%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO204+1 : 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 : n012.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 07:17:27 AM UTC 2026
% Result : Theorem 0.03s 0.32s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 7
% Syntax : Number of formulae : 36 ( 14 unt; 0 def)
% Number of atoms : 84 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 84 ( 36 ~; 32 |; 9 &)
% ( 0 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 46 ( 0 sgn 21 !; 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(ci1,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(X,line_connecting(X,Y)) ),
file('theBenchmark.p',ci1) ).
fof(ci2,axiom,
! [X,Y] :
( distinct_points(X,Y)
=> ~ apart_point_and_line(Y,line_connecting(X,Y)) ),
file('theBenchmark.p',ci2) ).
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(con,conjecture,
! [X,Y,Z] :
( ( ~ distinct_points(Y,Z)
& distinct_points(X,Y) )
=> ( ~ distinct_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( ~ distinct_points(Y,Z)
& distinct_points(X,Y) )
=> ( ~ distinct_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_16,plain,
~ distinct_points(A,A),
inference(clausify,[status(thm)],[apart1]) ).
cnf(c_19,plain,
( distinct_points(B,C)
| distinct_points(A,C)
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[apart4]) ).
cnf(c_22,plain,
( ~ apart_point_and_line(A,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci1]) ).
cnf(c_23,plain,
( ~ apart_point_and_line(B,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci2]) ).
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]) ).
fof(nnf_15,plain,
? [X,Y,Z] :
( ( distinct_lines(line_connecting(X,Y),line_connecting(X,Z))
| ~ distinct_points(X,Z) )
& ~ distinct_points(Y,Z)
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ( distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ distinct_points(sK0,sK2) )
& ~ distinct_points(sK1,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_15]) ).
cnf(c_30,negated_conjecture,
distinct_points(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_31,negated_conjecture,
~ distinct_points(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_32,negated_conjecture,
( distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2))
| ~ distinct_points(sK0,sK2) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_34,plain,
~ apart_point_and_line(sK1,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_30,c_23]) ).
cnf(c_35,plain,
~ apart_point_and_line(sK0,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_30,c_22]) ).
cnf(c_36,plain,
( distinct_points(sK1,A)
| distinct_points(sK0,A) ),
inference(resolve,[status(thm)],[c_30,c_19]) ).
cnf(c_59,plain,
( distinct_points(B,A)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_19,c_16]) ).
cnf(c_37,negated_conjecture,
~ distinct_points(sK2,sK1),
inference(resolve,[status(thm)],[c_59,c_31]) ).
cnf(c_60,plain,
( apart_point_and_line(sK1,A)
| ~ apart_point_and_line(sK2,A) ),
inference(resolve,[status(thm)],[c_27,c_37]) ).
cnf(c_38,plain,
~ apart_point_and_line(sK2,line_connecting(sK0,sK1)),
inference(resolve,[status(thm)],[c_60,c_34]) ).
cnf(c_39,plain,
distinct_points(sK0,sK2),
inference(resolve,[status(thm)],[c_36,c_31]) ).
cnf(c_44,negated_conjecture,
distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
inference(resolve,[status(thm)],[c_39,c_32]) ).
cnf(c_47,plain,
~ apart_point_and_line(sK2,line_connecting(sK0,sK2)),
inference(resolve,[status(thm)],[c_39,c_23]) ).
cnf(c_48,plain,
~ apart_point_and_line(sK0,line_connecting(sK0,sK2)),
inference(resolve,[status(thm)],[c_39,c_22]) ).
cnf(c_61,plain,
( apart_point_and_line(sK2,B)
| apart_point_and_line(sK2,A)
| apart_point_and_line(sK0,B)
| apart_point_and_line(sK0,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_26,c_39]) ).
cnf(c_62,plain,
( apart_point_and_line(sK2,A)
| apart_point_and_line(sK2,line_connecting(sK0,sK1))
| apart_point_and_line(sK0,A)
| ~ distinct_lines(line_connecting(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_61,c_35]) ).
cnf(c_63,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK2))
| apart_point_and_line(sK2,line_connecting(sK0,sK1))
| ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
inference(resolve,[status(thm)],[c_62,c_48]) ).
cnf(c_64,plain,
( apart_point_and_line(sK2,line_connecting(sK0,sK2))
| ~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)) ),
inference(resolve,[status(thm)],[c_63,c_38]) ).
cnf(c_65,plain,
~ distinct_lines(line_connecting(sK0,sK1),line_connecting(sK0,sK2)),
inference(resolve,[status(thm)],[c_64,c_47]) ).
cnf(c_58,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_44,c_65]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO204+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.03/0.30 % Computer : n012.cluster.edu
% 0.03/0.30 % Model : x86_64 x86_64
% 0.03/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/0.30 % Memory : 8046.5625MB
% 0.03/0.30 % OS : Linux 6.8.0-71-generic
% 0.03/0.30 % CPULimit : 300
% 0.03/0.30 % WCLimit : 300
% 0.03/0.30 % DateTime : Fri Sep 25 13:05:21 UTC 2026
% 0.03/0.30 % CPUTime :
% 0.03/0.30 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/0.30 % Process 2161802 was started by sandbox on n012,
% 0.03/0.30 % Fri Sep 25 13:05:21 2026
% 0.03/0.30 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.03/0.30
% 0.03/0.30 % From the command line: assign(max_seconds, 300).
% 0.03/0.32
% 0.03/0.32 % SZS status Theorem for theBenchmark
% 0.03/0.32
% 0.03/0.32 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.03/0.32 % Length of proof is 26.
% 0.03/0.32 % Level of proof is 5.
% 0.03/0.32 % Maximum clause weight is 18.000.
% 0.03/0.32 % Given clauses 29.
% 0.03/0.32
% 0.03/0.32 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------