%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV188+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 : n018.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 03:16:38 PM UTC 2026
% Result : Theorem 3.25s 1.31s
% Output : CNFRefutation 3.25s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 15 unt; 0 def)
% Number of atoms : 213 ( 49 equ)
% Maximal formula atoms : 26 ( 5 avg)
% Number of connectives : 273 ( 97 ~; 89 |; 60 &)
% ( 0 <=>; 27 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 5 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 : 17 ( 17 usr; 15 con; 0-3 aty)
% Number of variables : 79 ( 0 sgn 76 !; 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,
( ( ( gt(loopcounter,n1)
=> ! [X6] :
( ( leq(X6,n4)
& leq(n0,X6) )
=> a_select2(sigmaold_init,X6) = init ) )
& ( gt(loopcounter,n1)
=> ! [X5] :
( ( leq(X5,n4)
& leq(n0,X5) )
=> a_select2(rhoold_init,X5) = init ) )
& ( gt(loopcounter,n1)
=> ! [X4] :
( ( leq(X4,n4)
& leq(n0,X4) )
=> a_select2(muold_init,X4) = init ) )
& ! [X3] :
( ( leq(X3,n4)
& leq(n0,X3) )
=> a_select3(center_init,X3,n0) = 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 ) ) )
=> ! [X7] :
( ( leq(X7,tptp_minus_1)
& leq(n0,X7) )
=> a_select2(mu_init,X7) = init ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0116) ).
fof(f54,negated_conjecture,
~ ( ( ( gt(loopcounter,n1)
=> ! [X6] :
( ( leq(X6,n4)
& leq(n0,X6) )
=> a_select2(sigmaold_init,X6) = init ) )
& ( gt(loopcounter,n1)
=> ! [X5] :
( ( leq(X5,n4)
& leq(n0,X5) )
=> a_select2(rhoold_init,X5) = init ) )
& ( gt(loopcounter,n1)
=> ! [X4] :
( ( leq(X4,n4)
& leq(n0,X4) )
=> a_select2(muold_init,X4) = init ) )
& ! [X3] :
( ( leq(X3,n4)
& leq(n0,X3) )
=> a_select3(center_init,X3,n0) = 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 ) ) )
=> ! [X7] :
( ( leq(X7,tptp_minus_1)
& leq(n0,X7) )
=> a_select2(mu_init,X7) = init ) ),
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(f85,axiom,
! [X0] :
( ( leq(X0,n0)
& leq(n0,X0) )
=> X0 = n0 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',finite_domain_0) ).
fof(f94,plain,
( ( ~ gt(loopcounter,n1)
| ! [X6] :
( ~ leq(X6,n4)
| ~ leq(n0,X6)
| a_select2(sigmaold_init,X6) = init ) )
& ( ~ gt(loopcounter,n1)
| ! [X5] :
( ~ leq(X5,n4)
| ~ leq(n0,X5)
| a_select2(rhoold_init,X5) = init ) )
& ( ~ gt(loopcounter,n1)
| ! [X4] :
( ~ leq(X4,n4)
| ~ leq(n0,X4)
| a_select2(muold_init,X4) = init ) )
& ! [X3] :
( ~ leq(X3,n4)
| ~ leq(n0,X3)
| a_select3(center_init,X3,n0) = 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 ) )
& ? [X7] :
( leq(X7,tptp_minus_1)
& leq(n0,X7)
& init != a_select2(mu_init,X7) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f95,plain,
( ( ~ gt(loopcounter,n1)
| ! [X6] :
( ~ leq(X6,n4)
| ~ leq(n0,X6)
| a_select2(sigmaold_init,X6) = init ) )
& ( ~ gt(loopcounter,n1)
| ! [X5] :
( ~ leq(X5,n4)
| ~ leq(n0,X5)
| a_select2(rhoold_init,X5) = init ) )
& ( ~ gt(loopcounter,n1)
| ! [X4] :
( ~ leq(X4,n4)
| ~ leq(n0,X4)
| a_select2(muold_init,X4) = init ) )
& ! [X3] :
( ~ leq(X3,n4)
| ~ leq(n0,X3)
| a_select3(center_init,X3,n0) = 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 ) )
& ? [X7] :
( leq(X7,tptp_minus_1)
& leq(n0,X7)
& init != a_select2(mu_init,X7) ) ),
inference(flattening,[],[f94]) ).
