%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV180+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n004.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 : Sat Jun 21 05:31:39 AM UTC 2025
% Result : Theorem 0.20s 0.40s
% Output : Proof 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 27 ( 9 unt; 0 typ; 0 def)
% Number of atoms : 322 ( 90 equ)
% Maximal formula atoms : 82 ( 11 avg)
% Number of connectives : 403 ( 122 ~; 102 |; 131 &)
% ( 16 <=>; 32 =>; 0 <=; 0 <~>)
% Maximal formula depth : 21 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of FOOLs : 14 ( 14 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 8 ( 6 usr; 1 prp; 0-3 aty)
% Number of functors : 17 ( 17 usr; 15 con; 0-3 aty)
% Number of variables : 77 ( 75 !; 0 ?; 77 :)
% Comments :
%------------------------------------------------------------------------------
tff(init_type,type,
init: $i ).
tff(a_select2_type,type,
a_select2: ( $i * $i ) > $i ).
tff(pv86_type,type,
pv86: $i ).
tff(muold_init_type,type,
muold_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(rhoold_init_type,type,
rhoold_init: $i ).
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(n1_type,type,
n1: $i ).
tff(loopcounter_type,type,
loopcounter: $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(rho_init_type,type,
rho_init: $i ).
tff(q_init_type,type,
q_init: $i ).
tff(n135299_type,type,
n135299: $i ).
tff(1,plain,
( ( a_select2(muold_init,pv86) != init )
<=> ( a_select2(muold_init,pv86) != init ) ),
inference(rewrite,[status(thm)],[]) ).
tff(2,plain,
( ~ ( ( leq(n0,pv86)
& leq(pv86,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 ) ) )
& ! [J: $i] :
( ( leq(n0,J)
& leq(J,n4) )
=> ( a_select2(muold_init,J) = init ) )
& ! [K: $i] :
( ( leq(n0,K)
& leq(K,n4) )
=> ( a_select2(rhoold_init,K) = init ) )
& ! [L: $i] :
( ( leq(n0,L)
& leq(L,n4) )
=> ( a_select2(sigmaold_init,L) = init ) ) )
=> ( a_select2(muold_init,pv86) = init ) )
<=> ~ ( ~ ( leq(n0,pv86)
& leq(pv86,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 ) ) )
& ! [J: $i] :
( ~ ( leq(n0,J)
& leq(J,n4) )
| ( a_select2(muold_init,J) = init ) )
& ! [K: $i] :
( ~ ( leq(n0,K)
& leq(K,n4) )
| ( a_select2(rhoold_init,K) = init ) )
& ! [L: $i] :
( ~ ( leq(n0,L)
& leq(L,n4) )
| ( a_select2(sigmaold_init,L) = init ) ) )
| ( a_select2(muold_init,pv86) = init ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(3,axiom,
~ ( ( leq(n0,pv86)
& leq(pv86,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 ) ) )
& ! [J: $i] :
( ( leq(n0,J)
& leq(J,n4) )
=> ( a_select2(muold_init,J) = init ) )
& ! [K: $i] :
( ( leq(n0,K)
& leq(K,n4) )
=> ( a_select2(rhoold_init,K) = init ) )
& ! [L: $i] :
( ( leq(n0,L)
& leq(L,n4) )
=> ( a_select2(sigmaold_init,L) = init ) ) )
=> ( a_select2(muold_init,pv86) = init ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0076) ).
tff(4,plain,
~ ( ~ ( leq(n0,pv86)
& leq(pv86,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 ) ) )
& ! [J: $i] :
( ~ ( leq(n0,J)
& leq(J,n4) )
| ( a_select2(muold_init,J) = init ) )
& ! [K: $i] :
( ~ ( leq(n0,K)
& leq(K,n4) )
| ( a_select2(rhoold_init,K) = init ) )
& ! [L: $i] :
( ~ ( leq(n0,L)
& leq(L,n4) )
| ( a_select2(sigmaold_init,L) = init ) ) )
| ( a_select2(muold_init,pv86) = init ) ),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
a_select2(muold_init,pv86) != init,
inference(or_elim,[status(thm)],[4]) ).
tff(6,plain,
a_select2(muold_init,pv86) != init,
inference(modus_ponens,[status(thm)],[5,1]) ).
tff(7,plain,
^ [J: $i] :
refl(( ( ( a_select2(muold_init,J) = init )
| ~ leq(n0,J)
| ~ leq(J,n4) )
<=> ( ( a_select2(muold_init,J) = init )
| ~ leq(n0,J)
| ~ leq(J,n4) ) )),
inference(bind,[status(th)],[]) ).
tff(8,plain,
( ! [J: $i] :
( ( a_select2(muold_init,J) = init )
| ~ leq(n0,J)
| ~ leq(J,n4) )
<=> ! [J: $i] :
( ( a_select2(muold_init,J) = init )
| ~ leq(n0,J)
| ~ leq(J,n4) ) ),
inference(quant_intro,[status(thm)],[7]) ).
