%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV182+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 : n019.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 03:16:37 PM UTC 2026
% Result : Theorem 3.32s 1.27s
% Output : CNFRefutation 3.32s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 59 ( 27 unt; 0 def)
% Number of atoms : 246 ( 54 equ)
% Maximal formula atoms : 25 ( 4 avg)
% Number of connectives : 291 ( 104 ~; 96 |; 65 &)
% ( 1 <=>; 25 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 4 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 : 18 ( 18 usr; 14 con; 0-3 aty)
% Number of variables : 93 ( 0 sgn 90 !; 3 ?; 13 :)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox2/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/sandbox2/benchmark/Axioms/SWV003+0.ax',transitivity_leq) ).
fof(f8,axiom,
! [X0,X1] :
( gt(X1,X0)
=> leq(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_gt1) ).
fof(f9,axiom,
! [X0,X1] :
( ( X0 != X1
& leq(X0,X1) )
=> gt(X1,X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_gt2) ).
fof(f13,axiom,
! [X0,X1] :
( leq(X0,X1)
<=> gt(succ(X1),X0) ),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',leq_succ_gt_equiv) ).
fof(f30,axiom,
! [X0] : plus(n1,X0) = succ(X0),
file('/export/starexec/sandbox2/benchmark/Axioms/SWV003+0.ax',succ_plus_1_l) ).
fof(f53,conjecture,
( ( ( gt(loopcounter,n0)
=> ! [X5] :
( ( leq(X5,n4)
& leq(n0,X5) )
=> a_select2(sigma_init,X5) = init ) )
& ( gt(loopcounter,n0)
=> ! [X4] :
( ( leq(X4,n4)
& leq(n0,X4) )
=> a_select2(rho_init,X4) = init ) )
& ( gt(loopcounter,n0)
=> ! [X3] :
( ( leq(X3,n4)
& leq(n0,X3) )
=> a_select2(mu_init,X3) = init ) )
& ! [X2] :
( ( leq(X2,n4)
& leq(n0,X2) )
=> a_select3(center_init,X2,n0) = init )
& ! [X0] :
( ( leq(X0,n135299)
& leq(n0,X0) )
=> ! [X1] :
( ( leq(X1,n4)
& leq(n0,X1) )
=> a_select3(q_init,X0,X1) = init ) )
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76) )
=> ! [X6] :
( ( leq(X6,n4)
& leq(n0,X6) )
=> a_select2(rho_init,X6) = init ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cl5_nebula_init_0086) ).
fof(f54,negated_conjecture,
~ ( ( ( gt(loopcounter,n0)
=> ! [X5] :
( ( leq(X5,n4)
& leq(n0,X5) )
=> a_select2(sigma_init,X5) = init ) )
& ( gt(loopcounter,n0)
=> ! [X4] :
( ( leq(X4,n4)
& leq(n0,X4) )
=> a_select2(rho_init,X4) = init ) )
& ( gt(loopcounter,n0)
=> ! [X3] :
( ( leq(X3,n4)
& leq(n0,X3) )
=> a_select2(mu_init,X3) = init ) )
& ! [X2] :
( ( leq(X2,n4)
& leq(n0,X2) )
=> a_select3(center_init,X2,n0) = init )
& ! [X0] :
( ( leq(X0,n135299)
& leq(n0,X0) )
=> ! [X1] :
( ( leq(X1,n4)
& leq(n0,X1) )
=> a_select3(q_init,X0,X1) = init ) )
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76) )
=> ! [X6] :
( ( leq(X6,n4)
& leq(n0,X6) )
=> a_select2(rho_init,X6) = init ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
fof(f68,axiom,
gt(n1,n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',gt_1_0) ).
fof(f91,axiom,
succ(n0) = n1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',successor_1) ).
