%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO232+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Sep 24 08:40:02 AM UTC 2026
% Result : Theorem 0.14s 0.44s
% Output : Proof 0.14s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(a1_defns,axiom,
! [X,Y] :
( unequally_directed_opposite_lines(X,Y)
<=> unequally_directed_lines(X,reverse_line(Y)) ),
file('GEO009+0.ax',a1_defns) ).
fof(a2_defns,axiom,
! [X,Y] :
( right_apart_point(X,Y)
<=> left_apart_point(X,reverse_line(Y)) ),
file('GEO009+0.ax',a2_defns) ).
fof(a3_defns,axiom,
! [X,Y] :
( right_convergent_lines(X,Y)
<=> left_convergent_lines(X,reverse_line(Y)) ),
file('GEO009+0.ax',a3_defns) ).
fof(a4_defns,axiom,
! [X,Y] :
( equally_directed_lines(X,Y)
<=> ~ unequally_directed_lines(X,Y) ),
file('GEO009+0.ax',a4_defns) ).
fof(a5_defns,axiom,
! [X,Y] :
( equally_directed_opposite_lines(X,Y)
<=> ~ unequally_directed_opposite_lines(X,Y) ),
file('GEO009+0.ax',a5_defns) ).
fof(a6_defns,axiom,
! [A,L] :
( apart_point_and_line(A,L)
<=> ( right_apart_point(A,L)
| left_apart_point(A,L) ) ),
file('GEO009+0.ax',a6_defns) ).
fof(a7_defns,axiom,
! [L,M] :
( convergent_lines(L,M)
<=> ( unequally_directed_opposite_lines(L,M)
& unequally_directed_lines(L,M) ) ),
file('GEO009+0.ax',a7_defns) ).
fof(a8_defns,axiom,
! [A,B,L] :
( divides_points(L,A,B)
<=> ( ( left_apart_point(B,L)
& right_apart_point(A,L) )
| ( right_apart_point(B,L)
& left_apart_point(A,L) ) ) ),
file('GEO009+0.ax',a8_defns) ).
fof(ax4_defns,axiom,
! [L,A,B] :
( before_on_line(L,A,B)
<=> ( equally_directed_lines(L,line_connecting(A,B))
& incident_point_and_line(B,L)
& incident_point_and_line(A,L)
& distinct_points(A,B) ) ),
file('GEO009+0.ax',ax4_defns) ).
fof(a9_defns,axiom,
! [L,A,B,C] :
( between_on_line(L,A,B,C)
<=> ( ( before_on_line(L,B,A)
& before_on_line(L,C,B) )
| ( before_on_line(L,B,C)
& before_on_line(L,A,B) ) ) ),
file('GEO009+0.ax',a9_defns) ).
fof(ax1_basics,axiom,
! [A] : ~ distinct_points(A,A),
file('GEO009+0.ax',ax1_basics) ).
fof(ax2_basics,axiom,
! [A,B,C] :
( distinct_points(A,B)
=> ( distinct_points(B,C)
| distinct_points(A,C) ) ),
file('GEO009+0.ax',ax2_basics) ).
fof(ax3_basics,axiom,
! [L] : ~ distinct_lines(L,L),
file('GEO009+0.ax',ax3_basics) ).
fof(ax4_basics,axiom,
! [L,M,N] :
( distinct_lines(L,M)
=> ( distinct_lines(M,N)
| distinct_lines(L,N) ) ),
file('GEO009+0.ax',ax4_basics) ).
fof(ax5_basics,axiom,
! [L] : equally_directed_lines(L,L),
file('GEO009+0.ax',ax5_basics) ).
fof(ax6_basics,axiom,
! [L,M,N] :
( unequally_directed_lines(L,M)
=> ( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N) ) ),
file('GEO009+0.ax',ax6_basics) ).
fof(ax7_basics,axiom,
! [L,M,N] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
=> ( ( unequally_directed_lines(M,reverse_line(N))
& unequally_directed_lines(M,N) )
| ( unequally_directed_lines(L,reverse_line(N))
& unequally_directed_lines(L,N) ) ) ),
file('GEO009+0.ax',ax7_basics) ).
fof(ax8_basics,axiom,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
file('GEO009+0.ax',ax8_basics) ).
fof(ax9_basics,axiom,
! [L,M] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
=> ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ) ),
file('GEO009+0.ax',ax9_basics) ).
fof(ax10_basics,axiom,
! [A,L] :
~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) ),
file('GEO009+0.ax',ax10_basics) ).
fof(ax11_basics,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('GEO009+0.ax',ax11_basics) ).
fof(ax1_cons_objs,axiom,
! [A,B] :
( ( distinct_points(A,B)
& point(B)
& point(A) )
=> line(line_connecting(A,B)) ),
file('GEO009+0.ax',ax1_cons_objs) ).
fof(ax2_cons_objs,axiom,
! [L,M] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M)
& line(M)
& line(L) )
=> point(intersection_point(L,M)) ),
file('GEO009+0.ax',ax2_cons_objs) ).
fof(ax3_cons_objs,axiom,
! [L,A] :
( ( line(L)
& point(A) )
=> line(parallel_through_point(L,A)) ),
file('GEO009+0.ax',ax3_cons_objs) ).
fof(ax4_cons_objs,axiom,
! [L] :
( line(L)
=> line(reverse_line(L)) ),
file('GEO009+0.ax',ax4_cons_objs) ).
fof(ax5_cons_objs,axiom,
! [A,B] :
( distinct_points(A,B)
=> ( ~ apart_point_and_line(B,line_connecting(A,B))
& ~ apart_point_and_line(A,line_connecting(A,B)) ) ),
file('GEO009+0.ax',ax5_cons_objs) ).
fof(ax6_cons_objs,axiom,
! [L,M] :
( ( unequally_directed_lines(L,reverse_line(M))
& unequally_directed_lines(L,M) )
=> ( ~ apart_point_and_line(intersection_point(L,M),M)
& ~ apart_point_and_line(intersection_point(L,M),L) ) ),
file('GEO009+0.ax',ax6_cons_objs) ).