tff(9,plain,
^ [J: $i] :
trans(monotonicity(trans(monotonicity(rewrite(( ( leq(n0,J)
& leq(J,n4) )
<=> ~ ( ~ leq(n0,J)
| ~ leq(J,n4) ) )),
( ~ ( leq(n0,J)
& leq(J,n4) )
<=> ~ ~ ( ~ leq(n0,J)
| ~ leq(J,n4) ) )),
rewrite(( ~ ~ ( ~ leq(n0,J)
| ~ leq(J,n4) )
<=> ( ~ leq(n0,J)
| ~ leq(J,n4) ) )),
( ~ ( leq(n0,J)
& leq(J,n4) )
<=> ( ~ leq(n0,J)
| ~ leq(J,n4) ) )),
( ( ~ ( leq(n0,J)
& leq(J,n4) )
| ( a_select2(muold_init,J) = init ) )
<=> ( ~ leq(n0,J)
| ~ leq(J,n4)
| ( a_select2(muold_init,J) = init ) ) )),
rewrite(( ( ~ leq(n0,J)
| ~ leq(J,n4)
| ( a_select2(muold_init,J) = init ) )
<=> ( ( a_select2(muold_init,J) = init )
| ~ leq(n0,J)
| ~ leq(J,n4) ) )),
( ( ~ ( leq(n0,J)
& leq(J,n4) )
| ( a_select2(muold_init,J) = init ) )
<=> ( ( a_select2(muold_init,J) = init )
| ~ leq(n0,J)
| ~ leq(J,n4) ) )),
inference(bind,[status(th)],[]) ).
tff(10,plain,
( ! [J: $i] :
( ~ ( leq(n0,J)
& leq(J,n4) )
| ( a_select2(muold_init,J) = init ) )
<=> ! [J: $i] :
( ( a_select2(muold_init,J) = init )
| ~ leq(n0,J)
| ~ leq(J,n4) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,plain,
( ! [J: $i] :
( ~ ( leq(n0,J)
& leq(J,n4) )
| ( a_select2(muold_init,J) = init ) )
<=> ! [J: $i] :
( ~ ( leq(n0,J)
& leq(J,n4) )
| ( a_select2(muold_init,J) = init ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,plain,
( leq(n0,pv86)
& leq(pv86,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 ) ) )
& ! [J: $i] :
( ~ ( leq(n0,J)
& leq(J,n4) )
| ( a_select2(muold_init,J) = init ) )
& ! [K: $i] :
( ~ ( leq(n0,K)
& leq(K,n4) )
| ( a_select2(rhoold_init,K) = init ) )
& ! [L: $i] :
( ~ ( leq(n0,L)
& leq(L,n4) )
| ( a_select2(sigmaold_init,L) = init ) ) ),
inference(or_elim,[status(thm)],[4]) ).
tff(13,plain,
! [J: $i] :
( ~ ( leq(n0,J)
& leq(J,n4) )
| ( a_select2(muold_init,J) = init ) ),
inference(and_elim,[status(thm)],[12]) ).
tff(14,plain,
! [J: $i] :
( ~ ( leq(n0,J)
& leq(J,n4) )
| ( a_select2(muold_init,J) = init ) ),
inference(modus_ponens,[status(thm)],[13,11]) ).
tff(15,plain,
! [J: $i] :
( ~ ( leq(n0,J)
& leq(J,n4) )
| ( a_select2(muold_init,J) = init ) ),
inference(skolemize,[status(sab)],[14]) ).
tff(16,plain,
! [J: $i] :
( ( a_select2(muold_init,J) = init )
| ~ leq(n0,J)
| ~ leq(J,n4) ),
inference(modus_ponens,[status(thm)],[15,10]) ).
tff(17,plain,
! [J: $i] :
( ( a_select2(muold_init,J) = init )
| ~ leq(n0,J)
| ~ leq(J,n4) ),
inference(modus_ponens,[status(thm)],[16,8]) ).
tff(18,plain,
( leq(pv86,n4)
<=> leq(pv86,n4) ),
inference(rewrite,[status(thm)],[]) ).
tff(19,plain,
leq(pv86,n4),
inference(and_elim,[status(thm)],[12]) ).
tff(20,plain,
leq(pv86,n4),
inference(modus_ponens,[status(thm)],[19,18]) ).
tff(21,plain,
( leq(n0,pv86)
<=> leq(n0,pv86) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,plain,
leq(n0,pv86),
inference(and_elim,[status(thm)],[12]) ).
tff(23,plain,
leq(n0,pv86),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
( ( ~ ! [J: $i] :
( ( a_select2(muold_init,J) = init )
| ~ leq(n0,J)
| ~ leq(J,n4) )
| ( a_select2(muold_init,pv86) = init )
| ~ leq(n0,pv86)
| ~ leq(pv86,n4) )
<=> ( ~ ! [J: $i] :
( ( a_select2(muold_init,J) = init )
| ~ leq(n0,J)
| ~ leq(J,n4) )
| ( a_select2(muold_init,pv86) = init )
| ~ leq(n0,pv86)
| ~ leq(pv86,n4) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(25,plain,
( ~ ! [J: $i] :
( ( a_select2(muold_init,J) = init )
| ~ leq(n0,J)
| ~ leq(J,n4) )
| ( a_select2(muold_init,pv86) = init )
| ~ leq(n0,pv86)
| ~ leq(pv86,n4) ),
inference(quant_inst,[status(thm)],[]) ).
tff(26,plain,
( ~ ! [J: $i] :
( ( a_select2(muold_init,J) = init )
| ~ leq(n0,J)
| ~ leq(J,n4) )
| ( a_select2(muold_init,pv86) = init )
| ~ leq(n0,pv86)
| ~ leq(pv86,n4) ),
inference(modus_ponens,[status(thm)],[25,24]) ).
tff(27,plain,
$false,
inference(unit_resolution,[status(thm)],[26,23,20,17,6]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV180+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.07/0.12 % Command : run_E %s %d THM
% 0.13/0.33 % Computer : n004.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Fri Jun 20 09:30:38 EDT 2025
% 0.13/0.33 % CPUTime :
% 0.20/0.40 % SZS status Theorem
% 0.20/0.40 % SZS output start Proof
% See solution above
% 0.20/0.42 % E exiting
%------------------------------------------------------------------------------