%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO209+2 : 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 : n001.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 08:39:54 AM UTC 2026
% Result : Theorem 0.08s 5.39s
% Output : Proof 0.08s
% Verified :
% SZS Type : ERROR: Analysing output (MakeTreeStats fails)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X),
file('GEO008+0.ax',apart1) ).
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X),
file('GEO008+0.ax',apart2) ).
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('GEO008+0.ax',apart3) ).
fof(apart4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('GEO008+0.ax',apart4) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('GEO008+0.ax',apart5) ).
fof(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('GEO008+0.ax',apart6) ).
fof(con1,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ) ),
file('GEO008+0.ax',con1) ).
fof(con2,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,Y)
| apart_point_and_line(Z,X) )
=> distinct_points(Z,intersection_point(X,Y)) ) ),
file('GEO008+0.ax',con2) ).
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('GEO008+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('GEO008+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('GEO008+0.ax',ceq2) ).
fof(ceq3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('GEO008+0.ax',ceq3) ).
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(con,conjecture,
! [A,L,M,N] :
( ( ~ convergent_lines(N,L)
& ~ convergent_lines(M,L)
& ~ apart_point_and_line(A,N)
& ~ apart_point_and_line(A,M)
& apart_point_and_line(A,L) )
=> ~ distinct_lines(M,N) ),
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)],[apart6]) ).
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,Z] :
( ( distinct_points(Z,Y)
& distinct_points(Z,X) )
| ~ apart_point_and_line(Z,line_connecting(X,Y))
| ~ distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con1]) ).
fof(f_7_2,plain,
! [U_14,U_13,U_12] :
( ( distinct_points(U_12,U_13)
& distinct_points(U_12,U_14) )
| ~ apart_point_and_line(U_12,line_connecting(U_14,U_13))
| ~ distinct_points(U_14,U_13) ),
inference(variable_rename,[status(thm)],[f_7_1]) ).
fof(f_7_3,plain,
! [U_14,U_13] :
( ! [U_12] :
( ( distinct_points(U_12,U_13)
& distinct_points(U_12,U_14) )
| ~ apart_point_and_line(U_12,line_connecting(U_14,U_13)) )
| ~ distinct_points(U_14,U_13) ),
inference(miniscope,[status(thm)],[f_7_2]) ).
cnf(f_7_4,plain,
( distinct_points(U_12,U_14)
| ~ apart_point_and_line(U_12,line_connecting(U_14,U_13))
| ~ distinct_points(U_14,U_13) ),
inference(clausify,[status(thm)],[f_7_3]) ).
cnf(f_7_5,plain,
( distinct_points(U_12,U_13)
| ~ apart_point_and_line(U_12,line_connecting(U_14,U_13))
| ~ distinct_points(U_14,U_13) ),
inference(clausify,[status(thm)],[f_7_3]) ).
fof(f_8_1,plain,
! [X,Y,Z] :
( distinct_points(Z,intersection_point(X,Y))
| ( ~ apart_point_and_line(Z,Y)
& ~ apart_point_and_line(Z,X) )
| ~ convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[con2]) ).
fof(f_8_2,plain,
! [U_17,U_16,U_15] :
( distinct_points(U_15,intersection_point(U_17,U_16))
| ( ~ apart_point_and_line(U_15,U_16)
& ~ apart_point_and_line(U_15,U_17) )
| ~ convergent_lines(U_17,U_16) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
! [U_17,U_16] :
( ! [U_15] :
( distinct_points(U_15,intersection_point(U_17,U_16))
| ( ~ apart_point_and_line(U_15,U_16)
& ~ apart_point_and_line(U_15,U_17) ) )
| ~ convergent_lines(U_17,U_16) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_4,plain,
( ~ apart_point_and_line(U_15,U_17)
| distinct_points(U_15,intersection_point(U_17,U_16))
| ~ convergent_lines(U_17,U_16) ),
inference(clausify,[status(thm)],[f_8_3]) ).
cnf(f_8_5,plain,
( ~ apart_point_and_line(U_15,U_16)
| distinct_points(U_15,intersection_point(U_17,U_16))
| ~ convergent_lines(U_17,U_16) ),
inference(clausify,[status(thm)],[f_8_3]) ).
fof(f_9_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_9_2,plain,
! [U_21,U_20,U_19,U_18] :
( apart_point_and_line(U_20,U_18)
| apart_point_and_line(U_20,U_19)
| apart_point_and_line(U_21,U_18)
| apart_point_and_line(U_21,U_19)
| ~ distinct_lines(U_19,U_18)
| ~ distinct_points(U_21,U_20) ),
inference(variable_rename,[status(thm)],[f_9_1]) ).
