TSTP Solution File: SWV050+1 by Z3---4.8.9.0
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%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV050+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n007.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 : Thu Sep 29 15:09:46 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 42
% Syntax : Number of formulae : 71 ( 30 unt; 23 typ; 0 def)
% Number of atoms : 91 ( 86 equ)
% Maximal formula atoms : 10 ( 1 avg)
% Number of connectives : 58 ( 19 ~; 5 |; 16 &)
% ( 16 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 2 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 4 ( 4 fml; 0 var)
% Number of types : 1 ( 0 usr)
% Number of type conns : 14 ( 8 >; 6 *; 0 +; 0 <<)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 23 ( 23 usr; 15 con; 0-3 aty)
% Number of variables : 37 ( 33 !; 0 ?; 37 :)
% Comments :
%------------------------------------------------------------------------------
tff(sum_type,type,
sum: ( $i * $i * $i ) > $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(plus_type,type,
plus: ( $i * $i ) > $i ).
tff(abs_type,type,
abs: $i > $i ).
tff(a_select2_type,type,
a_select2: ( $i * $i ) > $i ).
tff(pv91_type,type,
pv91: $i ).
tff(sigmaold_type,type,
sigmaold: $i ).
tff(sigma_type,type,
sigma: $i ).
tff(minus_type,type,
minus: ( $i * $i ) > $i ).
tff(succ_type,type,
succ: $i > $i ).
tff(tptp_minus_1_type,type,
tptp_minus_1: $i ).
tff(pred_type,type,
pred: $i > $i ).
tff(n1_type,type,
n1: $i ).
tff(n0_type,type,
n0: $i ).
tff(pv89_type,type,
pv89: $i ).
tff(rhoold_type,type,
rhoold: $i ).
tff(rho_type,type,
rho: $i ).
tff(n5_type,type,
n5: $i ).
tff(pv88_type,type,
pv88: $i ).
tff(pv87_type,type,
pv87: $i ).
tff(muold_type,type,
muold: $i ).
tff(mu_type,type,
mu: $i ).
tff(pv86_type,type,
pv86: $i ).
tff(1,plain,
( ! [X: $i] : ( pred(succ(X)) = X )
<=> ! [X: $i] : ( pred(succ(X)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ! [X: $i] : ( pred(succ(X)) = X )
<=> ! [X: $i] : ( pred(succ(X)) = X ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
! [X: $i] : ( pred(succ(X)) = X ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_succ) ).
tff(4,plain,
! [X: $i] : ( pred(succ(X)) = X ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
! [X: $i] : ( pred(succ(X)) = X ),
inference(skolemize,[status(sab)],[4]) ).
tff(6,plain,
! [X: $i] : ( pred(succ(X)) = X ),
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
( ~ ! [X: $i] : ( pred(succ(X)) = X )
| ( pred(succ(tptp_minus_1)) = tptp_minus_1 ) ),
inference(quant_inst,[status(thm)],]) ).
tff(8,plain,
pred(succ(tptp_minus_1)) = tptp_minus_1,
inference(unit_resolution,[status(thm)],[7,6]) ).
tff(9,plain,
^ [X: $i] :
refl(
( ( minus(X,succ(succ(tptp_minus_1))) = pred(X) )
<=> ( minus(X,succ(succ(tptp_minus_1))) = pred(X) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [X: $i] : ( minus(X,succ(succ(tptp_minus_1))) = pred(X) )
<=> ! [X: $i] : ( minus(X,succ(succ(tptp_minus_1))) = pred(X) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [X: $i] :
rewrite(
( ( minus(X,n1) = pred(X) )
<=> ( minus(X,succ(succ(tptp_minus_1))) = pred(X) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [X: $i] : ( minus(X,n1) = pred(X) )
<=> ! [X: $i] : ( minus(X,succ(succ(tptp_minus_1))) = pred(X) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [X: $i] : ( minus(X,n1) = pred(X) )
<=> ! [X: $i] : ( minus(X,n1) = pred(X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,axiom,
! [X: $i] : ( minus(X,n1) = pred(X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
tff(15,plain,
! [X: $i] : ( minus(X,n1) = pred(X) ),
inference(modus_ponens,[status(thm)],[14,13]) ).
