47,plain,
( equally_directed_opposite_lines(X_38,X_39)
| unequally_directed_opposite_lines(X_38,X_39) ),
inference(subst,[],[refute_0_46:[bind(X,$fot(X_38)),bind(Y,$fot(X_39))]]) ).
cnf(refute_0_48,plain,
( ~ unequally_directed_opposite_lines(X,Y)
| unequally_directed_lines(X,reverse_line(Y)) ),
inference(canonicalize,[],[normalize_0_39]) ).
cnf(refute_0_49,plain,
( ~ unequally_directed_opposite_lines(X_38,X_39)
| unequally_directed_lines(X_38,reverse_line(X_39)) ),
inference(subst,[],[refute_0_48:[bind(X,$fot(X_38)),bind(Y,$fot(X_39))]]) ).
cnf(refute_0_50,plain,
( equally_directed_opposite_lines(X_38,X_39)
| unequally_directed_lines(X_38,reverse_line(X_39)) ),
inference(resolve,[$cnf( unequally_directed_opposite_lines(X_38,X_39) )],[refute_0_47,refute_0_49]) ).
cnf(refute_0_51,plain,
( equally_directed_opposite_lines(X_40,X_41)
| unequally_directed_lines(X_40,reverse_line(X_41)) ),
inference(subst,[],[refute_0_50:[bind(X_38,$fot(X_40)),bind(X_39,$fot(X_41))]]) ).
cnf(refute_0_52,plain,
( ~ equally_directed_lines(X_40,reverse_line(X_41))
| equally_directed_opposite_lines(X_40,X_41) ),
inference(resolve,[$cnf( unequally_directed_lines(X_40,reverse_line(X_41)) )],[refute_0_51,refute_0_45]) ).
cnf(refute_0_53,plain,
( ~ equally_directed_lines(reverse_line(X_43),reverse_line(X_43))
| equally_directed_opposite_lines(reverse_line(X_43),X_43) ),
inference(subst,[],[refute_0_52:[bind(X_40,$fot(reverse_line(X_43))),bind(X_41,$fot(X_43))]]) ).
cnf(refute_0_54,plain,
equally_directed_opposite_lines(reverse_line(X_43),X_43),
inference(resolve,[$cnf( equally_directed_lines(reverse_line(X_43),reverse_line(X_43)) )],[refute_0_44,refute_0_53]) ).
cnf(refute_0_55,plain,
equally_directed_opposite_lines(reverse_line(X_56),X_56),
inference(subst,[],[refute_0_54:[bind(X_43,$fot(X_56))]]) ).
cnf(refute_0_56,plain,
( ~ equally_directed_opposite_lines(X,Y)
| ~ unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_40]) ).
cnf(refute_0_57,plain,
( ~ equally_directed_opposite_lines(X_53,X_54)
| ~ unequally_directed_opposite_lines(X_53,X_54) ),
inference(subst,[],[refute_0_56:[bind(X,$fot(X_53)),bind(Y,$fot(X_54))]]) ).
cnf(refute_0_58,plain,
( ~ unequally_directed_lines(X,reverse_line(Y))
| unequally_directed_opposite_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_41]) ).
cnf(refute_0_59,plain,
( ~ unequally_directed_lines(X_47,reverse_line(X_48))
| unequally_directed_opposite_lines(X_47,X_48) ),
inference(subst,[],[refute_0_58:[bind(X,$fot(X_47)),bind(Y,$fot(X_48))]]) ).
cnf(refute_0_60,plain,
( unequally_directed_lines(X_47,X_48)
| unequally_directed_opposite_lines(X_47,X_48) ),
inference(resolve,[$cnf( unequally_directed_lines(X_47,reverse_line(X_48)) )],[refute_0_7,refute_0_59]) ).
cnf(refute_0_61,plain,
( unequally_directed_lines(X_53,X_54)
| unequally_directed_opposite_lines(X_53,X_54) ),
inference(subst,[],[refute_0_60:[bind(X_47,$fot(X_53)),bind(X_48,$fot(X_54))]]) ).
cnf(refute_0_62,plain,
( ~ equally_directed_opposite_lines(X_53,X_54)
| unequally_directed_lines(X_53,X_54) ),
inference(resolve,[$cnf( unequally_directed_opposite_lines(X_53,X_54) )],[refute_0_61,refute_0_57]) ).
