%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO214+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 : n020.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 0.22s 0.53s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 5
% Syntax : Number of formulae : 42 ( 18 unt; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 80 ( 30 ~; 32 |; 14 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 2 ( 2 usr; 2 con; 0-0 aty)
% Number of variables : 51 ( 0 sgn 37 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('GEO008+0.ax',apart3) ).
fof(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('GEO008+0.ax',apart6) ).
fof(occu1,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('GEO006+3.ax',occu1) ).
fof(oac1,axiom,
! [L,M,N] :
( ( unorthogonal_lines(L,M)
& convergent_lines(L,M) )
=> ( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) ) ) ),
file('GEO006+3.ax',oac1) ).
fof(con,conjecture,
! [L,M] :
( unorthogonal_lines(L,M)
=> unorthogonal_lines(M,L) ),
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)],[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_16_1,plain,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
inference(fof_nnf,[status(thm)],[occu1]) ).
fof(f_16_2,plain,
! [U_38,U_37] :
( unorthogonal_lines(U_38,U_37)
| convergent_lines(U_38,U_37) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
cnf(f_16_3,plain,
( unorthogonal_lines(U_38,U_37)
| convergent_lines(U_38,U_37) ),
inference(clausify,[status(thm)],[f_16_2]) ).
fof(f_17_1,plain,
! [L,M,N] :
( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) )
| ~ unorthogonal_lines(L,M)
| ~ convergent_lines(L,M) ),
inference(fof_nnf,[status(thm)],[oac1]) ).
fof(f_17_2,plain,
! [U_41,U_40,U_39] :
( ( unorthogonal_lines(U_40,U_39)
& convergent_lines(U_40,U_39) )
| ( unorthogonal_lines(U_41,U_39)
& convergent_lines(U_41,U_39) )
| ~ unorthogonal_lines(U_41,U_40)
| ~ convergent_lines(U_41,U_40) ),
inference(variable_rename,[status(thm)],[f_17_1]) ).
fof(f_17_3,plain,
! [U_41,U_40] :
( ! [U_39] :
( ( unorthogonal_lines(U_40,U_39)
& convergent_lines(U_40,U_39) )
| ( unorthogonal_lines(U_41,U_39)
& convergent_lines(U_41,U_39) ) )
| ~ unorthogonal_lines(U_41,U_40)
| ~ convergent_lines(U_41,U_40) ),
inference(miniscope,[status(thm)],[f_17_2]) ).
cnf(f_17_5,plain,
( unorthogonal_lines(U_40,U_39)
| convergent_lines(U_41,U_39)
| ~ unorthogonal_lines(U_41,U_40)
| ~ convergent_lines(U_41,U_40) ),
inference(clausify,[status(thm)],[f_17_3]) ).
fof(f_21_1,negated_conjecture,
~ ! [L,M] :
( unorthogonal_lines(L,M)
=> unorthogonal_lines(M,L) ),
inference(negate,[status(cth)],[con]) ).
fof(f_21_2,negated_conjecture,
? [L,M] :
( ~ unorthogonal_lines(M,L)
& unorthogonal_lines(L,M) ),
inference(fof_nnf,[status(thm)],[f_21_1]) ).
fof(f_21_3,negated_conjecture,
? [U_51,U_50] :
( ~ unorthogonal_lines(U_50,U_51)
& unorthogonal_lines(U_51,U_50) ),
inference(variable_rename,[status(thm)],[f_21_2]) ).
fof(f_21_4,negated_conjecture,
? [U_50] :
( ~ unorthogonal_lines(U_50,sK1)
& unorthogonal_lines(sK1,U_50) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_51,sK1)],[f_21_3]) ).
fof(f_21_5,negated_conjecture,
( ~ unorthogonal_lines(sK2,sK1)
& unorthogonal_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_50,sK2)],[f_21_4]) ).
fof(f_21_6,negated_conjecture,
( ~ unorthogonal_lines(sK2,sK1)
& unorthogonal_lines(sK1,sK2) ),
inference(definitional_conversion,[status(esa)],[f_21_5]) ).
cnf(f_21_7,negated_conjecture,
unorthogonal_lines(sK1,sK2),
inference(clausify,[status(thm)],[f_21_6]) ).
cnf(f_21_8,negated_conjecture,
~ unorthogonal_lines(sK2,sK1),
inference(clausify,[status(thm)],[f_21_6]) ).
cnf(t1,plain,
~ convergent_lines(sK2,sK2),
inference(start,[status(thm),parent(0:0)],[f_3_3]) ).
cnf(t2,plain,
( convergent_lines(sK1,sK2)
| ~ convergent_lines(sK2,sK1)
| convergent_lines(sK2,sK2) ),
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,
( unorthogonal_lines(sK2,sK1)
| convergent_lines(sK2,sK1) ),
inference(extension,[status(thm),parent(t2:2)],[f_16_3]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
~ unorthogonal_lines(sK2,sK1),
inference(extension,[status(thm),parent(t4:2)],[f_21_8]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( ~ unorthogonal_lines(sK1,sK2)
| convergent_lines(sK1,sK1)
| unorthogonal_lines(sK2,sK1)
| ~ convergent_lines(sK1,sK2) ),
inference(extension,[status(thm),parent(t2:3)],[f_17_5]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
~ unorthogonal_lines(sK2,sK1),
inference(extension,[status(thm),parent(t8:2)],[f_21_8]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
~ convergent_lines(sK1,sK1),
inference(extension,[status(thm),parent(t8:3)],[f_3_3]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t8:3]) ).
cnf(t14,plain,
unorthogonal_lines(sK1,sK2),
inference(extension,[status(thm),parent(t8:4)],[f_21_7]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO214+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
% 0.10/0.36 % Computer : n020.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Sat Sep 19 07:42:33 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.22/0.53 % SZS status Theorem for theBenchmark
% 0.22/0.53 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------