TSTP Solution File: NUM599+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM599+1 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n013.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 : Sun Sep 18 13:10:47 EDT 2022
% Result : Theorem 77.62s 49.45s
% Output : Proof 77.81s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 65
% Syntax : Number of formulae : 146 ( 38 unt; 18 typ; 0 def)
% Number of atoms : 1157 ( 383 equ)
% Maximal formula atoms : 32 ( 9 avg)
% Number of connectives : 1781 ( 812 ~; 659 |; 178 &)
% ( 82 <=>; 50 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of FOOLs : 60 ( 60 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 17 ( 12 >; 5 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 6 con; 0-2 aty)
% Number of variables : 243 ( 224 !; 0 ?; 243 :)
% Comments :
%------------------------------------------------------------------------------
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(tptp_fun_W3_17_type,type,
tptp_fun_W3_17: $i > $i ).
tff(xe_type,type,
xe: $i ).
tff(xN_type,type,
xN: $i ).
tff(tptp_fun_W2_18_type,type,
tptp_fun_W2_18: $i > $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(aFunction0_type,type,
aFunction0: $i > $o ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(xd_type,type,
xd: $i ).
tff(isCountable0_type,type,
isCountable0: $i > $o ).
tff(sdtlcdtrc0_type,type,
sdtlcdtrc0: ( $i * $i ) > $i ).
tff(xO_type,type,
xO: $i ).
tff(xT_type,type,
xT: $i ).
tff(1,plain,
( ( szDzozmdt0(xe) = szNzAzT0 )
<=> ( szDzozmdt0(xe) = szDzozmdt0(xN) ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( szDzozmdt0(xe) = szNzAzT0 )
<=> ( szDzozmdt0(xe) = szNzAzT0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
( aFunction0(xe)
& ( szDzozmdt0(xe) = szNzAzT0 )
& ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4660) ).
tff(4,plain,
( aFunction0(xe)
& ( szDzozmdt0(xe) = szNzAzT0 ) ),
inference(and_elim,[status(thm)],[3]) ).
tff(5,plain,
szDzozmdt0(xe) = szNzAzT0,
inference(and_elim,[status(thm)],[4]) ).
tff(6,plain,
szDzozmdt0(xe) = szNzAzT0,
inference(modus_ponens,[status(thm)],[5,2]) ).
tff(7,plain,
szDzozmdt0(xe) = szDzozmdt0(xN),
inference(modus_ponens,[status(thm)],[6,1]) ).
tff(8,plain,
szDzozmdt0(xN) = szDzozmdt0(xe),
inference(symmetry,[status(thm)],[7]) ).
tff(9,plain,
( aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN))
<=> aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(10,plain,
( aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe))
<=> aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN)) ),
inference(symmetry,[status(thm)],[9]) ).
tff(11,plain,
( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
<=> aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xN)) ),
inference(monotonicity,[status(thm)],[7]) ).
tff(12,plain,
( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xN))
<=> aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)) ),
inference(symmetry,[status(thm)],[11]) ).
tff(13,plain,
( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
<=> aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
<=> aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
( aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0)
& isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4930) ).
tff(16,plain,
aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0),
inference(and_elim,[status(thm)],[15]) ).
tff(17,plain,
aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szNzAzT0),
inference(modus_ponens,[status(thm)],[16,14]) ).
tff(18,plain,
aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)),
inference(modus_ponens,[status(thm)],[18,12]) ).
tff(20,plain,
( aFunction0(xe)
<=> aFunction0(xe) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
aFunction0(xe),
inference(and_elim,[status(thm)],[4]) ).
tff(22,plain,
aFunction0(xe),
inference(modus_ponens,[status(thm)],[21,20]) ).
tff(23,plain,
^ [W0: $i] :
refl(
( ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(24,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[23]) ).
tff(25,plain,
^ [W0: $i] :
rewrite(
( ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(26,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[25]) ).
tff(27,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ) ),
inference(transitivity,[status(thm)],[26,24]) ).