cnf(refute_0_63,plain,
( ~ equally_directed_opposite_lines(reverse_line(X_56),X_56)
| unequally_directed_lines(reverse_line(X_56),X_56) ),
inference(subst,[],[refute_0_62:[bind(X_53,$fot(reverse_line(X_56))),bind(X_54,$fot(X_56))]]) ).
cnf(refute_0_64,plain,
unequally_directed_lines(reverse_line(X_56),X_56),
inference(resolve,[$cnf( equally_directed_opposite_lines(reverse_line(X_56),X_56) )],[refute_0_55,refute_0_63]) ).
cnf(refute_0_65,plain,
unequally_directed_lines(reverse_line(X_241),X_241),
inference(subst,[],[refute_0_64:[bind(X_56,$fot(X_241))]]) ).
cnf(refute_0_66,plain,
( ~ unequally_directed_lines(reverse_line(X_241),X_241)
| unequally_directed_lines(X_241,X_242)
| unequally_directed_lines(reverse_line(X_241),X_242) ),
inference(subst,[],[refute_0_3:[bind(L,$fot(reverse_line(X_241))),bind(M,$fot(X_241)),bind(N,$fot(X_242))]]) ).
cnf(refute_0_67,plain,
( unequally_directed_lines(X_241,X_242)
| unequally_directed_lines(reverse_line(X_241),X_242) ),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(X_241),X_241) )],[refute_0_65,refute_0_66]) ).
cnf(refute_0_68,plain,
( unequally_directed_lines(X_243,X_244)
| unequally_directed_lines(reverse_line(X_243),X_244) ),
inference(subst,[],[refute_0_67:[bind(X_241,$fot(X_243)),bind(X_242,$fot(X_244))]]) ).
cnf(refute_0_69,plain,
( ~ equally_directed_lines(reverse_line(X_243),X_244)
| unequally_directed_lines(X_243,X_244) ),
inference(resolve,[$cnf( unequally_directed_lines(reverse_line(X_243),X_244) )],[refute_0_68,refute_0_43]) ).
cnf(refute_0_70,plain,
( ~ equally_directed_lines(reverse_line(X_245),reverse_line(X_245))
| unequally_directed_lines(X_245,reverse_line(X_245)) ),
inference(subst,[],[refute_0_69:[bind(X_243,$fot(X_245)),bind(X_244,$fot(reverse_line(X_245)))]]) ).
cnf(refute_0_71,plain,
unequally_directed_lines(X_245,reverse_line(X_245)),
inference(resolve,[$cnf( equally_directed_lines(reverse_line(X_245),reverse_line(X_245)) )],[refute_0_42,refute_0_70]) ).
cnf(refute_0_72,plain,
unequally_directed_lines(X_247,reverse_line(X_247)),
inference(subst,[],[refute_0_71:[bind(X_245,$fot(X_247))]]) ).
cnf(refute_0_73,plain,
~ unequally_directed_lines(X_247,X_247),
inference(resolve,[$cnf( unequally_directed_lines(X_247,reverse_line(X_247)) )],[refute_0_72,refute_0_40]) ).
cnf(refute_0_74,plain,
~ unequally_directed_lines(X_7906,X_7906),
inference(subst,[],[refute_0_73:[bind(X_247,$fot(X_7906))]]) ).
cnf(refute_0_75,plain,
( equally_directed_lines(X,Y)
| unequally_directed_lines(X,Y) ),
inference(canonicalize,[],[normalize_0_42]) ).
cnf(refute_0_76,plain,
( equally_directed_lines(X_240,X_241)
| unequally_directed_lines(X_240,X_241) ),
inference(subst,[],[refute_0_75:[bind(X,$fot(X_240)),bind(Y,$fot(X_241))]]) ).
cnf(refute_0_77,plain,
( ~ unequally_directed_lines(X_240,X_241)
| unequally_directed_lines(X_240,X_242)
| unequally_directed_lines(X_241,X_242) ),
inference(subst,[],[refute_0_3:[bind(L,$fot(X_240)),bind(M,$fot(X_241)),bind(N,$fot(X_242))]]) ).
cnf(refute_0_78,plain,
( equally_directed_lines(X_240,X_241)
| unequally_directed_lines(X_240,X_242)
| unequally_directed_lines(X_241,X_242) ),
inference(resolve,[$cnf( unequally_directed_lines(X_240,X_241) )],[refute_0_76,refute_0_77]) ).