fof(f94,plain,
( ( ~ gt(loopcounter,n0)
| ! [X5] :
( ~ leq(X5,n4)
| ~ leq(n0,X5)
| a_select2(sigma_init,X5) = init ) )
& ( ~ gt(loopcounter,n0)
| ! [X4] :
( ~ leq(X4,n4)
| ~ leq(n0,X4)
| a_select2(rho_init,X4) = init ) )
& ( ~ gt(loopcounter,n0)
| ! [X3] :
( ~ leq(X3,n4)
| ~ leq(n0,X3)
| a_select2(mu_init,X3) = init ) )
& ! [X2] :
( ~ leq(X2,n4)
| ~ leq(n0,X2)
| a_select3(center_init,X2,n0) = init )
& ! [X0] :
( ~ leq(X0,n135299)
| ~ leq(n0,X0)
| ! [X1] :
( ~ leq(X1,n4)
| ~ leq(n0,X1)
| a_select3(q_init,X0,X1) = init ) )
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76)
& ? [X6] :
( leq(X6,n4)
& leq(n0,X6)
& init != a_select2(rho_init,X6) ) ),
inference(ennf_transformation,[],[f54]) ).
fof(f95,plain,
( ( ~ gt(loopcounter,n0)
| ! [X5] :
( ~ leq(X5,n4)
| ~ leq(n0,X5)
| a_select2(sigma_init,X5) = init ) )
& ( ~ gt(loopcounter,n0)
| ! [X4] :
( ~ leq(X4,n4)
| ~ leq(n0,X4)
| a_select2(rho_init,X4) = init ) )
& ( ~ gt(loopcounter,n0)
| ! [X3] :
( ~ leq(X3,n4)
| ~ leq(n0,X3)
| a_select2(mu_init,X3) = init ) )
& ! [X2] :
( ~ leq(X2,n4)
| ~ leq(n0,X2)
| a_select3(center_init,X2,n0) = init )
& ! [X0] :
( ~ leq(X0,n135299)
| ~ leq(n0,X0)
| ! [X1] :
( ~ leq(X1,n4)
| ~ leq(n0,X1)
| a_select3(q_init,X0,X1) = init ) )
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76)
& ? [X6] :
( leq(X6,n4)
& leq(n0,X6)
& init != a_select2(rho_init,X6) ) ),
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(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,n0)
| ! [X6] :
( ~ leq(X6,n4)
| ~ leq(n0,X6)
| init = a_select2(sigma_init,X6) ) )
& ( ~ gt(loopcounter,n0)
| ! [X5] :
( ~ leq(X5,n4)
| ~ leq(n0,X5)
| init = a_select2(rho_init,X5) ) )
& ( ~ gt(loopcounter,n0)
| ! [X4] :
( ~ leq(X4,n4)
| ~ leq(n0,X4)
| init = a_select2(mu_init,X4) ) )
& ! [X3] :
( ~ leq(X3,n4)
| ~ leq(n0,X3)
| init = a_select3(center_init,X3,n0) )
& ! [X1] :
( ~ leq(X1,n135299)
| ~ leq(n0,X1)
| ! [X2] :
( ~ leq(X2,n4)
| ~ leq(n0,X2)
| init = a_select3(q_init,X1,X2) ) )
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76)
& ? [X0] :
( leq(X0,n4)
& leq(n0,X0)
& init != a_select2(rho_init,X0) ) ),
inference(rectify,[],[f95]) ).
fof(f118,plain,
( ( ~ gt(loopcounter,n0)
| ! [X6] :
( ~ leq(X6,n4)
| ~ leq(n0,X6)
| init = a_select2(sigma_init,X6) ) )
& ( ~ gt(loopcounter,n0)
| ! [X5] :
( ~ leq(X5,n4)
| ~ leq(n0,X5)
| init = a_select2(rho_init,X5) ) )
& ( ~ gt(loopcounter,n0)
| ! [X4] :
( ~ leq(X4,n4)
| ~ leq(n0,X4)
| init = a_select2(mu_init,X4) ) )
& ! [X3] :
( ~ leq(X3,n4)
| ~ leq(n0,X3)
| init = a_select3(center_init,X3,n0) )
& ! [X1] :
( ~ leq(X1,n135299)
| ~ leq(n0,X1)
| ! [X2] :
( ~ leq(X2,n4)
| ~ leq(n0,X2)
| init = a_select3(q_init,X1,X2) ) )
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76)
& leq(sK0,n4)
& leq(n0,sK0)
& init != a_select2(rho_init,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f117]) ).
