%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV157+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n004.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri Sep 25 03:16:33 PM UTC 2026
% Result : Theorem 3.36s 11.24s
% Output : CNFRefutation 3.36s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 4
% Syntax : Number of formulae : 38 ( 15 unt; 0 def)
% Number of atoms : 152 ( 51 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 169 ( 55 ~; 42 |; 60 &)
% ( 1 <=>; 11 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 11 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% 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 : 44 ( 0 sgn 41 !; 3 ?; 7 :)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [X0,X1] :
( ( X0 != X1
& leq(X0,X1) )
=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt2) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt_pred) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',pred_minus_1) ).
fof(f53,conjecture,
( ( ! [X1] :
( ( leq(X1,pred(pv10))
& leq(n0,X1) )
=> sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1 )
& ! [X0] :
( ( leq(X0,pred(pv47))
& leq(n0,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))))) )
& 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))))) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0007) ).
fof(f54,negated_conjecture,
~ ( ( ! [X1] :
( ( leq(X1,pred(pv10))
& leq(n0,X1) )
=> sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1 )
& ! [X0] :
( ( leq(X0,pred(pv47))
& leq(n0,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))))) )
& 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(negated_conjecture,[status(cth)],[f53]) ).
fof(f102,plain,
( ! [X1] :
( ~ leq(X1,pred(pv10))
| ~ leq(n0,X1)
| sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1 )
& ! [X0] :
( ~ leq(X0,pred(pv47))
| ~ leq(n0,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))))) )
& 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(ennf_transformation,[],[f54]) ).
fof(f103,plain,
( ! [X1] :
( ~ leq(X1,pred(pv10))
| ~ leq(n0,X1)
| sum(n0,n4,a_select3(q,X1,tptp_sum_index)) = n1 )
& ! [X0] :
( ~ leq(X0,pred(pv47))
| ~ leq(n0,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))))) )
& 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(flattening,[],[f102]) ).
fof(f106,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| gt(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f107,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| gt(X1,X0) ),
inference(flattening,[],[f106]) ).
fof(f126,plain,
( ! [X2] :
( ~ leq(X2,pred(pv10))
| ~ leq(n0,X2)
| n1 = sum(n0,n4,a_select3(q,X2,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))))
& ? [X0] :
( leq(X0,pv47)
& leq(n0,X0)
& pv47 != 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))))) ) ),
inference(rectify,[],[f103]) ).
fof(f127,plain,
( ! [X2] :
( ~ leq(X2,pred(pv10))
| ~ leq(n0,X2)
| n1 = sum(n0,n4,a_select3(q,X2,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))))
& leq(sK0,pv47)
& leq(n0,sK0)
& pv47 != sK0
& a_select3(q,pv10,sK0) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK0)),minus(a_select2(x,pv10),a_select2(mu,sK0))),tptp_minus_2),times(a_select2(sigma,sK0),a_select2(sigma,sK0)))),a_select2(rho,sK0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK0))),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(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f126]) ).
fof(f128,plain,
! [X0,X1] :
( ( ~ leq(X0,pred(X1))
| gt(X1,X0) )
& ( ~ gt(X1,X0)
| leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f132,plain,
! [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))))) ),
inference(cnf_transformation,[],[f127]) ).
fof(f137,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,[],[f127]) ).
fof(f138,plain,
leq(sK0,pv47),
inference(cnf_transformation,[],[f127]) ).
fof(f139,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f127]) ).
fof(f140,plain,
pv47 != sK0,
inference(cnf_transformation,[],[f127]) ).
fof(f141,plain,
a_select3(q,pv10,sK0) != divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK0)),minus(a_select2(x,pv10),a_select2(mu,sK0))),tptp_minus_2),times(a_select2(sigma,sK0),a_select2(sigma,sK0)))),a_select2(rho,sK0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK0))),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,[],[f127]) ).
fof(f143,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| gt(X1,X0) ),
inference(cnf_transformation,[],[f107]) ).
fof(f148,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,pred(X1)) ),
inference(cnf_transformation,[],[f128]) ).
fof(f184,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f221,plain,
! [X1] :
( ~ leq(X1,minus(pv47,n1))
| ~ 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))))) ),
inference(definition_unfolding,[],[f132,f184]) ).
fof(f225,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,minus(X1,n1)) ),
inference(definition_unfolding,[],[f148,f184]) ).
tcf(c_49,negated_conjecture,
divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK0)),minus(a_select2(x,pv10),a_select2(mu,sK0))),tptp_minus_2),times(a_select2(sigma,sK0),a_select2(sigma,sK0)))),a_select2(rho,sK0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK0))),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,sK0),
inference(cnf_transformation,[],[f141]) ).
tcf(c_50,negated_conjecture,
sK0 != pv47,
inference(cnf_transformation,[],[f140]) ).
tcf(c_51,negated_conjecture,
leq(n0,sK0),
inference(cnf_transformation,[],[f139]) ).
tcf(c_52,negated_conjecture,
leq(sK0,pv47),
inference(cnf_transformation,[],[f138]) ).
tcf(c_53,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,[],[f137]) ).
