%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM587+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n013.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 05:21:29 AM UTC 2025
% Result : Theorem 0.20s 0.56s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 28
% Syntax : Number of formulae : 69 ( 19 unt; 0 typ; 0 def)
% Number of atoms : 748 ( 6 equ)
% Maximal formula atoms : 36 ( 10 avg)
% Number of connectives : 1477 ( 813 ~; 564 |; 37 &)
% ( 51 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 13 ( 11 usr; 1 prp; 0-3 aty)
% Number of functors : 15 ( 15 usr; 8 con; 0-2 aty)
% Number of variables : 205 ( 198 !; 0 ?; 205 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(xc_type,type,
xc: $i ).
tff(xx_type,type,
xx: $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xi_type,type,
xi: $i ).
tff(xN_type,type,
xN: $i ).
tff(xQ_type,type,
xQ: $i ).
tff(xT_type,type,
xT: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(tptp_fun_W2_1_type,type,
tptp_fun_W2_1: ( $i * $i ) > $i ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xK_type,type,
xK: $i ).
tff(xS_type,type,
xS: $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(1,plain,
( ( xx = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
<=> ( xx = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( ( xx = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))) )
& aElementOf0(sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4263) ).
tff(3,plain,
xx = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xx = sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( aElementOf0(xx,sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> aElementOf0(sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( aElementOf0(sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> aElementOf0(xx,sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( aElementOf0(sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtlcdtrc0(xc,szDzozmdt0(xc)))
<=> aElementOf0(sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtlcdtrc0(xc,szDzozmdt0(xc))) ),
inference(rewrite,[status(thm)],[]) ).
tff(8,plain,
aElementOf0(sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(and_elim,[status(thm)],[2]) ).
tff(9,plain,
aElementOf0(sdtlpdtrp0(xc,sdtpldt0(xQ,szmzizndt0(sdtlpdtrp0(xN,xi)))),sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(modus_ponens,[status(thm)],[8,7]) ).
tff(10,plain,
aElementOf0(xx,sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(modus_ponens,[status(thm)],[9,6]) ).
tff(11,plain,
( aSet0(xT)
<=> aSet0(xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).
tff(13,plain,
aSet0(xT),
inference(and_elim,[status(thm)],[12]) ).
tff(14,plain,
aSet0(xT),
inference(modus_ponens,[status(thm)],[13,11]) ).
tff(15,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(16,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)],[15]) ).
tff(17,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(18,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)],[17]) ).
tff(19,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(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(quant_intro,[status(thm)],[19]) ).
tff(21,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)],[20,18]) ).
tff(22,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(23,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [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)],[22]) ).
tff(24,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(25,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ( ~ aSubsetOf0(W1,W0)
| ( aSet0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,W1)
| aElementOf0(W2,W0) ) ) )
& ( aSubsetOf0(W1,W0)
| ~ aSet0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_1(W1,W0),W1)
| aElementOf0(tptp_fun_W2_1(W1,W0),W0) ) ) ) )
<=> ! [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)],[24]) ).
tff(26,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(27,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(28,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)],[27]) ).
tff(29,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(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)],[29,28]) ).
tff(31,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)],[30,26]) ).
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(skolemize,[status(sab)],[31]) ).
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)],[32,25]) ).
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)],[33,23]) ).
tff(35,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)],[34,21]) ).
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) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[35,16]) ).
tff(37,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(38,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(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(monotonicity,[status(thm)],[38]) ).
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) ) ) ) ) )
<=> ( ~ ! [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)],[39,37]) ).
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] :
~ ( ~ ( 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(42,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)],[41,40]) ).
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) ) ) ) ),
inference(unit_resolution,[status(thm)],[42,36,14]) ).
tff(44,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(45,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(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(monotonicity,[status(thm)],[45]) ).
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) ) ) ) ) )
<=> ( ~ ! [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)],[46,44]) ).
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) ) ) ) )
| ~ ( ~ ( ~ 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(49,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)],[48,47]) ).
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) ) ) ) ),
inference(unit_resolution,[status(thm)],[49,43]) ).
tff(51,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(52,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)],[51,50]) ).
tff(53,plain,
( aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT)
<=> aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(54,axiom,
( aFunction0(xc)
& ( szDzozmdt0(xc) = slbdtsldtrb0(xS,xK) )
& aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3453) ).
tff(55,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(and_elim,[status(thm)],[54]) ).
tff(56,plain,
aSubsetOf0(sdtlcdtrc0(xc,szDzozmdt0(xc)),xT),
inference(modus_ponens,[status(thm)],[55,53]) ).
tff(57,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(58,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)],[57,56]) ).
tff(59,plain,
~ ( ~ aSet0(sdtlcdtrc0(xc,szDzozmdt0(xc)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ) ),
inference(unit_resolution,[status(thm)],[58,52]) ).
tff(60,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(61,plain,
! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) ),
inference(unit_resolution,[status(thm)],[60,59]) ).
tff(62,plain,
( ~ aElementOf0(xx,xT)
<=> ~ aElementOf0(xx,xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(63,axiom,
~ aElementOf0(xx,xT),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(64,plain,
~ aElementOf0(xx,xT),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
( ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(xx,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(xx,xT) )
<=> ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(xx,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(xx,xT) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(xx,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(xx,xT) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(W2,xT) )
| ~ aElementOf0(xx,sdtlcdtrc0(xc,szDzozmdt0(xc)))
| aElementOf0(xx,xT) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
~ aElementOf0(xx,sdtlcdtrc0(xc,szDzozmdt0(xc))),
inference(unit_resolution,[status(thm)],[67,64,61]) ).
tff(69,plain,
$false,
inference(unit_resolution,[status(thm)],[68,10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : NUM587+1 : TPTP v9.0.0. Released v4.0.0.
% 0.06/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Jun 20 01:31:23 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.20/0.56 % SZS status Theorem
% 0.20/0.56 % SZS output start Proof
% See solution above
% 0.20/0.58 % E exiting
%------------------------------------------------------------------------------