TSTP Solution File: SWV181+1 by Z3---4.8.9.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Z3---4.8.9.0
% Problem : SWV181+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : z3_tptp -proof -model -t:%d -file:%s
% Computer : n021.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 15:10:16 EDT 2022
% Result : Theorem 0.19s 0.43s
% Output : Proof 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 67
% Syntax : Number of formulae : 135 ( 34 unt; 20 typ; 0 def)
% Number of atoms : 615 ( 78 equ)
% Maximal formula atoms : 52 ( 5 avg)
% Number of connectives : 752 ( 288 ~; 247 |; 106 &)
% ( 77 <=>; 34 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of FOOLs : 36 ( 36 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 : 18 ( 18 usr; 15 con; 0-3 aty)
% Number of variables : 233 ( 212 !; 0 ?; 233 :)
% Comments :
%------------------------------------------------------------------------------
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(succ_type,type,
succ: $i > $i ).
tff(tptp_minus_1_type,type,
tptp_minus_1: $i ).
tff(loopcounter_type,type,
loopcounter: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(n0_type,type,
n0: $i ).
tff(n1_type,type,
n1: $i ).
tff(init_type,type,
init: $i ).
tff(a_select2_type,type,
a_select2: ( $i * $i ) > $i ).
tff(sigma_init_type,type,
sigma_init: $i ).
tff(n4_type,type,
n4: $i ).
tff(rho_init_type,type,
rho_init: $i ).
tff(mu_init_type,type,
mu_init: $i ).
tff(a_select3_type,type,
a_select3: ( $i * $i * $i ) > $i ).
tff(center_init_type,type,
center_init: $i ).
tff(q_init_type,type,
q_init: $i ).
tff(n135299_type,type,
n135299: $i ).
tff(pv76_type,type,
pv76: $i ).
tff(tptp_float_0_001_type,type,
tptp_float_0_001: $i ).
tff(muold_init_type,type,
muold_init: $i ).
tff(1,plain,
( gt(n1,n0)
<=> gt(succ(succ(tptp_minus_1)),succ(tptp_minus_1)) ),
inference(rewrite,[status(thm)],]) ).
tff(2,plain,
( gt(n1,n0)
<=> gt(n1,n0) ),
inference(rewrite,[status(thm)],]) ).
tff(3,axiom,
gt(n1,n0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_1_0) ).
tff(4,plain,
gt(n1,n0),
inference(modus_ponens,[status(thm)],[3,2]) ).
tff(5,plain,
gt(succ(succ(tptp_minus_1)),succ(tptp_minus_1)),
inference(modus_ponens,[status(thm)],[4,1]) ).
tff(6,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ gt(Y,X)
| leq(X,Y) )
<=> ( ~ gt(Y,X)
| leq(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(7,plain,
( ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ) ),
inference(quant_intro,[status(thm)],[6]) ).
tff(8,plain,
( ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(9,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( gt(Y,X)
=> leq(X,Y) )
<=> ( ~ gt(Y,X)
| leq(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(10,plain,
( ! [X: $i,Y: $i] :
( gt(Y,X)
=> leq(X,Y) )
<=> ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ) ),
inference(quant_intro,[status(thm)],[9]) ).
tff(11,axiom,
! [X: $i,Y: $i] :
( gt(Y,X)
=> leq(X,Y) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt1) ).
tff(12,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[11,10]) ).
tff(13,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[12,8]) ).
tff(14,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(skolemize,[status(sab)],[13]) ).
tff(15,plain,
! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) ),
inference(modus_ponens,[status(thm)],[14,7]) ).
tff(16,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(succ(succ(tptp_minus_1)),succ(tptp_minus_1))
| leq(succ(tptp_minus_1),succ(succ(tptp_minus_1))) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(succ(succ(tptp_minus_1)),succ(tptp_minus_1))
| leq(succ(tptp_minus_1),succ(succ(tptp_minus_1))) ) ),
inference(rewrite,[status(thm)],]) ).
tff(17,plain,
( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(succ(succ(tptp_minus_1)),succ(tptp_minus_1))
| leq(succ(tptp_minus_1),succ(succ(tptp_minus_1))) ),
inference(quant_inst,[status(thm)],]) ).