tcf(c_58,negated_conjecture,
! [X0: $i] :
( ( 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) )
| ~ leq(n0,X0)
| ~ leq(X0,minus(pv47,n1)) ),
inference(cnf_transformation,[],[f221]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( gt(X1,X0)
| ( X0 = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( leq(X1,minus(X0,n1))
| ~ gt(X0,X1) ),
inference(cnf_transformation,[],[f225]) ).
tcf(c_726,plain,
divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK0)),minus(a_select2(x,pv10),a_select2(mu,sK0))),tptp_minus_2),times(a_select2(sigma,sK0),a_select2(sigma,sK0)))),a_select2(rho,sK0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK0))),pv84) != a_select3(q,pv10,sK0),
inference(light_normalisation,[status(thm)],[c_49,c_53]) ).
tcf(c_727,plain,
! [X0: $i] :
( ( 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) )
| ~ leq(n0,X0)
| ~ leq(X0,minus(pv47,n1)) ),
inference(light_normalisation,[status(thm)],[c_58,c_53]) ).
tcf(c_1928,plain,
! [X0: $i] :
( ( 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) )
| ~ gt(pv47,X0)
| ~ leq(n0,X0) ),
inference(superposition,[status(thm)],[c_65,c_727]) ).
tcf(c_2212,plain,
( ( divide(divide(times(exp(divide(divide(times(minus(a_select2(x,pv10),a_select2(mu,sK0)),minus(a_select2(x,pv10),a_select2(mu,sK0))),tptp_minus_2),times(a_select2(sigma,sK0),a_select2(sigma,sK0)))),a_select2(rho,sK0)),times(sqrt(times(n2,tptp_pi)),a_select2(sigma,sK0))),pv84) = a_select3(q,pv10,sK0) )
| ~ gt(pv47,sK0) ),
inference(superposition,[status(thm)],[c_51,c_1928]) ).
tcf(c_2230,plain,
~ gt(pv47,sK0),
inference(forward_subsumption_resolution,[status(thm)],[c_2212,c_726]) ).
tcf(c_2701,plain,
( gt(pv47,sK0)
| ( sK0 = pv47 )
| ~ leq(sK0,pv47) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_2702,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2701,c_2230,c_50,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV157+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.05 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/10.39 % Computer : n004.cluster.edu
% 0.11/10.39 % Model : x86_64 x86_64
% 0.11/10.39 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/10.39 % Memory : 8046.5625MB
% 0.11/10.39 % OS : Linux 6.8.0-71-generic
% 0.11/10.39 % CPULimit : 300
% 0.11/10.39 % WCLimit : 300
% 0.11/10.39 % DateTime : Thu Sep 24 18:38:19 UTC 2026
% 0.11/10.39 % CPUTime :
% 0.11/10.39 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/10.43 Running first-order theorem proving
% 0.15/10.43 Running: /export/starexec/sandbox/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.15/10.44
% 0.15/10.44 % ======== iProver multi-core TPTP/SMT =========
% 0.15/10.44
% 0.15/10.45 % Detected problem language: tptp
% 0.15/10.46 % Proving...
% 3.36/11.24 % SZS status Started for theBenchmark.p
% 3.36/11.24 % SZS status Theorem for theBenchmark.p
% 3.36/11.24
% 3.36/11.24 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.36/11.24
% 3.36/11.24 % ------ iProver source info
% 3.36/11.24
% 3.36/11.24 % git: date: 2026-07-19 20:42:38 +0200
% 3.36/11.24 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.36/11.24 % git: non_committed_changes: false
% 3.36/11.24
% 3.36/11.24 % ------ Parsing...
% 3.36/11.24 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.36/11.24
% 3.36/11.24 % ------ Preprocessing... sup_sim: 12 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.36/11.24
% 3.36/11.24 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.36/11.24
% 3.36/11.24 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.36/11.24 % ------ Proving...
% 3.36/11.24 % ------ Problem Properties
% 3.36/11.24
% 3.36/11.24 %
% 3.36/11.24 % clauses 88
% 3.36/11.24 % conjectures 9
% 3.36/11.24 % EPR 56
% 3.36/11.24 % Horn 81
% 3.36/11.24 % unary 66
% 3.36/11.24 % binary 10
% 3.36/11.24 % lits 137
% 3.36/11.24 % lits eq 46
% 3.36/11.24 % fd_pure 0
% 3.36/11.24 % fd_pseudo 0
% 3.36/11.24 % fd_cond 6
% 3.36/11.24 % fd_pseudo_cond 2
% 3.36/11.24 % AC symbols 0
% 3.36/11.24
% 3.36/11.24 % ------ Schedule dynamic 5 is on
% 3.36/11.24
% 3.36/11.24 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.36/11.24
% 3.36/11.24
% 3.36/11.24 % ------
% 3.36/11.24 % Current options:
% 3.36/11.24 % ------
% 3.36/11.24
% 3.36/11.24
% 3.36/11.24 %
% 3.36/11.24
% 3.36/11.24 % ------ Proving...
% 3.36/11.24 %
% 3.36/11.24
% 3.36/11.24 % SZS status Theorem for theBenchmark.p
% 3.36/11.24
% 3.36/11.24 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.36/11.24
% 3.36/11.24
%------------------------------------------------------------------------------