TSTP Solution File: CAT016-4 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CAT016-4 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 17:29:48 EDT 2022
% Result : Unsatisfiable 0.14s 0.41s
% Output : Proof 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 18
% Syntax : Number of formulae : 37 ( 15 unt; 4 typ; 0 def)
% Number of atoms : 77 ( 13 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 74 ( 33 ~; 28 |; 0 &)
% ( 13 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 3 ( 3 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 4 ( 3 >; 1 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-2 aty)
% Number of variables : 44 ( 39 !; 0 ?; 44 :)
% Comments :
%------------------------------------------------------------------------------
tff(there_exists_type,type,
there_exists: $i > $o ).
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(domain_type,type,
domain: $i > $i ).
tff(a_type,type,
a: $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( compose(X,domain(X)) = X )
<=> ( compose(X,domain(X)) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( compose(X,domain(X)) = X )
<=> ! [X: $i] : ( compose(X,domain(X)) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( compose(X,domain(X)) = X )
<=> ! [X: $i] : ( compose(X,domain(X)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( compose(X,domain(X)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',compose_domain) ).
tff(5,plain,
! [X: $i] : ( compose(X,domain(X)) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( compose(X,domain(X)) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( compose(X,domain(X)) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( compose(X,domain(X)) = X )
| ( compose(a,domain(a)) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
compose(a,domain(a)) = a,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( there_exists(compose(a,domain(a)))
<=> there_exists(a) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( there_exists(a)
<=> there_exists(compose(a,domain(a))) ),
inference(symmetry,[status(thm)],[10]) ).
tff(12,plain,
( there_exists(a)
<=> there_exists(a) ),
inference(rewrite,[status(thm)],]) ).
tff(13,axiom,
there_exists(a),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',assume_a_exists) ).
tff(14,plain,
there_exists(a),
inference(modus_ponens,[status(thm)],[13,12]) ).
tff(15,plain,
there_exists(compose(a,domain(a))),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
( ~ there_exists(domain(a))
<=> ~ there_exists(domain(a)) ),
inference(rewrite,[status(thm)],]) ).
tff(17,axiom,
~ there_exists(domain(a)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_a_exists) ).
tff(18,plain,
~ there_exists(domain(a)),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
^ [Y: $i,X: $i] :
refl(
( ( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
<=> ( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(20,plain,
( ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
<=> ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
<=> ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
^ [Y: $i,X: $i] :
rewrite(
( ( ~ there_exists(compose(X,Y))
| there_exists(domain(X)) )
<=> ( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| there_exists(domain(X)) )
<=> ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,axiom,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| there_exists(domain(X)) ),
file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',composition_implies_domain) ).
tff(25,plain,
! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[25,21]) ).
tff(27,plain,
! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(skolemize,[status(sab)],[26]) ).
tff(28,plain,
! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ( ~ ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(domain(a))
| ~ there_exists(compose(a,domain(a))) )
<=> ( ~ ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(domain(a))
| ~ there_exists(compose(a,domain(a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ~ ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(domain(a))
| ~ there_exists(compose(a,domain(a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(31,plain,
( ~ ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(domain(a))
| ~ there_exists(compose(a,domain(a))) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
~ there_exists(compose(a,domain(a))),
inference(unit_resolution,[status(thm)],[31,28,18]) ).
tff(33,plain,
$false,
inference(unit_resolution,[status(thm)],[32,15]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : CAT016-4 : TPTP v8.1.0. Released v1.0.0.
% 0.12/0.14 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.36 % Computer : n013.cluster.edu
% 0.14/0.36 % Model : x86_64 x86_64
% 0.14/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36 % Memory : 8042.1875MB
% 0.14/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36 % CPULimit : 300
% 0.14/0.36 % WCLimit : 300
% 0.14/0.36 % DateTime : Tue Aug 30 06:20:16 EDT 2022
% 0.14/0.36 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.14/0.41 % SZS status Unsatisfiable
% 0.14/0.41 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------