TSTP Solution File: SWV172+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV172+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n001.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 15:10:14 EDT 2022
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 35
% Syntax : Number of formulae : 56 ( 12 unt; 22 typ; 0 def)
% Number of atoms : 309 ( 80 equ)
% Maximal formula atoms : 68 ( 9 avg)
% Number of connectives : 378 ( 118 ~; 98 |; 116 &)
% ( 20 <=>; 26 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 5 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of FOOLs : 15 ( 15 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 10 ( 5 >; 5 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 20 ( 20 usr; 17 con; 0-3 aty)
% Number of variables : 66 ( 63 !; 0 ?; 66 :)
% Comments :
%------------------------------------------------------------------------------
tff(init_type,type,
init: $i ).
tff(a_select2_type,type,
a_select2: ( $i * $i ) > $i ).
tff(pv54_type,type,
pv54: $i ).
tff(rho_init_type,type,
rho_init: $i ).
tff(sigmaold_init_type,type,
sigmaold_init: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(n4_type,type,
n4: $i ).
tff(n0_type,type,
n0: $i ).
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(n1_type,type,
n1: $i ).
tff(loopcounter_type,type,
loopcounter: $i ).
tff(rhoold_init_type,type,
rhoold_init: $i ).
tff(muold_init_type,type,
muold_init: $i ).
tff(a_select3_type,type,
a_select3: ( $i * $i * $i ) > $i ).
tff(center_init_type,type,
center_init: $i ).
tff(sigma_init_type,type,
sigma_init: $i ).
tff(mu_init_type,type,
mu_init: $i ).
tff(q_init_type,type,
q_init: $i ).
tff(n135299_type,type,
n135299: $i ).
tff(pv10_type,type,
pv10: $i ).
tff(succ_type,type,
succ: $i > $i ).
tff(tptp_minus_1_type,type,
tptp_minus_1: $i ).
tff(1,plain,
( ( a_select2(rho_init,pv54) != init )
<=> ( a_select2(rho_init,pv54) != init ) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( ~ ( ( leq(n0,pv10)
& leq(n0,pv54)
& leq(pv10,n135299)
& leq(pv54,n4)
& ! [A: $i] :
( ( leq(n0,A)
& leq(A,n135299) )
=> ! [B: $i] :
( ( leq(n0,B)
& leq(B,n4) )
=> ( a_select3(q_init,A,B) = init ) ) )
& ! [C: $i] :
( ( leq(n0,C)
& leq(C,n4) )
=> ( a_select2(rho_init,C) = init ) )
& ! [D: $i] :
( ( leq(n0,D)
& leq(D,n4) )
=> ( a_select2(mu_init,D) = init ) )
& ! [E: $i] :
( ( leq(n0,E)
& leq(E,n4) )
=> ( a_select2(sigma_init,E) = init ) )
& ! [F: $i] :
( ( leq(n0,F)
& leq(F,n4) )
=> ( a_select3(center_init,F,n0) = init ) )
& ( gt(loopcounter,n1)
=> ! [G: $i] :
( ( leq(n0,G)
& leq(G,n4) )
=> ( a_select2(muold_init,G) = init ) ) )
& ( gt(loopcounter,n1)
=> ! [H: $i] :
( ( leq(n0,H)
& leq(H,n4) )
=> ( a_select2(rhoold_init,H) = init ) ) )
& ( gt(loopcounter,n1)
=> ! [I: $i] :
( ( leq(n0,I)
& leq(I,n4) )
=> ( a_select2(sigmaold_init,I) = init ) ) ) )
=> ( a_select2(rho_init,pv54) = init ) )
<=> ~ ( ~ ( leq(n0,pv10)
& leq(n0,pv54)
& leq(pv10,n135299)
& leq(pv54,n4)
& ! [A: $i] :
( ~ ( leq(n0,A)
& leq(A,n135299) )
| ! [B: $i] :
( ~ ( leq(n0,B)
& leq(B,n4) )
| ( a_select3(q_init,A,B) = init ) ) )
& ! [C: $i] :
( ~ ( leq(n0,C)