tff(28,plain,
^ [W0: $i] :
rewrite(
( ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ~ ( aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
& aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0))
& ( tptp_fun_W2_18(W0) != tptp_fun_W3_17(W0) ) ) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ~ ( aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
& aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0))
& ( tptp_fun_W2_18(W0) != tptp_fun_W3_17(W0) ) ) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
^ [W0: $i] :
rewrite(
( ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ~ ( aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
& aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0))
& ( tptp_fun_W2_18(W0) != tptp_fun_W3_17(W0) ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ~ ( aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
& aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0))
& ( tptp_fun_W2_18(W0) != tptp_fun_W3_17(W0) ) ) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ~ ( aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
& aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0))
& ( tptp_fun_W2_18(W0) != tptp_fun_W3_17(W0) ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ~ ( aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
& aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0))
& ( tptp_fun_W2_18(W0) != tptp_fun_W3_17(W0) ) ) ) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
^ [W0: $i] :
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
quant_intro(
proof_bind(
^ [W2: $i,W3: $i] :
trans(
monotonicity(
rewrite(
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
<=> ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )),
( ( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
<=> ( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) ) )),
rewrite(
( ( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
<=> ( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) ) )),
( ( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
<=> ( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) ) ))),
( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
<=> ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) ) )),
( ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) )
<=> ( ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) )),
rewrite(
( ( ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) )
<=> ( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) ) ) )),
( ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) )
<=> ( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) ) ) )),
( ( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) )
<=> ( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) ) ) ) )),
rewrite(
( ( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) ) ) )
<=> ( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) )),
( ( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) )
<=> ( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ))),
( ! [W1: $i] :
( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) )
<=> ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) )),
( ( aFunction0(W0)
=> ! [W1: $i] :
( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) ) )
<=> ( aFunction0(W0)
=> ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ) )),
rewrite(
( ( aFunction0(W0)
=> ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ) )),
( ( aFunction0(W0)
=> ! [W1: $i] :
( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) ) )
<=> ( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [W0: $i] :
( aFunction0(W0)
=> ! [W1: $i] :
( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) ) )
<=> ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [W0: $i] :
( aFunction0(W0)
=> ! [W1: $i] :
( ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
=> ( ! [W2: $i,W3: $i] :
( ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) )
=> ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) ) )
=> isCountable0(sdtlcdtrc0(W0,W1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mImgCount) ).
tff(36,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ! [W2: $i,W3: $i] :
( ( sdtlpdtrp0(W0,W2) != sdtlpdtrp0(W0,W3) )
| ~ ( aElementOf0(W2,szDzozmdt0(W0))
& aElementOf0(W3,szDzozmdt0(W0))
& ( W2 != W3 ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ~ ( aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
& aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0))
& ( tptp_fun_W2_18(W0) != tptp_fun_W3_17(W0) ) ) )
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) ) ) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ ( aSubsetOf0(W1,szDzozmdt0(W0))
& isCountable0(W1) )
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ~ ( aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
& aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0))
& ( tptp_fun_W2_18(W0) != tptp_fun_W3_17(W0) ) ) ) ) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ),
inference(modus_ponens,[status(thm)],[39,29]) ).
tff(41,plain,
! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) ),
inference(modus_ponens,[status(thm)],[40,27]) ).
tff(42,plain,
( ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
| ~ aFunction0(xe)
| ! [W1: $i] :
( ~ isCountable0(W1)
| isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
| ~ aFunction0(xe)
| ! [W1: $i] :
( ~ isCountable0(W1)
| isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( ~ aFunction0(xe)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ) )
<=> ( ~ aFunction0(xe)
| ! [W1: $i] :
( ~ isCountable0(W1)
| isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
| ~ aFunction0(xe)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
| ~ aFunction0(xe)
| ! [W1: $i] :
( ~ isCountable0(W1)
| isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
| ~ aFunction0(xe)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
| ~ aFunction0(xe)
| ! [W1: $i] :
( ~ isCountable0(W1)
| isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
| ~ aFunction0(xe)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
( ~ ! [W0: $i] :
( ~ aFunction0(W0)
| ! [W1: $i] :
( isCountable0(sdtlcdtrc0(W0,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(W0))
| ~ isCountable0(W1)
| ~ ( ( sdtlpdtrp0(W0,tptp_fun_W2_18(W0)) != sdtlpdtrp0(W0,tptp_fun_W3_17(W0)) )
| ( tptp_fun_W2_18(W0) = tptp_fun_W3_17(W0) )
| ~ aElementOf0(tptp_fun_W2_18(W0),szDzozmdt0(W0))
| ~ aElementOf0(tptp_fun_W3_17(W0),szDzozmdt0(W0)) ) ) )
| ~ aFunction0(xe)
| ! [W1: $i] :
( ~ isCountable0(W1)
| isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
! [W1: $i] :
( ~ isCountable0(W1)
| isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ),
inference(unit_resolution,[status(thm)],[47,41,22]) ).
tff(49,plain,
( ~ isCountable0(xO)
<=> ~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))) ),
inference(rewrite,[status(thm)],]) ).
