TSTP Solution File: SET014-2 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SET014-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n016.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 05:04:45 EDT 2022
% Result : Unsatisfiable 0.12s 0.38s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 39
% Syntax : Number of formulae : 77 ( 17 unt; 7 typ; 0 def)
% Number of atoms : 319 ( 0 equ)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 421 ( 178 ~; 213 |; 0 &)
% ( 30 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 6 ( 6 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 4 >; 4 *; 0 +; 0 <<)
% Number of predicates : 5 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 190 ( 174 !; 0 ?; 190 :)
% Comments :
%------------------------------------------------------------------------------
tff(member_type,type,
member: ( $i * $i ) > $o ).
tff(as_type,type,
as: $i ).
tff(member_of_1_not_of_2_type,type,
member_of_1_not_of_2: ( $i * $i ) > $i ).
tff(cs_type,type,
cs: $i ).
tff(union_type,type,
union: ( $i * $i ) > $i ).
tff(bs_type,type,
bs: $i ).
tff(subset_type,type,
subset: ( $i * $i ) > $o ).
tff(1,plain,
( ~ subset(union(as,bs),cs)
<=> ~ subset(union(as,bs),cs) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ subset(union(as,bs),cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_a_union_b_subset_of_c) ).
tff(3,plain,
~ subset(union(as,bs),cs),
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/sandbox/benchmark/Axioms/SET002-0.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(union(as,bs),cs),cs)
| subset(union(as,bs),cs) )
<=> ( ~ ! [Subset: $i,Superset: $i] :
( ~ member(member_of_1_not_of_2(Subset,Superset),Superset)
| subset(Subset,Superset) )
| ~ member(member_of_1_not_of_2(union(as,bs),cs),cs)
| subset(union(as,bs),cs) ) ),
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(union(as,bs),cs),cs)
| subset(union(as,bs),cs) ),
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(union(as,bs),cs),cs)
| subset(union(as,bs),cs) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ member(member_of_1_not_of_2(union(as,bs),cs),cs),
inference(unit_resolution,[status(thm)],[13,10,3]) ).
tff(15,plain,
( subset(as,cs)
<=> subset(as,cs) ),
inference(rewrite,[status(thm)],]) ).
tff(16,axiom,
subset(as,cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_subset_of_c) ).
tff(17,plain,
subset(as,cs),
inference(modus_ponens,[status(thm)],[16,15]) ).
tff(18,plain,
^ [Subset: $i,Element: $i,Superset: $i] :
refl(
( ( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
<=> ( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ) )),
inference(bind,[status(th)],]) ).
tff(19,plain,
( ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
<=> ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ) ),
inference(quant_intro,[status(thm)],[18]) ).
tff(20,plain,
( ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
<=> ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
^ [Subset: $i,Element: $i,Superset: $i] :
rewrite(
( ( ~ member(Element,Subset)
| ~ subset(Subset,Superset)
| member(Element,Superset) )
<=> ( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ) )),
inference(bind,[status(th)],]) ).
tff(22,plain,
( ! [Subset: $i,Element: $i,Superset: $i] :
( ~ member(Element,Subset)
| ~ subset(Subset,Superset)
| member(Element,Superset) )
<=> ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ) ),
inference(quant_intro,[status(thm)],[21]) ).
tff(23,axiom,
! [Subset: $i,Element: $i,Superset: $i] :
( ~ member(Element,Subset)
| ~ subset(Subset,Superset)
| member(Element,Superset) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',membership_in_subsets) ).
tff(24,plain,
! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
inference(skolemize,[status(sab)],[25]) ).
tff(27,plain,
! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) ),
inference(modus_ponens,[status(thm)],[26,19]) ).
tff(28,plain,
( ( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| ~ subset(as,cs)
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),as) )
<=> ( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| ~ subset(as,cs)
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),as) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ subset(as,cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),as) )
<=> ( ~ subset(as,cs)
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),as) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
( ( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ subset(as,cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),as) )
<=> ( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| ~ subset(as,cs)
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),as) ) ),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
( ( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ subset(as,cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),as) )
<=> ( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| ~ subset(as,cs)
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),as) ) ),
inference(transitivity,[status(thm)],[30,28]) ).
tff(32,plain,
( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ subset(as,cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),as) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| ~ subset(as,cs)
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),as) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
~ member(member_of_1_not_of_2(union(as,bs),cs),as),
inference(unit_resolution,[status(thm)],[33,27,17,14]) ).
tff(35,plain,
( subset(bs,cs)
<=> subset(bs,cs) ),
inference(rewrite,[status(thm)],]) ).
tff(36,axiom,
subset(bs,cs),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',b_subset_of_c) ).
tff(37,plain,
subset(bs,cs),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
( ( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| ~ subset(bs,cs)
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),bs) )
<=> ( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| ~ subset(bs,cs)
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),bs) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ( member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ subset(bs,cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),bs) )
<=> ( ~ subset(bs,cs)
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),bs) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ subset(bs,cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),bs) )
<=> ( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| ~ subset(bs,cs)
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),bs) ) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(41,plain,
( ( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ subset(bs,cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),bs) )
<=> ( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| ~ subset(bs,cs)
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),bs) ) ),
inference(transitivity,[status(thm)],[40,38]) ).
