%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO205+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 : 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 07:17:28 AM UTC 2026
% Result : Theorem 0.03s 10.35s
% Output : CNFRefutation 0.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 15
% Syntax : Number of formulae : 64 ( 26 unt; 0 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 124 ( 55 ~; 49 |; 10 &)
% ( 2 <=>; 8 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 142 ( 38 sgn 38 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart2,axiom,
! [X] : ~ distinct_lines(X,X),
file('theBenchmark.p',apart2) ).
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('theBenchmark.p',apart3) ).
fof(apart5,axiom,
! [X,Y,Z] :
( distinct_lines(X,Y)
=> ( distinct_lines(Y,Z)
| distinct_lines(X,Z) ) ),
file('theBenchmark.p',apart5) ).
fof(ax6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('theBenchmark.p',ax6) ).
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(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
file('theBenchmark.p',ceq3) ).
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(ooc1,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('theBenchmark.p',ooc1) ).
fof(coipo1,axiom,
! [L,M] :
~ ( ~ unorthogonal_lines(L,M)
& ~ convergent_lines(L,M) ),
file('theBenchmark.p',coipo1) ).
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_lines(Y,Z)
& convergent_lines(X,Y) )
=> ( equal_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z) ) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [X,Y,Z] :
( ( equal_lines(Y,Z)
& convergent_lines(X,Y) )
=> ( equal_points(intersection_point(X,Y),intersection_point(X,Z))
& convergent_lines(X,Z) ) ),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_37,plain,
( distinct_points(A,B)
| equal_points(A,B) ),
inference(clausify,[status(thm)],[ax1]) ).
fof(nnf_36,plain,
? [X,Y,Z] :
( ( ~ equal_points(intersection_point(X,Y),intersection_point(X,Z))
| ~ convergent_lines(X,Z) )
& equal_lines(Y,Z)
& convergent_lines(X,Y) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( ( ~ equal_points(intersection_point(sK0,sK2),intersection_point(sK0,sK1))
| ~ convergent_lines(sK0,sK1) )
& equal_lines(sK2,sK1)
& convergent_lines(sK0,sK2) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK2,sK1]),skolemize(X,sK0),skolemize(Y,sK2),skolemize(Z,sK1)],[nnf_36]) ).
cnf(c_39,negated_conjecture,
( ~ equal_points(intersection_point(sK0,sK2),intersection_point(sK0,sK1))
| ~ convergent_lines(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_42,negated_conjecture,
equal_lines(sK2,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_49,negated_conjecture,
( distinct_points(intersection_point(sK0,sK2),intersection_point(sK0,sK1))
| ~ convergent_lines(sK0,sK1) ),
inference(resolve,[status(thm)],[c_39,c_37]) ).
cnf(c_50,negated_conjecture,
convergent_lines(sK0,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_59,plain,
( unorthogonal_lines(A,B)
| convergent_lines(A,B) ),
inference(clausify,[status(thm)],[coipo1]) ).
cnf(c_62,plain,
~ unorthogonal_lines(orthogonal_through_point(A,B),A),
inference(clausify,[status(thm)],[ooc1]) ).
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_71,plain,
( convergent_lines(A,C)
| distinct_lines(B,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ceq3]) ).
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_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_79,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_80,plain,
( distinct_lines(B,C)
| distinct_lines(A,C)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[apart5]) ).
cnf(c_82,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_83,plain,
~ distinct_lines(A,A),
inference(clausify,[status(thm)],[apart2]) ).
cnf(c_85,negated_conjecture,
~ distinct_lines(sK2,sK1),
inference(resolve,[status(thm)],[c_40,c_42]) ).
cnf(c_88,plain,
convergent_lines(orthogonal_through_point(A,B),A),
inference(resolve,[status(thm)],[c_62,c_59]) ).
cnf(c_89,plain,
~ distinct_lines(parallel_through_point(A,B),A),
inference(resolve,[status(thm)],[c_70,c_69]) ).
cnf(c_90,plain,
( convergent_lines(sK0,A)
| distinct_lines(sK2,A) ),
inference(resolve,[status(thm)],[c_71,c_50]) ).
cnf(c_256,plain,
( convergent_lines(B,A)
| ~ convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_79,c_82]) ).
cnf(c_95,plain,
~ convergent_lines(A,parallel_through_point(A,B)),
inference(resolve,[status(thm)],[c_256,c_69]) ).
cnf(c_257,plain,
( distinct_lines(C,A)
| ~ distinct_lines(parallel_through_point(A,B),C) ),
inference(resolve,[status(thm)],[c_80,c_89]) ).