tff(18,plain,
( ~ ! [X: $i,Y: $i] :
( ~ gt(Y,X)
| leq(X,Y) )
| ~ gt(succ(succ(tptp_minus_1)),succ(tptp_minus_1))
| leq(succ(tptp_minus_1),succ(succ(tptp_minus_1))) ),
inference(modus_ponens,[status(thm)],[17,16]) ).
tff(19,plain,
leq(succ(tptp_minus_1),succ(succ(tptp_minus_1))),
inference(unit_resolution,[status(thm)],[18,15,5]) ).
tff(20,plain,
( leq(n1,loopcounter)
<=> leq(succ(succ(tptp_minus_1)),loopcounter) ),
inference(rewrite,[status(thm)],]) ).
tff(21,plain,
( leq(n1,loopcounter)
<=> leq(n1,loopcounter) ),
inference(rewrite,[status(thm)],]) ).
tff(22,plain,
( ~ ( ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [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_select3(center_init,C,n0) = init ) )
& ( gt(loopcounter,n0)
=> ! [D: $i] :
( ( leq(n0,D)
& leq(D,n4) )
=> ( a_select2(mu_init,D) = init ) ) )
& ( gt(loopcounter,n0)
=> ! [E: $i] :
( ( leq(n0,E)
& leq(E,n4) )
=> ( a_select2(rho_init,E) = init ) ) )
& ( gt(loopcounter,n0)
=> ! [F: $i] :
( ( leq(n0,F)
& leq(F,n4) )
=> ( a_select2(sigma_init,F) = init ) ) ) )
=> ! [G: $i] :
( ( leq(n0,G)
& leq(G,n4) )
=> ( a_select2(muold_init,G) = init ) ) )
<=> ~ ( ~ ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [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_select3(center_init,C,n0) = init ) )
& ( ~ gt(loopcounter,n0)
| ! [D: $i] :
( ~ ( leq(n0,D)
& leq(D,n4) )
| ( a_select2(mu_init,D) = init ) ) )
& ( ~ gt(loopcounter,n0)
| ! [E: $i] :
( ~ ( leq(n0,E)
& leq(E,n4) )
| ( a_select2(rho_init,E) = init ) ) )
& ( ~ gt(loopcounter,n0)
| ! [F: $i] :
( ~ ( leq(n0,F)
& leq(F,n4) )
| ( a_select2(sigma_init,F) = init ) ) ) )
| ! [G: $i] :
( ~ ( leq(n0,G)
& leq(G,n4) )
| ( a_select2(muold_init,G) = init ) ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(23,axiom,
~ ( ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [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_select3(center_init,C,n0) = init ) )
& ( gt(loopcounter,n0)
=> ! [D: $i] :
( ( leq(n0,D)
& leq(D,n4) )
=> ( a_select2(mu_init,D) = init ) ) )
& ( gt(loopcounter,n0)
=> ! [E: $i] :
( ( leq(n0,E)
& leq(E,n4) )
=> ( a_select2(rho_init,E) = init ) ) )
& ( gt(loopcounter,n0)
=> ! [F: $i] :
( ( leq(n0,F)
& leq(F,n4) )
=> ( a_select2(sigma_init,F) = init ) ) ) )
=> ! [G: $i] :
( ( leq(n0,G)
& leq(G,n4) )
=> ( a_select2(muold_init,G) = init ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0081) ).
tff(24,plain,
~ ( ~ ( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [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_select3(center_init,C,n0) = init ) )
& ( ~ gt(loopcounter,n0)
| ! [D: $i] :
( ~ ( leq(n0,D)
& leq(D,n4) )
| ( a_select2(mu_init,D) = init ) ) )
& ( ~ gt(loopcounter,n0)
| ! [E: $i] :
( ~ ( leq(n0,E)
& leq(E,n4) )
| ( a_select2(rho_init,E) = init ) ) )
& ( ~ gt(loopcounter,n0)
| ! [F: $i] :
( ~ ( leq(n0,F)
& leq(F,n4) )
| ( a_select2(sigma_init,F) = init ) ) ) )
| ! [G: $i] :
( ~ ( leq(n0,G)
& leq(G,n4) )
| ( a_select2(muold_init,G) = init ) ) ),
inference(modus_ponens,[status(thm)],[23,22]) ).