& leq(C,n4) )
| ( a_select2(rho_init,C) = init ) )
& ! [D: $i] :
( ~ ( leq(n0,D)
& leq(D,n4) )
| ( a_select2(mu_init,D) = init ) )
& ! [E: $i] :
( ~ ( leq(n0,E)
& leq(E,n4) )
| ( a_select2(sigma_init,E) = init ) )
& ! [F: $i] :
( ~ ( leq(n0,F)
& leq(F,n4) )
| ( a_select3(center_init,F,n0) = init ) )
& ( ~ gt(loopcounter,n1)
| ! [G: $i] :
( ~ ( leq(n0,G)
& leq(G,n4) )
| ( a_select2(muold_init,G) = init ) ) )
& ( ~ gt(loopcounter,n1)
| ! [H: $i] :
( ~ ( leq(n0,H)
& leq(H,n4) )
| ( a_select2(rhoold_init,H) = init ) ) )
& ( ~ gt(loopcounter,n1)
| ! [I: $i] :
( ~ ( leq(n0,I)
& leq(I,n4) )
| ( a_select2(sigmaold_init,I) = init ) ) ) )
| ( a_select2(rho_init,pv54) = init ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
~ ( ( leq(n0,pv10)
& leq(n0,pv54)
& leq(pv10,n135299)
& leq(pv54,n4)
& ! [A: $i] :
( ( leq(n0,A)
& leq(A,n135299) )
=> ! [B: $i] :
( ( leq(n0,B)
& leq(B,n4) )
=> ( a_select3(q_init,A,B) = init ) ) )
& ! [C: $i] :
( ( leq(n0,C)
& leq(C,n4) )
=> ( a_select2(rho_init,C) = init ) )
& ! [D: $i] :
( ( leq(n0,D)
& leq(D,n4) )
=> ( a_select2(mu_init,D) = init ) )
& ! [E: $i] :
( ( leq(n0,E)
& leq(E,n4) )
=> ( a_select2(sigma_init,E) = init ) )
& ! [F: $i] :
( ( leq(n0,F)
& leq(F,n4) )
=> ( a_select3(center_init,F,n0) = init ) )
& ( gt(loopcounter,n1)
=> ! [G: $i] :
( ( leq(n0,G)
& leq(G,n4) )
=> ( a_select2(muold_init,G) = init ) ) )
& ( gt(loopcounter,n1)
=> ! [H: $i] :
( ( leq(n0,H)
& leq(H,n4) )
=> ( a_select2(rhoold_init,H) = init ) ) )
& ( gt(loopcounter,n1)
=> ! [I: $i] :
( ( leq(n0,I)
& leq(I,n4) )
=> ( a_select2(sigmaold_init,I) = init ) ) ) )
=> ( a_select2(rho_init,pv54) = init ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_init_0036) ).
tff(4,plain,
~ ( ~ ( leq(n0,pv10)
& leq(n0,pv54)
& leq(pv10,n135299)
& leq(pv54,n4)
& ! [A: $i] :
( ~ ( leq(n0,A)
& leq(A,n135299) )
| ! [B: $i] :
( ~ ( leq(n0,B)
& leq(B,n4) )
| ( a_select3(q_init,A,B) = init ) ) )
& ! [C: $i] :
( ~ ( leq(n0,C)
& leq(C,n4) )
| ( a_select2(rho_init,C) = init ) )
& ! [D: $i] :
( ~ ( leq(n0,D)
& leq(D,n4) )
| ( a_select2(mu_init,D) = init ) )
& ! [E: $i] :
( ~ ( leq(n0,E)
& leq(E,n4) )
| ( a_select2(sigma_init,E) = init ) )
& ! [F: $i] :
( ~ ( leq(n0,F)
& leq(F,n4) )
| ( a_select3(center_init,F,n0) = init ) )
& ( ~ gt(loopcounter,n1)
| ! [G: $i] :
( ~ ( leq(n0,G)
& leq(G,n4) )
| ( a_select2(muold_init,G) = init ) ) )
& ( ~ gt(loopcounter,n1)
| ! [H: $i] :
( ~ ( leq(n0,H)
& leq(H,n4) )
| ( a_select2(rhoold_init,H) = init ) ) )
& ( ~ gt(loopcounter,n1)
| ! [I: $i] :
( ~ ( leq(n0,I)
& leq(I,n4) )
| ( a_select2(sigmaold_init,I) = init ) ) ) )
| ( a_select2(rho_init,pv54) = init ) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
a_select2(rho_init,pv54) != init,
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
a_select2(rho_init,pv54) != init,
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
^ [C: $i] :
refl(
( ( ( a_select2(rho_init,C) = init )
| ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
<=> ( ( a_select2(rho_init,C) = init )
| ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) )),
inference(bind,[status(th)],]) ).
