TSTP Solution File: COL056-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : COL056-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 : Tue Sep 6 17:48:14 EDT 2022
% Result : Unsatisfiable 0.14s 0.39s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 16
% Syntax : Number of formulae : 29 ( 16 unt; 5 typ; 0 def)
% Number of atoms : 36 ( 33 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 24 ( 14 ~; 2 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 4 ( 2 >; 2 *; 0 +; 0 <<)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 50 ( 45 !; 0 ?; 50 :)
% Comments :
%------------------------------------------------------------------------------
tff(c_type,type,
c: $i ).
tff(response_type,type,
response: ( $i * $i ) > $i ).
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(b_type,type,
b: $i ).
tff(1,plain,
( ( response(a,b) = c )
<=> ( response(a,response(a,c)) = c ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( response(a,b) = c )
<=> ( response(a,b) = c ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
response(a,b) = c,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_to_b_responds_c) ).
tff(4,plain,
response(a,b) = c,
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
response(a,response(a,c)) = c,
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [W: $i,Y: $i,X: $i] :
refl(
( ( response(compose(X,Y),W) = response(X,response(Y,W)) )
<=> ( response(compose(X,Y),W) = response(X,response(Y,W)) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) )
<=> ! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) )
<=> ! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',composer_exists) ).
tff(10,plain,
! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) ),
inference(skolemize,[status(sab)],[10]) ).
tff(12,plain,
! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) ),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
( ~ ! [W: $i,Y: $i,X: $i] : ( response(compose(X,Y),W) = response(X,response(Y,W)) )
| ( response(compose(a,a),c) = response(a,response(a,c)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(14,plain,
response(compose(a,a),c) = response(a,response(a,c)),
inference(unit_resolution,[status(thm)],[13,12]) ).
tff(15,plain,
response(compose(a,a),c) = c,
inference(transitivity,[status(thm)],[14,5]) ).
tff(16,plain,
^ [W: $i,V: $i] :
refl(
( ( response(W,V) != V )
<=> ( response(W,V) != V ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [W: $i,V: $i] : ( response(W,V) != V )
<=> ! [W: $i,V: $i] : ( response(W,V) != V ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [W: $i,V: $i] : ( response(W,V) != V )
<=> ! [W: $i,V: $i] : ( response(W,V) != V ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
! [W: $i,V: $i] : ( response(W,V) != V ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_there_exists_a_happy_bird) ).
tff(20,plain,
! [W: $i,V: $i] : ( response(W,V) != V ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [W: $i,V: $i] : ( response(W,V) != V ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [W: $i,V: $i] : ( response(W,V) != V ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ~ ! [W: $i,V: $i] : ( response(W,V) != V )
| ( response(compose(a,a),c) != c ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
$false,
inference(unit_resolution,[status(thm)],[23,22,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : COL056-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n007.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Aug 30 10:21:16 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.14/0.39 % SZS status Unsatisfiable
% 0.14/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------