TSTP Solution File: NUM566+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM566+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:10:34 EDT 2022
% Result : Theorem 1.19s 1.01s
% Output : Proof 1.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 99
% Syntax : Number of formulae : 210 ( 46 unt; 20 typ; 0 def)
% Number of atoms : 1494 ( 111 equ)
% Maximal formula atoms : 36 ( 7 avg)
% Number of connectives : 2631 (1390 ~;1010 |; 97 &)
% ( 102 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 7 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 63 ( 63 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 13 >; 7 *; 0 +; 0 <<)
% Number of predicates : 19 ( 16 usr; 1 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 7 con; 0-2 aty)
% Number of variables : 449 ( 392 !; 36 ?; 449 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(xc_type,type,
xc: $i ).
tff(tptp_fun_W2_21_type,type,
tptp_fun_W2_21: ( $i * $i ) > $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(slbdtrb0_type,type,
slbdtrb0: $i > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(xS_type,type,
xS: $i ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xK_type,type,
xK: $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(xT_type,type,
xT: $i ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(1,plain,
( ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
<=> ( szDzozmdt0(xc) = slbdtsldtrb0(xS,sz00) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
<=> ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( aFunction0(xc)
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
tff(4,plain,
( aFunction0(xc)
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) ) ),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(and_elim,[status(thm)],[4]) ).
tff(6,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,xK),
inference(modus_ponens,[status(thm)],[5,2]) ).
tff(7,plain,
szDzozmdt0(xc) = slbdtsldtrb0(xS,sz00),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
( aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),szDzozmdt0(xc))
<=> aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00)) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00))
<=> aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),szDzozmdt0(xc)) ),
inference(symmetry,[status(thm)],[8]) ).
tff(10,plain,
( aSet0(xT)
<=> aSet0(xT) ),
inference(rewrite,[status(thm)],]) ).
tff(11,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).
tff(12,plain,
aSet0(xT),
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
aSet0(xT),
inference(modus_ponens,[status(thm)],[12,10]) ).
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)
| ~ ( ~ 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(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)
| ~ ( ~ 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)],[14]) ).
tff(16,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(17,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)],[16]) ).
tff(18,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(19,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)],[18]) ).
tff(20,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)],[19,17]) ).
tff(21,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(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) ) ) ) )
<=> ! [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)],[21]) ).
tff(23,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(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) ) ) ) )
<=> ! [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)],[23]) ).
tff(25,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(26,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(27,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)],[26]) ).
tff(28,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(29,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)],[28,27]) ).
tff(30,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)],[29,25]) ).
tff(31,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)],[30]) ).
tff(32,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)],[31,24]) ).
tff(33,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)],[32,22]) ).
tff(34,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)],[33,20]) ).
tff(35,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)],[34,15]) ).
tff(36,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(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [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(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( ( ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ aSet0(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(38,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(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [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(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[37]) ).
tff(39,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(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [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(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[38,36]) ).
tff(40,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(xT)
| ! [W1: $i] :
~ ( ~ ( aSubsetOf0(W1,xT)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(41,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(xT)
| ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) ),
inference(unit_resolution,[status(thm)],[41,35,13]) ).
tff(43,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) )
<=> ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(monotonicity,[status(thm)],[44]) ).
tff(46,plain,
( ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) )
<=> ( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[45,43]) ).
tff(47,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(48,plain,
( ~ ! [W1: $i] :
~ ( ~ ( ~ aSet0(W1)
| aSubsetOf0(W1,xT)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,xT),W1)
| aElementOf0(tptp_fun_W2_1(W1,xT),xT) ) )
| ~ ( ~ aSubsetOf0(W1,xT)
| ~ ( ~ aSet0(W1)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,xT) ) ) ) )
| ~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
~ ( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ) ),
inference(unit_resolution,[status(thm)],[48,42]) ).
tff(50,plain,
( ~ ( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ( ~ aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(tptp_fun_W2_1(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),xT) ) )
| ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(51,plain,
( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
<=> aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(rewrite,[status(thm)],]) ).
tff(53,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(and_elim,[status(thm)],[3]) ).
tff(54,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(modus_ponens,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(56,plain,
( ~ ( ~ aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) )
| ~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ) ),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ),
inference(unit_resolution,[status(thm)],[56,51]) ).
tff(58,plain,
( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ),
inference(tautology,[status(thm)],]) ).
tff(59,plain,
! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ),
inference(unit_resolution,[status(thm)],[58,57]) ).
