%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO237+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 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 08:40:04 AM UTC 2026
% Result : Theorem 0.13s 0.62s
% Output : Proof 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 3
% Syntax : Number of formulae : 28 ( 9 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 109 ( 43 ~; 23 |; 38 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-3 aty)
% Number of functors : 5 ( 5 usr; 4 con; 0-1 aty)
% Number of variables : 54 ( 5 sgn 33 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(div_def,axiom,
! [A,B,L] :
( divides_points(L,A,B)
<=> ( ( left_apart_point(B,L)
& left_apart_point(A,reverse_line(L)) )
| ( left_apart_point(B,reverse_line(L))
& left_apart_point(A,L) ) ) ),
file('GEO007+0.ax',div_def) ).
fof(oag10,axiom,
! [A,L] :
~ ( left_apart_point(A,reverse_line(L))
| left_apart_point(A,L) ),
file('GEO007+0.ax',oag10) ).
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_3_1,plain,
! [A,B,L] :
( ( divides_points(L,A,B)
| ( ( ~ left_apart_point(B,L)
| ~ left_apart_point(A,reverse_line(L)) )
& ( ~ left_apart_point(B,reverse_line(L))
| ~ left_apart_point(A,L) ) ) )
& ( ( left_apart_point(B,L)
& left_apart_point(A,reverse_line(L)) )
| ( left_apart_point(B,reverse_line(L))
& left_apart_point(A,L) )
| ~ divides_points(L,A,B) ) ),
inference(fof_nnf,[status(thm)],[div_def]) ).
fof(f_3_2,plain,
! [U_14,U_13,U_12] :
( ( divides_points(U_12,U_14,U_13)
| ( ( ~ left_apart_point(U_13,U_12)
| ~ left_apart_point(U_14,reverse_line(U_12)) )
& ( ~ left_apart_point(U_13,reverse_line(U_12))
| ~ left_apart_point(U_14,U_12) ) ) )
& ( ( left_apart_point(U_13,U_12)
& left_apart_point(U_14,reverse_line(U_12)) )
| ( left_apart_point(U_13,reverse_line(U_12))
& left_apart_point(U_14,U_12) )
| ~ divides_points(U_12,U_14,U_13) ) ),
inference(variable_rename,[status(thm)],[f_3_1]) ).
fof(f_3_3,plain,
( ! [U_20,U_18,U_16] :
( divides_points(U_16,U_20,U_18)
| ( ( ~ left_apart_point(U_18,U_16)
| ~ left_apart_point(U_20,reverse_line(U_16)) )
& ( ~ left_apart_point(U_18,reverse_line(U_16))
| ~ left_apart_point(U_20,U_16) ) ) )
& ! [U_19,U_17,U_15] :
( ( left_apart_point(U_17,U_15)
& left_apart_point(U_19,reverse_line(U_15)) )
| ( left_apart_point(U_17,reverse_line(U_15))
& left_apart_point(U_19,U_15) )
| ~ divides_points(U_15,U_19,U_17) ) ),
inference(miniscope,[status(thm)],[f_3_2]) ).
cnf(f_3_7,plain,
( left_apart_point(U_17,U_15)
| left_apart_point(U_17,reverse_line(U_15))
| ~ divides_points(U_15,U_19,U_17) ),
inference(clausify,[status(thm)],[f_3_3]) ).
fof(f_15_1,plain,
! [A,L] :
( ~ left_apart_point(A,reverse_line(L))
& ~ left_apart_point(A,L) ),
inference(fof_nnf,[status(thm)],[oag10]) ).
fof(f_15_2,plain,
! [U_62,U_61] :
( ~ left_apart_point(U_62,reverse_line(U_61))
& ~ left_apart_point(U_62,U_61) ),
inference(variable_rename,[status(thm)],[f_15_1]) ).
fof(f_15_3,plain,
( ! [U_66,U_64] : ~ left_apart_point(U_66,reverse_line(U_64))
& ! [U_65,U_63] : ~ left_apart_point(U_65,U_63) ),
inference(miniscope,[status(thm)],[f_15_2]) ).
cnf(f_15_4,plain,
~ left_apart_point(U_65,U_63),
inference(clausify,[status(thm)],[f_15_3]) ).
cnf(f_15_5,plain,
~ left_apart_point(U_66,reverse_line(U_64)),
inference(clausify,[status(thm)],[f_15_3]) ).
fof(f_32_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_32_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_32_1]) ).
fof(f_32_3,negated_conjecture,
? [U_110,U_109,U_108,U_107] :
( ~ divides_points(U_107,U_109,U_108)
& ~ divides_points(U_107,U_110,U_108)
& divides_points(U_107,U_110,U_109)
& apart_point_and_line(U_108,U_107) ),
inference(variable_rename,[status(thm)],[f_32_2]) ).
fof(f_32_4,negated_conjecture,
? [U_109,U_108,U_107] :
( ~ divides_points(U_107,U_109,U_108)
& ~ divides_points(U_107,sK1,U_108)
& divides_points(U_107,sK1,U_109)
& apart_point_and_line(U_108,U_107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_110,sK1)],[f_32_3]) ).
fof(f_32_5,negated_conjecture,
? [U_108,U_107] :
( ~ divides_points(U_107,sK2,U_108)
& ~ divides_points(U_107,sK1,U_108)
& divides_points(U_107,sK1,sK2)
& apart_point_and_line(U_108,U_107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_109,sK2)],[f_32_4]) ).
fof(f_32_6,negated_conjecture,
? [U_107] :
( ~ divides_points(U_107,sK2,sK3)
& ~ divides_points(U_107,sK1,sK3)
& divides_points(U_107,sK1,sK2)
& apart_point_and_line(sK3,U_107) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_108,sK3)],[f_32_5]) ).
fof(f_32_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_107,sK4)],[f_32_6]) ).
fof(f_32_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_32_7]) ).
cnf(f_32_10,negated_conjecture,
divides_points(sK4,sK1,sK2),
inference(clausify,[status(thm)],[f_32_8]) ).
cnf(t1,plain,
~ left_apart_point(sK2,sK4),
inference(start,[status(thm),parent(0:0)],[f_15_4]) ).
cnf(t2,plain,
( left_apart_point(sK2,reverse_line(sK4))
| ~ divides_points(sK4,sK1,sK2)
| left_apart_point(sK2,sK4) ),
inference(extension,[status(thm),parent(t1:1)],[f_3_7]) ).
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_32_10]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
cnf(t6,plain,
~ left_apart_point(sK2,reverse_line(sK4)),
inference(extension,[status(thm),parent(t2:3)],[f_15_5]) ).
cnf(t7,plain,
$false,
inference(connection,[status(thm),parent(t6:1)],[t6:1,t2:3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO237+1 : TPTP v9.3.1. Bugfixed v6.4.0.
% 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
% 0.10/0.54 % Computer : n020.cluster.edu
% 0.10/0.54 % Model : x86_64 x86_64
% 0.10/0.54 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.54 % Memory : 8046.5625MB
% 0.10/0.54 % OS : Linux 6.8.0-71-generic
% 0.10/0.54 % CPULimit : 300
% 0.10/0.54 % WCLimit : 300
% 0.10/0.54 % DateTime : Sat Sep 19 07:43:03 UTC 2026
% 0.10/0.55 % CPUTime :
% 0.13/0.62 % SZS status Theorem for theBenchmark
% 0.13/0.62 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------