%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO201+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 : n016.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 08:39:51 AM UTC 2026
% Result : Theorem 0.79s 1.12s
% Output : Proof 0.89s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X),
file('GEO006+0.ax',apart1) ).
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X),
file('GEO006+0.ax',apart2) ).
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('GEO006+0.ax',apart3) ).
fof(apart4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('GEO006+0.ax',apart4) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('GEO006+0.ax',apart5) ).
fof(ax6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('GEO006+0.ax',ax6) ).
fof(ci1,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('GEO006+0.ax',ci1) ).
fof(ci2,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('GEO006+0.ax',ci2) ).
fof(ci3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('GEO006+0.ax',ci3) ).
fof(ci4,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('GEO006+0.ax',ci4) ).
fof(cu1,axiom,
! [X,Y,U,V] :
( ( distinct_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('GEO006+0.ax',cu1) ).
fof(ceq1,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(Z,Y)
| distinct_points(X,Z) ) ),
file('GEO006+0.ax',ceq1) ).
fof(ceq2,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('GEO006+0.ax',ceq2) ).
fof(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('GEO006+0.ax',ceq3) ).
fof(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('GEO006+1.ax',p1) ).
fof(cp1,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('GEO006+2.ax',cp1) ).
fof(cp2,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('GEO006+2.ax',cp2) ).
fof(cup1,axiom,
! [X,Y,Z] :
( distinct_lines(Y,Z)
=> ( convergent_lines(Y,Z)
| apart_point_and_line(X,Z)
| apart_point_and_line(X,Y) ) ),
file('GEO006+2.ax',cup1) ).
fof(occu1,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('GEO006+3.ax',occu1) ).
fof(oac1,axiom,
! [L,M,N] :
( ( unorthogonal_lines(L,M)
& convergent_lines(L,M) )
=> ( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) ) ) ),
file('GEO006+3.ax',oac1) ).
fof(ooc1,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('GEO006+3.ax',ooc1) ).
fof(ooc2,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('GEO006+3.ax',ooc2) ).
fof(ouo1,axiom,
! [A,L,M,N] :
( distinct_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L) ) ),
file('GEO006+3.ax',ouo1) ).
fof(coipo1,axiom,
! [L,M] :
~ ( ~ unorthogonal_lines(L,M)
& ~ convergent_lines(L,M) ),
file('GEO006+4.ax',coipo1) ).
fof(cotno1,axiom,
! [L,M,N] :
( ( ( ~ unorthogonal_lines(L,N)
| ~ convergent_lines(L,N) )
& ( ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ) )
=> ( ~ unorthogonal_lines(M,N)
| ~ convergent_lines(M,N) ) ),
file('GEO006+4.ax',cotno1) ).
fof(couo1,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ convergent_lines(M,N) ),
file('GEO006+4.ax',couo1) ).
fof(con1,axiom,
! [A,B] :
( ( distinct_points(A,B)
& point(B)
& point(A) )
=> line(line_connecting(A,B)) ),
file('GEO006+5.ax',con1) ).
fof(int1,axiom,
! [L,M] :
( ( convergent_lines(L,M)
& line(M)
& line(L) )
=> point(intersection_point(L,M)) ),
file('GEO006+5.ax',int1) ).
fof(par1,axiom,
! [L,A] :
( ( point(A)
& line(L) )
=> line(parallel_through_point(L,A)) ),
file('GEO006+5.ax',par1) ).
fof(orth1,axiom,
! [L,A] :
( ( point(A)
& line(L) )
=> line(orthogonal_through_point(L,A)) ),
file('GEO006+5.ax',orth1) ).
fof(ax1,axiom,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,Y) ),
file('GEO006+6.ax',ax1) ).
fof(ax2,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('GEO006+6.ax',ax2) ).
fof(a3,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ),
file('GEO006+6.ax',a3) ).
fof(a4,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('GEO006+6.ax',a4) ).
fof(a5,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ),
file('GEO006+6.ax',a5) ).
fof(con,conjecture,
! [X,Y] :
( convergent_lines(X,Y)
=> equal_points(intersection_point(X,Y),intersection_point(Y,X)) ),
file('theBenchmark.p',con) ).
