%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO223+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 : n013.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 07:17:35 AM UTC 2026
% Result : Theorem 0.14s 0.48s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 44 ( 24 unt; 0 def)
% Number of atoms : 85 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 70 ( 29 ~; 34 |; 3 &)
% ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 100 ( 15 sgn 29 !; 2 ?)
% 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(apart6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('theBenchmark.p',apart6) ).
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(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(ooc2,axiom,
! [A,L] : ~ apart_point_and_line(A,orthogonal_through_point(L,A)),
file('theBenchmark.p',ooc2) ).
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] : ~ distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [A,L] : ~ distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_23,plain,
~ distinct_lines(A,A),
inference(clausify,[status(thm)],[apart2]) ).
cnf(c_24,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_26,plain,
( distinct_lines(B,C)
| distinct_lines(A,C)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[apart5]) ).
cnf(c_27,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[apart6]) ).
cnf(c_36,plain,
~ convergent_lines(parallel_through_point(A,B),A),
inference(clausify,[status(thm)],[cp1]) ).
cnf(c_37,plain,
~ apart_point_and_line(A,parallel_through_point(B,A)),
inference(clausify,[status(thm)],[cp2]) ).
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_44,plain,
~ apart_point_and_line(A,orthogonal_through_point(B,A)),
inference(clausify,[status(thm)],[ooc2]) ).
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] : distinct_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
distinct_lines(parallel_through_point(sK0,sK1),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,
distinct_lines(parallel_through_point(sK0,sK1),orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_297,plain,
( convergent_lines(B,A)
| ~ convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_27,c_24]) ).
cnf(c_48,plain,
~ convergent_lines(A,parallel_through_point(A,B)),
inference(resolve,[status(thm)],[c_297,c_36]) ).
cnf(c_50,plain,
convergent_lines(orthogonal_through_point(A,B),A),
inference(resolve,[status(thm)],[c_43,c_39]) ).
cnf(c_55,plain,
( distinct_lines(orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1),A)
| distinct_lines(parallel_through_point(sK0,sK1),A) ),
inference(resolve,[status(thm)],[c_46,c_26]) ).
cnf(c_78,plain,
( convergent_lines(A,C)
| convergent_lines(orthogonal_through_point(A,B),C) ),
inference(resolve,[status(thm)],[c_50,c_27]) ).
cnf(c_92,plain,
( convergent_lines(B,D)
| convergent_lines(orthogonal_through_point(A,C),D)
| convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_78,c_27]) ).
cnf(c_216,plain,
( convergent_lines(B,orthogonal_through_point(A,C))
| convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_92,c_24]) ).
cnf(c_234,plain,
convergent_lines(parallel_through_point(A,B),orthogonal_through_point(A,C)),
inference(resolve,[status(thm)],[c_216,c_48]) ).
cnf(c_298,plain,
( unorthogonal_lines(orthogonal_through_point(A,C),D)
| convergent_lines(parallel_through_point(A,B),D)
| ~ unorthogonal_lines(parallel_through_point(A,B),orthogonal_through_point(A,C)) ),
inference(resolve,[status(thm)],[c_40,c_234]) ).
cnf(c_299,plain,
( unorthogonal_lines(orthogonal_through_point(A,C),A)
| ~ unorthogonal_lines(parallel_through_point(A,B),orthogonal_through_point(A,C)) ),
inference(resolve,[status(thm)],[c_298,c_36]) ).
cnf(c_257,plain,
~ unorthogonal_lines(parallel_through_point(A,B),orthogonal_through_point(A,C)),
inference(resolve,[status(thm)],[c_299,c_43]) ).
cnf(c_267,plain,
distinct_lines(orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1),parallel_through_point(sK0,sK1)),
inference(resolve,[status(thm)],[c_55,c_23]) ).
cnf(c_300,plain,
( unorthogonal_lines(C,D)
| unorthogonal_lines(orthogonal_through_point(A,B),D)
| apart_point_and_line(B,C)
| ~ distinct_lines(orthogonal_through_point(A,B),C) ),
inference(resolve,[status(thm)],[c_45,c_44]) ).
cnf(c_301,plain,
( unorthogonal_lines(parallel_through_point(C,B),D)
| unorthogonal_lines(orthogonal_through_point(A,B),D)
| ~ distinct_lines(orthogonal_through_point(A,B),parallel_through_point(C,B)) ),
inference(resolve,[status(thm)],[c_300,c_37]) ).
cnf(c_302,plain,
( unorthogonal_lines(parallel_through_point(C,B),A)
| ~ distinct_lines(orthogonal_through_point(A,B),parallel_through_point(C,B)) ),
inference(resolve,[status(thm)],[c_301,c_43]) ).
cnf(c_295,plain,
~ distinct_lines(orthogonal_through_point(orthogonal_through_point(A,B),C),parallel_through_point(A,C)),
inference(resolve,[status(thm)],[c_302,c_257]) ).
cnf(c_296,plain,
$false,
inference(resolve,[status(thm)],[c_295,c_267]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO223+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.14/0.40 % Computer : n013.cluster.edu
% 0.14/0.40 % Model : x86_64 x86_64
% 0.14/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.40 % Memory : 8046.5625MB
% 0.14/0.40 % OS : Linux 6.8.0-71-generic
% 0.14/0.40 % CPULimit : 300
% 0.14/0.41 % WCLimit : 300
% 0.14/0.41 % DateTime : Fri Sep 25 13:07:36 UTC 2026
% 0.14/0.41 % CPUTime :
% 0.14/0.41 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.14/0.41 % Process 496102 was started by sandbox2 on n013,
% 0.14/0.41 % Fri Sep 25 13:07:36 2026
% 0.14/0.41 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.14/0.42
% 0.14/0.42 % From the command line: assign(max_seconds, 300).
% 0.14/0.48
% 0.14/0.48 % SZS status Theorem for theBenchmark
% 0.14/0.48
% 0.14/0.48 % Proof 1 at 0.04 (+ 0.02) seconds.
% 0.14/0.48 % Length of proof is 35.
% 0.14/0.48 % Level of proof is 9.
% 0.14/0.48 % Maximum clause weight is 32.000.
% 0.14/0.48 % Given clauses 55.
% 0.14/0.48
% 0.14/0.48 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------