TSTP Solution File: SET041-3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET041-3 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n029.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 20 05:05:05 EDT 2022
% Result : Unsatisfiable 0.19s 0.44s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 32
% Syntax : Number of formulae : 56 ( 13 unt; 9 typ; 0 def)
% Number of atoms : 187 ( 25 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 258 ( 122 ~; 118 |; 0 &)
% ( 18 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 6 >; 4 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 122 ( 111 !; 0 ?; 122 :)
% Comments :
%------------------------------------------------------------------------------
tff(subset_type,type,
subset: ( $i * $i ) > $o ).
tff(apply_type,type,
apply: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(a_function_type,type,
a_function: $i ).
tff(another_function_type,type,
another_function: $i ).
tff(compose_type,type,
compose: ( $i * $i ) > $i ).
tff(function_type,type,
function: $i > $o ).
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(domain_of_type,type,
domain_of: $i > $i ).
tff(1,plain,
( function(a_function)
<=> function(a_function) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
function(a_function),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_function) ).
tff(3,plain,
function(a_function),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Xg: $i,Xf: $i,X: $i] :
refl(
( ( ~ function(Xf)
| subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X))) )
<=> ( ~ function(Xf)
| subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X))) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X))) )
<=> ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X))) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X))) )
<=> ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_for_composition2) ).
tff(8,plain,
! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X))) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X))) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X))) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X))) )
| ~ function(a_function)
| subset(apply(compose(another_function,a_function),a),apply(another_function,apply(a_function,a))) )
<=> ( ~ ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X))) )
| ~ function(a_function)
| subset(apply(compose(another_function,a_function),a),apply(another_function,apply(a_function,a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X))) )
| ~ function(a_function)
| subset(apply(compose(another_function,a_function),a),apply(another_function,apply(a_function,a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| subset(apply(compose(Xg,Xf),X),apply(Xg,apply(Xf,X))) )
| ~ function(a_function)
| subset(apply(compose(another_function,a_function),a),apply(another_function,apply(a_function,a))) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
subset(apply(compose(another_function,a_function),a),apply(another_function,apply(a_function,a))),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( member(a,domain_of(a_function))
<=> member(a,domain_of(a_function)) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
member(a,domain_of(a_function)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',member_of_domain) ).
tff(17,plain,
member(a,domain_of(a_function)),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [Xg: $i,Xf: $i,X: $i] :
refl(
( ( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) )
<=> ( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) )
<=> ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) )
<=> ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [Xg: $i,Xf: $i,X: $i] :
rewrite(
( ( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) )
<=> ( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) )
<=> ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',apply_for_composition1) ).
tff(24,plain,
! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) )
| ~ function(a_function)
| ~ member(a,domain_of(a_function))
| subset(apply(another_function,apply(a_function,a)),apply(compose(another_function,a_function),a)) )
<=> ( ~ ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) )
| ~ function(a_function)
| ~ member(a,domain_of(a_function))
| subset(apply(another_function,apply(a_function,a)),apply(compose(another_function,a_function),a)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ~ ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) )
| ~ function(a_function)
| ~ member(a,domain_of(a_function))
| subset(apply(another_function,apply(a_function,a)),apply(compose(another_function,a_function),a)) ),
inference(quant_inst,[status(thm)],]) ).
tff(30,plain,
( ~ ! [Xg: $i,Xf: $i,X: $i] :
( ~ function(Xf)
| ~ member(X,domain_of(Xf))
| subset(apply(Xg,apply(Xf,X)),apply(compose(Xg,Xf),X)) )
| ~ function(a_function)
| ~ member(a,domain_of(a_function))
| subset(apply(another_function,apply(a_function,a)),apply(compose(another_function,a_function),a)) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
subset(apply(another_function,apply(a_function,a)),apply(compose(another_function,a_function),a)),
inference(unit_resolution,[status(thm)],[30,27,3,17]) ).
