TSTP Solution File: NUM576+3 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM576+3 : TPTP v8.1.0. Released v4.0.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n003.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 13:10:37 EDT 2022
% Result : Theorem 0.19s 0.56s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 39
% Syntax : Number of formulae : 84 ( 23 unt; 8 typ; 0 def)
% Number of atoms : 689 ( 65 equ)
% Maximal formula atoms : 20 ( 9 avg)
% Number of connectives : 924 ( 369 ~; 386 |; 90 &)
% ( 63 <=>; 16 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 58 ( 58 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 6 ( 4 >; 2 *; 0 +; 0 <<)
% Number of predicates : 9 ( 7 usr; 1 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-1 aty)
% Number of variables : 132 ( 116 !; 0 ?; 132 :)
% Comments :
%------------------------------------------------------------------------------
tff(sdtlseqdt0_type,type,
sdtlseqdt0: ( $i * $i ) > $o ).
tff(xi_type,type,
xi: $i ).
tff(xj_type,type,
xj: $i ).
tff(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(aElementOf0_type,type,
aElementOf0: ( $i * $i ) > $o ).
tff(szDzozmdt0_type,type,
szDzozmdt0: $i > $i ).
tff(xN_type,type,
xN: $i ).
tff(szNzAzT0_type,type,
szNzAzT0: $i ).
tff(1,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xi),xj)
<=> ~ sdtlseqdt0(szszuzczcdt0(xi),xj) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ ( ( xi != xj )
=> ( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ) )
<=> ~ ( ( xi = xj )
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ ( ( xi != xj )
=> ( sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__) ).
tff(4,plain,
~ ( ( xi = xj )
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
~ sdtlseqdt0(szszuzczcdt0(xi),xj),
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
~ sdtlseqdt0(szszuzczcdt0(xi),xj),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( aElementOf0(xj,szNzAzT0)
<=> aElementOf0(xj,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(8,plain,
( aElementOf0(xj,szNzAzT0)
<=> aElementOf0(xj,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(9,axiom,
( aElementOf0(xi,szNzAzT0)
& aElementOf0(xj,szNzAzT0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',m__3856) ).
tff(10,plain,
aElementOf0(xj,szNzAzT0),
inference(and_elim,[status(thm)],[9]) ).
tff(11,plain,
aElementOf0(xj,szNzAzT0),
inference(modus_ponens,[status(thm)],[10,8]) ).
tff(12,plain,
aElementOf0(xj,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[11,7]) ).
tff(13,plain,
( aElementOf0(xi,szNzAzT0)
<=> aElementOf0(xi,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( aElementOf0(xi,szNzAzT0)
<=> aElementOf0(xi,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
aElementOf0(xi,szNzAzT0),
inference(and_elim,[status(thm)],[9]) ).
tff(16,plain,
aElementOf0(xi,szNzAzT0),
inference(modus_ponens,[status(thm)],[15,14]) ).
tff(17,plain,
aElementOf0(xi,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[16,13]) ).
tff(18,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(19,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)],[18]) ).
tff(20,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(21,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)],[20]) ).
tff(22,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(23,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)],[22]) ).
tff(24,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(25,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(26,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)],[25]) ).
tff(27,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessTotal) ).
tff(28,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[27,26]) ).
tff(29,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[28,24]) ).
tff(30,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)],[29,23]) ).
tff(31,plain,
! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(skolemize,[status(sab)],[30]) ).
tff(32,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)],[31,21]) ).
tff(33,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)],[32,19]) ).
tff(34,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| sdtlseqdt0(xj,xi) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| sdtlseqdt0(xj,xi) ) ),
inference(rewrite,[status(thm)],]) ).
tff(35,plain,
( ( sdtlseqdt0(xj,xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN)) )
<=> ( sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| sdtlseqdt0(xj,xi) ) ),
inference(rewrite,[status(thm)],]) ).
tff(36,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(xj,xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| sdtlseqdt0(xj,xi) ) ),
inference(monotonicity,[status(thm)],[35]) ).
tff(37,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(xj,xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| sdtlseqdt0(xj,xi) ) ),
inference(transitivity,[status(thm)],[36,34]) ).
tff(38,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(xj,xi)
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN)) ),
inference(quant_inst,[status(thm)],]) ).
tff(39,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xi),xj)
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| sdtlseqdt0(xj,xi) ),
inference(modus_ponens,[status(thm)],[38,37]) ).
tff(40,plain,
sdtlseqdt0(xj,xi),
inference(unit_resolution,[status(thm)],[39,33,17,12,6]) ).
tff(41,plain,
( ~ sdtlseqdt0(szszuzczcdt0(xj),xi)
<=> ~ sdtlseqdt0(szszuzczcdt0(xj),xi) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
~ sdtlseqdt0(szszuzczcdt0(xj),xi),
inference(or_elim,[status(thm)],[4]) ).
tff(43,plain,
~ sdtlseqdt0(szszuzczcdt0(xj),xi),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| sdtlseqdt0(xi,xj) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| sdtlseqdt0(xi,xj) ) ),
inference(rewrite,[status(thm)],]) ).
tff(45,plain,
( ( sdtlseqdt0(xi,xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xj,szDzozmdt0(xN))
| ~ aElementOf0(xi,szDzozmdt0(xN)) )
<=> ( sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| sdtlseqdt0(xi,xj) ) ),
inference(rewrite,[status(thm)],]) ).
