%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM592+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n015.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sat Jun 21 05:21:30 AM UTC 2025
% Result : Theorem 0.48s 0.65s
% Output : Proof 0.48s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 29
% Syntax : Number of formulae : 82 ( 28 unt; 0 typ; 0 def)
% Number of atoms : 555 ( 120 equ)
% Maximal formula atoms : 24 ( 6 avg)
% Number of connectives : 800 ( 374 ~; 300 |; 83 &)
% ( 37 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 47 ( 47 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 16 ( 13 usr; 1 prp; 0-4 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 120 ( 91 !; 20 ?; 120 :)
% Comments :
%------------------------------------------------------------------------------
tff(xu_type,type,
xu: $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(tptp_fun_W2_21_type,type,
tptp_fun_W2_21: ( $i * $i ) > $i ).
tff(xX_type,type,
xX: $i ).
tff(xi_type,type,
xi: $i ).
tff(xC_type,type,
xC: $i ).
tff(xd_type,type,
xd: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xk_type,type,
xk: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xN_type,type,
xN: $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(xT_type,type,
xT: $i ).
tff(xY_type,type,
xY: $i ).
tff(1,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
( ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) )
<=> ~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
=> ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(13,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[13,10]) ).
tff(15,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
~ ? [W0: $i] :
( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[15,10]) ).
tff(17,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,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))))),refl($oeq(~ isCountable0(W1),~ isCountable0(W1))),
sk($oeq(~ ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ),
~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ))),
$oeq(~ ( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ),
( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ) )))),
$oeq(~ ? [W1: $i] :
( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ),
! [W1: $i] :
( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ) ))),
$oeq(~ ( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
& isCountable0(W1)
& ! [W2: $i] :
( ~ ( aSet0(W2)
& aElementOf0(W2,slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),W2) = W0 ) ) ) ),
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ))),
inference(bind,[status(th)],[]) ).
tff(18,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ isCountable0(W1)
| ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ),
inference(nnf-neg,[status(sab)],[16,17]) ).
tff(19,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ~ ( aSet0(tptp_fun_W2_21(W1,W0))
& aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) )
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[18,9]) ).
tff(20,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ),
inference(modus_ponens,[status(thm)],[19,7]) ).
tff(21,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) ),
inference(modus_ponens,[status(thm)],[20,5]) ).
tff(22,plain,
( aElementOf0(xu,xT)
<=> aElementOf0(xu,xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(23,axiom,
( aElementOf0(xu,xT)
& aSubsetOf0(xX,xY)
& isCountable0(xX)
& ! [W0: $i] :
( ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
=> ( sdtlpdtrp0(xd,W0) = xu ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4545) ).
tff(24,plain,
( aElementOf0(xu,xT)
& aSubsetOf0(xX,xY)
& isCountable0(xX) ),
inference(and_elim,[status(thm)],[23]) ).
tff(25,plain,
( aElementOf0(xu,xT)
& aSubsetOf0(xX,xY) ),
inference(and_elim,[status(thm)],[24]) ).
tff(26,plain,
aElementOf0(xu,xT),
inference(and_elim,[status(thm)],[25]) ).
tff(27,plain,
aElementOf0(xu,xT),
inference(modus_ponens,[status(thm)],[26,22]) ).
tff(28,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )
| ~ aElementOf0(xu,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(W1,xu))
| ~ aElementOf0(tptp_fun_W2_21(W1,xu),slbdtsldtrb0(W1,xk)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )
| ~ aElementOf0(xu,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(W1,xu))
| ~ aElementOf0(tptp_fun_W2_21(W1,xu),slbdtsldtrb0(W1,xk)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )
| ~ aElementOf0(xu,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(W1,xu))
| ~ aElementOf0(tptp_fun_W2_21(W1,xu),slbdtsldtrb0(W1,xk)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(30,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,W0)) = W0 )
| ~ aSet0(tptp_fun_W2_21(W1,W0))
| ~ aElementOf0(tptp_fun_W2_21(W1,W0),slbdtsldtrb0(W1,xk)) ) ) )
| ~ aElementOf0(xu,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(W1,xu))
| ~ aElementOf0(tptp_fun_W2_21(W1,xu),slbdtsldtrb0(W1,xk)) ) ) ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(W1,xu))
| ~ aElementOf0(tptp_fun_W2_21(W1,xu),slbdtsldtrb0(W1,xk)) ) ),
inference(unit_resolution,[status(thm)],[30,27,21]) ).
