%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : RNG099+1 : TPTP v9.0.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n016.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 05:24:11 AM UTC 2025
% Result : Theorem 4.66s 4.83s
% Output : Proof 4.70s
% Verified :
% SZS Type : Refutation
% Derivation depth : 19
% Number of leaves : 85
% Syntax : Number of formulae : 212 ( 54 unt; 0 typ; 0 def)
% Number of atoms : 2214 ( 8 equ)
% Maximal formula atoms : 56 ( 10 avg)
% Number of connectives : 4056 (2142 ~;1512 |; 172 &)
% ( 197 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 7 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of FOOLs : 88 ( 88 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 15 ( 12 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 8 con; 0-2 aty)
% Number of variables : 634 ( 591 !; 9 ?; 634 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdteqdtlpzmzozddtrp0_type,type,
sdteqdtlpzmzozddtrp0: ( $i * $i * $i ) > $o ).
tff(xJ_type,type,
xJ: $i ).
tff(xy_type,type,
xy: $i ).
tff(sdtpldt0_type,type,
sdtpldt0: ( $i * $i ) > $i ).
tff(sdtasdt0_type,type,
sdtasdt0: ( $i * $i ) > $i ).
tff(xb_type,type,
xb: $i ).
tff(xx_type,type,
xx: $i ).
tff(xa_type,type,
xa: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(smndt0_type,type,
smndt0: $i > $i ).
tff(xw_type,type,
xw: $i ).
tff(aElement0_type,type,
aElement0: $i > $o ).
tff(xI_type,type,
xI: $i ).
tff(aSet0_type,type,
aSet0: $i > $o ).
tff(aIdeal0_type,type,
aIdeal0: $i > $o ).
tff(tptp_fun_W2_9_type,type,
tptp_fun_W2_9: $i > $i ).
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(sz10_type,type,
sz10: $i ).
tff(1,plain,
( ( xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)) )
<=> ( xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,axiom,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1319) ).
tff(3,plain,
xw = sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),
inference(modus_ponens,[status(thm)],[2,1]) ).
tff(4,plain,
sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)) = xw,
inference(symmetry,[status(thm)],[3]) ).
tff(5,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)) = sdtpldt0(xw,smndt0(xy)),
inference(monotonicity,[status(thm)],[4]) ).
tff(6,plain,
( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ)
<=> aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ) ),
inference(monotonicity,[status(thm)],[5]) ).
tff(7,plain,
( aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) ),
inference(symmetry,[status(thm)],[6]) ).
tff(8,plain,
( aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ)
<=> aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ) ),
inference(rewrite,[status(thm)],[]) ).
tff(9,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1409) ).
tff(10,plain,
aElementOf0(sdtpldt0(xw,smndt0(xy)),xJ),
inference(modus_ponens,[status(thm)],[9,8]) ).
tff(11,plain,
aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ),
inference(modus_ponens,[status(thm)],[10,7]) ).
tff(12,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(13,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)],[12]) ).
tff(14,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(15,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)],[14]) ).
tff(16,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(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) ) ) ) ) )
| ~ ( 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)],[16]) ).
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) ) ) ) ) )
<=> ! [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)],[17,15]) ).
tff(19,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(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) ) ) ) ) )
<=> ! [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)],[19]) ).
tff(21,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(22,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)],[21]) ).
tff(23,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(24,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(25,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)],[24]) ).
tff(26,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/sandbox/benchmark/theBenchmark.p',mDefIdeal) ).
tff(27,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)],[26,25]) ).
tff(28,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)],[27,23]) ).
tff(29,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)],[28]) ).
tff(30,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)],[29,22]) ).
tff(31,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)],[30,20]) ).
tff(32,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)],[31,18]) ).
tff(33,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)],[32,13]) ).
tff(34,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)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),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) ) ) ) )
| ~ ( ~ 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) ) ) ) ) ) ) )
<=> ( ~ ! [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)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),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) ) ) ) )
| ~ ( ~ 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(rewrite,[status(thm)],[]) ).
tff(35,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)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),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) ) ) ) )
| ~ ( ~ 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(rewrite,[status(thm)],[]) ).
tff(36,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) ) ) ) ) ) ) )
<=> ( ~ ! [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)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),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) ) ) ) )
| ~ ( ~ 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(monotonicity,[status(thm)],[35]) ).
