%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM610+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 : Sat Jun 21 05:21:35 AM UTC 2025
% Result : Theorem 0.19s 0.49s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 38
% Syntax : Number of formulae : 105 ( 36 unt; 0 typ; 0 def)
% Number of atoms : 903 ( 13 equ)
% Maximal formula atoms : 36 ( 8 avg)
% Number of connectives : 1469 ( 717 ~; 545 |; 103 &)
% ( 81 <=>; 23 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 46 ( 46 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 227 ( 211 !; 0 ?; 227 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(xQ_type,type,
xQ: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(xe_type,type,
xe: $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xO_type,type,
xO: $i ).
tff(xP_type,type,
xP: $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(1,plain,
( aSet0(szNzAzT0)
<=> aSet0(szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mNATSet) ).
tff(3,plain,
aSet0(szNzAzT0),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
aSet0(szNzAzT0),
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(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) )
<=> ( ~ ! [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(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,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(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ),
inference(quant_inst,[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(szNzAzT0)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) ),
inference(unit_resolution,[status(thm)],[29,26,4]) ).
tff(31,plain,
( ~ ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,szNzAzT0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),W1)
| aElementOf0(tptp_fun_W2_1(W1,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(W1,szNzAzT0)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,szNzAzT0) ) ) ) )
| ~ ( ~ ( aSubsetOf0(xQ,szNzAzT0)
| ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xQ,szNzAzT0),xQ)
| aElementOf0(tptp_fun_W2_1(xQ,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(xQ,szNzAzT0)
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(32,plain,
~ ( ~ ( aSubsetOf0(xQ,szNzAzT0)
| ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xQ,szNzAzT0),xQ)
| aElementOf0(tptp_fun_W2_1(xQ,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(xQ,szNzAzT0)
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,szNzAzT0) ) ) ) ),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
( ~ ( aSubsetOf0(xQ,szNzAzT0)
| ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xQ,szNzAzT0),xQ)
| aElementOf0(tptp_fun_W2_1(xQ,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(xQ,szNzAzT0)
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(34,plain,
( ~ aSubsetOf0(xQ,szNzAzT0)
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(unit_resolution,[status(thm)],[33,32]) ).
tff(35,plain,
( ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
<=> ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,axiom,
( aSet0(xO)
& ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4891) ).
tff(37,plain,
xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(and_elim,[status(thm)],[36]) ).
tff(38,plain,
xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(modus_ponens,[status(thm)],[37,35]) ).
tff(39,plain,
sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) = xO,
inference(symmetry,[status(thm)],[38]) ).
tff(40,plain,
( ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) )
<=> ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(41,axiom,
( aSet0(xP)
& ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5164) ).
tff(42,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(and_elim,[status(thm)],[41]) ).
tff(43,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(modus_ponens,[status(thm)],[42,40]) ).
tff(44,plain,
sdtmndt0(xQ,szmzizndt0(xQ)) = xP,
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
<=> aSubsetOf0(xP,xO) ),
inference(monotonicity,[status(thm)],[44,39]) ).
tff(46,plain,
( aSubsetOf0(xP,xO)
<=> aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(symmetry,[status(thm)],[45]) ).
tff(47,plain,
( ~ aSubsetOf0(xP,xO)
<=> ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(monotonicity,[status(thm)],[46]) ).
tff(48,plain,
( ~ aSubsetOf0(xP,xO)
<=> ~ aSubsetOf0(xP,xO) ),
inference(rewrite,[status(thm)],[]) ).
tff(49,axiom,
~ aSubsetOf0(xP,xO),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(50,plain,
~ aSubsetOf0(xP,xO),
inference(modus_ponens,[status(thm)],[49,48]) ).
tff(51,plain,
~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[50,47]) ).
tff(52,plain,
( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
<=> aSubsetOf0(xP,xQ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(53,plain,
( aSubsetOf0(xP,xQ)
<=> aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ) ),
inference(symmetry,[status(thm)],[52]) ).
tff(54,plain,
( aSubsetOf0(xP,xQ)
<=> aSubsetOf0(xP,xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,axiom,
aSubsetOf0(xP,xQ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5195) ).
tff(56,plain,
aSubsetOf0(xP,xQ),
inference(modus_ponens,[status(thm)],[55,54]) ).
tff(57,plain,
aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ),
inference(modus_ponens,[status(thm)],[56,53]) ).
tff(58,plain,
( aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
<=> aSet0(xO) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(59,plain,
( aSet0(xO)
<=> aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(symmetry,[status(thm)],[58]) ).
tff(60,plain,
( aSet0(xO)
<=> aSet0(xO) ),
inference(rewrite,[status(thm)],[]) ).
tff(61,plain,
aSet0(xO),
inference(and_elim,[status(thm)],[36]) ).
tff(62,plain,
aSet0(xO),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[62,59]) ).
tff(64,plain,
( aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
<=> aSubsetOf0(xQ,xO) ),
inference(monotonicity,[status(thm)],[39]) ).
tff(65,plain,
( aSubsetOf0(xQ,xO)
<=> aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(symmetry,[status(thm)],[64]) ).
