%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : NUM552+3 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n007.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 05:21:22 AM UTC 2025
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 26
% Syntax : Number of formulae : 67 ( 15 unt; 0 typ; 0 def)
% Number of atoms : 984 ( 144 equ)
% Maximal formula atoms : 48 ( 14 avg)
% Number of connectives : 1718 ( 822 ~; 621 |; 183 &)
% ( 34 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 8 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 21 ( 21 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 161 ( 153 !; 1 ?; 161 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xT_type,type,
xT: $i ).
tff(xQ_type,type,
xQ: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(xk_type,type,
xk: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(slbdtsldtrb0_type,type,
slbdtsldtrb0: ( $i * $i ) > $i ).
tff(tptp_fun_W1_12_type,type,
tptp_fun_W1_12: $i > $i ).
tff(xS_type,type,
xS: $i ).
tff(slcrc0_type,type,
slcrc0: $i ).
tff(xx_type,type,
xx: $i ).
tff(1,plain,
^ [W0: $i] :
refl(( ~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [W0: $i] :
rewrite(( ~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(4,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[4,2]) ).
tff(6,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) ) )),
trans(monotonicity(rewrite(( ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) )
<=> ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) )),
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) )
<=> ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )),
rewrite(( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) )
<=> ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )),
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) )
<=> ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )),
( ( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) )),
rewrite(( ( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) )),
( ( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(7,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
^ [W0: $i] :
rewrite(( ( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) )
| ( sbrdtbr0(W0) != xk )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
<=> ( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) )),
inference(bind,[status(th)],[]) ).
tff(9,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) )
| ( sbrdtbr0(W0) != xk )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
<=> ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
( ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ~ ( ( aSubsetOf0(W0,xT)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
<=> ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ~ ( ( aSubsetOf0(W0,xT)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
^ [W0: $i] :
rewrite(( ( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
<=> ( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ~ ( ( aSubsetOf0(W0,xT)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ) )),
inference(bind,[status(th)],[]) ).
tff(12,plain,
( ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
<=> ! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ~ ( ( aSubsetOf0(W0,xT)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,axiom,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
& ! [W0: $i] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk))
& ~ ( ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
=> ( ~ ? [W0: $i] : aElementOf0(W0,slbdtsldtrb0(xS,xk))
| ( slbdtsldtrb0(xS,xk) = slcrc0 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2227) ).
tff(14,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
& ! [W0: $i] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
& aSubsetOf0(slbdtsldtrb0(xS,xk),slbdtsldtrb0(xT,xk)) ),
inference(and_elim,[status(thm)],[13]) ).
tff(15,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )
& ! [W0: $i] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ),
inference(and_elim,[status(thm)],[14]) ).
tff(16,plain,
( aSet0(slbdtsldtrb0(xS,xk))
& ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) )
& aSubsetOf0(W0,xS)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xS) ) )
| aSubsetOf0(W0,xS) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xS,xk)) ) )
& aSet0(slbdtsldtrb0(xT,xk))
& ! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ) ),
inference(and_elim,[status(thm)],[15]) ).
tff(17,plain,
! [W0: $i] :
( ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ( ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElementOf0(W1,xT) ) )
| aSubsetOf0(W0,xT) )
& ( sbrdtbr0(W0) = xk ) )
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ),
inference(and_elim,[status(thm)],[16]) ).
tff(18,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ~ ( ( aSubsetOf0(W0,xT)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ),
inference(modus_ponens,[status(thm)],[17,12]) ).
tff(19,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ~ ( ( aSubsetOf0(W0,xT)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
& ( sbrdtbr0(W0) = xk ) )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ),
inference(modus_ponens,[status(thm)],[18,10]) ).
tff(20,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) )
| ( sbrdtbr0(W0) != xk )
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ),
inference(skolemize,[status(sab)],[19]) ).
tff(21,plain,
! [W0: $i] :
( ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) )
& aSubsetOf0(W0,xT)
& ( sbrdtbr0(W0) = xk ) ) )
& ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ( ~ aSubsetOf0(W0,xT)
& ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,9]) ).
tff(22,plain,
! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,7]) ).
tff(23,plain,
! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[22,5]) ).
