%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO179+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/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 07:17:17 AM UTC 2026
% Result : Theorem 0.10s 5.39s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 27 ( 11 unt; 0 def)
% Number of atoms : 57 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 52 ( 22 ~; 16 |; 9 &)
% ( 0 <=>; 5 =>; 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 : 31 ( 0 sgn 13 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X),
file('theBenchmark.p',apart1) ).
fof(con1,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> ( distinct_points(Z,Y)
& distinct_points(Z,X) ) ) ),
file('theBenchmark.p',con1) ).
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] :
( ( apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) )
=> ( distinct_lines(line_connecting(X,Y),line_connecting(Z,Y))
& distinct_lines(line_connecting(X,Y),line_connecting(Z,X)) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) )
=> ( distinct_lines(line_connecting(X,Y),line_connecting(Z,Y))
& distinct_lines(line_connecting(X,Y),line_connecting(Z,X)) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_14,plain,
~ distinct_points(A,A),
inference(clausify,[status(thm)],[apart1]) ).
cnf(c_20,plain,
( distinct_points(C,A)
| ~ apart_point_and_line(C,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[con1]) ).
cnf(c_21,plain,
( distinct_points(C,B)
| ~ apart_point_and_line(C,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[con1]) ).
cnf(c_26,plain,
( apart_point_and_line(A,C)
| distinct_lines(B,C)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[ceq2]) ).
fof(nnf_13,plain,
? [X,Y,Z] :
( ( ~ distinct_lines(line_connecting(X,Y),line_connecting(Z,Y))
| ~ distinct_lines(line_connecting(X,Y),line_connecting(Z,X)) )
& apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ( ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK1))
| ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK0)) )
& apart_point_and_line(sK2,line_connecting(sK0,sK1))
& distinct_points(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X,sK0),skolemize(Y,sK1),skolemize(Z,sK2)],[nnf_13]) ).
cnf(c_28,negated_conjecture,
distinct_points(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_29,negated_conjecture,
apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_30,negated_conjecture,
( ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK1))
| ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK0)) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_31,plain,
( distinct_points(A,sK1)
| ~ apart_point_and_line(A,line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_28,c_21]) ).
cnf(c_32,plain,
( distinct_points(A,sK0)
| ~ apart_point_and_line(A,line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_28,c_20]) ).
cnf(c_36,plain,
( apart_point_and_line(sK2,A)
| distinct_lines(line_connecting(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_29,c_26]) ).
cnf(c_38,plain,
distinct_points(sK2,sK1),
inference(resolve,[status(thm)],[c_31,c_29]) ).
cnf(c_39,plain,
distinct_points(sK2,sK0),
inference(resolve,[status(thm)],[c_32,c_29]) ).
cnf(c_98,plain,
( distinct_points(A,sK2)
| ~ apart_point_and_line(A,line_connecting(sK2,sK1)) ),
inference(resolve,[status(thm)],[c_20,c_38]) ).
cnf(c_53,plain,
~ apart_point_and_line(sK2,line_connecting(sK2,sK1)),
inference(resolve,[status(thm)],[c_98,c_14]) ).
cnf(c_99,plain,
( distinct_points(A,sK2)
| ~ apart_point_and_line(A,line_connecting(sK2,sK0)) ),
inference(resolve,[status(thm)],[c_20,c_39]) ).
cnf(c_58,plain,
~ apart_point_and_line(sK2,line_connecting(sK2,sK0)),
inference(resolve,[status(thm)],[c_99,c_14]) ).
cnf(c_100,negated_conjecture,
( ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK0))
| apart_point_and_line(sK2,line_connecting(sK2,sK1)) ),
inference(resolve,[status(thm)],[c_36,c_30]) ).
cnf(c_85,negated_conjecture,
~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK0)),
inference(resolve,[status(thm)],[c_53,c_100]) ).
cnf(c_101,plain,
distinct_lines(line_connecting(sK0,sK1),line_connecting(sK2,sK0)),
inference(resolve,[status(thm)],[c_58,c_36]) ).
cnf(c_97,plain,
$false,
inference(resolve,[status(thm)],[c_85,c_101]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO179+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/5.36 % Computer : n006.cluster.edu
% 0.10/5.36 % Model : x86_64 x86_64
% 0.10/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.36 % Memory : 8046.5625MB
% 0.10/5.36 % 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 13:02:02 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 2978254 was started by sandbox on n006,
% 0.10/5.37 % Fri Sep 25 13:02:02 2026
% 0.10/5.37 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/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 0.01 (+ 0.00) seconds.
% 0.10/5.39 % Length of proof is 20.
% 0.10/5.39 % Level of proof is 6.
% 0.10/5.39 % Maximum clause weight is 24.000.
% 0.10/5.39 % Given clauses 35.
% 0.10/5.39
% 0.10/5.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------