%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO215+1 : 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 : 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 08:39:56 AM UTC 2026
% Result : Theorem 0.23s 0.52s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 54 ( 23 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 116 ( 52 ~; 44 |; 14 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 73 ( 0 sgn 49 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('GEO006+0.ax',apart3) ).
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(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('GEO006+0.ax',ceq3) ).
fof(ouo1,axiom,
! [A,L,M,N] :
( distinct_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L) ) ),
file('GEO006+3.ax',ouo1) ).
fof(con,conjecture,
! [L,M,N] :
( convergent_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N) ) ),
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_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_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_22_1,plain,
! [A,L,M,N] :
( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L)
| ~ distinct_lines(L,M) ),
inference(fof_nnf,[status(thm)],[ouo1]) ).
fof(f_22_2,plain,
! [U_52,U_51,U_50,U_49] :
( unorthogonal_lines(U_50,U_49)
| unorthogonal_lines(U_51,U_49)
| apart_point_and_line(U_52,U_50)
| apart_point_and_line(U_52,U_51)
| ~ distinct_lines(U_51,U_50) ),
inference(variable_rename,[status(thm)],[f_22_1]) ).
fof(f_22_3,plain,
! [U_52,U_51,U_50] :
( ! [U_49] :
( unorthogonal_lines(U_50,U_49)
| unorthogonal_lines(U_51,U_49) )
| apart_point_and_line(U_52,U_50)
| apart_point_and_line(U_52,U_51)
| ~ distinct_lines(U_51,U_50) ),
inference(miniscope,[status(thm)],[f_22_2]) ).
cnf(f_22_4,plain,
( unorthogonal_lines(U_50,U_49)
| unorthogonal_lines(U_51,U_49)
| apart_point_and_line(U_52,U_50)
| apart_point_and_line(U_52,U_51)
| ~ distinct_lines(U_51,U_50) ),
inference(clausify,[status(thm)],[f_22_3]) ).
fof(f_23_1,negated_conjecture,
~ ! [L,M,N] :
( convergent_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N) ) ),
inference(negate,[status(cth)],[con]) ).
fof(f_23_2,negated_conjecture,
? [L,M,N] :
( ~ unorthogonal_lines(M,N)
& ~ unorthogonal_lines(L,N)
& convergent_lines(L,M) ),
inference(fof_nnf,[status(thm)],[f_23_1]) ).
fof(f_23_3,negated_conjecture,
? [U_55,U_54,U_53] :
( ~ unorthogonal_lines(U_54,U_53)
& ~ unorthogonal_lines(U_55,U_53)
& convergent_lines(U_55,U_54) ),
inference(variable_rename,[status(thm)],[f_23_2]) ).
fof(f_23_4,negated_conjecture,
? [U_55,U_54] :
( ? [U_53] :
( ~ unorthogonal_lines(U_54,U_53)
& ~ unorthogonal_lines(U_55,U_53) )
& convergent_lines(U_55,U_54) ),
inference(miniscope,[status(thm)],[f_23_3]) ).
fof(f_23_5,negated_conjecture,
? [U_54] :
( ? [U_53] :
( ~ unorthogonal_lines(U_54,U_53)
& ~ unorthogonal_lines(sK1,U_53) )
& convergent_lines(sK1,U_54) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_55,sK1)],[f_23_4]) ).
fof(f_23_6,negated_conjecture,
( ? [U_53] :
( ~ unorthogonal_lines(sK2,U_53)
& ~ unorthogonal_lines(sK1,U_53) )
& convergent_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_54,sK2)],[f_23_5]) ).
fof(f_23_7,negated_conjecture,
( ~ unorthogonal_lines(sK2,sK3)
& ~ unorthogonal_lines(sK1,sK3)
& convergent_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_53,sK3)],[f_23_6]) ).
fof(f_23_8,negated_conjecture,
( ~ unorthogonal_lines(sK2,sK3)
& ~ unorthogonal_lines(sK1,sK3)
& convergent_lines(sK1,sK2) ),
inference(definitional_conversion,[status(esa)],[f_23_7]) ).
cnf(f_23_9,negated_conjecture,
convergent_lines(sK1,sK2),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_10,negated_conjecture,
~ unorthogonal_lines(sK1,sK3),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(f_23_11,negated_conjecture,
~ unorthogonal_lines(sK2,sK3),
inference(clausify,[status(thm)],[f_23_8]) ).
cnf(t1,plain,
( ~ apart_point_and_line(intersection_point(sK1,sK2),sK1)
| ~ convergent_lines(sK1,sK2) ),
inference(start,[status(thm),parent(0:0)],[f_9_3]) ).
cnf(t2,plain,
convergent_lines(sK1,sK2),
inference(extension,[status(thm),parent(t1:1)],[f_23_9]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(l1,lemma,
convergent_lines(sK1,sK2),
inference(lemma,[status(cth),parent(t1:1),below(0:0)],[t1:1]) ).
cnf(t4,plain,
( apart_point_and_line(intersection_point(sK1,sK2),sK2)
| unorthogonal_lines(sK1,sK3)
| unorthogonal_lines(sK2,sK3)
| ~ distinct_lines(sK2,sK1)
| apart_point_and_line(intersection_point(sK1,sK2),sK1) ),
inference(extension,[status(thm),parent(t1:2)],[f_22_4]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t1:2]) ).
cnf(t6,plain,
( convergent_lines(sK1,sK1)
| ~ convergent_lines(sK1,sK2)
| distinct_lines(sK2,sK1) ),
inference(extension,[status(thm),parent(t4:2)],[f_14_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
convergent_lines(sK1,sK2),
inference(extension,[status(thm),parent(t6:2)],[f_23_9]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t6:2]) ).
cnf(t10,plain,
~ convergent_lines(sK1,sK1),
inference(extension,[status(thm),parent(t6:3)],[f_3_3]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t6:3]) ).
cnf(t12,plain,
~ unorthogonal_lines(sK2,sK3),
inference(extension,[status(thm),parent(t4:3)],[f_23_11]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t4:3]) ).
cnf(t14,plain,
~ unorthogonal_lines(sK1,sK3),
inference(extension,[status(thm),parent(t4:4)],[f_23_10]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t4:4]) ).
cnf(t16,plain,
( ~ convergent_lines(sK1,sK2)
| ~ apart_point_and_line(intersection_point(sK1,sK2),sK2) ),
inference(extension,[status(thm),parent(t4:5)],[f_10_3]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t4:5]) ).
cnf(t18,plain,
convergent_lines(sK1,sK2),
inference(lemma_extension,[status(thm),parent(t16:2)],[l1:1]) ).
cnf(t19,plain,
$false,
inference(connection,[status(thm),parent(t18:1)],[t18:1,t16:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO215+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/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 : n015.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 07:44:48 UTC 2026
% 0.12/0.36 % CPUTime :
% 0.23/0.52 % SZS status Theorem for theBenchmark
% 0.23/0.52 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------