fof(f120,plain,
! [X0,X1] :
( ( ~ leq(X0,X1)
| gt(succ(X1),X0) )
& ( ~ gt(succ(X1),X0)
| leq(X0,X1) ) ),
inference(nnf_transformation,[],[f13]) ).
fof(f122,plain,
! [X5] :
( ~ gt(loopcounter,n0)
| ~ leq(X5,n4)
| ~ leq(n0,X5)
| init = a_select2(rho_init,X5) ),
inference(cnf_transformation,[],[f118]) ).
fof(f126,plain,
leq(n1,loopcounter),
inference(cnf_transformation,[],[f118]) ).
fof(f128,plain,
leq(sK0,n4),
inference(cnf_transformation,[],[f118]) ).
fof(f129,plain,
leq(n0,sK0),
inference(cnf_transformation,[],[f118]) ).
fof(f130,plain,
init != a_select2(rho_init,sK0),
inference(cnf_transformation,[],[f118]) ).
fof(f132,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| gt(X1,X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f134,plain,
! [X0,X1] :
( ~ gt(X1,X0)
| leq(X0,X1) ),
inference(cnf_transformation,[],[f100]) ).
fof(f135,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f140,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| gt(succ(X1),X0) ),
inference(cnf_transformation,[],[f120]) ).
fof(f143,plain,
! [X2,X0,X1] :
( ~ leq(X1,X2)
| ~ leq(X0,X1)
| leq(X0,X2) ),
inference(cnf_transformation,[],[f106]) ).
fof(f145,plain,
n1 = succ(n0),
inference(cnf_transformation,[],[f91]) ).
fof(f153,plain,
gt(n1,n0),
inference(cnf_transformation,[],[f68]) ).
fof(f193,plain,
! [X0] : succ(X0) = plus(n1,X0),
inference(cnf_transformation,[],[f30]) ).
fof(f199,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| gt(plus(n1,X1),X0) ),
inference(definition_unfolding,[],[f140,f193]) ).
fof(f201,plain,
n1 = plus(n1,n0),
inference(definition_unfolding,[],[f145,f193]) ).
tcf(c_49,negated_conjecture,
a_select2(rho_init,sK0) != init,
inference(cnf_transformation,[],[f130]) ).
tcf(c_50,negated_conjecture,
leq(n0,sK0),
inference(cnf_transformation,[],[f129]) ).
tcf(c_51,negated_conjecture,
leq(sK0,n4),
inference(cnf_transformation,[],[f128]) ).
tcf(c_53,negated_conjecture,
leq(n1,loopcounter),
inference(cnf_transformation,[],[f126]) ).
tcf(c_57,negated_conjecture,
! [X0: $i] :
( ( a_select2(rho_init,X0) = init )
| ~ gt(loopcounter,n0)
| ~ leq(n0,X0)
| ~ leq(X0,n4) ),
inference(cnf_transformation,[],[f122]) ).
tcf(c_60,plain,
! [X0: $i,X1: $i] :
( gt(X1,X0)
| ( X0 = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f132]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( leq(X1,X0)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_63,plain,
! [X0: $i] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f135]) ).
tcf(c_69,plain,
! [X0: $i,X1: $i] :
( gt(plus(n1,X1),X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f199]) ).
tcf(c_71,plain,
! [X0: $i,X1: $i,X2: $i] :
( leq(X2,X1)
| ~ leq(X2,X0)
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f143]) ).
tcf(c_73,plain,
plus(n1,n0) = n1,
inference(cnf_transformation,[],[f201]) ).
tcf(c_81,plain,
gt(n1,n0),
inference(cnf_transformation,[],[f153]) ).
tcf(c_123,plain,
~ gt(n1,n1),
inference(instantiation,[status(thm)],[c_63]) ).
