TSTP Solution File: NUM613+1 by Z3---4.8.9.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : NUM613+1 : 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 13:10:54 EDT 2022
% Result : Theorem 0.17s 0.44s
% Output : Proof 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 33
% Syntax : Number of formulae : 60 ( 18 unt; 12 typ; 0 def)
% Number of atoms : 299 ( 136 equ)
% Maximal formula atoms : 16 ( 6 avg)
% Number of connectives : 387 ( 164 ~; 143 |; 35 &)
% ( 34 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of FOOLs : 28 ( 28 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 8 ( 6 >; 2 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-3 aty)
% Number of functors : 11 ( 11 usr; 6 con; 0-2 aty)
% Number of variables : 58 ( 50 !; 0 ?; 58 :)
% Comments :
%------------------------------------------------------------------------------
tff(xk_type,type,
xk: $i ).
tff(sbrdtbr0_type,type,
sbrdtbr0: $i > $i ).
tff(sdtmndt0_type,type,
sdtmndt0: ( $i * $i ) > $i ).
tff(szmzizndt0_type,type,
szmzizndt0: $i > $i ).
tff(xQ_type,type,
xQ: $i ).
tff(xP_type,type,
xP: $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(szszuzczcdt0_type,type,
szszuzczcdt0: $i > $i ).
tff(xK_type,type,
xK: $i ).
tff(1,plain,
( ( sbrdtbr0(xP) != xk )
<=> ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ( sbrdtbr0(xP) != xk )
<=> ( sbrdtbr0(xP) != xk ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
sbrdtbr0(xP) != xk,
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__) ).
tff(4,plain,
sbrdtbr0(xP) != xk,
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) != xk,
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
<=> aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(7,plain,
( aElementOf0(sbrdtbr0(xP),szNzAzT0)
<=> aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(8,axiom,
( ( sbrdtbr0(xQ) = szszuzczcdt0(xk) )
& ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
& aElementOf0(sbrdtbr0(xP),szNzAzT0) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__5255) ).
tff(9,plain,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(and_elim,[status(thm)],[8]) ).
tff(10,plain,
aElementOf0(sbrdtbr0(xP),szNzAzT0),
inference(modus_ponens,[status(thm)],[9,7]) ).
tff(11,plain,
aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[10,6]) ).
tff(12,plain,
( ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) )
<=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = szszuzczcdt0(xk) ) ),
inference(rewrite,[status(thm)],]) ).
tff(13,plain,
( ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
<=> ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) )
<=> ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(15,plain,
( ( sbrdtbr0(xQ) = szszuzczcdt0(xk) )
& ( szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ) ) ),
inference(and_elim,[status(thm)],[8]) ).
tff(16,plain,
szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ),
inference(and_elim,[status(thm)],[15]) ).
tff(17,plain,
szszuzczcdt0(sbrdtbr0(xP)) = sbrdtbr0(xQ),
inference(modus_ponens,[status(thm)],[16,14]) ).
tff(18,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = sbrdtbr0(xQ),
inference(modus_ponens,[status(thm)],[17,13]) ).
tff(19,plain,
szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) = szszuzczcdt0(xk),
inference(modus_ponens,[status(thm)],[18,12]) ).
tff(20,plain,
( aElementOf0(xk,szNzAzT0)
<=> aElementOf0(xk,szDzozmdt0(xN)) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( aElementOf0(xk,szNzAzT0)
<=> aElementOf0(xk,szNzAzT0) ),
inference(rewrite,[status(thm)],]) ).
tff(22,axiom,
( aElementOf0(xk,szNzAzT0)
& ( szszuzczcdt0(xk) = xK ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',m__3533) ).
tff(23,plain,
aElementOf0(xk,szNzAzT0),
inference(and_elim,[status(thm)],[22]) ).
tff(24,plain,
aElementOf0(xk,szNzAzT0),
inference(modus_ponens,[status(thm)],[23,21]) ).
