%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM625+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n005.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 05:21:38 AM UTC 2025
% Result : Theorem 14.03s 14.18s
% Output : Proof 14.03s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 58
% Syntax : Number of formulae : 145 ( 43 unt; 0 typ; 0 def)
% Number of atoms : 2023 ( 400 equ)
% Maximal formula atoms : 56 ( 13 avg)
% Number of connectives : 3486 (1698 ~;1217 |; 206 &)
% ( 335 <=>; 30 =>; 0 <=; 0 <~>)
% Maximal formula depth : 22 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 90 ( 90 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 8 con; 0-3 aty)
% Number of variables : 475 ( 449 !; 0 ?; 475 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xQ_type,type,
xQ: $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xm_type,type,
xm: $i ).
tff(xe_type,type,
xe: $i ).
tff(xP_type,type,
xP: $i ).
tff(xx_type,type,
xx: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(tptp_fun_W3_3_type,type,
tptp_fun_W3_3: ( $i * $i * $i ) > $i ).
tff(xO_type,type,
xO: $i ).
tff(isCountable0_type,type,
isCountable0: $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(xp_type,type,
xp: $i ).
tff(1,plain,
( ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) )
<=> ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aSet0(xP)
& ( xP = sdtmndt0(xQ,szmzizndt0(xQ)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5164) ).
tff(3,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xP = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
sdtmndt0(xQ,szmzizndt0(xQ)) = xP,
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
( ( xx = sdtlpdtrp0(xe,xm) )
<=> ( xx = sdtlpdtrp0(xe,xm) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(7,axiom,
( aElementOf0(xm,szNzAzT0)
& ( xx = sdtlpdtrp0(xe,xm) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5389) ).
tff(8,plain,
xx = sdtlpdtrp0(xe,xm),
inference(and_elim,[status(thm)],[7]) ).
tff(9,plain,
xx = sdtlpdtrp0(xe,xm),
inference(modus_ponens,[status(thm)],[8,6]) ).
tff(10,plain,
sdtlpdtrp0(xe,xm) = xx,
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( aElementOf0(sdtlpdtrp0(xe,xm),sdtmndt0(xQ,szmzizndt0(xQ)))
<=> aElementOf0(xx,xP) ),
inference(monotonicity,[status(thm)],[10,5]) ).
tff(12,plain,
( aElementOf0(xx,xP)
<=> aElementOf0(sdtlpdtrp0(xe,xm),sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( aElementOf0(xx,xP)
<=> aElementOf0(xx,xP) ),
inference(rewrite,[status(thm)],[]) ).
tff(14,axiom,
aElementOf0(xx,xP),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5348) ).
tff(15,plain,
aElementOf0(xx,xP),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
aElementOf0(sdtlpdtrp0(xe,xm),sdtmndt0(xQ,szmzizndt0(xQ))),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
( aElementOf0(sdtlpdtrp0(xe,xm),szNzAzT0)
<=> aElementOf0(xx,szNzAzT0) ),
inference(monotonicity,[status(thm)],[10]) ).
tff(18,plain,
( aElementOf0(xx,szNzAzT0)
<=> aElementOf0(sdtlpdtrp0(xe,xm),szNzAzT0) ),
inference(symmetry,[status(thm)],[17]) ).
tff(19,plain,
( aElementOf0(xx,szNzAzT0)
<=> aElementOf0(xx,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(20,axiom,
( aElementOf0(xx,szNzAzT0)
& aElementOf0(xx,xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5365) ).
tff(21,plain,
aElementOf0(xx,szNzAzT0),
inference(and_elim,[status(thm)],[20]) ).
tff(22,plain,
aElementOf0(xx,szNzAzT0),
inference(modus_ponens,[status(thm)],[21,19]) ).
tff(23,plain,
aElementOf0(sdtlpdtrp0(xe,xm),szNzAzT0),
inference(modus_ponens,[status(thm)],[22,18]) ).
tff(24,plain,
( aSet0(szNzAzT0)
<=> aSet0(szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
tff(26,plain,
aSet0(szNzAzT0),
inference(and_elim,[status(thm)],[25]) ).