tff(60,plain,
( aFunction0(xc)
<=> aFunction0(xc) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
aFunction0(xc),
inference(and_elim,[status(thm)],[4]) ).
tff(62,plain,
aFunction0(xc),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
^ [W0: $i] :
refl(
( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
inference(bind,[status(th)],]) ).
tff(64,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(quant_intro,[status(thm)],[63]) ).
tff(65,plain,
^ [W0: $i] :
rewrite(
( ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(transitivity,[status(thm)],[66,64]) ).
tff(68,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
rewrite(
( ( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) )
<=> ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )),
( ( aFunction0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( aFunction0(W0)
=> ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
rewrite(
( ( aFunction0(W0)
=> ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
( ( aFunction0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [W0: $i] :
( aFunction0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,axiom,
! [W0: $i] :
( aFunction0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,szDzozmdt0(W0))
=> aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgRng) ).
tff(72,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(modus_ponens,[status(thm)],[72,68]) ).
tff(74,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(skolemize,[status(sab)],[73]) ).
tff(75,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) ),
inference(modus_ponens,[status(thm)],[74,67]) ).
tff(76,plain,
( ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
| ~ aFunction0(xc)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) )
<=> ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
| ~ aFunction0(xc)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
| ~ aFunction0(xc)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(W0))
| aElementOf0(sdtlpdtrp0(W0,W1),sdtlcdtrc0(W0,szDzozmdt0(W0))) ) )
| ~ aFunction0(xc)
| ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(unit_resolution,[status(thm)],[78,75,62]) ).
tff(80,plain,
( aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00))
<=> aElementOf0(slbdtrb0(sz00),szDzozmdt0(xc)) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
<=> aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00)) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00))
<=> aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)) ),
inference(rewrite,[status(thm)],]) ).
tff(83,axiom,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3476) ).
tff(84,plain,
aElementOf0(slcrc0,slbdtsldtrb0(xS,sz00)),
inference(modus_ponens,[status(thm)],[83,82]) ).
tff(85,plain,
aElementOf0(slbdtrb0(sz00),slbdtsldtrb0(xS,sz00)),
inference(modus_ponens,[status(thm)],[84,81]) ).
tff(86,plain,
aElementOf0(slbdtrb0(sz00),szDzozmdt0(xc)),
inference(modus_ponens,[status(thm)],[85,80]) ).
tff(87,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
| ~ aElementOf0(slbdtrb0(sz00),szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
| ~ aElementOf0(slbdtrb0(sz00),szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),sdtlcdtrc0(xc,szDzozmdt0(xc))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
| ~ aElementOf0(slbdtrb0(sz00),szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(quant_inst,[status(thm)],]) ).
tff(89,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,W1),sdtlcdtrc0(xc,szDzozmdt0(xc))) )
| ~ aElementOf0(slbdtrb0(sz00),szDzozmdt0(xc))
| aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(modus_ponens,[status(thm)],[88,87]) ).
tff(90,plain,
aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(unit_resolution,[status(thm)],[89,86,79]) ).
tff(91,plain,
( ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),xT) )
<=> ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),xT) ) ),
inference(rewrite,[status(thm)],]) ).
tff(92,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),xT) ),
inference(quant_inst,[status(thm)],]) ).
tff(93,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),xT) ),
inference(modus_ponens,[status(thm)],[92,91]) ).
tff(94,plain,
aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),xT),
inference(unit_resolution,[status(thm)],[93,90,59]) ).
tff(95,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(96,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[95]) ).
tff(97,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(98,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ) ),
inference(transitivity,[status(thm)],[98,96]) ).
tff(100,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(101,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(103,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( aElementOf0(W2,slbdtsldtrb0(W1,xK))
=> ( sdtlpdtrp0(xc,W2) = W0 ) ) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(104,axiom,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( aElementOf0(W2,slbdtsldtrb0(W1,xK))
=> ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(105,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[105,102]) ).
tff(107,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[106,102]) ).
tff(108,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[107,102]) ).
tff(109,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[108,101]) ).
tff(110,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[109,100]) ).
tff(111,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[110,100]) ).
tff(112,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[111,100]) ).
tff(113,plain,
^ [W0: $i] :
nnf_neg(refl($oeq(~ aElementOf0(W0,xT),~ aElementOf0(W0,xT))),
nnf_neg(
proof_bind(
^ [W1: $i] :
nnf_neg(refl($oeq(~ aSubsetOf0(W1,xS),~ aSubsetOf0(W1,xS))),refl($oeq(~ isCountable0(W1),~ isCountable0(W1))),
sk(
$oeq(
~ ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,W2) = W0 ) ),
~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ))),
$oeq(
~ ( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ),
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) )))),
$oeq(
~ ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ),
! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ))),
$oeq(
~ ( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ))),
inference(bind,[status(th)],]) ).
