%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV166+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 03:16:35 PM UTC 2026
% Result : Theorem 2.69s 1.08s
% Output : CNFRefutation 2.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 2
% Syntax : Number of formulae : 28 ( 15 unt; 1 def)
% Number of atoms : 258 ( 73 equ)
% Maximal formula atoms : 36 ( 9 avg)
% Number of connectives : 337 ( 113 ~; 98 |; 98 &)
% ( 0 <=>; 28 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 6 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 20 ( 20 usr; 17 con; 0-3 aty)
% Number of variables : 64 ( 0 sgn 61 !; 3 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f53,conjecture,
( ( ( gt(loopcounter,n1)
=> ! [X8] :
( ( leq(X8,n4)
& leq(n0,X8) )
=> a_select2(sigmaold_init,X8) = init ) )
& ( gt(loopcounter,n1)
=> ! [X7] :
( ( leq(X7,n4)
& leq(n0,X7) )
=> a_select2(rhoold_init,X7) = init ) )
& ( gt(loopcounter,n1)
=> ! [X6] :
( ( leq(X6,n4)
& leq(n0,X6) )
=> a_select2(muold_init,X6) = init ) )
& ! [X5] :
( ( leq(X5,n4)
& leq(n0,X5) )
=> a_select3(center_init,X5,n0) = init )
& ! [X4] :
( ( leq(X4,pred(pv40))
& leq(n0,X4) )
=> a_select2(sigma_init,X4) = init )
& ! [X3] :
( ( leq(X3,pred(pv40))
& leq(n0,X3) )
=> a_select2(mu_init,X3) = init )
& ! [X2] :
( ( leq(X2,n4)
& leq(n0,X2) )
=> a_select2(rho_init,X2) = init )
& ! [X0] :
( ( leq(X0,n135299)
& leq(n0,X0) )
=> ! [X1] :
( ( leq(X1,n4)
& leq(n0,X1) )
=> a_select3(q_init,X0,X1) = init ) )
& gt(loopcounter,n1)
& leq(pv40,n4)
& leq(n0,pv40)
& n0 != pv90 )
=> ! [X9] :
( ( leq(X9,n4)
& leq(n0,X9) )
=> a_select2(rhoold_init,X9) = init ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0006) ).
fof(f54,negated_conjecture,
~ ( ( ( gt(loopcounter,n1)
=> ! [X8] :
( ( leq(X8,n4)
& leq(n0,X8) )
=> a_select2(sigmaold_init,X8) = init ) )
& ( gt(loopcounter,n1)
=> ! [X7] :
( ( leq(X7,n4)
& leq(n0,X7) )
=> a_select2(rhoold_init,X7) = init ) )
& ( gt(loopcounter,n1)
=> ! [X6] :
( ( leq(X6,n4)
& leq(n0,X6) )
=> a_select2(muold_init,X6) = init ) )
& ! [X5] :
( ( leq(X5,n4)
& leq(n0,X5) )
=> a_select3(center_init,X5,n0) = init )
& ! [X4] :
( ( leq(X4,pred(pv40))
& leq(n0,X4) )
=> a_select2(sigma_init,X4) = init )
& ! [X3] :
( ( leq(X3,pred(pv40))
& leq(n0,X3) )
=> a_select2(mu_init,X3) = init )
& ! [X2] :
( ( leq(X2,n4)
& leq(n0,X2) )
=> a_select2(rho_init,X2) = init )
& ! [X0] :
( ( leq(X0,n135299)
& leq(n0,X0) )
=> ! [X1] :
( ( leq(X1,n4)
& leq(n0,X1) )
=> a_select3(q_init,X0,X1) = init ) )
& gt(loopcounter,n1)
& leq(pv40,n4)
& leq(n0,pv40)
& n0 != pv90 )
=> ! [X9] :
( ( leq(X9,n4)
& leq(n0,X9) )
=> a_select2(rhoold_init,X9) = init ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f143,plain,
( ( ~ gt(loopcounter,n1)
| ! [X8] :
( ~ leq(X8,n4)
| ~ leq(n0,X8)
| a_select2(sigmaold_init,X8) = init ) )
