%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SWV254-2 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n005.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 03:16:49 PM UTC 2026
% Result : Unsatisfiable 0.64s 11.41s
% Output : CNFRefutation 0.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 6
% Syntax : Number of formulae : 19 ( 14 unt; 0 def)
% Number of atoms : 29 ( 17 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 22 ( 12 ~; 10 |; 0 &)
% ( 0 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 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; 0-3 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 28 ( 0 sgn 28 !; 0 ?; 18 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X2,X0,X1] :
( c_SetInterval_OatLeastLessThan(X2,X1,X0) = c_emptyset
| ~ c_lessequals(X1,X2,X0)
| ~ class_Orderings_Oorder(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__empty_0) ).
fof(f2,axiom,
! [X0] : c_SetInterval_OatLeastLessThan(X0,c_Suc(X0),tc_nat) = c_insert(X0,c_emptyset,tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_SetInterval_OatLeastLessThan__singleton_0) ).
fof(f3,axiom,
! [X2,X0,X1] : c_emptyset != c_insert(X0,X1,X2),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_Set_Oempty__not__insert_0) ).
fof(f4,negated_conjecture,
! [X0] : c_lessequals(X0,v_x(X0),tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_0) ).
fof(f5,negated_conjecture,
! [X0] : v_x(X0) = v_nat,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cls_conjecture_1) ).
fof(f6,axiom,
class_Orderings_Oorder(tc_nat),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',clsarity_nat_3) ).
fof(f7,plain,
! [X0] : c_lessequals(X0,v_nat,tc_nat),
inference(definition_unfolding,[],[f4,f5]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_SetInterval_OatLeastLessThan(X1,X0,X2) = c_emptyset )
| ~ class_Orderings_Oorder(X2)
| ~ c_lessequals(X0,X1,X2) ),
inference(cnf_transformation,[],[f1]) ).
tcf(c_56,plain,
! [X0: $i] : c_SetInterval_OatLeastLessThan(X0,c_Suc(X0),tc_nat) = c_insert(X0,c_emptyset,tc_nat),
inference(cnf_transformation,[],[f2]) ).
tcf(c_57,plain,
! [X0: $i,X1: $i,X2: $i] : c_insert(X0,X1,X2) != c_emptyset,
inference(cnf_transformation,[],[f3]) ).
tcf(c_58,negated_conjecture,
! [X0: $i] : c_lessequals(X0,v_nat,tc_nat),
inference(cnf_transformation,[],[f7]) ).
tcf(c_59,plain,
class_Orderings_Oorder(tc_nat),
inference(cnf_transformation,[],[f6]) ).
tcf(c_88,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_SetInterval_OatLeastLessThan(X2,X1,X0) = c_emptyset )
| ~ c_lessequals(X1,X2,X0)
| ( X0 != tc_nat ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_59]) ).
tcf(c_89,plain,
! [X0: $i,X1: $i] :
( ( c_SetInterval_OatLeastLessThan(X1,X0,tc_nat) = c_emptyset )
| ~ c_lessequals(X0,X1,tc_nat) ),
inference(unflattening,[status(thm)],[c_88]) ).
tcf(c_99,plain,
! [X0: $i,X1: $i,X2: $i] :
( ( c_SetInterval_OatLeastLessThan(X2,X1,tc_nat) = c_emptyset )
| ( tc_nat != tc_nat )
| ( X2 != v_nat )
| ( X0 != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_58,c_89]) ).
tcf(c_100,plain,
! [X0: $i] : c_SetInterval_OatLeastLessThan(v_nat,X0,tc_nat) = c_emptyset,
inference(unflattening,[status(thm)],[c_99]) ).
tcf(c_116,plain,
! [X0: $i] : c_SetInterval_OatLeastLessThan(v_nat,X0,tc_nat) = c_emptyset,
inference(demodulation,[status(thm)],[c_100]) ).
tcf(c_152,plain,
c_insert(v_nat,c_emptyset,tc_nat) = c_emptyset,
inference(superposition,[status(thm)],[c_116,c_56]) ).
tcf(c_154,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_152,c_57]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SWV254-2 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.18/10.46 % Computer : n005.cluster.edu
% 0.18/10.46 % Model : x86_64 x86_64
% 0.18/10.46 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/10.46 % Memory : 8046.5625MB
% 0.18/10.46 % OS : Linux 6.8.0-71-generic
% 0.18/10.46 % CPULimit : 300
% 0.18/10.46 % WCLimit : 300
% 0.18/10.46 % DateTime : Thu Sep 24 18:53:58 UTC 2026
% 0.18/10.46 % CPUTime :
% 0.18/10.46 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.23/10.52 Running first-order theorem proving
% 0.23/10.52 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
% 0.23/10.54
% 0.23/10.54 % ======== iProver multi-core TPTP/SMT =========
% 0.23/10.54
% 0.23/10.54 % Detected problem language: tptp
% 0.23/10.56 % Proving...
% 0.64/11.41 % SZS status Started for theBenchmark.p
% 0.64/11.41 % SZS status Unsatisfiable for theBenchmark.p
% 0.64/11.41
% 0.64/11.41 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.64/11.41
% 0.64/11.41 % ------ iProver source info
% 0.64/11.41
% 0.64/11.41 % git: date: 2026-07-19 20:42:38 +0200
% 0.64/11.41 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.64/11.41 % git: non_committed_changes: false
% 0.64/11.41
% 0.64/11.41 % ------ Parsing...% successful
% 0.64/11.41
% 0.64/11.41
% 0.64/11.41 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.64/11.41
% 0.64/11.41 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 0.64/11.41
% 0.64/11.41 % ------ Preprocessing...% ------ preprocesses with Option_UEQ
% 0.64/11.41 gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.64/11.41
% 0.64/11.41 % ------ Preprocessing... sf_s rm: 0 0s sf_e
% 0.64/11.41 % ------ Proving...
% 0.64/11.41 % ------ Problem Properties
% 0.64/11.41
% 0.64/11.41 %
% 0.64/11.41 % clauses 3
% 0.64/11.41 % conjectures 0
% 0.64/11.41 % EPR 0
% 0.64/11.41 % Horn 3
% 0.64/11.41 % unary 3
% 0.64/11.41 % binary 0
% 0.64/11.41 % lits 3
% 0.64/11.41 % lits eq 3
% 0.64/11.41 % fd_pure 0
% 0.64/11.41 % fd_pseudo 0
% 0.64/11.41 % fd_cond 0
% 0.64/11.41 % fd_pseudo_cond 0
% 0.64/11.41 % AC symbols 0
% 0.64/11.41
% 0.64/11.41 % ------ Schedule UEQ
% 0.64/11.41
% 0.64/11.41 % ------ Option_UEQ Time Limit: 10.
% 0.64/11.41
% 0.64/11.41
% 0.64/11.41 % ------
% 0.64/11.41 % Current options:
% 0.64/11.41 % ------
% 0.64/11.41
% 0.64/11.41
% 0.64/11.41 %
% 0.64/11.41
% 0.64/11.41 % ------ Proving...
% 0.64/11.41 %
% 0.64/11.41
% 0.64/11.41 % SZS status Unsatisfiable for theBenchmark.p
% 0.64/11.41
% 0.64/11.41 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.64/11.41
% 0.64/11.41
%------------------------------------------------------------------------------