%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO225+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n015.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 08:40:00 AM UTC 2026
% Result : Theorem 0.09s 0.39s
% Output : Proof 0.09s
% 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(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(con,conjecture,
! [A,B] :
( ( distinct_points(A,B)
& point(B)
& point(A) )
=> ? [X] :
( line(X)
=> ( ~ apart_point_and_line(B,X)
& ~ apart_point_and_line(A,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,
! [A,B] :
( line(line_connecting(A,B))
| ~ distinct_points(A,B)
| ~ point(B)
| ~ point(A) ),
inference(fof_nnf,[status(thm)],[con1]) ).
fof(f_15_2,plain,
! [U_34,U_33] :
( line(line_connecting(U_34,U_33))
| ~ distinct_points(U_34,U_33)
| ~ point(U_33)
| ~ point(U_34) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( line(line_connecting(U_34,U_33))
| ~ distinct_points(U_34,U_33)
| ~ point(U_33)
| ~ point(U_34) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_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_16_2,plain,
! [U_36,U_35] :
( point(intersection_point(U_36,U_35))
| ~ convergent_lines(U_36,U_35)
| ~ line(U_35)
| ~ line(U_36) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( point(intersection_point(U_36,U_35))
| ~ convergent_lines(U_36,U_35)
| ~ line(U_35)
| ~ line(U_36) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [L,A] :
( line(parallel_through_point(L,A))
| ~ point(A)
| ~ line(L) ),
inference(fof_nnf,[status(thm)],[par1]) ).
fof(f_17_2,plain,
! [U_38,U_37] :
( line(parallel_through_point(U_38,U_37))
| ~ point(U_37)
| ~ line(U_38) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
cnf(f_17_3,plain,
( line(parallel_through_point(U_38,U_37))
| ~ point(U_37)
| ~ line(U_38) ),
inference(clausify,[status(thm)],[f_17_2]) ).
fof(f_18_1,plain,
! [L,A] :
( line(orthogonal_through_point(L,A))
| ~ point(A)
| ~ line(L) ),
inference(fof_nnf,[status(thm)],[orth1]) ).
fof(f_18_2,plain,
! [U_40,U_39] :
( line(orthogonal_through_point(U_40,U_39))
| ~ point(U_39)
| ~ line(U_40) ),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
( line(orthogonal_through_point(U_40,U_39))
| ~ point(U_39)
| ~ line(U_40) ),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,negated_conjecture,
~ ! [A,B] :
( ( distinct_points(A,B)
& point(B)
& point(A) )
=> ? [X] :
( line(X)
=> ( ~ apart_point_and_line(B,X)
& ~ apart_point_and_line(A,X) ) ) ),
inference(negate,[status(cth)],[con]) ).
fof(f_19_2,negated_conjecture,
? [A,B] :
( ! [X] :
( ( apart_point_and_line(B,X)
| apart_point_and_line(A,X) )
& line(X) )
& distinct_points(A,B)
& point(B)
& point(A) ),
inference(fof_nnf,[status(thm)],[f_19_1]) ).
fof(f_19_3,negated_conjecture,
? [U_43,U_42] :
( ! [U_41] :
( ( apart_point_and_line(U_42,U_41)
| apart_point_and_line(U_43,U_41) )
& line(U_41) )
& distinct_points(U_43,U_42)
& point(U_42)
& point(U_43) ),
inference(variable_rename,[status(thm)],[f_19_2]) ).
fof(f_19_4,negated_conjecture,
? [U_43,U_42] :
( ! [U_45] :
( apart_point_and_line(U_42,U_45)
| apart_point_and_line(U_43,U_45) )
& ! [U_44] : line(U_44)
& distinct_points(U_43,U_42)
& point(U_42)
& point(U_43) ),
inference(miniscope,[status(thm)],[f_19_3]) ).
fof(f_19_5,negated_conjecture,
? [U_42] :
( ! [U_45] :
( apart_point_and_line(U_42,U_45)
| apart_point_and_line(sK1,U_45) )
& ! [U_44] : line(U_44)
& distinct_points(sK1,U_42)
& point(U_42)
& point(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_43,sK1)],[f_19_4]) ).
fof(f_19_6,negated_conjecture,
( ! [U_45] :
( apart_point_and_line(sK2,U_45)
| apart_point_and_line(sK1,U_45) )
& ! [U_44] : line(U_44)
& distinct_points(sK1,sK2)
& point(sK2)
& point(sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_42,sK2)],[f_19_5]) ).
fof(f_19_7,negated_conjecture,
( ! [U_45] :
( apart_point_and_line(sK2,U_45)
| apart_point_and_line(sK1,U_45) )
& ! [U_44] : line(U_44)
& distinct_points(sK1,sK2)
& point(sK2)
& point(sK1) ),
inference(definitional_conversion,[status(esa)],[f_19_6]) ).
cnf(f_19_8,negated_conjecture,
point(sK1),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_9,negated_conjecture,
point(sK2),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_10,negated_conjecture,
distinct_points(sK1,sK2),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_11,negated_conjecture,
line(U_44),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(f_19_12,negated_conjecture,
( apart_point_and_line(sK2,U_45)
| apart_point_and_line(sK1,U_45) ),
inference(clausify,[status(thm)],[f_19_7]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO225+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.04 % Command : /export/starexec/sandbox2/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.34 % Computer : n015.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 19 07:45:03 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.39 % SZS status Theorem for theBenchmark
% 0.09/0.39 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------