TSTP Solution File: SET003-1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET003-1 : TPTP v8.1.0. Released v1.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n015.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 05:04:39 EDT 2022
% Result : Unsatisfiable 0.21s 0.40s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 27
% Syntax : Number of formulae : 51 ( 11 unt; 6 typ; 0 def)
% Number of atoms : 205 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 267 ( 117 ~; 128 |; 0 &)
% ( 22 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 10 ( 10 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 9 ( 4 >; 5 *; 0 +; 0 <<)
% Number of predicates : 8 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 136 ( 124 !; 0 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(aUa_type,type,
aUa: $i ).
tff(member_of_1_not_of_2_type,type,
member_of_1_not_of_2: ( $i * $i ) > $i ).
tff(a_type,type,
a: $i ).
tff(subset_type,type,
subset: ( $i * $i ) > $o ).
tff(union_type,type,
union: ( $i * $i * $i ) > $o ).
tff(1,plain,
( ~ subset(a,aUa)
<=> ~ subset(a,aUa) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ subset(a,aUa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_a_is_a_subset_of_aUa) ).
tff(3,plain,
~ subset(a,aUa),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [Subset: $i,Superset: $i] :
refl(
( ( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) )
<=> ( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ) )),
inference(bind,[status(th)],]) ).
tff(5,plain,
( ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) )
<=> ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
( ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) )
<=> ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,axiom,
! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',subsets_axiom2) ).
tff(8,plain,
! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ),
inference(modus_ponens,[status(thm)],[7,6]) ).
tff(9,plain,
! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ),
inference(skolemize,[status(sab)],[8]) ).
tff(10,plain,
! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) ),
inference(modus_ponens,[status(thm)],[9,5]) ).
tff(11,plain,
( ( ~ ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) )
| ~ member(member_of_1_not_of_2(a,aUa),aUa)
| subset(a,aUa) )
<=> ( ~ ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) )
| ~ member(member_of_1_not_of_2(a,aUa),aUa)
| subset(a,aUa) ) ),
inference(rewrite,[status(thm)],]) ).
tff(12,plain,
( ~ ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) )
| ~ member(member_of_1_not_of_2(a,aUa),aUa)
| subset(a,aUa) ),
inference(quant_inst,[status(thm)],]) ).
tff(13,plain,
( ~ ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) )
| ~ member(member_of_1_not_of_2(a,aUa),aUa)
| subset(a,aUa) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ member(member_of_1_not_of_2(a,aUa),aUa),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
^ [Subset: $i,Superset: $i] :
refl(
( ( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
<=> ( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ) )),
inference(bind,[status(th)],]) ).
tff(16,plain,
( ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
<=> ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,plain,
( ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
<=> ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ) ),
inference(rewrite,[status(thm)],]) ).
tff(18,axiom,
! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-0.ax',subsets_axiom1) ).
tff(19,plain,
! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
( ( ~ ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
| subset(a,aUa)
| member(member_of_1_not_of_2(a,aUa),a) )
<=> ( ~ ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
| subset(a,aUa)
| member(member_of_1_not_of_2(a,aUa),a) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
( ~ ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
| subset(a,aUa)
| member(member_of_1_not_of_2(a,aUa),a) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
( ~ ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
| subset(a,aUa)
| member(member_of_1_not_of_2(a,aUa),a) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
member(member_of_1_not_of_2(a,aUa),a),
inference(unit_resolution,[status(thm)],[24,21,3]) ).
tff(26,plain,
( union(a,a,aUa)
<=> union(a,a,aUa) ),
inference(rewrite,[status(thm)],]) ).
tff(27,axiom,
union(a,a,aUa),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_union_a_is_aUa) ).
tff(28,plain,
union(a,a,aUa),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
^ [Set1: $i,Set2: $i,Union: $i,Element: $i] :
refl(
( ( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) )
<=> ( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) )
<=> ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
( ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) )
<=> ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
^ [Set1: $i,Set2: $i,Union: $i,Element: $i] :
trans(
monotonicity(
rewrite(
( ( ~ union(Set1,Set2,Union)
| ~ member(Element,Set1) )
<=> ( ~ member(Element,Set1)
| ~ union(Set1,Set2,Union) ) )),
( ( ~ union(Set1,Set2,Union)
| ~ member(Element,Set1)
| member(Element,Union) )
<=> ( ~ member(Element,Set1)
| ~ union(Set1,Set2,Union)
| member(Element,Union) ) )),
rewrite(
( ( ~ member(Element,Set1)
| ~ union(Set1,Set2,Union)
| member(Element,Union) )
<=> ( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) ) )),
( ( ~ union(Set1,Set2,Union)
| ~ member(Element,Set1)
| member(Element,Union) )
<=> ( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) ) )),
inference(bind,[status(th)],]) ).