tff(25,plain,
aElementOf0(xk,szDzozmdt0(xN)),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
^ [W0: $i,W1: $i] :
refl(
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,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)) ) )),
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
rewrite(
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) )),
inference(bind,[status(th)],]) ).
tff(29,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ) ),
inference(quant_intro,[status(thm)],[28]) ).
tff(30,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
<=> ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )),
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
rewrite(
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
( ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
^ [W0: $i,W1: $i] :
trans(
monotonicity(
rewrite(
( ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) )
<=> ( ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ( W0 = W1 ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) )
<=> ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ( W0 = W1 ) ) ) )),
rewrite(
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ) )),
( ( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) )
<=> ( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) )
<=> ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [W0: $i,W1: $i] :
( ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) )
=> ( ( szszuzczcdt0(W0) = szszuzczcdt0(W1) )
=> ( W0 = W1 ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',mSuccEquSucc) ).
tff(36,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szNzAzT0)
& aElementOf0(W1,szNzAzT0) ) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(modus_ponens,[status(thm)],[37,31]) ).
tff(39,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ ( aElementOf0(W0,szDzozmdt0(xN))
& aElementOf0(W1,szDzozmdt0(xN)) ) ),
inference(skolemize,[status(sab)],[38]) ).
tff(40,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[39,29]) ).
tff(41,plain,
! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) ),
inference(modus_ponens,[status(thm)],[40,27]) ).
tff(42,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = xk )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) != szszuzczcdt0(xk) ) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = xk )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) != szszuzczcdt0(xk) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = xk )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) != szszuzczcdt0(xk) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) )
<=> ( ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = xk )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) != szszuzczcdt0(xk) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(44,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = xk )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) != szszuzczcdt0(xk) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = xk )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) != szszuzczcdt0(xk) ) ) ),
inference(monotonicity,[status(thm)],[43]) ).
tff(45,plain,
( ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = xk )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) != szszuzczcdt0(xk) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) )
<=> ( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = xk )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) != szszuzczcdt0(xk) ) ) ),
inference(transitivity,[status(thm)],[44,42]) ).
tff(46,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = xk )
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) != szszuzczcdt0(xk) )
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN)) ),
inference(quant_inst,[status(thm)],]) ).
tff(47,plain,
( ~ ! [W0: $i,W1: $i] :
( ( W0 = W1 )
| ( szszuzczcdt0(W0) != szszuzczcdt0(W1) )
| ~ aElementOf0(W1,szDzozmdt0(xN))
| ~ aElementOf0(W0,szDzozmdt0(xN)) )
| ( sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))) = xk )
| ~ aElementOf0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ))),szDzozmdt0(xN))
| ~ aElementOf0(xk,szDzozmdt0(xN))
| ( szszuzczcdt0(sbrdtbr0(sdtmndt0(xQ,szmzizndt0(xQ)))) != szszuzczcdt0(xk) ) ),
inference(modus_ponens,[status(thm)],[46,45]) ).
tff(48,plain,
$false,
inference(unit_resolution,[status(thm)],[47,41,25,19,11,5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.11 % Problem : NUM613+1 : TPTP v8.1.0. Released v4.0.0.
% 0.10/0.11 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.11/0.31 % Computer : n003.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Fri Sep 2 12:21:24 EDT 2022
% 0.11/0.32 % CPUTime :
% 0.11/0.32 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.11/0.32 Usage: tptp [options] [-file:]file
% 0.11/0.32 -h, -? prints this message.
% 0.11/0.32 -smt2 print SMT-LIB2 benchmark.
% 0.11/0.32 -m, -model generate model.
% 0.11/0.32 -p, -proof generate proof.
% 0.11/0.32 -c, -core generate unsat core of named formulas.
% 0.11/0.32 -st, -statistics display statistics.
% 0.11/0.32 -t:timeout set timeout (in second).
% 0.11/0.32 -smt2status display status in smt2 format instead of SZS.
% 0.11/0.32 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.11/0.32 -<param>:<value> configuration parameter and value.
% 0.11/0.32 -o:<output-file> file to place output in.
% 0.17/0.44 % SZS status Theorem
% 0.17/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------