%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM633+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n001.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 05:21:41 AM UTC 2025
% Result : Theorem 0.37s 0.60s
% Output : Proof 0.37s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 28
% Syntax : Number of formulae : 78 ( 24 unt; 0 typ; 0 def)
% Number of atoms : 513 ( 144 equ)
% Maximal formula atoms : 20 ( 6 avg)
% Number of connectives : 791 ( 389 ~; 293 |; 73 &)
% ( 30 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 33 ( 33 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 14 ( 11 usr; 1 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 9 con; 0-2 aty)
% Number of variables : 113 ( 84 !; 22 ?; 113 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xK_type,type,
xK: $i ).
tff(xO_type,type,
xO: $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(aSet0_type,type,
aSet0: $i > $o ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xc_type,type,
xc: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(xS_type,type,
xS: $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(xT_type,type,
xT: $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(1,plain,
( ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
<=> ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aSet0(xO)
& ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4891) ).
tff(3,plain,
xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) = xO,
inference(symmetry,[status(thm)],[4]) ).
tff(6,plain,
slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK) = slbdtsldtrb0(xO,xK),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
slbdtsldtrb0(xO,xK) = slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
<=> aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK)) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(9,plain,
( aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
<=> aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK)) ),
inference(symmetry,[status(thm)],[8]) ).
tff(10,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(13,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[12]) ).
tff(14,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ) ),
inference(transitivity,[status(thm)],[13,11]) ).
tff(15,plain,
^ [W0: $i] :
rewrite(( ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
<=> ( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(16,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ) ),
inference(quant_intro,[status(thm)],[15]) ).
tff(17,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(18,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(19,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/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(20,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)],[19,18]) ).
tff(21,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)],[20]) ).
tff(22,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)],[21,17]) ).
tff(23,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)],[22,17]) ).
tff(24,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)],[23,17]) ).
tff(25,plain,
^ [W0: $i] :
nnf_neg(refl($oeq(~ aElementOf0(W0,xT),~ aElementOf0(W0,xT))),
nnf_neg(proof_bind(^ [W1: $i] :
nnf_neg(refl($oeq(~ aSubsetOf0(W1,xS),~ aSubsetOf0(W1,xS))),refl($oeq(~ isCountable0(W1),~ isCountable0(W1))),
sk($oeq(~ ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ),
~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ))),
$oeq(~ ( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ),
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) )))),
$oeq(~ ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ),
! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ))),
$oeq(~ ( aElementOf0(W0,xT)
& ? [W1: $i] :
( aSubsetOf0(W1,xS)
& isCountable0(W1)
& ! [W2: $i] :
( ~ aElementOf0(W2,slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,W2) = W0 ) ) ) ),
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ))),
inference(bind,[status(th)],[]) ).
tff(26,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ aSubsetOf0(W1,xS)
| ~ isCountable0(W1)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ),
inference(nnf-neg,[status(sab)],[24,25]) ).
tff(27,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[26,16]) ).
tff(28,plain,
! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) ),
inference(modus_ponens,[status(thm)],[27,14]) ).
tff(29,plain,
( aElementOf0(szDzizrdt0(xd),xT)
<=> aElementOf0(szDzizrdt0(xd),xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(30,axiom,
( aElementOf0(szDzizrdt0(xd),xT)
& isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4854) ).
tff(31,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(and_elim,[status(thm)],[30]) ).
tff(32,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(modus_ponens,[status(thm)],[31,29]) ).
tff(33,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(35,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,W0),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,W0)) = W0 ) ) ) )
| ~ aElementOf0(szDzizrdt0(xd),xT)
| ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) ),
inference(modus_ponens,[status(thm)],[34,33]) ).
tff(36,plain,
! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(W1,szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ),
inference(unit_resolution,[status(thm)],[35,32,28]) ).
tff(37,plain,
( aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS)
<=> aSubsetOf0(xO,xS) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(38,plain,
( aSubsetOf0(xO,xS)
<=> aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS) ),
inference(symmetry,[status(thm)],[37]) ).
tff(39,plain,
( aSubsetOf0(xO,xS)
<=> aSubsetOf0(xO,xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
aSubsetOf0(xO,xS),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4998) ).
tff(41,plain,
aSubsetOf0(xO,xS),
inference(modus_ponens,[status(thm)],[40,39]) ).
tff(42,plain,
aSubsetOf0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xS),
inference(modus_ponens,[status(thm)],[41,38]) ).
