%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO204+3 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n019.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 07:17:28 AM UTC 2026
% Result : Theorem 0.17s 0.49s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 14
% Syntax : Number of formulae : 54 ( 20 unt; 0 def)
% Number of atoms : 118 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 107 ( 43 ~; 43 |; 9 &)
% ( 2 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 86 ( 7 sgn 37 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X),
file('theBenchmark.p',apart2) ).
fof(apart4,axiom,
! [X,Y,Z] :
( distinct_points(X,Y)
=> ( distinct_points(Y,Z)
| distinct_points(X,Z) ) ),
file('theBenchmark.p',apart4) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('theBenchmark.p',apart5) ).
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(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(p1,axiom,
! [X,Y] :
( distinct_lines(X,Y)
=> convergent_lines(X,Y) ),
file('theBenchmark.p',p1) ).
fof(cp1,axiom,
! [X,Y] : ~ convergent_lines(parallel_through_point(Y,X),Y),
file('theBenchmark.p',cp1) ).
fof(cp2,axiom,
! [X,Y] : ~ apart_point_and_line(X,parallel_through_point(Y,X)),
file('theBenchmark.p',cp2) ).
fof(ax1,axiom,
! [X,Y] :
( equal_points(X,Y)
<=> ~ distinct_points(X,Y) ),
file('theBenchmark.p',ax1) ).
fof(ax2,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('theBenchmark.p',ax2) ).
fof(con,conjecture,
! [X,Y,Z] :
( ( equal_points(Y,Z)
& distinct_points(X,Y) )
=> ( equal_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] :
( ( equal_points(Y,Z)
& distinct_points(X,Y) )
=> ( equal_lines(line_connecting(X,Y),line_connecting(X,Z))
& distinct_points(X,Z) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_38,plain,
( ~ distinct_points(A,B)
| ~ equal_points(A,B) ),
inference(clausify,[status(thm)],[ax1]) ).
fof(nnf_36,plain,
? [X,Y,Z] :
( ( ~ equal_lines(line_connecting(X,Y),line_connecting(X,Z))
| ~ distinct_points(X,Z) )
& equal_points(Y,Z)
& distinct_points(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ( ~ equal_lines(line_connecting(sK2,sK0),line_connecting(sK2,sK1))
| ~ distinct_points(sK2,sK1) )
& equal_points(sK0,sK1)
& distinct_points(sK2,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK0,sK1]),skolemize(X,sK2),skolemize(Y,sK0),skolemize(Z,sK1)],[nnf_36]) ).
cnf(c_39,negated_conjecture,
equal_points(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_40,plain,
( distinct_lines(A,B)
| equal_lines(A,B) ),
inference(clausify,[status(thm)],[ax2]) ).
cnf(c_41,negated_conjecture,
( ~ equal_lines(line_connecting(sK2,sK0),line_connecting(sK2,sK1))
| ~ distinct_points(sK2,sK1) ),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_49,negated_conjecture,
~ distinct_points(sK0,sK1),
inference(resolve,[status(thm)],[c_39,c_38]) ).
cnf(c_50,negated_conjecture,
distinct_points(sK2,sK0),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_68,plain,
~ apart_point_and_line(A,parallel_through_point(B,A)),
inference(clausify,[status(thm)],[cp2]) ).
cnf(c_69,plain,
~ convergent_lines(parallel_through_point(A,B),A),
inference(clausify,[status(thm)],[cp1]) ).
cnf(c_70,plain,
( convergent_lines(A,B)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_72,plain,
( apart_point_and_line(A,C)
| distinct_lines(B,C)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[ceq2]) ).
cnf(c_73,plain,
( apart_point_and_line(C,B)
| distinct_points(A,C)
| ~ apart_point_and_line(A,B) ),
inference(clausify,[status(thm)],[ceq1]) ).
cnf(c_74,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_77,plain,
( ~ apart_point_and_line(B,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci2]) ).
cnf(c_78,plain,
( ~ apart_point_and_line(A,line_connecting(A,B))
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[ci1]) ).
cnf(c_80,plain,
( distinct_lines(B,C)
| distinct_lines(A,C)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[apart5]) ).
cnf(c_81,plain,
( distinct_points(B,C)
| distinct_points(A,C)
| ~ distinct_points(A,B) ),
inference(clausify,[status(thm)],[apart4]) ).
cnf(c_83,plain,
~ distinct_lines(A,A),
inference(clausify,[status(thm)],[apart2]) ).
cnf(c_85,negated_conjecture,
( ~ distinct_points(sK2,sK1)
| distinct_lines(line_connecting(sK2,sK0),line_connecting(sK2,sK1)) ),
inference(resolve,[status(thm)],[c_40,c_41]) ).
cnf(c_88,plain,
~ distinct_lines(parallel_through_point(A,B),A),
inference(resolve,[status(thm)],[c_70,c_69]) ).