fof(ax7_cons_objs,axiom,
! [A,L] : ~ apart_point_and_line(A,parallel_through_point(L,A)),
file('GEO009+0.ax',ax7_cons_objs) ).
fof(ax8_cons_objs,axiom,
! [L] : ~ distinct_lines(L,reverse_line(L)),
file('GEO009+0.ax',ax8_cons_objs) ).
fof(ax9_cons_objs,axiom,
! [A,B] :
( distinct_points(A,B)
=> equally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A))) ),
file('GEO009+0.ax',ax9_cons_objs) ).
fof(ax10_cons_objs,axiom,
! [A,L] : equally_directed_lines(parallel_through_point(L,A),L),
file('GEO009+0.ax',ax10_cons_objs) ).
fof(ax1_uniq_cons,axiom,
! [A,B,L,M] :
( ( distinct_lines(L,M)
& distinct_points(A,B) )
=> ( left_apart_point(B,reverse_line(M))
| left_apart_point(A,reverse_line(M))
| left_apart_point(B,reverse_line(L))
| left_apart_point(A,reverse_line(L))
| left_apart_point(B,M)
| left_apart_point(A,M)
| left_apart_point(B,L)
| left_apart_point(A,L) ) ),
file('GEO009+0.ax',ax1_uniq_cons) ).
fof(ax2_uniq_cons,axiom,
! [A,B,L] :
( ( left_apart_point(A,L)
& distinct_points(A,B) )
=> ( left_convergent_lines(line_connecting(A,B),L)
| left_apart_point(B,L) ) ),
file('GEO009+0.ax',ax2_uniq_cons) ).
fof(ax1_subs,axiom,
! [A,B,L] :
( left_apart_point(A,L)
=> ( left_apart_point(B,L)
| distinct_points(A,B) ) ),
file('GEO009+0.ax',ax1_subs) ).
fof(ax2_subs,axiom,
! [A,L,M] :
( ( unequally_directed_lines(L,M)
& left_apart_point(A,L) )
=> ( left_apart_point(A,reverse_line(M))
| distinct_lines(L,M) ) ),
file('GEO009+0.ax',ax2_subs) ).
fof(ax3_subs,axiom,
! [L,M,N] :
( left_convergent_lines(L,M)
=> ( left_convergent_lines(L,N)
| unequally_directed_lines(M,N) ) ),
file('GEO009+0.ax',ax3_subs) ).
fof(con,conjecture,
! [L] : unequally_directed_opposite_lines(L,L),
file('theBenchmark.p',con) ).
fof(f_1_1,plain,
! [X,Y] :
( ( unequally_directed_opposite_lines(X,Y)
| ~ unequally_directed_lines(X,reverse_line(Y)) )
& ( unequally_directed_lines(X,reverse_line(Y))
| ~ unequally_directed_opposite_lines(X,Y) ) ),
inference(fof_nnf,[status(thm)],[a1_defns]) ).
fof(f_1_2,plain,
! [U_1,U_0] :
( ( unequally_directed_opposite_lines(U_1,U_0)
| ~ unequally_directed_lines(U_1,reverse_line(U_0)) )
& ( unequally_directed_lines(U_1,reverse_line(U_0))
| ~ unequally_directed_opposite_lines(U_1,U_0) ) ),
inference(variable_rename,[status(thm)],[f_1_1]) ).
fof(f_1_3,plain,
( ! [U_5,U_3] :
( unequally_directed_opposite_lines(U_5,U_3)
| ~ unequally_directed_lines(U_5,reverse_line(U_3)) )
& ! [U_4,U_2] :
( unequally_directed_lines(U_4,reverse_line(U_2))
| ~ unequally_directed_opposite_lines(U_4,U_2) ) ),
inference(miniscope,[status(thm)],[f_1_2]) ).
cnf(f_1_4,plain,
( unequally_directed_lines(U_4,reverse_line(U_2))
| ~ unequally_directed_opposite_lines(U_4,U_2) ),
inference(clausify,[status(thm)],[f_1_3]) ).
cnf(f_1_5,plain,
( unequally_directed_opposite_lines(U_5,U_3)
| ~ unequally_directed_lines(U_5,reverse_line(U_3)) ),
inference(clausify,[status(thm)],[f_1_3]) ).
fof(f_2_1,plain,
! [X,Y] :
( ( right_apart_point(X,Y)
| ~ left_apart_point(X,reverse_line(Y)) )
& ( left_apart_point(X,reverse_line(Y))
| ~ right_apart_point(X,Y) ) ),
inference(fof_nnf,[status(thm)],[a2_defns]) ).
fof(f_2_2,plain,
! [U_7,U_6] :
( ( right_apart_point(U_7,U_6)
| ~ left_apart_point(U_7,reverse_line(U_6)) )
& ( left_apart_point(U_7,reverse_line(U_6))
| ~ right_apart_point(U_7,U_6) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_11,U_9] :
( right_apart_point(U_11,U_9)
| ~ left_apart_point(U_11,reverse_line(U_9)) )
& ! [U_10,U_8] :
( left_apart_point(U_10,reverse_line(U_8))
| ~ right_apart_point(U_10,U_8) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( left_apart_point(U_10,reverse_line(U_8))
| ~ right_apart_point(U_10,U_8) ),
inference(clausify,[status(thm)],[f_2_3]) ).
cnf(f_2_5,plain,
( right_apart_point(U_11,U_9)
| ~ left_apart_point(U_11,reverse_line(U_9)) ),
inference(clausify,[status(thm)],[f_2_3]) ).
fof(f_3_1,plain,
! [X,Y] :
( ( right_convergent_lines(X,Y)
| ~ left_convergent_lines(X,reverse_line(Y)) )
& ( left_convergent_lines(X,reverse_line(Y))
| ~ right_convergent_lines(X,Y) ) ),
inference(fof_nnf,[status(thm)],[a3_defns]) ).