tff(50,plain,
( ~ isCountable0(xO)
<=> ~ isCountable0(xO) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
~ isCountable0(xO),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(52,plain,
~ isCountable0(xO),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
~ isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd)))),
inference(modus_ponens,[status(thm)],[52,49]) ).
tff(54,plain,
( isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
<=> isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(rewrite,[status(thm)],]) ).
tff(55,axiom,
( aElementOf0(szDzizrdt0(xd),xT)
& isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__4854) ).
tff(56,plain,
isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(and_elim,[status(thm)],[55]) ).
tff(57,plain,
isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd))),
inference(modus_ponens,[status(thm)],[56,54]) ).
tff(58,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
| isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) )
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
| isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) )
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
( ( ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
<=> ( isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) )
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(60,plain,
( ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) )
<=> ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
( ( ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
<=> ( ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ) ),
inference(monotonicity,[status(thm)],[60]) ).
tff(62,plain,
( ( ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
<=> ( isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) )
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)) ) ),
inference(transitivity,[status(thm)],[61,59]) ).
tff(63,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
| isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) )
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)) ) ),
inference(monotonicity,[status(thm)],[62]) ).
tff(64,plain,
( ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
<=> ( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
| isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) )
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)) ) ),
inference(transitivity,[status(thm)],[63,58]) ).
tff(65,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [W1: $i] :
( ~ isCountable0(W1)
| isCountable0(sdtlcdtrc0(xe,W1))
| ~ aSubsetOf0(W1,szDzozmdt0(xe))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ) )
| isCountable0(sdtlcdtrc0(xe,sdtlbdtrb0(xd,szDzizrdt0(xd))))
| ~ isCountable0(sdtlbdtrb0(xd,szDzizrdt0(xd)))
| ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) )
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
( ~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) )
| ~ aSubsetOf0(sdtlbdtrb0(xd,szDzizrdt0(xd)),szDzozmdt0(xe)) ),
inference(unit_resolution,[status(thm)],[66,57,53,48]) ).
tff(68,plain,
~ ( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ),
inference(unit_resolution,[status(thm)],[67,19]) ).
tff(69,plain,
( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe))
| aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)) ),
inference(tautology,[status(thm)],]) ).
tff(70,plain,
aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe)),
inference(unit_resolution,[status(thm)],[69,68]) ).
tff(71,plain,
aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[70,10]) ).
tff(72,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(75,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[74]) ).
tff(76,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
^ [W0: $i] :
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) )),
inference(bind,[status(th)],]) ).
tff(78,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ) ),
inference(quant_intro,[status(thm)],[77]) ).
tff(79,plain,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(and_elim,[status(thm)],[3]) ).
tff(80,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[79,78]) ).
tff(81,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[80,76]) ).
tff(82,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[81,75]) ).
tff(83,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(skolemize,[status(sab)],[82]) ).
tff(84,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) ),
inference(modus_ponens,[status(thm)],[83,73]) ).
tff(85,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(86,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(87,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ),
inference(modus_ponens,[status(thm)],[86,85]) ).
tff(88,plain,
( ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ),
inference(unit_resolution,[status(thm)],[87,84]) ).
tff(89,plain,
sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))),
inference(unit_resolution,[status(thm)],[88,71]) ).
tff(90,plain,
( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe))
| ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) = sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) ) ),
inference(tautology,[status(thm)],]) ).
tff(91,plain,
sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) = sdtlpdtrp0(xe,tptp_fun_W3_17(xe)),
inference(unit_resolution,[status(thm)],[90,68]) ).
tff(92,plain,
( aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN))
<=> aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe)) ),
inference(monotonicity,[status(thm)],[8]) ).
tff(93,plain,
( aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
<=> aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN)) ),
inference(symmetry,[status(thm)],[92]) ).
tff(94,plain,
( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe))
| aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe)) ),
inference(tautology,[status(thm)],]) ).
tff(95,plain,
aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe)),
inference(unit_resolution,[status(thm)],[94,68]) ).
tff(96,plain,
aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[95,93]) ).
tff(97,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(99,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,W0) = szmzizndt0(sdtlpdtrp0(xN,W0)) ) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) ) ),
inference(modus_ponens,[status(thm)],[98,97]) ).
tff(100,plain,
( ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN))
| ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) ) ),
inference(unit_resolution,[status(thm)],[99,84]) ).
tff(101,plain,
sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))),
inference(unit_resolution,[status(thm)],[100,96]) ).
tff(102,plain,
szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) = sdtlpdtrp0(xe,tptp_fun_W2_18(xe)),
inference(symmetry,[status(thm)],[101]) ).
