%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO206+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 : 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 08:39:53 AM UTC 2026
% Result : Theorem 0.11s 0.44s
% Output : Proof 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 41 ( 22 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 85 ( 42 ~; 25 |; 14 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 58 ( 2 sgn 39 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('GEO008+0.ax',apart6) ).
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,
! [X,Y,Z] :
( ( ~ convergent_lines(Y,Z)
& ~ apart_point_and_line(X,Y) )
=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ),
file('theBenchmark.p',con) ).
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_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,
~ ! [X,Y,Z] :
( ( ~ convergent_lines(Y,Z)
& ~ apart_point_and_line(X,Y) )
=> ~ distinct_lines(Y,parallel_through_point(Z,X)) ),
inference(negate,[status(cth)],[con]) ).
fof(f_16_2,negated_conjecture,
? [X,Y,Z] :
( distinct_lines(Y,parallel_through_point(Z,X))
& ~ convergent_lines(Y,Z)
& ~ apart_point_and_line(X,Y) ),
inference(fof_nnf,[status(thm)],[f_16_1]) ).
fof(f_16_3,negated_conjecture,
? [U_39,U_38,U_37] :
( distinct_lines(U_38,parallel_through_point(U_37,U_39))
& ~ convergent_lines(U_38,U_37)
& ~ apart_point_and_line(U_39,U_38) ),
inference(variable_rename,[status(thm)],[f_16_2]) ).
fof(f_16_4,negated_conjecture,
? [U_38,U_37] :
( distinct_lines(U_38,parallel_through_point(U_37,sK1))
& ~ convergent_lines(U_38,U_37)
& ~ apart_point_and_line(sK1,U_38) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_39,sK1)],[f_16_3]) ).
fof(f_16_5,negated_conjecture,
? [U_37] :
( distinct_lines(sK2,parallel_through_point(U_37,sK1))
& ~ convergent_lines(sK2,U_37)
& ~ apart_point_and_line(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_38,sK2)],[f_16_4]) ).
fof(f_16_6,negated_conjecture,
( distinct_lines(sK2,parallel_through_point(sK3,sK1))
& ~ convergent_lines(sK2,sK3)
& ~ apart_point_and_line(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_37,sK3)],[f_16_5]) ).
fof(f_16_7,negated_conjecture,
( distinct_lines(sK2,parallel_through_point(sK3,sK1))
& ~ convergent_lines(sK2,sK3)
& ~ apart_point_and_line(sK1,sK2) ),
inference(definitional_conversion,[status(esa)],[f_16_6]) ).
cnf(f_16_8,negated_conjecture,
~ apart_point_and_line(sK1,sK2),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_9,negated_conjecture,
~ convergent_lines(sK2,sK3),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_10,negated_conjecture,
distinct_lines(sK2,parallel_through_point(sK3,sK1)),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(t1,plain,
~ convergent_lines(parallel_through_point(sK3,sK1),sK3),
inference(start,[status(thm),parent(0:0)],[f_13_3]) ).
cnf(t2,plain,
( convergent_lines(sK2,sK3)
| ~ convergent_lines(sK2,parallel_through_point(sK3,sK1))
| convergent_lines(parallel_through_point(sK3,sK1),sK3) ),
inference(extension,[status(thm),parent(t1:1)],[f_6_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( apart_point_and_line(sK1,sK2)
| apart_point_and_line(sK1,parallel_through_point(sK3,sK1))
| ~ distinct_lines(sK2,parallel_through_point(sK3,sK1))
| convergent_lines(sK2,parallel_through_point(sK3,sK1)) ),
inference(extension,[status(thm),parent(t2:2)],[f_15_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
distinct_lines(sK2,parallel_through_point(sK3,sK1)),
inference(extension,[status(thm),parent(t4:2)],[f_16_10]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
~ apart_point_and_line(sK1,parallel_through_point(sK3,sK1)),
inference(extension,[status(thm),parent(t4:3)],[f_14_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t4:3]) ).
cnf(t10,plain,
~ apart_point_and_line(sK1,sK2),
inference(extension,[status(thm),parent(t4:4)],[f_16_8]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t4:4]) ).
cnf(t12,plain,
~ convergent_lines(sK2,sK3),
inference(extension,[status(thm),parent(t2:3)],[f_16_9]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO206+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
% 0.08/0.35 % Computer : n004.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Sat Sep 19 07:41:22 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.11/0.44 % SZS status Theorem for theBenchmark
% 0.11/0.44 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------