%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM598+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n003.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 05:21:32 AM UTC 2025
% Result : Theorem 31.31s 31.58s
% Output : Proof 31.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 62
% Syntax : Number of formulae : 171 ( 53 unt; 0 typ; 0 def)
% Number of atoms : 1255 ( 328 equ)
% Maximal formula atoms : 32 ( 7 avg)
% Number of connectives : 1790 ( 791 ~; 639 |; 189 &)
% ( 104 <=>; 67 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 85 ( 85 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 13 usr; 1 prp; 0-3 aty)
% Number of functors : 18 ( 18 usr; 8 con; 0-2 aty)
% Number of variables : 328 ( 302 !; 0 ?; 328 :)
% Comments :
%------------------------------------------------------------------------------
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(tptp_fun_W3_17_type,type,
tptp_fun_W3_17: $i > $i ).
tff(xe_type,type,
xe: $i ).
tff(xN_type,type,
xN: $i ).
tff(tptp_fun_W2_18_type,type,
tptp_fun_W2_18: $i > $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(xC_type,type,
xC: $i ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(xk_type,type,
xk: $i ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(xT_type,type,
xT: $i ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(xO_type,type,
xO: $i ).
tff(1,plain,
( ( szDzozmdt0(xe) = szNzAzT0 )
<=> ( szDzozmdt0(xe) = szNzAzT0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
( aFunction0(xe)
& ( szDzozmdt0(xe) = szNzAzT0 )
& ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4660) ).
tff(3,plain,
( aFunction0(xe)
& ( szDzozmdt0(xe) = szNzAzT0 ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(4,plain,
szDzozmdt0(xe) = szNzAzT0,
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
szDzozmdt0(xe) = szNzAzT0,
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
szNzAzT0 = szDzozmdt0(xe),
inference(symmetry,[status(thm)],[5]) ).
tff(7,plain,
( aElementOf0(tptp_fun_W3_17(xe),szNzAzT0)
<=> aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(8,plain,
( aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe))
<=> aElementOf0(tptp_fun_W3_17(xe),szNzAzT0) ),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( ( szDzozmdt0(xd) = szNzAzT0 )
<=> ( szDzozmdt0(xd) = szNzAzT0 ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,axiom,
( aFunction0(xd)
& ( szDzozmdt0(xd) = szNzAzT0 )
& ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ! [W1: $i] :
( ( aSet0(W1)
& aElementOf0(W1,slbdtsldtrb0(sdtlpdtrp0(xN,szszuzczcdt0(W0)),xk)) )
=> ( sdtlpdtrp0(xd,W0) = sdtlpdtrp0(sdtlpdtrp0(xC,W0),W1) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4730) ).
tff(11,plain,
( aFunction0(xd)
& ( szDzozmdt0(xd) = szNzAzT0 ) ),
inference(and_elim,[status(thm)],[10]) ).
tff(12,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(and_elim,[status(thm)],[11]) ).
tff(13,plain,
szDzozmdt0(xd) = szNzAzT0,
inference(modus_ponens,[status(thm)],[12,9]) ).
tff(14,plain,
szNzAzT0 = szDzozmdt0(xd),
inference(symmetry,[status(thm)],[13]) ).
tff(15,plain,
szDzozmdt0(xe) = szDzozmdt0(xd),
inference(transitivity,[status(thm)],[5,14]) ).
tff(16,plain,
( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
<=> aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)) ),
inference(monotonicity,[status(thm)],[15]) ).
tff(17,plain,
( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd))
<=> aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)) ),
inference(symmetry,[status(thm)],[16]) ).
tff(18,plain,
( aSet0(xT)
<=> aSet0(xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,axiom,
( aSet0(xT)
& isFinite0(xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3291) ).
tff(20,plain,
aSet0(xT),
inference(and_elim,[status(thm)],[19]) ).
tff(21,plain,
aSet0(xT),
inference(modus_ponens,[status(thm)],[20,18]) ).
tff(22,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(23,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(25,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(transitivity,[status(thm)],[25,23]) ).
tff(27,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(28,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) )
<=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
rewrite(( ( aSet0(W0)
=> ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) )),
inference(bind,[status(th)],[]) ).
tff(29,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mEOfElem) ).
tff(31,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[30,29]) ).
tff(32,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[31,27]) ).
tff(33,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[32]) ).
tff(34,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[33,26]) ).