fof(f_1_1,plain,
! [X] : ~ distinct_points(X,X),
inference(fof_nnf,[status(thm)],[apart1]) ).
fof(f_1_2,plain,
! [U_0] : ~ distinct_points(U_0,U_0),
inference(variable_rename,[status(thm)],[f_1_1]) ).
cnf(f_1_3,plain,
~ distinct_points(U_0,U_0),
inference(clausify,[status(thm)],[f_1_2]) ).
fof(f_2_1,plain,
! [X] : ~ distinct_lines(X,X),
inference(fof_nnf,[status(thm)],[apart2]) ).
fof(f_2_2,plain,
! [U_1] : ~ distinct_lines(U_1,U_1),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
~ distinct_lines(U_1,U_1),
inference(clausify,[status(thm)],[f_2_2]) ).
fof(f_3_1,plain,
! [X] : ~ convergent_lines(X,X),
inference(fof_nnf,[status(thm)],[apart3]) ).
fof(f_3_2,plain,
! [U_2] : ~ convergent_lines(U_2,U_2),
inference(variable_rename,[status(thm)],[f_3_1]) ).
cnf(f_3_3,plain,
~ convergent_lines(U_2,U_2),
inference(clausify,[status(thm)],[f_3_2]) ).
fof(f_4_1,plain,
! [X,Y,Z] :
( distinct_points(Y,Z)
| distinct_points(X,Z)
| ~ distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[apart4]) ).
fof(f_4_2,plain,
! [U_5,U_4,U_3] :
( distinct_points(U_4,U_3)
| distinct_points(U_5,U_3)
| ~ distinct_points(U_5,U_4) ),
inference(variable_rename,[status(thm)],[f_4_1]) ).
fof(f_4_3,plain,
! [U_5,U_4] :
( ! [U_3] :
( distinct_points(U_4,U_3)
| distinct_points(U_5,U_3) )
| ~ distinct_points(U_5,U_4) ),
inference(miniscope,[status(thm)],[f_4_2]) ).
cnf(f_4_4,plain,
( distinct_points(U_4,U_3)
| distinct_points(U_5,U_3)
| ~ distinct_points(U_5,U_4) ),
inference(clausify,[status(thm)],[f_4_3]) ).
fof(f_5_1,plain,
! [X,Y,Z] :
( distinct_lines(Y,Z)
| distinct_lines(X,Z)
| ~ distinct_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[apart5]) ).
fof(f_5_2,plain,
! [U_8,U_7,U_6] :
( distinct_lines(U_7,U_6)
| distinct_lines(U_8,U_6)
| ~ distinct_lines(U_8,U_7) ),
inference(variable_rename,[status(thm)],[f_5_1]) ).
fof(f_5_3,plain,
! [U_8,U_7] :
( ! [U_6] :
( distinct_lines(U_7,U_6)
| distinct_lines(U_8,U_6) )
| ~ distinct_lines(U_8,U_7) ),
inference(miniscope,[status(thm)],[f_5_2]) ).
cnf(f_5_4,plain,
( distinct_lines(U_7,U_6)
| distinct_lines(U_8,U_6)
| ~ distinct_lines(U_8,U_7) ),
inference(clausify,[status(thm)],[f_5_3]) ).
fof(f_6_1,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| convergent_lines(X,Z)
| ~ convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[ax6]) ).
fof(f_6_2,plain,
! [U_11,U_10,U_9] :
( convergent_lines(U_10,U_9)
| convergent_lines(U_11,U_9)
| ~ convergent_lines(U_11,U_10) ),
inference(variable_rename,[status(thm)],[f_6_1]) ).
fof(f_6_3,plain,
! [U_11,U_10] :
( ! [U_9] :
( convergent_lines(U_10,U_9)
| convergent_lines(U_11,U_9) )
| ~ convergent_lines(U_11,U_10) ),
inference(miniscope,[status(thm)],[f_6_2]) ).
cnf(f_6_4,plain,
( convergent_lines(U_10,U_9)
| convergent_lines(U_11,U_9)
| ~ convergent_lines(U_11,U_10) ),
inference(clausify,[status(thm)],[f_6_3]) ).
fof(f_7_1,plain,
! [X,Y] :
( ~ apart_point_and_line(X,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[ci1]) ).
