%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM538+2 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n012.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 05:21:19 AM UTC 2025
% Result : Theorem 0.23s 0.46s
% Output : Proof 0.23s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 58
% Syntax : Number of formulae : 150 ( 38 unt; 0 typ; 0 def)
% Number of atoms : 1173 ( 193 equ)
% Maximal formula atoms : 20 ( 7 avg)
% Number of connectives : 1597 ( 655 ~; 660 |; 76 &)
% ( 145 <=>; 61 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 81 ( 81 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-2 aty)
% Number of variables : 344 ( 323 !; 0 ?; 344 :)
% Comments :
%------------------------------------------------------------------------------
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(xS_type,type,
xS: $i ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(xx_type,type,
xx: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(isFinite0_type,type,
isFinite0: $i > $o ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(1,plain,
( aSet0(xS)
<=> aSet0(xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
aSet0(xS),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1522) ).
tff(3,plain,
aSet0(xS),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
^ [W0: $i] :
refl(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(5,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
inference(quant_intro,[status(thm)],[4]) ).
tff(6,plain,
^ [W0: $i] :
rewrite(( ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
inference(transitivity,[status(thm)],[7,5]) ).
tff(9,plain,
( ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(10,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) )
<=> ( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ))),
( ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) )
<=> ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ( aSet0(W0)
=> ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
rewrite(( ( aSet0(W0)
=> ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
( ( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(11,plain,
( ! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
<=> ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mConsDiff) ).
tff(13,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[13,9]) ).
tff(15,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) ),
inference(modus_ponens,[status(thm)],[15,8]) ).
tff(17,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
| ~ aSet0(xS)
| ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| ( sdtpldt0(sdtmndt0(xS,W1),W1) = xS ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
| ~ aSet0(xS)
| ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| ( sdtpldt0(sdtmndt0(xS,W1),W1) = xS ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(18,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
| ~ aSet0(xS)
| ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| ( sdtpldt0(sdtmndt0(xS,W1),W1) = xS ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(19,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( sdtpldt0(sdtmndt0(W0,W1),W1) = W0 ) ) )
| ~ aSet0(xS)
| ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| ( sdtpldt0(sdtmndt0(xS,W1),W1) = xS ) ) ),
inference(modus_ponens,[status(thm)],[18,17]) ).
tff(20,plain,
! [W1: $i] :
( ~ aElementOf0(W1,xS)
| ( sdtpldt0(sdtmndt0(xS,W1),W1) = xS ) ),
inference(unit_resolution,[status(thm)],[19,16,3]) ).
tff(21,plain,
( aElementOf0(xx,xS)
<=> aElementOf0(xx,xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
( isFinite0(xS)
& aElementOf0(xx,xS) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1522_02) ).
tff(23,plain,
aElementOf0(xx,xS),
inference(and_elim,[status(thm)],[22]) ).
tff(24,plain,
aElementOf0(xx,xS),
inference(modus_ponens,[status(thm)],[23,21]) ).
tff(25,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| ( sdtpldt0(sdtmndt0(xS,W1),W1) = xS ) )
| ~ aElementOf0(xx,xS)
| ( sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| ( sdtpldt0(sdtmndt0(xS,W1),W1) = xS ) )
| ~ aElementOf0(xx,xS)
| ( sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| ( sdtpldt0(sdtmndt0(xS,W1),W1) = xS ) )
| ~ aElementOf0(xx,xS)
| ( sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xS)
| ( sdtpldt0(sdtmndt0(xS,W1),W1) = xS ) )
| ~ aElementOf0(xx,xS)
| ( sdtpldt0(sdtmndt0(xS,xx),xx) = xS ) ),
inference(modus_ponens,[status(thm)],[26,25]) ).
tff(28,plain,
sdtpldt0(sdtmndt0(xS,xx),xx) = xS,
inference(unit_resolution,[status(thm)],[27,24,20]) ).
tff(29,plain,
xS = sdtpldt0(sdtmndt0(xS,xx),xx),
inference(symmetry,[status(thm)],[28]) ).