tff(37,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) ) ) ) ) ) ) )
<=> ( ~ ! [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)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),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) ) ) ) )
| ~ ( ~ 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(transitivity,[status(thm)],[36,34]) ).
tff(38,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(39,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)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),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) ) ) ) )
| ~ ( ~ 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(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
~ ( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),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) ) ) ) )
| ~ ( ~ 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)],[39,33]) ).
tff(41,plain,
( ~ ( aIdeal0(xI)
| ~ aSet0(xI)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xI),xI)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xI))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xI),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) ) ) ) )
| ~ ( ~ 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(42,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)],[41,40]) ).
tff(43,plain,
( aIdeal0(xI)
<=> aIdeal0(xI) ),
inference(rewrite,[status(thm)],[]) ).
tff(44,axiom,
( aIdeal0(xI)
& aIdeal0(xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1205) ).
tff(45,plain,
aIdeal0(xI),
inference(and_elim,[status(thm)],[44]) ).
tff(46,plain,
aIdeal0(xI),
inference(modus_ponens,[status(thm)],[45,43]) ).
tff(47,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(48,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)],[47,46]) ).
tff(49,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)],[48,42]) ).
tff(50,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) ) ) )
| aSet0(xI) ),
inference(tautology,[status(thm)],[]) ).
tff(51,plain,
aSet0(xI),
inference(unit_resolution,[status(thm)],[50,49]) ).
tff(52,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(53,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)],[52]) ).
tff(54,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(55,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)],[54]) ).
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(transitivity,[status(thm)],[55,53]) ).
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(rewrite,[status(thm)],[]) ).
tff(58,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(59,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)],[58]) ).
tff(60,axiom,
! [W0: $i] :
( aSet0(W0)
=> ! [W1: $i] :
( aElementOf0(W1,W0)
=> aElement0(W1) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mEOfElem) ).
tff(61,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[60,59]) ).
tff(62,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[61,57]) ).
tff(63,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(skolemize,[status(sab)],[62]) ).
tff(64,plain,
! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[63,56]) ).
tff(65,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xI)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xI)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(66,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xI)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(67,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xI)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ) ),
inference(modus_ponens,[status(thm)],[66,65]) ).
tff(68,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) ),
inference(unit_resolution,[status(thm)],[67,64,51]) ).
tff(69,plain,
( aElementOf0(xa,xI)
<=> aElementOf0(xa,xI) ),
inference(rewrite,[status(thm)],[]) ).
tff(70,axiom,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ)
& ( sdtpldt0(xa,xb) = sz10 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1294) ).
tff(71,plain,
( aElementOf0(xa,xI)
& aElementOf0(xb,xJ) ),
inference(and_elim,[status(thm)],[70]) ).
tff(72,plain,
aElementOf0(xa,xI),
inference(and_elim,[status(thm)],[71]) ).
tff(73,plain,
aElementOf0(xa,xI),
inference(modus_ponens,[status(thm)],[72,69]) ).
tff(74,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xa)
| ~ aElementOf0(xa,xI) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xa)
| ~ aElementOf0(xa,xI) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(75,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xa)
| ~ aElementOf0(xa,xI) ),
inference(quant_inst,[status(thm)],[]) ).
tff(76,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xI) )
| aElement0(xa)
| ~ aElementOf0(xa,xI) ),
inference(modus_ponens,[status(thm)],[75,74]) ).
tff(77,plain,
aElement0(xa),
inference(unit_resolution,[status(thm)],[76,73,68]) ).
tff(78,plain,
( aElement0(xy)
<=> aElement0(xy) ),
inference(rewrite,[status(thm)],[]) ).
tff(79,axiom,
( aElement0(xx)
& aElement0(xy) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1217) ).
tff(80,plain,
aElement0(xy),
inference(and_elim,[status(thm)],[79]) ).
tff(81,plain,
aElement0(xy),
inference(modus_ponens,[status(thm)],[80,78]) ).
tff(82,plain,
^ [W0: $i,W1: $i] :
refl(( ( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(83,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[82]) ).
tff(84,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aElement0(W0)
& aElement0(W1) )
<=> ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(( ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(( ( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(85,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[84]) ).
tff(86,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(87,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtasdt0(W0,W1)) )
<=> ( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(88,plain,
( ! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtasdt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) ),
inference(quant_intro,[status(thm)],[87]) ).
tff(89,axiom,
! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtasdt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB_02) ).
tff(90,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[89,88]) ).
tff(91,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[90,86]) ).
