%------------------------------------------------------------------------------
% File : ConnectPP---0.7.2
% Problem : GEO251+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 : n004.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 08:40:07 AM UTC 2026
% Result : Theorem 0.21s 0.48s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 3
% Syntax : Number of formulae : 24 ( 6 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 48 ( 24 ~; 9 |; 12 &)
% ( 1 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 2 sgn 26 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(a2_defns,axiom,
! [X,Y] :
( right_apart_point(X,Y)
<=> left_apart_point(X,reverse_line(Y)) ),
file('GEO009+0.ax',a2_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,L] :
( right_apart_point(B,parallel_through_point(L,A))
=> left_apart_point(A,parallel_through_point(L,B)) ),
file('theBenchmark.p',con) ).
fof(f_2_1,plain,
! [X,Y] :
( ( right_apart_point(X,Y)
| ~ left_apart_point(X,reverse_line(Y)) )
& ( left_apart_point(X,reverse_line(Y))
| ~ right_apart_point(X,Y) ) ),
inference(fof_nnf,[status(thm)],[a2_defns]) ).
fof(f_2_2,plain,
! [U_7,U_6] :
( ( right_apart_point(U_7,U_6)
| ~ left_apart_point(U_7,reverse_line(U_6)) )
& ( left_apart_point(U_7,reverse_line(U_6))
| ~ right_apart_point(U_7,U_6) ) ),
inference(variable_rename,[status(thm)],[f_2_1]) ).
fof(f_2_3,plain,
( ! [U_11,U_9] :
( right_apart_point(U_11,U_9)
| ~ left_apart_point(U_11,reverse_line(U_9)) )
& ! [U_10,U_8] :
( left_apart_point(U_10,reverse_line(U_8))
| ~ right_apart_point(U_10,U_8) ) ),
inference(miniscope,[status(thm)],[f_2_2]) ).
cnf(f_2_4,plain,
( left_apart_point(U_10,reverse_line(U_8))
| ~ right_apart_point(U_10,U_8) ),
inference(clausify,[status(thm)],[f_2_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,L] :
( right_apart_point(B,parallel_through_point(L,A))
=> left_apart_point(A,parallel_through_point(L,B)) ),
inference(negate,[status(cth)],[con]) ).
fof(f_37_2,negated_conjecture,
? [A,B,L] :
( ~ left_apart_point(A,parallel_through_point(L,B))
& right_apart_point(B,parallel_through_point(L,A)) ),
inference(fof_nnf,[status(thm)],[f_37_1]) ).
fof(f_37_3,negated_conjecture,
? [U_139,U_138,U_137] :
( ~ left_apart_point(U_139,parallel_through_point(U_137,U_138))
& right_apart_point(U_138,parallel_through_point(U_137,U_139)) ),
inference(variable_rename,[status(thm)],[f_37_2]) ).
fof(f_37_4,negated_conjecture,
? [U_138,U_137] :
( ~ left_apart_point(sK1,parallel_through_point(U_137,U_138))
& right_apart_point(U_138,parallel_through_point(U_137,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1]),skolemize(U_139,sK1)],[f_37_3]) ).
fof(f_37_5,negated_conjecture,
? [U_137] :
( ~ left_apart_point(sK1,parallel_through_point(U_137,sK2))
& right_apart_point(sK2,parallel_through_point(U_137,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(U_138,sK2)],[f_37_4]) ).
fof(f_37_6,negated_conjecture,
( ~ left_apart_point(sK1,parallel_through_point(sK3,sK2))
& right_apart_point(sK2,parallel_through_point(sK3,sK1)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3]),skolemize(U_137,sK3)],[f_37_5]) ).
fof(f_37_7,negated_conjecture,
( ~ left_apart_point(sK1,parallel_through_point(sK3,sK2))
& right_apart_point(sK2,parallel_through_point(sK3,sK1)) ),
inference(definitional_conversion,[status(esa)],[f_37_6]) ).
cnf(f_37_8,negated_conjecture,
right_apart_point(sK2,parallel_through_point(sK3,sK1)),
inference(clausify,[status(thm)],[f_37_7]) ).
cnf(t1,plain,
~ left_apart_point(sK2,reverse_line(parallel_through_point(sK3,sK1))),
inference(start,[status(thm),parent(0:0)],[f_20_4]) ).
cnf(t2,plain,
( ~ right_apart_point(sK2,parallel_through_point(sK3,sK1))
| left_apart_point(sK2,reverse_line(parallel_through_point(sK3,sK1))) ),
inference(extension,[status(thm),parent(t1:1)],[f_2_4]) ).
cnf(t3,plain,
$false,
inference(connection,[status(thm),parent(t2:1)],[t2:1,t1:1]) ).
cnf(t4,plain,
right_apart_point(sK2,parallel_through_point(sK3,sK1)),
inference(extension,[status(thm),parent(t2:2)],[f_37_8]) ).
cnf(t5,plain,
$false,
inference(connection,[status(thm),parent(t4:1)],[t4:1,t2:2]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO251+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
% 0.09/0.34 % Computer : n004.cluster.edu
% 0.09/0.34 % Model : x86_64 x86_64
% 0.09/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.34 % Memory : 8046.5625MB
% 0.09/0.34 % OS : Linux 6.8.0-71-generic
% 0.09/0.34 % CPULimit : 300
% 0.09/0.34 % WCLimit : 300
% 0.09/0.34 % DateTime : Sat Sep 19 07:42:34 UTC 2026
% 0.09/0.34 % CPUTime :
% 0.21/0.48 % SZS status Theorem for theBenchmark
% 0.21/0.48 % SZS output start Proof for theBenchmark
% See solution above
%------------------------------------------------------------------------------