tff(25,plain,
( leq(tptp_float_0_001,pv76)
& leq(n1,loopcounter)
& gt(n1,loopcounter)
& ! [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_select3(center_init,C,n0) = init ) )
& ( ~ gt(loopcounter,n0)
| ! [D: $i] :
( ~ ( leq(n0,D)
& leq(D,n4) )
| ( a_select2(mu_init,D) = init ) ) )
& ( ~ gt(loopcounter,n0)
| ! [E: $i] :
( ~ ( leq(n0,E)
& leq(E,n4) )
| ( a_select2(rho_init,E) = init ) ) )
& ( ~ gt(loopcounter,n0)
| ! [F: $i] :
( ~ ( leq(n0,F)
& leq(F,n4) )
| ( a_select2(sigma_init,F) = init ) ) ) ),
inference(or_elim,[status(thm)],[24]) ).
tff(26,plain,
leq(n1,loopcounter),
inference(and_elim,[status(thm)],[25]) ).
tff(27,plain,
leq(n1,loopcounter),
inference(modus_ponens,[status(thm)],[26,21]) ).
tff(28,plain,
leq(succ(succ(tptp_minus_1)),loopcounter),
inference(modus_ponens,[status(thm)],[27,20]) ).
tff(29,plain,
( ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
<=> ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ) ),
inference(rewrite,[status(thm)],]) ).
tff(30,plain,
^ [X: $i,Y: $i,Z: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( leq(X,Y)
& leq(Y,Z) )
<=> ~ ( ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
( ~ ( leq(X,Y)
& leq(Y,Z) )
<=> ~ ~ ( ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
rewrite(
( ~ ~ ( ~ leq(Y,Z)
| ~ leq(X,Y) )
<=> ( ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
( ~ ( leq(X,Y)
& leq(Y,Z) )
<=> ( ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
( ( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) )
<=> ( ~ leq(Y,Z)
| ~ leq(X,Y)
| leq(X,Z) ) )),
rewrite(
( ( ~ leq(Y,Z)
| ~ leq(X,Y)
| leq(X,Z) )
<=> ( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
( ( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) )
<=> ( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ) )),
inference(bind,[status(th)],]) ).
tff(31,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ) ),
inference(quant_intro,[status(thm)],[30]) ).
tff(32,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ) ),
inference(rewrite,[status(thm)],]) ).
tff(33,plain,
^ [X: $i,Y: $i,Z: $i] :
rewrite(
( ( ( leq(X,Y)
& leq(Y,Z) )
=> leq(X,Z) )
<=> ( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ) )),
inference(bind,[status(th)],]) ).
tff(34,plain,
( ! [X: $i,Y: $i,Z: $i] :
( ( leq(X,Y)
& leq(Y,Z) )
=> leq(X,Z) )
<=> ! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ) ),
inference(quant_intro,[status(thm)],[33]) ).
tff(35,axiom,
! [X: $i,Y: $i,Z: $i] :
( ( leq(X,Y)
& leq(Y,Z) )
=> leq(X,Z) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',transitivity_leq) ).
tff(36,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ),
inference(modus_ponens,[status(thm)],[35,34]) ).
tff(37,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ),
inference(modus_ponens,[status(thm)],[36,32]) ).
tff(38,plain,
! [X: $i,Y: $i,Z: $i] :
( ~ ( leq(X,Y)
& leq(Y,Z) )
| leq(X,Z) ),
inference(skolemize,[status(sab)],[37]) ).
tff(39,plain,
! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(modus_ponens,[status(thm)],[38,31]) ).
tff(40,plain,
! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) ),
inference(modus_ponens,[status(thm)],[39,29]) ).
tff(41,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| ~ leq(succ(tptp_minus_1),succ(succ(tptp_minus_1)))
| leq(succ(tptp_minus_1),loopcounter) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| ~ leq(succ(tptp_minus_1),succ(succ(tptp_minus_1)))
| leq(succ(tptp_minus_1),loopcounter) ) ),
inference(rewrite,[status(thm)],]) ).
tff(42,plain,
( ( leq(succ(tptp_minus_1),loopcounter)
| ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| ~ leq(succ(tptp_minus_1),succ(succ(tptp_minus_1))) )
<=> ( ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| ~ leq(succ(tptp_minus_1),succ(succ(tptp_minus_1)))
| leq(succ(tptp_minus_1),loopcounter) ) ),
inference(rewrite,[status(thm)],]) ).