tff(35,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(36,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(37,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xT)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) ),
inference(unit_resolution,[status(thm)],[37,34,21]) ).
tff(39,plain,
( aElementOf0(szDzizrdt0(xd),xT)
<=> aElementOf0(szDzizrdt0(xd),xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,axiom,
( aElementOf0(szDzizrdt0(xd),xT)
& isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4854) ).
tff(41,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(and_elim,[status(thm)],[40]) ).
tff(42,plain,
aElementOf0(szDzizrdt0(xd),xT),
inference(modus_ponens,[status(thm)],[41,39]) ).
tff(43,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(szDzizrdt0(xd))
| ~ aElementOf0(szDzizrdt0(xd),xT) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(szDzizrdt0(xd))
| ~ aElementOf0(szDzizrdt0(xd),xT) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(szDzizrdt0(xd))
| ~ aElementOf0(szDzizrdt0(xd),xT) ),
inference(quant_inst,[status(thm)],[]) ).
tff(45,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xT) )
| aElement0(szDzizrdt0(xd))
| ~ aElementOf0(szDzizrdt0(xd),xT) ),
inference(modus_ponens,[status(thm)],[44,43]) ).
tff(46,plain,
aElement0(szDzizrdt0(xd)),
inference(unit_resolution,[status(thm)],[45,42,38]) ).
tff(47,plain,
( aFunction0(xd)
<=> aFunction0(xd) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
aFunction0(xd),
inference(and_elim,[status(thm)],[11]) ).
tff(49,plain,
aFunction0(xd),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
^ [W0: $i,W1: $i] :
refl(( ( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
<=> ( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(51,plain,
( ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aFunction0(W0)
& aElement0(W1) )
<=> ~ ( ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
( ~ ( aFunction0(W0)
& aElement0(W1) )
<=> ~ ~ ( ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
rewrite(( ~ ~ ( ~ aElement0(W1)
| ~ aFunction0(W0) )
<=> ( ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
( ~ ( aFunction0(W0)
& aElement0(W1) )
<=> ( ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
( ( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) )
<=> ( ~ aElement0(W1)
| ~ aFunction0(W0)
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ) )),
rewrite(( ( ~ aElement0(W1)
| ~ aFunction0(W0)
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) )
<=> ( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
( ( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) )
<=> ( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(53,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) )
<=> ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(55,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aFunction0(W0)
& aElement0(W1) )
=> aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) )
<=> ( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ) )),
inference(bind,[status(th)],[]) ).
tff(56,plain,
( ! [W0: $i,W1: $i] :
( ( aFunction0(W0)
& aElement0(W1) )
=> aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [W0: $i,W1: $i] :
( ( aFunction0(W0)
& aElement0(W1) )
=> aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mPttSet) ).
tff(58,plain,
! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [W0: $i,W1: $i] :
( ~ ( aFunction0(W0)
& aElement0(W1) )
| aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0)) ),
inference(skolemize,[status(sab)],[59]) ).
tff(61,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ),
inference(modus_ponens,[status(thm)],[60,53]) ).
tff(62,plain,
! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) ),
inference(modus_ponens,[status(thm)],[61,51]) ).
tff(63,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
| ~ aFunction0(xd)
| ~ aElement0(szDzizrdt0(xd))
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
| ~ aFunction0(xd)
| ~ aElement0(szDzizrdt0(xd))
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(64,plain,
( ( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd))
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd) )
<=> ( ~ aFunction0(xd)
| ~ aElement0(szDzizrdt0(xd))
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd))
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
| ~ aFunction0(xd)
| ~ aElement0(szDzizrdt0(xd))
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)) ) ),
inference(monotonicity,[status(thm)],[64]) ).
tff(66,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd))
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
| ~ aFunction0(xd)
| ~ aElement0(szDzizrdt0(xd))
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)) ) ),
inference(transitivity,[status(thm)],[65,63]) ).
tff(67,plain,
( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd))
| ~ aElement0(szDzizrdt0(xd))
| ~ aFunction0(xd) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [W0: $i,W1: $i] :
( aSubsetOf0(sdtlbdtrb0(W0,W1),szDzozmdt0(W0))
| ~ aElement0(W1)
| ~ aFunction0(W0) )
| ~ aFunction0(xd)
| ~ aElement0(szDzizrdt0(xd))
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
( ~ aElement0(szDzizrdt0(xd))
| aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)) ),
inference(unit_resolution,[status(thm)],[68,62,49]) ).
