%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV164+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 : n011.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 3.63s 1.20s
% Output : CNFRefutation 3.63s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 15 unt; 0 def)
% Number of atoms : 105 ( 19 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 105 ( 37 ~; 29 |; 30 &)
% ( 0 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 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 : 25 ( 25 usr; 16 con; 0-3 aty)
% Number of variables : 43 ( 0 sgn 40 !; 3 ?; 8 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).
fof(f5,axiom,
! [X0,X1,X2] :
( ( leq(X1,X2)
& leq(X0,X1) )
=> leq(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',transitivity_leq) ).
fof(f8,axiom,
! [X0,X1] :
( gt(X1,X0)
=> leq(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',leq_gt1) ).
fof(f53,conjecture,
( ( ! [X0] :
( ( leq(X0,pred(pv10))
& leq(n0,X0) )
=> sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [X1] :
( ( leq(X1,tptp_minus_1)
& 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))))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_norm_0014) ).
fof(f54,negated_conjecture,
~ ( ( ! [X0] :
( ( leq(X0,pred(pv10))
& leq(n0,X0) )
=> sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10) )
=> ! [X1] :
( ( leq(X1,tptp_minus_1)
& 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(negated_conjecture,[status(cth)],[f53]) ).
fof(f61,axiom,
gt(n0,tptp_minus_1),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',gt_0_tptp_minus_1) ).
fof(f93,axiom,
! [X0] :
( ( leq(X0,n0)
& leq(n0,X0) )
=> X0 = n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
fof(f102,plain,
( ! [X0] :
( ~ leq(X0,pred(pv10))
| ~ leq(n0,X0)
| sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10)
& ? [X1] :
( leq(X1,tptp_minus_1)
& 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(ennf_transformation,[],[f54]) ).
fof(f103,plain,
( ! [X0] :
( ~ leq(X0,pred(pv10))
| ~ leq(n0,X0)
| sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 )
& leq(pv10,n135299)
& leq(n0,pv10)
& ? [X1] :
( leq(X1,tptp_minus_1)
& 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(flattening,[],[f102]) ).
fof(f104,plain,
! [X0] :
( ~ leq(X0,n0)
| ~ leq(n0,X0)
| X0 = n0 ),
inference(ennf_transformation,[],[f93]) ).
fof(f105,plain,
! [X0] :
( ~ leq(X0,n0)
| ~ leq(n0,X0)
| X0 = n0 ),
inference(flattening,[],[f104]) ).
fof(f110,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f111,plain,
! [X0,X1,X2] :
( ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f112,plain,
! [X0,X1,X2] :
( ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ),
inference(flattening,[],[f111]) ).
fof(f126,plain,
( ! [X1] :
( ~ leq(X1,pred(pv10))
| ~ leq(n0,X1)
| n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index)) )
& leq(pv10,n135299)
& leq(n0,pv10)
& ? [X0] :
( leq(X0,tptp_minus_1)
& 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))))) ) ),
inference(rectify,[],[f103]) ).
fof(f127,plain,
( ! [X1] :
( ~ leq(X1,pred(pv10))
| ~ leq(n0,X1)
| n1 = sum(n0,n4,a_select3(q,X1,tptp_sum_index)) )
& leq(pv10,n135299)
& leq(n0,pv10)
& leq(sK0,tptp_minus_1)
& leq(n0,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(f134,plain,
leq(sK0,tptp_minus_1),
inference(cnf_transformation,[],[f127]) ).
fof(f135,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f127]) ).
fof(f137,plain,
! [X0] :
( ~ leq(X0,n0)
| ~ leq(n0,X0)
| n0 = X0 ),
inference(cnf_transformation,[],[f105]) ).
fof(f150,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,X1) ),
inference(cnf_transformation,[],[f110]) ).
fof(f151,plain,
! [X2,X0,X1] :
( ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ),
inference(cnf_transformation,[],[f112]) ).
fof(f157,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[],[f61]) ).
fof(f200,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
tcf(c_50,negated_conjecture,
leq(n0,sK0),
inference(cnf_transformation,[],[f135]) ).