tff(43,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| leq(succ(tptp_minus_1),loopcounter)
| ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| ~ leq(succ(tptp_minus_1),succ(succ(tptp_minus_1))) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| ~ leq(succ(tptp_minus_1),succ(succ(tptp_minus_1)))
| leq(succ(tptp_minus_1),loopcounter) ) ),
inference(monotonicity,[status(thm)],[42]) ).
tff(44,plain,
( ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| leq(succ(tptp_minus_1),loopcounter)
| ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| ~ leq(succ(tptp_minus_1),succ(succ(tptp_minus_1))) )
<=> ( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| ~ leq(succ(tptp_minus_1),succ(succ(tptp_minus_1)))
| leq(succ(tptp_minus_1),loopcounter) ) ),
inference(transitivity,[status(thm)],[43,41]) ).
tff(45,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| leq(succ(tptp_minus_1),loopcounter)
| ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| ~ leq(succ(tptp_minus_1),succ(succ(tptp_minus_1))) ),
inference(quant_inst,[status(thm)],]) ).
tff(46,plain,
( ~ ! [X: $i,Y: $i,Z: $i] :
( leq(X,Z)
| ~ leq(Y,Z)
| ~ leq(X,Y) )
| ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| ~ leq(succ(tptp_minus_1),succ(succ(tptp_minus_1)))
| leq(succ(tptp_minus_1),loopcounter) ),
inference(modus_ponens,[status(thm)],[45,44]) ).
tff(47,plain,
leq(succ(tptp_minus_1),loopcounter),
inference(unit_resolution,[status(thm)],[46,40,28,19]) ).
tff(48,plain,
^ [X: $i,Y: $i] :
refl(
( ( leq(X,Y)
<=> gt(succ(Y),X) )
<=> ( leq(X,Y)
<=> gt(succ(Y),X) ) )),
inference(bind,[status(th)],]) ).
tff(49,plain,
( ! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) )
<=> ! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ) ),
inference(quant_intro,[status(thm)],[48]) ).
tff(50,plain,
( ! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) )
<=> ! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(51,axiom,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_succ_gt_equiv) ).
tff(52,plain,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
inference(modus_ponens,[status(thm)],[51,50]) ).
tff(53,plain,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
inference(skolemize,[status(sab)],[52]) ).
tff(54,plain,
! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) ),
inference(modus_ponens,[status(thm)],[53,49]) ).
tff(55,plain,
( ~ ! [X: $i,Y: $i] :
( leq(X,Y)
<=> gt(succ(Y),X) )
| ( leq(loopcounter,succ(tptp_minus_1))
<=> gt(succ(succ(tptp_minus_1)),loopcounter) ) ),
inference(quant_inst,[status(thm)],]) ).
tff(56,plain,
( leq(loopcounter,succ(tptp_minus_1))
<=> gt(succ(succ(tptp_minus_1)),loopcounter) ),
inference(unit_resolution,[status(thm)],[55,54]) ).
tff(57,plain,
( gt(n1,loopcounter)
<=> gt(succ(succ(tptp_minus_1)),loopcounter) ),
inference(rewrite,[status(thm)],]) ).
tff(58,plain,
( gt(n1,loopcounter)
<=> gt(n1,loopcounter) ),
inference(rewrite,[status(thm)],]) ).
tff(59,plain,
gt(n1,loopcounter),
inference(and_elim,[status(thm)],[25]) ).
tff(60,plain,
gt(n1,loopcounter),
inference(modus_ponens,[status(thm)],[59,58]) ).
tff(61,plain,
gt(succ(succ(tptp_minus_1)),loopcounter),
inference(modus_ponens,[status(thm)],[60,57]) ).
tff(62,plain,
( ~ ( leq(loopcounter,succ(tptp_minus_1))
<=> gt(succ(succ(tptp_minus_1)),loopcounter) )
| leq(loopcounter,succ(tptp_minus_1))
| ~ gt(succ(succ(tptp_minus_1)),loopcounter) ),
inference(tautology,[status(thm)],]) ).
tff(63,plain,
( ~ ( leq(loopcounter,succ(tptp_minus_1))
<=> gt(succ(succ(tptp_minus_1)),loopcounter) )
| leq(loopcounter,succ(tptp_minus_1)) ),
inference(unit_resolution,[status(thm)],[62,61]) ).
tff(64,plain,
leq(loopcounter,succ(tptp_minus_1)),
inference(unit_resolution,[status(thm)],[63,56]) ).