tff(92,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(skolemize,[status(sab)],[91]) ).
tff(93,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[92,85]) ).
tff(94,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[93,83]) ).
tff(95,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtasdt0(xy,xa))
| ~ aElement0(xa)
| ~ aElement0(xy) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtasdt0(xy,xa))
| ~ aElement0(xa)
| ~ aElement0(xy) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(96,plain,
( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtasdt0(xy,xa))
| ~ aElement0(xa)
| ~ aElement0(xy) ),
inference(quant_inst,[status(thm)],[]) ).
tff(97,plain,
( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtasdt0(xy,xa))
| ~ aElement0(xa)
| ~ aElement0(xy) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
( aElement0(sdtasdt0(xy,xa))
| ~ aElement0(xa) ),
inference(unit_resolution,[status(thm)],[97,94,81]) ).
tff(99,plain,
aElement0(sdtasdt0(xy,xa)),
inference(unit_resolution,[status(thm)],[98,77]) ).
tff(100,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)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),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) ) ) ) )
| ~ ( ~ 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) ) ) ) ) ) ) )
<=> ( ~ ! [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)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),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) ) ) ) )
| ~ ( ~ 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(rewrite,[status(thm)],[]) ).
tff(101,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)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),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) ) ) ) )
| ~ ( ~ 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(rewrite,[status(thm)],[]) ).
tff(102,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) ) ) ) ) ) ) )
<=> ( ~ ! [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)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),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) ) ) ) )
| ~ ( ~ 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(monotonicity,[status(thm)],[101]) ).
tff(103,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) ) ) ) ) ) ) )
<=> ( ~ ! [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)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),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) ) ) ) )
| ~ ( ~ 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(transitivity,[status(thm)],[102,100]) ).
tff(104,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(105,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)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),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) ) ) ) )
| ~ ( ~ 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(modus_ponens,[status(thm)],[104,103]) ).
tff(106,plain,
~ ( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),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) ) ) ) )
| ~ ( ~ 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)],[105,33]) ).
tff(107,plain,
( ~ ( aIdeal0(xJ)
| ~ aSet0(xJ)
| ~ ( ~ aElementOf0(tptp_fun_W1_8(xJ),xJ)
| ~ ( ~ ( ~ aElement0(tptp_fun_W2_10(xJ))
| aElementOf0(sdtasdt0(tptp_fun_W2_10(xJ),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) ) ) ) )
| ~ ( ~ 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(108,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)],[107,106]) ).
tff(109,plain,
( aIdeal0(xJ)
<=> aIdeal0(xJ) ),
inference(rewrite,[status(thm)],[]) ).
tff(110,plain,
aIdeal0(xJ),
inference(and_elim,[status(thm)],[44]) ).
tff(111,plain,
aIdeal0(xJ),
inference(modus_ponens,[status(thm)],[110,109]) ).
tff(112,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(113,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)],[112,111]) ).
tff(114,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)],[113,108]) ).
tff(115,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) ) ) )
| aSet0(xJ) ),
inference(tautology,[status(thm)],[]) ).
tff(116,plain,
aSet0(xJ),
inference(unit_resolution,[status(thm)],[115,114]) ).
tff(117,plain,
( ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xJ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xJ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(118,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xJ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(119,plain,
( ~ ! [W0: $i] :
( ~ aSet0(W0)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,W0) ) )
| ~ aSet0(xJ)
| ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ) ),
inference(modus_ponens,[status(thm)],[118,117]) ).
tff(120,plain,
! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) ),
inference(unit_resolution,[status(thm)],[119,64,116]) ).
tff(121,plain,
( aElementOf0(xb,xJ)
<=> aElementOf0(xb,xJ) ),
inference(rewrite,[status(thm)],[]) ).
tff(122,plain,
aElementOf0(xb,xJ),
inference(and_elim,[status(thm)],[71]) ).
tff(123,plain,
aElementOf0(xb,xJ),
inference(modus_ponens,[status(thm)],[122,121]) ).
tff(124,plain,
( ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xb)
| ~ aElementOf0(xb,xJ) )
<=> ( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xb)
| ~ aElementOf0(xb,xJ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(125,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xb)
| ~ aElementOf0(xb,xJ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(126,plain,
( ~ ! [W1: $i] :
( aElement0(W1)
| ~ aElementOf0(W1,xJ) )
| aElement0(xb)
| ~ aElementOf0(xb,xJ) ),
inference(modus_ponens,[status(thm)],[125,124]) ).