fof(f_7_2,plain,
! [U_13,U_12] :
( ~ apart_point_and_line(U_13,line_connecting(U_13,U_12))
| ~ distinct_points(U_13,U_12) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
cnf(f_7_3,plain,
( ~ apart_point_and_line(U_13,line_connecting(U_13,U_12))
| ~ distinct_points(U_13,U_12) ),
inference(clausify,[status(thm)],[f_7_2]) ).
fof(f_8_1,plain,
! [X,Y] :
( ~ apart_point_and_line(Y,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[ci2]) ).
fof(f_8_2,plain,
! [U_15,U_14] :
( ~ apart_point_and_line(U_14,line_connecting(U_15,U_14))
| ~ distinct_points(U_15,U_14) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
cnf(f_8_3,plain,
( ~ apart_point_and_line(U_14,line_connecting(U_15,U_14))
| ~ distinct_points(U_15,U_14) ),
inference(clausify,[status(thm)],[f_8_2]) ).
fof(f_9_1,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),X)
| ~ convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[ci3]) ).
fof(f_9_2,plain,
! [U_17,U_16] :
( ~ apart_point_and_line(intersection_point(U_17,U_16),U_17)
| ~ convergent_lines(U_17,U_16) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( ~ apart_point_and_line(intersection_point(U_17,U_16),U_17)
| ~ convergent_lines(U_17,U_16) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_1,plain,
! [X,Y] :
( ~ apart_point_and_line(intersection_point(X,Y),Y)
| ~ convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[ci4]) ).
fof(f_10_2,plain,
! [U_19,U_18] :
( ~ apart_point_and_line(intersection_point(U_19,U_18),U_18)
| ~ convergent_lines(U_19,U_18) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
( ~ apart_point_and_line(intersection_point(U_19,U_18),U_18)
| ~ convergent_lines(U_19,U_18) ),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_11_1,plain,
! [X,Y,U,V] :
( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U)
| ~ distinct_lines(U,V)
| ~ distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[cu1]) ).
fof(f_11_2,plain,
! [U_23,U_22,U_21,U_20] :
( apart_point_and_line(U_22,U_20)
| apart_point_and_line(U_22,U_21)
| apart_point_and_line(U_23,U_20)
| apart_point_and_line(U_23,U_21)
| ~ distinct_lines(U_21,U_20)
| ~ distinct_points(U_23,U_22) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
( apart_point_and_line(U_22,U_20)
| apart_point_and_line(U_22,U_21)
| apart_point_and_line(U_23,U_20)
| apart_point_and_line(U_23,U_21)
| ~ distinct_lines(U_21,U_20)
| ~ distinct_points(U_23,U_22) ),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_12_1,plain,
! [X,Y,Z] :
( apart_point_and_line(Z,Y)
| distinct_points(X,Z)
| ~ apart_point_and_line(X,Y) ),
inference(fof_nnf,[status(thm)],[ceq1]) ).
fof(f_12_2,plain,
! [U_26,U_25,U_24] :
( apart_point_and_line(U_24,U_25)
| distinct_points(U_26,U_24)
| ~ apart_point_and_line(U_26,U_25) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
fof(f_12_3,plain,
! [U_26,U_25] :
( ! [U_24] :
( apart_point_and_line(U_24,U_25)
| distinct_points(U_26,U_24) )
| ~ apart_point_and_line(U_26,U_25) ),
inference(miniscope,[status(thm)],[f_12_2]) ).
cnf(f_12_4,plain,
( apart_point_and_line(U_24,U_25)
| distinct_points(U_26,U_24)
| ~ apart_point_and_line(U_26,U_25) ),
inference(clausify,[status(thm)],[f_12_3]) ).
fof(f_13_1,plain,
! [X,Y,Z] :
( apart_point_and_line(X,Z)
| distinct_lines(Y,Z)
| ~ apart_point_and_line(X,Y) ),
inference(fof_nnf,[status(thm)],[ceq2]) ).
fof(f_13_2,plain,
! [U_29,U_28,U_27] :
( apart_point_and_line(U_29,U_27)
| distinct_lines(U_28,U_27)
| ~ apart_point_and_line(U_29,U_28) ),
inference(variable_rename,[status(thm)],[f_13_1]) ).