tff(24,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(xQ,xT) ) )
| ~ ( ( sbrdtbr0(xQ) != xk )
| aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ ( ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(xQ),xQ)
| aElementOf0(tptp_fun_W1_12(xQ),xT) ) )
| aSubsetOf0(xQ,xT) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(xQ,xT) ) )
| ~ ( ( sbrdtbr0(xQ) != xk )
| aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ ( ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(xQ),xQ)
| aElementOf0(tptp_fun_W1_12(xQ),xT) ) )
| aSubsetOf0(xQ,xT) ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ~ ( ~ ( ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ aSubsetOf0(xQ,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(xQ) != xk )
| ~ ( aSubsetOf0(xQ,xT)
| ~ ( ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(xQ),xQ)
| aElementOf0(tptp_fun_W1_12(xQ),xT) ) ) ) ) )
<=> ~ ( ~ ( ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(xQ,xT) ) )
| ~ ( ( sbrdtbr0(xQ) != xk )
| aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ ( ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(xQ),xQ)
| aElementOf0(tptp_fun_W1_12(xQ),xT) ) )
| aSubsetOf0(xQ,xT) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(26,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ aSubsetOf0(xQ,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(xQ) != xk )
| ~ ( aSubsetOf0(xQ,xT)
| ~ ( ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(xQ),xQ)
| aElementOf0(tptp_fun_W1_12(xQ),xT) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(xQ,xT) ) )
| ~ ( ( sbrdtbr0(xQ) != xk )
| aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ ( ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(xQ),xQ)
| aElementOf0(tptp_fun_W1_12(xQ),xT) ) )
| aSubsetOf0(xQ,xT) ) ) ) ) ),
inference(monotonicity,[status(thm)],[25]) ).
tff(27,plain,
( ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ aSubsetOf0(xQ,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(xQ) != xk )
| ~ ( aSubsetOf0(xQ,xT)
| ~ ( ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(xQ),xQ)
| aElementOf0(tptp_fun_W1_12(xQ),xT) ) ) ) ) ) )
<=> ( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(xQ,xT) ) )
| ~ ( ( sbrdtbr0(xQ) != xk )
| aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ ( ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(xQ),xQ)
| aElementOf0(tptp_fun_W1_12(xQ),xT) ) )
| aSubsetOf0(xQ,xT) ) ) ) ) ),
inference(transitivity,[status(thm)],[26,24]) ).
tff(28,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ aSubsetOf0(xQ,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(xQ) != xk )
| ~ ( aSubsetOf0(xQ,xT)
| ~ ( ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(xQ),xQ)
| aElementOf0(tptp_fun_W1_12(xQ),xT) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(29,plain,
( ~ ! [W0: $i] :
~ ( ~ ( ~ aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(W0)
| ( sbrdtbr0(W0) != xk )
| ~ aSubsetOf0(W0,xT)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| aElementOf0(W1,xT) ) ) )
| ~ ( aElementOf0(W0,slbdtsldtrb0(xT,xk))
| ( sbrdtbr0(W0) != xk )
| ~ ( aSubsetOf0(W0,xT)
| ~ ( ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(W0),W0)
| aElementOf0(tptp_fun_W1_12(W0),xT) ) ) ) ) )
| ~ ( ~ ( ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(xQ,xT) ) )
| ~ ( ( sbrdtbr0(xQ) != xk )
| aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ ( ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(xQ),xQ)
| aElementOf0(tptp_fun_W1_12(xQ),xT) ) )
| aSubsetOf0(xQ,xT) ) ) ) ),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
~ ( ~ ( ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(xQ,xT) ) )
| ~ ( ( sbrdtbr0(xQ) != xk )
| aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ ( ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(xQ),xQ)
| aElementOf0(tptp_fun_W1_12(xQ),xT) ) )
| aSubsetOf0(xQ,xT) ) ) ),
inference(unit_resolution,[status(thm)],[29,23]) ).
tff(31,plain,
( ~ ( ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(xQ,xT) ) )
| ~ ( ( sbrdtbr0(xQ) != xk )
| aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ ( ~ aSet0(xQ)
| ~ ( ~ aElementOf0(tptp_fun_W1_12(xQ),xQ)
| aElementOf0(tptp_fun_W1_12(xQ),xT) ) )
| aSubsetOf0(xQ,xT) ) )
| ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(xQ,xT) ) ),
inference(tautology,[status(thm)],[]) ).
tff(32,plain,
( ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(xQ,xT) ) ),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
( aElementOf0(xQ,slbdtsldtrb0(xS,xk))
<=> aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
inference(rewrite,[status(thm)],[]) ).
tff(34,axiom,
( aSet0(xQ)
& ! [W0: $i] :
( aElementOf0(W0,xQ)
=> aElementOf0(W0,xS) )
& aSubsetOf0(xQ,xS)
& ( sbrdtbr0(xQ) = xk )
& aElementOf0(xQ,slbdtsldtrb0(xS,xk)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__2270) ).
tff(35,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(and_elim,[status(thm)],[34]) ).
tff(36,plain,
aElementOf0(xQ,slbdtsldtrb0(xS,xk)),
inference(modus_ponens,[status(thm)],[35,33]) ).
