%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO220+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 : n001.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 08:39:59 AM UTC 2026
% Result : Theorem 0.12s 0.41s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 2
% Syntax : Number of formulae : 22 ( 9 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 56 ( 30 ~; 8 |; 15 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 27 ( 0 sgn 15 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(couo1,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ convergent_lines(M,N) ),
file('GEO006+4.ax',couo1) ).
fof(con,conjecture,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ convergent_lines(M,N) ),
file('theBenchmark.p',con) ).
fof(f_15_1,plain,
! [L,M,N] :
( ~ convergent_lines(M,N)
| unorthogonal_lines(L,N)
| unorthogonal_lines(L,M) ),
inference(fof_nnf,[status(thm)],[couo1]) ).
fof(f_15_2,plain,
! [U_37,U_36,U_35] :
( ~ convergent_lines(U_36,U_35)
| unorthogonal_lines(U_37,U_35)
| unorthogonal_lines(U_37,U_36) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
cnf(f_15_3,plain,
( ~ convergent_lines(U_36,U_35)
| unorthogonal_lines(U_37,U_35)
| unorthogonal_lines(U_37,U_36) ),
inference(clausify,[status(thm)],[f_15_2]) ).
fof(f_16_1,negated_conjecture,
~ ! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ convergent_lines(M,N) ),
inference(negate,[status(cth)],[con]) ).
fof(f_16_2,negated_conjecture,
? [L,M,N] :
( convergent_lines(M,N)
& ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) ),
inference(fof_nnf,[status(thm)],[f_16_1]) ).
fof(f_16_3,negated_conjecture,
? [U_40,U_39,U_38] :
( convergent_lines(U_39,U_38)
& ~ unorthogonal_lines(U_40,U_38)
& ~ unorthogonal_lines(U_40,U_39) ),
inference(variable_rename,[status(thm)],[f_16_2]) ).
fof(f_16_4,negated_conjecture,
? [U_39,U_38] :
( convergent_lines(U_39,U_38)
& ~ unorthogonal_lines(sK1,U_38)
& ~ unorthogonal_lines(sK1,U_39) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_40,sK1)],[f_16_3]) ).
fof(f_16_5,negated_conjecture,
? [U_38] :
( convergent_lines(sK2,U_38)
& ~ unorthogonal_lines(sK1,U_38)
& ~ unorthogonal_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_39,sK2)],[f_16_4]) ).
fof(f_16_6,negated_conjecture,
( convergent_lines(sK2,sK3)
& ~ unorthogonal_lines(sK1,sK3)
& ~ unorthogonal_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_38,sK3)],[f_16_5]) ).
fof(f_16_7,negated_conjecture,
( convergent_lines(sK2,sK3)
& ~ unorthogonal_lines(sK1,sK3)
& ~ unorthogonal_lines(sK1,sK2) ),
inference(definitional_conversion,[status(esa)],[f_16_6]) ).
cnf(f_16_8,negated_conjecture,
~ unorthogonal_lines(sK1,sK2),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_9,negated_conjecture,
~ unorthogonal_lines(sK1,sK3),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(f_16_10,negated_conjecture,
convergent_lines(sK2,sK3),
inference(clausify,[status(thm)],[f_16_7]) ).
cnf(t1,plain,
~ unorthogonal_lines(sK1,sK2),
inference(start,[status(thm),parent(0:0)],[f_16_8]) ).
cnf(t2,plain,
( unorthogonal_lines(sK1,sK3)
| ~ convergent_lines(sK2,sK3)
| unorthogonal_lines(sK1,sK2) ),
inference(extension,[status(thm),parent(t1:1)],[f_15_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
convergent_lines(sK2,sK3),
inference(extension,[status(thm),parent(t2:2)],[f_16_10]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
~ unorthogonal_lines(sK1,sK3),
inference(extension,[status(thm),parent(t2:3)],[f_16_9]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO220+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
% 0.08/0.35 % Computer : n001.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 07:47:08 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.12/0.41 % SZS status Theorem for theBenchmark
% 0.12/0.41 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------