%------------------------------------------------------------------------------
% File : Prover9---2026-6A
% Problem : GEO210+2 : 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 : n009.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 07:17:30 AM UTC 2026
% Result : Theorem 0.17s 0.45s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 4
% Syntax : Number of formulae : 18 ( 9 unt; 0 def)
% Number of atoms : 40 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 44 ( 22 ~; 13 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 30 ( 2 sgn 14 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
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,M] :
( ( ~ unorthogonal_lines(L,M)
& ~ apart_point_and_line(A,L) )
=> ~ distinct_lines(L,orthogonal_through_point(M,A)) ),
file('theBenchmark.p',con) ).
fof(con_neg,negated_conjecture,
~ ! [A,L,M] :
( ( ~ unorthogonal_lines(L,M)
& ~ apart_point_and_line(A,L) )
=> ~ distinct_lines(L,orthogonal_through_point(M,A)) ),
inference(assume_negation,[status(cth)],[con]) ).
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,M] :
( distinct_lines(L,orthogonal_through_point(M,A))
& ~ unorthogonal_lines(L,M)
& ~ apart_point_and_line(A,L) ),
inference(fof_nnf,[status(thm)],[con_neg]) ).
fof(sk_con_neg,plain,
( distinct_lines(sK1,orthogonal_through_point(sK2,sK0))
& ~ unorthogonal_lines(sK1,sK2)
& ~ apart_point_and_line(sK0,sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(A,sK0),skolemize(L,sK1),skolemize(M,sK2)],[nnf_21]) ).
cnf(c_46,negated_conjecture,
~ apart_point_and_line(sK0,sK1),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_47,negated_conjecture,
~ unorthogonal_lines(sK1,sK2),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_48,negated_conjecture,
distinct_lines(sK1,orthogonal_through_point(sK2,sK0)),
inference(split_conjunct,[status(thm)],[sk_con_neg]) ).
cnf(c_58,negated_conjecture,
( unorthogonal_lines(A,B)
| unorthogonal_lines(sK1,B)
| apart_point_and_line(sK0,A)
| ~ distinct_lines(sK1,A) ),
inference(resolve,[status(thm)],[c_45,c_46]) ).
cnf(c_59,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(A,sK0),B)
| unorthogonal_lines(sK1,B)
| ~ distinct_lines(sK1,orthogonal_through_point(A,sK0)) ),
inference(resolve,[status(thm)],[c_58,c_44]) ).
cnf(c_60,negated_conjecture,
( unorthogonal_lines(orthogonal_through_point(A,sK0),sK2)
| ~ distinct_lines(sK1,orthogonal_through_point(A,sK0)) ),
inference(resolve,[status(thm)],[c_59,c_47]) ).
cnf(c_61,negated_conjecture,
~ distinct_lines(sK1,orthogonal_through_point(sK2,sK0)),
inference(resolve,[status(thm)],[c_60,c_43]) ).
cnf(c_57,negated_conjecture,
$false,
inference(resolve,[status(thm)],[c_48,c_61]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : GEO210+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.17/0.42 % Computer : n009.cluster.edu
% 0.17/0.42 % Model : x86_64 x86_64
% 0.17/0.42 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.42 % Memory : 8046.5625MB
% 0.17/0.42 % OS : Linux 6.8.0-71-generic
% 0.17/0.42 % CPULimit : 300
% 0.17/0.42 % WCLimit : 300
% 0.17/0.42 % DateTime : Fri Sep 25 13:06:28 UTC 2026
% 0.17/0.42 % CPUTime :
% 0.17/0.42 % Prover9 (64) version 2026-6A, July 2026, CASC-J13.
% 0.17/0.42 % Process 1662147 was started by sandbox on n009,
% 0.17/0.42 % Fri Sep 25 13:06:28 2026
% 0.17/0.42 % The command was "/export/starexec/sandbox/solver/bin/prover9 -casc 300 -f /export/starexec/sandbox/benchmark/theBenchmark.p".
% 0.17/0.44
% 0.17/0.44 % From the command line: assign(max_seconds, 300).
% 0.17/0.45
% 0.17/0.45 % SZS status Theorem for theBenchmark
% 0.17/0.45
% 0.17/0.45 % Proof 1 at 0.00 (+ 0.00) seconds.
% 0.17/0.45 % Length of proof is 11.
% 0.17/0.45 % Level of proof is 2.
% 0.17/0.45 % Maximum clause weight is 15.000.
% 0.17/0.45 % Given clauses 26.
% 0.17/0.45
% 0.17/0.45 % SZS output start CNFRefutation for theBenchmark
% See solution above
%------------------------------------------------------------------------------