tff(8,plain,
( ! [C: $i] :
( ( a_select2(rho_init,C) = init )
| ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
<=> ! [C: $i] :
( ( a_select2(rho_init,C) = init )
| ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
^ [C: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( leq(succ(tptp_minus_1),C)
& leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
<=> ~ ( ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) )),
( ~ ( leq(succ(tptp_minus_1),C)
& leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
<=> ~ ~ ( ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) )),
rewrite(
( ~ ~ ( ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
<=> ( ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) )),
( ~ ( leq(succ(tptp_minus_1),C)
& leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
<=> ( ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) )),
( ( ~ ( leq(succ(tptp_minus_1),C)
& leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
| ( a_select2(rho_init,C) = init ) )
<=> ( ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1))))))
| ( a_select2(rho_init,C) = init ) ) )),
rewrite(
( ( ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1))))))
| ( a_select2(rho_init,C) = init ) )
<=> ( ( a_select2(rho_init,C) = init )
| ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) )),
( ( ~ ( leq(succ(tptp_minus_1),C)
& leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
| ( a_select2(rho_init,C) = init ) )
<=> ( ( a_select2(rho_init,C) = init )
| ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [C: $i] :
( ~ ( leq(succ(tptp_minus_1),C)
& leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
| ( a_select2(rho_init,C) = init ) )
<=> ! [C: $i] :
( ( a_select2(rho_init,C) = init )
| ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
^ [C: $i] :
rewrite(
( ( ~ ( leq(n0,C)
& leq(C,n4) )
| ( a_select2(rho_init,C) = init ) )
<=> ( ~ ( leq(succ(tptp_minus_1),C)
& leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
| ( a_select2(rho_init,C) = init ) ) )),
inference(bind,[status(th)],]) ).
tff(12,plain,
( ! [C: $i] :
( ~ ( leq(n0,C)
& leq(C,n4) )
| ( a_select2(rho_init,C) = init ) )
<=> ! [C: $i] :
( ~ ( leq(succ(tptp_minus_1),C)
& leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
| ( a_select2(rho_init,C) = init ) ) ),
inference(quant_intro,[status(thm)],[11]) ).
tff(13,plain,
( ! [C: $i] :
( ~ ( leq(n0,C)
& leq(C,n4) )
| ( a_select2(rho_init,C) = init ) )
<=> ! [C: $i] :
( ~ ( leq(n0,C)
& leq(C,n4) )
| ( a_select2(rho_init,C) = init ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(14,plain,
( leq(n0,pv10)
& leq(n0,pv54)
& leq(pv10,n135299)
& leq(pv54,n4)
& ! [A: $i] :
( ~ ( leq(n0,A)
& leq(A,n135299) )
| ! [B: $i] :
( ~ ( leq(n0,B)
& leq(B,n4) )
| ( a_select3(q_init,A,B) = init ) ) )
& ! [C: $i] :
( ~ ( leq(n0,C)
& leq(C,n4) )
| ( a_select2(rho_init,C) = init ) )
& ! [D: $i] :
( ~ ( leq(n0,D)
& leq(D,n4) )
| ( a_select2(mu_init,D) = init ) )
& ! [E: $i] :
( ~ ( leq(n0,E)
& leq(E,n4) )
| ( a_select2(sigma_init,E) = init ) )
& ! [F: $i] :
( ~ ( leq(n0,F)
& leq(F,n4) )
| ( a_select3(center_init,F,n0) = init ) )
& ( ~ gt(loopcounter,n1)
| ! [G: $i] :
( ~ ( leq(n0,G)
& leq(G,n4) )
| ( a_select2(muold_init,G) = init ) ) )
& ( ~ gt(loopcounter,n1)
| ! [H: $i] :
( ~ ( leq(n0,H)
& leq(H,n4) )
| ( a_select2(rhoold_init,H) = init ) ) )
& ( ~ gt(loopcounter,n1)
| ! [I: $i] :
( ~ ( leq(n0,I)
& leq(I,n4) )
| ( a_select2(sigmaold_init,I) = init ) ) ) ),
inference(or_elim,[status(thm)],[4]) ).
tff(15,plain,
! [C: $i] :
( ~ ( leq(n0,C)
& leq(C,n4) )
| ( a_select2(rho_init,C) = init ) ),
inference(and_elim,[status(thm)],[14]) ).
tff(16,plain,
! [C: $i] :
( ~ ( leq(n0,C)
& leq(C,n4) )
| ( a_select2(rho_init,C) = init ) ),
inference(modus_ponens,[status(thm)],[15,13]) ).