tff(32,plain,
( ( apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a) )
<=> ( apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_apply_for_composition3) ).
tff(34,plain,
apply(another_function,apply(a_function,a)) != apply(compose(another_function,a_function),a),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
( ! [Y: $i,X: $i] :
( ( X = Y )
| ~ subset(X,Y)
| ~ subset(Y,X) )
<=> ! [Y: $i,X: $i] :
( ( X = Y )
| ~ subset(X,Y)
| ~ subset(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ! [Y: $i,X: $i] :
( ( X = Y )
| ~ subset(X,Y)
| ~ subset(Y,X) )
<=> ! [Y: $i,X: $i] :
( ( X = Y )
| ~ subset(X,Y)
| ~ subset(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
^ [Y: $i,X: $i] :
rewrite(
( ( ~ subset(X,Y)
| ~ subset(Y,X)
| ( X = Y ) )
<=> ( ( X = Y )
| ~ subset(X,Y)
| ~ subset(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(38,plain,
( ! [Y: $i,X: $i] :
( ~ subset(X,Y)
| ~ subset(Y,X)
| ( X = Y ) )
<=> ! [Y: $i,X: $i] :
( ( X = Y )
| ~ subset(X,Y)
| ~ subset(Y,X) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,axiom,
! [Y: $i,X: $i] :
( ~ subset(X,Y)
| ~ subset(Y,X)
| ( X = Y ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',two_sets_equal) ).
tff(40,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ~ subset(X,Y)
| ~ subset(Y,X) ),
inference(modus_ponens,[status(thm)],[39,38]) ).
tff(41,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ~ subset(X,Y)
| ~ subset(Y,X) ),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ~ subset(X,Y)
| ~ subset(Y,X) ),
inference(skolemize,[status(sab)],[41]) ).
tff(43,plain,
! [Y: $i,X: $i] :
( ( X = Y )
| ~ subset(X,Y)
| ~ subset(Y,X) ),
inference(modus_ponens,[status(thm)],[42,35]) ).
tff(44,plain,
( ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ~ subset(X,Y)
| ~ subset(Y,X) )
| ( apply(another_function,apply(a_function,a)) = apply(compose(another_function,a_function),a) )
| ~ subset(apply(another_function,apply(a_function,a)),apply(compose(another_function,a_function),a))
| ~ subset(apply(compose(another_function,a_function),a),apply(another_function,apply(a_function,a))) )
<=> ( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ~ subset(X,Y)
| ~ subset(Y,X) )
| ( apply(another_function,apply(a_function,a)) = apply(compose(another_function,a_function),a) )
| ~ subset(apply(another_function,apply(a_function,a)),apply(compose(another_function,a_function),a))
| ~ subset(apply(compose(another_function,a_function),a),apply(another_function,apply(a_function,a))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ~ subset(X,Y)
| ~ subset(Y,X) )
| ( apply(another_function,apply(a_function,a)) = apply(compose(another_function,a_function),a) )
| ~ subset(apply(another_function,apply(a_function,a)),apply(compose(another_function,a_function),a))
| ~ subset(apply(compose(another_function,a_function),a),apply(another_function,apply(a_function,a))) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [Y: $i,X: $i] :
( ( X = Y )
| ~ subset(X,Y)
| ~ subset(Y,X) )
| ( apply(another_function,apply(a_function,a)) = apply(compose(another_function,a_function),a) )
| ~ subset(apply(another_function,apply(a_function,a)),apply(compose(another_function,a_function),a))
| ~ subset(apply(compose(another_function,a_function),a),apply(another_function,apply(a_function,a))) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
$false,
inference(unit_resolution,[status(thm)],[46,43,34,31,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET041-3 : TPTP v8.1.0. Released v1.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n029.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 : Sat Sep 3 01:53:00 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.
% 0.19/0.44 % SZS status Unsatisfiable
% 0.19/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------