%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO220+3 : TPTP v9.3.1. Released v4.0.0.
% 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 : 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 08:39:59 AM UTC 2026
% Result : Theorem 2.16s 2.46s
% Output : Proof 2.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 51 ( 19 unt; 0 def)
% Number of atoms : 114 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 109 ( 46 ~; 36 |; 21 &)
% ( 2 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 3 con; 0-0 aty)
% Number of variables : 70 ( 0 sgn 50 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X),
file('GEO006+0.ax',apart2) ).
fof(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('GEO006+0.ax',ceq3) ).
fof(couo1,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ convergent_lines(M,N) ),
file('GEO006+4.ax',couo1) ).
fof(a3,axiom,
! [X,Y] :
( parallel_lines(X,Y)
<=> ~ convergent_lines(X,Y) ),
file('GEO006+6.ax',a3) ).
fof(a5,axiom,
! [X,Y] :
( orthogonal_lines(X,Y)
<=> ~ unorthogonal_lines(X,Y) ),
file('GEO006+6.ax',a5) ).
fof(con,conjecture,
! [L,M,N] :
( ( orthogonal_lines(L,N)
& orthogonal_lines(L,M) )
=> parallel_lines(M,N) ),
file('theBenchmark.p',con) ).
fof(f_2_1,plain,
! [X] : ~ distinct_lines(X,X),
inference(fof_nnf,[status(thm)],[apart2]) ).
fof(f_2_2,plain,
! [U_1] : ~ distinct_lines(U_1,U_1),
inference(variable_rename,[status(thm)],[f_2_1]) ).
cnf(f_2_3,plain,
~ distinct_lines(U_1,U_1),
inference(clausify,[status(thm)],[f_2_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_26_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_26_2,plain,
! [U_62,U_61,U_60] :
( ~ convergent_lines(U_61,U_60)
| unorthogonal_lines(U_62,U_60)
| unorthogonal_lines(U_62,U_61) ),
inference(variable_rename,[status(thm)],[f_26_1]) ).
cnf(f_26_3,plain,
( ~ convergent_lines(U_61,U_60)
| unorthogonal_lines(U_62,U_60)
| unorthogonal_lines(U_62,U_61) ),
inference(clausify,[status(thm)],[f_26_2]) ).
fof(f_33_1,plain,
! [X,Y] :
( ( parallel_lines(X,Y)
| convergent_lines(X,Y) )
& ( ~ convergent_lines(X,Y)
| ~ parallel_lines(X,Y) ) ),
inference(fof_nnf,[status(thm)],[a3]) ).
fof(f_33_2,plain,
! [U_84,U_83] :
( ( parallel_lines(U_84,U_83)
| convergent_lines(U_84,U_83) )
& ( ~ convergent_lines(U_84,U_83)
| ~ parallel_lines(U_84,U_83) ) ),
inference(variable_rename,[status(thm)],[f_33_1]) ).
fof(f_33_3,plain,
( ! [U_88,U_86] :
( parallel_lines(U_88,U_86)
| convergent_lines(U_88,U_86) )
& ! [U_87,U_85] :
( ~ convergent_lines(U_87,U_85)
| ~ parallel_lines(U_87,U_85) ) ),
inference(miniscope,[status(thm)],[f_33_2]) ).
cnf(f_33_5,plain,
( parallel_lines(U_88,U_86)
| convergent_lines(U_88,U_86) ),
inference(clausify,[status(thm)],[f_33_3]) ).
fof(f_35_1,plain,
! [X,Y] :
( ( orthogonal_lines(X,Y)
| unorthogonal_lines(X,Y) )
& ( ~ unorthogonal_lines(X,Y)
| ~ orthogonal_lines(X,Y) ) ),
inference(fof_nnf,[status(thm)],[a5]) ).
fof(f_35_2,plain,
! [U_96,U_95] :
( ( orthogonal_lines(U_96,U_95)
| unorthogonal_lines(U_96,U_95) )
& ( ~ unorthogonal_lines(U_96,U_95)
| ~ orthogonal_lines(U_96,U_95) ) ),
inference(variable_rename,[status(thm)],[f_35_1]) ).
fof(f_35_3,plain,
( ! [U_100,U_98] :
( orthogonal_lines(U_100,U_98)
| unorthogonal_lines(U_100,U_98) )
& ! [U_99,U_97] :
( ~ unorthogonal_lines(U_99,U_97)
| ~ orthogonal_lines(U_99,U_97) ) ),
inference(miniscope,[status(thm)],[f_35_2]) ).
