TSTP Solution File: NUM533+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM533+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.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 : Sun Sep 18 13:10:19 EDT 2022
% Result : Theorem 0.19s 0.39s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 53
% Syntax : Number of formulae : 119 ( 22 unt; 7 typ; 0 def)
% Number of atoms : 1330 ( 0 equ)
% Maximal formula atoms : 36 ( 11 avg)
% Number of connectives : 2788 (1585 ~;1084 |; 41 &)
% ( 64 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 9 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 7 ( 4 >; 3 *; 0 +; 0 <<)
% Number of predicates : 10 ( 9 usr; 1 prp; 0-3 aty)
% Number of functors : 4 ( 4 usr; 3 con; 0-2 aty)
% Number of variables : 321 ( 314 !; 0 ?; 321 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xB_type,type,
xB: $i ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(xC_type,type,
xC: $i ).
tff(xA_type,type,
xA: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(1,plain,
( aSet0(xC)
<=> aSet0(xC) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
( aSet0(xA)
& aSet0(xB)
& aSet0(xC) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__522) ).
tff(3,plain,
aSet0(xC),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aSet0(xC),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
^ [W0: $i] :
refl(
( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(transitivity,[status(thm)],[10,8]) ).
tff(12,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(13,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
^ [W0: $i] :
rewrite(
( ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(15,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[14]) ).
tff(16,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
rewrite(
( ( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) )
<=> ( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ))),
( ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) )
<=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
rewrite(
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(18,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(quant_intro,[status(thm)],[17]) ).
tff(19,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefSub) ).
tff(20,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,16]) ).
tff(22,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(skolemize,[status(sab)],[21]) ).
tff(23,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[22,15]) ).
tff(24,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[23,13]) ).
tff(25,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
| ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) ),
inference(modus_ponens,[status(thm)],[24,11]) ).
tff(26,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[25,6]) ).
tff(27,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xC)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xC)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ( ~ aSet0(xC)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xC)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) ) )
<=> ( ~ aSet0(xC)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xC)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xC)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xC)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[28]) ).
tff(30,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xC)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xC)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xC)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[29,27]) ).
tff(31,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xC)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xC)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(32,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xC)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[31,30]) ).
tff(33,plain,
! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) ),
inference(unit_resolution,[status(thm)],[32,26,4]) ).
tff(34,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xA,xC)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xA,xC)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xC) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xA,xC)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xA,xC)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xC) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ~ ( ~ ( ~ aSet0(xA)
| aSubsetOf0(xA,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xA,xC)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xC) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(xA,xC)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xA,xC)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xC) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) )
| ~ ( ~ ( ~ aSet0(xA)
| aSubsetOf0(xA,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xA,xC)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xC) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xA,xC)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xA,xC)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xC) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) )
| ~ ( ~ ( ~ aSet0(xA)
| aSubsetOf0(xA,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xA,xC)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xC) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xA,xC)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xA,xC)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xC) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) )
| ~ ( ~ ( ~ aSet0(xA)
| aSubsetOf0(xA,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xA,xC)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xC) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xA,xC)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xA,xC)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xC) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
~ ( ~ ( aSubsetOf0(xA,xC)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xA,xC)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xC) ) ) ) ),
inference(unit_resolution,[status(thm)],[39,33]) ).
tff(41,plain,
( ~ ( aSubsetOf0(xA,xC)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xA,xC)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xC) ) ) )
| aSubsetOf0(xA,xC)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) ),
inference(tautology,[status(thm)],]) ).
tff(42,plain,
( aSubsetOf0(xA,xC)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) ),
inference(unit_resolution,[status(thm)],[41,40]) ).
tff(43,plain,
( ~ aSubsetOf0(xA,xC)
<=> ~ aSubsetOf0(xA,xC) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ~ ( ( aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) )
=> aSubsetOf0(xA,xC) )
<=> ~ ( ~ ( aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) )
| aSubsetOf0(xA,xC) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,axiom,
~ ( ( aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) )
=> aSubsetOf0(xA,xC) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(46,plain,
~ ( ~ ( aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) )
| aSubsetOf0(xA,xC) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
~ aSubsetOf0(xA,xC),
inference(or_elim,[status(thm)],[46]) ).
tff(48,plain,
~ aSubsetOf0(xA,xC),
inference(modus_ponens,[status(thm)],[47,43]) ).
tff(49,plain,
( aSet0(xA)
<=> aSet0(xA) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( aSet0(xA)
& aSet0(xB) ),
inference(and_elim,[status(thm)],[2]) ).
tff(51,plain,
aSet0(xA),
inference(and_elim,[status(thm)],[50]) ).
tff(52,plain,
aSet0(xA),
inference(modus_ponens,[status(thm)],[51,49]) ).
tff(53,plain,
( ~ ( aSubsetOf0(xA,xC)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) )
| aSubsetOf0(xA,xC)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) ),
inference(tautology,[status(thm)],]) ).
