%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV159+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 : n016.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 2.41s 1.08s
% Output : CNFRefutation 2.41s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 5
% Syntax : Number of formulae : 30 ( 18 unt; 3 def)
% Number of atoms : 137 ( 46 equ)
% Maximal formula atoms : 15 ( 4 avg)
% Number of connectives : 135 ( 41 ~; 26 |; 58 &)
% ( 0 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 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 : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 26 ( 26 usr; 17 con; 0-3 aty)
% Number of variables : 23 ( 0 sgn 20 !; 3 ?; 2 :)
% Comments :
%------------------------------------------------------------------------------
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,a_select3(q,X2,tptp_sum_index)) = n1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_norm_0009) ).
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,a_select3(q,X2,tptp_sum_index)) = n1 ) ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f151,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,a_select3(q,X2,tptp_sum_index)) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f152,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,a_select3(q,X2,tptp_sum_index)) ) ),
inference(flattening,[],[f151]) ).
fof(f205,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,a_select3(q,X0,tptp_sum_index)) ) ),
inference(rectify,[],[f152]) ).
fof(f206,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(sK31,pred(pv10))
& leq(n0,sK31)
& pv10 != sK31
& n1 != sum(n0,n4,a_select3(q,sK31,tptp_sum_index)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(X0,sK31)],[f205]) ).
fof(f297,plain,
! [X0] : minus(X0,n1) = pred(X0),
inference(cnf_transformation,[],[f39]) ).
fof(f317,plain,
! [X2] :
( ~ leq(X2,pred(pv10))
| ~ leq(n0,X2)
| n1 = sum(n0,n4,a_select3(q,X2,tptp_sum_index)) ),
inference(cnf_transformation,[],[f206]) ).
fof(f324,plain,
leq(sK31,pred(pv10)),
inference(cnf_transformation,[],[f206]) ).
fof(f325,plain,
leq(n0,sK31),
inference(cnf_transformation,[],[f206]) ).
fof(f327,plain,
n1 != sum(n0,n4,a_select3(q,sK31,tptp_sum_index)),
inference(cnf_transformation,[],[f206]) ).
fof(f396,plain,
leq(sK31,minus(pv10,n1)),
inference(definition_unfolding,[],[f324,f297]) ).
fof(f398,plain,
! [X2] :
( ~ leq(X2,minus(pv10,n1))
| ~ leq(n0,X2)
| n1 = sum(n0,n4,a_select3(q,X2,tptp_sum_index)) ),
inference(definition_unfolding,[],[f317,f297]) ).
tcf(c_157,negated_conjecture,
sum(n0,n4,a_select3(q,sK31,tptp_sum_index)) != n1,
inference(cnf_transformation,[],[f327]) ).
tcf(c_159,negated_conjecture,
leq(n0,sK31),
inference(cnf_transformation,[],[f325]) ).
tcf(c_160,negated_conjecture,
leq(sK31,minus(pv10,n1)),
inference(cnf_transformation,[],[f396]) ).
tcf(c_167,negated_conjecture,
! [X0: $i] :
( ( sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 )
| ~ leq(n0,X0)
| ~ leq(X0,minus(pv10,n1)) ),
inference(cnf_transformation,[],[f398]) ).
tcf(c_5915,definition,
iPr_def_14 = minus(pv10,n1),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_5929,definition,
iPr_def_28 = a_select3(q,sK31,tptp_sum_index),
introduced(definition,[new_symbols(definition,[iPr_def_28])],[]) ).
tcf(c_5930,definition,
iPr_def_29 = sum(n0,n4,iPr_def_28),
introduced(definition,[new_symbols(definition,[iPr_def_29])],[]) ).
tcf(c_5932,negated_conjecture,
! [X0: $i] :
( ( sum(n0,n4,a_select3(q,X0,tptp_sum_index)) = n1 )
| ~ leq(n0,X0)
| ~ leq(X0,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_167,c_5915]) ).
tcf(c_5938,negated_conjecture,
leq(sK31,iPr_def_14),
inference(demodulation,[status(thm)],[c_160]) ).