tff(66,plain,
( aSubsetOf0(xQ,xO)
<=> aSubsetOf0(xQ,xO) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,axiom,
( aSubsetOf0(xQ,xO)
& ( xQ != slcrc0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5093) ).
tff(68,plain,
aSubsetOf0(xQ,xO),
inference(and_elim,[status(thm)],[67]) ).
tff(69,plain,
aSubsetOf0(xQ,xO),
inference(modus_ponens,[status(thm)],[68,66]) ).
tff(70,plain,
aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[69,65]) ).
tff(71,plain,
( aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
<=> aSet0(xP) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(72,plain,
( aSet0(xP)
<=> aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(symmetry,[status(thm)],[71]) ).
tff(73,plain,
( aSet0(xP)
<=> aSet0(xP) ),
inference(rewrite,[status(thm)],[]) ).
tff(74,plain,
aSet0(xP),
inference(and_elim,[status(thm)],[41]) ).
tff(75,plain,
aSet0(xP),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
aSet0(sdtmndt0(xQ,szmzizndt0(xQ))),
inference(modus_ponens,[status(thm)],[75,72]) ).
tff(77,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
<=> ( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(78,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
<=> ~ ( ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1) ) )),
( ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
<=> ~ ~ ( ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1) ) )),
rewrite(( ~ ~ ( ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1) )
<=> ( ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1) ) )),
( ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
<=> ( ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1) ) )),
trans(monotonicity(rewrite(( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
<=> ~ ( ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ) )),
( ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
<=> ~ ~ ( ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ) )),
rewrite(( ~ ~ ( ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) )
<=> ( ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ) )),
( ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
<=> ( ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ) )),
( ( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) )
<=> ( aSubsetOf0(W0,W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) ) )),
rewrite(( ( aSubsetOf0(W0,W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W2)
| ~ aSet0(W1)
| ~ aSet0(W0) )
<=> ( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) ) )),
( ( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) )
<=> ( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
<=> ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) )),
rewrite(( ( ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
=> aSubsetOf0(W0,W2) )
<=> ( ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| aSubsetOf0(W0,W2) ) )),
( ( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
=> ( ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
=> aSubsetOf0(W0,W2) ) )
<=> ( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
=> ( ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| aSubsetOf0(W0,W2) ) ) )),
rewrite(( ( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
=> ( ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| aSubsetOf0(W0,W2) ) )
<=> ( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) ) )),
( ( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
=> ( ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
=> aSubsetOf0(W0,W2) ) )
<=> ( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
=> ( ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
=> aSubsetOf0(W0,W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) )
=> ( ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
=> aSubsetOf0(W0,W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSubTrans) ).
tff(85,plain,
! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ ( aSubsetOf0(W0,W1)
& aSubsetOf0(W1,W2) )
| ~ ( aSet0(W0)
& aSet0(W1)
& aSet0(W2) ) ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) ),
inference(modus_ponens,[status(thm)],[87,80]) ).
tff(89,plain,
! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) ),
inference(modus_ponens,[status(thm)],[88,78]) ).
tff(90,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ( aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) )
<=> ( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ) ),
inference(transitivity,[status(thm)],[92,90]) ).
tff(94,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( aSubsetOf0(W0,W2)
| ~ aSet0(W2)
| ~ aSubsetOf0(W1,W2)
| ~ aSet0(W1)
| ~ aSubsetOf0(W0,W1)
| ~ aSet0(W0) )
| ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
( ~ aSet0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ aSubsetOf0(xQ,sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSet0(xQ)
| ~ aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),xQ)
| aSubsetOf0(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(unit_resolution,[status(thm)],[95,89]) ).
tff(97,plain,
~ aSet0(xQ),
inference(unit_resolution,[status(thm)],[96,76,70,63,57,51]) ).
tff(98,plain,
( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,szNzAzT0) )
| aSet0(xQ) ),
inference(tautology,[status(thm)],[]) ).
tff(99,plain,
( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,szNzAzT0) ) ),
inference(unit_resolution,[status(thm)],[98,97]) ).
tff(100,plain,
( aSubsetOf0(xQ,szNzAzT0)
<=> aSubsetOf0(xQ,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5106) ).
tff(102,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
( ~ ( ~ aSubsetOf0(xQ,szNzAzT0)
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ aSubsetOf0(xQ,szNzAzT0)
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(104,plain,
( ~ ( ~ aSubsetOf0(xQ,szNzAzT0)
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(unit_resolution,[status(thm)],[103,102]) ).
tff(105,plain,
$false,
inference(unit_resolution,[status(thm)],[104,99,34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUM610+1 : TPTP v9.0.0. Released v4.0.0.
% 0.00/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n007.cluster.edu
% 0.11/0.33 % Model : x86_64 x86_64
% 0.11/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33 % Memory : 8042.1875MB
% 0.11/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33 % CPULimit : 300
% 0.11/0.33 % WCLimit : 300
% 0.11/0.33 % DateTime : Fri Jun 20 01:36:50 EDT 2025
% 0.11/0.33 % CPUTime :
% 0.19/0.49 % SZS status Theorem
% 0.19/0.49 % SZS output start Proof
% See solution above
% 0.19/0.50 % E exiting
%------------------------------------------------------------------------------