%------------------------------------------------------------------------------
% File : CSE_E---1.7
% Problem : SWV158+1 : TPTP v9.2.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% Computer : n010.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 : Tue May 5 05:20:57 PM UTC 2026
% Result : Theorem 1.33s 1.73s
% Output : CNFRefutation 1.33s
% Verified :
% SZS Type : Refutation
% Derivation depth : 4
% Number of leaves : 1
% Syntax : Number of formulae : 7 ( 4 unt; 0 def)
% Number of atoms : 49 ( 18 equ)
% Maximal formula atoms : 15 ( 7 avg)
% Number of connectives : 49 ( 7 ~; 4 |; 28 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 17 con; 0-3 aty)
% Number of variables : 8 ( 0 sgn 8 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(cl5_nebula_norm_0008,conjecture,
( ( 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)
& ! [X14] :
( ( leq(n0,X14)
& leq(X14,pred(pv47)) )
=> a_select3(q,pv10,X14) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X14)),minus(a_select2(x,pv10),a_select2(mu,X14))),tptp_minus_2),times(a_select2(sigma,X14),a_select2(sigma,X14)))),a_select2(rho,X14)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X14))),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))))) )
& ! [X18] :
( ( leq(n0,X18)
& leq(X18,pred(pv10)) )
=> sum(n0,n4,a_select3(q,X18,tptp_sum_index)) = n1 ) )
=> ! [X4] :
( ( leq(n0,X4)
& leq(X4,pv47) )
=> ( pv47 = X4
=> 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) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X4)),minus(a_select2(x,pv10),a_select2(mu,X4))),tptp_minus_2),times(a_select2(sigma,X4),a_select2(sigma,X4)))),a_select2(rho,X4)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X4))),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))))) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0008) ).
fof(c_0_1,negated_conjecture,
~ ( ( 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)
& ! [X14] :
( ( leq(n0,X14)
& leq(X14,pred(pv47)) )
=> a_select3(q,pv10,X14) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X14)),minus(a_select2(x,pv10),a_select2(mu,X14))),tptp_minus_2),times(a_select2(sigma,X14),a_select2(sigma,X14)))),a_select2(rho,X14)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X14))),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))))) )
& ! [X18] :
( ( leq(n0,X18)
& leq(X18,pred(pv10)) )
=> sum(n0,n4,a_select3(q,X18,tptp_sum_index)) = n1 ) )
=> ! [X4] :
( ( leq(n0,X4)
& leq(X4,pv47) )
=> ( pv47 = X4
=> 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) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X4)),minus(a_select2(x,pv10),a_select2(mu,X4))),tptp_minus_2),times(a_select2(sigma,X4),a_select2(sigma,X4)))),a_select2(rho,X4)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X4))),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))))) ) ) ),
inference(assume_negation,[status(cth)],[cl5_nebula_norm_0008]) ).
fof(c_0_2,negated_conjecture,
! [X357,X358] :
( 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)
& ( ~ leq(n0,X357)
| ~ leq(X357,pred(pv47))
| a_select3(q,pv10,X357) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X357)),minus(a_select2(x,pv10),a_select2(mu,X357))),tptp_minus_2),times(a_select2(sigma,X357),a_select2(sigma,X357)))),a_select2(rho,X357)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X357))),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,X358)
| ~ leq(X358,pred(pv10))
| sum(n0,n4,a_select3(q,X358,tptp_sum_index)) = n1 )
& leq(n0,esk24_0)
& leq(esk24_0,pv47)
& pv47 = esk24_0
& 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) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,esk24_0)),minus(a_select2(x,pv10),a_select2(mu,esk24_0))),tptp_minus_2),times(a_select2(sigma,esk24_0),a_select2(sigma,esk24_0)))),a_select2(rho,esk24_0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,esk24_0))),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))))) ),
inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_1])])])]) ).
cnf(c_0_3,negated_conjecture,
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) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,esk24_0)),minus(a_select2(x,pv10),a_select2(mu,esk24_0))),tptp_minus_2),times(a_select2(sigma,esk24_0),a_select2(sigma,esk24_0)))),a_select2(rho,esk24_0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,esk24_0))),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))))),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_4,negated_conjecture,
pv47 = esk24_0,
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_5,negated_conjecture,
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)))),
inference(split_conjunct,[status(thm)],[c_0_2]) ).
cnf(c_0_6,negated_conjecture,
$false,
inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_3,c_0_4]),c_0_4]),c_0_4]),c_0_4]),c_0_4]),c_0_4]),c_0_5])]),
[proof] ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SWV158+1 : TPTP v9.2.1. Bugfixed v3.3.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/lemma_parallel_prover %s --lemma-prover /export/starexec/sandbox2/solver/bin/cse --final-prover /export/starexec/sandbox2/solver/bin/eprover --proof-time %d --global-time-limit %d
% 0.16/0.33 % Computer : n010.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue May 5 04:57:21 EDT 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.34 % start to proof: theBenchmark
% 1.33/1.73 % Version : CSE_E---1.7
% 1.33/1.73 % Problem : theBenchmark.p
% 1.33/1.73 % SZS status Theorem for theBenchmark.p
% 1.33/1.73 % SZS output start CNFRefutation
% See solution above
% 1.33/1.73 % Total time : 1.374s
%------------------------------------------------------------------------------