tff(17,plain,
! [C: $i] :
( ~ ( leq(succ(tptp_minus_1),C)
& leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
| ( a_select2(rho_init,C) = init ) ),
inference(modus_ponens,[status(thm)],[16,12]) ).
tff(18,plain,
! [C: $i] :
( ~ ( leq(succ(tptp_minus_1),C)
& leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
| ( a_select2(rho_init,C) = init ) ),
inference(skolemize,[status(sab)],[17]) ).
tff(19,plain,
! [C: $i] :
( ( a_select2(rho_init,C) = init )
| ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) ),
inference(modus_ponens,[status(thm)],[18,10]) ).
tff(20,plain,
! [C: $i] :
( ( a_select2(rho_init,C) = init )
| ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) ),
inference(modus_ponens,[status(thm)],[19,8]) ).
tff(21,plain,
( leq(pv54,n4)
<=> leq(pv54,succ(succ(succ(succ(succ(tptp_minus_1)))))) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( leq(pv54,n4)
<=> leq(pv54,n4) ),
inference(rewrite,[status(thm)],]) ).
tff(23,plain,
leq(pv54,n4),
inference(and_elim,[status(thm)],[14]) ).
tff(24,plain,
leq(pv54,n4),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
leq(pv54,succ(succ(succ(succ(succ(tptp_minus_1)))))),
inference(modus_ponens,[status(thm)],[24,21]) ).
tff(26,plain,
( leq(n0,pv54)
<=> leq(succ(tptp_minus_1),pv54) ),
inference(rewrite,[status(thm)],]) ).
tff(27,plain,
( leq(n0,pv54)
<=> leq(n0,pv54) ),
inference(rewrite,[status(thm)],]) ).
tff(28,plain,
leq(n0,pv54),
inference(and_elim,[status(thm)],[14]) ).
tff(29,plain,
leq(n0,pv54),
inference(modus_ponens,[status(thm)],[28,27]) ).
tff(30,plain,
leq(succ(tptp_minus_1),pv54),
inference(modus_ponens,[status(thm)],[29,26]) ).
tff(31,plain,
( ( ~ ! [C: $i] :
( ( a_select2(rho_init,C) = init )
| ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
| ( a_select2(rho_init,pv54) = init )
| ~ leq(succ(tptp_minus_1),pv54)
| ~ leq(pv54,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
<=> ( ~ ! [C: $i] :
( ( a_select2(rho_init,C) = init )
| ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
| ( a_select2(rho_init,pv54) = init )
| ~ leq(succ(tptp_minus_1),pv54)
| ~ leq(pv54,succ(succ(succ(succ(succ(tptp_minus_1)))))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(32,plain,
( ~ ! [C: $i] :
( ( a_select2(rho_init,C) = init )
| ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
| ( a_select2(rho_init,pv54) = init )
| ~ leq(succ(tptp_minus_1),pv54)
| ~ leq(pv54,succ(succ(succ(succ(succ(tptp_minus_1)))))) ),
inference(quant_inst,[status(thm)],]) ).
tff(33,plain,
( ~ ! [C: $i] :
( ( a_select2(rho_init,C) = init )
| ~ leq(succ(tptp_minus_1),C)
| ~ leq(C,succ(succ(succ(succ(succ(tptp_minus_1)))))) )
| ( a_select2(rho_init,pv54) = init )
| ~ leq(succ(tptp_minus_1),pv54)
| ~ leq(pv54,succ(succ(succ(succ(succ(tptp_minus_1)))))) ),
inference(modus_ponens,[status(thm)],[32,31]) ).
tff(34,plain,
$false,
inference(unit_resolution,[status(thm)],[33,30,25,20,6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV172+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.07/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.14/0.34 % Computer : n001.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Sun Sep 4 02:01:12 EDT 2022
% 0.14/0.35 % CPUTime :
% 0.14/0.35 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.14/0.35 Usage: tptp [options] [-file:]file
% 0.14/0.35 -h, -? prints this message.
% 0.14/0.35 -smt2 print SMT-LIB2 benchmark.
% 0.14/0.35 -m, -model generate model.
% 0.14/0.35 -p, -proof generate proof.
% 0.14/0.35 -c, -core generate unsat core of named formulas.
% 0.14/0.35 -st, -statistics display statistics.
% 0.14/0.35 -t:timeout set timeout (in second).
% 0.14/0.35 -smt2status display status in smt2 format instead of SZS.
% 0.14/0.35 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.14/0.35 -<param>:<value> configuration parameter and value.
% 0.14/0.35 -o:<output-file> file to place output in.
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% See solution above
%------------------------------------------------------------------------------