tff(114,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ),
inference(nnf-neg,[status(sab)],[112,113]) ).
tff(115,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[114,99]) ).
tff(116,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(117,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(118,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
| ~ aElementOf0(sdtlpdtrp0(xc,slbdtrb0(sz00)),xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) ) ),
inference(modus_ponens,[status(thm)],[117,116]) ).
tff(119,plain,
! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) ),
inference(unit_resolution,[status(thm)],[118,115,94]) ).
tff(120,plain,
( aSet0(szNzAzT0)
<=> aSet0(szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(121,axiom,
( aSet0(szNzAzT0)
& isCountable0(szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mNATSet) ).
tff(122,plain,
aSet0(szNzAzT0),
inference(and_elim,[status(thm)],[121]) ).
tff(123,plain,
aSet0(szNzAzT0),
inference(modus_ponens,[status(thm)],[122,120]) ).
tff(124,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(125,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(126,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)],[125,124]) ).
tff(127,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)],[126,35,123]) ).
tff(128,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(xS,szNzAzT0)
| ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),xS)
| aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(129,plain,
~ ( ~ ( aSubsetOf0(xS,szNzAzT0)
| ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),xS)
| aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ) ),
inference(unit_resolution,[status(thm)],[128,127]) ).
tff(130,plain,
( ~ ( aSubsetOf0(xS,szNzAzT0)
| ~ aSet0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),xS)
| aElementOf0(tptp_fun_W2_1(xS,szNzAzT0),szNzAzT0) ) )
| ~ ( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(131,plain,
( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(unit_resolution,[status(thm)],[130,129]) ).
tff(132,plain,
( aSubsetOf0(xS,szNzAzT0)
<=> aSubsetOf0(xS,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(133,axiom,
( aSubsetOf0(xS,szNzAzT0)
& isCountable0(xS) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3435) ).
tff(134,plain,
aSubsetOf0(xS,szNzAzT0),
inference(and_elim,[status(thm)],[133]) ).
tff(135,plain,
aSubsetOf0(xS,szNzAzT0),
inference(modus_ponens,[status(thm)],[134,132]) ).
tff(136,plain,
( ~ ( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(137,plain,
( ~ ( ~ aSubsetOf0(xS,szNzAzT0)
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) )
| ~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ) ),
inference(unit_resolution,[status(thm)],[136,135]) ).
tff(138,plain,
~ ( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) ) ),
inference(unit_resolution,[status(thm)],[137,131]) ).
tff(139,plain,
( ~ aSet0(xS)
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,xS)
| aElementOf0(W2,szNzAzT0) )
| aSet0(xS) ),
inference(tautology,[status(thm)],]) ).
tff(140,plain,
aSet0(xS),
inference(unit_resolution,[status(thm)],[139,138]) ).
tff(141,plain,
^ [W0: $i] :
refl(
( ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) )),
inference(bind,[status(th)],]) ).
tff(142,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(rewrite,[status(thm)],]) ).
tff(144,plain,
^ [W0: $i] :
rewrite(
( ( aSet0(W0)
=> aSubsetOf0(W0,W0) )
<=> ( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) )),
inference(bind,[status(th)],]) ).
tff(145,plain,
( ! [W0: $i] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ) ),
inference(quant_intro,[status(thm)],[144]) ).
tff(146,axiom,
! [W0: $i] :
( aSet0(W0)
=> aSubsetOf0(W0,W0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mSubRefl) ).
tff(147,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[146,145]) ).
tff(148,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[147,143]) ).
tff(149,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(skolemize,[status(sab)],[148]) ).
tff(150,plain,
! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) ),
inference(modus_ponens,[status(thm)],[149,142]) ).
tff(151,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(xS)
| aSubsetOf0(xS,xS) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(xS)
| aSubsetOf0(xS,xS) ) ),
inference(rewrite,[status(thm)],]) ).
tff(152,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(xS)
| aSubsetOf0(xS,xS) ),
inference(quant_inst,[status(thm)],]) ).
tff(153,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| aSubsetOf0(W0,W0) )
| ~ aSet0(xS)
| aSubsetOf0(xS,xS) ),
inference(modus_ponens,[status(thm)],[152,151]) ).
tff(154,plain,
aSubsetOf0(xS,xS),
inference(unit_resolution,[status(thm)],[153,150,140]) ).