tff(70,plain,
aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xd)),
inference(unit_resolution,[status(thm)],[69,46]) ).
tff(71,plain,
aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)),
inference(modus_ponens,[status(thm)],[70,17]) ).
tff(72,plain,
( ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) )
<=> ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(73,axiom,
( aSet0(xO)
& ( xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__4891) ).
tff(74,plain,
xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(and_elim,[status(thm)],[73]) ).
tff(75,plain,
xO = sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(modus_ponens,[status(thm)],[74,72]) ).
tff(76,plain,
sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))) = xO,
inference(symmetry,[status(thm)],[75]) ).
tff(77,plain,
( isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
<=> isCountable0(xO) ),
inference(monotonicity,[status(thm)],[76]) ).
tff(78,plain,
( isCountable0(xO)
<=> isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(symmetry,[status(thm)],[77]) ).
tff(79,plain,
( ~ isCountable0(xO)
<=> ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(monotonicity,[status(thm)],[78]) ).
tff(80,plain,
( ~ isCountable0(xO)
<=> ~ isCountable0(xO) ),
inference(rewrite,[status(thm)],[]) ).
tff(81,axiom,
~ isCountable0(xO),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(82,plain,
~ isCountable0(xO),
inference(modus_ponens,[status(thm)],[81,80]) ).
tff(83,plain,
~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[82,79]) ).
tff(84,plain,
( aFunction0(xe)
<=> aFunction0(xe) ),
inference(rewrite,[status(thm)],[]) ).
tff(85,plain,
aFunction0(xe),
inference(and_elim,[status(thm)],[3]) ).
tff(86,plain,
aFunction0(xe),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
^ [W0: $i] :
refl(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,plain,
^ [W0: $i] :
rewrite(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(90,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[89]) ).
tff(91,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ) ),
inference(transitivity,[status(thm)],[90,88]) ).
tff(92,plain,
^ [W0: $i] :
rewrite(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ~ ( aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
& aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0))
& ( tptp_fun_W2_18(W0) != tptp_fun_W3_17(W0) ) ) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(93,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ~ ( aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
& aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0))
& ( tptp_fun_W2_18(W0) != tptp_fun_W3_17(W0) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[92]) ).
tff(94,plain,
^ [W0: $i] :
rewrite(( ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ~ ( aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
& aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0))
& ( tptp_fun_W2_18(W0) != tptp_fun_W3_17(W0) ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ~ ( aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
& aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0))
& ( tptp_fun_W2_18(W0) != tptp_fun_W3_17(W0) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(95,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ~ ( aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
& aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0))
& ( tptp_fun_W2_18(W0) != tptp_fun_W3_17(W0) ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ~ ( aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
& aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0))
& ( tptp_fun_W2_18(W0) != tptp_fun_W3_17(W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(97,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
trans(monotonicity(trans(monotonicity(quant_intro(proof_bind(^ [W2: $i,W3: $i] :
trans(monotonicity(rewrite(( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
<=> ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )),
( ( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
<=> ( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) ) )),
rewrite(( ( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
<=> ( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) ) )),
( ( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
<=> ( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) ) ))),
( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
<=> ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) ) )),
( ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) )
<=> ( ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) )),
rewrite(( ( ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) )
<=> ( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) ) ) )),
( ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) )
<=> ( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) ) ) )),
( ( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) )
<=> ( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) ) ) ) )),
rewrite(( ( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) ) ) )
<=> ( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) )),
( ( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) )
<=> ( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ))),
( ! [W1: $i] :
( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) )
<=> ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) )),
( ( aFunction0(W0)
=> ! [W1: $i] :
( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) ) )
<=> ( aFunction0(W0)
=> ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ) )),
rewrite(( ( aFunction0(W0)
=> ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ) )),
( ( aFunction0(W0)
=> ! [W1: $i] :
( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(98,plain,
( ! [W0: $i] :
( aFunction0(W0)
=> ! [W1: $i] :
( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ) ),
inference(quant_intro,[status(thm)],[97]) ).
tff(99,axiom,
! [W0: $i] :
( aFunction0(W0)
=> ! [W1: $i] :
( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mImgCount) ).
tff(100,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ),
inference(modus_ponens,[status(thm)],[99,98]) ).
tff(101,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ),
inference(modus_ponens,[status(thm)],[100,96]) ).
