%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO193+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 : 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 07:17:23 AM UTC 2026
% Result : Theorem 0.14s 5.60s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 18
% Number of leaves : 8
% Syntax : Number of formulae : 51 ( 19 unt; 0 def)
% Number of atoms : 123 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 35 ~; 49 |; 13 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 61 ( 0 sgn 24 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('theBenchmark.p',apart3) ).
fof(ax6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('theBenchmark.p',ax6) ).
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(cu1,axiom,
! [X,Y,U,V] :
( ( distinct_lines(U,V)
& distinct_points(X,Y) )
=> ( apart_point_and_line(Y,V)
| apart_point_and_line(Y,U)
| apart_point_and_line(X,V)
| apart_point_and_line(X,U) ) ),
file('theBenchmark.p',cu1) ).
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(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('theBenchmark.p',ceq3) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> apart_point_and_line(intersection_point(Z,Y),X) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) )
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> apart_point_and_line(intersection_point(Z,Y),X) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_18,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_21,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ax6]) ).
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_26,plain,
( apart_point_and_line(B,D)
| apart_point_and_line(B,C)
| apart_point_and_line(A,D)
| apart_point_and_line(A,C)
| ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[cu1]) ).
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]) ).
cnf(c_29,plain,
( convergent_lines(A,C)
| distinct_lines(B,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ceq3]) ).
fof(nnf_15,plain,
? [X,Y,Z] :
( ~ apart_point_and_line(intersection_point(Z,Y),X)
& apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Z)
& convergent_lines(Z,Y)
& convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ~ apart_point_and_line(intersection_point(sK2,sK1),sK0)
& apart_point_and_line(intersection_point(sK0,sK1),sK2)
& convergent_lines(sK0,sK2)
& convergent_lines(sK2,sK1)
& convergent_lines(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(Y,sK1),skolemize(Z,sK2)],[nnf_15]) ).
cnf(c_30,negated_conjecture,
convergent_lines(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_31,negated_conjecture,
convergent_lines(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_33,negated_conjecture,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_34,negated_conjecture,
~ apart_point_and_line(intersection_point(sK2,sK1),sK0),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_36,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK1),
inference(resolve,[status(thm)],[c_30,c_25]) ).
cnf(c_37,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_30,c_24]) ).
cnf(c_38,plain,
( convergent_lines(sK1,A)
| convergent_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_30,c_21]) ).
cnf(c_40,plain,
~ apart_point_and_line(intersection_point(sK2,sK1),sK1),
inference(resolve,[status(thm)],[c_31,c_25]) ).
cnf(c_41,plain,
~ apart_point_and_line(intersection_point(sK2,sK1),sK2),
inference(resolve,[status(thm)],[c_31,c_24]) ).
cnf(c_48,plain,
( apart_point_and_line(A,sK2)
| distinct_points(intersection_point(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_33,c_27]) ).
cnf(c_53,plain,
( convergent_lines(A,B)
| convergent_lines(sK1,B)
| convergent_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_38,c_21]) ).
cnf(c_148,plain,
( convergent_lines(sK1,sK0)
| convergent_lines(sK0,sK0) ),
inference(factor,[status(thm)],[c_53]) ).
cnf(c_54,plain,
convergent_lines(sK1,sK0),
inference(resolve,[status(thm)],[c_18,c_148]) ).
cnf(c_56,plain,
~ apart_point_and_line(intersection_point(sK1,sK0),sK0),
inference(resolve,[status(thm)],[c_54,c_25]) ).
cnf(c_57,plain,
~ apart_point_and_line(intersection_point(sK1,sK0),sK1),
inference(resolve,[status(thm)],[c_54,c_24]) ).
cnf(c_96,plain,
( convergent_lines(A,sK1)
| convergent_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_53,c_18]) ).
cnf(c_107,plain,
( convergent_lines(A,B)
| distinct_lines(sK1,B)
| convergent_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_96,c_29]) ).
cnf(c_149,plain,
( distinct_lines(sK1,sK0)
| convergent_lines(sK0,sK0) ),
inference(factor,[status(thm)],[c_107]) ).
cnf(c_110,plain,
distinct_lines(sK1,sK0),
inference(resolve,[status(thm)],[c_18,c_149]) ).