tff(54,plain,
( ~ ( aSubsetOf0(xA,xC)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) )
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) ),
inference(unit_resolution,[status(thm)],[53,52,48]) ).
tff(55,plain,
~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ),
inference(unit_resolution,[status(thm)],[54,42]) ).
tff(56,plain,
( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC)
| ~ aElementOf0(tptp_fun_W2_1(xA,xC),xC) ),
inference(tautology,[status(thm)],]) ).
tff(57,plain,
~ aElementOf0(tptp_fun_W2_1(xA,xC),xC),
inference(unit_resolution,[status(thm)],[56,55]) ).
tff(58,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xB,xC)
| ~ aSet0(xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xB,xC),xB)
| aElementOf0(tptp_fun_W2_1(xB,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xB,xC)
| ~ aSet0(xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xB,xC),xB)
| aElementOf0(tptp_fun_W2_1(xB,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ~ ( ~ ( ~ aSet0(xB)
| aSubsetOf0(xB,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xB,xC),xB)
| aElementOf0(tptp_fun_W2_1(xB,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(xB,xC)
| ~ aSet0(xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xB,xC),xB)
| aElementOf0(tptp_fun_W2_1(xB,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) )
| ~ ( ~ ( ~ aSet0(xB)
| aSubsetOf0(xB,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xB,xC),xB)
| aElementOf0(tptp_fun_W2_1(xB,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xB,xC)
| ~ aSet0(xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xB,xC),xB)
| aElementOf0(tptp_fun_W2_1(xB,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[59]) ).
tff(61,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) )
| ~ ( ~ ( ~ aSet0(xB)
| aSubsetOf0(xB,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xB,xC),xB)
| aElementOf0(tptp_fun_W2_1(xB,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xB,xC)
| ~ aSet0(xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xB,xC),xB)
| aElementOf0(tptp_fun_W2_1(xB,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[60,58]) ).
tff(62,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) )
| ~ ( ~ ( ~ aSet0(xB)
| aSubsetOf0(xB,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xB,xC),xB)
| aElementOf0(tptp_fun_W2_1(xB,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(63,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xC)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xC),W1)
| aElementOf0(tptp_fun_W2_1(W1,xC),xC) ) )
| ~ ( ~ aSubsetOf0(W1,xC)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xC) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xB,xC)
| ~ aSet0(xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xB,xC),xB)
| aElementOf0(tptp_fun_W2_1(xB,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
~ ( ~ ( aSubsetOf0(xB,xC)
| ~ aSet0(xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xB,xC),xB)
| aElementOf0(tptp_fun_W2_1(xB,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) ) ),
inference(unit_resolution,[status(thm)],[63,33]) ).
tff(65,plain,
( ~ ( aSubsetOf0(xB,xC)
| ~ aSet0(xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xB,xC),xB)
| aElementOf0(tptp_fun_W2_1(xB,xC),xC) ) )
| ~ ( ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) )
| ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(66,plain,
( ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) ),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
( aSubsetOf0(xB,xC)
<=> aSubsetOf0(xB,xC) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
( aSubsetOf0(xA,xB)
& aSubsetOf0(xB,xC) ),
inference(or_elim,[status(thm)],[46]) ).
tff(69,plain,
aSubsetOf0(xB,xC),
inference(and_elim,[status(thm)],[68]) ).
tff(70,plain,
aSubsetOf0(xB,xC),
inference(modus_ponens,[status(thm)],[69,67]) ).
tff(71,plain,
( ~ ( ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) )
| ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(72,plain,
( ~ ( ~ aSubsetOf0(xB,xC)
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) )
| ~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ) ),
inference(unit_resolution,[status(thm)],[71,70]) ).
tff(73,plain,
~ ( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ),
inference(unit_resolution,[status(thm)],[72,66]) ).
tff(74,plain,
( ~ aSet0(xB)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) )
| ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ) ),
inference(tautology,[status(thm)],]) ).
tff(75,plain,
! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) ),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
( ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) )
| ~ aElementOf0(tptp_fun_W2_1(xA,xC),xB)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) )
<=> ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) )
| ~ aElementOf0(tptp_fun_W2_1(xA,xC),xB)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) )
| ~ aElementOf0(tptp_fun_W2_1(xA,xC),xB)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xB)
| aElementOf0(W2,xC) )
| ~ aElementOf0(tptp_fun_W2_1(xA,xC),xB)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
~ aElementOf0(tptp_fun_W2_1(xA,xC),xB),
inference(unit_resolution,[status(thm)],[78,75,57]) ).
tff(80,plain,
( ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xC)
| aElementOf0(tptp_fun_W2_1(xA,xC),xA) ),
inference(tautology,[status(thm)],]) ).
tff(81,plain,
aElementOf0(tptp_fun_W2_1(xA,xC),xA),
inference(unit_resolution,[status(thm)],[80,55]) ).
