%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO222+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 0.13s 10.47s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 10
% Syntax : Number of formulae : 45 ( 18 unt; 0 def)
% Number of atoms : 97 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 84 ( 32 ~; 43 |; 3 &)
% ( 0 <=>; 6 =>; 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 : 98 ( 13 sgn 26 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(apart3,axiom,
! [X] : ~ convergent_lines(X,X),
file('theBenchmark.p',apart3) ).
fof(ax6,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(Y,Z)
| convergent_lines(X,Z) ) ),
file('theBenchmark.p',ax6) ).
fof(ci3,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),X) ),
file('theBenchmark.p',ci3) ).
fof(ci4,axiom,
! [X,Y] :
( convergent_lines(X,Y)
=> ~ apart_point_and_line(intersection_point(X,Y),Y) ),
file('theBenchmark.p',ci4) ).
fof(ceq3,axiom,
! [X,Y,Z] :
( convergent_lines(X,Y)
=> ( convergent_lines(X,Z)
| distinct_lines(Y,Z) ) ),
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_26,plain,
~ convergent_lines(A,A),
inference(clausify,[status(thm)],[apart3]) ).
cnf(c_29,plain,
( convergent_lines(B,C)
| convergent_lines(A,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ax6]) ).
cnf(c_32,plain,
( ~ apart_point_and_line(intersection_point(A,B),A)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci3]) ).
cnf(c_33,plain,
( ~ apart_point_and_line(intersection_point(A,B),B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ci4]) ).
cnf(c_37,plain,
( convergent_lines(A,C)
| distinct_lines(B,C)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[ceq3]) ).
cnf(c_41,plain,
( unorthogonal_lines(A,B)
| convergent_lines(A,B) ),
inference(clausify,[status(thm)],[occu1]) ).
cnf(c_42,plain,
( unorthogonal_lines(B,C)
| convergent_lines(A,C)
| ~ unorthogonal_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[oac1]) ).
cnf(c_44,plain,
( unorthogonal_lines(B,C)
| unorthogonal_lines(A,C)
| ~ unorthogonal_lines(A,B)
| ~ convergent_lines(A,B) ),
inference(clausify,[status(thm)],[oac1]) ).
cnf(c_45,plain,
~ unorthogonal_lines(orthogonal_through_point(A,B),A),
inference(clausify,[status(thm)],[ooc1]) ).
cnf(c_47,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_23,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_23]) ).
cnf(c_48,negated_conjecture,
convergent_lines(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_52,plain,
convergent_lines(orthogonal_through_point(A,B),A),
inference(resolve,[status(thm)],[c_45,c_41]) ).
cnf(c_78,plain,
( convergent_lines(A,C)
| convergent_lines(orthogonal_through_point(A,B),C) ),
inference(resolve,[status(thm)],[c_52,c_29]) ).
cnf(c_91,plain,
( convergent_lines(B,D)
| convergent_lines(orthogonal_through_point(A,C),D)
| convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_78,c_29]) ).
cnf(c_92,plain,
convergent_lines(A,orthogonal_through_point(A,B)),
inference(resolve,[status(thm)],[c_78,c_26]) ).
cnf(c_97,plain,
~ apart_point_and_line(intersection_point(A,orthogonal_through_point(A,B)),orthogonal_through_point(A,B)),
inference(resolve,[status(thm)],[c_92,c_33]) ).
cnf(c_98,plain,
~ apart_point_and_line(intersection_point(A,orthogonal_through_point(A,B)),A),
inference(resolve,[status(thm)],[c_92,c_32]) ).
cnf(c_238,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_42,c_92]) ).
cnf(c_239,plain,
( unorthogonal_lines(orthogonal_through_point(A,B),A)
| ~ unorthogonal_lines(A,orthogonal_through_point(A,B)) ),
inference(resolve,[status(thm)],[c_238,c_26]) ).
