%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : GRA010+2 : TPTP v9.0.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n008.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 05:06:37 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 : 9 ( 2 unt; 0 typ; 0 def)
% Number of atoms : 109 ( 15 equ)
% Maximal formula atoms : 14 ( 12 avg)
% Number of connectives : 117 ( 24 ~; 19 |; 51 &)
% ( 6 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 11 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 7 ( 7 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 2 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 81 ( 61 !; 17 ?; 81 :)
% Comments :
%------------------------------------------------------------------------------
tff(number_of_in_type,type,
number_of_in: ( $i * $i ) > $i ).
tff(triangles_type,type,
triangles: $i ).
tff(sequential_pairs_type,type,
sequential_pairs: $i ).
tff(triangle_type,type,
triangle: ( $i * $i * $i ) > $o ).
tff(sequential_type,type,
sequential: ( $i * $i ) > $o ).
tff(on_path_type,type,
on_path: ( $i * $i ) > $o ).
tff(path_type,type,
path: ( $i * $i * $i ) > $o ).
tff(complete_type,type,
complete: $o ).
tff(1,plain,
( ~ ( complete
=> ! [P: $i,V1: $i,V2: $i] :
( ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
=> ? [E3: $i] : triangle(E1,E2,E3) ) )
=> ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ) )
<=> ~ ( ~ complete
| ! [P: $i,V1: $i,V2: $i] :
( ~ ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ~ ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
| ? [E3: $i] : triangle(E1,E2,E3) ) )
| ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
~ ( complete
=> ! [P: $i,V1: $i,V2: $i] :
( ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
=> ? [E3: $i] : triangle(E1,E2,E3) ) )
=> ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',complete_means_sequential_pairs_and_triangles) ).
tff(3,plain,
~ ( ~ complete
| ! [P: $i,V1: $i,V2: $i] :
( ~ ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ~ ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
| ? [E3: $i] : triangle(E1,E2,E3) ) )
| ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ) ),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
~ ! [P: $i,V1: $i,V2: $i] :
( ~ ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ~ ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
| ? [E3: $i] : triangle(E1,E2,E3) ) )
| ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ),
inference(or_elim,[status(thm)],[3]) ).
tff(5,plain,
^ [P: $i,V1: $i,V2: $i] :
trans(monotonicity(rewrite(( ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
=> ? [E3: $i] : triangle(E1,E2,E3) ) )
<=> ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ~ ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
| ? [E3: $i] : triangle(E1,E2,E3) ) ) )),
( ( ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
=> ? [E3: $i] : triangle(E1,E2,E3) ) )
=> ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) )
<=> ( ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ~ ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
| ? [E3: $i] : triangle(E1,E2,E3) ) )
=> ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ) )),
rewrite(( ( ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ~ ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
| ? [E3: $i] : triangle(E1,E2,E3) ) )
=> ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) )
<=> ( ~ ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ~ ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
| ? [E3: $i] : triangle(E1,E2,E3) ) )
| ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ) )),
( ( ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
=> ? [E3: $i] : triangle(E1,E2,E3) ) )
=> ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) )
<=> ( ~ ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ~ ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
| ? [E3: $i] : triangle(E1,E2,E3) ) )
| ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ) )),
inference(bind,[status(th)],[]) ).
tff(6,plain,
( ! [P: $i,V1: $i,V2: $i] :
( ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
=> ? [E3: $i] : triangle(E1,E2,E3) ) )
=> ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) )
<=> ! [P: $i,V1: $i,V2: $i] :
( ~ ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ~ ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
| ? [E3: $i] : triangle(E1,E2,E3) ) )
| ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,axiom,
! [P: $i,V1: $i,V2: $i] :
( ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
=> ? [E3: $i] : triangle(E1,E2,E3) ) )
=> ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sequential_pairs_and_triangles) ).
tff(8,plain,
! [P: $i,V1: $i,V2: $i] :
( ~ ( path(V1,V2,P)
& ! [E1: $i,E2: $i] :
( ~ ( on_path(E1,P)
& on_path(E2,P)
& sequential(E1,E2) )
| ? [E3: $i] : triangle(E1,E2,E3) ) )
| ( number_of_in(sequential_pairs,P) = number_of_in(triangles,P) ) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
$false,
inference(unit_resolution,[status(thm)],[8,4]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : GRA010+2 : TPTP v9.0.0. Bugfixed v3.2.0.
% 0.07/0.13 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n008.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 15:23:03 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
% 0.12/0.38 % E exiting
%------------------------------------------------------------------------------