tff(30,plain,
sbrdtbr0(xS) = sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(monotonicity,[status(thm)],[29]) ).
tff(31,plain,
sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = sbrdtbr0(xS),
inference(symmetry,[status(thm)],[30]) ).
tff(32,plain,
^ [W0: $i] :
refl(( ~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) )
<=> ~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) ) )),
inference(bind,[status(th)],[]) ).
tff(33,plain,
( ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) )
<=> ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) ) ),
inference(quant_intro,[status(thm)],[32]) ).
tff(34,plain,
^ [W0: $i] :
trans(trans(monotonicity(rewrite(( ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) )
<=> ~ ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) ) )),
( ( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) ) )
<=> ( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ~ ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) ) ) )),
rewrite(( ( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ~ ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) ) )
<=> ~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) ) )),
( ( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) ) )
<=> ~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) ) )),
rewrite(( ~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) )
<=> ~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) ) )),
( ( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) ) )
<=> ~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) ) )),
inference(bind,[status(th)],[]) ).
tff(35,plain,
( ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) ) )
<=> ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,plain,
( ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) ) )
<=> ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(37,plain,
( ~ ( ( aSet0(sdtmndt0(xS,xx))
& ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) ) ) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ) )
<=> ~ ( ~ ( aSet0(sdtmndt0(xS,xx))
& ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) ) ) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(38,axiom,
~ ( ( aSet0(sdtmndt0(xS,xx))
& ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) ) ) )
=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(39,plain,
~ ( ~ ( aSet0(sdtmndt0(xS,xx))
& ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) ) ) )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS) ) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
( aSet0(sdtmndt0(xS,xx))
& ! [W0: $i] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) ) ) ),
inference(or_elim,[status(thm)],[39]) ).
tff(41,plain,
! [W0: $i] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) ) ),
inference(and_elim,[status(thm)],[40]) ).
tff(42,plain,
! [W0: $i] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) ) ),
inference(modus_ponens,[status(thm)],[41,36]) ).
tff(43,plain,
! [W0: $i] :
( aElementOf0(W0,sdtmndt0(xS,xx))
<=> ( aElement0(W0)
& aElementOf0(W0,xS)
& ( W0 != xx ) ) ),
inference(skolemize,[status(sab)],[42]) ).
tff(44,plain,
! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) ),
inference(modus_ponens,[status(thm)],[43,35]) ).
tff(45,plain,
! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) ),
inference(modus_ponens,[status(thm)],[44,33]) ).
tff(46,plain,
( ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElementOf0(xx,sdtmndt0(xS,xx)) )
<=> ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElementOf0(xx,sdtmndt0(xS,xx)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(47,plain,
( ~ ( ( ~ aElement0(xx)
| ~ aElementOf0(xx,xS)
| ( xx = xx ) )
<=> aElementOf0(xx,sdtmndt0(xS,xx)) )
<=> ~ aElementOf0(xx,sdtmndt0(xS,xx)) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ ( ( ~ aElement0(xx)
| ~ aElementOf0(xx,xS)
| ( xx = xx ) )
<=> aElementOf0(xx,sdtmndt0(xS,xx)) ) )
<=> ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElementOf0(xx,sdtmndt0(xS,xx)) ) ),
inference(monotonicity,[status(thm)],[47]) ).
tff(49,plain,
( ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ ( ( ~ aElement0(xx)
| ~ aElementOf0(xx,xS)
| ( xx = xx ) )
<=> aElementOf0(xx,sdtmndt0(xS,xx)) ) )
<=> ( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElementOf0(xx,sdtmndt0(xS,xx)) ) ),
inference(transitivity,[status(thm)],[48,46]) ).
tff(50,plain,
( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ ( ( ~ aElement0(xx)
| ~ aElementOf0(xx,xS)
| ( xx = xx ) )
<=> aElementOf0(xx,sdtmndt0(xS,xx)) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(51,plain,
( ~ ! [W0: $i] :
~ ( ( ~ aElement0(W0)
| ~ aElementOf0(W0,xS)
| ( W0 = xx ) )
<=> aElementOf0(W0,sdtmndt0(xS,xx)) )
| ~ aElementOf0(xx,sdtmndt0(xS,xx)) ),
inference(modus_ponens,[status(thm)],[50,49]) ).