tff(27,plain,
aSet0(szNzAzT0),
inference(modus_ponens,[status(thm)],[26,24]) ).
tff(28,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(31,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(transitivity,[status(thm)],[31,29]) ).
tff(33,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
rewrite(( ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
tff(37,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[39,32]) ).
tff(41,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(42,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(43,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(szNzAzT0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) ),
inference(unit_resolution,[status(thm)],[43,40,27]) ).
tff(45,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) )
| aElement0(sdtlpdtrp0(xe,xm))
| ~ aElementOf0(sdtlpdtrp0(xe,xm),szNzAzT0) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) )
| aElement0(sdtlpdtrp0(xe,xm))
| ~ aElementOf0(sdtlpdtrp0(xe,xm),szNzAzT0) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) )
| aElement0(sdtlpdtrp0(xe,xm))
| ~ aElementOf0(sdtlpdtrp0(xe,xm),szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,szNzAzT0) )
| aElement0(sdtlpdtrp0(xe,xm))
| ~ aElementOf0(sdtlpdtrp0(xe,xm),szNzAzT0) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
aElement0(sdtlpdtrp0(xe,xm)),
inference(unit_resolution,[status(thm)],[47,44,23]) ).
tff(49,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(50,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)],[49]) ).
tff(51,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(52,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)],[51]) ).
tff(53,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(54,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)],[53]) ).
tff(55,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)],[54,52]) ).
tff(56,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(57,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)],[56]) ).
tff(58,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(59,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)],[58]) ).
tff(60,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(61,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(62,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)],[61]) ).
tff(63,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aSubsetOf0(W1,W0)
<=> ( aSet0(W1)
& ! [W2: $i] :
( aElementOf0(W2,W1)
=> aElementOf0(W2,W0) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefSub) ).
tff(64,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)],[63,62]) ).
tff(65,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)],[64,60]) ).
tff(66,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)],[65]) ).
tff(67,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)],[66,59]) ).
tff(68,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)],[67,57]) ).
tff(69,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)],[68,55]) ).
tff(70,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)],[69,50]) ).
tff(71,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(72,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(73,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)],[72,71]) ).
tff(74,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)],[73,70,27]) ).
tff(75,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(76,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)],[75,74]) ).
tff(77,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(78,plain,
( ~ aSubsetOf0(xQ,szNzAzT0)
| ~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(unit_resolution,[status(thm)],[77,76]) ).
tff(79,plain,
( aSubsetOf0(xQ,szNzAzT0)
<=> aSubsetOf0(xQ,szNzAzT0) ),
inference(rewrite,[status(thm)],[]) ).
tff(80,axiom,
aSubsetOf0(xQ,szNzAzT0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5106) ).
tff(81,plain,
aSubsetOf0(xQ,szNzAzT0),
inference(modus_ponens,[status(thm)],[80,79]) ).
tff(82,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(83,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)],[82,81]) ).
tff(84,plain,
~ ( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,szNzAzT0) ) ),
inference(unit_resolution,[status(thm)],[83,78]) ).
tff(85,plain,
( ~ aSet0(xQ)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xQ)
| aElementOf0(W2,szNzAzT0) )
| aSet0(xQ) ),
inference(tautology,[status(thm)],[]) ).
tff(86,plain,
aSet0(xQ),
inference(unit_resolution,[status(thm)],[85,84]) ).
tff(87,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
^ [W0: $i,W1: $i] :
refl(( ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(92,plain,
( ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,plain,
( ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) ) ),
inference(transitivity,[status(thm)],[92,90]) ).