fof(f96,plain,
! [X0] :
( ~ leq(X0,n0)
| ~ leq(n0,X0)
| X0 = n0 ),
inference(ennf_transformation,[],[f85]) ).
fof(f97,plain,
! [X0] :
( ~ leq(X0,n0)
| ~ leq(n0,X0)
| X0 = n0 ),
inference(flattening,[],[f96]) ).
fof(f100,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,X1) ),
inference(ennf_transformation,[],[f8]) ).
fof(f105,plain,
! [X0,X1,X2] :
( ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ),
inference(ennf_transformation,[],[f5]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ),
inference(flattening,[],[f105]) ).
fof(f117,plain,
( ( ~ gt(loopcounter,n1)
| ! [X7] :
( ~ leq(X7,n4)
| ~ leq(n0,X7)
| init = a_select2(sigmaold_init,X7) ) )
& ( ~ gt(loopcounter,n1)
| ! [X6] :
( ~ leq(X6,n4)
| ~ leq(n0,X6)
| init = a_select2(rhoold_init,X6) ) )
& ( ~ gt(loopcounter,n1)
| ! [X5] :
( ~ leq(X5,n4)
| ~ leq(n0,X5)
| init = a_select2(muold_init,X5) ) )
& ! [X4] :
( ~ leq(X4,n4)
| ~ leq(n0,X4)
| init = a_select3(center_init,X4,n0) )
& ! [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) ) )
& ? [X0] :
( leq(X0,tptp_minus_1)
& leq(n0,X0)
& init != a_select2(mu_init,X0) ) ),
inference(rectify,[],[f95]) ).
fof(f118,plain,
( ( ~ gt(loopcounter,n1)
| ! [X7] :
( ~ leq(X7,n4)
| ~ leq(n0,X7)
| init = a_select2(sigmaold_init,X7) ) )
& ( ~ gt(loopcounter,n1)
| ! [X6] :
( ~ leq(X6,n4)
| ~ leq(n0,X6)
| init = a_select2(rhoold_init,X6) ) )
& ( ~ gt(loopcounter,n1)
| ! [X5] :
( ~ leq(X5,n4)
| ~ leq(n0,X5)
| init = a_select2(muold_init,X5) ) )
& ! [X4] :
( ~ leq(X4,n4)
| ~ leq(n0,X4)
| init = a_select3(center_init,X4,n0) )
& ! [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(sK0,tptp_minus_1)
& leq(n0,sK0)
& init != a_select2(mu_init,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f117]) ).
fof(f127,plain,
leq(sK0,tptp_minus_1),
inference(cnf_transformation,[],[f118]) ).
fof(f128,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f118]) ).
fof(f130,plain,
! [X0] :
( ~ leq(X0,n0)
| ~ leq(n0,X0)
| n0 = X0 ),
inference(cnf_transformation,[],[f97]) ).
fof(f133,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f134,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f142,plain,
! [X2,X0,X1] :
( ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ),
inference(cnf_transformation,[],[f106]) ).
fof(f147,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[],[f61]) ).
tcf(c_50,negated_conjecture,
leq(n0,sK0),
inference(cnf_transformation,[],[f128]) ).
tcf(c_51,negated_conjecture,
leq(sK0,tptp_minus_1),
inference(cnf_transformation,[],[f127]) ).
tcf(c_58,plain,
! [X0: $i] :
( ( X0 = n0 )
| ~ leq(n0,X0)
| ~ leq(X0,n0) ),
inference(cnf_transformation,[],[f130]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( leq(X1,X0)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_62,plain,
! [X0: $i] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f134]) ).
tcf(c_70,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(X2,X1)
| ~ leq(X2,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f142]) ).
tcf(c_75,plain,
gt(n0,tptp_minus_1),
inference(cnf_transformation,[],[f147]) ).