fof(f_13_3,plain,
! [U_29,U_28] :
( ! [U_27] :
( apart_point_and_line(U_29,U_27)
| distinct_lines(U_28,U_27) )
| ~ apart_point_and_line(U_29,U_28) ),
inference(miniscope,[status(thm)],[f_13_2]) ).
cnf(f_13_4,plain,
( apart_point_and_line(U_29,U_27)
| distinct_lines(U_28,U_27)
| ~ apart_point_and_line(U_29,U_28) ),
inference(clausify,[status(thm)],[f_13_3]) ).
fof(f_14_1,plain,
! [X,Y,Z] :
( convergent_lines(X,Z)
| distinct_lines(Y,Z)
| ~ convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[ceq3]) ).
fof(f_14_2,plain,
! [U_32,U_31,U_30] :
( convergent_lines(U_32,U_30)
| distinct_lines(U_31,U_30)
| ~ convergent_lines(U_32,U_31) ),
inference(variable_rename,[status(thm)],[f_14_1]) ).
fof(f_14_3,plain,
! [U_32,U_31] :
( ! [U_30] :
( convergent_lines(U_32,U_30)
| distinct_lines(U_31,U_30) )
| ~ convergent_lines(U_32,U_31) ),
inference(miniscope,[status(thm)],[f_14_2]) ).
cnf(f_14_4,plain,
( convergent_lines(U_32,U_30)
| distinct_lines(U_31,U_30)
| ~ convergent_lines(U_32,U_31) ),
inference(clausify,[status(thm)],[f_14_3]) ).
fof(f_15_1,plain,
! [X,Y] :
( convergent_lines(X,Y)
| ~ distinct_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[p1]) ).
fof(f_15_2,plain,
! [U_34,U_33] :
( convergent_lines(U_34,U_33)
| ~ distinct_lines(U_34,U_33) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( convergent_lines(U_34,U_33)
| ~ distinct_lines(U_34,U_33) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(fof_nnf,[status(thm)],[cp1]) ).
fof(f_16_2,plain,
! [U_36,U_35] : ~ convergent_lines(parallel_through_point(U_35,U_36),U_35),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
~ convergent_lines(parallel_through_point(U_35,U_36),U_35),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(fof_nnf,[status(thm)],[cp2]) ).
fof(f_17_2,plain,
! [U_38,U_37] : ~ apart_point_and_line(U_38,parallel_through_point(U_37,U_38)),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
~ apart_point_and_line(U_38,parallel_through_point(U_37,U_38)),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [X,Y,Z] :
( convergent_lines(Y,Z)
| apart_point_and_line(X,Z)
| apart_point_and_line(X,Y)
| ~ distinct_lines(Y,Z) ),
inference(fof_nnf,[status(thm)],[cup1]) ).
fof(f_18_2,plain,
! [U_41,U_40,U_39] :
( convergent_lines(U_40,U_39)
| apart_point_and_line(U_41,U_39)
| apart_point_and_line(U_41,U_40)
| ~ distinct_lines(U_40,U_39) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( convergent_lines(U_40,U_39)
| apart_point_and_line(U_41,U_39)
| apart_point_and_line(U_41,U_40)
| ~ distinct_lines(U_40,U_39) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(fof_nnf,[status(thm)],[occu1]) ).
fof(f_19_2,plain,
! [U_43,U_42] :
( unorthogonal_lines(U_43,U_42)
| convergent_lines(U_43,U_42) ),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
( unorthogonal_lines(U_43,U_42)
| convergent_lines(U_43,U_42) ),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_1,plain,
! [L,M,N] :
( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ),
inference(fof_nnf,[status(thm)],[oac1]) ).
