TSTP Solution File: SWV157+1 by iProver---3.8
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- Process Solution
%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SWV157+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n028.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 Aug 31 22:31:23 EDT 2023
% Result : Theorem 0.52s 1.22s
% Output : CNFRefutation 0.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 15 unt; 0 def)
% Number of atoms : 174 ( 60 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 193 ( 59 ~; 41 |; 75 &)
% ( 1 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 17 con; 0-3 aty)
% Number of variables : 48 ( 0 sgn; 37 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( ( X0 != X1
& leq(X0,X1) )
=> gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt2) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',leq_gt_pred) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',pred_minus_1) ).
fof(f53,conjecture,
( ( ! [X17] :
( ( leq(X17,pred(pv10))
& leq(n0,X17) )
=> n1 = sum(n0,n4,a_select3(q,X17,tptp_sum_index)) )
& ! [X13] :
( ( leq(X13,pred(pv47))
& leq(n0,X13) )
=> a_select3(q,pv10,X13) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X13)),minus(a_select2(x,pv10),a_select2(mu,X13))),tptp_minus_2),times(a_select2(sigma,X13),a_select2(sigma,X13)))),a_select2(rho,X13)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X13))),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(pv47,n4)
& leq(pv10,n135299)
& leq(n0,pv47)
& 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)))) )
=> ! [X3] :
( ( leq(X3,pv47)
& leq(n0,X3) )
=> ( pv47 != X3
=> a_select3(q,pv10,X3) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X3)),minus(a_select2(x,pv10),a_select2(mu,X3))),tptp_minus_2),times(a_select2(sigma,X3),a_select2(sigma,X3)))),a_select2(rho,X3)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X3))),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_0007) ).
fof(f54,negated_conjecture,
~ ( ( ! [X17] :
( ( leq(X17,pred(pv10))
& leq(n0,X17) )
=> n1 = sum(n0,n4,a_select3(q,X17,tptp_sum_index)) )
& ! [X13] :
( ( leq(X13,pred(pv47))
& leq(n0,X13) )
=> a_select3(q,pv10,X13) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X13)),minus(a_select2(x,pv10),a_select2(mu,X13))),tptp_minus_2),times(a_select2(sigma,X13),a_select2(sigma,X13)))),a_select2(rho,X13)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X13))),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(pv47,n4)
& leq(pv10,n135299)
& leq(n0,pv47)
& 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)))) )
=> ! [X3] :
( ( leq(X3,pv47)
& leq(n0,X3) )
=> ( pv47 != X3
=> a_select3(q,pv10,X3) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X3)),minus(a_select2(x,pv10),a_select2(mu,X3))),tptp_minus_2),times(a_select2(sigma,X3),a_select2(sigma,X3)))),a_select2(rho,X3)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X3))),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(negated_conjecture,[],[f53]) ).
fof(f122,plain,
~ ( ( ! [X0] :
( ( leq(X0,pred(pv10))
& leq(n0,X0) )
=> n1 = sum(n0,n4,a_select3(q,X0,tptp_sum_index)) )
& ! [X1] :
( ( leq(X1,pred(pv47))
& leq(n0,X1) )
=> a_select3(q,pv10,X1) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),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(pv47,n4)
& leq(pv10,n135299)
& leq(n0,pv47)
& 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)))) )
=> ! [X2] :
( ( leq(X2,pv47)
& leq(n0,X2) )
=> ( pv47 != X2
=> a_select3(q,pv10,X2) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X2)),minus(a_select2(x,pv10),a_select2(mu,X2))),tptp_minus_2),times(a_select2(sigma,X2),a_select2(sigma,X2)))),a_select2(rho,X2)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X2))),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(rectify,[],[f54]) ).
fof(f129,plain,
! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ),
inference(ennf_transformation,[],[f9]) ).
fof(f130,plain,
! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ),
inference(flattening,[],[f129]) ).
fof(f164,plain,
( ? [X2] :
( a_select3(q,pv10,X2) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X2)),minus(a_select2(x,pv10),a_select2(mu,X2))),tptp_minus_2),times(a_select2(sigma,X2),a_select2(sigma,X2)))),a_select2(rho,X2)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X2))),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)))))
& pv47 != X2
& leq(X2,pv47)
& leq(n0,X2) )
& ! [X0] :
( n1 = sum(n0,n4,a_select3(q,X0,tptp_sum_index))
| ~ leq(X0,pred(pv10))
| ~ leq(n0,X0) )
& ! [X1] :
( a_select3(q,pv10,X1) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),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(X1,pred(pv47))
| ~ leq(n0,X1) )
& leq(pv47,n4)
& leq(pv10,n135299)
& leq(n0,pv47)
& 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)))) ),
inference(ennf_transformation,[],[f122]) ).