tcf(c_1605,plain,
( ( a_select2(rho_init,sK0) = init )
| ~ gt(loopcounter,n0)
| ~ leq(sK0,n4) ),
inference(superposition,[status(thm)],[c_50,c_57]) ).
tcf(c_1606,plain,
~ gt(loopcounter,n0),
inference(forward_subsumption_resolution,[status(thm)],[c_1605,c_49,c_51]) ).
tcf(c_1701,plain,
leq(n0,n1),
inference(superposition,[status(thm)],[c_81,c_62]) ).
tcf(c_1904,plain,
! [X0: $i] :
( gt(n1,X0)
| ~ leq(X0,n0) ),
inference(superposition,[status(thm)],[c_73,c_69]) ).
tcf(c_1938,plain,
( gt(n1,n1)
| ~ leq(n1,n0) ),
inference(instantiation,[status(thm)],[c_1904]) ).
tcf(c_3314,plain,
! [X0: $i] :
( leq(X0,loopcounter)
| ~ leq(X0,n1) ),
inference(superposition,[status(thm)],[c_53,c_71]) ).
tcf(c_3484,plain,
leq(n0,loopcounter),
inference(superposition,[status(thm)],[c_1701,c_3314]) ).
tcf(c_3561,plain,
( gt(loopcounter,n0)
| ( n0 = loopcounter ) ),
inference(superposition,[status(thm)],[c_3484,c_60]) ).
tcf(c_3562,plain,
n0 = loopcounter,
inference(forward_subsumption_resolution,[status(thm)],[c_3561,c_1606]) ).
tcf(c_3586,plain,
leq(n1,n0),
inference(demodulation,[status(thm)],[c_53,c_3562]) ).
tcf(c_3591,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_3586,c_1938,c_123]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV182+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.35 % Computer : n019.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Thu Sep 24 18:42:19 UTC 2026
% 0.10/0.35 % CPUTime :
% 0.10/0.35 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.39 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
% 0.14/0.40
% 0.14/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.40
% 0.14/0.40 % Detected problem language: tptp
% 0.14/0.41 % Proving...
% 3.32/1.27 % SZS status Started for theBenchmark.p
% 3.32/1.27 % SZS status Theorem for theBenchmark.p
% 3.32/1.27
% 3.32/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.32/1.27
% 3.32/1.27 % ------ iProver source info
% 3.32/1.27
% 3.32/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 3.32/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.32/1.27 % git: non_committed_changes: false
% 3.32/1.27
% 3.32/1.27 % ------ Parsing...
% 3.32/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.32/1.27
% 3.32/1.27 % ------ Preprocessing... sup_sim: 10 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.32/1.27
% 3.32/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.32/1.27
% 3.32/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.32/1.27 % ------ Proving...
% 3.32/1.27 % ------ Problem Properties
% 3.32/1.27
% 3.32/1.27 %
% 3.32/1.27 % clauses 73
% 3.32/1.27 % conjectures 10
% 3.32/1.27 % EPR 45
% 3.32/1.27 % Horn 66
% 3.32/1.27 % unary 51
% 3.32/1.27 % binary 7
% 3.32/1.27 % lits 130
% 3.32/1.27 % lits eq 44
% 3.32/1.27 % fd_pure 0
% 3.32/1.27 % fd_pseudo 0
% 3.32/1.27 % fd_cond 6
% 3.32/1.27 % fd_pseudo_cond 2
% 3.32/1.27 % AC symbols 0
% 3.32/1.27
% 3.32/1.27 % ------ Schedule dynamic 5 is on
% 3.32/1.27
% 3.32/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.32/1.27
% 3.32/1.27
% 3.32/1.27 % ------
% 3.32/1.27 % Current options:
% 3.32/1.27 % ------
% 3.32/1.27
% 3.32/1.27
% 3.32/1.27 %
% 3.32/1.27
% 3.32/1.27 % ------ Proving...
% 3.32/1.27 %
% 3.32/1.27
% 3.32/1.27 % SZS status Theorem for theBenchmark.p
% 3.32/1.27
% 3.32/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.32/1.27
% 3.32/1.27
%------------------------------------------------------------------------------