tff(16,plain,
! [X: $i] : ( minus(X,succ(succ(tptp_minus_1))) = pred(X) ),
inference(modus_ponens,[status(thm)],[15,12]) ).
tff(17,plain,
! [X: $i] : ( minus(X,succ(succ(tptp_minus_1))) = pred(X) ),
inference(skolemize,[status(sab)],[16]) ).
tff(18,plain,
! [X: $i] : ( minus(X,succ(succ(tptp_minus_1))) = pred(X) ),
inference(modus_ponens,[status(thm)],[17,10]) ).
tff(19,plain,
( ~ ! [X: $i] : ( minus(X,succ(succ(tptp_minus_1))) = pred(X) )
| ( minus(succ(tptp_minus_1),succ(succ(tptp_minus_1))) = pred(succ(tptp_minus_1)) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(20,plain,
minus(succ(tptp_minus_1),succ(succ(tptp_minus_1))) = pred(succ(tptp_minus_1)),
inference(unit_resolution,[status(thm)],[19,18]) ).
tff(21,plain,
minus(succ(tptp_minus_1),succ(succ(tptp_minus_1))) = tptp_minus_1,
inference(transitivity,[status(thm)],[20,8]) ).
tff(22,plain,
sum(succ(tptp_minus_1),minus(succ(tptp_minus_1),succ(succ(tptp_minus_1))),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) = sum(succ(tptp_minus_1),tptp_minus_1,divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))),
inference(monotonicity,[status(thm)],[21]) ).
tff(23,plain,
sum(succ(tptp_minus_1),tptp_minus_1,divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) = sum(succ(tptp_minus_1),minus(succ(tptp_minus_1),succ(succ(tptp_minus_1))),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))),
inference(symmetry,[status(thm)],[22]) ).
tff(24,plain,
^ [Body: $i] :
refl(
( ( sum(succ(tptp_minus_1),tptp_minus_1,Body) = succ(tptp_minus_1) )
<=> ( sum(succ(tptp_minus_1),tptp_minus_1,Body) = succ(tptp_minus_1) ) )),
inference(bind,[status(th)],]) ).
tff(25,plain,
( ! [Body: $i] : ( sum(succ(tptp_minus_1),tptp_minus_1,Body) = succ(tptp_minus_1) )
<=> ! [Body: $i] : ( sum(succ(tptp_minus_1),tptp_minus_1,Body) = succ(tptp_minus_1) ) ),
inference(quant_intro,[status(thm)],[24]) ).
tff(26,plain,
^ [Body: $i] :
rewrite(
( ( sum(n0,tptp_minus_1,Body) = n0 )
<=> ( sum(succ(tptp_minus_1),tptp_minus_1,Body) = succ(tptp_minus_1) ) )),
inference(bind,[status(th)],]) ).
tff(27,plain,
( ! [Body: $i] : ( sum(n0,tptp_minus_1,Body) = n0 )
<=> ! [Body: $i] : ( sum(succ(tptp_minus_1),tptp_minus_1,Body) = succ(tptp_minus_1) ) ),
inference(quant_intro,[status(thm)],[26]) ).
tff(28,plain,
( ! [Body: $i] : ( sum(n0,tptp_minus_1,Body) = n0 )
<=> ! [Body: $i] : ( sum(n0,tptp_minus_1,Body) = n0 ) ),
inference(rewrite,[status(thm)],]) ).
tff(29,axiom,
! [Body: $i] : ( sum(n0,tptp_minus_1,Body) = n0 ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',sum_plus_base) ).
tff(30,plain,
! [Body: $i] : ( sum(n0,tptp_minus_1,Body) = n0 ),
inference(modus_ponens,[status(thm)],[29,28]) ).
