%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV181+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 : n008.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 3.17s 1.19s
% Output : CNFRefutation 3.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 10 unt; 0 def)
% Number of atoms : 231 ( 53 equ)
% Maximal formula atoms : 26 ( 6 avg)
% Number of connectives : 292 ( 98 ~; 100 |; 70 &)
% ( 0 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 16 ( 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 : 17 ( 17 usr; 15 con; 0-3 aty)
% Number of variables : 83 ( 0 sgn 80 !; 3 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] :
( X0 = X1
| gt(X1,X0)
| gt(X0,X1) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',totality) ).
fof(f2,axiom,
! [X0,X1,X2] :
( ( gt(X1,X2)
& gt(X0,X1) )
=> gt(X0,X2) ),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',transitivity_gt) ).
fof(f3,axiom,
! [X0] : ~ gt(X0,X0),
file('/export/starexec/sandbox/benchmark/Axioms/SWV003+0.ax',irreflexivity_gt) ).
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(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 ) )
& gt(n1,loopcounter)
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76) )
=> ! [X6] :
( ( leq(X6,n4)
& leq(n0,X6) )
=> a_select2(muold_init,X6) = init ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cl5_nebula_init_0081) ).
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 ) )
& gt(n1,loopcounter)
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76) )
=> ! [X6] :
( ( leq(X6,n4)
& leq(n0,X6) )
=> a_select2(muold_init,X6) = init ) ),
inference(negated_conjecture,[status(cth)],[f53]) ).
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 ) )
& gt(n1,loopcounter)
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76)
& ? [X6] :
( leq(X6,n4)
& leq(n0,X6)
& init != a_select2(muold_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 ) )
& gt(n1,loopcounter)
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76)
& ? [X6] :
( leq(X6,n4)
& leq(n0,X6)
& init != a_select2(muold_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(f101,plain,
! [X0,X1,X2] :
( ~ gt(X1,X2)
| ~ gt(X0,X1)
| gt(X0,X2) ),
inference(ennf_transformation,[],[f2]) ).
fof(f102,plain,
! [X0,X1,X2] :
( ~ gt(X1,X2)
| ~ gt(X0,X1)
| gt(X0,X2) ),
inference(flattening,[],[f101]) ).
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) ) )
& gt(n1,loopcounter)
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76)
& ? [X0] :
( leq(X0,n4)
& leq(n0,X0)
& init != a_select2(muold_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) ) )
& gt(n1,loopcounter)
& leq(n1,loopcounter)
& leq(tptp_float_0_001,pv76)
& leq(sK0,n4)
& leq(n0,sK0)
& init != a_select2(muold_init,sK0) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f117]) ).
fof(f126,plain,
gt(n1,loopcounter),
inference(cnf_transformation,[],[f118]) ).
fof(f127,plain,
leq(n1,loopcounter),
inference(cnf_transformation,[],[f118]) ).
fof(f133,plain,
! [X0,X1] :
( X0 = X1
| ~ leq(X0,X1)
| gt(X1,X0) ),
inference(cnf_transformation,[],[f99]) ).
fof(f134,plain,
! [X0,X1] :
( X0 = X1
| gt(X1,X0)
| gt(X0,X1) ),
inference(cnf_transformation,[],[f1]) ).
fof(f136,plain,
! [X0] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f137,plain,
! [X2,X0,X1] :
( ~ gt(X1,X2)
| ~ gt(X0,X1)
| gt(X0,X2) ),
inference(cnf_transformation,[],[f102]) ).
tcf(c_53,negated_conjecture,
leq(n1,loopcounter),
inference(cnf_transformation,[],[f127]) ).
tcf(c_54,negated_conjecture,
gt(n1,loopcounter),
inference(cnf_transformation,[],[f126]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( gt(X1,X0)
| ( X0 = X1 )
| ~ leq(X0,X1) ),
inference(cnf_transformation,[],[f133]) ).
tcf(c_62,plain,
! [X0: $i,X1: $i] :
( gt(X1,X0)
| gt(X0,X1)
| ( X0 = X1 ) ),
inference(cnf_transformation,[],[f134]) ).
tcf(c_64,plain,
! [X0: $i] : ~ gt(X0,X0),
inference(cnf_transformation,[],[f136]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i,X2: $i] :
( gt(X2,X1)
| ~ gt(X2,X0)
| ~ gt(X0,X1) ),
inference(cnf_transformation,[],[f137]) ).
tcf(c_124,plain,
~ gt(n1,n1),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_131,plain,
( gt(n1,n1)
| ( n1 = n1 ) ),
inference(instantiation,[status(thm)],[c_62]) ).
