%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO192+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 : n006.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 07:17:22 AM UTC 2026
% Result : Theorem 0.12s 0.38s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 28 ( 12 unt; 0 def)
% Number of atoms : 56 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 50 ( 22 ~; 14 |; 6 &)
% ( 0 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 35 ( 0 sgn 17 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X),
file('theBenchmark.p',apart2) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('theBenchmark.p',apart5) ).
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(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,Z] :
( convergent_lines(X,Y)
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> ( distinct_lines(Y,Z)
& distinct_lines(X,Z) ) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( apart_point_and_line(intersection_point(X,Y),Z)
=> ( distinct_lines(Y,Z)
& distinct_lines(X,Z) ) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_17,plain,
~ distinct_lines(A,A),
inference(clausify,[status(thm)],[apart2]) ).
cnf(c_20,plain,
( distinct_lines(B,C)
| distinct_lines(A,C)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[apart5]) ).
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_28,plain,
( apart_point_and_line(A,C)
| distinct_lines(B,C)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[ceq2]) ).
fof(nnf_15,plain,
? [X,Y,Z] :
( ( ~ distinct_lines(Y,Z)
| ~ distinct_lines(X,Z) )
& apart_point_and_line(intersection_point(X,Y),Z)
& convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ( ~ distinct_lines(sK1,sK2)
| ~ distinct_lines(sK0,sK2) )
& apart_point_and_line(intersection_point(sK0,sK1),sK2)
& 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,
apart_point_and_line(intersection_point(sK0,sK1),sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_32,negated_conjecture,
( ~ distinct_lines(sK1,sK2)
| ~ distinct_lines(sK0,sK2) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_34,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK1),
inference(resolve,[status(thm)],[c_30,c_25]) ).
cnf(c_35,plain,
~ apart_point_and_line(intersection_point(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_30,c_24]) ).
cnf(c_37,plain,
( apart_point_and_line(intersection_point(sK0,sK1),A)
| distinct_lines(sK2,A) ),
inference(resolve,[status(thm)],[c_31,c_28]) ).
cnf(c_63,plain,
distinct_lines(sK2,sK0),
inference(resolve,[status(thm)],[c_37,c_35]) ).
cnf(c_64,plain,
distinct_lines(sK2,sK1),
inference(resolve,[status(thm)],[c_37,c_34]) ).
cnf(c_83,plain,
( distinct_lines(sK0,A)
| distinct_lines(sK2,A) ),
inference(resolve,[status(thm)],[c_63,c_20]) ).
cnf(c_95,plain,
distinct_lines(sK0,sK2),
inference(resolve,[status(thm)],[c_83,c_17]) ).
cnf(c_99,negated_conjecture,
~ distinct_lines(sK1,sK2),
inference(resolve,[status(thm)],[c_95,c_32]) ).
cnf(c_111,plain,
( distinct_lines(B,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_20,c_17]) ).
cnf(c_112,negated_conjecture,
~ distinct_lines(sK2,sK1),
inference(resolve,[status(thm)],[c_111,c_99]) ).
cnf(c_110,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_64,c_112]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO192+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n006.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Fri Sep 25 13:03:29 UTC 2026
% 0.07/0.36 % CPUTime :
% 0.12/0.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.12/0.36 % Process 2982697 was started by sandbox2 on n006,
% 0.12/0.36 % Fri Sep 25 13:03:29 2026
% 0.12/0.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.12/0.36
% 0.12/0.36 % From the command line: assign(max_seconds, 300).
% 0.12/0.38
% 0.12/0.38 % SZS status Theorem for theBenchmark
% 0.12/0.38
% 0.12/0.38 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.12/0.38 % Length of proof is 23.
% 0.12/0.38 % Level of proof is 7.
% 0.12/0.38 % Maximum clause weight is 18.000.
% 0.12/0.38 % Given clauses 43.
% 0.12/0.38
% 0.12/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------