tff(46,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(xi,xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xj,szDzozmdt0(xN))
| ~ aElementOf0(xi,szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| sdtlseqdt0(xi,xj) ) ),
inference(monotonicity,[status(thm)],[45]) ).
tff(47,plain,
( ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(xi,xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xj,szDzozmdt0(xN))
| ~ aElementOf0(xi,szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| sdtlseqdt0(xi,xj) ) ),
inference(transitivity,[status(thm)],[46,44]) ).
tff(48,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(xi,xj)
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xj,szDzozmdt0(xN))
| ~ aElementOf0(xi,szDzozmdt0(xN)) ),
inference(quant_inst,[status(thm)],]) ).
tff(49,plain,
( ~ ! [W0: $i,W1: $i] :
( sdtlseqdt0(W0,W1)
| sdtlseqdt0(szszuzczcdt0(W1),W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| sdtlseqdt0(szszuzczcdt0(xj),xi)
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| sdtlseqdt0(xi,xj) ),
inference(modus_ponens,[status(thm)],[48,47]) ).
tff(50,plain,
sdtlseqdt0(xi,xj),
inference(unit_resolution,[status(thm)],[49,33,17,12,43]) ).
tff(51,plain,
( ( xi != xj )
<=> ( xi != xj ) ),
inference(rewrite,[status(thm)],]) ).
tff(52,plain,
xi != xj,
inference(or_elim,[status(thm)],[4]) ).
tff(53,plain,
xi != xj,
inference(modus_ponens,[status(thm)],[52,51]) ).
tff(54,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) )
<=> ( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],]) ).
tff(55,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[54]) ).
tff(56,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ~ ( ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ~ ~ ( ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) ) )),
rewrite(
( ~ ~ ( ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1) ) )),
( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
<=> ( ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,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)) ) )),
( ( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ sdtlseqdt0(W0,W1)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) ) )),
( ( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) ) )),
inference(bind,[status(th)],]) ).
tff(57,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) ) ),
inference(quant_intro,[status(thm)],[56]) ).
tff(58,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )),
( ( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ( ( W0 = W1 )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) )),
rewrite(
( ( ( W0 = W1 )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
( ( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
inference(bind,[status(th)],]) ).
tff(59,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
inference(quant_intro,[status(thm)],[58]) ).
tff(60,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(61,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) )
<=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) ) )),
rewrite(
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) )),
inference(bind,[status(th)],]) ).
tff(62,plain,
( ! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ) ),
inference(quant_intro,[status(thm)],[61]) ).
tff(63,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',mLessASymm) ).
tff(64,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[63,62]) ).
tff(65,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) ) ),
inference(modus_ponens,[status(thm)],[64,60]) ).
tff(66,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(modus_ponens,[status(thm)],[65,59]) ).
tff(67,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ ( sdtlseqdt0(W0,W1)
& sdtlseqdt0(W1,W0) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(skolemize,[status(sab)],[66]) ).
tff(68,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[67,57]) ).
tff(69,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) ),
inference(modus_ponens,[status(thm)],[68,55]) ).
tff(70,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) )
| ( xi = xj )
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| ~ sdtlseqdt0(xi,xj)
| ~ sdtlseqdt0(xj,xi) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) )
| ( xi = xj )
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| ~ sdtlseqdt0(xi,xj)
| ~ sdtlseqdt0(xj,xi) ) ),
inference(rewrite,[status(thm)],]) ).
tff(71,plain,
( ( ( xi = xj )
| ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(xj,szDzozmdt0(xN))
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ sdtlseqdt0(xi,xj) )
<=> ( ( xi = xj )
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| ~ sdtlseqdt0(xi,xj)
| ~ sdtlseqdt0(xj,xi) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) )
| ( xi = xj )
| ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(xj,szDzozmdt0(xN))
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ sdtlseqdt0(xi,xj) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) )
| ( xi = xj )
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| ~ sdtlseqdt0(xi,xj)
| ~ sdtlseqdt0(xj,xi) ) ),
inference(monotonicity,[status(thm)],[71]) ).
tff(73,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) )
| ( xi = xj )
| ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(xj,szDzozmdt0(xN))
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ sdtlseqdt0(xi,xj) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) )
| ( xi = xj )
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| ~ sdtlseqdt0(xi,xj)
| ~ sdtlseqdt0(xj,xi) ) ),
inference(transitivity,[status(thm)],[72,70]) ).
tff(74,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) )
| ( xi = xj )
| ~ sdtlseqdt0(xj,xi)
| ~ aElementOf0(xj,szDzozmdt0(xN))
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ sdtlseqdt0(xi,xj) ),
inference(quant_inst,[status(thm)],]) ).
tff(75,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ~ sdtlseqdt0(W1,W0)
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN))
| ~ sdtlseqdt0(W0,W1) )
| ( xi = xj )
| ~ aElementOf0(xi,szDzozmdt0(xN))
| ~ aElementOf0(xj,szDzozmdt0(xN))
| ~ sdtlseqdt0(xi,xj)
| ~ sdtlseqdt0(xj,xi) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
$false,
inference(unit_resolution,[status(thm)],[75,69,17,12,53,50,40]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12 % Problem : NUM576+3 : TPTP v8.1.0. Released v4.0.0.
% 0.08/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n003.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 11:58:24 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.
% 0.19/0.56 % SZS status Theorem
% 0.19/0.56 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------