TSTP Solution File: CAT017-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : CAT017-3 : 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 0.12s 0.38s
% Output : Proof 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 24
% Syntax : Number of formulae : 55 ( 18 unt; 5 typ; 0 def)
% Number of atoms : 126 ( 33 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 131 ( 59 ~; 52 |; 0 &)
% ( 20 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 5 ( 4 >; 1 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 1 con; 0-2 aty)
% Number of variables : 70 ( 63 !; 0 ?; 70 :)
% Comments :
%------------------------------------------------------------------------------
tff(there_exists_type,type,
there_exists: $i > $o ).
tff(domain_type,type,
domain: $i > $i ).
tff(codomain_type,type,
codomain: $i > $i ).
tff(a_type,type,
a: $i ).
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i] :
refl(
( ( compose(codomain(X),X) = X )
<=> ( compose(codomain(X),X) = X ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [X: $i] : ( compose(codomain(X),X) = X )
<=> ! [X: $i] : ( compose(codomain(X),X) = X ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i] : ( compose(codomain(X),X) = X )
<=> ! [X: $i] : ( compose(codomain(X),X) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(4,axiom,
! [X: $i] : ( compose(codomain(X),X) = X ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',compose_codomain) ).
tff(5,plain,
! [X: $i] : ( compose(codomain(X),X) = X ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i] : ( compose(codomain(X),X) = X ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i] : ( compose(codomain(X),X) = X ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i] : ( compose(codomain(X),X) = X )
| ( compose(codomain(a),a) = a ) ),
inference(quant_inst,[status(thm)],]) ).
tff(9,plain,
compose(codomain(a),a) = a,
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( there_exists(compose(codomain(a),a))
<=> there_exists(a) ),
inference(monotonicity,[status(thm)],[9]) ).
tff(11,plain,
( there_exists(a)
<=> there_exists(compose(codomain(a),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/sandbox2/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(codomain(a),a)),
inference(modus_ponens,[status(thm)],[14,11]) ).
tff(16,plain,
^ [Y: $i,X: $i] :
refl(
( ( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
<=> ( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ) )),
inference(bind,[status(th)],]) ).
tff(17,plain,
( ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
<=> ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ) ),
inference(quant_intro,[status(thm)],[16]) ).
tff(18,plain,
( ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
<=> ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(19,axiom,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',domain_codomain_composition1) ).
tff(20,plain,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
inference(skolemize,[status(sab)],[20]) ).
tff(22,plain,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) ),
inference(modus_ponens,[status(thm)],[21,17]) ).
tff(23,plain,
( ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(a),a))
| ( domain(codomain(a)) = codomain(a) ) )
<=> ( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(a),a))
| ( domain(codomain(a)) = codomain(a) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(24,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(a),a))
| ( domain(codomain(a)) = codomain(a) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(25,plain,
( ~ ! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| ( domain(X) = codomain(Y) ) )
| ~ there_exists(compose(codomain(a),a))
| ( domain(codomain(a)) = codomain(a) ) ),
inference(modus_ponens,[status(thm)],[24,23]) ).
tff(26,plain,
( ~ there_exists(compose(codomain(a),a))
| ( domain(codomain(a)) = codomain(a) ) ),
inference(unit_resolution,[status(thm)],[25,22]) ).
tff(27,plain,
domain(codomain(a)) = codomain(a),
inference(unit_resolution,[status(thm)],[26,15]) ).
tff(28,plain,
( there_exists(domain(codomain(a)))
<=> there_exists(codomain(a)) ),
inference(monotonicity,[status(thm)],[27]) ).
tff(29,plain,
( there_exists(codomain(a))
<=> there_exists(domain(codomain(a))) ),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
( ~ there_exists(codomain(a))
<=> ~ there_exists(domain(codomain(a))) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ~ there_exists(codomain(a))
<=> ~ there_exists(codomain(a)) ),
inference(rewrite,[status(thm)],]) ).
tff(32,axiom,
~ there_exists(codomain(a)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_codomain_of_a_exists) ).
tff(33,plain,
~ there_exists(codomain(a)),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ there_exists(domain(codomain(a))),
inference(modus_ponens,[status(thm)],[33,30]) ).
tff(35,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(36,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)],[35]) ).
tff(37,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(38,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(39,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)],[38]) ).
tff(40,axiom,
! [Y: $i,X: $i] :
( ~ there_exists(compose(X,Y))
| there_exists(domain(X)) ),
file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',composition_implies_domain) ).
tff(41,plain,
! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[41,37]) ).
tff(43,plain,
! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) ),
inference(modus_ponens,[status(thm)],[43,36]) ).
tff(45,plain,
( ( ~ ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(domain(codomain(a)))
| ~ there_exists(compose(codomain(a),a)) )
<=> ( ~ ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(domain(codomain(a)))
| ~ there_exists(compose(codomain(a),a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ~ ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(domain(codomain(a)))
| ~ there_exists(compose(codomain(a),a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
( ~ ! [Y: $i,X: $i] :
( there_exists(domain(X))
| ~ there_exists(compose(X,Y)) )
| there_exists(domain(codomain(a)))
| ~ there_exists(compose(codomain(a),a)) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
( there_exists(domain(codomain(a)))
| ~ there_exists(compose(codomain(a),a)) ),
inference(unit_resolution,[status(thm)],[47,44]) ).
tff(49,plain,
there_exists(domain(codomain(a))),
inference(unit_resolution,[status(thm)],[48,15]) ).
tff(50,plain,
$false,
inference(unit_resolution,[status(thm)],[49,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : CAT017-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n013.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue Aug 30 06:24:02 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 0.12/0.38 % SZS status Unsatisfiable
% 0.12/0.38 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------