tff(94,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(W0)
& aElement0(W1) )
<=> ~ ( ~ aElement0(W1)
| ~ aSet0(W0) ) )),
( ~ ( aSet0(W0)
& aElement0(W1) )
<=> ~ ~ ( ~ aElement0(W1)
| ~ aSet0(W0) ) )),
rewrite(( ~ ~ ( ~ aElement0(W1)
| ~ aSet0(W0) )
<=> ( ~ aElement0(W1)
| ~ aSet0(W0) ) )),
( ~ ( aSet0(W0)
& aElement0(W1) )
<=> ( ~ aElement0(W1)
| ~ aSet0(W0) ) )),
quant_intro(proof_bind(^ [W2: $i] :
trans(monotonicity(rewrite(( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
<=> ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) ) )),
trans(monotonicity(trans(monotonicity(trans(trans(monotonicity(rewrite(( ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) )
<=> ~ ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) )),
( ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) )
<=> ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ~ ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) ) )),
rewrite(( ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ~ ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) ) )
<=> ~ ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )),
( ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) )
<=> ~ ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )),
rewrite(( ~ ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) )
<=> ~ ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )),
( ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) )
<=> ~ ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )),
( ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) )
<=> ~ ~ ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )),
rewrite(( ~ ~ ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) )
<=> ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )),
( ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) )
<=> ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )),
( ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) )
<=> ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) )),
rewrite(( ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )
<=> ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) )),
( ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) )
<=> ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) )),
( ( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) )
<=> ( ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) )),
rewrite(( ( ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) )
<=> ~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) )),
( ( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) )
<=> ~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) ))),
( ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) )),
( ( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) ) )),
rewrite(( ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) ) )),
( ( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) )
<=> ( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) )
<=> ( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(97,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[96]) ).
tff(98,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(99,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W2: $i] :
rewrite(( ( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
<=> ( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ))),
( ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
<=> ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) )),
( ( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) )
<=> ( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ) )),
rewrite(( ( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) )
<=> ( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ) )),
( ( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) )
<=> ( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(100,plain,
( ! [W0: $i,W1: $i] :
( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[99]) ).
tff(101,axiom,
! [W0: $i,W1: $i] :
( ( aSet0(W0)
& aElement0(W1) )
=> ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefDiff) ).
tff(102,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( W2 = sdtmndt0(W0,W1) )
<=> ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[102,98]) ).
tff(104,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) ),
inference(skolemize,[status(sab)],[103]) ).
tff(105,plain,
! [W0: $i,W1: $i] :
( ~ ( aSet0(W0)
& aElement0(W1) )
| ! [W2: $i] :
( ( ( W2 != sdtmndt0(W0,W1) )
| ( aSet0(W2)
& ! [W3: $i] :
( aElementOf0(W3,W2)
<=> ( aElement0(W3)
& aElementOf0(W3,W0)
& ( W3 != W1 ) ) ) ) )
& ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ~ ( aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2)
<=> ( aElement0(tptp_fun_W3_3(W2,W1,W0))
& aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
& ( tptp_fun_W3_3(W2,W1,W0) != W1 ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[104,97]) ).
tff(106,plain,
! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[105,95]) ).
tff(107,plain,
! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) )
| ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) ) ) ),
inference(modus_ponens,[status(thm)],[106,93]) ).
tff(108,plain,
! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[107,88]) ).
tff(109,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aSet0(xQ)
| ~ aElement0(sdtlpdtrp0(xe,xm))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aSet0(xQ)
| ~ aElement0(sdtlpdtrp0(xe,xm))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
( ( ~ aElement0(sdtlpdtrp0(xe,xm))
| ~ aSet0(xQ)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aSet0(xQ)
| ~ aElement0(sdtlpdtrp0(xe,xm))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
^ [W2: $i] :
rewrite(( ~ ( ~ ( ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) )
<=> ~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(112,plain,
( ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) )
<=> ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(quant_intro,[status(thm)],[111]) ).
tff(113,plain,
( ( ~ aElement0(sdtlpdtrp0(xe,xm))
| ~ aSet0(xQ)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aElement0(sdtlpdtrp0(xe,xm))
| ~ aSet0(xQ)
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[112]) ).
tff(114,plain,
( ( ~ aElement0(sdtlpdtrp0(xe,xm))
| ~ aSet0(xQ)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ aSet0(xQ)
| ~ aElement0(sdtlpdtrp0(xe,xm))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[113,110]) ).
