%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO239+3 : TPTP v9.3.1. Released v4.0.0.
% 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 : n003.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 08:40:04 AM UTC 2026
% Result : Theorem 0.21s 0.48s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 29 ( 12 unt; 0 def)
% Number of atoms : 59 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 55 ( 25 ~; 10 |; 17 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 43 ( 2 sgn 28 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ax1_basics,axiom,
! [A] : ~ distinct_points(A,A),
file('GEO009+0.ax',ax1_basics) ).
fof(ax10_basics,axiom,
! [A,L] :
~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) ),
file('GEO009+0.ax',ax10_basics) ).
fof(ax1_subs,axiom,
! [A,B,L] :
( left_apart_point(A,L)
=> ( left_apart_point(B,L)
| distinct_points(A,B) ) ),
file('GEO009+0.ax',ax1_subs) ).
fof(con,conjecture,
! [A,B,L] :
( ( left_apart_point(B,L)
& incident_point_and_line(A,L) )
=> left_convergent_lines(L,line_connecting(A,B)) ),
file('theBenchmark.p',con) ).
fof(f_11_1,plain,
! [A] : ~ distinct_points(A,A),
inference(fof_nnf,[status(thm)],[ax1_basics]) ).
fof(f_11_2,plain,
! [U_72] : ~ distinct_points(U_72,U_72),
inference(variable_rename,[status(thm)],[f_11_1]) ).
cnf(f_11_3,plain,
~ distinct_points(U_72,U_72),
inference(clausify,[status(thm)],[f_11_2]) ).
fof(f_20_1,plain,
! [A,L] :
( ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L) ),
inference(fof_nnf,[status(thm)],[ax10_basics]) ).
fof(f_20_2,plain,
! [U_92,U_91] :
( ~ left_apart_point(U_92,reverse_line(U_91))
& ~ left_apart_point(U_92,U_91) ),
inference(variable_rename,[status(thm)],[f_20_1]) ).
fof(f_20_3,plain,
( ! [U_96,U_94] : ~ left_apart_point(U_96,reverse_line(U_94))
& ! [U_95,U_93] : ~ left_apart_point(U_95,U_93) ),
inference(miniscope,[status(thm)],[f_20_2]) ).
cnf(f_20_4,plain,
~ left_apart_point(U_95,U_93),
inference(clausify,[status(thm)],[f_20_3]) ).
fof(f_34_1,plain,
! [A,B,L] :
( left_apart_point(B,L)
| distinct_points(A,B)
| ~ left_apart_point(A,L) ),
inference(fof_nnf,[status(thm)],[ax1_subs]) ).
fof(f_34_2,plain,
! [U_130,U_129,U_128] :
( left_apart_point(U_129,U_128)
| distinct_points(U_130,U_129)
| ~ left_apart_point(U_130,U_128) ),
inference(variable_rename,[status(thm)],[f_34_1]) ).
cnf(f_34_3,plain,
( left_apart_point(U_129,U_128)
| distinct_points(U_130,U_129)
| ~ left_apart_point(U_130,U_128) ),
inference(clausify,[status(thm)],[f_34_2]) ).
fof(f_37_1,negated_conjecture,
~ ! [A,B,L] :
( ( left_apart_point(B,L)
& incident_point_and_line(A,L) )
=> left_convergent_lines(L,line_connecting(A,B)) ),
inference(negate,[status(cth)],[con]) ).
fof(f_37_2,negated_conjecture,
? [A,B,L] :
( ~ left_convergent_lines(L,line_connecting(A,B))
& left_apart_point(B,L)
& incident_point_and_line(A,L) ),
inference(fof_nnf,[status(thm)],[f_37_1]) ).
fof(f_37_3,negated_conjecture,
? [U_139,U_138,U_137] :
( ~ left_convergent_lines(U_137,line_connecting(U_139,U_138))
& left_apart_point(U_138,U_137)
& incident_point_and_line(U_139,U_137) ),
inference(variable_rename,[status(thm)],[f_37_2]) ).
fof(f_37_4,negated_conjecture,
? [U_138,U_137] :
( ~ left_convergent_lines(U_137,line_connecting(sK1,U_138))
& left_apart_point(U_138,U_137)
& incident_point_and_line(sK1,U_137) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_139,sK1)],[f_37_3]) ).
fof(f_37_5,negated_conjecture,
? [U_137] :
( ~ left_convergent_lines(U_137,line_connecting(sK1,sK2))
& left_apart_point(sK2,U_137)
& incident_point_and_line(sK1,U_137) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_138,sK2)],[f_37_4]) ).
fof(f_37_6,negated_conjecture,
( ~ left_convergent_lines(sK3,line_connecting(sK1,sK2))
& left_apart_point(sK2,sK3)
& incident_point_and_line(sK1,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_137,sK3)],[f_37_5]) ).
fof(f_37_7,negated_conjecture,
( ~ left_convergent_lines(sK3,line_connecting(sK1,sK2))
& left_apart_point(sK2,sK3)
& incident_point_and_line(sK1,sK3) ),
inference(definitional_conversion,[status(esa)],[f_37_6]) ).
cnf(f_37_9,negated_conjecture,
left_apart_point(sK2,sK3),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(t1,plain,
~ distinct_points(sK2,sK2),
inference(start,[status(thm),parent(0:0)],[f_11_3]) ).
cnf(t2,plain,
( left_apart_point(sK2,sK3)
| ~ left_apart_point(sK2,sK3)
| distinct_points(sK2,sK2) ),
inference(extension,[status(thm),parent(t1:1)],[f_34_3]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
left_apart_point(sK2,sK3),
inference(extension,[status(thm),parent(t2:2)],[f_37_9]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
~ left_apart_point(sK2,sK3),
inference(extension,[status(thm),parent(t2:3)],[f_20_4]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO239+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/sandbox/solver/bin/connect++ --verbosity 1 --no-colour --tptp-proof --schedule default --timeout 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n003.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Sat Sep 19 07:43:43 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.21/0.48 % SZS status Theorem for theBenchmark
% 0.21/0.48 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------