tcf(c_51,negated_conjecture,
leq(sK0,tptp_minus_1),
inference(cnf_transformation,[],[f134]) ).
tcf(c_55,plain,
! [X0: $i] :
( ( X0 = n0 )
| ~ leq(n0,X0)
| ~ leq(X0,n0) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( leq(X1,X0)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[],[f150]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(X2,X1)
| ~ leq(X2,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f151]) ).
tcf(c_75,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[],[f157]) ).
tcf(c_117,plain,
! [X0: $i] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f200]) ).
tcf(c_1775,plain,
leq(tptp_minus_1,n0),
inference(superposition,[status(thm)],[c_75,c_68]) ).
tcf(c_3090,plain,
! [X0: $i] :
( leq(X0,tptp_minus_1)
| ~ leq(X0,sK0) ),
inference(superposition,[status(thm)],[c_51,c_69]) ).
tcf(c_3311,plain,
leq(n0,tptp_minus_1),
inference(superposition,[status(thm)],[c_50,c_3090]) ).
tcf(c_3597,plain,
( ( n0 = tptp_minus_1 )
| ~ leq(tptp_minus_1,n0) ),
inference(superposition,[status(thm)],[c_3311,c_55]) ).
tcf(c_3598,plain,
n0 = tptp_minus_1,
inference(forward_subsumption_resolution,[status(thm)],[c_3597,c_1775]) ).
tcf(c_3634,plain,
gt(n0,n0),
inference(demodulation,[status(thm)],[c_75,c_3598]) ).
tcf(c_3647,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_3634,c_117]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV164+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.37 % Computer : n011.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Thu Sep 24 18:39:12 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.41 Running first-order theorem proving
% 0.11/0.41 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
% 0.11/0.42
% 0.11/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.42
% 0.11/0.42 % Detected problem language: tptp
% 0.11/0.43 % Proving...
% 3.63/1.20 % SZS status Started for theBenchmark.p
% 3.63/1.20 % SZS status Theorem for theBenchmark.p
% 3.63/1.20
% 3.63/1.20 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.63/1.20
% 3.63/1.20 % ------ iProver source info
% 3.63/1.20
% 3.63/1.20 % git: date: 2026-07-19 20:42:38 +0200
% 3.63/1.20 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.63/1.20 % git: non_committed_changes: false
% 3.63/1.20
% 3.63/1.20 % ------ Parsing...
% 3.63/1.20 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.63/1.20
% 3.63/1.20 % ------ Preprocessing... sup_sim: 10 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.63/1.20
% 3.63/1.20 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.63/1.20
% 3.63/1.20 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.63/1.20 % ------ Proving...
% 3.63/1.20 % ------ Problem Properties
% 3.63/1.20
% 3.63/1.20 %
% 3.63/1.20 % clauses 83
% 3.63/1.20 % conjectures 6
% 3.63/1.20 % EPR 53
% 3.63/1.20 % Horn 76
% 3.63/1.20 % unary 62
% 3.63/1.20 % binary 10
% 3.63/1.20 % lits 130
% 3.63/1.20 % lits eq 43
% 3.63/1.20 % fd_pure 0
% 3.63/1.20 % fd_pseudo 0
% 3.63/1.20 % fd_cond 6
% 3.63/1.20 % fd_pseudo_cond 2
% 3.63/1.20 % AC symbols 0
% 3.63/1.20
% 3.63/1.20 % ------ Schedule dynamic 5 is on
% 3.63/1.20
% 3.63/1.20 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.63/1.20
% 3.63/1.20
% 3.63/1.20 % ------
% 3.63/1.20 % Current options:
% 3.63/1.20 % ------
% 3.63/1.20
% 3.63/1.20
% 3.63/1.20 %
% 3.63/1.20
% 3.63/1.20 % ------ Proving...
% 3.63/1.20 %
% 3.63/1.20
% 3.63/1.20 % SZS status Theorem for theBenchmark.p
% 3.63/1.20
% 3.63/1.20 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.63/1.20
% 3.63/1.20
%------------------------------------------------------------------------------