%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO222+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 : n004.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 07:17:34 AM UTC 2026
% Result : Theorem 0.12s 5.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 40 ( 19 unt; 0 def)
% Number of atoms : 83 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 72 ( 29 ~; 34 |; 3 &)
% ( 0 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 6 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 6 sgn 25 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart1,axiom,
! [X] : ~ distinct_points(X,X),
file('theBenchmark.p',apart1) ).
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('theBenchmark.p',apart3) ).
fof(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('theBenchmark.p',apart6) ).
fof(con2,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( ( apart_point_and_line(Z,Y)
| apart_point_and_line(Z,X) )
=> distinct_points(Z,intersection_point(X,Y)) ) ),
file('theBenchmark.p',con2) ).
fof(ceq3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> distinct_lines(X,Y) ),
file('theBenchmark.p',ceq3) ).
fof(occu1,axiom,
! [L,M] :
( unorthogonal_lines(L,M)
| convergent_lines(L,M) ),
file('theBenchmark.p',occu1) ).
fof(oac1,axiom,
! [L,M,N] :
( ( unorthogonal_lines(L,M)
& convergent_lines(L,M) )
=> ( ( unorthogonal_lines(M,N)
& convergent_lines(M,N) )
| ( unorthogonal_lines(L,N)
& convergent_lines(L,N) ) ) ),
file('theBenchmark.p',oac1) ).
fof(ooc1,axiom,
! [A,L] : ~ unorthogonal_lines(orthogonal_through_point(L,A),L),
file('theBenchmark.p',ooc1) ).
fof(ouo1,axiom,
! [A,L,M,N] :
( distinct_lines(L,M)
=> ( unorthogonal_lines(M,N)
| unorthogonal_lines(L,N)
| apart_point_and_line(A,M)
| apart_point_and_line(A,L) ) ),
file('theBenchmark.p',ouo1) ).
fof(con,conjecture,
! [A,L] : ~ convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [A,L] : ~ convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_22,plain,
~ distinct_points(A,A),
inference(clausify,[status(thm)],[apart1]) ).
cnf(c_24,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_27,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[apart6]) ).
cnf(c_30,plain,
( distinct_points(C,intersection_point(A,B))
| ~ apart_point_and_line(C,A)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[con2]) ).
cnf(c_31,plain,
( distinct_points(C,intersection_point(A,B))
| ~ apart_point_and_line(C,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[con2]) ).
cnf(c_35,plain,
( distinct_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ceq3]) ).
cnf(c_39,plain,
( unorthogonal_lines(A,B)
| convergent_lines(A,B) ),
inference(clausify,[status(thm)],[occu1]) ).
cnf(c_40,plain,
( unorthogonal_lines(B,C)
| convergent_lines(A,C)
| ~ unorthogonal_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[oac1]) ).
cnf(c_43,plain,
~ unorthogonal_lines(orthogonal_through_point(A,B),A),
inference(clausify,[status(thm)],[ooc1]) ).
cnf(c_45,plain,
( unorthogonal_lines(B,D)
| unorthogonal_lines(A,D)
| apart_point_and_line(C,B)
| apart_point_and_line(C,A)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[ouo1]) ).
fof(nnf_21,plain,
? [A,L] : convergent_lines(L,orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
convergent_lines(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(A,sK1),skolemize(L,sK0)],[nnf_21]) ).
cnf(c_46,negated_conjecture,
convergent_lines(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_50,plain,
convergent_lines(orthogonal_through_point(A,B),A),
inference(resolve,[status(thm)],[c_43,c_39]) ).
cnf(c_52,plain,
distinct_lines(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),
inference(resolve,[status(thm)],[c_46,c_35]) ).
cnf(c_234,negated_conjecture,
( distinct_points(A,intersection_point(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)))
| ~ apart_point_and_line(A,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)) ),
inference(resolve,[status(thm)],[c_31,c_46]) ).
cnf(c_54,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),
inference(resolve,[status(thm)],[c_234,c_22]) ).
cnf(c_235,negated_conjecture,
( distinct_points(A,intersection_point(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)))
| ~ apart_point_and_line(A,sK0) ),
inference(resolve,[status(thm)],[c_30,c_46]) ).
cnf(c_55,negated_conjecture,
~ apart_point_and_line(intersection_point(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),sK0),
inference(resolve,[status(thm)],[c_235,c_22]) ).
cnf(c_76,plain,
( convergent_lines(A,C)
| convergent_lines(orthogonal_through_point(A,B),C) ),
inference(resolve,[status(thm)],[c_50,c_27]) ).
cnf(c_86,plain,
convergent_lines(A,orthogonal_through_point(A,B)),
inference(resolve,[status(thm)],[c_76,c_24]) ).
cnf(c_236,plain,
( unorthogonal_lines(orthogonal_through_point(A,B),C)
| convergent_lines(A,C)
| ~ unorthogonal_lines(A,orthogonal_through_point(A,B)) ),
inference(resolve,[status(thm)],[c_40,c_86]) ).
cnf(c_237,plain,
( unorthogonal_lines(orthogonal_through_point(A,B),A)
| ~ unorthogonal_lines(A,orthogonal_through_point(A,B)) ),
inference(resolve,[status(thm)],[c_236,c_24]) ).
cnf(c_89,plain,
~ unorthogonal_lines(A,orthogonal_through_point(A,B)),
inference(resolve,[status(thm)],[c_237,c_43]) ).
cnf(c_238,plain,
( unorthogonal_lines(A,B)
| unorthogonal_lines(sK0,B)
| apart_point_and_line(intersection_point(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),A)
| ~ distinct_lines(sK0,A) ),
inference(resolve,[status(thm)],[c_45,c_55]) ).
cnf(c_239,plain,
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1),A)
| unorthogonal_lines(sK0,A)
| ~ distinct_lines(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)) ),
inference(resolve,[status(thm)],[c_238,c_54]) ).
cnf(c_240,plain,
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1),orthogonal_through_point(sK0,A))
| ~ distinct_lines(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)) ),
inference(resolve,[status(thm)],[c_239,c_89]) ).
cnf(c_241,plain,
~ distinct_lines(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),
inference(resolve,[status(thm)],[c_240,c_43]) ).
cnf(c_233,plain,
$false,
inference(resolve,[status(thm)],[c_52,c_241]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : GEO222+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/5.36 % Computer : n004.cluster.edu
% 0.07/5.36 % Model : x86_64 x86_64
% 0.07/5.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.36 % Memory : 8046.5625MB
% 0.07/5.36 % OS : Linux 6.8.0-71-generic
% 0.07/5.36 % CPULimit : 300
% 0.07/5.36 % WCLimit : 300
% 0.07/5.36 % DateTime : Fri Sep 25 13:08:12 UTC 2026
% 0.07/5.36 % CPUTime :
% 0.07/5.36 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.07/5.36 % Process 3233536 was started by sandbox2 on n004,
% 0.07/5.36 % Fri Sep 25 13:08:12 2026
% 0.07/5.36 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.07/5.37
% 0.07/5.37 % From the command line: assign(max_seconds, 300).
% 0.12/5.40
% 0.12/5.40 % SZS status Theorem for theBenchmark
% 0.12/5.40
% 0.12/5.40 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.12/5.40 % Length of proof is 29.
% 0.12/5.40 % Level of proof is 6.
% 0.12/5.40 % Maximum clause weight is 37.000.
% 0.12/5.40 % Given clauses 52.
% 0.12/5.40
% 0.12/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------