fof(f165,plain,
( ? [X2] :
( a_select3(q,pv10,X2) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X2)),minus(a_select2(x,pv10),a_select2(mu,X2))),tptp_minus_2),times(a_select2(sigma,X2),a_select2(sigma,X2)))),a_select2(rho,X2)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X2))),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)))))
& pv47 != X2
& leq(X2,pv47)
& leq(n0,X2) )
& ! [X0] :
( n1 = sum(n0,n4,a_select3(q,X0,tptp_sum_index))
| ~ leq(X0,pred(pv10))
| ~ leq(n0,X0) )
& ! [X1] :
( a_select3(q,pv10,X1) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X1)),minus(a_select2(x,pv10),a_select2(mu,X1))),tptp_minus_2),times(a_select2(sigma,X1),a_select2(sigma,X1)))),a_select2(rho,X1)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X1))),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(X1,pred(pv47))
| ~ leq(n0,X1) )
& leq(pv47,n4)
& leq(pv10,n135299)
& leq(n0,pv47)
& 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)))) ),
inference(flattening,[],[f164]) ).
fof(f185,plain,
! [X0,X1] :
( ( leq(X0,pred(X1))
| ~ gt(X1,X0) )
& ( gt(X1,X0)
| ~ leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f232,plain,
( ? [X0] :
( a_select3(q,pv10,X0) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),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)))))
& pv47 != X0
& leq(X0,pv47)
& leq(n0,X0) )
& ! [X1] :
( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
| ~ leq(X1,pred(pv10))
| ~ leq(n0,X1) )
& ! [X2] :
( a_select3(q,pv10,X2) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X2)),minus(a_select2(x,pv10),a_select2(mu,X2))),tptp_minus_2),times(a_select2(sigma,X2),a_select2(sigma,X2)))),a_select2(rho,X2)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X2))),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(X2,pred(pv47))
| ~ leq(n0,X2) )
& leq(pv47,n4)
& leq(pv10,n135299)
& leq(n0,pv47)
& 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)))) ),
inference(rectify,[],[f165]) ).
fof(f233,plain,
( ? [X0] :
( a_select3(q,pv10,X0) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),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)))))
& pv47 != X0
& leq(X0,pv47)
& leq(n0,X0) )
=> ( a_select3(q,pv10,sK31) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK31))),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)))))
& pv47 != sK31
& leq(sK31,pv47)
& leq(n0,sK31) ) ),
introduced(choice_axiom,[]) ).
fof(f234,plain,
( a_select3(q,pv10,sK31) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK31))),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)))))
& pv47 != sK31
& leq(sK31,pv47)
& leq(n0,sK31)
& ! [X1] :
( n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index))
| ~ leq(X1,pred(pv10))
| ~ leq(n0,X1) )
& ! [X2] :
( a_select3(q,pv10,X2) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X2)),minus(a_select2(x,pv10),a_select2(mu,X2))),tptp_minus_2),times(a_select2(sigma,X2),a_select2(sigma,X2)))),a_select2(rho,X2)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X2))),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(X2,pred(pv47))
| ~ leq(n0,X2) )
& leq(pv47,n4)
& leq(pv10,n135299)
& leq(n0,pv47)
& 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)))) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK31])],[f232,f233]) ).
fof(f241,plain,
! [X0,X1] :
( gt(X1,X0)
| X0 = X1
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f130]) ).
fof(f243,plain,
! [X0,X1] :
( leq(X0,pred(X1))
| ~ gt(X1,X0) ),
inference(cnf_transformation,[],[f185]) ).
fof(f325,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f345,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)))),
inference(cnf_transformation,[],[f234]) ).
fof(f350,plain,
! [X2] :
( a_select3(q,pv10,X2) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X2)),minus(a_select2(x,pv10),a_select2(mu,X2))),tptp_minus_2),times(a_select2(sigma,X2),a_select2(sigma,X2)))),a_select2(rho,X2)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X2))),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(X2,pred(pv47))
| ~ leq(n0,X2) ),
inference(cnf_transformation,[],[f234]) ).
fof(f352,plain,
leq(n0,sK31),
inference(cnf_transformation,[],[f234]) ).
fof(f353,plain,
leq(sK31,pv47),
inference(cnf_transformation,[],[f234]) ).
fof(f354,plain,
pv47 != sK31,
inference(cnf_transformation,[],[f234]) ).
fof(f355,plain,
a_select3(q,pv10,sK31) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK31))),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(cnf_transformation,[],[f234]) ).
fof(f403,plain,
! [X0,X1] :
( leq(X0,minus(X1,n1))
| ~ gt(X1,X0) ),
inference(definition_unfolding,[],[f243,f325]) ).
fof(f425,plain,
! [X2] :
( a_select3(q,pv10,X2) = divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X2)),minus(a_select2(x,pv10),a_select2(mu,X2))),tptp_minus_2),times(a_select2(sigma,X2),a_select2(sigma,X2)))),a_select2(rho,X2)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X2))),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(X2,minus(pv47,n1))
| ~ leq(n0,X2) ),
inference(definition_unfolding,[],[f350,f325]) ).
cnf(c_55,plain,
( ~ leq(X0,X1)
| X0 = X1
| gt(X1,X0) ),
inference(cnf_transformation,[],[f241]) ).
cnf(c_56,plain,
( ~ gt(X0,X1)
| leq(X1,minus(X0,n1)) ),
inference(cnf_transformation,[],[f403]) ).
cnf(c_157,negated_conjecture,
divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK31))),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))))) != a_select3(q,pv10,sK31),
inference(cnf_transformation,[],[f355]) ).
