TSTP Solution File: NUM633+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM633+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:11:04 EDT 2022
% Result : Theorem 0.62s 0.64s
% Output : Proof 0.65s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 56
% Syntax : Number of formulae : 99 ( 17 unt; 25 typ; 0 def)
% Number of atoms : 605 ( 171 equ)
% Maximal formula atoms : 20 ( 8 avg)
% Number of connectives : 947 ( 455 ~; 336 |; 117 &)
% ( 33 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 7 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 39 ( 39 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 20 ( 13 >; 7 *; 0 +; 0 <<)
% Number of predicates : 16 ( 13 usr; 1 prp; 0-4 aty)
% Number of functors : 21 ( 21 usr; 12 con; 0-2 aty)
% Number of variables : 136 ( 91 !; 38 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(xN_type,type,
xN: $i ).
tff(tptp_fun_W2_25_type,type,
tptp_fun_W2_25: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(xe_type,type,
xe: $i ).
tff(slbdtrb0_type,type,
slbdtrb0: $i > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xc_type,type,
xc: $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(xk_type,type,
xk: $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(xT_type,type,
xT: $i ).
tff(xK_type,type,
xK: $i ).
tff(xS_type,type,
xS: $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(xO_type,type,
xO: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(1,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(7,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,sdtlpdtrp0(xN,sz00))
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(8,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(9,plain,
( ~ ( ! [W0: $i] :
( aElementOf0(W0,slbdtsldtrb0(xO,xK))
=> ( ( W0 != slcrc0 )
& aSubsetOf0(W0,szNzAzT0)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
=> ? [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,slbdtsldtrb0(xO,xK))
| ( ( W0 != slcrc0 )
& aSubsetOf0(W0,szNzAzT0)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
| ? [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(10,axiom,
~ ( ! [W0: $i] :
( aElementOf0(W0,slbdtsldtrb0(xO,xK))
=> ( ( W0 != slcrc0 )
& aSubsetOf0(W0,szNzAzT0)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
=> ? [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/sandbox/benchmark/theBenchmark.p',m__) ).
tff(11,plain,
~ ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ( ( W0 != slcrc0 )
& aSubsetOf0(W0,szNzAzT0)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
| ? [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)],[10,9]) ).
tff(12,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(or_elim,[status(thm)],[11]) ).
tff(13,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)],[12,8]) ).
tff(14,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)],[13,8]) ).
tff(15,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)],[14,8]) ).
tff(16,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[15,7]) ).
tff(17,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[16,6]) ).
tff(18,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[17,6]) ).
tff(19,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[18,6]) ).
tff(20,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,sdtlpdtrp0(xN,sz00)),~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00)))),refl($oeq(~ isCountable0(W1),~ isCountable0(W1))),
sk(
$oeq(
~ ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,W2) = W0 ) ),
~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ))),
$oeq(
~ ( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ),
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) )))),
$oeq(
~ ? [W1: $i] :
( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ),
! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ))),
$oeq(
~ ( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ))),
inference(bind,[status(th)],]) ).
tff(21,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ),
inference(nnf-neg,[status(sab)],[19,20]) ).
tff(22,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[21,5]) ).
tff(23,plain,
( aElementOf0(szDzizrdt0(xd),xT)
<=> aElementOf0(szDzizrdt0(xd),xT) ),
inference(rewrite,[status(thm)],]) ).
tff(24,axiom,
( aElementOf0(szDzizrdt0(xd),xT)
& isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4854) ).
tff(25,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(and_elim,[status(thm)],[24]) ).
tff(26,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(modus_ponens,[status(thm)],[25,23]) ).
tff(27,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(29,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ),
inference(unit_resolution,[status(thm)],[29,26,22]) ).
tff(31,plain,
( aSubsetOf0(xO,xS)
<=> aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00)) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( aSubsetOf0(xO,xS)
<=> aSubsetOf0(xO,xS) ),
inference(rewrite,[status(thm)],]) ).
tff(33,axiom,
aSubsetOf0(xO,xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4998) ).
tff(34,plain,
aSubsetOf0(xO,xS),
inference(modus_ponens,[status(thm)],[33,32]) ).
tff(35,plain,
aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00)),
inference(modus_ponens,[status(thm)],[34,31]) ).
tff(36,plain,
( isCountable0(xO)
<=> isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(rewrite,[status(thm)],]) ).
tff(37,plain,
( isCountable0(xO)
<=> isCountable0(xO) ),
inference(rewrite,[status(thm)],]) ).