tff(103,plain,
szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) = szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))),
inference(transitivity,[status(thm)],[102,91,89]) ).
tff(104,plain,
( ( sdtlpdtrp0(xe,tptp_fun_W2_18(xe)) != sdtlpdtrp0(xe,tptp_fun_W3_17(xe)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xe))
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xe))
| ( tptp_fun_W2_18(xe) != tptp_fun_W3_17(xe) ) ),
inference(tautology,[status(thm)],]) ).
tff(105,plain,
tptp_fun_W2_18(xe) != tptp_fun_W3_17(xe),
inference(unit_resolution,[status(thm)],[104,68]) ).
tff(106,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
inference(bind,[status(th)],]) ).
tff(107,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN))
& ( W0 != W1 ) )
<=> ~ ( ( W0 = W1 )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN))
& ( W0 != W1 ) )
<=> ~ ~ ( ( W0 = W1 )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ~ ~ ( ( W0 = W1 )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN))
& ( W0 != W1 ) )
<=> ( ( W0 = W1 )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN))
& ( W0 != W1 ) ) )
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ( W0 = W1 )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ( W0 = W1 )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN))
& ( W0 != W1 ) ) )
<=> ( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
inference(bind,[status(th)],]) ).
tff(109,plain,
( ! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN))
& ( W0 != W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) ),
inference(quant_intro,[status(thm)],[108]) ).
tff(110,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) )
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN))
& ( W0 != W1 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(111,plain,
( ! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN))
& ( W0 != W1 ) ) ) ),
inference(quant_intro,[status(thm)],[110]) ).
tff(112,plain,
( ! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(113,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
<=> ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
=> ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ) )
<=> ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
=> ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ) ) )),
rewrite(
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
=> ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ) )
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
=> ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ) )
<=> ( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(114,plain,
( ! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
=> ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) ) ),
inference(quant_intro,[status(thm)],[113]) ).
tff(115,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) )
=> ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3821) ).
tff(116,plain,
! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) ),
inference(modus_ponens,[status(thm)],[115,114]) ).
tff(117,plain,
! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0)
& ( W0 != W1 ) ) ),
inference(modus_ponens,[status(thm)],[116,112]) ).
tff(118,plain,
! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN))
& ( W0 != W1 ) ) ),
inference(modus_ponens,[status(thm)],[117,111]) ).
tff(119,plain,
! [W0: $i,W1: $i] :
( ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN))
& ( W0 != W1 ) ) ),
inference(skolemize,[status(sab)],[118]) ).
tff(120,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[119,109]) ).
tff(121,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[120,107]) ).
tff(122,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN))
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN))
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(123,plain,
( ( ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN)) )
<=> ( ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN))
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(124,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN))
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ) ),
inference(monotonicity,[status(thm)],[123]) ).
tff(125,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN))
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ) ),
inference(transitivity,[status(thm)],[124,122]) ).
tff(126,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN)) ),
inference(quant_inst,[status(thm)],]) ).
tff(127,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szmzizndt0(sdtlpdtrp0(xN,W0)) != szmzizndt0(sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( tptp_fun_W2_18(xe) = tptp_fun_W3_17(xe) )
| ~ aElementOf0(tptp_fun_W3_17(xe),szDzozmdt0(xN))
| ~ aElementOf0(tptp_fun_W2_18(xe),szDzozmdt0(xN))
| ( szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W2_18(xe))) != szmzizndt0(sdtlpdtrp0(xN,tptp_fun_W3_17(xe))) ) ),
inference(modus_ponens,[status(thm)],[126,125]) ).
tff(128,plain,
$false,
inference(unit_resolution,[status(thm)],[127,121,105,71,96,103]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : NUM599+1 : TPTP v8.1.0. Released v4.0.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n013.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Fri Sep 2 12:10:02 EDT 2022
% 0.12/0.34 % CPUTime :
% 0.12/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.35 Usage: tptp [options] [-file:]file
% 0.12/0.35 -h, -? prints this message.
% 0.12/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.35 -m, -model generate model.
% 0.12/0.35 -p, -proof generate proof.
% 0.12/0.35 -c, -core generate unsat core of named formulas.
% 0.12/0.35 -st, -statistics display statistics.
% 0.12/0.35 -t:timeout set timeout (in second).
% 0.12/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.35 -<param>:<value> configuration parameter and value.
% 0.12/0.35 -o:<output-file> file to place output in.
% 77.62/49.45 % SZS status Theorem
% 77.62/49.45 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------