cnf(refute_0_79,plain,
( equally_directed_lines(X_7906,X_7905)
| unequally_directed_lines(X_7905,X_7906)
| unequally_directed_lines(X_7906,X_7906) ),
inference(subst,[],[refute_0_78:[bind(X_240,$fot(X_7906)),bind(X_241,$fot(X_7905)),bind(X_242,$fot(X_7906))]]) ).
cnf(refute_0_80,plain,
( equally_directed_lines(X_7906,X_7905)
| unequally_directed_lines(X_7905,X_7906) ),
inference(resolve,[$cnf( unequally_directed_lines(X_7906,X_7906) )],[refute_0_79,refute_0_74]) ).
cnf(refute_0_81,plain,
( equally_directed_lines(X_7908,X_7907)
| unequally_directed_lines(X_7907,X_7908) ),
inference(subst,[],[refute_0_80:[bind(X_7905,$fot(X_7907)),bind(X_7906,$fot(X_7908))]]) ).
cnf(refute_0_82,plain,
( ~ equally_directed_lines(X_7907,X_7908)
| equally_directed_lines(X_7908,X_7907) ),
inference(resolve,[$cnf( unequally_directed_lines(X_7907,X_7908) )],[refute_0_81,refute_0_34]) ).
cnf(refute_0_83,plain,
( ~ equally_directed_lines(skolemFOFtoCNF_L,line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A))
| equally_directed_lines(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A),skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_82:[bind(X_7907,$fot(skolemFOFtoCNF_L)),bind(X_7908,$fot(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A)))]]) ).
cnf(refute_0_84,plain,
( ~ before_on_line(L,A,B)
| equally_directed_lines(L,line_connecting(A,B)) ),
inference(canonicalize,[],[normalize_0_43]) ).
cnf(refute_0_85,plain,
( ~ before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| equally_directed_lines(skolemFOFtoCNF_L,line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) ),
inference(subst,[],[refute_0_84:[bind(A,$fot(skolemFOFtoCNF_B)),bind(B,$fot(skolemFOFtoCNF_A)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_86,plain,
( ~ before_on_line(L,A,B)
| ~ before_on_line(L,B,C)
| between_on_line(L,A,B,C) ),
inference(canonicalize,[],[normalize_0_44]) ).
cnf(refute_0_87,plain,
( ~ before_on_line(skolemFOFtoCNF_L,A,skolemFOFtoCNF_B)
| ~ before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| between_on_line(skolemFOFtoCNF_L,A,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_86:[bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_A)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_88,plain,
( ~ before_on_line(skolemFOFtoCNF_L,A,skolemFOFtoCNF_B)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| between_on_line(skolemFOFtoCNF_L,A,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_22,refute_0_87]) ).
cnf(refute_0_89,plain,
( ~ before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_88:[bind(A,$fot(skolemFOFtoCNF_C))]]) ).
cnf(refute_0_90,plain,
( ~ between_on_line(L,A,B,C)
| before_on_line(L,A,B)
| before_on_line(L,C,B) ),
inference(canonicalize,[],[normalize_0_45]) ).
cnf(refute_0_91,plain,
( ~ between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B) ),
inference(subst,[],[refute_0_90:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_92,plain,
( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B) ),
inference(resolve,[$cnf( between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_19,refute_0_91]) ).
cnf(refute_0_93,plain,
( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B) )],[refute_0_92,refute_0_89]) ).
cnf(refute_0_94,plain,
~ between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A),
inference(canonicalize,[],[normalize_0_46]) ).
cnf(refute_0_95,plain,
before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B),
inference(resolve,[$cnf( between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_93,refute_0_94]) ).
cnf(refute_0_96,plain,
( ~ before_on_line(L,B,A)
| ~ before_on_line(L,C,B)
| between_on_line(L,A,B,C) ),
inference(canonicalize,[],[normalize_0_47]) ).
cnf(refute_0_97,plain,
( ~ before_on_line(skolemFOFtoCNF_L,C,skolemFOFtoCNF_B)
| ~ before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,C) ),
inference(subst,[],[refute_0_96:[bind(A,$fot(skolemFOFtoCNF_C)),bind(B,$fot(skolemFOFtoCNF_B)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_98,plain,
( ~ between_on_line(L,A,B,C)
| before_on_line(L,B,A)
| before_on_line(L,B,C) ),
inference(canonicalize,[],[normalize_0_48]) ).
