TSTP Solution File: RNG089+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : RNG089+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n017.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 : Tue Sep 20 03:18:20 EDT 2022
% Result : Theorem 0.22s 0.47s
% Output : Proof 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 55
% Syntax : Number of formulae : 105 ( 19 unt; 17 typ; 0 def)
% Number of atoms : 968 ( 1 equ)
% Maximal formula atoms : 28 ( 11 avg)
% Number of connectives : 1975 (1109 ~; 744 |; 72 &)
% ( 41 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 8 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 14 ( 10 >; 4 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 13 ( 13 usr; 7 con; 0-2 aty)
% Number of variables : 302 ( 296 !; 0 ?; 302 :)
% Comments :
%------------------------------------------------------------------------------
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(xJ_type,type,
xJ: $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xl_type,type,
xl: $i ).
tff(xz_type,type,
xz: $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aIdeal0_type,type,
aIdeal0: $i > $o ).
tff(tptp_fun_W1_8_type,type,
tptp_fun_W1_8: $i > $i ).
tff(tptp_fun_W2_10_type,type,
tptp_fun_W2_10: $i > $i ).
tff(tptp_fun_W2_9_type,type,
tptp_fun_W2_9: $i > $i ).
tff(xI_type,type,
xI: $i ).
tff(xk_type,type,
xk: $i ).
tff(xx_type,type,
xx: $i ).
tff(sdtpldt1_type,type,
sdtpldt1: ( $i * $i ) > $i ).
tff(xy_type,type,
xy: $i ).
tff(1,plain,
^ [W0: $i] :
rewrite(
( ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(2,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
^ [W0: $i] :
refl(
( ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(4,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[3]) ).
tff(5,plain,
^ [W0: $i] :
rewrite(
( ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(6,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[5]) ).
tff(7,plain,
( ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) ),
inference(transitivity,[status(thm)],[6,4]) ).
tff(8,plain,
^ [W0: $i] :
trans(
monotonicity(
rewrite(
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
<=> ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )),
rewrite(
( ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
<=> ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )),
( ( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ( ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
rewrite(
( ( ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
( ( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(9,plain,
( ! [W0: $i] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[8]) ).
tff(10,plain,
^ [W0: $i] :
rewrite(
( ( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( ~ ~ aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(11,plain,
( ! [W0: $i] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( ~ ~ aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) )
<=> ! [W0: $i] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[10]) ).
tff(12,plain,
( ! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
<=> ! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
^ [W0: $i] :
rewrite(
( ( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
<=> ( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(14,plain,
( ! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
<=> ! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[13]) ).
tff(15,axiom,
! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( aElementOf0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,W0)
=> aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( aElement0(W2)
=> aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mDefIdeal) ).
tff(16,plain,
! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
! [W0: $i] :
( aIdeal0(W0)
<=> ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [W0: $i] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( ~ ~ aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [W0: $i] :
( ( ~ aIdeal0(W0)
| ( aSet0(W0)
& ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
& ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
& ( aIdeal0(W0)
| ~ aSet0(W0)
| ( aElementOf0(tptp_fun_W1_8(W0),W0)
& ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[18,11]) ).
tff(20,plain,
! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[19,9]) ).
tff(21,plain,
! [W0: $i] :
~ ( ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) )
| ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[20,7]) ).
tff(22,plain,
! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[21,2]) ).
tff(23,plain,
( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(xJ),xJ)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xJ),tptp_fun_W2_9(xJ)),xJ) )
| ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),tptp_fun_W1_8(xJ)),xJ) ) ) ) )
| ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(24,plain,
~ ( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(xJ),xJ)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xJ),tptp_fun_W2_9(xJ)),xJ) )
| ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),tptp_fun_W1_8(xJ)),xJ) ) ) ) )
| ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[23,22]) ).
tff(25,plain,
( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(xJ),xJ)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xJ),tptp_fun_W2_9(xJ)),xJ) )
| ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),tptp_fun_W1_8(xJ)),xJ) ) ) ) )
| ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) )
| ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(26,plain,
( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[25,24]) ).
tff(27,plain,
( aIdeal0(xJ)
<=> aIdeal0(xJ) ),
inference(rewrite,[status(thm)],]) ).
tff(28,axiom,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__870) ).
tff(29,plain,
aIdeal0(xJ),
inference(and_elim,[status(thm)],[28]) ).