tff(115,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElement0(sdtlpdtrp0(xe,xm))
| ~ aSet0(xQ)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aSet0(xQ)
| ~ aElement0(sdtlpdtrp0(xe,xm))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[114]) ).
tff(116,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElement0(sdtlpdtrp0(xe,xm))
| ~ aSet0(xQ)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aSet0(xQ)
| ~ aElement0(sdtlpdtrp0(xe,xm))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[115,109]) ).
tff(117,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aElement0(sdtlpdtrp0(xe,xm))
| ~ aSet0(xQ)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ aElement0(W1)
| ~ aSet0(W0)
| ! [W2: $i] :
~ ( ~ ( ( W2 = sdtmndt0(W0,W1) )
| ~ aSet0(W2)
| ( ( ~ aElement0(tptp_fun_W3_3(W2,W1,W0))
| ~ aElementOf0(tptp_fun_W3_3(W2,W1,W0),W0)
| ( tptp_fun_W3_3(W2,W1,W0) = W1 ) )
<=> aElementOf0(tptp_fun_W3_3(W2,W1,W0),W2) ) )
| ~ ( ( W2 != sdtmndt0(W0,W1) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,W0)
| ( W3 = W1 ) )
<=> aElementOf0(W3,W2) ) ) ) ) )
| ~ aSet0(xQ)
| ~ aElement0(sdtlpdtrp0(xe,xm))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
( ~ aSet0(xQ)
| ~ aElement0(sdtlpdtrp0(xe,xm))
| ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[118,108]) ).
tff(120,plain,
! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) ),
inference(unit_resolution,[status(thm)],[119,86,48]) ).
tff(121,plain,
( ~ ! [W2: $i] :
~ ( ~ ( ~ aSet0(W2)
| ( W2 = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(W2,sdtlpdtrp0(xe,xm),xQ),W2) ) )
| ~ ( ( W2 != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(W2)
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,W2) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtmndt0(xQ,szmzizndt0(xQ)) = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xe,xm),xQ),sdtmndt0(xQ,szmzizndt0(xQ))) ) )
| ~ ( ( sdtmndt0(xQ,szmzizndt0(xQ)) != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(122,plain,
~ ( ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtmndt0(xQ,szmzizndt0(xQ)) = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xe,xm),xQ),sdtmndt0(xQ,szmzizndt0(xQ))) ) )
| ~ ( ( sdtmndt0(xQ,szmzizndt0(xQ)) != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ) ),
inference(unit_resolution,[status(thm)],[121,120]) ).
tff(123,plain,
( ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ( sdtmndt0(xQ,szmzizndt0(xQ)) = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ( ( ~ aElement0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xe,xm),xQ))
| ~ aElementOf0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xe,xm),xQ),xQ)
| ( tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xe,xm),xQ) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(tptp_fun_W3_3(sdtmndt0(xQ,szmzizndt0(xQ)),sdtlpdtrp0(xe,xm),xQ),sdtmndt0(xQ,szmzizndt0(xQ))) ) )
| ~ ( ( sdtmndt0(xQ,szmzizndt0(xQ)) != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ( sdtmndt0(xQ,szmzizndt0(xQ)) != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(124,plain,
( ( sdtmndt0(xQ,szmzizndt0(xQ)) != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ),
inference(unit_resolution,[status(thm)],[123,122]) ).
tff(125,plain,
( ( xp = szmzizndt0(xQ) )
<=> ( xp = szmzizndt0(xQ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(126,axiom,
xp = szmzizndt0(xQ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5147) ).
tff(127,plain,
xp = szmzizndt0(xQ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
( ( xp = xx )
<=> ( xp = xx ) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,axiom,
xp = xx,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__5496) ).
tff(130,plain,
xp = xx,
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
xx = xp,
inference(symmetry,[status(thm)],[130]) ).
tff(132,plain,
sdtlpdtrp0(xe,xm) = szmzizndt0(xQ),
inference(transitivity,[status(thm)],[10,131,127]) ).
