%------------------------------------------------------------------------------
% File : Z3---4.15.1
% Problem : SWV160+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp
% Command : run_E %s %d THM
% Computer : n002.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 05:31:37 AM UTC 2025
% Result : Theorem 0.21s 0.44s
% Output : Proof 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 12
% Syntax : Number of formulae : 27 ( 10 unt; 0 typ; 0 def)
% Number of atoms : 111 ( 18 equ)
% Maximal formula atoms : 29 ( 4 avg)
% Number of connectives : 113 ( 31 ~; 15 |; 34 &)
% ( 23 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 17 ( 5 avg)
% Maximal term depth : 12 ( 2 avg)
% Number of FOOLs : 2 ( 2 fml; 0 var)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 27 ( 27 usr; 16 con; 0-3 aty)
% Number of variables : 40 ( 37 !; 0 ?; 40 :)
% Comments :
%------------------------------------------------------------------------------
tff(gt_type,type,
gt: ( $i * $i ) > $o ).
tff(pv10_type,type,
pv10: $i ).
tff(leq_type,type,
leq: ( $i * $i ) > $o ).
tff(pred_type,type,
pred: $i > $i ).
tff(n1_type,type,
n1: $i ).
tff(sum_type,type,
sum: ( $i * $i * $i ) > $i ).
tff(a_select3_type,type,
a_select3: ( $i * $i * $i ) > $i ).
tff(tptp_sum_index_type,type,
tptp_sum_index: $i ).
tff(q_type,type,
q: $i ).
tff(n4_type,type,
n4: $i ).
tff(n0_type,type,
n0: $i ).
tff(divide_type,type,
divide: ( $i * $i ) > $i ).
tff(times_type,type,
times: ( $i * $i ) > $i ).
tff(a_select2_type,type,
a_select2: ( $i * $i ) > $i ).
tff(sigma_type,type,
sigma: $i ).
tff(sqrt_type,type,
sqrt: $i > $i ).
tff(tptp_pi_type,type,
tptp_pi: $i ).
tff(n2_type,type,
n2: $i ).
tff(rho_type,type,
rho: $i ).
tff(exp_type,type,
exp: $i > $i ).
tff(tptp_minus_2_type,type,
tptp_minus_2: $i ).
tff(minus_type,type,
minus: ( $i * $i ) > $i ).
tff(mu_type,type,
mu: $i ).
tff(x_type,type,
x: $i ).
tff(pv47_type,type,
pv47: $i ).
tff(n135299_type,type,
n135299: $i ).
tff(pv84_type,type,
pv84: $i ).
tff(cond_type,type,
cond: ( $i * $i * $i ) > $i ).
tff(tptp_term_equals_type,type,
tptp_term_equals: ( $i * $i ) > $i ).
tff(1,plain,
^ [X: $i,Y: $i] :
refl(( ( leq(X,pred(Y))
<=> gt(Y,X) )
<=> ( leq(X,pred(Y))
<=> gt(Y,X) ) )),
inference(bind,[status(th)],[]) ).
tff(2,plain,
( ! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) )
<=> ! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ) ),
inference(quant_intro,[status(thm)],[1]) ).
tff(3,plain,
( ! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) )
<=> ! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(4,axiom,
! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt_pred) ).
tff(5,plain,
! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
inference(modus_ponens,[status(thm)],[4,3]) ).
tff(6,plain,
! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
inference(skolemize,[status(sab)],[5]) ).
tff(7,plain,
! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) ),
inference(modus_ponens,[status(thm)],[6,2]) ).
tff(8,plain,
( ~ ! [X: $i,Y: $i] :
( leq(X,pred(Y))
<=> gt(Y,X) )
| ( leq(pv10,pred(pv10))
<=> gt(pv10,pv10) ) ),
inference(quant_inst,[status(thm)],[]) ).
tff(9,plain,
( leq(pv10,pred(pv10))
<=> gt(pv10,pv10) ),
inference(unit_resolution,[status(thm)],[8,7]) ).
tff(10,plain,
( leq(pv10,pred(pv10))
<=> leq(pv10,pred(pv10)) ),
inference(rewrite,[status(thm)],[]) ).
tff(11,plain,
( ~ ( ( ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))) )
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [A: $i] :
( ( leq(n0,A)
& leq(A,pred(pv47)) )
=> ( a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) )
& ! [B: $i] :
( ( leq(n0,B)
& leq(B,pred(pv10)) )
=> ( sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) ) )
=> ! [C: $i] :
( ( leq(n0,C)
& leq(C,pred(pv10)) )
=> ( ( pv10 = C )
=> ( sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,C,tptp_sum_index))) = n1 ) ) ) )
<=> ~ ( ( sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,pv10,tptp_sum_index))) = n1 )
| ~ leq(pv10,pred(pv10))
| ~ leq(n0,pv10)
| ~ ( ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))) )
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [A: $i] :
( ~ ( leq(n0,A)
& leq(A,pred(pv47)) )
| ( a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) )
& ! [B: $i] :
( ~ ( leq(n0,B)
& leq(B,pred(pv10)) )
| ( sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) ) ) ) ),
inference(rewrite,[status(thm)],[]) ).