& ( ~ gt(loopcounter,n1)
| ! [X7] :
( ~ leq(X7,n4)
| ~ leq(n0,X7)
| a_select2(rhoold_init,X7) = init ) )
& ( ~ gt(loopcounter,n1)
| ! [X6] :
( ~ leq(X6,n4)
| ~ leq(n0,X6)
| a_select2(muold_init,X6) = init ) )
& ! [X5] :
( ~ leq(X5,n4)
| ~ leq(n0,X5)
| a_select3(center_init,X5,n0) = init )
& ! [X4] :
( ~ leq(X4,pred(pv40))
| ~ leq(n0,X4)
| a_select2(sigma_init,X4) = init )
& ! [X3] :
( ~ leq(X3,pred(pv40))
| ~ leq(n0,X3)
| a_select2(mu_init,X3) = init )
& ! [X2] :
( ~ leq(X2,n4)
| ~ leq(n0,X2)
| a_select2(rho_init,X2) = init )
& ! [X0] :
( ~ leq(X0,n135299)
| ~ leq(n0,X0)
| ! [X1] :
( ~ leq(X1,n4)
| ~ leq(n0,X1)
| a_select3(q_init,X0,X1) = init ) )
& gt(loopcounter,n1)
& leq(pv40,n4)
& leq(n0,pv40)
& n0 != pv90
& ? [X9] :
( leq(X9,n4)
& leq(n0,X9)
& init != a_select2(rhoold_init,X9) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f144,plain,
( ( ~ gt(loopcounter,n1)
| ! [X8] :
( ~ leq(X8,n4)
| ~ leq(n0,X8)
| a_select2(sigmaold_init,X8) = init ) )
& ( ~ gt(loopcounter,n1)
| ! [X7] :
( ~ leq(X7,n4)
| ~ leq(n0,X7)
| a_select2(rhoold_init,X7) = init ) )
& ( ~ gt(loopcounter,n1)
| ! [X6] :
( ~ leq(X6,n4)
| ~ leq(n0,X6)
| a_select2(muold_init,X6) = init ) )
& ! [X5] :
( ~ leq(X5,n4)
| ~ leq(n0,X5)
| a_select3(center_init,X5,n0) = init )
& ! [X4] :
( ~ leq(X4,pred(pv40))
| ~ leq(n0,X4)
| a_select2(sigma_init,X4) = init )
& ! [X3] :
( ~ leq(X3,pred(pv40))
| ~ leq(n0,X3)
| a_select2(mu_init,X3) = init )
& ! [X2] :
( ~ leq(X2,n4)
| ~ leq(n0,X2)
| a_select2(rho_init,X2) = init )
& ! [X0] :
( ~ leq(X0,n135299)
| ~ leq(n0,X0)
| ! [X1] :
( ~ leq(X1,n4)
| ~ leq(n0,X1)
| a_select3(q_init,X0,X1) = init ) )
& gt(loopcounter,n1)
& leq(pv40,n4)
& leq(n0,pv40)
& n0 != pv90
& ? [X9] :
( leq(X9,n4)
& leq(n0,X9)
& init != a_select2(rhoold_init,X9) ) ),
inference(flattening,[],[f143]) ).
fof(f197,plain,
( ( ~ gt(loopcounter,n1)
| ! [X9] :
( ~ leq(X9,n4)
| ~ leq(n0,X9)
| init = a_select2(sigmaold_init,X9) ) )
& ( ~ gt(loopcounter,n1)
| ! [X8] :
( ~ leq(X8,n4)
| ~ leq(n0,X8)
| init = a_select2(rhoold_init,X8) ) )
& ( ~ gt(loopcounter,n1)
| ! [X7] :
( ~ leq(X7,n4)
| ~ leq(n0,X7)
| init = a_select2(muold_init,X7) ) )
& ! [X6] :
( ~ leq(X6,n4)
| ~ leq(n0,X6)
| init = a_select3(center_init,X6,n0) )
& ! [X5] :
( ~ leq(X5,pred(pv40))
| ~ leq(n0,X5)
| init = a_select2(sigma_init,X5) )
& ! [X4] :
( ~ leq(X4,pred(pv40))
| ~ leq(n0,X4)
| init = a_select2(mu_init,X4) )
& ! [X3] :
( ~ leq(X3,n4)
| ~ leq(n0,X3)
| init = a_select2(rho_init,X3) )
& ! [X1] :
( ~ leq(X1,n135299)
| ~ leq(n0,X1)
| ! [X2] :
( ~ leq(X2,n4)
| ~ leq(n0,X2)
| init = a_select3(q_init,X1,X2) ) )
& gt(loopcounter,n1)
& leq(pv40,n4)
& leq(n0,pv40)
& n0 != pv90
& ? [X0] :
( leq(X0,n4)
& leq(n0,X0)
& init != a_select2(rhoold_init,X0) ) ),
inference(rectify,[],[f144]) ).