tff(30,plain,
aIdeal0(xJ),
inference(modus_ponens,[status(thm)],[29,27]) ).
tff(31,plain,
( ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) )
| ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(32,plain,
( ~ ( ~ aIdeal0(xJ)
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) )
| ~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[31,30]) ).
tff(33,plain,
~ ( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ),
inference(unit_resolution,[status(thm)],[32,26]) ).
tff(34,plain,
( ~ aSet0(xJ)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) )
| ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(35,plain,
! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) ),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
( aElementOf0(xl,xJ)
<=> aElementOf0(xl,xJ) ),
inference(rewrite,[status(thm)],]) ).
tff(37,axiom,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ)
& ( xx = sdtpldt0(xk,xl) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__934) ).
tff(38,plain,
( aElementOf0(xk,xI)
& aElementOf0(xl,xJ) ),
inference(and_elim,[status(thm)],[37]) ).
tff(39,plain,
aElementOf0(xl,xJ),
inference(and_elim,[status(thm)],[38]) ).
tff(40,plain,
aElementOf0(xl,xJ),
inference(modus_ponens,[status(thm)],[39,36]) ).
tff(41,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) )
| ~ aElementOf0(xl,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(xl,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) )
| ~ aElementOf0(xl,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(xl,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) )
| ~ aElementOf0(xl,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(xl,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(43,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(W1,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xJ) ) ) )
| ~ aElementOf0(xl,xJ)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(xl,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) ) ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(xl,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) ) ),
inference(unit_resolution,[status(thm)],[43,40,35]) ).
tff(45,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xJ)
| aElementOf0(sdtpldt0(xl,W2),xJ) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) )
| ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) ) ),
inference(tautology,[status(thm)],]) ).
tff(46,plain,
! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) ),
inference(unit_resolution,[status(thm)],[45,44]) ).
tff(47,plain,
( aElement0(xz)
<=> aElement0(xz) ),
inference(rewrite,[status(thm)],]) ).
tff(48,axiom,
( aElementOf0(xx,sdtpldt1(xI,xJ))
& aElementOf0(xy,sdtpldt1(xI,xJ))
& aElement0(xz) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__901) ).
tff(49,plain,
aElement0(xz),
inference(and_elim,[status(thm)],[48]) ).
tff(50,plain,
aElement0(xz),
inference(modus_ponens,[status(thm)],[49,47]) ).
tff(51,plain,
( ( ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) )
| ~ aElement0(xz)
| aElementOf0(sdtasdt0(xz,xl),xJ) )
<=> ( ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) )
| ~ aElement0(xz)
| aElementOf0(sdtasdt0(xz,xl),xJ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
( ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) )
| ~ aElement0(xz)
| aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(quant_inst,[status(thm)],]) ).
tff(53,plain,
( ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xl),xJ) )
| ~ aElement0(xz)
| aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
aElementOf0(sdtasdt0(xz,xl),xJ),
inference(unit_resolution,[status(thm)],[53,50,46]) ).
tff(55,plain,
( ~ ! [W0: $i] :
~ ( ~ ( aIdeal0(W0)
| ~ aSet0(W0)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(W0),W0)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(W0),W0)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(W0),tptp_fun_W2_9(W0)),W0) )
| ~ ( ~ aElement0(tptp_fun_W2_10(W0))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(W0),tptp_fun_W1_8(W0)),W0) ) ) ) )
| ~ ( ~ aIdeal0(W0)
| ~ ( ~ aSet0(W0)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,W0)
| aElementOf0(sdtpldt0(W1,W2),W0) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),W0) ) ) ) ) ) )
| ~ ( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(xI),xI)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xI),tptp_fun_W2_9(xI)),xI) )
| ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),tptp_fun_W1_8(xI)),xI) ) ) ) )
| ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
~ ( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(xI),xI)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xI),tptp_fun_W2_9(xI)),xI) )
| ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),tptp_fun_W1_8(xI)),xI) ) ) ) )
| ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[55,22]) ).
tff(57,plain,
( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElementOf0(tptp_fun_W2_9(xI),xI)
| aElementOf0(sdtpldt0(tptp_fun_W1_8(xI),tptp_fun_W2_9(xI)),xI) )
| ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),tptp_fun_W1_8(xI)),xI) ) ) ) )
| ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) )
| ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(58,plain,
( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[57,56]) ).