tff(31,plain,
! [Body: $i] : ( sum(succ(tptp_minus_1),tptp_minus_1,Body) = succ(tptp_minus_1) ),
inference(modus_ponens,[status(thm)],[30,27]) ).
tff(32,plain,
! [Body: $i] : ( sum(succ(tptp_minus_1),tptp_minus_1,Body) = succ(tptp_minus_1) ),
inference(skolemize,[status(sab)],[31]) ).
tff(33,plain,
! [Body: $i] : ( sum(succ(tptp_minus_1),tptp_minus_1,Body) = succ(tptp_minus_1) ),
inference(modus_ponens,[status(thm)],[32,25]) ).
tff(34,plain,
( ~ ! [Body: $i] : ( sum(succ(tptp_minus_1),tptp_minus_1,Body) = succ(tptp_minus_1) )
| ( sum(succ(tptp_minus_1),tptp_minus_1,divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) = succ(tptp_minus_1) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(35,plain,
sum(succ(tptp_minus_1),tptp_minus_1,divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) = succ(tptp_minus_1),
inference(unit_resolution,[status(thm)],[34,33]) ).
tff(36,plain,
succ(tptp_minus_1) = sum(succ(tptp_minus_1),tptp_minus_1,divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))),
inference(symmetry,[status(thm)],[35]) ).
tff(37,plain,
succ(tptp_minus_1) = sum(succ(tptp_minus_1),minus(succ(tptp_minus_1),succ(succ(tptp_minus_1))),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))),
inference(transitivity,[status(thm)],[36,23]) ).
tff(38,plain,
( ( n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) )
<=> ( succ(tptp_minus_1) != sum(succ(tptp_minus_1),minus(succ(tptp_minus_1),succ(succ(tptp_minus_1))),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(39,plain,
( ( n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) )
<=> ( n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(40,plain,
( ~ ( ( n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) )
& ( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) )
& ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) )
<=> ( n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(41,plain,
( ~ ( ( ( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) )
& ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) )
=> ( ( n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) )
& ( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) )
& ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) ) )
<=> ~ ( ~ ( ( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) )
& ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) )
| ( ( n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) )
& ( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) )
& ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,axiom,
~ ( ( ( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) )
& ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) )
=> ( ( n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) )
& ( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) )
& ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0022) ).
tff(43,plain,
~ ( ~ ( ( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) )
& ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) )
| ( ( n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) )
& ( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) )
& ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) ) ),
inference(modus_ponens,[status(thm)],[42,41]) ).
tff(44,plain,
~ ( ( n0 = sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))) )
& ( pv86 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(mu,pv87),a_select2(muold,pv87))),plus(abs(a_select2(mu,pv87)),abs(a_select2(muold,pv87))))) )
& ( pv88 = sum(n0,minus(n5,n1),divide(abs(minus(a_select2(rho,pv89),a_select2(rhoold,pv89))),plus(abs(a_select2(rho,pv89)),abs(a_select2(rhoold,pv89))))) ) ),
inference(or_elim,[status(thm)],[43]) ).
tff(45,plain,
n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))),
inference(modus_ponens,[status(thm)],[44,40]) ).
tff(46,plain,
n0 != sum(n0,minus(n0,n1),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))),
inference(modus_ponens,[status(thm)],[45,39]) ).
tff(47,plain,
succ(tptp_minus_1) != sum(succ(tptp_minus_1),minus(succ(tptp_minus_1),succ(succ(tptp_minus_1))),divide(abs(minus(a_select2(sigma,pv91),a_select2(sigmaold,pv91))),plus(abs(a_select2(sigma,pv91)),abs(a_select2(sigmaold,pv91))))),
inference(modus_ponens,[status(thm)],[46,38]) ).
tff(48,plain,
$false,
inference(unit_resolution,[status(thm)],[47,37]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV050+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.34 % Computer : n007.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 : Sun Sep 4 00:57:34 EDT 2022
% 0.12/0.34 % 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.
% 0.19/0.43 % SZS status Theorem
% 0.19/0.43 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------