tff(127,plain,
aElement0(xb),
inference(unit_resolution,[status(thm)],[126,123,120]) ).
tff(128,plain,
( aElement0(xx)
<=> aElement0(xx) ),
inference(rewrite,[status(thm)],[]) ).
tff(129,plain,
aElement0(xx),
inference(and_elim,[status(thm)],[79]) ).
tff(130,plain,
aElement0(xx),
inference(modus_ponens,[status(thm)],[129,128]) ).
tff(131,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtasdt0(xx,xb))
| ~ aElement0(xb)
| ~ aElement0(xx) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtasdt0(xx,xb))
| ~ aElement0(xb)
| ~ aElement0(xx) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(132,plain,
( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtasdt0(xx,xb))
| ~ aElement0(xb)
| ~ aElement0(xx) ),
inference(quant_inst,[status(thm)],[]) ).
tff(133,plain,
( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtasdt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtasdt0(xx,xb))
| ~ aElement0(xb)
| ~ aElement0(xx) ),
inference(modus_ponens,[status(thm)],[132,131]) ).
tff(134,plain,
( aElement0(sdtasdt0(xx,xb))
| ~ aElement0(xb) ),
inference(unit_resolution,[status(thm)],[133,94,130]) ).
tff(135,plain,
aElement0(sdtasdt0(xx,xb)),
inference(unit_resolution,[status(thm)],[134,127]) ).
tff(136,plain,
^ [W0: $i,W1: $i] :
refl(( ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(137,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[136]) ).
tff(138,plain,
^ [W0: $i,W1: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aElement0(W0)
& aElement0(W1) )
<=> ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(( ~ ~ ( ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1) )
<=> ( ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(( ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(139,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[138]) ).
tff(140,plain,
( ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(141,plain,
^ [W0: $i,W1: $i] :
rewrite(( ( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) )
<=> ( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) )),
inference(bind,[status(th)],[]) ).
tff(142,plain,
( ! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) )
<=> ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ) ),
inference(quant_intro,[status(thm)],[141]) ).
tff(143,axiom,
! [W0: $i,W1: $i] :
( ( aElement0(W0)
& aElement0(W1) )
=> aElement0(sdtpldt0(W0,W1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSortsB) ).
tff(144,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[143,142]) ).
tff(145,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(modus_ponens,[status(thm)],[144,140]) ).
tff(146,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ ( aElement0(W0)
& aElement0(W1) ) ),
inference(skolemize,[status(sab)],[145]) ).
tff(147,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[146,139]) ).
tff(148,plain,
! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[147,137]) ).
tff(149,plain,
( ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(150,plain,
( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(quant_inst,[status(thm)],[]) ).
tff(151,plain,
( ~ ! [W0: $i,W1: $i] :
( aElement0(sdtpldt0(W0,W1))
| ~ aElement0(W1)
| ~ aElement0(W0) )
| aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(modus_ponens,[status(thm)],[150,149]) ).
tff(152,plain,
( aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aElement0(sdtasdt0(xx,xb))
| ~ aElement0(sdtasdt0(xy,xa)) ),
inference(unit_resolution,[status(thm)],[151,148]) ).
tff(153,plain,
aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))),
inference(unit_resolution,[status(thm)],[152,135,99]) ).
tff(154,plain,
^ [W0: $i,W1: $i,W2: $i] :
refl(( ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(155,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[154]) ).
tff(156,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
<=> ~ ( ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
<=> ~ ~ ( ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
rewrite(( ~ ~ ( ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
<=> ( ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ~ ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
<=> ( ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( ~ ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) )
<=> ( ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0)
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ) )),
rewrite(( ( ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0)
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) )
<=> ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
( ( ~ ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) )
<=> ( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) )),
inference(bind,[status(th)],[]) ).
tff(157,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ) ),
inference(quant_intro,[status(thm)],[156]) ).
tff(158,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(159,plain,
^ [W0: $i,W1: $i,W2: $i] :
trans(monotonicity(rewrite(( ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
<=> ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) ) )),
( ( ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) )
<=> ( ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ) )),
rewrite(( ( ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) )
<=> ( ~ ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ) )),
( ( ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) )
<=> ( ~ ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ) )),
inference(bind,[status(th)],[]) ).
