%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO237+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 : n016.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 0.09s 0.43s
% Output : Proof 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 27 ( 8 unt; 0 def)
% Number of atoms : 93 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 108 ( 42 ~; 23 |; 38 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 52 ( 2 sgn 33 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a8_defns,axiom,
! [A,B,L] :
( divides_points(L,A,B)
<=> ( ( left_apart_point(B,L)
& right_apart_point(A,L) )
| ( right_apart_point(B,L)
& left_apart_point(A,L) ) ) ),
file('GEO009+0.ax',a8_defns) ).
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(con,conjecture,
! [A,B,C,L] :
( apart_point_and_line(C,L)
=> ( divides_points(L,A,B)
=> ( divides_points(L,B,C)
| divides_points(L,A,C) ) ) ),
file('theBenchmark.p',con) ).
fof(f_8_1,plain,
! [A,B,L] :
( ( divides_points(L,A,B)
| ( ( ~ left_apart_point(B,L)
| ~ right_apart_point(A,L) )
& ( ~ right_apart_point(B,L)
| ~ left_apart_point(A,L) ) ) )
& ( ( left_apart_point(B,L)
& right_apart_point(A,L) )
| ( right_apart_point(B,L)
& left_apart_point(A,L) )
| ~ divides_points(L,A,B) ) ),
inference(fof_nnf,[status(thm)],[a8_defns]) ).
fof(f_8_2,plain,
! [U_44,U_43,U_42] :
( ( divides_points(U_42,U_44,U_43)
| ( ( ~ left_apart_point(U_43,U_42)
| ~ right_apart_point(U_44,U_42) )
& ( ~ right_apart_point(U_43,U_42)
| ~ left_apart_point(U_44,U_42) ) ) )
& ( ( left_apart_point(U_43,U_42)
& right_apart_point(U_44,U_42) )
| ( right_apart_point(U_43,U_42)
& left_apart_point(U_44,U_42) )
| ~ divides_points(U_42,U_44,U_43) ) ),
inference(variable_rename,[status(thm)],[f_8_1]) ).
fof(f_8_3,plain,
( ! [U_50,U_48,U_46] :
( divides_points(U_46,U_50,U_48)
| ( ( ~ left_apart_point(U_48,U_46)
| ~ right_apart_point(U_50,U_46) )
& ( ~ right_apart_point(U_48,U_46)
| ~ left_apart_point(U_50,U_46) ) ) )
& ! [U_49,U_47,U_45] :
( ( left_apart_point(U_47,U_45)
& right_apart_point(U_49,U_45) )
| ( right_apart_point(U_47,U_45)
& left_apart_point(U_49,U_45) )
| ~ divides_points(U_45,U_49,U_47) ) ),
inference(miniscope,[status(thm)],[f_8_2]) ).
cnf(f_8_5,plain,
( left_apart_point(U_47,U_45)
| left_apart_point(U_49,U_45)
| ~ divides_points(U_45,U_49,U_47) ),
inference(clausify,[status(thm)],[f_8_3]) ).
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_37_1,negated_conjecture,
~ ! [A,B,C,L] :
( apart_point_and_line(C,L)
=> ( divides_points(L,A,B)
=> ( divides_points(L,B,C)
| divides_points(L,A,C) ) ) ),
inference(negate,[status(cth)],[con]) ).
fof(f_37_2,negated_conjecture,
? [A,B,C,L] :
( ~ divides_points(L,B,C)
& ~ divides_points(L,A,C)
& divides_points(L,A,B)
& apart_point_and_line(C,L) ),
inference(fof_nnf,[status(thm)],[f_37_1]) ).
fof(f_37_3,negated_conjecture,
? [U_140,U_139,U_138,U_137] :
( ~ divides_points(U_137,U_139,U_138)
& ~ divides_points(U_137,U_140,U_138)
& divides_points(U_137,U_140,U_139)
& apart_point_and_line(U_138,U_137) ),
inference(variable_rename,[status(thm)],[f_37_2]) ).
fof(f_37_4,negated_conjecture,
? [U_139,U_138,U_137] :
( ~ divides_points(U_137,U_139,U_138)
& ~ divides_points(U_137,sK1,U_138)
& divides_points(U_137,sK1,U_139)
& apart_point_and_line(U_138,U_137) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_140,sK1)],[f_37_3]) ).
fof(f_37_5,negated_conjecture,
? [U_138,U_137] :
( ~ divides_points(U_137,sK2,U_138)
& ~ divides_points(U_137,sK1,U_138)
& divides_points(U_137,sK1,sK2)
& apart_point_and_line(U_138,U_137) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_139,sK2)],[f_37_4]) ).
fof(f_37_6,negated_conjecture,
? [U_137] :
( ~ divides_points(U_137,sK2,sK3)
& ~ divides_points(U_137,sK1,sK3)
& divides_points(U_137,sK1,sK2)
& apart_point_and_line(sK3,U_137) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_138,sK3)],[f_37_5]) ).
fof(f_37_7,negated_conjecture,
( ~ divides_points(sK4,sK2,sK3)
& ~ divides_points(sK4,sK1,sK3)
& divides_points(sK4,sK1,sK2)
& apart_point_and_line(sK3,sK4) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(U_137,sK4)],[f_37_6]) ).
fof(f_37_8,negated_conjecture,
( ~ divides_points(sK4,sK2,sK3)
& ~ divides_points(sK4,sK1,sK3)
& divides_points(sK4,sK1,sK2)
& apart_point_and_line(sK3,sK4) ),
inference(definitional_conversion,[status(esa)],[f_37_7]) ).
cnf(f_37_10,negated_conjecture,
divides_points(sK4,sK1,sK2),
inference(clausify,[status(thm)],[f_37_8]) ).
cnf(t1,plain,
~ left_apart_point(sK2,sK4),
inference(start,[status(thm),parent(0:0)],[f_20_4]) ).
cnf(t2,plain,
( left_apart_point(sK1,sK4)
| ~ divides_points(sK4,sK1,sK2)
| left_apart_point(sK2,sK4) ),
inference(extension,[status(thm),parent(t1:1)],[f_8_5]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
divides_points(sK4,sK1,sK2),
inference(extension,[status(thm),parent(t2:2)],[f_37_10]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
~ left_apart_point(sK1,sK4),
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 : GEO237+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
% 0.09/0.36 % Computer : n016.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 07:46:50 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.43 % SZS status Theorem for theBenchmark
% 0.09/0.43 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------