%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO241+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 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 : n005.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 08:40:05 AM UTC 2026
% Result : Theorem 0.41s 0.67s
% Output : Proof 0.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 30 ( 12 unt; 0 def)
% Number of atoms : 70 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 74 ( 34 ~; 12 |; 25 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 46 ( 2 sgn 31 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(oag5,axiom,
! [L] : ~ unequally_directed_lines(L,L),
file('GEO007+0.ax',oag5) ).
fof(oag11,axiom,
! [L,M] :
~ ( left_convergent_lines(L,reverse_line(M))
| left_convergent_lines(L,M) ),
file('GEO007+0.ax',oag11) ).
fof(oagsub3,axiom,
! [L,M,N] :
( left_convergent_lines(L,M)
=> ( left_convergent_lines(L,N)
| unequally_directed_lines(M,N) ) ),
file('GEO007+0.ax',oagsub3) ).
fof(con,conjecture,
! [A,B,L] :
( ( left_convergent_lines(L,line_connecting(A,B))
& distinct_points(A,B)
& ~ apart_point_and_line(A,L) )
=> left_apart_point(B,L) ),
file('theBenchmark.p',con) ).
fof(f_10_1,plain,
! [L] : ~ unequally_directed_lines(L,L),
inference(fof_nnf,[status(thm)],[oag5]) ).
fof(f_10_2,plain,
! [U_50] : ~ unequally_directed_lines(U_50,U_50),
inference(variable_rename,[status(thm)],[f_10_1]) ).
cnf(f_10_3,plain,
~ unequally_directed_lines(U_50,U_50),
inference(clausify,[status(thm)],[f_10_2]) ).
fof(f_16_1,plain,
! [L,M] :
( ~ left_convergent_lines(L,reverse_line(M))
& ~ left_convergent_lines(L,M) ),
inference(fof_nnf,[status(thm)],[oag11]) ).
fof(f_16_2,plain,
! [U_68,U_67] :
( ~ left_convergent_lines(U_68,reverse_line(U_67))
& ~ left_convergent_lines(U_68,U_67) ),
inference(variable_rename,[status(thm)],[f_16_1]) ).
fof(f_16_3,plain,
( ! [U_72,U_70] : ~ left_convergent_lines(U_72,reverse_line(U_70))
& ! [U_71,U_69] : ~ left_convergent_lines(U_71,U_69) ),
inference(miniscope,[status(thm)],[f_16_2]) ).
cnf(f_16_4,plain,
~ left_convergent_lines(U_71,U_69),
inference(clausify,[status(thm)],[f_16_3]) ).
fof(f_31_1,plain,
! [L,M,N] :
( left_convergent_lines(L,N)
| unequally_directed_lines(M,N)
| ~ left_convergent_lines(L,M) ),
inference(fof_nnf,[status(thm)],[oagsub3]) ).
fof(f_31_2,plain,
! [U_106,U_105,U_104] :
( left_convergent_lines(U_106,U_104)
| unequally_directed_lines(U_105,U_104)
| ~ left_convergent_lines(U_106,U_105) ),
inference(variable_rename,[status(thm)],[f_31_1]) ).
fof(f_31_3,plain,
! [U_106,U_105] :
( ! [U_104] :
( left_convergent_lines(U_106,U_104)
| unequally_directed_lines(U_105,U_104) )
| ~ left_convergent_lines(U_106,U_105) ),
inference(miniscope,[status(thm)],[f_31_2]) ).
cnf(f_31_4,plain,
( left_convergent_lines(U_106,U_104)
| unequally_directed_lines(U_105,U_104)
| ~ left_convergent_lines(U_106,U_105) ),
inference(clausify,[status(thm)],[f_31_3]) ).
fof(f_32_1,negated_conjecture,
~ ! [A,B,L] :
( ( left_convergent_lines(L,line_connecting(A,B))
& distinct_points(A,B)
& ~ apart_point_and_line(A,L) )
=> left_apart_point(B,L) ),
inference(negate,[status(cth)],[con]) ).
fof(f_32_2,negated_conjecture,
? [A,B,L] :
( ~ left_apart_point(B,L)
& left_convergent_lines(L,line_connecting(A,B))
& distinct_points(A,B)
& ~ apart_point_and_line(A,L) ),
inference(fof_nnf,[status(thm)],[f_32_1]) ).
fof(f_32_3,negated_conjecture,
? [U_109,U_108,U_107] :
( ~ left_apart_point(U_108,U_107)
& left_convergent_lines(U_107,line_connecting(U_109,U_108))
& distinct_points(U_109,U_108)
& ~ apart_point_and_line(U_109,U_107) ),
inference(variable_rename,[status(thm)],[f_32_2]) ).
fof(f_32_4,negated_conjecture,
? [U_108,U_107] :
( ~ left_apart_point(U_108,U_107)
& left_convergent_lines(U_107,line_connecting(sK1,U_108))
& distinct_points(sK1,U_108)
& ~ apart_point_and_line(sK1,U_107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_109,sK1)],[f_32_3]) ).
fof(f_32_5,negated_conjecture,
? [U_107] :
( ~ left_apart_point(sK2,U_107)
& left_convergent_lines(U_107,line_connecting(sK1,sK2))
& distinct_points(sK1,sK2)
& ~ apart_point_and_line(sK1,U_107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_108,sK2)],[f_32_4]) ).
fof(f_32_6,negated_conjecture,
( ~ left_apart_point(sK2,sK3)
& left_convergent_lines(sK3,line_connecting(sK1,sK2))
& distinct_points(sK1,sK2)
& ~ apart_point_and_line(sK1,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_107,sK3)],[f_32_5]) ).
fof(f_32_7,negated_conjecture,
( ~ left_apart_point(sK2,sK3)
& left_convergent_lines(sK3,line_connecting(sK1,sK2))
& distinct_points(sK1,sK2)
& ~ apart_point_and_line(sK1,sK3) ),
inference(definitional_conversion,[status(esa)],[f_32_6]) ).
cnf(f_32_10,negated_conjecture,
left_convergent_lines(sK3,line_connecting(sK1,sK2)),
inference(clausify,[status(thm)],[f_32_7]) ).
cnf(t1,plain,
~ unequally_directed_lines(line_connecting(sK1,sK2),line_connecting(sK1,sK2)),
inference(start,[status(thm),parent(0:0)],[f_10_3]) ).
cnf(t2,plain,
( left_convergent_lines(sK3,line_connecting(sK1,sK2))
| ~ left_convergent_lines(sK3,line_connecting(sK1,sK2))
| unequally_directed_lines(line_connecting(sK1,sK2),line_connecting(sK1,sK2)) ),
inference(extension,[status(thm),parent(t1:1)],[f_31_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
left_convergent_lines(sK3,line_connecting(sK1,sK2)),
inference(extension,[status(thm),parent(t2:2)],[f_32_10]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
~ left_convergent_lines(sK3,line_connecting(sK1,sK2)),
inference(extension,[status(thm),parent(t2:3)],[f_16_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO241+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 0.00/0.04 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
% 0.12/0.37 % Computer : n005.cluster.edu
% 0.12/0.37 % Model : x86_64 x86_64
% 0.12/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.37 % Memory : 8046.5625MB
% 0.12/0.37 % OS : Linux 6.8.0-71-generic
% 0.12/0.37 % CPULimit : 300
% 0.12/0.37 % WCLimit : 300
% 0.12/0.37 % DateTime : Sat Sep 19 07:42:18 UTC 2026
% 0.12/0.37 % CPUTime :
% 0.41/0.67 % SZS status Theorem for theBenchmark
% 0.41/0.67 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------