tff(52,plain,
~ aElementOf0(xx,sdtmndt0(xS,xx)),
inference(unit_resolution,[status(thm)],[51,45]) ).
tff(53,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(54,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)],[53]) ).
tff(55,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(56,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)],[55]) ).
tff(57,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)],[56,54]) ).
tff(58,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(59,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(60,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)],[59]) ).
tff(61,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
tff(62,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[61,60]) ).
tff(63,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[62,58]) ).
tff(64,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[63]) ).
tff(65,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[64,57]) ).
tff(66,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xS)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xS)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xS)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(68,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xS)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) ) ),
inference(modus_ponens,[status(thm)],[67,66]) ).
tff(69,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) ),
inference(unit_resolution,[status(thm)],[68,65,3]) ).
tff(70,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) )
| aElement0(xx)
| ~ aElementOf0(xx,xS) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) )
| aElement0(xx)
| ~ aElementOf0(xx,xS) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(71,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) )
| aElement0(xx)
| ~ aElementOf0(xx,xS) ),
inference(quant_inst,[status(thm)],[]) ).
tff(72,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xS) )
| aElement0(xx)
| ~ aElementOf0(xx,xS) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
aElement0(xx),
inference(unit_resolution,[status(thm)],[72,24,69]) ).
tff(74,plain,
^ [W0: $i] :
refl(( ( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) )
<=> ( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(75,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
^ [W0: $i] :
rewrite(( ( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) )
<=> ( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(77,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) ) ),
inference(quant_intro,[status(thm)],[76]) ).
tff(78,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) ) ),
inference(transitivity,[status(thm)],[77,75]) ).
tff(79,plain,
^ [W0: $i] :
rewrite(( ( ~ aElement0(W0)
| ! [W1: $i] :
( isFinite0(sdtmndt0(W1,W0))
| ~ ( aSet0(W1)
& isFinite0(W1) ) ) )
<=> ( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(80,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( isFinite0(sdtmndt0(W1,W0))
| ~ ( aSet0(W1)
& isFinite0(W1) ) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) ) ),
inference(quant_intro,[status(thm)],[79]) ).
tff(81,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( isFinite0(sdtmndt0(W1,W0))
| ~ ( aSet0(W1)
& isFinite0(W1) ) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( isFinite0(sdtmndt0(W1,W0))
| ~ ( aSet0(W1)
& isFinite0(W1) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(82,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
rewrite(( ( ( aSet0(W1)
& isFinite0(W1) )
=> isFinite0(sdtmndt0(W1,W0)) )
<=> ( isFinite0(sdtmndt0(W1,W0))
| ~ ( aSet0(W1)
& isFinite0(W1) ) ) ))),
( ! [W1: $i] :
( ( aSet0(W1)
& isFinite0(W1) )
=> isFinite0(sdtmndt0(W1,W0)) )
<=> ! [W1: $i] :
( isFinite0(sdtmndt0(W1,W0))
| ~ ( aSet0(W1)
& isFinite0(W1) ) ) )),
( ( aElement0(W0)
=> ! [W1: $i] :
( ( aSet0(W1)
& isFinite0(W1) )
=> isFinite0(sdtmndt0(W1,W0)) ) )
<=> ( aElement0(W0)
=> ! [W1: $i] :
( isFinite0(sdtmndt0(W1,W0))
| ~ ( aSet0(W1)
& isFinite0(W1) ) ) ) )),
rewrite(( ( aElement0(W0)
=> ! [W1: $i] :
( isFinite0(sdtmndt0(W1,W0))
| ~ ( aSet0(W1)
& isFinite0(W1) ) ) )
<=> ( ~ aElement0(W0)
| ! [W1: $i] :
( isFinite0(sdtmndt0(W1,W0))
| ~ ( aSet0(W1)
& isFinite0(W1) ) ) ) )),
( ( aElement0(W0)
=> ! [W1: $i] :
( ( aSet0(W1)
& isFinite0(W1) )
=> isFinite0(sdtmndt0(W1,W0)) ) )
<=> ( ~ aElement0(W0)
| ! [W1: $i] :
( isFinite0(sdtmndt0(W1,W0))
| ~ ( aSet0(W1)
& isFinite0(W1) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [W0: $i] :
( aElement0(W0)
=> ! [W1: $i] :
( ( aSet0(W1)
& isFinite0(W1) )
=> isFinite0(sdtmndt0(W1,W0)) ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( isFinite0(sdtmndt0(W1,W0))
| ~ ( aSet0(W1)
& isFinite0(W1) ) ) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,axiom,
! [W0: $i] :
( aElement0(W0)
=> ! [W1: $i] :
( ( aSet0(W1)
& isFinite0(W1) )
=> isFinite0(sdtmndt0(W1,W0)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mFDiffSet) ).