tff(155,plain,
( isCountable0(xS)
<=> isCountable0(xS) ),
inference(rewrite,[status(thm)],]) ).
tff(156,plain,
isCountable0(xS),
inference(and_elim,[status(thm)],[133]) ).
tff(157,plain,
isCountable0(xS),
inference(modus_ponens,[status(thm)],[156,155]) ).
tff(158,plain,
( ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) )
| ~ isCountable0(xS)
| ~ aSubsetOf0(xS,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) )
| ~ isCountable0(xS)
| ~ aSubsetOf0(xS,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(159,plain,
( ( ~ aSubsetOf0(xS,xS)
| ~ isCountable0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) )
<=> ( ~ isCountable0(xS)
| ~ aSubsetOf0(xS,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(160,plain,
( ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) )
| ~ aSubsetOf0(xS,xS)
| ~ isCountable0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) )
| ~ isCountable0(xS)
| ~ aSubsetOf0(xS,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) ) ),
inference(monotonicity,[status(thm)],[159]) ).
tff(161,plain,
( ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) )
| ~ aSubsetOf0(xS,xS)
| ~ isCountable0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) )
| ~ isCountable0(xS)
| ~ aSubsetOf0(xS,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) ) ),
inference(transitivity,[status(thm)],[160,158]) ).
tff(162,plain,
( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) )
| ~ aSubsetOf0(xS,xS)
| ~ isCountable0(xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(163,plain,
( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(W1,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(W1,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) )
| ~ isCountable0(xS)
| ~ aSubsetOf0(xS,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) ),
inference(modus_ponens,[status(thm)],[162,161]) ).
tff(164,plain,
~ ( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ),
inference(unit_resolution,[status(thm)],[163,157,154,119]) ).
tff(165,plain,
( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) )
| aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00)) ),
inference(tautology,[status(thm)],]) ).
tff(166,plain,
aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00)),
inference(unit_resolution,[status(thm)],[165,164]) ).
tff(167,plain,
aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),szDzozmdt0(xc)),
inference(modus_ponens,[status(thm)],[166,9]) ).
tff(168,plain,
( ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) )
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) != sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ),
inference(tautology,[status(thm)],]) ).
tff(169,plain,
sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) != sdtlpdtrp0(xc,slbdtrb0(sz00)),
inference(unit_resolution,[status(thm)],[168,164]) ).
tff(170,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) )),
inference(bind,[status(th)],]) ).
tff(171,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) ),
inference(quant_intro,[status(thm)],[170]) ).
tff(172,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) )),
inference(bind,[status(th)],]) ).
tff(173,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) ),
inference(quant_intro,[status(thm)],[172]) ).
tff(174,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) )),
inference(bind,[status(th)],]) ).
tff(175,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) ),
inference(quant_intro,[status(thm)],[174]) ).
tff(176,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(177,plain,
^ [W0: $i] :
rewrite(
( ( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
=> ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) )),
inference(bind,[status(th)],]) ).
tff(178,plain,
( ! [W0: $i] :
( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
=> ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ) ),
inference(quant_intro,[status(thm)],[177]) ).
tff(179,axiom,
! [W0: $i] :
( aElementOf0(W0,slbdtsldtrb0(xS,sz00))
=> ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3507) ).
tff(180,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ),
inference(modus_ponens,[status(thm)],[179,178]) ).
tff(181,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slcrc0) ) ),
inference(modus_ponens,[status(thm)],[180,176]) ).
tff(182,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,sz00))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ),
inference(modus_ponens,[status(thm)],[181,175]) ).
tff(183,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ),
inference(modus_ponens,[status(thm)],[182,173]) ).
tff(184,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ),
inference(skolemize,[status(sab)],[183]) ).
tff(185,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ),
inference(modus_ponens,[status(thm)],[184,171]) ).
tff(186,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) )
| ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) )
| ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(187,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) )
| ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(188,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) )
| ~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00)))) = sdtlpdtrp0(xc,slbdtrb0(sz00)) ) ),
inference(modus_ponens,[status(thm)],[187,186]) ).
tff(189,plain,
~ aElementOf0(tptp_fun_W2_21(xS,sdtlpdtrp0(xc,slbdtrb0(sz00))),szDzozmdt0(xc)),
inference(unit_resolution,[status(thm)],[188,185,169]) ).
tff(190,plain,
$false,
inference(unit_resolution,[status(thm)],[189,167]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.11 % Problem : NUM566+1 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 11:47:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.19/1.01 % SZS status Theorem
% 1.19/1.01 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------