%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO174+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 : Sun Sep 27 07:17:15 AM UTC 2026
% Result : Theorem 0.18s 0.47s
% Output : CNFRefutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 4
% Syntax : Number of formulae : 21 ( 8 unt; 0 def)
% Number of atoms : 48 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 44 ( 17 ~; 12 |; 10 &)
% ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 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; 4 con; 0-2 aty)
% Number of variables : 28 ( 0 sgn 15 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(ci1,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('theBenchmark.p',ci1) ).
fof(ci2,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('theBenchmark.p',ci2) ).
fof(ceq2,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(X,Z)
| distinct_lines(Y,Z) ) ),
file('theBenchmark.p',ceq2) ).
fof(con,conjecture,
! [X,Y,U,V] :
( ( ( apart_point_and_line(Y,U)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> distinct_lines(U,line_connecting(X,Y)) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( ( apart_point_and_line(Y,U)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> distinct_lines(U,line_connecting(X,Y)) ),
inference(assume_negation,[status(cth)],[con]) ).
fof(nnf_36,plain,
? [X,Y,U,V] :
( ~ distinct_lines(U,line_connecting(X,Y))
& ( apart_point_and_line(Y,U)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ distinct_lines(sK0,line_connecting(sK1,sK2))
& ( apart_point_and_line(sK2,sK0)
| apart_point_and_line(sK1,sK0) )
& convergent_lines(sK0,sK3)
& distinct_points(sK1,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1,sK2,sK0,sK3]),skolemize(X,sK1),skolemize(Y,sK2),skolemize(U,sK0),skolemize(V,sK3)],[nnf_36]) ).
cnf(c_47,negated_conjecture,
~ distinct_lines(sK0,line_connecting(sK1,sK2)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_48,negated_conjecture,
( apart_point_and_line(sK2,sK0)
| apart_point_and_line(sK1,sK0) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_50,negated_conjecture,
distinct_points(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_72,plain,
( apart_point_and_line(A,C)
| distinct_lines(B,C)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[ceq2]) ).
cnf(c_77,plain,
( ~ apart_point_and_line(B,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci2]) ).
cnf(c_78,plain,
( ~ apart_point_and_line(A,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci1]) ).
cnf(c_105,plain,
~ apart_point_and_line(sK2,line_connecting(sK1,sK2)),
inference(resolve,[status(thm)],[c_77,c_50]) ).
cnf(c_106,plain,
~ apart_point_and_line(sK1,line_connecting(sK1,sK2)),
inference(resolve,[status(thm)],[c_78,c_50]) ).
cnf(c_183,negated_conjecture,
( apart_point_and_line(A,line_connecting(sK1,sK2))
| ~ apart_point_and_line(A,sK0) ),
inference(resolve,[status(thm)],[c_72,c_47]) ).
cnf(c_140,negated_conjecture,
~ apart_point_and_line(sK2,sK0),
inference(resolve,[status(thm)],[c_183,c_105]) ).
cnf(c_143,negated_conjecture,
apart_point_and_line(sK1,sK0),
inference(resolve,[status(thm)],[c_140,c_48]) ).
cnf(c_184,negated_conjecture,
( apart_point_and_line(A,line_connecting(sK1,sK2))
| ~ apart_point_and_line(A,sK0) ),
inference(resolve,[status(thm)],[c_72,c_47]) ).
cnf(c_185,negated_conjecture,
~ apart_point_and_line(sK1,sK0),
inference(resolve,[status(thm)],[c_184,c_106]) ).
cnf(c_182,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_143,c_185]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO174+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.43 % Computer : n009.cluster.edu
% 0.18/0.43 % Model : x86_64 x86_64
% 0.18/0.43 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.43 % Memory : 8046.5625MB
% 0.18/0.43 % OS : Linux 6.8.0-71-generic
% 0.18/0.43 % CPULimit : 300
% 0.18/0.43 % WCLimit : 300
% 0.18/0.43 % DateTime : Fri Sep 25 13:01:29 UTC 2026
% 0.18/0.43 % CPUTime :
% 0.18/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.18/0.44 % Process 1651671 was started by sandbox2 on n009,
% 0.18/0.44 % Fri Sep 25 13:01:29 2026
% 0.18/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.18/0.45
% 0.18/0.45 % From the command line: assign(max_seconds, 300).
% 0.18/0.47
% 0.18/0.47 % SZS status Theorem for theBenchmark
% 0.18/0.47
% 0.18/0.47 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.18/0.47 % Length of proof is 15.
% 0.18/0.47 % Level of proof is 5.
% 0.18/0.47 % Maximum clause weight is 18.000.
% 0.18/0.47 % Given clauses 53.
% 0.18/0.47
% 0.18/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------