tcf(c_5939,negated_conjecture,
leq(n0,sK31),
inference(demodulation,[status(thm)],[c_159]) ).
tcf(c_5941,negated_conjecture,
iPr_def_29 != n1,
inference(demodulation,[status(thm)],[c_157,c_5929,c_5930]) ).
tcf(c_9126,plain,
( ( sum(n0,n4,a_select3(q,sK31,tptp_sum_index)) = n1 )
| ~ leq(sK31,iPr_def_14) ),
inference(superposition,[status(thm)],[c_5939,c_5932]) ).
tcf(c_9133,plain,
( ( n1 = iPr_def_29 )
| ~ leq(sK31,iPr_def_14) ),
inference(light_normalisation,[status(thm)],[c_9126,c_5929,c_5930]) ).
tcf(c_9134,plain,
n1 = iPr_def_29,
inference(forward_subsumption_resolution,[status(thm)],[c_9133,c_5938]) ).
tcf(c_9138,plain,
iPr_def_29 != iPr_def_29,
inference(demodulation,[status(thm)],[c_5941,c_9134]) ).
tcf(c_9139,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_9138]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV159+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.37 % Computer : n016.cluster.edu
% 0.08/0.37 % Model : x86_64 x86_64
% 0.08/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.37 % Memory : 8046.5625MB
% 0.08/0.37 % OS : Linux 6.8.0-71-generic
% 0.08/0.37 % CPULimit : 300
% 0.08/0.37 % WCLimit : 300
% 0.08/0.38 % DateTime : Thu Sep 24 18:43:43 UTC 2026
% 0.08/0.38 % CPUTime :
% 0.08/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.08/0.42 Running first-order theorem proving
% 0.08/0.42 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
% 0.08/0.43
% 0.08/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.08/0.43
% 0.08/0.43 % Detected problem language: tptp
% 0.08/0.44 % Proving...
% 2.41/1.08 % SZS status Started for theBenchmark.p
% 2.41/1.08 % SZS status Theorem for theBenchmark.p
% 2.41/1.08
% 2.41/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.41/1.08
% 2.41/1.08 % ------ iProver source info
% 2.41/1.08
% 2.41/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 2.41/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.41/1.08 % git: non_committed_changes: false
% 2.41/1.08
% 2.41/1.08 % ------ Parsing...
% 2.41/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.41/1.08
% 2.41/1.08 % ------ Preprocessing... sup_sim: 16 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.41/1.08
% 2.41/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.41/1.08
% 2.41/1.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.41/1.08 % ------ Proving...
% 2.41/1.08 % ------ Problem Properties
% 2.41/1.08
% 2.41/1.08 %
% 2.41/1.08 % clauses 186
% 2.41/1.08 % conjectures 10
% 2.41/1.08 % EPR 60
% 2.41/1.08 % Horn 136
% 2.41/1.08 % unary 90
% 2.41/1.08 % binary 34
% 2.41/1.08 % lits 529
% 2.41/1.08 % lits eq 138
% 2.41/1.08 % fd_pure 0
% 2.41/1.08 % fd_pseudo 0
% 2.41/1.08 % fd_cond 6
% 2.41/1.08 % fd_pseudo_cond 4
% 2.41/1.08 % AC symbols 0
% 2.41/1.08
% 2.41/1.08 % ------ Schedule dynamic 5 is on
% 2.41/1.08
% 2.41/1.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.41/1.08
% 2.41/1.08
% 2.41/1.08 % ------
% 2.41/1.08 % Current options:
% 2.41/1.08 % ------
% 2.41/1.08
% 2.41/1.08
% 2.41/1.08 %
% 2.41/1.08
% 2.41/1.08 % ------ Proving...
% 2.41/1.08 %
% 2.41/1.08
% 2.41/1.08 % SZS status Theorem for theBenchmark.p
% 2.41/1.08
% 2.41/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.41/1.09
% 2.41/1.09
%------------------------------------------------------------------------------