fof(f_3_2,plain,
! [U_13,U_12] :
( ( right_convergent_lines(U_13,U_12)
| ~ left_convergent_lines(U_13,reverse_line(U_12)) )
& ( left_convergent_lines(U_13,reverse_line(U_12))
| ~ right_convergent_lines(U_13,U_12) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_17,U_15] :
( right_convergent_lines(U_17,U_15)
| ~ left_convergent_lines(U_17,reverse_line(U_15)) )
& ! [U_16,U_14] :
( left_convergent_lines(U_16,reverse_line(U_14))
| ~ right_convergent_lines(U_16,U_14) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_4,plain,
( left_convergent_lines(U_16,reverse_line(U_14))
| ~ right_convergent_lines(U_16,U_14) ),
inference(clausify,[status(thm)],[f_3_3]) ).
cnf(f_3_5,plain,
( right_convergent_lines(U_17,U_15)
| ~ left_convergent_lines(U_17,reverse_line(U_15)) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_4_1,plain,
! [X,Y] :
( ( equally_directed_lines(X,Y)
| unequally_directed_lines(X,Y) )
& ( ~ unequally_directed_lines(X,Y)
| ~ equally_directed_lines(X,Y) ) ),
inference(fof_nnf,[status(thm)],[a4_defns]) ).
fof(f_4_2,plain,
! [U_19,U_18] :
( ( equally_directed_lines(U_19,U_18)
| unequally_directed_lines(U_19,U_18) )
& ( ~ unequally_directed_lines(U_19,U_18)
| ~ equally_directed_lines(U_19,U_18) ) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
( ! [U_23,U_21] :
( equally_directed_lines(U_23,U_21)
| unequally_directed_lines(U_23,U_21) )
& ! [U_22,U_20] :
( ~ unequally_directed_lines(U_22,U_20)
| ~ equally_directed_lines(U_22,U_20) ) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( ~ unequally_directed_lines(U_22,U_20)
| ~ equally_directed_lines(U_22,U_20) ),
inference(clausify,[status(thm)],[f_4_3]) ).
cnf(f_4_5,plain,
( equally_directed_lines(U_23,U_21)
| unequally_directed_lines(U_23,U_21) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [X,Y] :
( ( equally_directed_opposite_lines(X,Y)
| unequally_directed_opposite_lines(X,Y) )
& ( ~ unequally_directed_opposite_lines(X,Y)
| ~ equally_directed_opposite_lines(X,Y) ) ),
inference(fof_nnf,[status(thm)],[a5_defns]) ).
fof(f_5_2,plain,
! [U_25,U_24] :
( ( equally_directed_opposite_lines(U_25,U_24)
| unequally_directed_opposite_lines(U_25,U_24) )
& ( ~ unequally_directed_opposite_lines(U_25,U_24)
| ~ equally_directed_opposite_lines(U_25,U_24) ) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
( ! [U_29,U_27] :
( equally_directed_opposite_lines(U_29,U_27)
| unequally_directed_opposite_lines(U_29,U_27) )
& ! [U_28,U_26] :
( ~ unequally_directed_opposite_lines(U_28,U_26)
| ~ equally_directed_opposite_lines(U_28,U_26) ) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( ~ unequally_directed_opposite_lines(U_28,U_26)
| ~ equally_directed_opposite_lines(U_28,U_26) ),
inference(clausify,[status(thm)],[f_5_3]) ).
cnf(f_5_5,plain,
( equally_directed_opposite_lines(U_29,U_27)
| unequally_directed_opposite_lines(U_29,U_27) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [A,L] :
( ( apart_point_and_line(A,L)
| ( ~ right_apart_point(A,L)
& ~ left_apart_point(A,L) ) )
& ( right_apart_point(A,L)
| left_apart_point(A,L)
| ~ apart_point_and_line(A,L) ) ),
inference(fof_nnf,[status(thm)],[a6_defns]) ).
fof(f_6_2,plain,
! [U_31,U_30] :
( ( apart_point_and_line(U_31,U_30)
| ( ~ right_apart_point(U_31,U_30)
& ~ left_apart_point(U_31,U_30) ) )
& ( right_apart_point(U_31,U_30)
| left_apart_point(U_31,U_30)
| ~ apart_point_and_line(U_31,U_30) ) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
( ! [U_35,U_33] :
( apart_point_and_line(U_35,U_33)
| ( ~ right_apart_point(U_35,U_33)
& ~ left_apart_point(U_35,U_33) ) )
& ! [U_34,U_32] :
( right_apart_point(U_34,U_32)
| left_apart_point(U_34,U_32)
| ~ apart_point_and_line(U_34,U_32) ) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( right_apart_point(U_34,U_32)
| left_apart_point(U_34,U_32)
| ~ apart_point_and_line(U_34,U_32) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_5,plain,
( ~ left_apart_point(U_35,U_33)
| apart_point_and_line(U_35,U_33) ),
inference(clausify,[status(thm)],[f_6_3]) ).
cnf(f_6_6,plain,
( ~ right_apart_point(U_35,U_33)
| apart_point_and_line(U_35,U_33) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [L,M] :
( ( convergent_lines(L,M)
| ~ unequally_directed_opposite_lines(L,M)
| ~ unequally_directed_lines(L,M) )
& ( ( unequally_directed_opposite_lines(L,M)
& unequally_directed_lines(L,M) )
| ~ convergent_lines(L,M) ) ),
inference(fof_nnf,[status(thm)],[a7_defns]) ).