cnf(c_159,negated_conjecture,
( apart_point_and_line(sK1,A)
| ~ apart_point_and_line(sK0,A) ),
inference(resolve,[status(thm)],[c_73,c_49]) ).
cnf(c_89,negated_conjecture,
~ apart_point_and_line(sK0,parallel_through_point(A,sK1)),
inference(resolve,[status(thm)],[c_159,c_68]) ).
cnf(c_91,plain,
( apart_point_and_line(sK0,B)
| apart_point_and_line(sK0,A)
| apart_point_and_line(sK2,B)
| apart_point_and_line(sK2,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_74,c_50]) ).
cnf(c_92,plain,
~ apart_point_and_line(sK0,line_connecting(sK2,sK0)),
inference(resolve,[status(thm)],[c_77,c_50]) ).
cnf(c_93,plain,
~ apart_point_and_line(sK2,line_connecting(sK2,sK0)),
inference(resolve,[status(thm)],[c_78,c_50]) ).
cnf(c_95,plain,
( distinct_points(sK0,A)
| distinct_points(sK2,A) ),
inference(resolve,[status(thm)],[c_81,c_50]) ).
cnf(c_160,plain,
( distinct_lines(B,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_80,c_83]) ).
cnf(c_101,plain,
~ distinct_lines(A,parallel_through_point(A,B)),
inference(resolve,[status(thm)],[c_160,c_88]) ).
cnf(c_119,plain,
distinct_points(sK2,sK1),
inference(resolve,[status(thm)],[c_95,c_49]) ).
cnf(c_121,negated_conjecture,
distinct_lines(line_connecting(sK2,sK0),line_connecting(sK2,sK1)),
inference(resolve,[status(thm)],[c_119,c_85]) ).
cnf(c_123,plain,
~ apart_point_and_line(sK2,line_connecting(sK2,sK1)),
inference(resolve,[status(thm)],[c_119,c_78]) ).
cnf(c_161,negated_conjecture,
( apart_point_and_line(sK0,line_connecting(sK2,sK1))
| apart_point_and_line(sK0,line_connecting(sK2,sK0))
| apart_point_and_line(sK2,line_connecting(sK2,sK1))
| apart_point_and_line(sK2,line_connecting(sK2,sK0)) ),
inference(resolve,[status(thm)],[c_121,c_91]) ).
cnf(c_162,negated_conjecture,
( apart_point_and_line(sK0,line_connecting(sK2,sK1))
| apart_point_and_line(sK0,line_connecting(sK2,sK0))
| apart_point_and_line(sK2,line_connecting(sK2,sK1)) ),
inference(resolve,[status(thm)],[c_93,c_161]) ).
cnf(c_163,negated_conjecture,
( apart_point_and_line(sK0,line_connecting(sK2,sK1))
| apart_point_and_line(sK0,line_connecting(sK2,sK0)) ),
inference(resolve,[status(thm)],[c_123,c_162]) ).
cnf(c_145,negated_conjecture,
apart_point_and_line(sK0,line_connecting(sK2,sK1)),
inference(resolve,[status(thm)],[c_92,c_163]) ).
cnf(c_164,plain,
( apart_point_and_line(A,parallel_through_point(B,C))
| ~ apart_point_and_line(A,B) ),
inference(resolve,[status(thm)],[c_72,c_101]) ).
cnf(c_157,plain,
~ apart_point_and_line(sK0,A),
inference(resolve,[status(thm)],[c_164,c_89]) ).
cnf(c_158,plain,
$false,
inference(resolve,[status(thm)],[c_157,c_145]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : GEO204+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.17/0.44 % Computer : n019.cluster.edu
% 0.17/0.44 % Model : x86_64 x86_64
% 0.17/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.44 % Memory : 8046.5625MB
% 0.17/0.44 % OS : Linux 6.8.0-71-generic
% 0.17/0.44 % CPULimit : 300
% 0.17/0.44 % WCLimit : 300
% 0.17/0.44 % DateTime : Fri Sep 25 13:05:49 UTC 2026
% 0.17/0.44 % CPUTime :
% 0.17/0.44 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.44 % Process 2815845 was started by sandbox2 on n019,
% 0.17/0.44 % Fri Sep 25 13:05:49 2026
% 0.17/0.44 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.17/0.46
% 0.17/0.46 % From the command line: assign(max_seconds, 300).
% 0.17/0.49
% 0.17/0.49 % SZS status Theorem for theBenchmark
% 0.17/0.49
% 0.17/0.49 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.17/0.49 % Length of proof is 45.
% 0.17/0.49 % Level of proof is 6.
% 0.17/0.49 % Maximum clause weight is 18.000.
% 0.17/0.49 % Given clauses 56.
% 0.17/0.49
% 0.17/0.49 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------