%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO188+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 : 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 07:17:21 AM UTC 2026
% Result : Theorem 0.19s 0.50s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 14 unt; 0 def)
% Number of atoms : 94 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 88 ( 31 ~; 34 |; 16 &)
% ( 0 <=>; 7 =>; 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 : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 49 ( 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] :
( ( ~ apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(Y,Z)
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> ~ apart_point_and_line(X,line_connecting(Z,Y)) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(Y,Z)
& distinct_points(X,Z)
& distinct_points(X,Y) )
=> ~ apart_point_and_line(X,line_connecting(Z,Y)) ),
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(X,line_connecting(Z,Y))
& ~ apart_point_and_line(Z,line_connecting(X,Y))
& distinct_points(Y,Z)
& distinct_points(X,Z)
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( apart_point_and_line(sK0,line_connecting(sK2,sK1))
& ~ apart_point_and_line(sK2,line_connecting(sK0,sK1))
& distinct_points(sK1,sK2)
& distinct_points(sK0,sK2)
& 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_30,negated_conjecture,
distinct_points(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_31,negated_conjecture,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_32,negated_conjecture,
apart_point_and_line(sK0,line_connecting(sK2,sK1)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_105,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_105,c_14]) ).
cnf(c_106,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_106,c_14]) ).
cnf(c_39,plain,
( distinct_points(sK2,A)
| distinct_points(sK1,A) ),
inference(resolve,[status(thm)],[c_30,c_17]) ).
cnf(c_42,plain,
( apart_point_and_line(sK0,A)
| distinct_lines(line_connecting(sK2,sK1),A) ),
inference(resolve,[status(thm)],[c_32,c_26]) ).
cnf(c_59,plain,
distinct_points(sK2,sK1),
inference(resolve,[status(thm)],[c_39,c_14]) ).
cnf(c_107,plain,
( distinct_points(A,sK1)
| ~ apart_point_and_line(A,line_connecting(sK2,sK1)) ),
inference(resolve,[status(thm)],[c_21,c_59]) ).
cnf(c_61,plain,
~ apart_point_and_line(sK1,line_connecting(sK2,sK1)),
inference(resolve,[status(thm)],[c_107,c_14]) ).
cnf(c_108,plain,
( distinct_points(A,sK2)
| ~ apart_point_and_line(A,line_connecting(sK2,sK1)) ),
inference(resolve,[status(thm)],[c_20,c_59]) ).
cnf(c_62,plain,
~ apart_point_and_line(sK2,line_connecting(sK2,sK1)),
inference(resolve,[status(thm)],[c_108,c_14]) ).
cnf(c_71,plain,
distinct_lines(line_connecting(sK2,sK1),line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_42,c_35]) ).
cnf(c_109,negated_conjecture,
( apart_point_and_line(sK2,B)
| apart_point_and_line(sK2,A)
| apart_point_and_line(sK1,B)
| apart_point_and_line(sK1,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_24,c_30]) ).
cnf(c_110,negated_conjecture,
( apart_point_and_line(sK2,A)
| apart_point_and_line(sK2,line_connecting(sK2,sK1))
| apart_point_and_line(sK1,A)
| ~ distinct_lines(line_connecting(sK2,sK1),A) ),
inference(resolve,[status(thm)],[c_109,c_61]) ).
cnf(c_111,negated_conjecture,
( apart_point_and_line(sK2,line_connecting(sK0,sK1))
| apart_point_and_line(sK2,line_connecting(sK2,sK1))
| ~ distinct_lines(line_connecting(sK2,sK1),line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_110,c_34]) ).
cnf(c_112,negated_conjecture,
( apart_point_and_line(sK2,line_connecting(sK0,sK1))
| ~ distinct_lines(line_connecting(sK2,sK1),line_connecting(sK0,sK1)) ),
inference(resolve,[status(thm)],[c_111,c_62]) ).
cnf(c_113,negated_conjecture,
~ distinct_lines(line_connecting(sK2,sK1),line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_112,c_31]) ).
cnf(c_104,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_71,c_113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO188+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.19/0.44 % Computer : n026.cluster.edu
% 0.19/0.44 % Model : x86_64 x86_64
% 0.19/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.44 % Memory : 8046.5625MB
% 0.19/0.44 % OS : Linux 6.8.0-71-generic
% 0.19/0.44 % CPULimit : 300
% 0.19/0.44 % WCLimit : 300
% 0.19/0.44 % DateTime : Fri Sep 25 13:06:11 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.19/0.45 % Process 2582264 was started by sandbox2 on n026,
% 0.19/0.45 % Fri Sep 25 13:06:11 2026
% 0.19/0.45 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.19/0.47
% 0.19/0.47 % From the command line: assign(max_seconds, 300).
% 0.19/0.50
% 0.19/0.50 % SZS status Theorem for theBenchmark
% 0.19/0.50
% 0.19/0.50 % Proof 1 at 0.02 (+ 0.01) seconds.
% 0.19/0.50 % Length of proof is 25.
% 0.19/0.50 % Level of proof is 5.
% 0.19/0.50 % Maximum clause weight is 23.000.
% 0.19/0.50 % Given clauses 50.
% 0.19/0.50
% 0.19/0.50 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------