tff(85,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( isFinite0(sdtmndt0(W1,W0))
| ~ ( aSet0(W1)
& isFinite0(W1) ) ) ),
inference(modus_ponens,[status(thm)],[84,83]) ).
tff(86,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( isFinite0(sdtmndt0(W1,W0))
| ~ ( aSet0(W1)
& isFinite0(W1) ) ) ),
inference(modus_ponens,[status(thm)],[85,81]) ).
tff(87,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( isFinite0(sdtmndt0(W1,W0))
| ~ ( aSet0(W1)
& isFinite0(W1) ) ) ),
inference(skolemize,[status(sab)],[86]) ).
tff(88,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) ),
inference(modus_ponens,[status(thm)],[87,80]) ).
tff(89,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) ),
inference(modus_ponens,[status(thm)],[88,78]) ).
tff(90,plain,
( ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) )
| ~ aElement0(xx)
| ! [W1: $i] :
( ~ isFinite0(W1)
| ~ aSet0(W1)
| isFinite0(sdtmndt0(W1,xx)) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) )
| ~ aElement0(xx)
| ! [W1: $i] :
( ~ isFinite0(W1)
| ~ aSet0(W1)
| isFinite0(sdtmndt0(W1,xx)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(91,plain,
( ( ~ aElement0(xx)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,xx))
| ~ aSet0(W1) ) )
<=> ( ~ aElement0(xx)
| ! [W1: $i] :
( ~ isFinite0(W1)
| ~ aSet0(W1)
| isFinite0(sdtmndt0(W1,xx)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(92,plain,
( ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) )
| ~ aElement0(xx)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,xx))
| ~ aSet0(W1) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) )
| ~ aElement0(xx)
| ! [W1: $i] :
( ~ isFinite0(W1)
| ~ aSet0(W1)
| isFinite0(sdtmndt0(W1,xx)) ) ) ),
inference(monotonicity,[status(thm)],[91]) ).
tff(93,plain,
( ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) )
| ~ aElement0(xx)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,xx))
| ~ aSet0(W1) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) )
| ~ aElement0(xx)
| ! [W1: $i] :
( ~ isFinite0(W1)
| ~ aSet0(W1)
| isFinite0(sdtmndt0(W1,xx)) ) ) ),
inference(transitivity,[status(thm)],[92,90]) ).
tff(94,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) )
| ~ aElement0(xx)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,xx))
| ~ aSet0(W1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(95,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ! [W1: $i] :
( ~ isFinite0(W1)
| isFinite0(sdtmndt0(W1,W0))
| ~ aSet0(W1) ) )
| ~ aElement0(xx)
| ! [W1: $i] :
( ~ isFinite0(W1)
| ~ aSet0(W1)
| isFinite0(sdtmndt0(W1,xx)) ) ),
inference(modus_ponens,[status(thm)],[94,93]) ).
tff(96,plain,
! [W1: $i] :
( ~ isFinite0(W1)
| ~ aSet0(W1)
| isFinite0(sdtmndt0(W1,xx)) ),
inference(unit_resolution,[status(thm)],[95,89,73]) ).