cnf(c_150,plain,
( apart_point_and_line(B,sK0)
| apart_point_and_line(B,sK1)
| apart_point_and_line(A,sK0)
| apart_point_and_line(A,sK1)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_26,c_110]) ).
cnf(c_151,plain,
( apart_point_and_line(A,sK0)
| apart_point_and_line(A,sK1)
| apart_point_and_line(intersection_point(sK1,sK0),sK0)
| ~ distinct_points(intersection_point(sK1,sK0),A) ),
inference(resolve,[status(thm)],[c_150,c_57]) ).
cnf(c_152,plain,
( apart_point_and_line(A,sK0)
| apart_point_and_line(A,sK1)
| ~ distinct_points(intersection_point(sK1,sK0),A) ),
inference(resolve,[status(thm)],[c_151,c_56]) ).
cnf(c_153,plain,
( apart_point_and_line(intersection_point(sK2,sK1),sK0)
| ~ distinct_points(intersection_point(sK1,sK0),intersection_point(sK2,sK1)) ),
inference(resolve,[status(thm)],[c_152,c_40]) ).
cnf(c_115,negated_conjecture,
~ distinct_points(intersection_point(sK1,sK0),intersection_point(sK2,sK1)),
inference(resolve,[status(thm)],[c_153,c_34]) ).
cnf(c_154,plain,
( apart_point_and_line(B,sK0)
| apart_point_and_line(B,sK1)
| apart_point_and_line(A,sK0)
| apart_point_and_line(A,sK1)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_26,c_110]) ).
cnf(c_155,plain,
( apart_point_and_line(A,sK0)
| apart_point_and_line(A,sK1)
| apart_point_and_line(intersection_point(sK0,sK1),sK0)
| ~ distinct_points(intersection_point(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_154,c_36]) ).
cnf(c_156,plain,
( apart_point_and_line(A,sK0)
| apart_point_and_line(A,sK1)
| ~ distinct_points(intersection_point(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_155,c_37]) ).
cnf(c_157,plain,
( apart_point_and_line(intersection_point(sK1,sK0),sK0)
| ~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)) ),
inference(resolve,[status(thm)],[c_156,c_57]) ).
cnf(c_119,plain,
~ distinct_points(intersection_point(sK0,sK1),intersection_point(sK1,sK0)),
inference(resolve,[status(thm)],[c_157,c_56]) ).
cnf(c_158,plain,
( apart_point_and_line(intersection_point(sK2,sK1),A)
| ~ apart_point_and_line(intersection_point(sK1,sK0),A) ),
inference(resolve,[status(thm)],[c_27,c_115]) ).
cnf(c_131,plain,
~ apart_point_and_line(intersection_point(sK1,sK0),sK2),
inference(resolve,[status(thm)],[c_158,c_41]) ).
cnf(c_159,plain,
apart_point_and_line(intersection_point(sK1,sK0),sK2),
inference(resolve,[status(thm)],[c_119,c_48]) ).
cnf(c_147,plain,
$false,
inference(resolve,[status(thm)],[c_131,c_159]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO193+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/5.57 % Computer : n009.cluster.edu
% 0.09/5.57 % Model : x86_64 x86_64
% 0.09/5.57 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/5.57 % Memory : 8046.5625MB
% 0.09/5.57 % OS : Linux 6.8.0-71-generic
% 0.09/5.57 % CPULimit : 300
% 0.09/5.57 % WCLimit : 300
% 0.09/5.57 % DateTime : Fri Sep 25 13:04:36 UTC 2026
% 0.09/5.58 % CPUTime :
% 0.09/5.58 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/5.58 % Process 1659012 was started by sandbox2 on n009,
% 0.09/5.58 % Fri Sep 25 13:04:36 2026
% 0.09/5.58 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/5.59
% 0.09/5.59 % From the command line: assign(max_seconds, 300).
% 0.14/5.60
% 0.14/5.60 % SZS status Theorem for theBenchmark
% 0.14/5.60
% 0.14/5.60 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.14/5.60 % Length of proof is 36.
% 0.14/5.60 % Level of proof is 9.
% 0.14/5.60 % Maximum clause weight is 18.000.
% 0.14/5.60 % Given clauses 73.
% 0.14/5.60
% 0.14/5.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------