TSTP Solution File: GRA010+2 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : GRA010+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 : Fri Sep 16 20:47:29 EDT 2022
% Result : Theorem 0.06s 0.28s
% Output : Proof 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 12
% Syntax : Number of formulae : 17 ( 2 unt; 8 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 : 12 ( 5 >; 7 *; 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
% 0.00/0.06 % Problem : GRA010+2 : TPTP v8.1.0. Bugfixed v3.2.0.
% 0.00/0.07 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.06/0.25 % Computer : n021.cluster.edu
% 0.06/0.25 % Model : x86_64 x86_64
% 0.06/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.25 % Memory : 8042.1875MB
% 0.06/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.25 % CPULimit : 300
% 0.06/0.25 % WCLimit : 300
% 0.06/0.25 % DateTime : Wed Aug 31 13:19:42 EDT 2022
% 0.06/0.25 % CPUTime :
% 0.06/0.26 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.06/0.26 Usage: tptp [options] [-file:]file
% 0.06/0.26 -h, -? prints this message.
% 0.06/0.26 -smt2 print SMT-LIB2 benchmark.
% 0.06/0.26 -m, -model generate model.
% 0.06/0.26 -p, -proof generate proof.
% 0.06/0.26 -c, -core generate unsat core of named formulas.
% 0.06/0.26 -st, -statistics display statistics.
% 0.06/0.26 -t:timeout set timeout (in second).
% 0.06/0.26 -smt2status display status in smt2 format instead of SZS.
% 0.06/0.26 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.06/0.26 -<param>:<value> configuration parameter and value.
% 0.06/0.26 -o:<output-file> file to place output in.
% 0.06/0.28 % SZS status Theorem
% 0.06/0.28 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------