tff(38,axiom,
( aSet0(xO)
& isCountable0(xO) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4908) ).
tff(39,plain,
isCountable0(xO),
inference(and_elim,[status(thm)],[38]) ).
tff(40,plain,
isCountable0(xO),
inference(modus_ponens,[status(thm)],[39,37]) ).
tff(41,plain,
isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[40,36]) ).
tff(42,plain,
( ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( ~ aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
<=> ( ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
| ~ aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
( ~ ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtlpdtrp0(xN,sz00))
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
| ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),sdtlpdtrp0(xN,sz00))
| ~ ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
~ ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ),
inference(unit_resolution,[status(thm)],[47,41,35,30]) ).
tff(49,plain,
( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) )
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) ) ),
inference(tautology,[status(thm)],]) ).
tff(50,plain,
sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd),
inference(unit_resolution,[status(thm)],[49,48]) ).
tff(51,plain,
( ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ),
inference(tautology,[status(thm)],]) ).
tff(52,plain,
( ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN)) ),
inference(unit_resolution,[status(thm)],[51,50]) ).
tff(53,plain,
( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) )
| aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk))) ),
inference(tautology,[status(thm)],]) ).
tff(54,plain,
aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk))),
inference(unit_resolution,[status(thm)],[53,48]) ).
tff(55,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( ( W0 != slbdtrb0(sz00) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) )
<=> ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )),
( ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( ( W0 != slbdtrb0(sz00) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) )),
rewrite(
( ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) )),
( ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( ( W0 != slbdtrb0(sz00) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(58,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( ( W0 != slbdtrb0(sz00) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) ),
inference(quant_intro,[status(thm)],[57]) ).
tff(59,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ( ( W0 != slcrc0 )
& aSubsetOf0(W0,szNzAzT0)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( ( W0 != slbdtrb0(sz00) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(60,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ( ( W0 != slcrc0 )
& aSubsetOf0(W0,szNzAzT0)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( ( W0 != slbdtrb0(sz00) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ( ( W0 != slcrc0 )
& aSubsetOf0(W0,szNzAzT0)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ( ( W0 != slcrc0 )
& aSubsetOf0(W0,szNzAzT0)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(62,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ( ( W0 != slcrc0 )
& aSubsetOf0(W0,szNzAzT0)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ),
inference(or_elim,[status(thm)],[11]) ).
tff(63,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ( ( W0 != slcrc0 )
& aSubsetOf0(W0,szNzAzT0)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( ( W0 != slbdtrb0(sz00) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ),
inference(modus_ponens,[status(thm)],[63,60]) ).
tff(65,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ( ( W0 != slbdtrb0(sz00) )
& aSubsetOf0(W0,szDzozmdt0(xN))
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ),
inference(skolemize,[status(sab)],[64]) ).
tff(66,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ),
inference(modus_ponens,[status(thm)],[65,58]) ).
tff(67,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ),
inference(modus_ponens,[status(thm)],[66,56]) ).
tff(68,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN)) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(69,plain,
( ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) ) ) )
<=> ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(70,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN)) ) ) ),
inference(monotonicity,[status(thm)],[69]) ).
tff(71,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN)) ) ) ),
inference(transitivity,[status(thm)],[70,68]) ).
tff(72,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(73,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( W0 = slbdtrb0(sz00) )
| ~ aSubsetOf0(W0,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szszuzczcdt0(xk)))
| ~ ( ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xc))
| ( tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slbdtrb0(sz00) )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szDzozmdt0(xN)) ) ),
inference(modus_ponens,[status(thm)],[72,71]) ).
tff(74,plain,
$false,
inference(unit_resolution,[status(thm)],[73,67,54,52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM633+1 : TPTP v8.1.0. Released v4.0.0.
% 0.03/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.13/0.33 % Computer : n019.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Sep 2 12:34:20 EDT 2022
% 0.13/0.33 % CPUTime :
% 0.13/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.13/0.34 Usage: tptp [options] [-file:]file
% 0.13/0.34 -h, -? prints this message.
% 0.13/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.13/0.34 -m, -model generate model.
% 0.13/0.34 -p, -proof generate proof.
% 0.13/0.34 -c, -core generate unsat core of named formulas.
% 0.13/0.34 -st, -statistics display statistics.
% 0.13/0.34 -t:timeout set timeout (in second).
% 0.13/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.13/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.13/0.34 -<param>:<value> configuration parameter and value.
% 0.13/0.34 -o:<output-file> file to place output in.
% 0.62/0.64 % SZS status Theorem
% 0.62/0.64 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------