tff(65,plain,
^ [X: $i] :
refl(
( ( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) )
<=> ( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) ) )),
inference(bind,[status(th)],]) ).
tff(66,plain,
( ! [X: $i] :
( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) )
<=> ! [X: $i] :
( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) ) ),
inference(quant_intro,[status(thm)],[65]) ).
tff(67,plain,
^ [X: $i] :
trans(
monotonicity(
trans(
monotonicity(
rewrite(
( ( leq(succ(tptp_minus_1),X)
& leq(X,succ(tptp_minus_1)) )
<=> ~ ( ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) ) )),
( ~ ( leq(succ(tptp_minus_1),X)
& leq(X,succ(tptp_minus_1)) )
<=> ~ ~ ( ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) ) )),
rewrite(
( ~ ~ ( ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) )
<=> ( ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) ) )),
( ~ ( leq(succ(tptp_minus_1),X)
& leq(X,succ(tptp_minus_1)) )
<=> ( ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) ) )),
( ( ~ ( leq(succ(tptp_minus_1),X)
& leq(X,succ(tptp_minus_1)) )
| ( X = succ(tptp_minus_1) ) )
<=> ( ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1))
| ( X = succ(tptp_minus_1) ) ) )),
rewrite(
( ( ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1))
| ( X = succ(tptp_minus_1) ) )
<=> ( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) ) )),
( ( ~ ( leq(succ(tptp_minus_1),X)
& leq(X,succ(tptp_minus_1)) )
| ( X = succ(tptp_minus_1) ) )
<=> ( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) ) )),
inference(bind,[status(th)],]) ).
tff(68,plain,
( ! [X: $i] :
( ~ ( leq(succ(tptp_minus_1),X)
& leq(X,succ(tptp_minus_1)) )
| ( X = succ(tptp_minus_1) ) )
<=> ! [X: $i] :
( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) ) ),
inference(quant_intro,[status(thm)],[67]) ).
tff(69,plain,
^ [X: $i] :
rewrite(
( ( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) )
<=> ( ~ ( leq(succ(tptp_minus_1),X)
& leq(X,succ(tptp_minus_1)) )
| ( X = succ(tptp_minus_1) ) ) )),
inference(bind,[status(th)],]) ).
tff(70,plain,
( ! [X: $i] :
( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) )
<=> ! [X: $i] :
( ~ ( leq(succ(tptp_minus_1),X)
& leq(X,succ(tptp_minus_1)) )
| ( X = succ(tptp_minus_1) ) ) ),
inference(quant_intro,[status(thm)],[69]) ).
tff(71,plain,
( ! [X: $i] :
( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) )
<=> ! [X: $i] :
( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) ) ),
inference(rewrite,[status(thm)],]) ).
tff(72,plain,
^ [X: $i] :
rewrite(
( ( ( leq(n0,X)
& leq(X,n0) )
=> ( X = n0 ) )
<=> ( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) ) )),
inference(bind,[status(th)],]) ).
tff(73,plain,
( ! [X: $i] :
( ( leq(n0,X)
& leq(X,n0) )
=> ( X = n0 ) )
<=> ! [X: $i] :
( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) ) ),
inference(quant_intro,[status(thm)],[72]) ).
tff(74,axiom,
! [X: $i] :
( ( leq(n0,X)
& leq(X,n0) )
=> ( X = n0 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
tff(75,plain,
! [X: $i] :
( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) ),
inference(modus_ponens,[status(thm)],[74,73]) ).
tff(76,plain,
! [X: $i] :
( ~ ( leq(n0,X)
& leq(X,n0) )
| ( X = n0 ) ),
inference(modus_ponens,[status(thm)],[75,71]) ).
tff(77,plain,
! [X: $i] :
( ~ ( leq(succ(tptp_minus_1),X)
& leq(X,succ(tptp_minus_1)) )
| ( X = succ(tptp_minus_1) ) ),
inference(modus_ponens,[status(thm)],[76,70]) ).
tff(78,plain,
! [X: $i] :
( ~ ( leq(succ(tptp_minus_1),X)
& leq(X,succ(tptp_minus_1)) )
| ( X = succ(tptp_minus_1) ) ),
inference(skolemize,[status(sab)],[77]) ).
tff(79,plain,
! [X: $i] :
( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) ),
inference(modus_ponens,[status(thm)],[78,68]) ).