fof(f_7_2,plain,
! [U_37,U_36] :
( ( convergent_lines(U_37,U_36)
| ~ unequally_directed_opposite_lines(U_37,U_36)
| ~ unequally_directed_lines(U_37,U_36) )
& ( ( unequally_directed_opposite_lines(U_37,U_36)
& unequally_directed_lines(U_37,U_36) )
| ~ convergent_lines(U_37,U_36) ) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
( ! [U_41,U_39] :
( convergent_lines(U_41,U_39)
| ~ unequally_directed_opposite_lines(U_41,U_39)
| ~ unequally_directed_lines(U_41,U_39) )
& ! [U_40,U_38] :
( ( unequally_directed_opposite_lines(U_40,U_38)
& unequally_directed_lines(U_40,U_38) )
| ~ convergent_lines(U_40,U_38) ) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( unequally_directed_lines(U_40,U_38)
| ~ convergent_lines(U_40,U_38) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( unequally_directed_opposite_lines(U_40,U_38)
| ~ convergent_lines(U_40,U_38) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_6,plain,
( convergent_lines(U_41,U_39)
| ~ unequally_directed_opposite_lines(U_41,U_39)
| ~ unequally_directed_lines(U_41,U_39) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [A,B,L] :
( ( divides_points(L,A,B)
| ( ( ~ left_apart_point(B,L)
| ~ right_apart_point(A,L) )
& ( ~ right_apart_point(B,L)
| ~ left_apart_point(A,L) ) ) )
& ( ( left_apart_point(B,L)
& right_apart_point(A,L) )
| ( right_apart_point(B,L)
& left_apart_point(A,L) )
| ~ divides_points(L,A,B) ) ),
inference(fof_nnf,[status(thm)],[a8_defns]) ).
fof(f_8_2,plain,
! [U_44,U_43,U_42] :
( ( divides_points(U_42,U_44,U_43)
| ( ( ~ left_apart_point(U_43,U_42)
| ~ right_apart_point(U_44,U_42) )
& ( ~ right_apart_point(U_43,U_42)
| ~ left_apart_point(U_44,U_42) ) ) )
& ( ( left_apart_point(U_43,U_42)
& right_apart_point(U_44,U_42) )
| ( right_apart_point(U_43,U_42)
& left_apart_point(U_44,U_42) )
| ~ divides_points(U_42,U_44,U_43) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_50,U_48,U_46] :
( divides_points(U_46,U_50,U_48)
| ( ( ~ left_apart_point(U_48,U_46)
| ~ right_apart_point(U_50,U_46) )
& ( ~ right_apart_point(U_48,U_46)
| ~ left_apart_point(U_50,U_46) ) ) )
& ! [U_49,U_47,U_45] :
( ( left_apart_point(U_47,U_45)
& right_apart_point(U_49,U_45) )
| ( right_apart_point(U_47,U_45)
& left_apart_point(U_49,U_45) )
| ~ divides_points(U_45,U_49,U_47) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( right_apart_point(U_49,U_45)
| left_apart_point(U_49,U_45)
| ~ divides_points(U_45,U_49,U_47) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( left_apart_point(U_47,U_45)
| left_apart_point(U_49,U_45)
| ~ divides_points(U_45,U_49,U_47) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_6,plain,
( right_apart_point(U_49,U_45)
| right_apart_point(U_47,U_45)
| ~ divides_points(U_45,U_49,U_47) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_7,plain,
( left_apart_point(U_47,U_45)
| right_apart_point(U_47,U_45)
| ~ divides_points(U_45,U_49,U_47) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_8,plain,
( ~ right_apart_point(U_48,U_46)
| ~ left_apart_point(U_50,U_46)
| divides_points(U_46,U_50,U_48) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_9,plain,
( ~ left_apart_point(U_48,U_46)
| ~ right_apart_point(U_50,U_46)
| divides_points(U_46,U_50,U_48) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_1,plain,
! [L,A,B] :
( ( before_on_line(L,A,B)
| ~ equally_directed_lines(L,line_connecting(A,B))
| ~ incident_point_and_line(B,L)
| ~ incident_point_and_line(A,L)
| ~ distinct_points(A,B) )
& ( ( equally_directed_lines(L,line_connecting(A,B))
& incident_point_and_line(B,L)
& incident_point_and_line(A,L)
& distinct_points(A,B) )
| ~ before_on_line(L,A,B) ) ),
inference(fof_nnf,[status(thm)],[ax4_defns]) ).
fof(f_9_2,plain,
! [U_53,U_52,U_51] :
( ( before_on_line(U_53,U_52,U_51)
| ~ equally_directed_lines(U_53,line_connecting(U_52,U_51))
| ~ incident_point_and_line(U_51,U_53)
| ~ incident_point_and_line(U_52,U_53)
| ~ distinct_points(U_52,U_51) )
& ( ( equally_directed_lines(U_53,line_connecting(U_52,U_51))
& incident_point_and_line(U_51,U_53)
& incident_point_and_line(U_52,U_53)
& distinct_points(U_52,U_51) )
| ~ before_on_line(U_53,U_52,U_51) ) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
fof(f_9_3,plain,
( ! [U_59,U_57,U_55] :
( before_on_line(U_59,U_57,U_55)
| ~ equally_directed_lines(U_59,line_connecting(U_57,U_55))
| ~ incident_point_and_line(U_55,U_59)
| ~ incident_point_and_line(U_57,U_59)
| ~ distinct_points(U_57,U_55) )
& ! [U_58,U_56,U_54] :
( ( equally_directed_lines(U_58,line_connecting(U_56,U_54))
& incident_point_and_line(U_54,U_58)
& incident_point_and_line(U_56,U_58)
& distinct_points(U_56,U_54) )
| ~ before_on_line(U_58,U_56,U_54) ) ),
inference(miniscope,[status(thm)],[f_9_2]) ).
cnf(f_9_4,plain,
( distinct_points(U_56,U_54)
| ~ before_on_line(U_58,U_56,U_54) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_5,plain,
( incident_point_and_line(U_56,U_58)
| ~ before_on_line(U_58,U_56,U_54) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_6,plain,
( incident_point_and_line(U_54,U_58)
| ~ before_on_line(U_58,U_56,U_54) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_7,plain,
( equally_directed_lines(U_58,line_connecting(U_56,U_54))
| ~ before_on_line(U_58,U_56,U_54) ),
inference(clausify,[status(thm)],[f_9_3]) ).
cnf(f_9_8,plain,
( before_on_line(U_59,U_57,U_55)
| ~ equally_directed_lines(U_59,line_connecting(U_57,U_55))
| ~ incident_point_and_line(U_55,U_59)
| ~ incident_point_and_line(U_57,U_59)
| ~ distinct_points(U_57,U_55) ),
inference(clausify,[status(thm)],[f_9_3]) ).