fof(f_20_2,plain,
! [U_46,U_45,U_44] :
( ( unorthogonal_lines(U_45,U_44)
& convergent_lines(U_45,U_44) )
| ( unorthogonal_lines(U_46,U_44)
& convergent_lines(U_46,U_44) )
| ~ unorthogonal_lines(U_46,U_45)
| ~ convergent_lines(U_46,U_45) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_46,U_45] :
( ! [U_44] :
( ( unorthogonal_lines(U_45,U_44)
& convergent_lines(U_45,U_44) )
| ( unorthogonal_lines(U_46,U_44)
& convergent_lines(U_46,U_44) ) )
| ~ unorthogonal_lines(U_46,U_45)
| ~ convergent_lines(U_46,U_45) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( convergent_lines(U_45,U_44)
| convergent_lines(U_46,U_44)
| ~ unorthogonal_lines(U_46,U_45)
| ~ convergent_lines(U_46,U_45) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_5,plain,
( unorthogonal_lines(U_45,U_44)
| convergent_lines(U_46,U_44)
| ~ unorthogonal_lines(U_46,U_45)
| ~ convergent_lines(U_46,U_45) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_6,plain,
( convergent_lines(U_45,U_44)
| unorthogonal_lines(U_46,U_44)
| ~ unorthogonal_lines(U_46,U_45)
| ~ convergent_lines(U_46,U_45) ),
inference(clausify,[status(thm)],[f_20_3]) ).
cnf(f_20_7,plain,
( unorthogonal_lines(U_45,U_44)
| unorthogonal_lines(U_46,U_44)
| ~ unorthogonal_lines(U_46,U_45)
| ~ convergent_lines(U_46,U_45) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(fof_nnf,[status(thm)],[ooc1]) ).
fof(f_21_2,plain,
! [U_48,U_47] : ~ unorthogonal_lines(orthogonal_through_point(U_47,U_48),U_47),
inference(variable_rename,[status(thm)],[f_21_1]) ).
cnf(f_21_3,plain,
~ unorthogonal_lines(orthogonal_through_point(U_47,U_48),U_47),
inference(clausify,[status(thm)],[f_21_2]) ).
fof(f_22_1,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(fof_nnf,[status(thm)],[ooc2]) ).
fof(f_22_2,plain,
! [U_50,U_49] : ~ apart_point_and_line(U_50,orthogonal_through_point(U_49,U_50)),
inference(variable_rename,[status(thm)],[f_22_1]) ).
cnf(f_22_3,plain,
~ apart_point_and_line(U_50,orthogonal_through_point(U_49,U_50)),
inference(clausify,[status(thm)],[f_22_2]) ).
fof(f_23_1,plain,
! [A,L,M,N] :
( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L)
| ~ distinct_lines(L,M) ),
inference(fof_nnf,[status(thm)],[ouo1]) ).
fof(f_23_2,plain,
! [U_54,U_53,U_52,U_51] :
( unorthogonal_lines(U_52,U_51)
| unorthogonal_lines(U_53,U_51)
| apart_point_and_line(U_54,U_52)
| apart_point_and_line(U_54,U_53)
| ~ distinct_lines(U_53,U_52) ),
inference(variable_rename,[status(thm)],[f_23_1]) ).
fof(f_23_3,plain,
! [U_54,U_53,U_52] :
( ! [U_51] :
( unorthogonal_lines(U_52,U_51)
| unorthogonal_lines(U_53,U_51) )
| apart_point_and_line(U_54,U_52)
| apart_point_and_line(U_54,U_53)
| ~ distinct_lines(U_53,U_52) ),
inference(miniscope,[status(thm)],[f_23_2]) ).
cnf(f_23_4,plain,
( unorthogonal_lines(U_52,U_51)
| unorthogonal_lines(U_53,U_51)
| apart_point_and_line(U_54,U_52)
| apart_point_and_line(U_54,U_53)
| ~ distinct_lines(U_53,U_52) ),
inference(clausify,[status(thm)],[f_23_3]) ).
fof(f_24_1,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(fof_nnf,[status(thm)],[coipo1]) ).
fof(f_24_2,plain,
! [U_56,U_55] :
( unorthogonal_lines(U_56,U_55)
| convergent_lines(U_56,U_55) ),
inference(variable_rename,[status(thm)],[f_24_1]) ).
cnf(f_24_3,plain,
( unorthogonal_lines(U_56,U_55)
| convergent_lines(U_56,U_55) ),
inference(clausify,[status(thm)],[f_24_2]) ).
fof(f_25_1,plain,
! [L,M,N] :
( ~ unorthogonal_lines(M,N)
| ~ convergent_lines(M,N)
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| ( unorthogonal_lines(L,M)
& convergent_lines(L,M) ) ),
inference(fof_nnf,[status(thm)],[cotno1]) ).
