TSTP Solution File: NUM627+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM627+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 18 13:11:00 EDT 2022
% Result : Theorem 1.10s 0.95s
% Output : Proof 1.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 59
% Syntax : Number of formulae : 120 ( 28 unt; 17 typ; 0 def)
% Number of atoms : 878 ( 41 equ)
% Maximal formula atoms : 24 ( 8 avg)
% Number of connectives : 1296 ( 587 ~; 486 |; 123 &)
% ( 71 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 66 ( 66 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 13 ( 8 >; 5 *; 0 +; 0 <<)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 14 ( 14 usr; 9 con; 0-2 aty)
% Number of variables : 241 ( 217 !; 0 ?; 241 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xn_type,type,
xn: $i ).
tff(xm_type,type,
xm: $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(sdtlpdtrp0_type,type,
sdtlpdtrp0: ( $i * $i ) > $i ).
tff(xN_type,type,
xN: $i ).
tff(aSubsetOf0_type,type,
aSubsetOf0: ( $i * $i ) > $o ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(xe_type,type,
xe: $i ).
tff(xx_type,type,
xx: $i ).
tff(xd_type,type,
xd: $i ).
tff(szDzizrdt0_type,type,
szDzizrdt0: $i > $i ).
tff(sdtlbdtrb0_type,type,
sdtlbdtrb0: ( $i * $i ) > $i ).
tff(xp_type,type,
xp: $i ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(sz00_type,type,
sz00: $i ).
tff(1,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
<=> ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,axiom,
~ ( ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xn))
=> aElementOf0(W0,sdtlpdtrp0(xN,xm)) )
| aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5461) ).
tff(3,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
inference(or_elim,[status(thm)],[2]) ).
tff(4,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)),
inference(modus_ponens,[status(thm)],[3,1]) ).
tff(5,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) )
| aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm)) ),
inference(tautology,[status(thm)],]) ).
tff(6,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ),
inference(unit_resolution,[status(thm)],[5,4]) ).
tff(7,plain,
( aElementOf0(xm,szNzAzT0)
<=> aElementOf0(xm,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
( aElementOf0(xm,szNzAzT0)
<=> aElementOf0(xm,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
( aElementOf0(xm,szNzAzT0)
& ( xx = sdtlpdtrp0(xe,xm) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5389) ).
tff(10,plain,
aElementOf0(xm,szNzAzT0),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
aElementOf0(xm,szNzAzT0),
inference(modus_ponens,[status(thm)],[10,8]) ).
tff(12,plain,
aElementOf0(xm,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
( aElementOf0(xn,szDzozmdt0(xd))
<=> aElementOf0(xn,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( aElementOf0(xn,szDzozmdt0(xd))
<=> aElementOf0(xn,szDzozmdt0(xd)) ),
inference(rewrite,[status(thm)],]) ).
tff(15,axiom,
( aElementOf0(xn,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0)
& ( sdtlpdtrp0(xe,xn) = xp ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5309) ).
tff(16,plain,
( aElementOf0(xn,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd)))
& aElementOf0(xn,szNzAzT0) ),
inference(and_elim,[status(thm)],[15]) ).
tff(17,plain,
( aElementOf0(xn,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) )
& aElementOf0(xn,sdtlbdtrb0(xd,szDzizrdt0(xd))) ),
inference(and_elim,[status(thm)],[16]) ).
tff(18,plain,
( aElementOf0(xn,szDzozmdt0(xd))
& ( sdtlpdtrp0(xd,xn) = szDzizrdt0(xd) ) ),
inference(and_elim,[status(thm)],[17]) ).
tff(19,plain,
aElementOf0(xn,szDzozmdt0(xd)),
inference(and_elim,[status(thm)],[18]) ).
tff(20,plain,
aElementOf0(xn,szDzozmdt0(xd)),
inference(modus_ponens,[status(thm)],[19,14]) ).
tff(21,plain,
aElementOf0(xn,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[20,13]) ).
tff(22,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) ) )),
inference(bind,[status(th)],]) ).
tff(23,plain,
( ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) ) ),
inference(quant_intro,[status(thm)],[22]) ).
tff(24,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ),
inference(transitivity,[status(thm)],[27,25]) ).
tff(29,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
<=> ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )),
trans(
monotonicity(
rewrite(
( ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ~ ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ~ ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ( ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ( ~ sdtlseqdt0(W1,W0)
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
( ( ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
inference(bind,[status(th)],]) ).
