%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO193+2 : TPTP v9.3.1. Released v3.3.0.
% 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 : n009.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 08:39:48 AM UTC 2026
% Result : Theorem 11.45s 11.71s
% Output : Proof 11.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 61 ( 33 unt; 0 def)
% Number of atoms : 147 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 135 ( 49 ~; 46 |; 32 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 39 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X),
file('GEO008+0.ax',apart1) ).
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(ceq3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('GEO008+0.ax',ceq3) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> apart_point_and_line(intersection_point(Z,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_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_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,negated_conjecture,
~ ! [X,Y,Z] :
( ( convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> apart_point_and_line(intersection_point(Z,Y),X) ) ),
inference(negate,[status(cth)],[con]) ).
fof(f_13_2,negated_conjecture,
? [X,Y,Z] :
( ~ apart_point_and_line(intersection_point(Z,Y),X)
& apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[f_13_1]) ).
fof(f_13_3,negated_conjecture,
? [U_32,U_31,U_30] :
( ~ apart_point_and_line(intersection_point(U_30,U_31),U_32)
& apart_point_and_line(intersection_point(U_32,U_31),U_30)
& convergent_lines(U_32,U_30)
& convergent_lines(U_30,U_31)
& convergent_lines(U_32,U_31) ),
inference(variable_rename,[status(thm)],[f_13_2]) ).
fof(f_13_4,negated_conjecture,
? [U_31,U_30] :
( ~ apart_point_and_line(intersection_point(U_30,U_31),sK1)
& apart_point_and_line(intersection_point(sK1,U_31),U_30)
& convergent_lines(sK1,U_30)
& convergent_lines(U_30,U_31)
& convergent_lines(sK1,U_31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_32,sK1)],[f_13_3]) ).
fof(f_13_5,negated_conjecture,
? [U_30] :
( ~ apart_point_and_line(intersection_point(U_30,sK2),sK1)
& apart_point_and_line(intersection_point(sK1,sK2),U_30)
& convergent_lines(sK1,U_30)
& convergent_lines(U_30,sK2)
& convergent_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_31,sK2)],[f_13_4]) ).
fof(f_13_6,negated_conjecture,
( ~ apart_point_and_line(intersection_point(sK3,sK2),sK1)
& apart_point_and_line(intersection_point(sK1,sK2),sK3)
& convergent_lines(sK1,sK3)
& convergent_lines(sK3,sK2)
& convergent_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_30,sK3)],[f_13_5]) ).
fof(f_13_7,negated_conjecture,
( ~ apart_point_and_line(intersection_point(sK3,sK2),sK1)
& apart_point_and_line(intersection_point(sK1,sK2),sK3)
& convergent_lines(sK1,sK3)
& convergent_lines(sK3,sK2)
& convergent_lines(sK1,sK2) ),
inference(definitional_conversion,[status(esa)],[f_13_6]) ).
cnf(f_13_8,negated_conjecture,
convergent_lines(sK1,sK2),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_9,negated_conjecture,
convergent_lines(sK3,sK2),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_11,negated_conjecture,
apart_point_and_line(intersection_point(sK1,sK2),sK3),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(f_13_12,negated_conjecture,
~ apart_point_and_line(intersection_point(sK3,sK2),sK1),
inference(clausify,[status(thm)],[f_13_7]) ).
cnf(t1,plain,
~ apart_point_and_line(intersection_point(sK3,sK2),sK1),
inference(start,[status(thm),parent(0:0)],[f_13_12]) ).
cnf(t2,plain,
( ~ distinct_lines(sK1,sK2)
| apart_point_and_line(intersection_point(sK1,sK2),sK1)
| apart_point_and_line(intersection_point(sK1,sK2),sK2)
| apart_point_and_line(intersection_point(sK3,sK2),sK2)
| ~ distinct_points(intersection_point(sK1,sK2),intersection_point(sK3,sK2))
| apart_point_and_line(intersection_point(sK3,sK2),sK1) ),
inference(extension,[status(thm),parent(t1:1)],[f_9_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( ~ apart_point_and_line(intersection_point(sK1,sK2),sK3)
| ~ convergent_lines(sK3,sK2)
| distinct_points(intersection_point(sK1,sK2),intersection_point(sK3,sK2)) ),
inference(extension,[status(thm),parent(t2:2)],[f_8_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
convergent_lines(sK3,sK2),
inference(extension,[status(thm),parent(t4:2)],[f_13_9]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
apart_point_and_line(intersection_point(sK1,sK2),sK3),
inference(extension,[status(thm),parent(t4:3)],[f_13_11]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
( distinct_points(intersection_point(sK3,sK2),intersection_point(sK3,sK2))
| ~ convergent_lines(sK3,sK2)
| ~ apart_point_and_line(intersection_point(sK3,sK2),sK2) ),
inference(extension,[status(thm),parent(t2:3)],[f_8_5]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:3]) ).
cnf(t12,plain,
convergent_lines(sK3,sK2),
inference(extension,[status(thm),parent(t10:2)],[f_13_9]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
~ distinct_points(intersection_point(sK3,sK2),intersection_point(sK3,sK2)),
inference(extension,[status(thm),parent(t10:3)],[f_1_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
cnf(t16,plain,
( distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK2))
| ~ convergent_lines(sK1,sK2)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK2) ),
inference(extension,[status(thm),parent(t2:4)],[f_8_5]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t2:4]) ).
cnf(t18,plain,
convergent_lines(sK1,sK2),
inference(extension,[status(thm),parent(t16:2)],[f_13_8]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
cnf(t20,plain,
~ distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK2)),
inference(extension,[status(thm),parent(t16:3)],[f_1_3]) ).
cnf(t21,plain,
$false,
inference(connection,[status(thm),parent(t20:1)],[t20:1,t16:3]) ).
cnf(t22,plain,
( distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK2))
| ~ convergent_lines(sK1,sK2)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK1) ),
inference(extension,[status(thm),parent(t2:5)],[f_8_4]) ).
cnf(t23,plain,
$false,
inference(connection,[status(thm),parent(t22:1)],[t22:1,t2:5]) ).
cnf(t24,plain,
convergent_lines(sK1,sK2),
inference(extension,[status(thm),parent(t22:2)],[f_13_8]) ).
cnf(t25,plain,
$false,
inference(connection,[status(thm),parent(t24:1)],[t24:1,t22:2]) ).
cnf(t26,plain,
~ distinct_points(intersection_point(sK1,sK2),intersection_point(sK1,sK2)),
inference(extension,[status(thm),parent(t22:3)],[f_1_3]) ).
cnf(t27,plain,
$false,
inference(connection,[status(thm),parent(t26:1)],[t26:1,t22:3]) ).
cnf(t28,plain,
( ~ convergent_lines(sK1,sK2)
| distinct_lines(sK1,sK2) ),
inference(extension,[status(thm),parent(t2:6)],[f_12_3]) ).
cnf(t29,plain,
$false,
inference(connection,[status(thm),parent(t28:1)],[t28:1,t2:6]) ).
cnf(t30,plain,
convergent_lines(sK1,sK2),
inference(extension,[status(thm),parent(t28:2)],[f_13_8]) ).
cnf(t31,plain,
$false,
inference(connection,[status(thm),parent(t30:1)],[t30:1,t28:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO193+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n009.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Sat Sep 19 07:40:42 UTC 2026
% 0.11/0.36 % CPUTime :
% 11.45/11.71 % SZS status Theorem for theBenchmark
% 11.45/11.71 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------