cnf(c_158,negated_conjecture,
sK31 != pv47,
inference(cnf_transformation,[],[f354]) ).
cnf(c_159,negated_conjecture,
leq(sK31,pv47),
inference(cnf_transformation,[],[f353]) ).
cnf(c_160,negated_conjecture,
leq(n0,sK31),
inference(cnf_transformation,[],[f352]) ).
cnf(c_162,negated_conjecture,
( ~ leq(X0,minus(pv47,n1))
| ~ leq(n0,X0)
| divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),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))))) = a_select3(q,pv10,X0) ),
inference(cnf_transformation,[],[f425]) ).
cnf(c_167,negated_conjecture,
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)))) = pv84,
inference(cnf_transformation,[],[f345]) ).
cnf(c_2560,plain,
divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK31))),pv84) != a_select3(q,pv10,sK31),
inference(light_normalisation,[status(thm)],[c_157,c_167]) ).
cnf(c_2577,plain,
( ~ leq(X0,minus(pv47,n1))
| ~ leq(n0,X0)
| divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),pv84) = a_select3(q,pv10,X0) ),
inference(light_normalisation,[status(thm)],[c_162,c_167]) ).
cnf(c_9094,plain,
( ~ gt(pv47,X0)
| ~ leq(n0,X0)
| divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,X0)),minus(a_select2(x,pv10),a_select2(mu,X0))),tptp_minus_2),times(a_select2(sigma,X0),a_select2(sigma,X0)))),a_select2(rho,X0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,X0))),pv84) = a_select3(q,pv10,X0) ),
inference(superposition,[status(thm)],[c_56,c_2577]) ).
cnf(c_10825,plain,
( sK31 = pv47
| gt(pv47,sK31) ),
inference(superposition,[status(thm)],[c_159,c_55]) ).
cnf(c_10883,plain,
gt(pv47,sK31),
inference(forward_subsumption_resolution,[status(thm)],[c_10825,c_158]) ).
cnf(c_11038,plain,
( ~ leq(n0,sK31)
| divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK31)),minus(a_select2(x,pv10),a_select2(mu,sK31))),tptp_minus_2),times(a_select2(sigma,sK31),a_select2(sigma,sK31)))),a_select2(rho,sK31)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK31))),pv84) = a_select3(q,pv10,sK31) ),
inference(superposition,[status(thm)],[c_10883,c_9094]) ).
cnf(c_11041,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_11038,c_2560,c_160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SWV157+1 : TPTP v8.1.2. Bugfixed v3.3.0.
% 0.07/0.13 % Command : run_iprover %s %d THM
% 0.13/0.34 % Computer : n028.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 : Tue Aug 29 07:34:11 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.20/0.48 Running first-order theorem proving
% 0.20/0.48 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.52/1.22 % SZS status Started for theBenchmark.p
% 0.52/1.22 % SZS status Theorem for theBenchmark.p
% 0.52/1.22
% 0.52/1.22 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 0.52/1.22
% 0.52/1.22 ------ iProver source info
% 0.52/1.22
% 0.52/1.22 git: date: 2023-05-31 18:12:56 +0000
% 0.52/1.22 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 0.52/1.22 git: non_committed_changes: false
% 0.52/1.22 git: last_make_outside_of_git: false
% 0.52/1.22
% 0.52/1.22 ------ Parsing...
% 0.52/1.22 ------ Clausification by vclausify_rel & Parsing by iProver...
% 0.52/1.22
% 0.52/1.22 ------ Preprocessing... sup_sim: 18 sf_s rm: 1 0s sf_e pe_s pe_e
% 0.52/1.22
% 0.52/1.22 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 0.52/1.22
% 0.52/1.22 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.52/1.22 ------ Proving...
% 0.52/1.22 ------ Problem Properties
% 0.52/1.22
% 0.52/1.22
% 0.52/1.22 clauses 166
% 0.52/1.22 conjectures 9
% 0.52/1.22 EPR 58
% 0.52/1.22 Horn 116
% 0.52/1.22 unary 70
% 0.52/1.22 binary 34
% 0.52/1.22 lits 509
% 0.52/1.22 lits eq 118
% 0.52/1.22 fd_pure 0
% 0.52/1.22 fd_pseudo 0
% 0.52/1.22 fd_cond 6
% 0.52/1.22 fd_pseudo_cond 4
% 0.52/1.22 AC symbols 0
% 0.52/1.22
% 0.52/1.22 ------ Schedule dynamic 5 is on
% 0.52/1.22
% 0.52/1.22 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.52/1.22
% 0.52/1.22
% 0.52/1.22 ------
% 0.52/1.22 Current options:
% 0.52/1.22 ------
% 0.52/1.22
% 0.52/1.22
% 0.52/1.22
% 0.52/1.22
% 0.52/1.22 ------ Proving...
% 0.52/1.22
% 0.52/1.22
% 0.52/1.22 % SZS status Theorem for theBenchmark.p
% 0.52/1.22
% 0.52/1.22 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.52/1.22
% 0.52/1.22
%------------------------------------------------------------------------------