%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV160+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n020.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 03:16:34 PM UTC 2026
% Result : Theorem 2.62s 1.10s
% Output : CNFRefutation 2.62s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 4
% Syntax : Number of formulae : 22 ( 11 unt; 0 def)
% Number of atoms : 113 ( 33 equ)
% Maximal formula atoms : 15 ( 5 avg)
% Number of connectives : 120 ( 29 ~; 21 |; 59 &)
% ( 1 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 5 avg)
% Maximal term depth : 12 ( 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 : 28 ( 28 usr; 17 con; 0-3 aty)
% Number of variables : 32 ( 0 sgn 29 !; 3 ?; 3 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).
fof(f10,axiom,
! [X0,X1] :
( leq(X0,pred(X1))
<=> gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_gt_pred) ).
fof(f39,axiom,
! [X0] : minus(X0,n1) = pred(X0),
file('/export/starexec/sandbox2/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,pred(pv10))
& leq(n0,X2) )
=> ( pv10 = X2
=> 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,X2,tptp_sum_index))) = n1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0010) ).
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,pred(pv10))
& leq(n0,X2) )
=> ( pv10 = X2
=> 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,X2,tptp_sum_index))) = n1 ) ) ),
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,pred(pv10))
& leq(n0,X2)
& pv10 = X2
& 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,X2,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,pred(pv10))
& leq(n0,X2)
& pv10 = X2
& 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,X2,tptp_sum_index))) ) ),
inference(flattening,[],[f102]) ).
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,pred(pv10))
& leq(n0,X0)
& pv10 = X0
& 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,X0,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,pred(pv10))
& leq(n0,sK0)
& pv10 = sK0
& 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,sK0,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(f138,plain,
leq(sK0,pred(pv10)),
inference(cnf_transformation,[],[f127]) ).
fof(f140,plain,
pv10 = sK0,
inference(cnf_transformation,[],[f127]) ).
fof(f147,plain,
! [X0,X1] :
( ~ leq(X0,pred(X1))
| gt(X1,X0) ),
inference(cnf_transformation,[],[f128]) ).
fof(f184,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f200,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f222,plain,
leq(sK0,minus(sK0,n1)),
inference(definition_unfolding,[],[f138,f184,f140]) ).
fof(f231,plain,
! [X0,X1] :
( ~ leq(X0,minus(X1,n1))
| gt(X1,X0) ),
inference(definition_unfolding,[],[f147,f184]) ).
tcf(c_51,negated_conjecture,
leq(sK0,minus(sK0,n1)),
inference(cnf_transformation,[],[f222]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( gt(X1,X0)
| ~ leq(X0,minus(X1,n1)) ),
inference(cnf_transformation,[],[f231]) ).
tcf(c_116,plain,
! [X0: $i] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f200]) ).
tcf(c_2534,plain,
gt(sK0,sK0),
inference(superposition,[status(thm)],[c_51,c_65]) ).
tcf(c_2538,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_2534,c_116]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV160+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n020.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 18:40:03 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 Running: /export/starexec/sandbox2/solver/bin/iproveropt-multi-core.sh -d -n -l tptp -s fof_schedule -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 2.62/1.10 % SZS status Started for theBenchmark.p
% 2.62/1.10 % SZS status Theorem for theBenchmark.p
% 2.62/1.10
% 2.62/1.10 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.62/1.10
% 2.62/1.10 % ------ iProver source info
% 2.62/1.10
% 2.62/1.10 % git: date: 2026-07-19 20:42:38 +0200
% 2.62/1.10 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.62/1.10 % git: non_committed_changes: false
% 2.62/1.10
% 2.62/1.10 % ------ Parsing...
% 2.62/1.10 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.62/1.10
% 2.62/1.10 % ------ Preprocessing... sup_sim: 11 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.62/1.10
% 2.62/1.10 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.62/1.10
% 2.62/1.10 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.62/1.10 % ------ Proving...
% 2.62/1.10 % ------ Problem Properties
% 2.62/1.10
% 2.62/1.10 %
% 2.62/1.10 % clauses 86
% 2.62/1.10 % conjectures 8
% 2.62/1.10 % EPR 53
% 2.62/1.10 % Horn 79
% 2.62/1.10 % unary 64
% 2.62/1.10 % binary 10
% 2.62/1.10 % lits 135
% 2.62/1.10 % lits eq 45
% 2.62/1.10 % fd_pure 0
% 2.62/1.10 % fd_pseudo 0
% 2.62/1.10 % fd_cond 6
% 2.62/1.10 % fd_pseudo_cond 2
% 2.62/1.10 % AC symbols 0
% 2.62/1.10
% 2.62/1.10 % ------ Schedule dynamic 5 is on
% 2.62/1.10
% 2.62/1.10 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.62/1.10
% 2.62/1.10
% 2.62/1.10 % ------
% 2.62/1.10 % Current options:
% 2.62/1.10 % ------
% 2.62/1.10
% 2.62/1.10
% 2.62/1.10 %
% 2.62/1.10
% 2.62/1.10 % ------ Proving...
% 2.62/1.10 %
% 2.62/1.10
% 2.62/1.10 % SZS status Theorem for theBenchmark.p
% 2.62/1.10
% 2.62/1.10 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.62/1.10
% 2.62/1.10
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