tff(12,axiom,
~ ( ( ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))) )
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [A: $i] :
( ( leq(n0,A)
& leq(A,pred(pv47)) )
=> ( a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) )
& ! [B: $i] :
( ( leq(n0,B)
& leq(B,pred(pv10)) )
=> ( sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) ) )
=> ! [C: $i] :
( ( leq(n0,C)
& leq(C,pred(pv10)) )
=> ( ( pv10 = C )
=> ( sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,C,tptp_sum_index))) = n1 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0010) ).
tff(13,plain,
~ ( ( sum(n0,n4,cond(tptp_term_equals(pv47,tptp_sum_index),divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,pv47)),minus(a_select2(x,pv10),a_select2(mu,pv47))),tptp_minus_2),times(a_select2(sigma,pv47),a_select2(sigma,pv47)))),a_select2(rho,pv47)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,pv47))),pv84),a_select3(q,pv10,tptp_sum_index))) = n1 )
| ~ leq(pv10,pred(pv10))
| ~ leq(n0,pv10)
| ~ ( ( pv84 = sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index)))) )
& leq(n0,pv10)
& leq(n0,pv47)
& leq(pv10,n135299)
& leq(pv47,n4)
& ! [A: $i] :
( ~ ( leq(n0,A)
& leq(A,pred(pv47)) )
| ( a_select3(q,pv10,A) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,A)),minus(a_select2(x,pv10),a_select2(mu,A))),tptp_minus_2),times(a_select2(sigma,A),a_select2(sigma,A)))),a_select2(rho,A)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,A))),sum(n0,n4,divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index)),minus(a_select2(x,pv10),a_select2(mu,tptp_sum_index))),tptp_minus_2),times(a_select2(sigma,tptp_sum_index),a_select2(sigma,tptp_sum_index)))),a_select2(rho,tptp_sum_index)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,tptp_sum_index))))) ) )
& ! [B: $i] :
( ~ ( leq(n0,B)
& leq(B,pred(pv10)) )
| ( sum(n0,n4,a_select3(q,B,tptp_sum_index)) = n1 ) ) ) ),
inference(modus_ponens,[status(thm)],[12,11]) ).
tff(14,plain,
leq(pv10,pred(pv10)),
inference(or_elim,[status(thm)],[13]) ).
tff(15,plain,
leq(pv10,pred(pv10)),
inference(modus_ponens,[status(thm)],[14,10]) ).
tff(16,plain,
( ~ ( leq(pv10,pred(pv10))
<=> gt(pv10,pv10) )
| ~ leq(pv10,pred(pv10))
| gt(pv10,pv10) ),
inference(tautology,[status(thm)],[]) ).
tff(17,plain,
( ~ ( leq(pv10,pred(pv10))
<=> gt(pv10,pv10) )
| gt(pv10,pv10) ),
inference(unit_resolution,[status(thm)],[16,15]) ).
tff(18,plain,
gt(pv10,pv10),
inference(unit_resolution,[status(thm)],[17,9]) ).
tff(19,plain,
^ [X: $i] :
refl(( ~ gt(X,X)
<=> ~ gt(X,X) )),
inference(bind,[status(th)],[]) ).
tff(20,plain,
( ! [X: $i] : ~ gt(X,X)
<=> ! [X: $i] : ~ gt(X,X) ),
inference(quant_intro,[status(thm)],[19]) ).
tff(21,plain,
( ! [X: $i] : ~ gt(X,X)
<=> ! [X: $i] : ~ gt(X,X) ),
inference(rewrite,[status(thm)],[]) ).
tff(22,axiom,
! [X: $i] : ~ gt(X,X),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).
tff(23,plain,
! [X: $i] : ~ gt(X,X),
inference(modus_ponens,[status(thm)],[22,21]) ).
tff(24,plain,
! [X: $i] : ~ gt(X,X),
inference(skolemize,[status(sab)],[23]) ).
tff(25,plain,
! [X: $i] : ~ gt(X,X),
inference(modus_ponens,[status(thm)],[24,20]) ).
tff(26,plain,
( ~ ! [X: $i] : ~ gt(X,X)
| ~ gt(pv10,pv10) ),
inference(quant_inst,[status(thm)],[]) ).
tff(27,plain,
$false,
inference(unit_resolution,[status(thm)],[26,25,18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.13 % Problem : SWV160+1 : TPTP v9.0.0. Bugfixed v3.3.0.
% 0.09/0.13 % Command : run_E %s %d THM
% 0.13/0.34 % Computer : n002.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Fri Jun 20 09:32:01 EDT 2025
% 0.13/0.35 % CPUTime :
% 0.21/0.44 % SZS status Theorem
% 0.21/0.44 % SZS output start Proof
% See solution above
% 0.21/0.46 % E exiting
%------------------------------------------------------------------------------