%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO223+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 07:17:35 AM UTC 2026
% Result : Theorem 0.09s 0.40s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 49 ( 24 unt; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 6 ( 1 avg)
% Number of connectives : 82 ( 39 ~; 31 |; 5 &)
% ( 1 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 107 ( 19 sgn 31 !; 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(ax6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('theBenchmark.p',ax6) ).
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(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(coipo1,axiom,
! [L,M] :
~ ( ~ unorthogonal_lines(L,M)
& ~ convergent_lines(L,M) ),
file('theBenchmark.p',coipo1) ).
fof(couo1,axiom,
! [L,M,N] :
( ( ~ unorthogonal_lines(L,N)
& ~ unorthogonal_lines(L,M) )
=> ~ convergent_lines(M,N) ),
file('theBenchmark.p',couo1) ).
fof(ax2,axiom,
! [X,Y] :
( equal_lines(X,Y)
<=> ~ distinct_lines(X,Y) ),
file('theBenchmark.p',ax2) ).
fof(con,conjecture,
! [A,L] : equal_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] : equal_lines(parallel_through_point(L,A),orthogonal_through_point(orthogonal_through_point(L,A),A)),
inference(assume_negation,[status(cth)],[con]) ).
cnf(c_39,plain,
( distinct_lines(A,B)
| equal_lines(A,B) ),
inference(clausify,[status(thm)],[ax2]) ).
fof(nnf_36,plain,
? [A,L] : ~ equal_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,
~ equal_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_36]) ).
cnf(c_40,negated_conjecture,
~ equal_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_52,plain,
( ~ convergent_lines(B,C)
| unorthogonal_lines(A,C)
| unorthogonal_lines(A,B) ),
inference(clausify,[status(thm)],[couo1]) ).
cnf(c_56,plain,
( unorthogonal_lines(A,B)
| convergent_lines(A,B) ),
inference(clausify,[status(thm)],[coipo1]) ).
cnf(c_59,plain,
~ unorthogonal_lines(orthogonal_through_point(A,B),A),
inference(clausify,[status(thm)],[ooc1]) ).
cnf(c_61,plain,
( convergent_lines(B,C)
| unorthogonal_lines(A,C)
| ~ unorthogonal_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[oac1]) ).
cnf(c_62,plain,
( unorthogonal_lines(B,C)
| convergent_lines(A,C)
| ~ unorthogonal_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[oac1]) ).
cnf(c_66,plain,
~ convergent_lines(parallel_through_point(A,B),A),
inference(clausify,[status(thm)],[cp1]) ).
cnf(c_67,plain,
( convergent_lines(A,B)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[p1]) ).
cnf(c_68,plain,
( convergent_lines(A,C)
| distinct_lines(B,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ceq3]) ).
cnf(c_76,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_77,plain,
( distinct_lines(B,C)
| distinct_lines(A,C)
| ~ distinct_lines(A,B) ),
inference(clausify,[status(thm)],[apart5]) ).
cnf(c_79,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_80,plain,
~ distinct_lines(A,A),
inference(clausify,[status(thm)],[apart2]) ).
cnf(c_82,negated_conjecture,
distinct_lines(parallel_through_point(sK0,sK1),orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),
inference(resolve,[status(thm)],[c_39,c_40]) ).
cnf(c_83,plain,
convergent_lines(orthogonal_through_point(A,B),A),
inference(resolve,[status(thm)],[c_59,c_56]) ).
cnf(c_84,plain,
~ distinct_lines(parallel_through_point(A,B),A),
inference(resolve,[status(thm)],[c_67,c_66]) ).
cnf(c_88,plain,
convergent_lines(parallel_through_point(sK0,sK1),orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),
inference(resolve,[status(thm)],[c_82,c_67]) ).
cnf(c_90,plain,
( convergent_lines(A,C)
| convergent_lines(orthogonal_through_point(A,B),C) ),
inference(resolve,[status(thm)],[c_83,c_76]) ).
cnf(c_91,plain,
( convergent_lines(orthogonal_through_point(A,C),B)
| distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_83,c_68]) ).
cnf(c_166,plain,
( distinct_lines(B,A)
| ~ distinct_lines(A,B) ),
inference(resolve,[status(thm)],[c_77,c_80]) ).
cnf(c_97,plain,
~ distinct_lines(A,parallel_through_point(A,B)),
inference(resolve,[status(thm)],[c_166,c_84]) ).
cnf(c_110,plain,
convergent_lines(A,orthogonal_through_point(A,B)),
inference(resolve,[status(thm)],[c_90,c_79]) ).
cnf(c_167,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_62,c_110]) ).
cnf(c_168,plain,
( unorthogonal_lines(orthogonal_through_point(A,B),A)
| ~ unorthogonal_lines(A,orthogonal_through_point(A,B)) ),
inference(resolve,[status(thm)],[c_167,c_79]) ).
cnf(c_117,plain,
~ unorthogonal_lines(A,orthogonal_through_point(A,B)),
inference(resolve,[status(thm)],[c_168,c_59]) ).
cnf(c_119,plain,
convergent_lines(orthogonal_through_point(A,B),parallel_through_point(A,C)),
inference(resolve,[status(thm)],[c_91,c_97]) ).
cnf(c_169,plain,
( convergent_lines(parallel_through_point(A,C),D)
| unorthogonal_lines(orthogonal_through_point(A,B),D)
| ~ unorthogonal_lines(orthogonal_through_point(A,B),parallel_through_point(A,C)) ),
inference(resolve,[status(thm)],[c_61,c_119]) ).
cnf(c_170,plain,
( convergent_lines(parallel_through_point(A,C),A)
| ~ unorthogonal_lines(orthogonal_through_point(A,B),parallel_through_point(A,C)) ),
inference(resolve,[status(thm)],[c_169,c_59]) ).
cnf(c_142,plain,
~ unorthogonal_lines(orthogonal_through_point(A,B),parallel_through_point(A,C)),
inference(resolve,[status(thm)],[c_170,c_66]) ).
cnf(c_171,plain,
( ~ convergent_lines(parallel_through_point(A,D),C)
| unorthogonal_lines(orthogonal_through_point(A,B),C) ),
inference(resolve,[status(thm)],[c_52,c_142]) ).
cnf(c_164,plain,
~ convergent_lines(parallel_through_point(A,B),orthogonal_through_point(orthogonal_through_point(A,C),D)),
inference(resolve,[status(thm)],[c_171,c_117]) ).
cnf(c_165,plain,
$false,
inference(resolve,[status(thm)],[c_164,c_88]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO223+3 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n019.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Fri Sep 25 13:08:03 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.37 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.09/0.37 % Process 2823304 was started by sandbox2 on n019,
% 0.09/0.37 % Fri Sep 25 13:08:03 2026
% 0.09/0.37 % The command was "/export/starexec/sandbox2/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox2/benchmark/theBenchmark.p".
% 0.09/0.38
% 0.09/0.38 % From the command line: assign(max_seconds, 300).
% 0.09/0.40
% 0.09/0.40 % SZS status Theorem for theBenchmark
% 0.09/0.40
% 0.09/0.40 % Proof 1 at 0.00 (+ 0.01) seconds.
% 0.09/0.40 % Length of proof is 40.
% 0.09/0.40 % Level of proof is 7.
% 0.09/0.40 % Maximum clause weight is 29.000.
% 0.09/0.40 % Given clauses 54.
% 0.09/0.40
% 0.09/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------