tff(80,plain,
! [X: $i] :
( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) ),
inference(modus_ponens,[status(thm)],[79,66]) ).
tff(81,plain,
( ( ~ ! [X: $i] :
( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) )
| ~ leq(loopcounter,succ(tptp_minus_1))
| ( loopcounter = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),loopcounter) )
<=> ( ~ ! [X: $i] :
( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) )
| ~ leq(loopcounter,succ(tptp_minus_1))
| ( loopcounter = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),loopcounter) ) ),
inference(rewrite,[status(thm)],]) ).
tff(82,plain,
( ( ( loopcounter = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),loopcounter)
| ~ leq(loopcounter,succ(tptp_minus_1)) )
<=> ( ~ leq(loopcounter,succ(tptp_minus_1))
| ( loopcounter = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),loopcounter) ) ),
inference(rewrite,[status(thm)],]) ).
tff(83,plain,
( ( ~ ! [X: $i] :
( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) )
| ( loopcounter = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),loopcounter)
| ~ leq(loopcounter,succ(tptp_minus_1)) )
<=> ( ~ ! [X: $i] :
( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) )
| ~ leq(loopcounter,succ(tptp_minus_1))
| ( loopcounter = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),loopcounter) ) ),
inference(monotonicity,[status(thm)],[82]) ).
tff(84,plain,
( ( ~ ! [X: $i] :
( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) )
| ( loopcounter = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),loopcounter)
| ~ leq(loopcounter,succ(tptp_minus_1)) )
<=> ( ~ ! [X: $i] :
( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) )
| ~ leq(loopcounter,succ(tptp_minus_1))
| ( loopcounter = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),loopcounter) ) ),
inference(transitivity,[status(thm)],[83,81]) ).
tff(85,plain,
( ~ ! [X: $i] :
( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) )
| ( loopcounter = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),loopcounter)
| ~ leq(loopcounter,succ(tptp_minus_1)) ),
inference(quant_inst,[status(thm)],]) ).
tff(86,plain,
( ~ ! [X: $i] :
( ( X = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),X)
| ~ leq(X,succ(tptp_minus_1)) )
| ~ leq(loopcounter,succ(tptp_minus_1))
| ( loopcounter = succ(tptp_minus_1) )
| ~ leq(succ(tptp_minus_1),loopcounter) ),
inference(modus_ponens,[status(thm)],[85,84]) ).
tff(87,plain,
loopcounter = succ(tptp_minus_1),
inference(unit_resolution,[status(thm)],[86,80,64,47]) ).
tff(88,plain,
succ(tptp_minus_1) = loopcounter,
inference(symmetry,[status(thm)],[87]) ).
tff(89,plain,
( gt(succ(tptp_minus_1),succ(tptp_minus_1))
<=> gt(loopcounter,succ(tptp_minus_1)) ),
inference(monotonicity,[status(thm)],[88]) ).
tff(90,plain,
( gt(loopcounter,succ(tptp_minus_1))
<=> gt(succ(tptp_minus_1),succ(tptp_minus_1)) ),
inference(symmetry,[status(thm)],[89]) ).
tff(91,plain,
^ [X: $i,Y: $i] :
refl(
( ( ~ leq(succ(X),Y)
| gt(Y,X) )
<=> ( ~ leq(succ(X),Y)
| gt(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(92,plain,
( ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
<=> ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ) ),
inference(quant_intro,[status(thm)],[91]) ).
tff(93,plain,
( ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
<=> ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ) ),
inference(rewrite,[status(thm)],]) ).
tff(94,plain,
^ [X: $i,Y: $i] :
rewrite(
( ( leq(succ(X),Y)
=> gt(Y,X) )
<=> ( ~ leq(succ(X),Y)
| gt(Y,X) ) )),
inference(bind,[status(th)],]) ).
tff(95,plain,
( ! [X: $i,Y: $i] :
( leq(succ(X),Y)
=> gt(Y,X) )
<=> ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ) ),
inference(quant_intro,[status(thm)],[94]) ).
tff(96,axiom,
! [X: $i,Y: $i] :
( leq(succ(X),Y)
=> gt(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_succ_gt) ).
tff(97,plain,
! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(modus_ponens,[status(thm)],[96,95]) ).
tff(98,plain,
! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(modus_ponens,[status(thm)],[97,93]) ).