tff(160,plain,
( ! [W0: $i,W1: $i,W2: $i] :
( ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) )
<=> ! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ) ),
inference(quant_intro,[status(thm)],[159]) ).
tff(161,axiom,
! [W0: $i,W1: $i,W2: $i] :
( ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
=> ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mDefMod) ).
tff(162,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ),
inference(modus_ponens,[status(thm)],[161,160]) ).
tff(163,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ),
inference(modus_ponens,[status(thm)],[162,158]) ).
tff(164,plain,
! [W0: $i,W1: $i,W2: $i] :
( ~ ( aElement0(W0)
& aElement0(W1)
& aIdeal0(W2) )
| ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) ) ),
inference(skolemize,[status(sab)],[163]) ).
tff(165,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[164,157]) ).
tff(166,plain,
! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) ),
inference(modus_ponens,[status(thm)],[165,155]) ).
tff(167,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xy)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aIdeal0(xJ)
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xy)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aIdeal0(xJ)
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(168,plain,
( ( ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) )
| ~ aIdeal0(xJ)
| ~ aElement0(xy)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))) )
<=> ( ~ aElement0(xy)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aIdeal0(xJ)
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(169,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) )
| ~ aIdeal0(xJ)
| ~ aElement0(xy)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xy)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aIdeal0(xJ)
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) ) ) ),
inference(monotonicity,[status(thm)],[168]) ).
tff(170,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) )
| ~ aIdeal0(xJ)
| ~ aElement0(xy)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xy)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aIdeal0(xJ)
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) ) ) ),
inference(transitivity,[status(thm)],[169,167]) ).
tff(171,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) )
| ~ aIdeal0(xJ)
| ~ aElement0(xy)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(172,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xy)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aIdeal0(xJ)
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) ) ),
inference(modus_ponens,[status(thm)],[171,170]) ).
tff(173,plain,
( ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) ) ),
inference(unit_resolution,[status(thm)],[172,166,111,81]) ).
tff(174,plain,
( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) ),
inference(unit_resolution,[status(thm)],[173,153]) ).
tff(175,plain,
( ~ ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) )
| sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ)
| ~ aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xy)),xJ) ),
inference(tautology,[status(thm)],[]) ).
tff(176,plain,
sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ),
inference(unit_resolution,[status(thm)],[175,174,11]) ).
tff(177,plain,
sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)) = sdtpldt0(xw,smndt0(xx)),
inference(monotonicity,[status(thm)],[4]) ).
tff(178,plain,
( aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI)
<=> aElementOf0(sdtpldt0(xw,smndt0(xx)),xI) ),
inference(monotonicity,[status(thm)],[177]) ).
tff(179,plain,
( aElementOf0(sdtpldt0(xw,smndt0(xx)),xI)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) ),
inference(symmetry,[status(thm)],[178]) ).
tff(180,plain,
( aElementOf0(sdtpldt0(xw,smndt0(xx)),xI)
<=> aElementOf0(sdtpldt0(xw,smndt0(xx)),xI) ),
inference(rewrite,[status(thm)],[]) ).
tff(181,axiom,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__1332) ).
tff(182,plain,
aElementOf0(sdtpldt0(xw,smndt0(xx)),xI),
inference(modus_ponens,[status(thm)],[181,180]) ).
tff(183,plain,
aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI),
inference(modus_ponens,[status(thm)],[182,179]) ).
tff(184,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xx)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aIdeal0(xI)
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) ) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xx)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aIdeal0(xI)
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(185,plain,
( ( ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) )
| ~ aIdeal0(xI)
| ~ aElement0(xx)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))) )
<=> ( ~ aElement0(xx)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aIdeal0(xI)
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(186,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) )
| ~ aIdeal0(xI)
| ~ aElement0(xx)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xx)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aIdeal0(xI)
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) ) ) ),
inference(monotonicity,[status(thm)],[185]) ).
tff(187,plain,
( ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) )
| ~ aIdeal0(xI)
| ~ aElement0(xx)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))) )
<=> ( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xx)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aIdeal0(xI)
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) ) ) ),
inference(transitivity,[status(thm)],[186,184]) ).
tff(188,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) )
| ~ aIdeal0(xI)
| ~ aElement0(xx)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb))) ),
inference(quant_inst,[status(thm)],[]) ).