tcf(c_1803,plain,
leq(tptp_minus_1,n0),
inference(superposition,[status(thm)],[c_75,c_61]) ).
tcf(c_4049,plain,
! [X0: $i] :
( leq(X0,tptp_minus_1)
| ~ leq(X0,sK0) ),
inference(superposition,[status(thm)],[c_51,c_70]) ).
tcf(c_4192,plain,
leq(n0,tptp_minus_1),
inference(superposition,[status(thm)],[c_50,c_4049]) ).
tcf(c_4374,plain,
( ( n0 = tptp_minus_1 )
| ~ leq(tptp_minus_1,n0) ),
inference(superposition,[status(thm)],[c_4192,c_58]) ).
tcf(c_4375,plain,
n0 = tptp_minus_1,
inference(forward_subsumption_resolution,[status(thm)],[c_4374,c_1803]) ).
tcf(c_4404,plain,
gt(n0,n0),
inference(demodulation,[status(thm)],[c_75,c_4375]) ).
tcf(c_4423,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_4404,c_62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV188+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.12/0.60 % Computer : n018.cluster.edu
% 0.12/0.60 % Model : x86_64 x86_64
% 0.12/0.60 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.60 % Memory : 8046.5625MB
% 0.12/0.60 % OS : Linux 6.8.0-71-generic
% 0.12/0.60 % CPULimit : 300
% 0.12/0.60 % WCLimit : 300
% 0.12/0.60 % DateTime : Thu Sep 24 18:45:06 UTC 2026
% 0.12/0.60 % CPUTime :
% 0.12/0.60 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.15/0.64 Running first-order theorem proving
% 0.15/0.64 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
% 0.15/0.66
% 0.15/0.66 % ======== iProver multi-core TPTP/SMT =========
% 0.15/0.66
% 0.15/0.66 % Detected problem language: tptp
% 0.15/0.67 % Proving...
% 3.25/1.31 % SZS status Started for theBenchmark.p
% 3.25/1.31 % SZS status Theorem for theBenchmark.p
% 3.25/1.31
% 3.25/1.31 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.25/1.31
% 3.25/1.31 % ------ iProver source info
% 3.25/1.31
% 3.25/1.31 % git: date: 2026-07-19 20:42:38 +0200
% 3.25/1.31 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.25/1.31 % git: non_committed_changes: false
% 3.25/1.31
% 3.25/1.31 % ------ Parsing...
% 3.25/1.31 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.25/1.31
% 3.25/1.31 % ------ Preprocessing... sup_sim: 10 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.25/1.31
% 3.25/1.31 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.25/1.31
% 3.25/1.31 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.25/1.31 % ------ Proving...
% 3.25/1.31 % ------ Problem Properties
% 3.25/1.31
% 3.25/1.31 %
% 3.25/1.31 % clauses 72
% 3.25/1.31 % conjectures 9
% 3.25/1.31 % EPR 43
% 3.25/1.31 % Horn 65
% 3.25/1.31 % unary 49
% 3.25/1.31 % binary 7
% 3.25/1.31 % lits 131
% 3.25/1.31 % lits eq 45
% 3.25/1.31 % fd_pure 0
% 3.25/1.31 % fd_pseudo 0
% 3.25/1.31 % fd_cond 6
% 3.25/1.31 % fd_pseudo_cond 2
% 3.25/1.31 % AC symbols 0
% 3.25/1.31
% 3.25/1.31 % ------ Schedule dynamic 5 is on
% 3.25/1.31
% 3.25/1.31 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.25/1.31
% 3.25/1.31
% 3.25/1.31 % ------
% 3.25/1.31 % Current options:
% 3.25/1.31 % ------
% 3.25/1.31
% 3.25/1.31
% 3.25/1.31 %
% 3.25/1.31
% 3.25/1.31 % ------ Proving...
% 3.25/1.31 %
% 3.25/1.31
% 3.25/1.31 % SZS status Theorem for theBenchmark.p
% 3.25/1.31
% 3.25/1.31 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.25/1.31
%------------------------------------------------------------------------------