fof(f198,plain,
( ( ~ gt(loopcounter,n1)
| ! [X9] :
( ~ leq(X9,n4)
| ~ leq(n0,X9)
| init = a_select2(sigmaold_init,X9) ) )
& ( ~ gt(loopcounter,n1)
| ! [X8] :
( ~ leq(X8,n4)
| ~ leq(n0,X8)
| init = a_select2(rhoold_init,X8) ) )
& ( ~ gt(loopcounter,n1)
| ! [X7] :
( ~ leq(X7,n4)
| ~ leq(n0,X7)
| init = a_select2(muold_init,X7) ) )
& ! [X6] :
( ~ leq(X6,n4)
| ~ leq(n0,X6)
| init = a_select3(center_init,X6,n0) )
& ! [X5] :
( ~ leq(X5,pred(pv40))
| ~ leq(n0,X5)
| init = a_select2(sigma_init,X5) )
& ! [X4] :
( ~ leq(X4,pred(pv40))
| ~ leq(n0,X4)
| init = a_select2(mu_init,X4) )
& ! [X3] :
( ~ leq(X3,n4)
| ~ leq(n0,X3)
| init = a_select2(rho_init,X3) )
& ! [X1] :
( ~ leq(X1,n135299)
| ~ leq(n0,X1)
| ! [X2] :
( ~ leq(X2,n4)
| ~ leq(n0,X2)
| init = a_select3(q_init,X1,X2) ) )
& gt(loopcounter,n1)
& leq(pv40,n4)
& leq(n0,pv40)
& n0 != pv90
& leq(sK31,n4)
& leq(n0,sK31)
& init != a_select2(rhoold_init,sK31) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK31]),skolemize(X0,sK31)],[f197]) ).
fof(f310,plain,
! [X8] :
( ~ gt(loopcounter,n1)
| ~ leq(X8,n4)
| ~ leq(n0,X8)
| init = a_select2(rhoold_init,X8) ),
inference(cnf_transformation,[],[f198]) ).
fof(f317,plain,
gt(loopcounter,n1),
inference(cnf_transformation,[],[f198]) ).
fof(f321,plain,
leq(sK31,n4),
inference(cnf_transformation,[],[f198]) ).
fof(f322,plain,
leq(n0,sK31),
inference(cnf_transformation,[],[f198]) ).
fof(f323,plain,
init != a_select2(rhoold_init,sK31),
inference(cnf_transformation,[],[f198]) ).
tcf(c_157,negated_conjecture,
a_select2(rhoold_init,sK31) != init,
inference(cnf_transformation,[],[f323]) ).
tcf(c_158,negated_conjecture,
leq(n0,sK31),
inference(cnf_transformation,[],[f322]) ).
tcf(c_159,negated_conjecture,
leq(sK31,n4),
inference(cnf_transformation,[],[f321]) ).
tcf(c_163,negated_conjecture,
gt(loopcounter,n1),
inference(cnf_transformation,[],[f317]) ).
tcf(c_170,negated_conjecture,
! [X0: $i] :
( ( a_select2(rhoold_init,X0) = init )
| ~ gt(loopcounter,n1)
| ~ leq(n0,X0)
| ~ leq(X0,n4) ),
inference(cnf_transformation,[],[f310]) ).
tcf(c_312,plain,
! [X0: $i] :
( ( a_select2(rhoold_init,X0) = init )
| ~ leq(X0,n4)
| ~ leq(n0,X0) ),
inference(global_subsumption_just,[status(thm)],[c_170,c_163,c_170]) ).