fof(f_10_1,plain,
! [L,A,B,C] :
( ( between_on_line(L,A,B,C)
| ( ( ~ before_on_line(L,B,A)
| ~ before_on_line(L,C,B) )
& ( ~ before_on_line(L,B,C)
| ~ before_on_line(L,A,B) ) ) )
& ( ( before_on_line(L,B,A)
& before_on_line(L,C,B) )
| ( before_on_line(L,B,C)
& before_on_line(L,A,B) )
| ~ between_on_line(L,A,B,C) ) ),
inference(fof_nnf,[status(thm)],[a9_defns]) ).
fof(f_10_2,plain,
! [U_63,U_62,U_61,U_60] :
( ( between_on_line(U_63,U_62,U_61,U_60)
| ( ( ~ before_on_line(U_63,U_61,U_62)
| ~ before_on_line(U_63,U_60,U_61) )
& ( ~ before_on_line(U_63,U_61,U_60)
| ~ before_on_line(U_63,U_62,U_61) ) ) )
& ( ( before_on_line(U_63,U_61,U_62)
& before_on_line(U_63,U_60,U_61) )
| ( before_on_line(U_63,U_61,U_60)
& before_on_line(U_63,U_62,U_61) )
| ~ between_on_line(U_63,U_62,U_61,U_60) ) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
( ! [U_71,U_69,U_67,U_65] :
( between_on_line(U_71,U_69,U_67,U_65)
| ( ( ~ before_on_line(U_71,U_67,U_69)
| ~ before_on_line(U_71,U_65,U_67) )
& ( ~ before_on_line(U_71,U_67,U_65)
| ~ before_on_line(U_71,U_69,U_67) ) ) )
& ! [U_70,U_68,U_66,U_64] :
( ( before_on_line(U_70,U_66,U_68)
& before_on_line(U_70,U_64,U_66) )
| ( before_on_line(U_70,U_66,U_64)
& before_on_line(U_70,U_68,U_66) )
| ~ between_on_line(U_70,U_68,U_66,U_64) ) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( before_on_line(U_70,U_64,U_66)
| before_on_line(U_70,U_68,U_66)
| ~ between_on_line(U_70,U_68,U_66,U_64) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_5,plain,
( before_on_line(U_70,U_66,U_68)
| before_on_line(U_70,U_68,U_66)
| ~ between_on_line(U_70,U_68,U_66,U_64) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_6,plain,
( before_on_line(U_70,U_64,U_66)
| before_on_line(U_70,U_66,U_64)
| ~ between_on_line(U_70,U_68,U_66,U_64) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_7,plain,
( before_on_line(U_70,U_66,U_68)
| before_on_line(U_70,U_66,U_64)
| ~ between_on_line(U_70,U_68,U_66,U_64) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_8,plain,
( ~ before_on_line(U_71,U_67,U_65)
| ~ before_on_line(U_71,U_69,U_67)
| between_on_line(U_71,U_69,U_67,U_65) ),
inference(clausify,[status(thm)],[f_10_3]) ).
cnf(f_10_9,plain,
( ~ before_on_line(U_71,U_67,U_69)
| ~ before_on_line(U_71,U_65,U_67)
| between_on_line(U_71,U_69,U_67,U_65) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_1,plain,
! [A] : ~ distinct_points(A,A),
inference(fof_nnf,[status(thm)],[ax1_basics]) ).
fof(f_11_2,plain,
! [U_72] : ~ distinct_points(U_72,U_72),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
~ distinct_points(U_72,U_72),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [A,B,C] :
( distinct_points(B,C)
| distinct_points(A,C)
| ~ distinct_points(A,B) ),
inference(fof_nnf,[status(thm)],[ax2_basics]) ).
fof(f_12_2,plain,
! [U_75,U_74,U_73] :
( distinct_points(U_74,U_73)
| distinct_points(U_75,U_73)
| ~ distinct_points(U_75,U_74) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_75,U_74] :
( ! [U_73] :
( distinct_points(U_74,U_73)
| distinct_points(U_75,U_73) )
| ~ distinct_points(U_75,U_74) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( distinct_points(U_74,U_73)
| distinct_points(U_75,U_73)
| ~ distinct_points(U_75,U_74) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [L] : ~ distinct_lines(L,L),
inference(fof_nnf,[status(thm)],[ax3_basics]) ).
fof(f_13_2,plain,
! [U_76] : ~ distinct_lines(U_76,U_76),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
~ distinct_lines(U_76,U_76),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [L,M,N] :
( distinct_lines(M,N)
| distinct_lines(L,N)
| ~ distinct_lines(L,M) ),
inference(fof_nnf,[status(thm)],[ax4_basics]) ).
fof(f_14_2,plain,
! [U_79,U_78,U_77] :
( distinct_lines(U_78,U_77)
| distinct_lines(U_79,U_77)
| ~ distinct_lines(U_79,U_78) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_79,U_78] :
( ! [U_77] :
( distinct_lines(U_78,U_77)
| distinct_lines(U_79,U_77) )
| ~ distinct_lines(U_79,U_78) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( distinct_lines(U_78,U_77)
| distinct_lines(U_79,U_77)
| ~ distinct_lines(U_79,U_78) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [L] : equally_directed_lines(L,L),
inference(fof_nnf,[status(thm)],[ax5_basics]) ).
fof(f_15_2,plain,
! [U_80] : equally_directed_lines(U_80,U_80),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
equally_directed_lines(U_80,U_80),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [L,M,N] :
( unequally_directed_lines(M,N)
| unequally_directed_lines(L,N)
| ~ unequally_directed_lines(L,M) ),
inference(fof_nnf,[status(thm)],[ax6_basics]) ).