tff(59,plain,
( aIdeal0(xI)
<=> aIdeal0(xI) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
aIdeal0(xI),
inference(and_elim,[status(thm)],[28]) ).
tff(61,plain,
aIdeal0(xI),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
( ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) )
| ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(63,plain,
( ~ ( ~ aIdeal0(xI)
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) )
| ~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ) ),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
~ ( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ),
inference(unit_resolution,[status(thm)],[63,58]) ).
tff(65,plain,
( ~ aSet0(xI)
| ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) )
| ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ) ),
inference(tautology,[status(thm)],]) ).
tff(66,plain,
! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) ),
inference(unit_resolution,[status(thm)],[65,64]) ).
tff(67,plain,
( aElementOf0(xk,xI)
<=> aElementOf0(xk,xI) ),
inference(rewrite,[status(thm)],]) ).
tff(68,plain,
aElementOf0(xk,xI),
inference(and_elim,[status(thm)],[38]) ).
tff(69,plain,
aElementOf0(xk,xI),
inference(modus_ponens,[status(thm)],[68,67]) ).
tff(70,plain,
( ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) )
| ~ aElementOf0(xk,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(xk,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) ) ) )
<=> ( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) )
| ~ aElementOf0(xk,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(xk,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) )
| ~ aElementOf0(xk,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(xk,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(72,plain,
( ~ ! [W1: $i] :
( ~ aElementOf0(W1,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(W1,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,W1),xI) ) ) )
| ~ aElementOf0(xk,xI)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(xk,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) ) ) ),
inference(modus_ponens,[status(thm)],[71,70]) ).
tff(73,plain,
~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(xk,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) ) ),
inference(unit_resolution,[status(thm)],[72,69,66]) ).
tff(74,plain,
( ~ ! [W2: $i] :
( ~ aElementOf0(W2,xI)
| aElementOf0(sdtpldt0(xk,W2),xI) )
| ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) )
| ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) ) ),
inference(tautology,[status(thm)],]) ).
tff(75,plain,
! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) ),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
( ( ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) )
| ~ aElement0(xz)
| aElementOf0(sdtasdt0(xz,xk),xI) )
<=> ( ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) )
| ~ aElement0(xz)
| aElementOf0(sdtasdt0(xz,xk),xI) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) )
| ~ aElement0(xz)
| aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [W2: $i] :
( ~ aElement0(W2)
| aElementOf0(sdtasdt0(W2,xk),xI) )
| ~ aElement0(xz)
| aElementOf0(sdtasdt0(xz,xk),xI) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
aElementOf0(sdtasdt0(xz,xk),xI),
inference(unit_resolution,[status(thm)],[78,50,75]) ).
tff(80,plain,
( ~ ~ ( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) )
<=> ( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(81,plain,
( ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) )
<=> ~ ( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) )
<=> ~ ~ ( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ) ),
inference(monotonicity,[status(thm)],[81]) ).
tff(83,plain,
( ~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) )
<=> ( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ) ),
inference(transitivity,[status(thm)],[82,80]) ).
tff(84,plain,
( ~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) )
<=> ~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(85,axiom,
~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(86,plain,
~ ( aElementOf0(sdtasdt0(xz,xk),xI)
& aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
( ~ aElementOf0(sdtasdt0(xz,xk),xI)
| ~ aElementOf0(sdtasdt0(xz,xl),xJ) ),
inference(modus_ponens,[status(thm)],[86,83]) ).
tff(88,plain,
$false,
inference(unit_resolution,[status(thm)],[87,79,54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : RNG089+1 : TPTP v8.1.0. Released v4.0.0.
% 0.04/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.35 % Computer : n017.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Fri Sep 2 21:47:38 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.36 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.36 Usage: tptp [options] [-file:]file
% 0.14/0.36 -h, -? prints this message.
% 0.14/0.36 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.36 -m, -model generate model.
% 0.14/0.36 -p, -proof generate proof.
% 0.14/0.36 -c, -core generate unsat core of named formulas.
% 0.14/0.36 -st, -statistics display statistics.
% 0.14/0.36 -t:timeout set timeout (in second).
% 0.14/0.36 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.36 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.36 -<param>:<value> configuration parameter and value.
% 0.14/0.36 -o:<output-file> file to place output in.
% 0.22/0.47 % SZS status Theorem
% 0.22/0.47 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------