tff(33,plain,
( ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ union(Set1,Set2,Union)
| ~ member(Element,Set1)
| member(Element,Union) )
<=> ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,axiom,
! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ union(Set1,Set2,Union)
| ~ member(Element,Set1)
| member(Element,Union) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SET001-1.ax',member_of_set1_is_member_of_union) ).
tff(35,plain,
! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) ),
inference(modus_ponens,[status(thm)],[35,31]) ).
tff(37,plain,
! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) ),
inference(skolemize,[status(sab)],[36]) ).
tff(38,plain,
! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) ),
inference(modus_ponens,[status(thm)],[37,30]) ).
tff(39,plain,
( ( ~ ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) )
| member(member_of_1_not_of_2(a,aUa),aUa)
| ~ member(member_of_1_not_of_2(a,aUa),a)
| ~ union(a,a,aUa) )
<=> ( ~ ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) )
| member(member_of_1_not_of_2(a,aUa),aUa)
| ~ member(member_of_1_not_of_2(a,aUa),a)
| ~ union(a,a,aUa) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( ~ member(member_of_1_not_of_2(a,aUa),a)
| member(member_of_1_not_of_2(a,aUa),aUa)
| ~ union(a,a,aUa) )
<=> ( member(member_of_1_not_of_2(a,aUa),aUa)
| ~ member(member_of_1_not_of_2(a,aUa),a)
| ~ union(a,a,aUa) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ( ~ ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) )
| ~ member(member_of_1_not_of_2(a,aUa),a)
| member(member_of_1_not_of_2(a,aUa),aUa)
| ~ union(a,a,aUa) )
<=> ( ~ ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) )
| member(member_of_1_not_of_2(a,aUa),aUa)
| ~ member(member_of_1_not_of_2(a,aUa),a)
| ~ union(a,a,aUa) ) ),
inference(monotonicity,[status(thm)],[40]) ).
tff(42,plain,
( ( ~ ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) )
| ~ member(member_of_1_not_of_2(a,aUa),a)
| member(member_of_1_not_of_2(a,aUa),aUa)
| ~ union(a,a,aUa) )
<=> ( ~ ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) )
| member(member_of_1_not_of_2(a,aUa),aUa)
| ~ member(member_of_1_not_of_2(a,aUa),a)
| ~ union(a,a,aUa) ) ),
inference(transitivity,[status(thm)],[41,39]) ).
tff(43,plain,
( ~ ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) )
| ~ member(member_of_1_not_of_2(a,aUa),a)
| member(member_of_1_not_of_2(a,aUa),aUa)
| ~ union(a,a,aUa) ),
inference(quant_inst,[status(thm)],]) ).
tff(44,plain,
( ~ ! [Set1: $i,Set2: $i,Union: $i,Element: $i] :
( ~ member(Element,Set1)
| member(Element,Union)
| ~ union(Set1,Set2,Union) )
| member(member_of_1_not_of_2(a,aUa),aUa)
| ~ member(member_of_1_not_of_2(a,aUa),a)
| ~ union(a,a,aUa) ),
inference(modus_ponens,[status(thm)],[43,42]) ).
tff(45,plain,
$false,
inference(unit_resolution,[status(thm)],[44,38,28,25,14]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET003-1 : TPTP v8.1.0. Released v1.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.35 % Computer : n015.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Sat Sep 3 01:11:39 EDT 2022
% 0.13/0.35 % CPUTime :
% 0.13/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.35 Usage: tptp [options] [-file:]file
% 0.13/0.35 -h, -? prints this message.
% 0.13/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.35 -m, -model generate model.
% 0.13/0.35 -p, -proof generate proof.
% 0.13/0.35 -c, -core generate unsat core of named formulas.
% 0.13/0.35 -st, -statistics display statistics.
% 0.13/0.35 -t:timeout set timeout (in second).
% 0.13/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.35 -<param>:<value> configuration parameter and value.
% 0.13/0.35 -o:<output-file> file to place output in.
% 0.21/0.40 % SZS status Unsatisfiable
% 0.21/0.40 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------