fof(f_16_2,plain,
! [U_83,U_82,U_81] :
( unequally_directed_lines(U_82,U_81)
| unequally_directed_lines(U_83,U_81)
| ~ unequally_directed_lines(U_83,U_82) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
! [U_83,U_82] :
( ! [U_81] :
( unequally_directed_lines(U_82,U_81)
| unequally_directed_lines(U_83,U_81) )
| ~ unequally_directed_lines(U_83,U_82) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
( unequally_directed_lines(U_82,U_81)
| unequally_directed_lines(U_83,U_81)
| ~ unequally_directed_lines(U_83,U_82) ),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_17_1,plain,
! [L,M,N] :
( ( unequally_directed_lines(M,reverse_line(N))
& unequally_directed_lines(M,N) )
| ( unequally_directed_lines(L,reverse_line(N))
& unequally_directed_lines(L,N) )
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(fof_nnf,[status(thm)],[ax7_basics]) ).
fof(f_17_2,plain,
! [U_86,U_85,U_84] :
( ( unequally_directed_lines(U_85,reverse_line(U_84))
& unequally_directed_lines(U_85,U_84) )
| ( unequally_directed_lines(U_86,reverse_line(U_84))
& unequally_directed_lines(U_86,U_84) )
| ~ unequally_directed_lines(U_86,reverse_line(U_85))
| ~ unequally_directed_lines(U_86,U_85) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_86,U_85] :
( ! [U_84] :
( ( unequally_directed_lines(U_85,reverse_line(U_84))
& unequally_directed_lines(U_85,U_84) )
| ( unequally_directed_lines(U_86,reverse_line(U_84))
& unequally_directed_lines(U_86,U_84) ) )
| ~ unequally_directed_lines(U_86,reverse_line(U_85))
| ~ unequally_directed_lines(U_86,U_85) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
cnf(f_17_4,plain,
( unequally_directed_lines(U_85,U_84)
| unequally_directed_lines(U_86,U_84)
| ~ unequally_directed_lines(U_86,reverse_line(U_85))
| ~ unequally_directed_lines(U_86,U_85) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_5,plain,
( unequally_directed_lines(U_85,reverse_line(U_84))
| unequally_directed_lines(U_86,U_84)
| ~ unequally_directed_lines(U_86,reverse_line(U_85))
| ~ unequally_directed_lines(U_86,U_85) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_6,plain,
( unequally_directed_lines(U_85,U_84)
| unequally_directed_lines(U_86,reverse_line(U_84))
| ~ unequally_directed_lines(U_86,reverse_line(U_85))
| ~ unequally_directed_lines(U_86,U_85) ),
inference(clausify,[status(thm)],[f_17_3]) ).
cnf(f_17_7,plain,
( unequally_directed_lines(U_85,reverse_line(U_84))
| unequally_directed_lines(U_86,reverse_line(U_84))
| ~ unequally_directed_lines(U_86,reverse_line(U_85))
| ~ unequally_directed_lines(U_86,U_85) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_18_1,plain,
! [L,M] :
( unequally_directed_lines(L,reverse_line(M))
| unequally_directed_lines(L,M) ),
inference(fof_nnf,[status(thm)],[ax8_basics]) ).
fof(f_18_2,plain,
! [U_88,U_87] :
( unequally_directed_lines(U_88,reverse_line(U_87))
| unequally_directed_lines(U_88,U_87) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( unequally_directed_lines(U_88,reverse_line(U_87))
| unequally_directed_lines(U_88,U_87) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [L,M] :
( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M)
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(fof_nnf,[status(thm)],[ax9_basics]) ).
fof(f_19_2,plain,
! [U_90,U_89] :
( left_convergent_lines(U_90,reverse_line(U_89))
| left_convergent_lines(U_90,U_89)
| ~ unequally_directed_lines(U_90,reverse_line(U_89))
| ~ unequally_directed_lines(U_90,U_89) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( left_convergent_lines(U_90,reverse_line(U_89))
| left_convergent_lines(U_90,U_89)
| ~ unequally_directed_lines(U_90,reverse_line(U_89))
| ~ unequally_directed_lines(U_90,U_89) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [A,L] :
( ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L) ),
inference(fof_nnf,[status(thm)],[ax10_basics]) ).
fof(f_20_2,plain,
! [U_92,U_91] :
( ~ left_apart_point(U_92,reverse_line(U_91))
& ~ left_apart_point(U_92,U_91) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_96,U_94] : ~ left_apart_point(U_96,reverse_line(U_94))
& ! [U_95,U_93] : ~ left_apart_point(U_95,U_93) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
~ left_apart_point(U_95,U_93),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
~ left_apart_point(U_96,reverse_line(U_94)),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(fof_nnf,[status(thm)],[ax11_basics]) ).
fof(f_21_2,plain,
! [U_98,U_97] :
( ~ left_convergent_lines(U_98,reverse_line(U_97))
& ~ left_convergent_lines(U_98,U_97) ),
inference(variable_rename,[status(thm)],[f_21_1]) ).
fof(f_21_3,plain,
( ! [U_102,U_100] : ~ left_convergent_lines(U_102,reverse_line(U_100))
& ! [U_101,U_99] : ~ left_convergent_lines(U_101,U_99) ),
inference(miniscope,[status(thm)],[f_21_2]) ).
cnf(f_21_4,plain,
~ left_convergent_lines(U_101,U_99),
inference(clausify,[status(thm)],[f_21_3]) ).
cnf(f_21_5,plain,
~ left_convergent_lines(U_102,reverse_line(U_100)),
inference(clausify,[status(thm)],[f_21_3]) ).
fof(f_22_1,plain,
! [A,B] :
( line(line_connecting(A,B))
| ~ distinct_points(A,B)
| ~ point(B)
| ~ point(A) ),
inference(fof_nnf,[status(thm)],[ax1_cons_objs]) ).
fof(f_22_2,plain,
! [U_104,U_103] :
( line(line_connecting(U_104,U_103))
| ~ distinct_points(U_104,U_103)
| ~ point(U_103)
| ~ point(U_104) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
( line(line_connecting(U_104,U_103))
| ~ distinct_points(U_104,U_103)
| ~ point(U_103)
| ~ point(U_104) ),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [L,M] :
( point(intersection_point(L,M))
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M)
| ~ line(M)
| ~ line(L) ),
inference(fof_nnf,[status(thm)],[ax2_cons_objs]) ).