tff(30,plain,
( ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ),
inference(quant_intro,[status(thm)],[29]) ).
tff(31,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )),
rewrite(
( ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
<=> ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )),
( ( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
rewrite(
( ( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
( ( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
inference(bind,[status(th)],]) ).
tff(32,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
inference(quant_intro,[status(thm)],[31]) ).
tff(33,plain,
( ! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(34,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
<=> ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )),
( ( sdtlseqdt0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( sdtlseqdt0(W1,W0)
=> ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
rewrite(
( ( sdtlseqdt0(W1,W0)
=> ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
( ( sdtlseqdt0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )
<=> ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ) )),
rewrite(
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )
<=> ( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )
<=> ( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )),
inference(bind,[status(th)],]) ).
tff(35,plain,
( ! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) )
<=> ! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ),
inference(quant_intro,[status(thm)],[34]) ).
tff(36,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W1,W0)
=> ( ! [W2: $i] :
( aElementOf0(W2,sdtlpdtrp0(xN,W0))
=> aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3754) ).
tff(37,plain,
! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ),
inference(modus_ponens,[status(thm)],[36,35]) ).
tff(38,plain,
! [W0: $i,W1: $i] :
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ),
inference(modus_ponens,[status(thm)],[37,33]) ).
tff(39,plain,
! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(modus_ponens,[status(thm)],[38,32]) ).
tff(40,plain,
! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ( ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
& aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(skolemize,[status(sab)],[39]) ).
tff(41,plain,
! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ),
inference(modus_ponens,[status(thm)],[40,30]) ).
tff(42,plain,
! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) )
| ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1)) ) ),
inference(modus_ponens,[status(thm)],[41,28]) ).
tff(43,plain,
! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) ),
inference(modus_ponens,[status(thm)],[42,23]) ).
tff(44,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ sdtlseqdt0(xm,xn)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xn),sdtlpdtrp0(xN,xm))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xn))
| aElementOf0(W2,sdtlpdtrp0(xN,xm)) ) ) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
~ sdtlseqdt0(xm,xn),
inference(unit_resolution,[status(thm)],[46,43,21,12,6]) ).
tff(48,plain,
^ [W0: $i] :
refl(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(51,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[50]) ).
tff(52,plain,
^ [W0: $i] :
rewrite(
( ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(53,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[52]) ).
tff(54,plain,
( ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(55,plain,
^ [W0: $i] :
rewrite(
( ( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ) )),
inference(bind,[status(th)],]) ).
tff(56,plain,
( ! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) )
<=> ! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ) ),
inference(quant_intro,[status(thm)],[55]) ).
tff(57,axiom,
! [W0: $i] :
( aElementOf0(W0,szNzAzT0)
=> ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccNum) ).
tff(58,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[57,56]) ).
tff(59,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szNzAzT0)
| ( aElementOf0(szszuzczcdt0(W0),szNzAzT0)
& ( szszuzczcdt0(W0) != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[58,54]) ).
tff(60,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) ),
inference(modus_ponens,[status(thm)],[59,53]) ).
tff(61,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ( aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
& ( szszuzczcdt0(W0) != sz00 ) ) ),
inference(skolemize,[status(sab)],[60]) ).
tff(62,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ),
inference(modus_ponens,[status(thm)],[61,51]) ).
tff(63,plain,
! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) ),
inference(modus_ponens,[status(thm)],[62,49]) ).
tff(64,plain,
( ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 ) ) )
<=> ( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(65,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(66,plain,
( ~ ! [W0: $i] :
( ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(W0),szDzozmdt0(xN))
| ( szszuzczcdt0(W0) = sz00 ) ) )
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 ) ) ),
inference(modus_ponens,[status(thm)],[65,64]) ).
tff(67,plain,
~ ( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 ) ),
inference(unit_resolution,[status(thm)],[66,63,21]) ).
tff(68,plain,
( ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ( szszuzczcdt0(xn) = sz00 )
| aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN)) ),
inference(tautology,[status(thm)],]) ).
tff(69,plain,
aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN)),
inference(unit_resolution,[status(thm)],[68,67]) ).
tff(70,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
<=> ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(rewrite,[status(thm)],]) ).
tff(71,axiom,
~ ( ! [W0: $i] :
( aElementOf0(W0,sdtlpdtrp0(xN,xm))
=> aElementOf0(W0,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
| aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5442) ).
tff(72,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(or_elim,[status(thm)],[71]) ).
tff(73,plain,
~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))),
inference(modus_ponens,[status(thm)],[72,70]) ).