cnf(f_35_4,plain,
( ~ unorthogonal_lines(U_99,U_97)
| ~ orthogonal_lines(U_99,U_97) ),
inference(clausify,[status(thm)],[f_35_3]) ).
fof(f_36_1,negated_conjecture,
~ ! [L,M,N] :
( ( orthogonal_lines(L,N)
& orthogonal_lines(L,M) )
=> parallel_lines(M,N) ),
inference(negate,[status(cth)],[con]) ).
fof(f_36_2,negated_conjecture,
? [L,M,N] :
( ~ parallel_lines(M,N)
& orthogonal_lines(L,N)
& orthogonal_lines(L,M) ),
inference(fof_nnf,[status(thm)],[f_36_1]) ).
fof(f_36_3,negated_conjecture,
? [U_103,U_102,U_101] :
( ~ parallel_lines(U_102,U_101)
& orthogonal_lines(U_103,U_101)
& orthogonal_lines(U_103,U_102) ),
inference(variable_rename,[status(thm)],[f_36_2]) ).
fof(f_36_4,negated_conjecture,
? [U_102,U_101] :
( ~ parallel_lines(U_102,U_101)
& orthogonal_lines(sK1,U_101)
& orthogonal_lines(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] :
( ~ parallel_lines(sK2,U_101)
& orthogonal_lines(sK1,U_101)
& orthogonal_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_102,sK2)],[f_36_4]) ).
fof(f_36_6,negated_conjecture,
( ~ parallel_lines(sK2,sK3)
& orthogonal_lines(sK1,sK3)
& orthogonal_lines(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_101,sK3)],[f_36_5]) ).
fof(f_36_7,negated_conjecture,
( ~ parallel_lines(sK2,sK3)
& orthogonal_lines(sK1,sK3)
& orthogonal_lines(sK1,sK2) ),
inference(definitional_conversion,[status(esa)],[f_36_6]) ).
cnf(f_36_8,negated_conjecture,
orthogonal_lines(sK1,sK2),
inference(clausify,[status(thm)],[f_36_7]) ).
cnf(f_36_9,negated_conjecture,
orthogonal_lines(sK1,sK3),
inference(clausify,[status(thm)],[f_36_7]) ).
cnf(f_36_10,negated_conjecture,
~ parallel_lines(sK2,sK3),
inference(clausify,[status(thm)],[f_36_7]) ).
cnf(t1,plain,
~ distinct_lines(sK3,sK3),
inference(start,[status(thm),parent(0:0)],[f_2_3]) ).
cnf(t2,plain,
( convergent_lines(sK2,sK3)
| ~ convergent_lines(sK2,sK3)
| distinct_lines(sK3,sK3) ),
inference(extension,[status(thm),parent(t1:1)],[f_14_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
( parallel_lines(sK2,sK3)
| convergent_lines(sK2,sK3) ),
inference(extension,[status(thm),parent(t2:2)],[f_33_5]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
~ parallel_lines(sK2,sK3),
inference(extension,[status(thm),parent(t4:2)],[f_36_10]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t4:2]) ).
cnf(t8,plain,
( unorthogonal_lines(sK1,sK3)
| unorthogonal_lines(sK1,sK2)
| ~ convergent_lines(sK2,sK3) ),
inference(extension,[status(thm),parent(t2:3)],[f_26_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:3]) ).
cnf(t10,plain,
( ~ orthogonal_lines(sK1,sK2)
| ~ unorthogonal_lines(sK1,sK2) ),
inference(extension,[status(thm),parent(t8:2)],[f_35_4]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t8:2]) ).
cnf(t12,plain,
orthogonal_lines(sK1,sK2),
inference(extension,[status(thm),parent(t10:2)],[f_36_8]) ).
cnf(t13,plain,
$false,
inference(connection,[status(thm),parent(t12:1)],[t12:1,t10:2]) ).
cnf(t14,plain,
( ~ orthogonal_lines(sK1,sK3)
| ~ unorthogonal_lines(sK1,sK3) ),
inference(extension,[status(thm),parent(t8:3)],[f_35_4]) ).
cnf(t15,plain,
$false,
inference(connection,[status(thm),parent(t14:1)],[t14:1,t8:3]) ).
cnf(t16,plain,
orthogonal_lines(sK1,sK3),
inference(extension,[status(thm),parent(t14:2)],[f_36_9]) ).
cnf(t17,plain,
$false,
inference(connection,[status(thm),parent(t16:1)],[t16:1,t14:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO220+3 : TPTP v9.3.1. Released v4.0.0.
% 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
% 0.10/0.36 % 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
% 0.10/0.37 % CPUTime :
% 2.16/2.46 % SZS status Theorem for theBenchmark
% 2.16/2.46 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------