tff(82,plain,
( aSet0(xB)
<=> aSet0(xB) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
aSet0(xB),
inference(and_elim,[status(thm)],[50]) ).
tff(84,plain,
aSet0(xB),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xB)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xB)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ( ~ aSet0(xB)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xB)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) ) )
<=> ( ~ aSet0(xB)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(87,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xB)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xB)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xB)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[86]) ).
tff(88,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xB)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xB)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xB)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[87,85]) ).
tff(89,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xB)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xB)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(90,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) )
| ~ ( ~ aSubsetOf0(W1,W0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) ) ) )
| ~ aSet0(xB)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) ),
inference(unit_resolution,[status(thm)],[90,26,84]) ).
tff(92,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xA,xB)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xB),xA)
| aElementOf0(tptp_fun_W2_1(xA,xB),xB) ) )
| ~ ( ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xA,xB)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xB),xA)
| aElementOf0(tptp_fun_W2_1(xA,xB),xB) ) )
| ~ ( ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(93,plain,
( ~ ( ~ ( ~ aSet0(xA)
| aSubsetOf0(xA,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xB),xA)
| aElementOf0(tptp_fun_W2_1(xA,xB),xB) ) )
| ~ ( ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(xA,xB)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xB),xA)
| aElementOf0(tptp_fun_W2_1(xA,xB),xB) ) )
| ~ ( ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) )
| ~ ( ~ ( ~ aSet0(xA)
| aSubsetOf0(xA,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xB),xA)
| aElementOf0(tptp_fun_W2_1(xA,xB),xB) ) )
| ~ ( ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xA,xB)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xB),xA)
| aElementOf0(tptp_fun_W2_1(xA,xB),xB) ) )
| ~ ( ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[93]) ).
tff(95,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) )
| ~ ( ~ ( ~ aSet0(xA)
| aSubsetOf0(xA,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xB),xA)
| aElementOf0(tptp_fun_W2_1(xA,xB),xB) ) )
| ~ ( ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xA,xB)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xB),xA)
| aElementOf0(tptp_fun_W2_1(xA,xB),xB) ) )
| ~ ( ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[94,92]) ).
tff(96,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) )
| ~ ( ~ ( ~ aSet0(xA)
| aSubsetOf0(xA,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xB),xA)
| aElementOf0(tptp_fun_W2_1(xA,xB),xB) ) )
| ~ ( ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(97,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xB)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xB),W1)
| aElementOf0(tptp_fun_W2_1(W1,xB),xB) ) )
| ~ ( ~ aSubsetOf0(W1,xB)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xB) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xA,xB)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xB),xA)
| aElementOf0(tptp_fun_W2_1(xA,xB),xB) ) )
| ~ ( ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
~ ( ~ ( aSubsetOf0(xA,xB)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xB),xA)
| aElementOf0(tptp_fun_W2_1(xA,xB),xB) ) )
| ~ ( ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) ) ),
inference(unit_resolution,[status(thm)],[97,91]) ).
tff(99,plain,
( ~ ( aSubsetOf0(xA,xB)
| ~ aSet0(xA)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xA,xB),xA)
| aElementOf0(tptp_fun_W2_1(xA,xB),xB) ) )
| ~ ( ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) )
| ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(100,plain,
( ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) ),
inference(unit_resolution,[status(thm)],[99,98]) ).
tff(101,plain,
( aSubsetOf0(xA,xB)
<=> aSubsetOf0(xA,xB) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
aSubsetOf0(xA,xB),
inference(and_elim,[status(thm)],[68]) ).
tff(103,plain,
aSubsetOf0(xA,xB),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
( ~ ( ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) )
| ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(105,plain,
( ~ ( ~ aSubsetOf0(xA,xB)
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) )
| ~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ) ),
inference(unit_resolution,[status(thm)],[104,103]) ).
tff(106,plain,
~ ( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ),
inference(unit_resolution,[status(thm)],[105,100]) ).
tff(107,plain,
( ~ aSet0(xA)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) )
| ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ) ),
inference(tautology,[status(thm)],]) ).
tff(108,plain,
! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) ),
inference(unit_resolution,[status(thm)],[107,106]) ).
tff(109,plain,
( ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) )
| ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xB) )
<=> ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) )
| ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xB) ) ),
inference(rewrite,[status(thm)],]) ).
tff(110,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) )
| ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xB) ),
inference(quant_inst,[status(thm)],]) ).
tff(111,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xA)
| aElementOf0(W2,xB) )
| ~ aElementOf0(tptp_fun_W2_1(xA,xC),xA)
| aElementOf0(tptp_fun_W2_1(xA,xC),xB) ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,plain,
$false,
inference(unit_resolution,[status(thm)],[111,108,81,79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM533+1 : TPTP v8.1.0. Released v4.0.0.
% 0.06/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n019.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 : Fri Sep 2 11:35:20 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.
% 0.19/0.39 % SZS status Theorem
% 0.19/0.39 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------