fof(f_23_2,plain,
! [U_106,U_105] :
( point(intersection_point(U_106,U_105))
| ~ unequally_directed_lines(U_106,reverse_line(U_105))
| ~ unequally_directed_lines(U_106,U_105)
| ~ line(U_105)
| ~ line(U_106) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
cnf(f_23_3,plain,
( point(intersection_point(U_106,U_105))
| ~ unequally_directed_lines(U_106,reverse_line(U_105))
| ~ unequally_directed_lines(U_106,U_105)
| ~ line(U_105)
| ~ line(U_106) ),
inference(clausify,[status(thm)],[f_23_2]) ).
fof(f_24_1,plain,
! [L,A] :
( line(parallel_through_point(L,A))
| ~ line(L)
| ~ point(A) ),
inference(fof_nnf,[status(thm)],[ax3_cons_objs]) ).
fof(f_24_2,plain,
! [U_108,U_107] :
( line(parallel_through_point(U_108,U_107))
| ~ line(U_108)
| ~ point(U_107) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( line(parallel_through_point(U_108,U_107))
| ~ line(U_108)
| ~ point(U_107) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [L] :
( line(reverse_line(L))
| ~ line(L) ),
inference(fof_nnf,[status(thm)],[ax4_cons_objs]) ).
fof(f_25_2,plain,
! [U_109] :
( line(reverse_line(U_109))
| ~ line(U_109) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( line(reverse_line(U_109))
| ~ line(U_109) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [A,B] :
( ( ~ apart_point_and_line(B,line_connecting(A,B))
& ~ apart_point_and_line(A,line_connecting(A,B)) )
| ~ distinct_points(A,B) ),
inference(fof_nnf,[status(thm)],[ax5_cons_objs]) ).
fof(f_26_2,plain,
! [U_111,U_110] :
( ( ~ apart_point_and_line(U_110,line_connecting(U_111,U_110))
& ~ apart_point_and_line(U_111,line_connecting(U_111,U_110)) )
| ~ distinct_points(U_111,U_110) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( ~ apart_point_and_line(U_111,line_connecting(U_111,U_110))
| ~ distinct_points(U_111,U_110) ),
inference(clausify,[status(thm)],[f_26_2]) ).
cnf(f_26_4,plain,
( ~ apart_point_and_line(U_110,line_connecting(U_111,U_110))
| ~ distinct_points(U_111,U_110) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [L,M] :
( ( ~ apart_point_and_line(intersection_point(L,M),M)
& ~ apart_point_and_line(intersection_point(L,M),L) )
| ~ unequally_directed_lines(L,reverse_line(M))
| ~ unequally_directed_lines(L,M) ),
inference(fof_nnf,[status(thm)],[ax6_cons_objs]) ).
fof(f_27_2,plain,
! [U_113,U_112] :
( ( ~ apart_point_and_line(intersection_point(U_113,U_112),U_112)
& ~ apart_point_and_line(intersection_point(U_113,U_112),U_113) )
| ~ unequally_directed_lines(U_113,reverse_line(U_112))
| ~ unequally_directed_lines(U_113,U_112) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( ~ apart_point_and_line(intersection_point(U_113,U_112),U_113)
| ~ unequally_directed_lines(U_113,reverse_line(U_112))
| ~ unequally_directed_lines(U_113,U_112) ),
inference(clausify,[status(thm)],[f_27_2]) ).
cnf(f_27_4,plain,
( ~ apart_point_and_line(intersection_point(U_113,U_112),U_112)
| ~ unequally_directed_lines(U_113,reverse_line(U_112))
| ~ unequally_directed_lines(U_113,U_112) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [A,L] : ~ apart_point_and_line(A,parallel_through_point(L,A)),
inference(fof_nnf,[status(thm)],[ax7_cons_objs]) ).
fof(f_28_2,plain,
! [U_115,U_114] : ~ apart_point_and_line(U_115,parallel_through_point(U_114,U_115)),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
~ apart_point_and_line(U_115,parallel_through_point(U_114,U_115)),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [L] : ~ distinct_lines(L,reverse_line(L)),
inference(fof_nnf,[status(thm)],[ax8_cons_objs]) ).
fof(f_29_2,plain,
! [U_116] : ~ distinct_lines(U_116,reverse_line(U_116)),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
~ distinct_lines(U_116,reverse_line(U_116)),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [A,B] :
( equally_directed_lines(line_connecting(A,B),reverse_line(line_connecting(B,A)))
| ~ distinct_points(A,B) ),
inference(fof_nnf,[status(thm)],[ax9_cons_objs]) ).
fof(f_30_2,plain,
! [U_118,U_117] :
( equally_directed_lines(line_connecting(U_118,U_117),reverse_line(line_connecting(U_117,U_118)))
| ~ distinct_points(U_118,U_117) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( equally_directed_lines(line_connecting(U_118,U_117),reverse_line(line_connecting(U_117,U_118)))
| ~ distinct_points(U_118,U_117) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [A,L] : equally_directed_lines(parallel_through_point(L,A),L),
inference(fof_nnf,[status(thm)],[ax10_cons_objs]) ).
fof(f_31_2,plain,
! [U_120,U_119] : equally_directed_lines(parallel_through_point(U_119,U_120),U_119),
inference(variable_rename,[status(thm)],[f_31_1]) ).
cnf(f_31_3,plain,
equally_directed_lines(parallel_through_point(U_119,U_120),U_119),
inference(clausify,[status(thm)],[f_31_2]) ).
fof(f_32_1,plain,
! [A,B,L,M] :
( left_apart_point(B,reverse_line(M))
| left_apart_point(A,reverse_line(M))
| left_apart_point(B,reverse_line(L))
| left_apart_point(A,reverse_line(L))
| left_apart_point(B,M)
| left_apart_point(A,M)
| left_apart_point(B,L)
| left_apart_point(A,L)
| ~ distinct_lines(L,M)
| ~ distinct_points(A,B) ),
inference(fof_nnf,[status(thm)],[ax1_uniq_cons]) ).