tff(133,plain,
sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) = sdtmndt0(xQ,szmzizndt0(xQ)),
inference(monotonicity,[status(thm)],[132]) ).
tff(134,plain,
sdtmndt0(xQ,szmzizndt0(xQ)) = sdtmndt0(xQ,sdtlpdtrp0(xe,xm)),
inference(symmetry,[status(thm)],[133]) ).
tff(135,plain,
( ~ ( ( sdtmndt0(xQ,szmzizndt0(xQ)) != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) ) ) )
| ( sdtmndt0(xQ,szmzizndt0(xQ)) != sdtmndt0(xQ,sdtlpdtrp0(xe,xm)) )
| ~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) ) ) ),
inference(tautology,[status(thm)],[]) ).
tff(136,plain,
~ ( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(unit_resolution,[status(thm)],[135,134,124]) ).
tff(137,plain,
( ~ aSet0(sdtmndt0(xQ,szmzizndt0(xQ)))
| ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) )
| ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(tautology,[status(thm)],[]) ).
tff(138,plain,
! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(unit_resolution,[status(thm)],[137,136]) ).
tff(139,plain,
( ( ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ aElementOf0(sdtlpdtrp0(xe,xm),sdtmndt0(xQ,szmzizndt0(xQ))) )
<=> ( ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ aElementOf0(sdtlpdtrp0(xe,xm),sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,plain,
( ~ ( ( ~ aElement0(sdtlpdtrp0(xe,xm))
| ~ aElementOf0(sdtlpdtrp0(xe,xm),xQ)
| ( sdtlpdtrp0(xe,xm) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(sdtlpdtrp0(xe,xm),sdtmndt0(xQ,szmzizndt0(xQ))) )
<=> ~ aElementOf0(sdtlpdtrp0(xe,xm),sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
( ( ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( ( ~ aElement0(sdtlpdtrp0(xe,xm))
| ~ aElementOf0(sdtlpdtrp0(xe,xm),xQ)
| ( sdtlpdtrp0(xe,xm) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(sdtlpdtrp0(xe,xm),sdtmndt0(xQ,szmzizndt0(xQ))) ) )
<=> ( ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ aElementOf0(sdtlpdtrp0(xe,xm),sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(monotonicity,[status(thm)],[140]) ).
tff(142,plain,
( ( ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( ( ~ aElement0(sdtlpdtrp0(xe,xm))
| ~ aElementOf0(sdtlpdtrp0(xe,xm),xQ)
| ( sdtlpdtrp0(xe,xm) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(sdtlpdtrp0(xe,xm),sdtmndt0(xQ,szmzizndt0(xQ))) ) )
<=> ( ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ aElementOf0(sdtlpdtrp0(xe,xm),sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(transitivity,[status(thm)],[141,139]) ).
tff(143,plain,
( ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ ( ( ~ aElement0(sdtlpdtrp0(xe,xm))
| ~ aElementOf0(sdtlpdtrp0(xe,xm),xQ)
| ( sdtlpdtrp0(xe,xm) = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(sdtlpdtrp0(xe,xm),sdtmndt0(xQ,szmzizndt0(xQ))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(144,plain,
( ~ ! [W3: $i] :
~ ( ( ~ aElement0(W3)
| ~ aElementOf0(W3,xQ)
| ( W3 = sdtlpdtrp0(xe,xm) ) )
<=> aElementOf0(W3,sdtmndt0(xQ,szmzizndt0(xQ))) )
| ~ aElementOf0(sdtlpdtrp0(xe,xm),sdtmndt0(xQ,szmzizndt0(xQ))) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
$false,
inference(unit_resolution,[status(thm)],[144,138,16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : NUM625+1 : TPTP v9.0.0. Released v4.0.0.
% 0.11/0.12 % Command : run_E %s %d THM
% 0.11/0.33 % Computer : n005.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 :
% 14.03/14.18 % SZS status Theorem
% 14.03/14.18 % SZS output start Proof
% See solution above
% 14.03/14.26 % E exiting
%------------------------------------------------------------------------------