cnf(refute_0_99,plain,
( ~ between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(subst,[],[refute_0_98:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B)),bind(C,$fot(skolemFOFtoCNF_C)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_100,plain,
( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_C) ),
inference(resolve,[$cnf( between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_19,refute_0_99]) ).
cnf(refute_0_101,plain,
( ~ before_on_line(skolemFOFtoCNF_L,C,skolemFOFtoCNF_B)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,C) ),
inference(resolve,[$cnf( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_C) )],[refute_0_100,refute_0_97]) ).
cnf(refute_0_102,plain,
( ~ before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(subst,[],[refute_0_101:[bind(C,$fot(skolemFOFtoCNF_A))]]) ).
cnf(refute_0_103,plain,
( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A)
| between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) ),
inference(resolve,[$cnf( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_95,refute_0_102]) ).
cnf(refute_0_104,plain,
before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A),
inference(resolve,[$cnf( between_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_C,skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_103,refute_0_94]) ).
cnf(refute_0_105,plain,
equally_directed_lines(skolemFOFtoCNF_L,line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A)),
inference(resolve,[$cnf( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_B,skolemFOFtoCNF_A) )],[refute_0_104,refute_0_85]) ).
cnf(refute_0_106,plain,
equally_directed_lines(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A),skolemFOFtoCNF_L),
inference(resolve,[$cnf( equally_directed_lines(skolemFOFtoCNF_L,line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A)) )],[refute_0_105,refute_0_83]) ).
cnf(refute_0_107,plain,
unequally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_L),
inference(resolve,[$cnf( equally_directed_lines(line_connecting(skolemFOFtoCNF_B,skolemFOFtoCNF_A),skolemFOFtoCNF_L) )],[refute_0_106,refute_0_33]) ).
cnf(refute_0_108,plain,
~ equally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_L),
inference(resolve,[$cnf( unequally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_L) )],[refute_0_107,refute_0_1]) ).
cnf(refute_0_109,plain,
( ~ equally_directed_lines(skolemFOFtoCNF_L,line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B))
| equally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_L) ),
inference(subst,[],[refute_0_82:[bind(X_7907,$fot(skolemFOFtoCNF_L)),bind(X_7908,$fot(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B)))]]) ).
cnf(refute_0_110,plain,
( ~ before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B)
| equally_directed_lines(skolemFOFtoCNF_L,line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B)) ),
inference(subst,[],[refute_0_84:[bind(A,$fot(skolemFOFtoCNF_A)),bind(B,$fot(skolemFOFtoCNF_B)),bind(L,$fot(skolemFOFtoCNF_L))]]) ).
cnf(refute_0_111,plain,
equally_directed_lines(skolemFOFtoCNF_L,line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B)),
inference(resolve,[$cnf( before_on_line(skolemFOFtoCNF_L,skolemFOFtoCNF_A,skolemFOFtoCNF_B) )],[refute_0_95,refute_0_110]) ).
cnf(refute_0_112,plain,
equally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_L),
inference(resolve,[$cnf( equally_directed_lines(skolemFOFtoCNF_L,line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B)) )],[refute_0_111,refute_0_109]) ).
cnf(refute_0_113,plain,
$false,
inference(resolve,[$cnf( equally_directed_lines(line_connecting(skolemFOFtoCNF_A,skolemFOFtoCNF_B),skolemFOFtoCNF_L) )],[refute_0_112,refute_0_108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : GEO258+3 : TPTP v8.1.0. Released v4.0.0.
% 0.00/0.10 % Command : metis --show proof --show saturation %s
% 0.08/0.28 % Computer : n032.cluster.edu
% 0.08/0.28 % Model : x86_64 x86_64
% 0.08/0.28 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.28 % Memory : 8042.1875MB
% 0.08/0.28 % OS : Linux 3.10.0-693.el7.x86_64
% 0.08/0.28 % CPULimit : 300
% 0.08/0.28 % WCLimit : 600
% 0.08/0.28 % DateTime : Sat Jun 18 13:17:47 EDT 2022
% 0.08/0.29 % CPUTime :
% 0.08/0.29 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
% 21.73/21.97 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p
% 21.73/21.97
% 21.73/21.97 % SZS output start CNFRefutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 21.80/21.99
%------------------------------------------------------------------------------