cnf(c_104,plain,
~ distinct_lines(parallel_through_point(A,B),parallel_through_point(A,C)),
inference(resolve,[status(thm)],[c_257,c_89]) ).
cnf(c_258,plain,
( distinct_lines(B,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_80,c_83]) ).
cnf(c_106,plain,
~ distinct_lines(A,parallel_through_point(A,B)),
inference(resolve,[status(thm)],[c_258,c_89]) ).
cnf(c_112,plain,
( convergent_lines(orthogonal_through_point(A,C),B)
| distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_88,c_71]) ).
cnf(c_132,plain,
convergent_lines(sK0,sK1),
inference(resolve,[status(thm)],[c_90,c_85]) ).
cnf(c_135,negated_conjecture,
distinct_points(intersection_point(sK0,sK2),intersection_point(sK0,sK1)),
inference(resolve,[status(thm)],[c_132,c_49]) ).
cnf(c_259,plain,
( convergent_lines(B,parallel_through_point(A,C))
| ~ convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_79,c_95]) ).
cnf(c_140,plain,
~ convergent_lines(A,parallel_through_point(parallel_through_point(A,B),C)),
inference(resolve,[status(thm)],[c_259,c_69]) ).
cnf(c_260,plain,
( apart_point_and_line(A,parallel_through_point(B,D))
| ~ apart_point_and_line(A,parallel_through_point(B,C)) ),
inference(resolve,[status(thm)],[c_72,c_104]) ).
cnf(c_195,plain,
~ apart_point_and_line(A,parallel_through_point(B,C)),
inference(resolve,[status(thm)],[c_260,c_68]) ).
cnf(c_261,plain,
( apart_point_and_line(A,parallel_through_point(B,C))
| ~ apart_point_and_line(A,B) ),
inference(resolve,[status(thm)],[c_72,c_106]) ).
cnf(c_223,plain,
~ apart_point_and_line(A,B),
inference(resolve,[status(thm)],[c_261,c_195]) ).
cnf(c_262,plain,
( apart_point_and_line(B,D)
| apart_point_and_line(B,C)
| apart_point_and_line(A,D)
| ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_223,c_74]) ).
cnf(c_263,plain,
( apart_point_and_line(B,D)
| apart_point_and_line(B,C)
| ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_223,c_262]) ).
cnf(c_264,plain,
( apart_point_and_line(B,D)
| ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_223,c_263]) ).
cnf(c_227,plain,
( ~ distinct_lines(C,D)
| ~ distinct_points(A,B) ),
inference(resolve,[status(thm)],[c_223,c_264]) ).
cnf(c_252,plain,
( distinct_lines(C,D)
| distinct_lines(A,D)
| convergent_lines(orthogonal_through_point(A,B),C) ),
inference(resolve,[status(thm)],[c_112,c_80]) ).
cnf(c_253,plain,
~ distinct_lines(A,B),
inference(resolve,[status(thm)],[c_227,c_135]) ).
cnf(c_265,plain,
( distinct_lines(C,D)
| convergent_lines(orthogonal_through_point(A,B),C) ),
inference(resolve,[status(thm)],[c_253,c_252]) ).
cnf(c_254,plain,
convergent_lines(orthogonal_through_point(A,B),C),
inference(resolve,[status(thm)],[c_253,c_265]) ).
cnf(c_255,plain,
$false,
inference(resolve,[status(thm)],[c_254,c_140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : GEO205+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.02 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.03/10.32 % Computer : n012.cluster.edu
% 0.03/10.32 % Model : x86_64 x86_64
% 0.03/10.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.03/10.32 % Memory : 8046.5625MB
% 0.03/10.32 % OS : Linux 6.8.0-71-generic
% 0.03/10.32 % CPULimit : 300
% 0.03/10.32 % WCLimit : 300
% 0.03/10.32 % DateTime : Fri Sep 25 13:05:19 UTC 2026
% 0.03/10.32 % CPUTime :
% 0.03/10.32 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.03/10.32 % Process 2161425 was started by sandbox2 on n012,
% 0.03/10.32 % Fri Sep 25 13:05:19 2026
% 0.03/10.32 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.03/10.33
% 0.03/10.33 % From the command line: assign(max_seconds, 300).
% 0.03/10.35
% 0.03/10.35 % SZS status Theorem for theBenchmark
% 0.03/10.35
% 0.03/10.35 % Proof 1 at 0.01 (+ 0.00) seconds.
% 0.03/10.35 % Length of proof is 51.
% 0.03/10.35 % Level of proof is 9.
% 0.03/10.35 % Maximum clause weight is 18.000.
% 0.03/10.35 % Given clauses 83.
% 0.03/10.35
% 0.03/10.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------