%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV167+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 : n015.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 4.24s 1.33s
% Output : CNFRefutation 4.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 3
% Syntax : Number of formulae : 31 ( 11 unt; 0 def)
% Number of atoms : 266 ( 83 equ)
% Maximal formula atoms : 36 ( 8 avg)
% Number of connectives : 343 ( 108 ~; 105 |; 100 &)
% ( 1 <=>; 29 =>; 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 : 4 ( 2 usr; 1 prp; 0-2 aty)
% Number of functors : 19 ( 19 usr; 16 con; 0-3 aty)
% Number of variables : 80 ( 0 sgn 77 !; 3 ?; 6 :)
% 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(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 ) )
& leq(pv40,n4)
& leq(n0,pv40)
& a_select2(sigma_init,pv40) = init
& a_select2(mu_init,pv40) = init )
=> ! [X9] :
( ( leq(X9,pv40)
& leq(n0,X9) )
=> a_select2(mu_init,X9) = init ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0011) ).
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 ) )
& leq(pv40,n4)
& leq(n0,pv40)
& a_select2(sigma_init,pv40) = init
& a_select2(mu_init,pv40) = init )
=> ! [X9] :
( ( leq(X9,pv40)
& leq(n0,X9) )
=> a_select2(mu_init,X9) = init ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f94,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 ) )
& leq(pv40,n4)
& leq(n0,pv40)
& a_select2(sigma_init,pv40) = init
& a_select2(mu_init,pv40) = init
& ? [X9] :
( leq(X9,pv40)
& leq(n0,X9)
& init != a_select2(mu_init,X9) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f95,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 ) )
& leq(pv40,n4)
& leq(n0,pv40)
& a_select2(sigma_init,pv40) = init
& a_select2(mu_init,pv40) = init
& ? [X9] :
( leq(X9,pv40)
& leq(n0,X9)
& init != a_select2(mu_init,X9) ) ),
inference(flattening,[],[f94]) ).
fof(f98,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| gt(X1,X0) ),
inference(ennf_transformation,[],[f9]) ).
fof(f99,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| gt(X1,X0) ),
inference(flattening,[],[f98]) ).
fof(f117,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) ) )
& leq(pv40,n4)
& leq(n0,pv40)
& a_select2(sigma_init,pv40) = init
& a_select2(mu_init,pv40) = init
& ? [X0] :
( leq(X0,pv40)
& leq(n0,X0)
& init != a_select2(mu_init,X0) ) ),
inference(rectify,[],[f95]) ).
fof(f118,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) ) )
& leq(pv40,n4)
& leq(n0,pv40)
& a_select2(sigma_init,pv40) = init
& a_select2(mu_init,pv40) = init
& leq(sK0,pv40)
& leq(n0,sK0)
& init != a_select2(mu_init,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f117]) ).
fof(f119,plain,
! [X0,X1] :
( ( ~ leq(X0,pred(X1))
| gt(X1,X0) )
& ( ~ gt(X1,X0)
| leq(X0,pred(X1)) ) ),
inference(nnf_transformation,[],[f10]) ).
fof(f127,plain,
! [X4] :
( ~ leq(X4,pred(pv40))
| ~ leq(n0,X4)
| init = a_select2(mu_init,X4) ),
inference(cnf_transformation,[],[f118]) ).
fof(f133,plain,
a_select2(mu_init,pv40) = init,
inference(cnf_transformation,[],[f118]) ).
fof(f134,plain,
leq(sK0,pv40),
inference(cnf_transformation,[],[f118]) ).
fof(f135,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f118]) ).
fof(f136,plain,
init != a_select2(mu_init,sK0),
inference(cnf_transformation,[],[f118]) ).
fof(f138,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| gt(X1,X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f143,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,pred(X1)) ),
inference(cnf_transformation,[],[f119]) ).
tcf(c_49,negated_conjecture,
a_select2(mu_init,sK0) != init,
inference(cnf_transformation,[],[f136]) ).
tcf(c_50,negated_conjecture,
leq(n0,sK0),
inference(cnf_transformation,[],[f135]) ).
tcf(c_51,negated_conjecture,
leq(sK0,pv40),
inference(cnf_transformation,[],[f134]) ).
tcf(c_52,negated_conjecture,
a_select2(mu_init,pv40) = init,
inference(cnf_transformation,[],[f133]) ).