tff(43,plain,
( isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
<=> isCountable0(xO) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(44,plain,
( isCountable0(xO)
<=> isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(symmetry,[status(thm)],[43]) ).
tff(45,plain,
( isCountable0(xO)
<=> isCountable0(xO) ),
inference(rewrite,[status(thm)],[]) ).
tff(46,axiom,
( aSet0(xO)
& isCountable0(xO) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4908) ).
tff(47,plain,
isCountable0(xO),
inference(and_elim,[status(thm)],[46]) ).
tff(48,plain,
isCountable0(xO),
inference(modus_ponens,[status(thm)],[47,45]) ).
tff(49,plain,
isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[48,44]) ).
tff(50,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,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))),xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,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))),xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,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))),xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(52,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| ~ aSubsetOf0(W1,xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(W1,szDzizrdt0(xd)),slbdtsldtrb0(W1,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))),xS)
| ~ ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ) ),
inference(modus_ponens,[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))),xK))
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ),
inference(unit_resolution,[status(thm)],[52,49,42,36]) ).
tff(54,plain,
( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),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))),xK)) ),
inference(tautology,[status(thm)],[]) ).
tff(55,plain,
aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),xK)),
inference(unit_resolution,[status(thm)],[54,53]) ).
tff(56,plain,
aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK)),
inference(modus_ponens,[status(thm)],[55,9]) ).
tff(57,plain,
( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),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(58,plain,
sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) != szDzizrdt0(xd),
inference(unit_resolution,[status(thm)],[57,53]) ).
tff(59,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)) = slcrc0 )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ( sdtlpdtrp0(xc,tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd))) = szDzizrdt0(xd) ) ),
inference(tautology,[status(thm)],[]) ).
tff(60,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)) = slcrc0 )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0) ),
inference(unit_resolution,[status(thm)],[59,58]) ).
tff(61,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( W0 = slcrc0 )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( W0 = slcrc0 )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(62,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(quant_intro,[status(thm)],[61]) ).
tff(63,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(xO,xK))
| ~ ( ( W0 = slcrc0 )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(64,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(quant_intro,[status(thm)],[63]) ).
tff(65,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(66,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)],[20]) ).
tff(67,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)],[66,65]) ).
tff(68,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ( ( W0 != slcrc0 )
& aSubsetOf0(W0,szNzAzT0)
& aElementOf0(W0,szDzozmdt0(xc))
& ( sdtlpdtrp0(xc,W0) = szDzizrdt0(xd) ) ) ),
inference(skolemize,[status(sab)],[67]) ).
tff(69,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)],[68,64]) ).
tff(70,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)],[69,62]) ).
tff(71,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( W0 = slcrc0 )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,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)) = slcrc0 )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( W0 = slcrc0 )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,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)) = slcrc0 )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(72,plain,
( ( ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ 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(xO,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)) = slcrc0 )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( W0 = slcrc0 )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ 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(xO,xK))
| ~ ( ( W0 = slcrc0 )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,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)) = slcrc0 )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0) ) ) ),
inference(monotonicity,[status(thm)],[72]) ).
tff(74,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( W0 = slcrc0 )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ 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(xO,xK))
| ~ ( ( W0 = slcrc0 )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,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)) = slcrc0 )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0) ) ) ),
inference(transitivity,[status(thm)],[73,71]) ).
tff(75,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( W0 = slcrc0 )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK))
| ~ ( ( tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)) = slcrc0 )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0)
| ~ 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(76,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xO,xK))
| ~ ( ( W0 = slcrc0 )
| ~ aSubsetOf0(W0,szNzAzT0)
| ~ aElementOf0(W0,szDzozmdt0(xc))
| ( sdtlpdtrp0(xc,W0) != szDzizrdt0(xd) ) ) )
| ~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,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)) = slcrc0 )
| ~ aSubsetOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
~ aElementOf0(tptp_fun_W2_25(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),szDzizrdt0(xd)),slbdtsldtrb0(xO,xK)),
inference(unit_resolution,[status(thm)],[76,70,60]) ).
tff(78,plain,
$false,
inference(unit_resolution,[status(thm)],[77,56]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM633+1 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.34 % Computer : n001.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 01:41:34 EDT 2025
% 0.12/0.34 % CPUTime :
% 0.37/0.60 % SZS status Theorem
% 0.37/0.60 % SZS output start Proof
% See solution above
% 0.37/0.62 % E exiting
%------------------------------------------------------------------------------