tff(74,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) )
| aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn))) ),
inference(tautology,[status(thm)],]) ).
tff(75,plain,
( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ),
inference(unit_resolution,[status(thm)],[74,73]) ).
tff(76,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(77,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(78,plain,
( ~ ! [W0: $i,W1: $i] :
( ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,W0),sdtlpdtrp0(xN,W1))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,W0))
| aElementOf0(W2,sdtlpdtrp0(xN,W1)) ) ) )
| ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN))
| ~ aElementOf0(xm,szDzozmdt0(xN))
| ~ ( ~ aSubsetOf0(sdtlpdtrp0(xN,xm),sdtlpdtrp0(xN,szszuzczcdt0(xn)))
| ~ ! [W2: $i] :
( ~ aElementOf0(W2,sdtlpdtrp0(xN,xm))
| aElementOf0(W2,sdtlpdtrp0(xN,szszuzczcdt0(xn))) ) ) ),
inference(modus_ponens,[status(thm)],[77,76]) ).
tff(79,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(szszuzczcdt0(xn),szDzozmdt0(xN)) ),
inference(unit_resolution,[status(thm)],[78,43,12,75]) ).
tff(80,plain,
~ sdtlseqdt0(szszuzczcdt0(xn),xm),
inference(unit_resolution,[status(thm)],[79,69]) ).
tff(81,plain,
^ [W0: $i,W1: $i] :
refl(
( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
inference(bind,[status(th)],]) ).
tff(82,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) ),
inference(quant_intro,[status(thm)],[81]) ).
tff(83,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ~ ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ~ ~ ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
<=> ( ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
inference(bind,[status(th)],]) ).
tff(84,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) ),
inference(quant_intro,[status(thm)],[83]) ).
tff(85,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )),
( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
rewrite(
( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
( ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
inference(bind,[status(th)],]) ).
tff(86,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
inference(quant_intro,[status(thm)],[85]) ).
tff(87,plain,
( ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(88,plain,
^ [W0: $i,W1: $i] :
rewrite(
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0) ) )
<=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ) )),
inference(bind,[status(th)],]) ).
tff(89,plain,
( ! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0) ) )
<=> ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ) ),
inference(quant_intro,[status(thm)],[88]) ).
tff(90,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mLessTotal) ).
tff(91,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[90,89]) ).
tff(92,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[91,87]) ).
tff(93,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(modus_ponens,[status(thm)],[92,86]) ).
tff(94,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(skolemize,[status(sab)],[93]) ).
tff(95,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[94,84]) ).
tff(96,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[95,82]) ).
tff(97,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(98,plain,
( ( sdtlseqdt0(xm,xn)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ aElementOf0(xm,szDzozmdt0(xN)) )
<=> ( sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(99,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(xm,xn)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ aElementOf0(xm,szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) ) ),
inference(monotonicity,[status(thm)],[98]) ).
tff(100,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(xm,xn)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ aElementOf0(xm,szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) ) ),
inference(transitivity,[status(thm)],[99,97]) ).
tff(101,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(xm,xn)
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xn,szDzozmdt0(xN))
| ~ aElementOf0(xm,szDzozmdt0(xN)) ),
inference(quant_inst,[status(thm)],]) ).
tff(102,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xn),xm)
| ~ aElementOf0(xm,szDzozmdt0(xN))
| sdtlseqdt0(xm,xn)
| ~ aElementOf0(xn,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[101,100]) ).
tff(103,plain,
$false,
inference(unit_resolution,[status(thm)],[102,96,21,12,80,47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.11 % Problem : NUM627+3 : TPTP v8.1.0. Released v4.0.0.
% 0.11/0.12 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.33 % Computer : n012.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Fri Sep 2 12:28:19 EDT 2022
% 0.12/0.33 % CPUTime :
% 0.12/0.34 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.34 Usage: tptp [options] [-file:]file
% 0.12/0.34 -h, -? prints this message.
% 0.12/0.34 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.34 -m, -model generate model.
% 0.12/0.34 -p, -proof generate proof.
% 0.12/0.34 -c, -core generate unsat core of named formulas.
% 0.12/0.34 -st, -statistics display statistics.
% 0.12/0.34 -t:timeout set timeout (in second).
% 0.12/0.34 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.34 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.34 -<param>:<value> configuration parameter and value.
% 0.12/0.34 -o:<output-file> file to place output in.
% 1.10/0.95 % SZS status Theorem
% 1.10/0.95 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------