fof(f_32_2,plain,
! [U_124,U_123,U_122,U_121] :
( left_apart_point(U_123,reverse_line(U_121))
| left_apart_point(U_124,reverse_line(U_121))
| left_apart_point(U_123,reverse_line(U_122))
| left_apart_point(U_124,reverse_line(U_122))
| left_apart_point(U_123,U_121)
| left_apart_point(U_124,U_121)
| left_apart_point(U_123,U_122)
| left_apart_point(U_124,U_122)
| ~ distinct_lines(U_122,U_121)
| ~ distinct_points(U_124,U_123) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
cnf(f_32_3,plain,
( left_apart_point(U_123,reverse_line(U_121))
| left_apart_point(U_124,reverse_line(U_121))
| left_apart_point(U_123,reverse_line(U_122))
| left_apart_point(U_124,reverse_line(U_122))
| left_apart_point(U_123,U_121)
| left_apart_point(U_124,U_121)
| left_apart_point(U_123,U_122)
| left_apart_point(U_124,U_122)
| ~ distinct_lines(U_122,U_121)
| ~ distinct_points(U_124,U_123) ),
inference(clausify,[status(thm)],[f_32_2]) ).
fof(f_33_1,plain,
! [A,B,L] :
( left_convergent_lines(line_connecting(A,B),L)
| left_apart_point(B,L)
| ~ left_apart_point(A,L)
| ~ distinct_points(A,B) ),
inference(fof_nnf,[status(thm)],[ax2_uniq_cons]) ).
fof(f_33_2,plain,
! [U_127,U_126,U_125] :
( left_convergent_lines(line_connecting(U_127,U_126),U_125)
| left_apart_point(U_126,U_125)
| ~ left_apart_point(U_127,U_125)
| ~ distinct_points(U_127,U_126) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
cnf(f_33_3,plain,
( left_convergent_lines(line_connecting(U_127,U_126),U_125)
| left_apart_point(U_126,U_125)
| ~ left_apart_point(U_127,U_125)
| ~ distinct_points(U_127,U_126) ),
inference(clausify,[status(thm)],[f_33_2]) ).
fof(f_34_1,plain,
! [A,B,L] :
( left_apart_point(B,L)
| distinct_points(A,B)
| ~ left_apart_point(A,L) ),
inference(fof_nnf,[status(thm)],[ax1_subs]) ).
fof(f_34_2,plain,
! [U_130,U_129,U_128] :
( left_apart_point(U_129,U_128)
| distinct_points(U_130,U_129)
| ~ left_apart_point(U_130,U_128) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( left_apart_point(U_129,U_128)
| distinct_points(U_130,U_129)
| ~ left_apart_point(U_130,U_128) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_35_1,plain,
! [A,L,M] :
( left_apart_point(A,reverse_line(M))
| distinct_lines(L,M)
| ~ unequally_directed_lines(L,M)
| ~ left_apart_point(A,L) ),
inference(fof_nnf,[status(thm)],[ax2_subs]) ).
fof(f_35_2,plain,
! [U_133,U_132,U_131] :
( left_apart_point(U_133,reverse_line(U_131))
| distinct_lines(U_132,U_131)
| ~ unequally_directed_lines(U_132,U_131)
| ~ left_apart_point(U_133,U_132) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
cnf(f_35_3,plain,
( left_apart_point(U_133,reverse_line(U_131))
| distinct_lines(U_132,U_131)
| ~ unequally_directed_lines(U_132,U_131)
| ~ left_apart_point(U_133,U_132) ),
inference(clausify,[status(thm)],[f_35_2]) ).
fof(f_36_1,plain,
! [L,M,N] :
( left_convergent_lines(L,N)
| unequally_directed_lines(M,N)
| ~ left_convergent_lines(L,M) ),
inference(fof_nnf,[status(thm)],[ax3_subs]) ).
fof(f_36_2,plain,
! [U_136,U_135,U_134] :
( left_convergent_lines(U_136,U_134)
| unequally_directed_lines(U_135,U_134)
| ~ left_convergent_lines(U_136,U_135) ),
inference(variable_rename,[status(thm)],[f_36_1]) ).
fof(f_36_3,plain,
! [U_136,U_135] :
( ! [U_134] :
( left_convergent_lines(U_136,U_134)
| unequally_directed_lines(U_135,U_134) )
| ~ left_convergent_lines(U_136,U_135) ),
inference(miniscope,[status(thm)],[f_36_2]) ).
cnf(f_36_4,plain,
( left_convergent_lines(U_136,U_134)
| unequally_directed_lines(U_135,U_134)
| ~ left_convergent_lines(U_136,U_135) ),
inference(clausify,[status(thm)],[f_36_3]) ).
fof(f_37_1,negated_conjecture,
~ ! [L] : unequally_directed_opposite_lines(L,L),
inference(negate,[status(cth)],[con]) ).
fof(f_37_2,negated_conjecture,
? [L] : ~ unequally_directed_opposite_lines(L,L),
inference(fof_nnf,[status(thm)],[f_37_1]) ).
fof(f_37_3,negated_conjecture,
? [U_137] : ~ unequally_directed_opposite_lines(U_137,U_137),
inference(variable_rename,[status(thm)],[f_37_2]) ).
fof(f_37_4,negated_conjecture,
~ unequally_directed_opposite_lines(sK1,sK1),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_137,sK1)],[f_37_3]) ).
fof(f_37_5,negated_conjecture,
~ unequally_directed_opposite_lines(sK1,sK1),
inference(definitional_conversion,[status(esa)],[f_37_4]) ).
cnf(f_37_6,negated_conjecture,
~ unequally_directed_opposite_lines(sK1,sK1),
inference(clausify,[status(thm)],[f_37_5]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO232+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n006.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 07:41:58 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.14/0.44 % SZS status Theorem for theBenchmark
% 0.14/0.44 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------