tcf(c_58,negated_conjecture,
! [X0: $i] :
( ( a_select2(mu_init,X0) = init )
| ~ leq(n0,X0)
| ~ leq(X0,pred(pv40)) ),
inference(cnf_transformation,[],[f127]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( gt(X1,X0)
| ( X0 = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f138]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( leq(X1,pred(X0))
| ~ gt(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_2225,plain,
! [X0: $i] :
( ( a_select2(mu_init,X0) = init )
| ~ gt(pv40,X0)
| ~ leq(n0,X0) ),
inference(superposition,[status(thm)],[c_69,c_58]) ).
tcf(c_3411,plain,
( gt(pv40,sK0)
| ( sK0 = pv40 ) ),
inference(superposition,[status(thm)],[c_51,c_65]) ).
tcf(c_4191,plain,
( ( sK0 = pv40 )
| ( a_select2(mu_init,sK0) = init )
| ~ leq(n0,sK0) ),
inference(superposition,[status(thm)],[c_3411,c_2225]) ).
tcf(c_4199,plain,
sK0 = pv40,
inference(forward_subsumption_resolution,[status(thm)],[c_4191,c_49,c_50]) ).
tcf(c_4210,plain,
a_select2(mu_init,pv40) != init,
inference(demodulation,[status(thm)],[c_49,c_4199]) ).
tcf(c_4213,plain,
$false,
inference(ground_joinability,[status(thm)],[c_4210,c_52]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV167+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.40 % Computer : n015.cluster.edu
% 0.11/0.40 % Model : x86_64 x86_64
% 0.11/0.40 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.40 % Memory : 8046.5625MB
% 0.11/0.40 % OS : Linux 6.8.0-71-generic
% 0.11/0.40 % CPULimit : 300
% 0.11/0.40 % WCLimit : 300
% 0.11/0.40 % DateTime : Thu Sep 24 18:43:11 UTC 2026
% 0.11/0.41 % CPUTime :
% 0.11/0.41 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.11/0.44 Running first-order theorem proving
% 0.11/0.44 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
% 0.11/0.46
% 0.11/0.46 % ======== iProver multi-core TPTP/SMT =========
% 0.11/0.46
% 0.11/0.46 % Detected problem language: tptp
% 0.17/0.47 % Proving...
% 4.24/1.33 % SZS status Started for theBenchmark.p
% 4.24/1.33 % SZS status Theorem for theBenchmark.p
% 4.24/1.33
% 4.24/1.33 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 4.24/1.33
% 4.24/1.33 % ------ iProver source info
% 4.24/1.33
% 4.24/1.33 % git: date: 2026-07-19 20:42:38 +0200
% 4.24/1.33 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 4.24/1.33 % git: non_committed_changes: false
% 4.24/1.33
% 4.24/1.33 % ------ Parsing...
% 4.24/1.33 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 4.24/1.33
% 4.24/1.33 % ------ Preprocessing... sup_sim: 10 sf_s rm: 1 0s sf_e pe_s pe_e %
% 4.24/1.33
% 4.24/1.33 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 4.24/1.33
% 4.24/1.33 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 4.24/1.33 % ------ Proving...
% 4.24/1.33 % ------ Problem Properties
% 4.24/1.33
% 4.24/1.33 %
% 4.24/1.33 % clauses 82
% 4.24/1.33 % conjectures 15
% 4.24/1.33 % EPR 45
% 4.24/1.33 % Horn 75
% 4.24/1.33 % unary 55
% 4.24/1.33 % binary 9
% 4.24/1.33 % lits 147
% 4.24/1.33 % lits eq 51
% 4.24/1.33 % fd_pure 0
% 4.24/1.33 % fd_pseudo 0
% 4.24/1.33 % fd_cond 6
% 4.24/1.33 % fd_pseudo_cond 2
% 4.24/1.33 % AC symbols 0
% 4.24/1.33
% 4.24/1.33 % ------ Schedule dynamic 5 is on
% 4.24/1.33
% 4.24/1.33 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 4.24/1.33
% 4.24/1.33
% 4.24/1.33 % ------
% 4.24/1.33 % Current options:
% 4.24/1.33 % ------
% 4.24/1.33
% 4.24/1.33
% 4.24/1.33 %
% 4.24/1.33
% 4.24/1.33 % ------ Proving...
% 4.24/1.33 %
% 4.24/1.33
% 4.24/1.33 % SZS status Theorem for theBenchmark.p
% 4.24/1.33
% 4.24/1.33 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 4.24/1.33
% 4.24/1.33
%------------------------------------------------------------------------------