%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GEO220+2 : TPTP v9.0.0. Released v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:06:01 AM UTC 2025
% Result : Theorem 0.12s 0.37s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 4
% Syntax : Number of formulae : 8 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 32 ( 0 equ)
% Maximal formula atoms : 6 ( 4 avg)
% Number of connectives : 62 ( 39 ~; 5 |; 10 &)
% ( 3 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 7 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of FOOLs : 1 ( 1 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 4 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 0 ( 0 usr; 0 con; --- aty)
% Number of variables : 27 ( 24 !; 0 ?; 27 :)
% Comments :
%------------------------------------------------------------------------------
tff(unorthogonal_lines_type,type,
unorthogonal_lines: ( $i * $i ) > $o ).
tff(convergent_lines_type,type,
convergent_lines: ( $i * $i ) > $o ).
tff(1,plain,
( ~ ! [L: $i,M: $i,N: $i] :
( ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) )
=> ~ convergent_lines(M,N) )
<=> ~ ! [L: $i,M: $i,N: $i] :
( ~ convergent_lines(M,N)
| ~ ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ ! [L: $i,M: $i,N: $i] :
( ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) )
=> ~ convergent_lines(M,N) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',con) ).
tff(3,plain,
~ ! [L: $i,M: $i,N: $i] :
( ~ convergent_lines(M,N)
| ~ ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) ) ),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [L: $i,M: $i,N: $i] :
rewrite(( ( ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) )
=> ~ convergent_lines(M,N) )
<=> ( ~ convergent_lines(M,N)
| ~ ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [L: $i,M: $i,N: $i] :
( ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) )
=> ~ convergent_lines(M,N) )
<=> ! [L: $i,M: $i,N: $i] :
( ~ convergent_lines(M,N)
| ~ ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,axiom,
! [L: $i,M: $i,N: $i] :
( ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) )
=> ~ convergent_lines(M,N) ),
file('/export/starexec/sandbox2/benchmark/Axioms/GEO006+4.ax',couo1) ).
tff(7,plain,
! [L: $i,M: $i,N: $i] :
( ~ convergent_lines(M,N)
| ~ ( ~ unorthogonal_lines(L,M)
& ~ unorthogonal_lines(L,N) ) ),
inference(modus_ponens,[status(thm)],[6,5]) ).
tff(8,plain,
$false,
inference(unit_resolution,[status(thm)],[7,3]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : GEO220+2 : TPTP v9.0.0. Released v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n016.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Thu Jun 19 14:42:17 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.12/0.37 % SZS status Theorem
% 0.12/0.37 % SZS output start Proof
% See solution above
% 0.12/0.37 % E exiting
%------------------------------------------------------------------------------