tff(42,plain,
( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ subset(bs,cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),bs) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
( ~ ! [Subset: $i,Element: $i,Superset: $i] :
( member(Element,Superset)
| ~ subset(Subset,Superset)
| ~ member(Element,Subset) )
| ~ subset(bs,cs)
| member(member_of_1_not_of_2(union(as,bs),cs),cs)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),bs) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
~ member(member_of_1_not_of_2(union(as,bs),cs),bs),
inference(unit_resolution,[status(thm)],[43,27,37,14]) ).
tff(45,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(46,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)],[45]) ).
tff(47,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(48,axiom,
! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',subsets_axiom1) ).
tff(49,plain,
! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
inference(skolemize,[status(sab)],[49]) ).
tff(51,plain,
! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) ),
inference(modus_ponens,[status(thm)],[50,46]) ).
tff(52,plain,
( ( ~ ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
| subset(union(as,bs),cs)
| member(member_of_1_not_of_2(union(as,bs),cs),union(as,bs)) )
<=> ( ~ ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
| subset(union(as,bs),cs)
| member(member_of_1_not_of_2(union(as,bs),cs),union(as,bs)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
( ~ ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
| subset(union(as,bs),cs)
| member(member_of_1_not_of_2(union(as,bs),cs),union(as,bs)) ),
inference(quant_inst,[status(thm)],]) ).
tff(54,plain,
( ~ ! [Subset: $i,Superset: $i] :
( subset(Subset,Superset)
| member(member_of_1_not_of_2(Subset,Superset),Subset) )
| subset(union(as,bs),cs)
| member(member_of_1_not_of_2(union(as,bs),cs),union(as,bs)) ),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
member(member_of_1_not_of_2(union(as,bs),cs),union(as,bs)),
inference(unit_resolution,[status(thm)],[54,51,3]) ).
tff(56,plain,
^ [Xs: $i,X: $i,Ys: $i] :
refl(
( ( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) )
<=> ( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [Xs: $i,X: $i,Ys: $i] :
( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) )
<=> ! [Xs: $i,X: $i,Ys: $i] :
( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [Xs: $i,X: $i,Ys: $i] :
( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) )
<=> ! [Xs: $i,X: $i,Ys: $i] :
( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
^ [Xs: $i,X: $i,Ys: $i] :
rewrite(
( ( ~ member(X,union(Xs,Ys))
| member(X,Xs)
| member(X,Ys) )
<=> ( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [Xs: $i,X: $i,Ys: $i] :
( ~ member(X,union(Xs,Ys))
| member(X,Xs)
| member(X,Ys) )
<=> ! [Xs: $i,X: $i,Ys: $i] :
( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,axiom,
! [Xs: $i,X: $i,Ys: $i] :
( ~ member(X,union(Xs,Ys))
| member(X,Xs)
| member(X,Ys) ),
file('/export/starexec/sandbox/benchmark/Axioms/SET002-0.ax',member_of_union_is_member_of_one_set) ).
tff(62,plain,
! [Xs: $i,X: $i,Ys: $i] :
( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [Xs: $i,X: $i,Ys: $i] :
( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [Xs: $i,X: $i,Ys: $i] :
( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [Xs: $i,X: $i,Ys: $i] :
( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ( ~ ! [Xs: $i,X: $i,Ys: $i] :
( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) )
| member(member_of_1_not_of_2(union(as,bs),cs),bs)
| member(member_of_1_not_of_2(union(as,bs),cs),as)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),union(as,bs)) )
<=> ( ~ ! [Xs: $i,X: $i,Ys: $i] :
( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) )
| member(member_of_1_not_of_2(union(as,bs),cs),bs)
| member(member_of_1_not_of_2(union(as,bs),cs),as)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),union(as,bs)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(67,plain,
( ~ ! [Xs: $i,X: $i,Ys: $i] :
( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) )
| member(member_of_1_not_of_2(union(as,bs),cs),bs)
| member(member_of_1_not_of_2(union(as,bs),cs),as)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),union(as,bs)) ),
inference(quant_inst,[status(thm)],]) ).
tff(68,plain,
( ~ ! [Xs: $i,X: $i,Ys: $i] :
( member(X,Ys)
| member(X,Xs)
| ~ member(X,union(Xs,Ys)) )
| member(member_of_1_not_of_2(union(as,bs),cs),bs)
| member(member_of_1_not_of_2(union(as,bs),cs),as)
| ~ member(member_of_1_not_of_2(union(as,bs),cs),union(as,bs)) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
( member(member_of_1_not_of_2(union(as,bs),cs),bs)
| member(member_of_1_not_of_2(union(as,bs),cs),as) ),
inference(unit_resolution,[status(thm)],[68,65,55]) ).
tff(70,plain,
$false,
inference(unit_resolution,[status(thm)],[69,44,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.11 % Problem : SET014-2 : TPTP v8.1.0. Bugfixed v2.1.0.
% 0.07/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n016.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 : Sat Sep 3 01:26:51 EDT 2022
% 0.12/0.33 % 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
%------------------------------------------------------------------------------