fof(f_25_2,plain,
! [U_59,U_58,U_57] :
( ~ unorthogonal_lines(U_58,U_57)
| ~ convergent_lines(U_58,U_57)
| ( unorthogonal_lines(U_59,U_57)
& convergent_lines(U_59,U_57) )
| ( unorthogonal_lines(U_59,U_58)
& convergent_lines(U_59,U_58) ) ),
inference(variable_rename,[status(thm)],[f_25_1]) ).
cnf(f_25_3,plain,
( convergent_lines(U_59,U_57)
| convergent_lines(U_59,U_58)
| ~ unorthogonal_lines(U_58,U_57)
| ~ convergent_lines(U_58,U_57) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_4,plain,
( unorthogonal_lines(U_59,U_57)
| convergent_lines(U_59,U_58)
| ~ unorthogonal_lines(U_58,U_57)
| ~ convergent_lines(U_58,U_57) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_5,plain,
( convergent_lines(U_59,U_57)
| unorthogonal_lines(U_59,U_58)
| ~ unorthogonal_lines(U_58,U_57)
| ~ convergent_lines(U_58,U_57) ),
inference(clausify,[status(thm)],[f_25_2]) ).
cnf(f_25_6,plain,
( unorthogonal_lines(U_59,U_57)
| unorthogonal_lines(U_59,U_58)
| ~ unorthogonal_lines(U_58,U_57)
| ~ convergent_lines(U_58,U_57) ),
inference(clausify,[status(thm)],[f_25_2]) ).
fof(f_26_1,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(fof_nnf,[status(thm)],[couo1]) ).
fof(f_26_2,plain,
! [U_62,U_61,U_60] :
( ~ convergent_lines(U_61,U_60)
| unorthogonal_lines(U_62,U_60)
| unorthogonal_lines(U_62,U_61) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( ~ convergent_lines(U_61,U_60)
| unorthogonal_lines(U_62,U_60)
| unorthogonal_lines(U_62,U_61) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_27_1,plain,
! [A,B] :
( line(line_connecting(A,B))
| ~ distinct_points(A,B)
| ~ point(B)
| ~ point(A) ),
inference(fof_nnf,[status(thm)],[con1]) ).
fof(f_27_2,plain,
! [U_64,U_63] :
( line(line_connecting(U_64,U_63))
| ~ distinct_points(U_64,U_63)
| ~ point(U_63)
| ~ point(U_64) ),
inference(variable_rename,[status(thm)],[f_27_1]) ).
cnf(f_27_3,plain,
( line(line_connecting(U_64,U_63))
| ~ distinct_points(U_64,U_63)
| ~ point(U_63)
| ~ point(U_64) ),
inference(clausify,[status(thm)],[f_27_2]) ).
fof(f_28_1,plain,
! [L,M] :
( point(intersection_point(L,M))
| ~ convergent_lines(L,M)
| ~ line(M)
| ~ line(L) ),
inference(fof_nnf,[status(thm)],[int1]) ).
fof(f_28_2,plain,
! [U_66,U_65] :
( point(intersection_point(U_66,U_65))
| ~ convergent_lines(U_66,U_65)
| ~ line(U_65)
| ~ line(U_66) ),
inference(variable_rename,[status(thm)],[f_28_1]) ).
cnf(f_28_3,plain,
( point(intersection_point(U_66,U_65))
| ~ convergent_lines(U_66,U_65)
| ~ line(U_65)
| ~ line(U_66) ),
inference(clausify,[status(thm)],[f_28_2]) ).
fof(f_29_1,plain,
! [L,A] :
( line(parallel_through_point(L,A))
| ~ point(A)
| ~ line(L) ),
inference(fof_nnf,[status(thm)],[par1]) ).
fof(f_29_2,plain,
! [U_68,U_67] :
( line(parallel_through_point(U_68,U_67))
| ~ point(U_67)
| ~ line(U_68) ),
inference(variable_rename,[status(thm)],[f_29_1]) ).
cnf(f_29_3,plain,
( line(parallel_through_point(U_68,U_67))
| ~ point(U_67)
| ~ line(U_68) ),
inference(clausify,[status(thm)],[f_29_2]) ).