cnf(f_9_3,plain,
( apart_point_and_line(U_20,U_18)
| apart_point_and_line(U_20,U_19)
| apart_point_and_line(U_21,U_18)
| apart_point_and_line(U_21,U_19)
| ~ distinct_lines(U_19,U_18)
| ~ distinct_points(U_21,U_20) ),
inference(clausify,[status(thm)],[f_9_2]) ).
fof(f_10_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_10_2,plain,
! [U_24,U_23,U_22] :
( apart_point_and_line(U_22,U_23)
| distinct_points(U_24,U_22)
| ~ apart_point_and_line(U_24,U_23) ),
inference(variable_rename,[status(thm)],[f_10_1]) ).
fof(f_10_3,plain,
! [U_24,U_23] :
( ! [U_22] :
( apart_point_and_line(U_22,U_23)
| distinct_points(U_24,U_22) )
| ~ apart_point_and_line(U_24,U_23) ),
inference(miniscope,[status(thm)],[f_10_2]) ).
cnf(f_10_4,plain,
( apart_point_and_line(U_22,U_23)
| distinct_points(U_24,U_22)
| ~ apart_point_and_line(U_24,U_23) ),
inference(clausify,[status(thm)],[f_10_3]) ).
fof(f_11_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_11_2,plain,
! [U_27,U_26,U_25] :
( apart_point_and_line(U_27,U_25)
| distinct_lines(U_26,U_25)
| ~ apart_point_and_line(U_27,U_26) ),
inference(variable_rename,[status(thm)],[f_11_1]) ).
fof(f_11_3,plain,
! [U_27,U_26] :
( ! [U_25] :
( apart_point_and_line(U_27,U_25)
| distinct_lines(U_26,U_25) )
| ~ apart_point_and_line(U_27,U_26) ),
inference(miniscope,[status(thm)],[f_11_2]) ).
cnf(f_11_4,plain,
( apart_point_and_line(U_27,U_25)
| distinct_lines(U_26,U_25)
| ~ apart_point_and_line(U_27,U_26) ),
inference(clausify,[status(thm)],[f_11_3]) ).
fof(f_12_1,plain,
! [X,Y] :
( distinct_lines(X,Y)
| ~ convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[ceq3]) ).
fof(f_12_2,plain,
! [U_29,U_28] :
( distinct_lines(U_29,U_28)
| ~ convergent_lines(U_29,U_28) ),
inference(variable_rename,[status(thm)],[f_12_1]) ).
cnf(f_12_3,plain,
( distinct_lines(U_29,U_28)
| ~ convergent_lines(U_29,U_28) ),
inference(clausify,[status(thm)],[f_12_2]) ).
fof(f_13_1,plain,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
inference(fof_nnf,[status(thm)],[cp1]) ).
fof(f_13_2,plain,
! [U_31,U_30] : ~ convergent_lines(parallel_through_point(U_30,U_31),U_30),
inference(variable_rename,[status(thm)],[f_13_1]) ).
cnf(f_13_3,plain,
~ convergent_lines(parallel_through_point(U_30,U_31),U_30),
inference(clausify,[status(thm)],[f_13_2]) ).
fof(f_14_1,plain,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
inference(fof_nnf,[status(thm)],[cp2]) ).
fof(f_14_2,plain,
! [U_33,U_32] : ~ apart_point_and_line(U_33,parallel_through_point(U_32,U_33)),
inference(variable_rename,[status(thm)],[f_14_1]) ).
cnf(f_14_3,plain,
~ apart_point_and_line(U_33,parallel_through_point(U_32,U_33)),
inference(clausify,[status(thm)],[f_14_2]) ).
fof(f_15_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_15_2,plain,
! [U_36,U_35,U_34] :
( convergent_lines(U_35,U_34)
| apart_point_and_line(U_36,U_34)
| apart_point_and_line(U_36,U_35)
| ~ distinct_lines(U_35,U_34) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( convergent_lines(U_35,U_34)
| apart_point_and_line(U_36,U_34)
| apart_point_and_line(U_36,U_35)
| ~ distinct_lines(U_35,U_34) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,negated_conjecture,
~ ! [A,L,M,N] :
( ( ~ convergent_lines(N,L)
& ~ convergent_lines(M,L)
& ~ apart_point_and_line(A,N)
& ~ apart_point_and_line(A,M)
& apart_point_and_line(A,L) )
=> ~ distinct_lines(M,N) ),
inference(negate,[status(cth)],[con]) ).