tff(99,plain,
! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(skolemize,[status(sab)],[98]) ).
tff(100,plain,
! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) ),
inference(modus_ponens,[status(thm)],[99,92]) ).
tff(101,plain,
( ( ~ ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
| ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| gt(loopcounter,succ(tptp_minus_1)) )
<=> ( ~ ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
| ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| gt(loopcounter,succ(tptp_minus_1)) ) ),
inference(rewrite,[status(thm)],]) ).
tff(102,plain,
( ~ ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
| ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| gt(loopcounter,succ(tptp_minus_1)) ),
inference(quant_inst,[status(thm)],]) ).
tff(103,plain,
( ~ ! [X: $i,Y: $i] :
( ~ leq(succ(X),Y)
| gt(Y,X) )
| ~ leq(succ(succ(tptp_minus_1)),loopcounter)
| gt(loopcounter,succ(tptp_minus_1)) ),
inference(modus_ponens,[status(thm)],[102,101]) ).
tff(104,plain,
gt(loopcounter,succ(tptp_minus_1)),
inference(unit_resolution,[status(thm)],[103,100,28]) ).
tff(105,plain,
gt(succ(tptp_minus_1),succ(tptp_minus_1)),
inference(modus_ponens,[status(thm)],[104,90]) ).
tff(106,plain,
^ [X: $i] :
refl(
( ~ gt(X,X)
<=> ~ gt(X,X) )),
inference(bind,[status(th)],]) ).
tff(107,plain,
( ! [X: $i] : ~ gt(X,X)
<=> ! [X: $i] : ~ gt(X,X) ),
inference(quant_intro,[status(thm)],[106]) ).
tff(108,plain,
( ! [X: $i] : ~ gt(X,X)
<=> ! [X: $i] : ~ gt(X,X) ),
inference(rewrite,[status(thm)],]) ).
tff(109,axiom,
! [X: $i] : ~ gt(X,X),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).
tff(110,plain,
! [X: $i] : ~ gt(X,X),
inference(modus_ponens,[status(thm)],[109,108]) ).
tff(111,plain,
! [X: $i] : ~ gt(X,X),
inference(skolemize,[status(sab)],[110]) ).
tff(112,plain,
! [X: $i] : ~ gt(X,X),
inference(modus_ponens,[status(thm)],[111,107]) ).
tff(113,plain,
( ~ ! [X: $i] : ~ gt(X,X)
| ~ gt(succ(tptp_minus_1),succ(tptp_minus_1)) ),
inference(quant_inst,[status(thm)],]) ).
tff(114,plain,
~ gt(succ(tptp_minus_1),succ(tptp_minus_1)),
inference(unit_resolution,[status(thm)],[113,112]) ).
tff(115,plain,
$false,
inference(unit_resolution,[status(thm)],[114,105]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SWV181+1 : TPTP v8.1.0. Bugfixed v3.3.0.
% 0.11/0.13 % Command : z3_tptp -proof -model -t:%d -file:%s
% 0.12/0.32 % Computer : n021.cluster.edu
% 0.12/0.32 % Model : x86_64 x86_64
% 0.12/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.32 % Memory : 8042.1875MB
% 0.12/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.32 % CPULimit : 300
% 0.12/0.32 % WCLimit : 300
% 0.12/0.32 % DateTime : Sun Sep 4 01:37:00 EDT 2022
% 0.12/0.32 % CPUTime :
% 0.12/0.33 Z3tptp [4.8.9.0] (c) 2006-20**. Microsoft Corp.
% 0.12/0.33 Usage: tptp [options] [-file:]file
% 0.12/0.33 -h, -? prints this message.
% 0.12/0.33 -smt2 print SMT-LIB2 benchmark.
% 0.12/0.33 -m, -model generate model.
% 0.12/0.33 -p, -proof generate proof.
% 0.12/0.33 -c, -core generate unsat core of named formulas.
% 0.12/0.33 -st, -statistics display statistics.
% 0.12/0.33 -t:timeout set timeout (in second).
% 0.12/0.33 -smt2status display status in smt2 format instead of SZS.
% 0.12/0.33 -check_status check the status produced by Z3 against annotation in benchmark.
% 0.12/0.33 -<param>:<value> configuration parameter and value.
% 0.12/0.33 -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
%------------------------------------------------------------------------------