%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO176+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 07:17:16 AM UTC 2026
% Result : Theorem 0.10s 5.39s
% Output : CNFRefutation 0.10s
% 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 : 4 ( 3 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(ci3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('theBenchmark.p',ci3) ).
fof(ci4,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('theBenchmark.p',ci4) ).
fof(ceq1,axiom,
! [X,Y,Z] :
( apart_point_and_line(X,Y)
=> ( apart_point_and_line(Z,Y)
| distinct_points(X,Z) ) ),
file('theBenchmark.p',ceq1) ).
fof(con,conjecture,
! [X,Y,U,V] :
( ( ( apart_point_and_line(X,V)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> distinct_points(X,intersection_point(U,V)) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,U,V] :
( ( ( apart_point_and_line(X,V)
| apart_point_and_line(X,U) )
& convergent_lines(U,V)
& distinct_points(X,Y) )
=> distinct_points(X,intersection_point(U,V)) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_24,plain,
( ~ apart_point_and_line(intersection_point(A,B),A)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci3]) ).
cnf(c_25,plain,
( ~ apart_point_and_line(intersection_point(A,B),B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci4]) ).
cnf(c_27,plain,
( apart_point_and_line(C,B)
| distinct_points(A,C)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[ceq1]) ).
fof(nnf_15,plain,
? [X,Y,U,V] :
( ~ distinct_points(X,intersection_point(U,V))
& ( apart_point_and_line(X,V)
| 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_points(sK2,intersection_point(sK0,sK1))
& ( apart_point_and_line(sK2,sK1)
| apart_point_and_line(sK2,sK0) )
& convergent_lines(sK0,sK1)
& distinct_points(sK2,sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3,sK0,sK1]),skolemize(X,sK2),skolemize(Y,sK3),skolemize(U,sK0),skolemize(V,sK1)],[nnf_15]) ).
cnf(c_31,negated_conjecture,
convergent_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_32,negated_conjecture,
( apart_point_and_line(sK2,sK1)
| apart_point_and_line(sK2,sK0) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_33,negated_conjecture,
~ distinct_points(sK2,intersection_point(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_39,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK1),
inference(resolve,[status(thm)],[c_31,c_25]) ).
cnf(c_40,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_31,c_24]) ).
cnf(c_60,negated_conjecture,
( apart_point_and_line(intersection_point(sK0,sK1),A)
| ~ apart_point_and_line(sK2,A) ),
inference(resolve,[status(thm)],[c_27,c_33]) ).
cnf(c_46,negated_conjecture,
~ apart_point_and_line(sK2,sK1),
inference(resolve,[status(thm)],[c_60,c_39]) ).
cnf(c_47,negated_conjecture,
apart_point_and_line(sK2,sK0),
inference(resolve,[status(thm)],[c_46,c_32]) ).
cnf(c_61,negated_conjecture,
( apart_point_and_line(intersection_point(sK0,sK1),A)
| ~ apart_point_and_line(sK2,A) ),
inference(resolve,[status(thm)],[c_27,c_33]) ).
cnf(c_62,negated_conjecture,
~ apart_point_and_line(sK2,sK0),
inference(resolve,[status(thm)],[c_61,c_40]) ).
cnf(c_59,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_47,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO176+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/5.37 % Computer : n026.cluster.edu
% 0.10/5.37 % Model : x86_64 x86_64
% 0.10/5.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.37 % Memory : 8046.5625MB
% 0.10/5.37 % OS : Linux 6.8.0-71-generic
% 0.10/5.37 % CPULimit : 300
% 0.10/5.37 % WCLimit : 300
% 0.10/5.37 % DateTime : Fri Sep 25 13:04:31 UTC 2026
% 0.10/5.37 % CPUTime :
% 0.10/5.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.10/5.37 % Process 2576272 was started by sandbox2 on n026,
% 0.10/5.37 % Fri Sep 25 13:04:31 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.10/5.38
% 0.10/5.38 % From the command line: assign(max_seconds, 300).
% 0.10/5.39
% 0.10/5.39 % SZS status Theorem for theBenchmark
% 0.10/5.39
% 0.10/5.39 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.10/5.39 % Length of proof is 15.
% 0.10/5.39 % Level of proof is 5.
% 0.10/5.39 % Maximum clause weight is 9.000.
% 0.10/5.39 % Given clauses 28.
% 0.10/5.39
% 0.10/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------