tff(32,plain,
( ( xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))) )
<=> ( xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(33,axiom,
( ( xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))) )
& ( xd = sdtlpdtrp0(xC,xi) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4448_02) ).
tff(34,plain,
xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(and_elim,[status(thm)],[33]) ).
tff(35,plain,
xY = sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))),
inference(modus_ponens,[status(thm)],[34,32]) ).
tff(36,plain,
sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))) = xY,
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
( aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
<=> aSubsetOf0(xX,xY) ),
inference(monotonicity,[status(thm)],[36]) ).
tff(38,plain,
( aSubsetOf0(xX,xY)
<=> aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))) ),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
( aSubsetOf0(xX,xY)
<=> aSubsetOf0(xX,xY) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
aSubsetOf0(xX,xY),
inference(and_elim,[status(thm)],[25]) ).
tff(41,plain,
aSubsetOf0(xX,xY),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(modus_ponens,[status(thm)],[41,38]) ).
tff(43,plain,
( isCountable0(xX)
<=> isCountable0(xX) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
isCountable0(xX),
inference(and_elim,[status(thm)],[24]) ).
tff(45,plain,
isCountable0(xX),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(W1,xu))
| ~ aElementOf0(tptp_fun_W2_21(W1,xu),slbdtsldtrb0(W1,xk)) ) )
| ~ isCountable0(xX)
| ~ aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk)) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(W1,xu))
| ~ aElementOf0(tptp_fun_W2_21(W1,xu),slbdtsldtrb0(W1,xk)) ) )
| ~ isCountable0(xX)
| ~ aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(W1,xu))
| ~ aElementOf0(tptp_fun_W2_21(W1,xu),slbdtsldtrb0(W1,xk)) ) )
| ~ isCountable0(xX)
| ~ aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(W1,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(W1,xu))
| ~ aElementOf0(tptp_fun_W2_21(W1,xu),slbdtsldtrb0(W1,xk)) ) )
| ~ isCountable0(xX)
| ~ aSubsetOf0(xX,sdtmndt0(sdtlpdtrp0(xN,xi),szmzizndt0(sdtlpdtrp0(xN,xi))))
| ~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk)) ) ),
inference(modus_ponens,[status(thm)],[47,46]) ).
tff(49,plain,
~ ( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk)) ),
inference(unit_resolution,[status(thm)],[48,45,42,31]) ).
tff(50,plain,
( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk))
| aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk)) ),
inference(tautology,[status(thm)],[]) ).
tff(51,plain,
aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk)),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,plain,
( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk))
| aSet0(tptp_fun_W2_21(xX,xu)) ),
inference(tautology,[status(thm)],[]) ).
tff(53,plain,
aSet0(tptp_fun_W2_21(xX,xu)),
inference(unit_resolution,[status(thm)],[52,49]) ).
tff(54,plain,
^ [W0: $i] :
refl(( ( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
<=> ( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) ) )),
inference(bind,[status(th)],[]) ).
tff(55,plain,
( ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
<=> ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
<=> ~ ( ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) ) )),
( ~ ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
<=> ~ ~ ( ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) ) )),
rewrite(( ~ ~ ( ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
<=> ( ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) ) )),
( ~ ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
<=> ( ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) ) )),
( ( ~ ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ( sdtlpdtrp0(xd,W0) = xu ) )
<=> ( ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ( sdtlpdtrp0(xd,W0) = xu ) ) )),
rewrite(( ( ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk))
| ( sdtlpdtrp0(xd,W0) = xu ) )
<=> ( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) ) )),
( ( ~ ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ( sdtlpdtrp0(xd,W0) = xu ) )
<=> ( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) ) )),
inference(bind,[status(th)],[]) ).
tff(57,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ( sdtlpdtrp0(xd,W0) = xu ) )
<=> ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ( sdtlpdtrp0(xd,W0) = xu ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ( sdtlpdtrp0(xd,W0) = xu ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(59,plain,
^ [W0: $i] :
rewrite(( ( ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
=> ( sdtlpdtrp0(xd,W0) = xu ) )
<=> ( ~ ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ( sdtlpdtrp0(xd,W0) = xu ) ) )),
inference(bind,[status(th)],[]) ).