tff(102,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ~ ( aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
& aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0))
& ( tptp_fun_W2_18(W0) != tptp_fun_W3_17(W0) ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ),
inference(skolemize,[status(sab)],[101]) ).
tff(103,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ~ ( aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
& aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0))
& ( tptp_fun_W2_18(W0) != tptp_fun_W3_17(W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[102,95]) ).
tff(104,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ),
inference(modus_ponens,[status(thm)],[103,93]) ).
tff(105,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ),
inference(modus_ponens,[status(thm)],[104,91]) ).
tff(106,plain,
( ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
| ~ aFunction0(xe)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(xe,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
| ~ aFunction0(xe)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(xe,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(107,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
| ~ aFunction0(xe)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(xe,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(108,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
| ~ aFunction0(xe)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(xe,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ) ),
inference(modus_ponens,[status(thm)],[107,106]) ).
tff(109,plain,
! [W1: $i] :
( isCountable0(sdtlcdtrc0(xe,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ),
inference(unit_resolution,[status(thm)],[108,105,86]) ).
tff(110,plain,
( isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(rewrite,[status(thm)],[]) ).
tff(111,plain,
isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(and_elim,[status(thm)],[40]) ).
tff(112,plain,
isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(modus_ponens,[status(thm)],[111,110]) ).
tff(113,plain,
( ( ~ ! [W1: $i] :
( isCountable0(sdtlcdtrc0(xe,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
| isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
<=> ( ~ ! [W1: $i] :
( isCountable0(sdtlcdtrc0(xe,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
| isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(114,plain,
( ~ ! [W1: $i] :
( isCountable0(sdtlcdtrc0(xe,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
| isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(115,plain,
( ~ ! [W1: $i] :
( isCountable0(sdtlcdtrc0(xe,W1))
| ~ isCountable0(W1)
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
| isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ),
inference(modus_ponens,[status(thm)],[114,113]) ).
tff(116,plain,
( isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ),
inference(unit_resolution,[status(thm)],[115,112,109]) ).
tff(117,plain,
~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ),
inference(unit_resolution,[status(thm)],[116,83,71]) ).
tff(118,plain,
( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe))
| aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ),
inference(tautology,[status(thm)],[]) ).
tff(119,plain,
aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)),
inference(unit_resolution,[status(thm)],[118,117]) ).
tff(120,plain,
aElementOf0(tptp_fun_W3_17(xe),szNzAzT0),
inference(modus_ponens,[status(thm)],[119,8]) ).
tff(121,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(122,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[121]) ).
tff(123,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(124,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,szNzAzT0)
=> ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(125,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[124]) ).
tff(126,plain,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(and_elim,[status(thm)],[2]) ).
tff(127,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[127,123]) ).
tff(129,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(skolemize,[status(sab)],[128]) ).
tff(130,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[129,122]) ).
tff(131,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szNzAzT0)
| ( sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szNzAzT0)
| ( sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szNzAzT0)
| ( sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szNzAzT0)
| ( sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
( ~ aElementOf0(tptp_fun_W3_17(xe),szNzAzT0)
| ( sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ),
inference(unit_resolution,[status(thm)],[133,130]) ).
tff(135,plain,
sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))),
inference(unit_resolution,[status(thm)],[134,120]) ).
tff(136,plain,
( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe))
| ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) = sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) ) ),
inference(tautology,[status(thm)],[]) ).
tff(137,plain,
sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) = sdtlpdtrp0(xe,tptp_fun_W3_17(xe)),
inference(unit_resolution,[status(thm)],[136,117]) ).
tff(138,plain,
( aElementOf0(tptp_fun_W2_18(xe),szNzAzT0)
<=> aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe)) ),
inference(monotonicity,[status(thm)],[6]) ).
tff(139,plain,
( aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
<=> aElementOf0(tptp_fun_W2_18(xe),szNzAzT0) ),
inference(symmetry,[status(thm)],[138]) ).
tff(140,plain,
( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe))
| aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe)) ),
inference(tautology,[status(thm)],[]) ).
tff(141,plain,
aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe)),
inference(unit_resolution,[status(thm)],[140,117]) ).
tff(142,plain,
aElementOf0(tptp_fun_W2_18(xe),szNzAzT0),
inference(modus_ponens,[status(thm)],[141,139]) ).
tff(143,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szNzAzT0)
| ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szNzAzT0)
| ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(144,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szNzAzT0)
| ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(145,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szNzAzT0)
| ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) ) ),
inference(modus_ponens,[status(thm)],[144,143]) ).