tcf(c_313,negated_conjecture,
! [X0: $i] :
( ( a_select2(rhoold_init,X0) = init )
| ~ leq(n0,X0)
| ~ leq(X0,n4) ),
inference(renaming,[status(thm)],[c_312]) ).
tcf(c_5972,definition,
iPr_def_11 = a_select2(rhoold_init,sK31),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_5974,negated_conjecture,
! [X0: $i] :
( ( a_select2(rhoold_init,X0) = init )
| ~ leq(n0,X0)
| ~ leq(X0,n4) ),
inference(demodulation,[status(thm)],[c_313]) ).
tcf(c_5985,negated_conjecture,
leq(sK31,n4),
inference(demodulation,[status(thm)],[c_159]) ).
tcf(c_5986,negated_conjecture,
leq(n0,sK31),
inference(demodulation,[status(thm)],[c_158]) ).
tcf(c_5987,negated_conjecture,
iPr_def_11 != init,
inference(demodulation,[status(thm)],[c_157,c_5972]) ).
tcf(c_9037,plain,
( ( a_select2(rhoold_init,sK31) = init )
| ~ leq(sK31,n4) ),
inference(superposition,[status(thm)],[c_5986,c_5974]) ).
tcf(c_9040,plain,
( ( init = iPr_def_11 )
| ~ leq(sK31,n4) ),
inference(light_normalisation,[status(thm)],[c_9037,c_5972]) ).
tcf(c_9041,plain,
init = iPr_def_11,
inference(forward_subsumption_resolution,[status(thm)],[c_9040,c_5985]) ).
tcf(c_9046,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_5987,c_9041]) ).
tcf(c_9047,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_9046]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SWV166+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.09/0.36 % Computer : n004.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Thu Sep 24 18:39:50 UTC 2026
% 0.02/0.37 % CPUTime :
% 0.02/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.02/0.40 Running first-order theorem proving
% 0.02/0.40 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
% 0.02/0.42
% 0.02/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.02/0.42
% 0.02/0.42 % Detected problem language: tptp
% 0.02/0.43 % Proving...
% 2.69/1.08 % SZS status Started for theBenchmark.p
% 2.69/1.08 % SZS status Theorem for theBenchmark.p
% 2.69/1.08
% 2.69/1.08 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.69/1.08
% 2.69/1.08 % ------ iProver source info
% 2.69/1.08
% 2.69/1.08 % git: date: 2026-07-19 20:42:38 +0200
% 2.69/1.08 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.69/1.08 % git: non_committed_changes: false
% 2.69/1.08
% 2.69/1.08 % ------ Parsing...
% 2.69/1.08 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.69/1.08
% 2.69/1.08 % ------ Preprocessing... sup_sim: 15 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.69/1.08
% 2.69/1.08 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.69/1.08
% 2.69/1.08 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.69/1.08 % ------ Proving...
% 2.69/1.08 % ------ Problem Properties
% 2.69/1.08
% 2.69/1.08 %
% 2.69/1.08 % clauses 164
% 2.69/1.08 % conjectures 15
% 2.69/1.08 % EPR 50
% 2.69/1.08 % Horn 114
% 2.69/1.08 % unary 62
% 2.69/1.08 % binary 34
% 2.69/1.08 % lits 521
% 2.69/1.08 % lits eq 125
% 2.69/1.08 % fd_pure 0
% 2.69/1.08 % fd_pseudo 0
% 2.69/1.08 % fd_cond 6
% 2.69/1.08 % fd_pseudo_cond 4
% 2.69/1.08 % AC symbols 0
% 2.69/1.08
% 2.69/1.08 % ------ Schedule dynamic 5 is on
% 2.69/1.08
% 2.69/1.08 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.69/1.08
% 2.69/1.08
% 2.69/1.08 % ------
% 2.69/1.08 % Current options:
% 2.69/1.08 % ------
% 2.69/1.08
% 2.69/1.08
% 2.69/1.08 %
% 2.69/1.08
% 2.69/1.08 % ------ Proving...
% 2.69/1.08 %
% 2.69/1.08
% 2.69/1.08 % SZS status Theorem for theBenchmark.p
% 2.69/1.08
% 2.69/1.08 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.69/1.08
% 2.69/1.08
%------------------------------------------------------------------------------