%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO181+2 : 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 : n003.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 07:17:18 AM UTC 2026
% Result : Theorem 0.06s 0.38s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 6
% Syntax : Number of formulae : 40 ( 15 unt; 0 def)
% Number of atoms : 91 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 79 ( 28 ~; 36 |; 6 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 51 ( 0 sgn 20 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X),
file('theBenchmark.p',apart1) ).
fof(apart4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('theBenchmark.p',apart4) ).
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(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(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] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> apart_point_and_line(Y,line_connecting(X,Z)) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,Z] :
( distinct_points(X,Y)
=> ( apart_point_and_line(Z,line_connecting(X,Y))
=> apart_point_and_line(Y,line_connecting(X,Z)) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_14,plain,
~ distinct_points(A,A),
inference(clausify,[status(thm)],[apart1]) ).
cnf(c_17,plain,
( distinct_points(B,C)
| distinct_points(A,C)
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[apart4]) ).
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_24,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_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] :
( ~ apart_point_and_line(Y,line_connecting(X,Z))
& 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,
( ~ apart_point_and_line(sK1,line_connecting(sK0,sK2))
& 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,
~ apart_point_and_line(sK1,line_connecting(sK0,sK2)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
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_33,plain,
( distinct_points(sK1,A)
| distinct_points(sK0,A) ),
inference(resolve,[status(thm)],[c_28,c_17]) ).
cnf(c_208,negated_conjecture,
( distinct_points(A,sK1)
| ~ apart_point_and_line(A,line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_21,c_28]) ).
cnf(c_34,negated_conjecture,
~ apart_point_and_line(sK1,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_208,c_14]) ).
cnf(c_209,negated_conjecture,
( distinct_points(A,sK0)
| ~ apart_point_and_line(A,line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_20,c_28]) ).
cnf(c_35,negated_conjecture,
~ apart_point_and_line(sK0,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_209,c_14]) ).
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_39,plain,
distinct_points(sK2,sK0),
inference(resolve,[status(thm)],[c_32,c_29]) ).
cnf(c_47,plain,
( distinct_points(sK0,A)
| distinct_points(sK2,A) ),
inference(resolve,[status(thm)],[c_39,c_17]) ).
cnf(c_53,plain,
distinct_points(sK1,sK0),
inference(resolve,[status(thm)],[c_33,c_14]) ).
cnf(c_91,plain,
distinct_points(sK0,sK2),
inference(resolve,[status(thm)],[c_47,c_14]) ).
cnf(c_210,plain,
( distinct_points(A,sK2)
| ~ apart_point_and_line(A,line_connecting(sK0,sK2)) ),
inference(resolve,[status(thm)],[c_21,c_91]) ).
cnf(c_99,plain,
~ apart_point_and_line(sK2,line_connecting(sK0,sK2)),
inference(resolve,[status(thm)],[c_210,c_14]) ).
cnf(c_211,plain,
( distinct_points(A,sK0)
| ~ apart_point_and_line(A,line_connecting(sK0,sK2)) ),
inference(resolve,[status(thm)],[c_20,c_91]) ).
cnf(c_100,plain,
~ apart_point_and_line(sK0,line_connecting(sK0,sK2)),
inference(resolve,[status(thm)],[c_211,c_14]) ).
cnf(c_201,plain,
distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
inference(resolve,[status(thm)],[c_99,c_36]) ).
cnf(c_212,plain,
( apart_point_and_line(sK0,B)
| apart_point_and_line(sK0,A)
| apart_point_and_line(sK1,B)
| apart_point_and_line(sK1,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_24,c_53]) ).
cnf(c_213,plain,
( apart_point_and_line(sK0,A)
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| apart_point_and_line(sK1,A)
| ~ distinct_lines(line_connecting(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_212,c_34]) ).
cnf(c_214,negated_conjecture,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| apart_point_and_line(sK0,line_connecting(sK0,sK1))
| ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
inference(resolve,[status(thm)],[c_213,c_30]) ).
cnf(c_215,negated_conjecture,
( apart_point_and_line(sK0,line_connecting(sK0,sK2))
| ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
inference(resolve,[status(thm)],[c_214,c_35]) ).
cnf(c_216,negated_conjecture,
~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
inference(resolve,[status(thm)],[c_215,c_100]) ).
cnf(c_207,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_201,c_216]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO181+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.06/0.33 % Computer : n003.cluster.edu
% 0.06/0.33 % Model : x86_64 x86_64
% 0.06/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.33 % Memory : 8046.5625MB
% 0.06/0.33 % OS : Linux 6.8.0-71-generic
% 0.06/0.33 % CPULimit : 300
% 0.06/0.33 % WCLimit : 300
% 0.06/0.33 % DateTime : Fri Sep 25 13:04:08 UTC 2026
% 0.06/0.34 % CPUTime :
% 0.06/0.34 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.06/0.34 % Process 231721 was started by sandbox2 on n003,
% 0.06/0.34 % Fri Sep 25 13:04:08 2026
% 0.06/0.34 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.06/0.35
% 0.06/0.35 % From the command line: assign(max_seconds, 300).
% 0.06/0.38
% 0.06/0.38 % SZS status Theorem for theBenchmark
% 0.06/0.38
% 0.06/0.38 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.06/0.38 % Length of proof is 28.
% 0.06/0.38 % Level of proof is 8.
% 0.06/0.38 % Maximum clause weight is 23.000.
% 0.06/0.38 % Given clauses 55.
% 0.06/0.38
% 0.06/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------