tff(146,plain,
( ~ aElementOf0(tptp_fun_W2_18(xe),szNzAzT0)
| ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) ) ),
inference(unit_resolution,[status(thm)],[145,130]) ).
tff(147,plain,
sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))),
inference(unit_resolution,[status(thm)],[146,142]) ).
tff(148,plain,
szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) = sdtlpdtrp0(xe,tptp_fun_W2_18(xe)),
inference(symmetry,[status(thm)],[147]) ).
tff(149,plain,
szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))),
inference(transitivity,[status(thm)],[148,137,135]) ).
tff(150,plain,
( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe))
| ( tptp_fun_W2_18(xe) != tptp_fun_W3_17(xe) ) ),
inference(tautology,[status(thm)],[]) ).
tff(151,plain,
tptp_fun_W2_18(xe) != tptp_fun_W3_17(xe),
inference(unit_resolution,[status(thm)],[150,117]) ).
tff(152,plain,
^ [W0: $i,W1: $i] :
refl(( ( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
<=> ( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(153,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[152]) ).
tff(154,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
<=> ~ ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
<=> ~ ~ ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
rewrite(( ~ ~ ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) )
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
rewrite(( ( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ( W0 = W1 )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
<=> ( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
( ( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) )
<=> ( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) )),
inference(bind,[status(th)],[]) ).
tff(155,plain,
( ! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ) ),
inference(quant_intro,[status(thm)],[154]) ).
tff(156,plain,
( ! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(157,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(rewrite(( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
<=> ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
=> ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ) )
<=> ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
=> ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ) ) )),
rewrite(( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
=> ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ) )
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
=> ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ) )
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(158,plain,
( ! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
=> ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) ) ),
inference(quant_intro,[status(thm)],[157]) ).
tff(159,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
=> ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3821) ).
tff(160,plain,
! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) ),
inference(modus_ponens,[status(thm)],[159,158]) ).
tff(161,plain,
! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) ),
inference(modus_ponens,[status(thm)],[160,156]) ).
tff(162,plain,
! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) ),
inference(skolemize,[status(sab)],[161]) ).
tff(163,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[162,155]) ).
tff(164,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) ),
inference(modus_ponens,[status(thm)],[163,153]) ).
tff(165,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szNzAzT0)
| ~ aElementOf0(tptp_fun_W2_18(xe),szNzAzT0)
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szNzAzT0)
| ~ aElementOf0(tptp_fun_W2_18(xe),szNzAzT0)
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(166,plain,
( ( ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szNzAzT0)
| ~ aElementOf0(tptp_fun_W2_18(xe),szNzAzT0) )
<=> ( ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szNzAzT0)
| ~ aElementOf0(tptp_fun_W2_18(xe),szNzAzT0)
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(167,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szNzAzT0)
| ~ aElementOf0(tptp_fun_W2_18(xe),szNzAzT0) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szNzAzT0)
| ~ aElementOf0(tptp_fun_W2_18(xe),szNzAzT0)
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ) ),
inference(monotonicity,[status(thm)],[166]) ).
tff(168,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szNzAzT0)
| ~ aElementOf0(tptp_fun_W2_18(xe),szNzAzT0) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szNzAzT0)
| ~ aElementOf0(tptp_fun_W2_18(xe),szNzAzT0)
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ) ),
inference(transitivity,[status(thm)],[167,165]) ).
tff(169,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szNzAzT0)
| ~ aElementOf0(tptp_fun_W2_18(xe),szNzAzT0) ),
inference(quant_inst,[status(thm)],[]) ).
tff(170,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szNzAzT0)
| ~ aElementOf0(W0,szNzAzT0) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szNzAzT0)
| ~ aElementOf0(tptp_fun_W2_18(xe),szNzAzT0)
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ),
inference(modus_ponens,[status(thm)],[169,168]) ).
tff(171,plain,
$false,
inference(unit_resolution,[status(thm)],[170,164,151,120,142,149]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : NUM598+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.12 % Command : run_E %s %d THM
% 0.12/0.33 % Computer : n003.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Jun 20 01:33:39 EDT 2025
% 0.12/0.34 % CPUTime :
% 31.31/31.58 % SZS status Theorem
% 31.31/31.58 % SZS output start Proof
% See solution above
% 31.47/31.72 % E exiting
%------------------------------------------------------------------------------