cnf(c_100,plain,
~ unorthogonal_lines(A,orthogonal_through_point(A,B)),
inference(resolve,[status(thm)],[c_239,c_45]) ).
cnf(c_240,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1),A)
| unorthogonal_lines(sK0,A)
| ~ unorthogonal_lines(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)) ),
inference(resolve,[status(thm)],[c_44,c_48]) ).
cnf(c_241,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1),orthogonal_through_point(sK0,A))
| ~ unorthogonal_lines(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)) ),
inference(resolve,[status(thm)],[c_240,c_100]) ).
cnf(c_105,negated_conjecture,
~ unorthogonal_lines(sK0,orthogonal_through_point(orthogonal_through_point(sK0,sK1),sK1)),
inference(resolve,[status(thm)],[c_241,c_45]) ).
cnf(c_201,plain,
( convergent_lines(B,orthogonal_through_point(A,C))
| convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_91,c_26]) ).
cnf(c_220,plain,
( convergent_lines(B,D)
| distinct_lines(orthogonal_through_point(A,C),D)
| convergent_lines(A,B) ),
inference(resolve,[status(thm)],[c_201,c_37]) ).
cnf(c_242,plain,
( distinct_lines(orthogonal_through_point(A,B),A)
| convergent_lines(A,A) ),
inference(factor,[status(thm)],[c_220]) ).
cnf(c_223,plain,
distinct_lines(orthogonal_through_point(A,B),A),
inference(resolve,[status(thm)],[c_26,c_242]) ).
cnf(c_243,plain,
( unorthogonal_lines(C,D)
| unorthogonal_lines(orthogonal_through_point(A,B),D)
| apart_point_and_line(intersection_point(A,orthogonal_through_point(A,B)),C)
| ~ distinct_lines(orthogonal_through_point(A,B),C) ),
inference(resolve,[status(thm)],[c_47,c_97]) ).
cnf(c_244,plain,
( unorthogonal_lines(A,C)
| unorthogonal_lines(orthogonal_through_point(A,B),C)
| ~ distinct_lines(orthogonal_through_point(A,B),A) ),
inference(resolve,[status(thm)],[c_243,c_98]) ).
cnf(c_245,plain,
( unorthogonal_lines(A,orthogonal_through_point(orthogonal_through_point(A,B),C))
| ~ distinct_lines(orthogonal_through_point(A,B),A) ),
inference(resolve,[status(thm)],[c_244,c_100]) ).
cnf(c_246,plain,
~ distinct_lines(orthogonal_through_point(sK0,sK1),sK0),
inference(resolve,[status(thm)],[c_245,c_105]) ).
cnf(c_237,plain,
$false,
inference(resolve,[status(thm)],[c_223,c_246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : GEO222+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.13/10.42 % Computer : n017.cluster.edu
% 0.13/10.42 % Model : x86_64 x86_64
% 0.13/10.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/10.42 % Memory : 8046.5625MB
% 0.13/10.42 % OS : Linux 6.8.0-71-generic
% 0.13/10.42 % CPULimit : 300
% 0.13/10.42 % WCLimit : 300
% 0.13/10.42 % DateTime : Fri Sep 25 13:02:58 UTC 2026
% 0.13/10.43 % CPUTime :
% 0.13/10.43 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.13/10.43 % Process 2335104 was started by sandbox on n017,
% 0.13/10.43 % Fri Sep 25 13:02:58 2026
% 0.13/10.43 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.13/10.44
% 0.13/10.44 % From the command line: assign(max_seconds, 300).
% 0.13/10.47
% 0.13/10.47 % SZS status Theorem for theBenchmark
% 0.13/10.47
% 0.13/10.47 % Proof 1 at 0.01 (+ 0.01) seconds.
% 0.13/10.47 % Length of proof is 33.
% 0.13/10.47 % Level of proof is 8.
% 0.13/10.47 % Maximum clause weight is 24.000.
% 0.13/10.47 % Given clauses 50.
% 0.13/10.47
% 0.13/10.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------