%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU161+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% Computer : n009.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 02:55:40 PM UTC 2026
% Result : Theorem 1.68s 1.27s
% Output : CNFRefutation 1.68s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 25 ( 17 unt; 2 def)
% Number of atoms : 42 ( 21 equ)
% Maximal formula atoms : 2 ( 1 avg)
% Number of connectives : 19 ( 11 ~; 3 |; 2 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 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 : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 20 ( 0 sgn 18 !; 2 ?; 4 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f6,conjecture,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f7,negated_conjecture,
~ ! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(f11,plain,
? [X0,X1] :
( in(X0,X1)
& set_union2(singleton(X0),X1) != X1 ),
inference(ennf_transformation,[],[f7]) ).
fof(f12,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(ennf_transformation,[],[f8]) ).
fof(f13,plain,
( in(sK0,sK1)
& sK1 != set_union2(singleton(sK0),sK1) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1]),skolemize(X0,sK0),skolemize(X1,sK1)],[f11]) ).
fof(f14,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f1]) ).
fof(f17,plain,
in(sK0,sK1),
inference(cnf_transformation,[],[f13]) ).
fof(f18,plain,
sK1 != set_union2(singleton(sK0),sK1),
inference(cnf_transformation,[],[f13]) ).
fof(f19,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(cnf_transformation,[],[f12]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f14]) ).
tcf(c_52,negated_conjecture,
set_union2(singleton(sK0),sK1) != sK1,
inference(cnf_transformation,[],[f18]) ).
tcf(c_53,negated_conjecture,
in(sK0,sK1),
inference(cnf_transformation,[],[f17]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( ( set_union2(singleton(X0),X1) = X1 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f19]) ).
tcf(c_76,plain,
set_union2(sK1,singleton(sK0)) != sK1,
inference(demodulation,[status(thm)],[c_52,c_49]) ).
tcf(c_87,definition,
iPr_def_10 = singleton(sK0),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_88,definition,
iPr_def_11 = set_union2(sK1,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_89,plain,
iPr_def_11 != sK1,
inference(demodulation,[status(thm)],[c_76,c_87,c_88]) ).
tcf(c_90,negated_conjecture,
in(sK0,sK1),
inference(demodulation,[status(thm)],[c_53]) ).
tcf(c_194,plain,
set_union2(iPr_def_10,sK1) = iPr_def_11,
inference(demodulation,[status(thm)],[c_88,c_49]) ).
tcf(c_202,plain,
set_union2(singleton(sK0),sK1) = sK1,
inference(superposition,[status(thm)],[c_90,c_54]) ).
tcf(c_203,plain,
sK1 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_202,c_87,c_194]) ).
tcf(c_206,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_89,c_203]) ).
tcf(c_208,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_206]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU161+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.36 % Computer : n009.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
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Thu Sep 24 12:59:43 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.36 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.39 Running first-order theorem proving
% 0.10/0.39 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
% 0.10/0.40
% 0.10/0.40 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.40
% 0.10/0.40 % Detected problem language: tptp
% 0.10/0.42 % Proving...
% 1.68/1.27 % SZS status Started for theBenchmark.p
% 1.68/1.27 % SZS status Theorem for theBenchmark.p
% 1.68/1.27
% 1.68/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 1.68/1.27
% 1.68/1.27 % ------ iProver source info
% 1.68/1.27
% 1.68/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 1.68/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 1.68/1.27 % git: non_committed_changes: false
% 1.68/1.27
% 1.68/1.27 % ------ Parsing...
% 1.68/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 1.68/1.27
% 1.68/1.27 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 1.68/1.27
% 1.68/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 1.68/1.27
% 1.68/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.68/1.27 % ------ Proving...
% 1.68/1.27 % ------ Problem Properties
% 1.68/1.27
% 1.68/1.27 %
% 1.68/1.27 % clauses 8
% 1.68/1.27 % conjectures 1
% 1.68/1.27 % EPR 3
% 1.68/1.27 % Horn 8
% 1.68/1.27 % unary 6
% 1.68/1.27 % binary 2
% 1.68/1.27 % lits 10
% 1.68/1.27 % lits eq 6
% 1.68/1.27 % fd_pure 0
% 1.68/1.27 % fd_pseudo 0
% 1.68/1.27 % fd_cond 0
% 1.68/1.27 % fd_pseudo_cond 0
% 1.68/1.27 % AC symbols 0
% 1.68/1.27
% 1.68/1.27 % ------ Schedule dynamic 5 is on
% 1.68/1.27
% 1.68/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.68/1.27
% 1.68/1.27
% 1.68/1.27 % ------
% 1.68/1.27 % Current options:
% 1.68/1.27 % ------
% 1.68/1.27
% 1.68/1.27
% 1.68/1.27 %
% 1.68/1.27
% 1.68/1.27 % ------ Proving...
% 1.68/1.27 %
% 1.68/1.27
% 1.68/1.27 % SZS status Theorem for theBenchmark.p
% 1.68/1.27
% 1.68/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.68/1.27
% 1.68/1.27
%------------------------------------------------------------------------------