tff(60,plain,
( ! [W0: $i] :
( ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
=> ( sdtlpdtrp0(xd,W0) = xu ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ( sdtlpdtrp0(xd,W0) = xu ) ) ),
inference(quant_intro,[status(thm)],[59]) ).
tff(61,plain,
! [W0: $i] :
( ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
=> ( sdtlpdtrp0(xd,W0) = xu ) ),
inference(and_elim,[status(thm)],[23]) ).
tff(62,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ( sdtlpdtrp0(xd,W0) = xu ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ( sdtlpdtrp0(xd,W0) = xu ) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ( sdtlpdtrp0(xd,W0) = xu ) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) ),
inference(modus_ponens,[status(thm)],[65,55]) ).
tff(67,plain,
( ( ~ ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk))
| ( sdtlpdtrp0(xd,tptp_fun_W2_21(xX,xu)) = xu ) )
<=> ( ~ ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk))
| ( sdtlpdtrp0(xd,tptp_fun_W2_21(xX,xu)) = xu ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(68,plain,
( ( ( sdtlpdtrp0(xd,tptp_fun_W2_21(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk)) )
<=> ( ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk))
| ( sdtlpdtrp0(xd,tptp_fun_W2_21(xX,xu)) = xu ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(69,plain,
( ( ~ ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ( sdtlpdtrp0(xd,tptp_fun_W2_21(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk)) )
<=> ( ~ ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk))
| ( sdtlpdtrp0(xd,tptp_fun_W2_21(xX,xu)) = xu ) ) ),
inference(monotonicity,[status(thm)],[68]) ).
tff(70,plain,
( ( ~ ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ( sdtlpdtrp0(xd,tptp_fun_W2_21(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk)) )
<=> ( ~ ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk))
| ( sdtlpdtrp0(xd,tptp_fun_W2_21(xX,xu)) = xu ) ) ),
inference(transitivity,[status(thm)],[69,67]) ).
tff(71,plain,
( ~ ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ( sdtlpdtrp0(xd,tptp_fun_W2_21(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [W0: $i] :
( ( sdtlpdtrp0(xd,W0) = xu )
| ~ aSet0(W0)
| ~ aElementOf0(W0,slbdtsldtrb0(xX,xk)) )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk))
| ( sdtlpdtrp0(xd,tptp_fun_W2_21(xX,xu)) = xu ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
sdtlpdtrp0(xd,tptp_fun_W2_21(xX,xu)) = xu,
inference(unit_resolution,[status(thm)],[72,66,53,51]) ).
tff(74,plain,
( ( xd = sdtlpdtrp0(xC,xi) )
<=> ( xd = sdtlpdtrp0(xC,xi) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
xd = sdtlpdtrp0(xC,xi),
inference(and_elim,[status(thm)],[33]) ).
tff(76,plain,
xd = sdtlpdtrp0(xC,xi),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
sdtlpdtrp0(xd,tptp_fun_W2_21(xX,xu)) = sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(xX,xu)),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(xX,xu)) = sdtlpdtrp0(xd,tptp_fun_W2_21(xX,xu)),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(xX,xu)) = xu,
inference(transitivity,[status(thm)],[78,73]) ).
tff(80,plain,
( ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(xX,xu)) = xu )
| ~ aSet0(tptp_fun_W2_21(xX,xu))
| ~ aElementOf0(tptp_fun_W2_21(xX,xu),slbdtsldtrb0(xX,xk))
| ( sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(xX,xu)) != xu ) ),
inference(tautology,[status(thm)],[]) ).
tff(81,plain,
sdtlpdtrp0(sdtlpdtrp0(xC,xi),tptp_fun_W2_21(xX,xu)) != xu,
inference(unit_resolution,[status(thm)],[80,49]) ).
tff(82,plain,
$false,
inference(unit_resolution,[status(thm)],[81,79]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : NUM592+1 : TPTP v9.0.0. Released v4.0.0.
% 0.12/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n015.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 01:32:25 EDT 2025
% 0.13/0.34 % CPUTime :
% 0.48/0.65 % SZS status Theorem
% 0.48/0.65 % SZS output start Proof
% See solution above
% 0.48/0.66 % E exiting
%------------------------------------------------------------------------------