tff(97,plain,
( isFinite0(xS)
<=> isFinite0(xS) ),
inference(rewrite,[status(thm)],[]) ).
tff(98,plain,
isFinite0(xS),
inference(and_elim,[status(thm)],[22]) ).
tff(99,plain,
isFinite0(xS),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
( ( ~ ! [W1: $i] :
( ~ isFinite0(W1)
| ~ aSet0(W1)
| isFinite0(sdtmndt0(W1,xx)) )
| ~ aSet0(xS)
| ~ isFinite0(xS)
| isFinite0(sdtmndt0(xS,xx)) )
<=> ( ~ ! [W1: $i] :
( ~ isFinite0(W1)
| ~ aSet0(W1)
| isFinite0(sdtmndt0(W1,xx)) )
| ~ aSet0(xS)
| ~ isFinite0(xS)
| isFinite0(sdtmndt0(xS,xx)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(101,plain,
( ( ~ isFinite0(xS)
| ~ aSet0(xS)
| isFinite0(sdtmndt0(xS,xx)) )
<=> ( ~ aSet0(xS)
| ~ isFinite0(xS)
| isFinite0(sdtmndt0(xS,xx)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(102,plain,
( ( ~ ! [W1: $i] :
( ~ isFinite0(W1)
| ~ aSet0(W1)
| isFinite0(sdtmndt0(W1,xx)) )
| ~ isFinite0(xS)
| ~ aSet0(xS)
| isFinite0(sdtmndt0(xS,xx)) )
<=> ( ~ ! [W1: $i] :
( ~ isFinite0(W1)
| ~ aSet0(W1)
| isFinite0(sdtmndt0(W1,xx)) )
| ~ aSet0(xS)
| ~ isFinite0(xS)
| isFinite0(sdtmndt0(xS,xx)) ) ),
inference(monotonicity,[status(thm)],[101]) ).
tff(103,plain,
( ( ~ ! [W1: $i] :
( ~ isFinite0(W1)
| ~ aSet0(W1)
| isFinite0(sdtmndt0(W1,xx)) )
| ~ isFinite0(xS)
| ~ aSet0(xS)
| isFinite0(sdtmndt0(xS,xx)) )
<=> ( ~ ! [W1: $i] :
( ~ isFinite0(W1)
| ~ aSet0(W1)
| isFinite0(sdtmndt0(W1,xx)) )
| ~ aSet0(xS)
| ~ isFinite0(xS)
| isFinite0(sdtmndt0(xS,xx)) ) ),
inference(transitivity,[status(thm)],[102,100]) ).
tff(104,plain,
( ~ ! [W1: $i] :
( ~ isFinite0(W1)
| ~ aSet0(W1)
| isFinite0(sdtmndt0(W1,xx)) )
| ~ isFinite0(xS)
| ~ aSet0(xS)
| isFinite0(sdtmndt0(xS,xx)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(105,plain,
( ~ ! [W1: $i] :
( ~ isFinite0(W1)
| ~ aSet0(W1)
| isFinite0(sdtmndt0(W1,xx)) )
| ~ aSet0(xS)
| ~ isFinite0(xS)
| isFinite0(sdtmndt0(xS,xx)) ),
inference(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
isFinite0(sdtmndt0(xS,xx)),
inference(unit_resolution,[status(thm)],[105,3,99,96]) ).
tff(107,plain,
( aSet0(sdtmndt0(xS,xx))
<=> aSet0(sdtmndt0(xS,xx)) ),
inference(rewrite,[status(thm)],[]) ).
tff(108,plain,
aSet0(sdtmndt0(xS,xx)),
inference(and_elim,[status(thm)],[40]) ).
tff(109,plain,
aSet0(sdtmndt0(xS,xx)),
inference(modus_ponens,[status(thm)],[108,107]) ).
tff(110,plain,
^ [W0: $i] :
refl(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(111,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,plain,
^ [W0: $i] :
rewrite(( ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(113,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) ),
inference(quant_intro,[status(thm)],[112]) ).