tff(37,plain,
^ [W0: $i] :
refl(( ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )),
inference(bind,[status(th)],[]) ).
tff(38,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ),
inference(quant_intro,[status(thm)],[37]) ).
tff(39,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(40,plain,
^ [W0: $i] :
rewrite(( ( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
<=> ( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) )),
inference(bind,[status(th)],[]) ).
tff(41,plain,
( ! [W0: $i] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ) ),
inference(quant_intro,[status(thm)],[40]) ).
tff(42,plain,
! [W0: $i] :
( aElementOf0(W0,slbdtsldtrb0(xS,xk))
=> aElementOf0(W0,slbdtsldtrb0(xT,xk)) ),
inference(and_elim,[status(thm)],[15]) ).
tff(43,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ),
inference(modus_ponens,[status(thm)],[43,39]) ).
tff(45,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ),
inference(skolemize,[status(sab)],[44]) ).
tff(46,plain,
! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) ),
inference(modus_ponens,[status(thm)],[45,38]) ).
tff(47,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
| ~ aElementOf0(xQ,slbdtsldtrb0(xS,xk))
| aElementOf0(xQ,slbdtsldtrb0(xT,xk)) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
| ~ aElementOf0(xQ,slbdtsldtrb0(xS,xk))
| aElementOf0(xQ,slbdtsldtrb0(xT,xk)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(48,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
| ~ aElementOf0(xQ,slbdtsldtrb0(xS,xk))
| aElementOf0(xQ,slbdtsldtrb0(xT,xk)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(49,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,slbdtsldtrb0(xS,xk))
| aElementOf0(W0,slbdtsldtrb0(xT,xk)) )
| ~ aElementOf0(xQ,slbdtsldtrb0(xS,xk))
| aElementOf0(xQ,slbdtsldtrb0(xT,xk)) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
aElementOf0(xQ,slbdtsldtrb0(xT,xk)),
inference(unit_resolution,[status(thm)],[49,46,36]) ).
tff(51,plain,
( ~ ( ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(xQ,xT) ) )
| ~ aElementOf0(xQ,slbdtsldtrb0(xT,xk))
| ~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(xQ,xT) ) ),
inference(tautology,[status(thm)],[]) ).
tff(52,plain,
~ ( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(xQ,xT) ),
inference(unit_resolution,[status(thm)],[51,50,32]) ).
tff(53,plain,
( ~ aSet0(xQ)
| ( sbrdtbr0(xQ) != xk )
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aSubsetOf0(xQ,xT)
| ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) ) ),
inference(tautology,[status(thm)],[]) ).
tff(54,plain,
! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) ),
inference(unit_resolution,[status(thm)],[53,52]) ).
tff(55,plain,
( ~ aElementOf0(xx,xT)
<=> ~ aElementOf0(xx,xT) ),
inference(rewrite,[status(thm)],[]) ).
tff(56,plain,
( ~ ( aElementOf0(xx,xQ)
=> aElementOf0(xx,xT) )
<=> ~ ( ~ aElementOf0(xx,xQ)
| aElementOf0(xx,xT) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(57,axiom,
~ ( aElementOf0(xx,xQ)
=> aElementOf0(xx,xT) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(58,plain,
~ ( ~ aElementOf0(xx,xQ)
| aElementOf0(xx,xT) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
~ aElementOf0(xx,xT),
inference(or_elim,[status(thm)],[58]) ).
tff(60,plain,
~ aElementOf0(xx,xT),
inference(modus_ponens,[status(thm)],[59,55]) ).
tff(61,plain,
( aElementOf0(xx,xQ)
<=> aElementOf0(xx,xQ) ),
inference(rewrite,[status(thm)],[]) ).
tff(62,plain,
aElementOf0(xx,xQ),
inference(or_elim,[status(thm)],[58]) ).
tff(63,plain,
aElementOf0(xx,xQ),
inference(modus_ponens,[status(thm)],[62,61]) ).
tff(64,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aElementOf0(xx,xQ)
| aElementOf0(xx,xT) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aElementOf0(xx,xQ)
| aElementOf0(xx,xT) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(65,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aElementOf0(xx,xQ)
| aElementOf0(xx,xT) ),
inference(quant_inst,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xQ)
| aElementOf0(W1,xT) )
| ~ aElementOf0(xx,xQ)
| aElementOf0(xx,xT) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
$false,
inference(unit_resolution,[status(thm)],[66,63,60,54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM552+3 : TPTP v9.0.0. Released v4.0.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.12/0.32 % Computer : n007.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % 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 01:26:35 EDT 2025
% 0.12/0.33 % CPUTime :
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% See solution above
% 0.19/0.45 % E exiting
%------------------------------------------------------------------------------