fof(f_30_1,plain,
! [L,A] :
( line(orthogonal_through_point(L,A))
| ~ point(A)
| ~ line(L) ),
inference(fof_nnf,[status(thm)],[orth1]) ).
fof(f_30_2,plain,
! [U_70,U_69] :
( line(orthogonal_through_point(U_70,U_69))
| ~ point(U_69)
| ~ line(U_70) ),
inference(variable_rename,[status(thm)],[f_30_1]) ).
cnf(f_30_3,plain,
( line(orthogonal_through_point(U_70,U_69))
| ~ point(U_69)
| ~ line(U_70) ),
inference(clausify,[status(thm)],[f_30_2]) ).
fof(f_31_1,plain,
! [X,Y] :
( ( equal_points(X,Y)
| distinct_points(X,Y) )
& ( ~ distinct_points(X,Y)
| ~ equal_points(X,Y) ) ),
inference(fof_nnf,[status(thm)],[ax1]) ).
fof(f_31_2,plain,
! [U_72,U_71] :
( ( equal_points(U_72,U_71)
| distinct_points(U_72,U_71) )
& ( ~ distinct_points(U_72,U_71)
| ~ equal_points(U_72,U_71) ) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
( ! [U_76,U_74] :
( equal_points(U_76,U_74)
| distinct_points(U_76,U_74) )
& ! [U_75,U_73] :
( ~ distinct_points(U_75,U_73)
| ~ equal_points(U_75,U_73) ) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( ~ distinct_points(U_75,U_73)
| ~ equal_points(U_75,U_73) ),
inference(clausify,[status(thm)],[f_31_3]) ).
cnf(f_31_5,plain,
( equal_points(U_76,U_74)
| distinct_points(U_76,U_74) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,plain,
! [X,Y] :
( ( equal_lines(X,Y)
| distinct_lines(X,Y) )
& ( ~ distinct_lines(X,Y)
| ~ equal_lines(X,Y) ) ),
inference(fof_nnf,[status(thm)],[ax2]) ).
fof(f_32_2,plain,
! [U_78,U_77] :
( ( equal_lines(U_78,U_77)
| distinct_lines(U_78,U_77) )
& ( ~ distinct_lines(U_78,U_77)
| ~ equal_lines(U_78,U_77) ) ),
inference(variable_rename,[status(thm)],[f_32_1]) ).
fof(f_32_3,plain,
( ! [U_82,U_80] :
( equal_lines(U_82,U_80)
| distinct_lines(U_82,U_80) )
& ! [U_81,U_79] :
( ~ distinct_lines(U_81,U_79)
| ~ equal_lines(U_81,U_79) ) ),
inference(miniscope,[status(thm)],[f_32_2]) ).
cnf(f_32_4,plain,
( ~ distinct_lines(U_81,U_79)
| ~ equal_lines(U_81,U_79) ),
inference(clausify,[status(thm)],[f_32_3]) ).
cnf(f_32_5,plain,
( equal_lines(U_82,U_80)
| distinct_lines(U_82,U_80) ),
inference(clausify,[status(thm)],[f_32_3]) ).
fof(f_33_1,plain,
! [X,Y] :
( ( parallel_lines(X,Y)
| convergent_lines(X,Y) )
& ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ) ),
inference(fof_nnf,[status(thm)],[a3]) ).
fof(f_33_2,plain,
! [U_84,U_83] :
( ( parallel_lines(U_84,U_83)
| convergent_lines(U_84,U_83) )
& ( ~ convergent_lines(U_84,U_83)
| ~ parallel_lines(U_84,U_83) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_88,U_86] :
( parallel_lines(U_88,U_86)
| convergent_lines(U_88,U_86) )
& ! [U_87,U_85] :
( ~ convergent_lines(U_87,U_85)
| ~ parallel_lines(U_87,U_85) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
cnf(f_33_4,plain,
( ~ convergent_lines(U_87,U_85)
| ~ parallel_lines(U_87,U_85) ),
inference(clausify,[status(thm)],[f_33_3]) ).