tff(114,plain,
( ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) ),
inference(transitivity,[status(thm)],[113,111]) ).
tff(115,plain,
^ [W0: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aSet0(W0)
& isFinite0(W0) )
<=> ~ ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
( ~ ( aSet0(W0)
& isFinite0(W0) )
<=> ~ ~ ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
rewrite(( ~ ~ ( ~ aSet0(W0)
| ~ isFinite0(W0) )
<=> ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
( ~ ( aSet0(W0)
& isFinite0(W0) )
<=> ( ~ aSet0(W0)
| ~ isFinite0(W0) ) )),
( ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ( ~ aSet0(W0)
| ~ isFinite0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) )),
rewrite(( ( ~ aSet0(W0)
| ~ isFinite0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) )),
( ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(116,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) ),
inference(quant_intro,[status(thm)],[115]) ).
tff(117,plain,
( ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
^ [W0: $i] :
trans(monotonicity(quant_intro(proof_bind(^ [W1: $i] :
trans(monotonicity(rewrite(( ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) )
<=> ( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) )),
( ( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) )
<=> ( aElement0(W1)
=> ( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) )),
rewrite(( ( aElement0(W1)
=> ( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) )
<=> ( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )),
( ( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) )
<=> ( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ))),
( ! [W1: $i] :
( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) )
<=> ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )),
( ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) )
<=> ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) )),
rewrite(( ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
<=> ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) )),
( ( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) )
<=> ( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(119,plain,
( ! [W0: $i] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) )
<=> ! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ) ),
inference(quant_intro,[status(thm)],[118]) ).
tff(120,axiom,
! [W0: $i] :
( ( aSet0(W0)
& isFinite0(W0) )
=> ! [W1: $i] :
( aElement0(W1)
=> ( ~ aElementOf0(W1,W0)
=> ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mCardCons) ).
tff(121,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[120,119]) ).
tff(122,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[121,117]) ).
tff(123,plain,
! [W0: $i] :
( ~ ( aSet0(W0)
& isFinite0(W0) )
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ),
inference(skolemize,[status(sab)],[122]) ).
tff(124,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[123,116]) ).
tff(125,plain,
! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[124,114]) ).
tff(126,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
| ~ aSet0(sdtmndt0(xS,xx))
| ~ isFinite0(sdtmndt0(xS,xx))
| ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
| ~ aSet0(sdtmndt0(xS,xx))
| ~ isFinite0(sdtmndt0(xS,xx))
| ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(127,plain,
( ( ~ isFinite0(sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ) )
<=> ( ~ aSet0(sdtmndt0(xS,xx))
| ~ isFinite0(sdtmndt0(xS,xx))
| ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(128,plain,
^ [W1: $i] :
rewrite(( ( aElementOf0(W1,sdtmndt0(xS,xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) )
| ~ aElement0(W1) )
<=> ( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ) )),
inference(bind,[status(th)],[]) ).
tff(129,plain,
( ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) )
| ~ aElement0(W1) )
<=> ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ) ),
inference(quant_intro,[status(thm)],[128]) ).
tff(130,plain,
( ( ~ isFinite0(sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) )
| ~ aElement0(W1) ) )
<=> ( ~ isFinite0(sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ) ) ),
inference(monotonicity,[status(thm)],[129]) ).
tff(131,plain,
( ( ~ isFinite0(sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) )
| ~ aElement0(W1) ) )
<=> ( ~ aSet0(sdtmndt0(xS,xx))
| ~ isFinite0(sdtmndt0(xS,xx))
| ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ) ) ),
inference(transitivity,[status(thm)],[130,127]) ).
tff(132,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
| ~ isFinite0(sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) )
| ~ aElement0(W1) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
| ~ aSet0(sdtmndt0(xS,xx))
| ~ isFinite0(sdtmndt0(xS,xx))
| ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ) ) ),
inference(monotonicity,[status(thm)],[131]) ).
tff(133,plain,
( ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
| ~ isFinite0(sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) )
| ~ aElement0(W1) ) )
<=> ( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
| ~ aSet0(sdtmndt0(xS,xx))
| ~ isFinite0(sdtmndt0(xS,xx))
| ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ) ) ),
inference(transitivity,[status(thm)],[132,126]) ).
