%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU161+3 : TPTP v9.3.1. Released v3.2.0.
% 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 2.00s 1.35s
% Output : CNFRefutation 2.00s
% 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(f3,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f8,conjecture,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t46_zfmisc_1) ).
fof(f9,negated_conjecture,
~ ! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,axiom,
! [X0,X1] :
( in(X0,X1)
=> set_union2(singleton(X0),X1) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',l23_zfmisc_1) ).
fof(f15,plain,
? [X0,X1] :
( in(X0,X1)
& set_union2(singleton(X0),X1) != X1 ),
inference(ennf_transformation,[],[f9]) ).
fof(f16,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(ennf_transformation,[],[f10]) ).
fof(f19,plain,
( in(sK2,sK3)
& sK3 != set_union2(singleton(sK2),sK3) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f15]) ).
fof(f22,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f3]) ).
fof(f27,plain,
in(sK2,sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f28,plain,
sK3 != set_union2(singleton(sK2),sK3),
inference(cnf_transformation,[],[f19]) ).
fof(f29,plain,
! [X0,X1] :
( ~ in(X0,X1)
| set_union2(singleton(X0),X1) = X1 ),
inference(cnf_transformation,[],[f16]) ).
tcf(c_51,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f22]) ).
tcf(c_56,negated_conjecture,
set_union2(singleton(sK2),sK3) != sK3,
inference(cnf_transformation,[],[f28]) ).
tcf(c_57,negated_conjecture,
in(sK2,sK3),
inference(cnf_transformation,[],[f27]) ).
tcf(c_58,plain,
! [X0: $i,X1: $i] :
( ( set_union2(singleton(X0),X1) = X1 )
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f29]) ).
tcf(c_101,plain,
set_union2(sK3,singleton(sK2)) != sK3,
inference(demodulation,[status(thm)],[c_56,c_51]) ).
tcf(c_113,definition,
iPr_def_10 = singleton(sK2),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_114,definition,
iPr_def_11 = set_union2(sK3,iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_11])],[]) ).
tcf(c_115,plain,
iPr_def_11 != sK3,
inference(demodulation,[status(thm)],[c_101,c_113,c_114]) ).
tcf(c_116,negated_conjecture,
in(sK2,sK3),
inference(demodulation,[status(thm)],[c_57]) ).
tcf(c_257,plain,
set_union2(iPr_def_10,sK3) = iPr_def_11,
inference(demodulation,[status(thm)],[c_114,c_51]) ).
tcf(c_285,plain,
set_union2(singleton(sK2),sK3) = sK3,
inference(superposition,[status(thm)],[c_116,c_58]) ).
tcf(c_286,plain,
sK3 = iPr_def_11,
inference(light_normalisation,[status(thm)],[c_285,c_113,c_257]) ).
tcf(c_288,plain,
iPr_def_11 != iPr_def_11,
inference(demodulation,[status(thm)],[c_115,c_286]) ).
tcf(c_290,plain,
$false,
inference(equality_resolution_simp,[status(thm)],[c_288]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU161+3 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.10/0.37 % Computer : n009.cluster.edu
% 0.10/0.37 % Model : x86_64 x86_64
% 0.10/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.37 % Memory : 8046.5625MB
% 0.10/0.37 % 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 12:59:58 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 Running run_iprover 300 /export/starexec/sandbox/benchmark/theBenchmark.p THM
% 0.16/0.43 Running first-order theorem proving
% 0.16/0.43 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
% 0.16/0.45
% 0.16/0.45 % ======== iProver multi-core TPTP/SMT =========
% 0.16/0.45
% 0.16/0.45 % Detected problem language: tptp
% 0.16/0.48 % Proving...
% 2.00/1.35 % SZS status Started for theBenchmark.p
% 2.00/1.35 % SZS status Theorem for theBenchmark.p
% 2.00/1.35
% 2.00/1.35 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.00/1.35
% 2.00/1.35 % ------ iProver source info
% 2.00/1.35
% 2.00/1.35 % git: date: 2026-07-19 20:42:38 +0200
% 2.00/1.35 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.00/1.35 % git: non_committed_changes: false
% 2.00/1.35
% 2.00/1.35 % ------ Parsing...
% 2.00/1.35 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.00/1.35
% 2.00/1.35 % ------ Preprocessing... sup_sim: 1 sf_s rm: 1 0s sf_e pe_s pe_e %
% 2.00/1.35
% 2.00/1.35 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.00/1.35
% 2.00/1.35 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.00/1.35 % ------ Proving...
% 2.00/1.35 % ------ Problem Properties
% 2.00/1.35
% 2.00/1.35 %
% 2.00/1.35 % clauses 12
% 2.00/1.35 % conjectures 1
% 2.00/1.35 % EPR 5
% 2.00/1.35 % Horn 12
% 2.00/1.35 % unary 8
% 2.00/1.35 % binary 4
% 2.00/1.35 % lits 16
% 2.00/1.35 % lits eq 6
% 2.00/1.35 % fd_pure 0
% 2.00/1.35 % fd_pseudo 0
% 2.00/1.35 % fd_cond 0
% 2.00/1.35 % fd_pseudo_cond 0
% 2.00/1.35 % AC symbols 0
% 2.00/1.35
% 2.00/1.35 % ------ Schedule dynamic 5 is on
% 2.00/1.35
% 2.00/1.35 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.00/1.35
% 2.00/1.35
% 2.00/1.35 % ------
% 2.00/1.35 % Current options:
% 2.00/1.35 % ------
% 2.00/1.35
% 2.00/1.35
% 2.00/1.35 %
% 2.00/1.35
% 2.00/1.35 % ------ Proving...
% 2.00/1.35 %
% 2.00/1.35
% 2.00/1.35 % SZS status Theorem for theBenchmark.p
% 2.00/1.35
% 2.00/1.35 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.00/1.35
% 2.00/1.35
%------------------------------------------------------------------------------