tcf(c_714,plain,
! [X0: $i,X1: $i,X2: $i,X3: $i] :
( gt(X0,X2)
| ~ gt(X1,X3)
| ( X2 != X3 )
| ( X0 != X1 ) ),
theory(equality) ).
tcf(c_2038,plain,
! [X0: $i] :
( gt(X0,loopcounter)
| ~ gt(n1,loopcounter)
| ~ gt(X0,n1) ),
inference(instantiation,[status(thm)],[c_65]) ).
tcf(c_2444,plain,
! [X0: $i,X1: $i] :
( gt(X0,X1)
| ~ gt(n1,loopcounter)
| ( X1 != loopcounter )
| ( X0 != n1 ) ),
inference(instantiation,[status(thm)],[c_714]) ).
tcf(c_2445,plain,
( gt(n1,n1)
| ~ gt(n1,loopcounter)
| ( n1 != loopcounter )
| ( n1 != n1 ) ),
inference(instantiation,[status(thm)],[c_2444]) ).
tcf(c_2788,plain,
( gt(loopcounter,loopcounter)
| ~ gt(loopcounter,n1)
| ~ gt(n1,loopcounter) ),
inference(instantiation,[status(thm)],[c_2038]) ).
tcf(c_2789,plain,
~ gt(loopcounter,loopcounter),
inference(instantiation,[status(thm)],[c_64]) ).
tcf(c_2890,plain,
! [X0: $i] :
( gt(loopcounter,X0)
| ( X0 = loopcounter )
| ~ leq(X0,loopcounter) ),
inference(instantiation,[status(thm)],[c_61]) ).
tcf(c_2891,plain,
( gt(loopcounter,n1)
| ( n1 = loopcounter )
| ~ leq(n1,loopcounter) ),
inference(instantiation,[status(thm)],[c_2890]) ).
tcf(c_2892,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_2891,c_2789,c_2788,c_2445,c_131,c_124,c_53,c_54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SWV181+1 : TPTP v9.3.1. Bugfixed v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n008.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.37 % CPULimit : 300
% 0.10/0.37 % WCLimit : 300
% 0.10/0.37 % DateTime : Thu Sep 24 18:42:39 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.40 Running first-order theorem proving
% 0.10/0.41 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
% 0.10/0.42
% 0.10/0.42 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.42
% 0.10/0.42 % Detected problem language: tptp
% 0.10/0.43 % Proving...
% 3.17/1.19 % SZS status Started for theBenchmark.p
% 3.17/1.19 % SZS status Theorem for theBenchmark.p
% 3.17/1.19
% 3.17/1.19 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 3.17/1.19
% 3.17/1.19 % ------ iProver source info
% 3.17/1.19
% 3.17/1.19 % git: date: 2026-07-19 20:42:38 +0200
% 3.17/1.19 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 3.17/1.19 % git: non_committed_changes: false
% 3.17/1.19
% 3.17/1.19 % ------ Parsing...
% 3.17/1.19 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 3.17/1.19
% 3.17/1.19 % ------ Preprocessing... sup_sim: 10 sf_s rm: 1 0s sf_e pe_s pe_e %
% 3.17/1.19
% 3.17/1.19 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 3.17/1.19
% 3.17/1.19 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 3.17/1.19 % ------ Proving...
% 3.17/1.19 % ------ Problem Properties
% 3.17/1.19
% 3.17/1.19 %
% 3.17/1.19 % clauses 74
% 3.17/1.19 % conjectures 11
% 3.17/1.19 % EPR 46
% 3.17/1.19 % Horn 67
% 3.17/1.19 % unary 52
% 3.17/1.19 % binary 7
% 3.17/1.19 % lits 131
% 3.17/1.19 % lits eq 44
% 3.17/1.19 % fd_pure 0
% 3.17/1.19 % fd_pseudo 0
% 3.17/1.19 % fd_cond 6
% 3.17/1.19 % fd_pseudo_cond 2
% 3.17/1.19 % AC symbols 0
% 3.17/1.19
% 3.17/1.19 % ------ Schedule dynamic 5 is on
% 3.17/1.19
% 3.17/1.19 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 3.17/1.19
% 3.17/1.19
% 3.17/1.19 % ------
% 3.17/1.19 % Current options:
% 3.17/1.19 % ------
% 3.17/1.19
% 3.17/1.19
% 3.17/1.19 %
% 3.17/1.19
% 3.17/1.19 % ------ Proving...
% 3.17/1.19 %
% 3.17/1.19
% 3.17/1.19 % SZS status Theorem for theBenchmark.p
% 3.17/1.19
% 3.17/1.19 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 3.17/1.19
% 3.17/1.19
%------------------------------------------------------------------------------