tff(134,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
| ~ isFinite0(sdtmndt0(xS,xx))
| ~ aSet0(sdtmndt0(xS,xx))
| ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) )
| ~ aElement0(W1) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(135,plain,
( ~ ! [W0: $i] :
( ~ isFinite0(W0)
| ~ aSet0(W0)
| ! [W1: $i] :
( aElementOf0(W1,W0)
| ( sbrdtbr0(sdtpldt0(W0,W1)) = szszuzczcdt0(sbrdtbr0(W0)) )
| ~ aElement0(W1) ) )
| ~ aSet0(sdtmndt0(xS,xx))
| ~ isFinite0(sdtmndt0(xS,xx))
| ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ) ),
inference(modus_ponens,[status(thm)],[134,133]) ).
tff(136,plain,
( ~ isFinite0(sdtmndt0(xS,xx))
| ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ) ),
inference(unit_resolution,[status(thm)],[135,125,109]) ).
tff(137,plain,
! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ),
inference(unit_resolution,[status(thm)],[136,106]) ).
tff(138,plain,
( ( ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) )
| ~ aElement0(xx)
| aElementOf0(xx,sdtmndt0(xS,xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) )
<=> ( ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) )
| ~ aElement0(xx)
| aElementOf0(xx,sdtmndt0(xS,xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(139,plain,
( ( aElementOf0(xx,sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) )
<=> ( ~ aElement0(xx)
| aElementOf0(xx,sdtmndt0(xS,xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(140,plain,
( ( ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) )
| aElementOf0(xx,sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) )
<=> ( ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) )
| ~ aElement0(xx)
| aElementOf0(xx,sdtmndt0(xS,xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ) ),
inference(monotonicity,[status(thm)],[139]) ).
tff(141,plain,
( ( ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) )
| aElementOf0(xx,sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) )
<=> ( ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) )
| ~ aElement0(xx)
| aElementOf0(xx,sdtmndt0(xS,xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ) ),
inference(transitivity,[status(thm)],[140,138]) ).
tff(142,plain,
( ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) )
| aElementOf0(xx,sdtmndt0(xS,xx))
| ~ aElement0(xx)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(143,plain,
( ~ ! [W1: $i] :
( aElementOf0(W1,sdtmndt0(xS,xx))
| ~ aElement0(W1)
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),W1)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) )
| ~ aElement0(xx)
| aElementOf0(xx,sdtmndt0(xS,xx))
| ( sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) ) ),
inference(modus_ponens,[status(thm)],[142,141]) ).
tff(144,plain,
sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)) = szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))),
inference(unit_resolution,[status(thm)],[143,137,73,52]) ).
tff(145,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(sdtpldt0(sdtmndt0(xS,xx),xx)),
inference(symmetry,[status(thm)],[144]) ).
tff(146,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) = sbrdtbr0(xS),
inference(transitivity,[status(thm)],[145,31]) ).
tff(147,plain,
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS) )
<=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(148,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(or_elim,[status(thm)],[39]) ).
tff(149,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xS,xx))) != sbrdtbr0(xS),
inference(modus_ponens,[status(thm)],[148,147]) ).
tff(150,plain,
$false,
inference(unit_resolution,[status(thm)],[149,146]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.14 % Problem : NUM538+2 : TPTP v9.0.0. Released v4.0.0.
% 0.08/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n012.cluster.edu
% 0.15/0.36 % Model : x86_64 x86_64
% 0.15/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36 % Memory : 8042.1875MB
% 0.15/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36 % CPULimit : 300
% 0.15/0.36 % WCLimit : 300
% 0.15/0.36 % DateTime : Fri Jun 20 01:22:55 EDT 2025
% 0.15/0.36 % CPUTime :
% 0.23/0.46 % SZS status Theorem
% 0.23/0.46 % SZS output start Proof
% See solution above
% 0.23/0.49 % E exiting
%------------------------------------------------------------------------------