tff(189,plain,
( ~ ! [W0: $i,W1: $i,W2: $i] :
( ( sdteqdtlpzmzozddtrp0(W0,W1,W2)
<=> aElementOf0(sdtpldt0(W0,smndt0(W1)),W2) )
| ~ aIdeal0(W2)
| ~ aElement0(W1)
| ~ aElement0(W0) )
| ~ aElement0(xx)
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ aIdeal0(xI)
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) ) ),
inference(modus_ponens,[status(thm)],[188,187]) ).
tff(190,plain,
( ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) ) ),
inference(unit_resolution,[status(thm)],[189,166,46,130]) ).
tff(191,plain,
( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) ),
inference(unit_resolution,[status(thm)],[190,153]) ).
tff(192,plain,
( ~ ( sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
<=> aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) )
| sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
| ~ aElementOf0(sdtpldt0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),smndt0(xx)),xI) ),
inference(tautology,[status(thm)],[]) ).
tff(193,plain,
sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI),
inference(unit_resolution,[status(thm)],[192,191,183]) ).
tff(194,plain,
^ [W0: $i] :
refl(( ( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) )
<=> ( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )),
inference(bind,[status(th)],[]) ).
tff(195,plain,
( ! [W0: $i] :
( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
inference(quant_intro,[status(thm)],[194]) ).
tff(196,plain,
^ [W0: $i] :
trans(monotonicity(rewrite(( ( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) )
<=> ~ ( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )),
( ~ ( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) )
<=> ~ ~ ( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )),
rewrite(( ~ ~ ( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) )
<=> ( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )),
( ~ ( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) )
<=> ( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) )),
inference(bind,[status(th)],[]) ).
tff(197,plain,
( ! [W0: $i] :
~ ( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) )
<=> ! [W0: $i] :
( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
inference(quant_intro,[status(thm)],[196]) ).
tff(198,plain,
( ~ ? [W0: $i] :
( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) )
<=> ~ ? [W0: $i] :
( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(199,plain,
( ~ ? [W0: $i] :
( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) )
<=> ~ ? [W0: $i] :
( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(200,axiom,
~ ? [W0: $i] :
( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(201,plain,
~ ? [W0: $i] :
( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) ),
inference(modus_ponens,[status(thm)],[200,199]) ).
tff(202,plain,
~ ? [W0: $i] :
( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) ),
inference(modus_ponens,[status(thm)],[201,198]) ).
tff(203,plain,
~ ? [W0: $i] :
( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) ),
inference(modus_ponens,[status(thm)],[202,198]) ).
tff(204,plain,
~ ? [W0: $i] :
( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) ),
inference(modus_ponens,[status(thm)],[203,198]) ).
tff(205,plain,
^ [W0: $i] :
refl($oeq(~ ( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) ),
~ ( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) ))),
inference(bind,[status(th)],[]) ).
tff(206,plain,
! [W0: $i] :
~ ( aElement0(W0)
& sdteqdtlpzmzozddtrp0(W0,xx,xI)
& sdteqdtlpzmzozddtrp0(W0,xy,xJ) ),
inference(nnf-neg,[status(sab)],[204,205]) ).
tff(207,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) ),
inference(modus_ponens,[status(thm)],[206,197]) ).
tff(208,plain,
! [W0: $i] :
( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) ),
inference(modus_ponens,[status(thm)],[207,195]) ).
tff(209,plain,
( ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) )
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
| ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ) )
<=> ( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) )
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
| ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(210,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) )
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
| ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(211,plain,
( ~ ! [W0: $i] :
( ~ aElement0(W0)
| ~ sdteqdtlpzmzozddtrp0(W0,xx,xI)
| ~ sdteqdtlpzmzozddtrp0(W0,xy,xJ) )
| ~ aElement0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)))
| ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xx,xI)
| ~ sdteqdtlpzmzozddtrp0(sdtpldt0(sdtasdt0(xy,xa),sdtasdt0(xx,xb)),xy,xJ) ),
inference(modus_ponens,[status(thm)],[210,209]) ).
tff(212,plain,
$false,
inference(unit_resolution,[status(thm)],[211,208,153,193,176]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.14 % Problem : RNG099+1 : TPTP v9.0.0. Released v4.0.0.
% 0.03/0.14 % Command : run_E %s %d THM
% 0.15/0.36 % Computer : n016.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 03:20:47 EDT 2025
% 0.15/0.36 % CPUTime :
% 4.66/4.83 % SZS status Theorem
% 4.66/4.83 % SZS output start Proof
% See solution above
% 4.70/4.88 % E exiting
%------------------------------------------------------------------------------