cnf(f_33_5,plain,
( parallel_lines(U_88,U_86)
| convergent_lines(U_88,U_86) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_34_1,plain,
! [X,Y] :
( ( incident_point_and_line(X,Y)
| apart_point_and_line(X,Y) )
& ( ~ apart_point_and_line(X,Y)
| ~ incident_point_and_line(X,Y) ) ),
inference(fof_nnf,[status(thm)],[a4]) ).
fof(f_34_2,plain,
! [U_90,U_89] :
( ( incident_point_and_line(U_90,U_89)
| apart_point_and_line(U_90,U_89) )
& ( ~ apart_point_and_line(U_90,U_89)
| ~ incident_point_and_line(U_90,U_89) ) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
fof(f_34_3,plain,
( ! [U_94,U_92] :
( incident_point_and_line(U_94,U_92)
| apart_point_and_line(U_94,U_92) )
& ! [U_93,U_91] :
( ~ apart_point_and_line(U_93,U_91)
| ~ incident_point_and_line(U_93,U_91) ) ),
inference(miniscope,[status(thm)],[f_34_2]) ).
cnf(f_34_4,plain,
( ~ apart_point_and_line(U_93,U_91)
| ~ incident_point_and_line(U_93,U_91) ),
inference(clausify,[status(thm)],[f_34_3]) ).
cnf(f_34_5,plain,
( incident_point_and_line(U_94,U_92)
| apart_point_and_line(U_94,U_92) ),
inference(clausify,[status(thm)],[f_34_3]) ).
fof(f_35_1,plain,
! [X,Y] :
( ( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) )
& ( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(fof_nnf,[status(thm)],[a5]) ).
fof(f_35_2,plain,
! [U_96,U_95] :
( ( orthogonal_lines(U_96,U_95)
| unorthogonal_lines(U_96,U_95) )
& ( ~ unorthogonal_lines(U_96,U_95)
| ~ orthogonal_lines(U_96,U_95) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_100,U_98] :
( orthogonal_lines(U_100,U_98)
| unorthogonal_lines(U_100,U_98) )
& ! [U_99,U_97] :
( ~ unorthogonal_lines(U_99,U_97)
| ~ orthogonal_lines(U_99,U_97) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( ~ unorthogonal_lines(U_99,U_97)
| ~ orthogonal_lines(U_99,U_97) ),
inference(clausify,[status(thm)],[f_35_3]) ).
cnf(f_35_5,plain,
( orthogonal_lines(U_100,U_98)
| unorthogonal_lines(U_100,U_98) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,negated_conjecture,
~ ! [X,Y] :
( convergent_lines(X,Y)
=> equal_points(intersection_point(X,Y),intersection_point(Y,X)) ),
inference(negate,[status(cth)],[con]) ).
fof(f_36_2,negated_conjecture,
? [X,Y] :
( ~ equal_points(intersection_point(X,Y),intersection_point(Y,X))
& convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[f_36_1]) ).
fof(f_36_3,negated_conjecture,
? [U_102,U_101] :
( ~ equal_points(intersection_point(U_102,U_101),intersection_point(U_101,U_102))
& convergent_lines(U_102,U_101) ),
inference(variable_rename,[status(thm)],[f_36_2]) ).
fof(f_36_4,negated_conjecture,
? [U_101] :
( ~ equal_points(intersection_point(sK1,U_101),intersection_point(U_101,sK1))
& convergent_lines(sK1,U_101) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_102,sK1)],[f_36_3]) ).
fof(f_36_5,negated_conjecture,
( ~ equal_points(intersection_point(sK1,sK2),intersection_point(sK2,sK1))
& convergent_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_101,sK2)],[f_36_4]) ).
fof(f_36_6,negated_conjecture,
( ~ equal_points(intersection_point(sK1,sK2),intersection_point(sK2,sK1))
& convergent_lines(sK1,sK2) ),
inference(definitional_conversion,[status(esa)],[f_36_5]) ).
cnf(f_36_7,negated_conjecture,
convergent_lines(sK1,sK2),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(f_36_8,negated_conjecture,
~ equal_points(intersection_point(sK1,sK2),intersection_point(sK2,sK1)),
inference(clausify,[status(thm)],[f_36_6]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO201+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
% 0.08/0.36 % Computer : n016.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Sat Sep 19 07:45:52 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.79/1.12 % SZS status Theorem for theBenchmark
% 0.79/1.12 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------