fof(f_16_2,negated_conjecture,
? [A,L,M,N] :
( distinct_lines(M,N)
& ~ convergent_lines(N,L)
& ~ convergent_lines(M,L)
& ~ apart_point_and_line(A,N)
& ~ apart_point_and_line(A,M)
& apart_point_and_line(A,L) ),
inference(fof_nnf,[status(thm)],[f_16_1]) ).
fof(f_16_3,negated_conjecture,
? [U_40,U_39,U_38,U_37] :
( distinct_lines(U_38,U_37)
& ~ convergent_lines(U_37,U_39)
& ~ convergent_lines(U_38,U_39)
& ~ apart_point_and_line(U_40,U_37)
& ~ apart_point_and_line(U_40,U_38)
& apart_point_and_line(U_40,U_39) ),
inference(variable_rename,[status(thm)],[f_16_2]) ).
fof(f_16_4,negated_conjecture,
? [U_39,U_38,U_37] :
( distinct_lines(U_38,U_37)
& ~ convergent_lines(U_37,U_39)
& ~ convergent_lines(U_38,U_39)
& ~ apart_point_and_line(sK1,U_37)
& ~ apart_point_and_line(sK1,U_38)
& apart_point_and_line(sK1,U_39) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_40,sK1)],[f_16_3]) ).
fof(f_16_5,negated_conjecture,
? [U_38,U_37] :
( distinct_lines(U_38,U_37)
& ~ convergent_lines(U_37,sK2)
& ~ convergent_lines(U_38,sK2)
& ~ apart_point_and_line(sK1,U_37)
& ~ apart_point_and_line(sK1,U_38)
& apart_point_and_line(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_39,sK2)],[f_16_4]) ).
fof(f_16_6,negated_conjecture,
? [U_37] :
( distinct_lines(sK3,U_37)
& ~ convergent_lines(U_37,sK2)
& ~ convergent_lines(sK3,sK2)
& ~ apart_point_and_line(sK1,U_37)
& ~ apart_point_and_line(sK1,sK3)
& apart_point_and_line(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_38,sK3)],[f_16_5]) ).
fof(f_16_7,negated_conjecture,
( distinct_lines(sK3,sK4)
& ~ convergent_lines(sK4,sK2)
& ~ convergent_lines(sK3,sK2)
& ~ apart_point_and_line(sK1,sK4)
& ~ apart_point_and_line(sK1,sK3)
& apart_point_and_line(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_37,sK4)],[f_16_6]) ).
fof(f_16_8,negated_conjecture,
( distinct_lines(sK3,sK4)
& ~ convergent_lines(sK4,sK2)
& ~ convergent_lines(sK3,sK2)
& ~ apart_point_and_line(sK1,sK4)
& ~ apart_point_and_line(sK1,sK3)
& apart_point_and_line(sK1,sK2) ),
inference(definitional_conversion,[status(esa)],[f_16_7]) ).
cnf(f_16_9,negated_conjecture,
apart_point_and_line(sK1,sK2),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_10,negated_conjecture,
~ apart_point_and_line(sK1,sK3),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_11,negated_conjecture,
~ apart_point_and_line(sK1,sK4),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_12,negated_conjecture,
~ convergent_lines(sK3,sK2),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_13,negated_conjecture,
~ convergent_lines(sK4,sK2),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(f_16_14,negated_conjecture,
distinct_lines(sK3,sK4),
inference(clausify,[status(thm)],[f_16_8]) ).
cnf(sat_proved,plain,
$false,
inference(cadical,[status(thm)],[]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO209+2 : 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
% 0.08/5.36 % Computer : n001.cluster.edu
% 0.08/5.36 % Model : x86_64 x86_64
% 0.08/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/5.36 % Memory : 8046.5625MB
% 0.08/5.36 % OS : Linux 6.8.0-71-generic
% 0.08/5.36 % CPULimit : 300
% 0.08/5.36 % WCLimit : 300
% 0.08/5.36 % DateTime : Sat Sep 19 07:46:59 UTC 2026
% 0.08/5.36 % CPUTime :
% 0.08/5.39 % SZS status Theorem for theBenchmark
% 0.08/5.39 % SZS output start Proof for theBenchmark
% See solution above
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