%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO210+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 : n013.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 08:39:55 AM UTC 2026
% Result : Theorem 0.10s 0.45s
% Output : Proof 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 35 ( 21 unt; 0 def)
% Number of atoms : 75 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 78 ( 38 ~; 23 |; 14 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 51 ( 2 sgn 34 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ooc1,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('GEO006+3.ax',ooc1) ).
fof(ooc2,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('GEO006+3.ax',ooc2) ).
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,
! [A,L,M] :
( ( ~ unorthogonal_lines(L,M)
& ~ apart_point_and_line(A,L) )
=> ~ distinct_lines(L,orthogonal_through_point(M,A)) ),
file('theBenchmark.p',con) ).
fof(f_18_1,plain,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
inference(fof_nnf,[status(thm)],[ooc1]) ).
fof(f_18_2,plain,
! [U_43,U_42] : ~ unorthogonal_lines(orthogonal_through_point(U_42,U_43),U_42),
inference(variable_rename,[status(thm)],[f_18_1]) ).
cnf(f_18_3,plain,
~ unorthogonal_lines(orthogonal_through_point(U_42,U_43),U_42),
inference(clausify,[status(thm)],[f_18_2]) ).
fof(f_19_1,plain,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
inference(fof_nnf,[status(thm)],[ooc2]) ).
fof(f_19_2,plain,
! [U_45,U_44] : ~ apart_point_and_line(U_45,orthogonal_through_point(U_44,U_45)),
inference(variable_rename,[status(thm)],[f_19_1]) ).
cnf(f_19_3,plain,
~ apart_point_and_line(U_45,orthogonal_through_point(U_44,U_45)),
inference(clausify,[status(thm)],[f_19_2]) ).
fof(f_20_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_20_2,plain,
! [U_49,U_48,U_47,U_46] :
( unorthogonal_lines(U_47,U_46)
| unorthogonal_lines(U_48,U_46)
| apart_point_and_line(U_49,U_47)
| apart_point_and_line(U_49,U_48)
| ~ distinct_lines(U_48,U_47) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
! [U_49,U_48,U_47] :
( ! [U_46] :
( unorthogonal_lines(U_47,U_46)
| unorthogonal_lines(U_48,U_46) )
| apart_point_and_line(U_49,U_47)
| apart_point_and_line(U_49,U_48)
| ~ distinct_lines(U_48,U_47) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
( unorthogonal_lines(U_47,U_46)
| unorthogonal_lines(U_48,U_46)
| apart_point_and_line(U_49,U_47)
| apart_point_and_line(U_49,U_48)
| ~ distinct_lines(U_48,U_47) ),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_21_1,negated_conjecture,
~ ! [A,L,M] :
( ( ~ unorthogonal_lines(L,M)
& ~ apart_point_and_line(A,L) )
=> ~ distinct_lines(L,orthogonal_through_point(M,A)) ),
inference(negate,[status(cth)],[con]) ).
fof(f_21_2,negated_conjecture,
? [A,L,M] :
( distinct_lines(L,orthogonal_through_point(M,A))
& ~ unorthogonal_lines(L,M)
& ~ apart_point_and_line(A,L) ),
inference(fof_nnf,[status(thm)],[f_21_1]) ).
fof(f_21_3,negated_conjecture,
? [U_52,U_51,U_50] :
( distinct_lines(U_51,orthogonal_through_point(U_50,U_52))
& ~ unorthogonal_lines(U_51,U_50)
& ~ apart_point_and_line(U_52,U_51) ),
inference(variable_rename,[status(thm)],[f_21_2]) ).
fof(f_21_4,negated_conjecture,
? [U_51,U_50] :
( distinct_lines(U_51,orthogonal_through_point(U_50,sK1))
& ~ unorthogonal_lines(U_51,U_50)
& ~ apart_point_and_line(sK1,U_51) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_52,sK1)],[f_21_3]) ).
fof(f_21_5,negated_conjecture,
? [U_50] :
( distinct_lines(sK2,orthogonal_through_point(U_50,sK1))
& ~ unorthogonal_lines(sK2,U_50)
& ~ apart_point_and_line(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_51,sK2)],[f_21_4]) ).
fof(f_21_6,negated_conjecture,
( distinct_lines(sK2,orthogonal_through_point(sK3,sK1))
& ~ unorthogonal_lines(sK2,sK3)
& ~ apart_point_and_line(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_50,sK3)],[f_21_5]) ).
fof(f_21_7,negated_conjecture,
( distinct_lines(sK2,orthogonal_through_point(sK3,sK1))
& ~ unorthogonal_lines(sK2,sK3)
& ~ apart_point_and_line(sK1,sK2) ),
inference(definitional_conversion,[status(esa)],[f_21_6]) ).
cnf(f_21_8,negated_conjecture,
~ apart_point_and_line(sK1,sK2),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_9,negated_conjecture,
~ unorthogonal_lines(sK2,sK3),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(f_21_10,negated_conjecture,
distinct_lines(sK2,orthogonal_through_point(sK3,sK1)),
inference(clausify,[status(thm)],[f_21_7]) ).
cnf(t1,plain,
~ unorthogonal_lines(orthogonal_through_point(sK3,sK1),sK3),
inference(start,[status(thm),parent(0:0)],[f_18_3]) ).
cnf(t2,plain,
( apart_point_and_line(sK1,sK2)
| apart_point_and_line(sK1,orthogonal_through_point(sK3,sK1))
| unorthogonal_lines(sK2,sK3)
| ~ distinct_lines(sK2,orthogonal_through_point(sK3,sK1))
| unorthogonal_lines(orthogonal_through_point(sK3,sK1),sK3) ),
inference(extension,[status(thm),parent(t1:1)],[f_20_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
distinct_lines(sK2,orthogonal_through_point(sK3,sK1)),
inference(extension,[status(thm),parent(t2:2)],[f_21_10]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
~ unorthogonal_lines(sK2,sK3),
inference(extension,[status(thm),parent(t2:3)],[f_21_9]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
cnf(t8,plain,
~ apart_point_and_line(sK1,orthogonal_through_point(sK3,sK1)),
inference(extension,[status(thm),parent(t2:4)],[f_19_3]) ).
cnf(t9,plain,
$false,
inference(connection,[status(thm),parent(t8:1)],[t8:1,t2:4]) ).
cnf(t10,plain,
~ apart_point_and_line(sK1,sK2),
inference(extension,[status(thm),parent(t2:5)],[f_21_8]) ).
cnf(t11,plain,
$false,
inference(connection,[status(thm),parent(t10:1)],[t10:1,t2:5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO210+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
% 0.10/0.38 % Computer : n013.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Sat Sep 19 07:40:51 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.45 % SZS status Theorem for theBenchmark
% 0.10/0.45 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------