%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO188+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 : n004.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 08:39:46 AM UTC 2026
% Result : Theorem 25.45s 25.72s
% Output : Proof 25.45s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 8
% Syntax : Number of formulae : 55 ( 24 unt; 0 def)
% Number of atoms : 128 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 118 ( 45 ~; 34 |; 33 &)
% ( 1 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 85 ( 2 sgn 61 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('GEO006+0.ax',apart3) ).
fof(ax6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('GEO006+0.ax',ax6) ).
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(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(a4,axiom,
! [X,Y] :
( incident_point_and_line(X,Y)
<=> ~ apart_point_and_line(X,Y) ),
file('GEO006+6.ax',a4) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( incident_point_and_line(Z,line_connecting(X,Y))
& distinct_points(Y,Z)
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> incident_point_and_line(X,line_connecting(Z,Y)) ),
file('theBenchmark.p',con) ).
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_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_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_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_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_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_36_1,negated_conjecture,
~ ! [X,Y,Z] :
( ( incident_point_and_line(Z,line_connecting(X,Y))
& distinct_points(Y,Z)
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> incident_point_and_line(X,line_connecting(Z,Y)) ),
inference(negate,[status(cth)],[con]) ).
fof(f_36_2,negated_conjecture,
? [X,Y,Z] :
( ~ incident_point_and_line(X,line_connecting(Z,Y))
& incident_point_and_line(Z,line_connecting(X,Y))
& distinct_points(Y,Z)
& distinct_points(X,Z)
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[f_36_1]) ).
fof(f_36_3,negated_conjecture,
? [U_103,U_102,U_101] :
( ~ incident_point_and_line(U_103,line_connecting(U_101,U_102))
& incident_point_and_line(U_101,line_connecting(U_103,U_102))
& distinct_points(U_102,U_101)
& distinct_points(U_103,U_101)
& distinct_points(U_103,U_102) ),
inference(variable_rename,[status(thm)],[f_36_2]) ).
fof(f_36_4,negated_conjecture,
? [U_102,U_101] :
( ~ incident_point_and_line(sK1,line_connecting(U_101,U_102))
& incident_point_and_line(U_101,line_connecting(sK1,U_102))
& distinct_points(U_102,U_101)
& distinct_points(sK1,U_101)
& distinct_points(sK1,U_102) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_103,sK1)],[f_36_3]) ).
fof(f_36_5,negated_conjecture,
? [U_101] :
( ~ incident_point_and_line(sK1,line_connecting(U_101,sK2))
& incident_point_and_line(U_101,line_connecting(sK1,sK2))
& distinct_points(sK2,U_101)
& distinct_points(sK1,U_101)
& distinct_points(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_102,sK2)],[f_36_4]) ).
fof(f_36_6,negated_conjecture,
( ~ incident_point_and_line(sK1,line_connecting(sK3,sK2))
& incident_point_and_line(sK3,line_connecting(sK1,sK2))
& distinct_points(sK2,sK3)
& distinct_points(sK1,sK3)
& distinct_points(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_101,sK3)],[f_36_5]) ).
fof(f_36_7,negated_conjecture,
( ~ incident_point_and_line(sK1,line_connecting(sK3,sK2))
& incident_point_and_line(sK3,line_connecting(sK1,sK2))
& distinct_points(sK2,sK3)
& distinct_points(sK1,sK3)
& distinct_points(sK1,sK2) ),
inference(definitional_conversion,[status(esa)],[f_36_6]) ).
cnf(f_36_12,negated_conjecture,
~ incident_point_and_line(sK1,line_connecting(sK3,sK2)),
inference(clausify,[status(thm)],[f_36_7]) ).
cnf(t1,plain,
~ apart_point_and_line(sK1,parallel_through_point(line_connecting(sK3,sK2),sK1)),
inference(start,[status(thm),parent(0:0)],[f_17_3]) ).
cnf(t2,plain,
( distinct_lines(line_connecting(sK3,sK2),parallel_through_point(line_connecting(sK3,sK2),sK1))
| ~ apart_point_and_line(sK1,line_connecting(sK3,sK2))
| apart_point_and_line(sK1,parallel_through_point(line_connecting(sK3,sK2),sK1)) ),
inference(extension,[status(thm),parent(t1:1)],[f_13_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( incident_point_and_line(sK1,line_connecting(sK3,sK2))
| apart_point_and_line(sK1,line_connecting(sK3,sK2)) ),
inference(extension,[status(thm),parent(t2:2)],[f_34_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
~ incident_point_and_line(sK1,line_connecting(sK3,sK2)),
inference(extension,[status(thm),parent(t4:2)],[f_36_12]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( convergent_lines(line_connecting(sK3,sK2),parallel_through_point(line_connecting(sK3,sK2),sK1))
| ~ distinct_lines(line_connecting(sK3,sK2),parallel_through_point(line_connecting(sK3,sK2),sK1)) ),
inference(extension,[status(thm),parent(t2:3)],[f_15_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
( convergent_lines(line_connecting(sK3,sK2),line_connecting(sK3,sK2))
| convergent_lines(parallel_through_point(line_connecting(sK3,sK2),sK1),line_connecting(sK3,sK2))
| ~ convergent_lines(line_connecting(sK3,sK2),parallel_through_point(line_connecting(sK3,sK2),sK1)) ),
inference(extension,[status(thm),parent(t8:2)],[f_6_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
~ convergent_lines(parallel_through_point(line_connecting(sK3,sK2),sK1),line_connecting(sK3,sK2)),
inference(extension,[status(thm),parent(t10:2)],[f_16_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
~ convergent_lines(line_connecting(sK3,sK2),line_connecting(sK3,sK2)),
inference(extension,[status(thm),parent(t10:3)],[f_3_3]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t10:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO188+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.03 This is a FOF_THM_RFO_NEQ problem
% 0.00/0.03 % 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 : n004.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 07:40:19 UTC 2026
% 0.08/0.36 % CPUTime :
% 25.45/25.72 % SZS status Theorem for theBenchmark
% 25.45/25.72 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------