%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU169+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% Computer : n017.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 02:55:44 PM UTC 2026
% Result : Theorem 2.72s 1.27s
% Output : CNFRefutation 2.72s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 8
% Syntax : Number of formulae : 54 ( 22 unt; 1 def)
% Number of atoms : 190 ( 30 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 209 ( 76 ~; 80 |; 38 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 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 : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-3 aty)
% Number of variables : 94 ( 0 sgn 86 !; 8 ?; 16 :)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',commutativity_k2_xboole_0) ).
fof(f9,axiom,
! [X0,X1] :
( X1 = powerset(X0)
<=> ! [X2] :
( in(X2,X1)
<=> subset(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d1_zfmisc_1) ).
fof(f10,axiom,
! [X0,X1] :
( ( empty(X0)
=> ( element(X1,X0)
<=> empty(X1) ) )
& ( ~ empty(X0)
=> ( element(X1,X0)
<=> in(X1,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_subset_1) ).
fof(f12,axiom,
! [X0,X1,X2] :
( X2 = set_union2(X0,X1)
<=> ! [X3] :
( in(X3,X2)
<=> ( in(X3,X1)
| in(X3,X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d2_xboole_0) ).
fof(f33,axiom,
! [X0] : ~ empty(powerset(X0)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',fc1_subset_1) ).
fof(f47,conjecture,
! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l3_subset_1) ).
fof(f48,negated_conjecture,
~ ! [X0,X1] :
( element(X1,powerset(X0))
=> ! [X2] :
( in(X2,X1)
=> in(X2,X0) ) ),
inference(negated_conjecture,[status(cth)],[f47]) ).
fof(f62,axiom,
! [X0,X1] :
( subset(X0,X1)
=> set_union2(X0,X1) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t12_xboole_1) ).
fof(f120,plain,
! [X0,X1] :
( ( ~ empty(X0)
| ( element(X1,X0)
<=> empty(X1) ) )
& ( empty(X0)
| ( element(X1,X0)
<=> in(X1,X0) ) ) ),
inference(ennf_transformation,[],[f10]) ).
fof(f129,plain,
? [X0,X1] :
( element(X1,powerset(X0))
& ? [X2] :
( in(X2,X1)
& ~ in(X2,X0) ) ),
inference(ennf_transformation,[],[f48]) ).
fof(f139,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(ennf_transformation,[],[f62]) ).
fof(f178,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X2] :
( ( ~ in(X2,X1)
| subset(X2,X0) )
& ( ~ subset(X2,X0)
| in(X2,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(nnf_transformation,[],[f9]) ).
fof(f179,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ? [X2] :
( ( in(X2,X1)
| subset(X2,X0) )
& ( ~ in(X2,X1)
| ~ subset(X2,X0) ) )
| X1 = powerset(X0) ) ),
inference(rectify,[],[f178]) ).
fof(f180,plain,
! [X0,X1] :
( ( powerset(X0) != X1
| ! [X3] :
( ( ~ in(X3,X1)
| subset(X3,X0) )
& ( ~ subset(X3,X0)
| in(X3,X1) ) ) )
& ( ( ( in(sK2(X0,X1),X1)
| subset(sK2(X0,X1),X0) )
& ( ~ in(sK2(X0,X1),X1)
| ~ subset(sK2(X0,X1),X0) ) )
| X1 = powerset(X0) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2]),skolemize(X2,sK2(X0,X1))],[f179]) ).
fof(f181,plain,
! [X0,X1] :
( ( ~ empty(X0)
| ( ( ~ element(X1,X0)
| empty(X1) )
& ( ~ empty(X1)
| element(X1,X0) ) ) )
& ( empty(X0)
| ( ( ~ element(X1,X0)
| in(X1,X0) )
& ( ~ in(X1,X0)
| element(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f120]) ).
fof(f186,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(nnf_transformation,[],[f12]) ).
fof(f187,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X3] :
( ( ~ in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ( ~ in(X3,X1)
& ~ in(X3,X0) )
| in(X3,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(flattening,[],[f186]) ).
fof(f188,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ? [X3] :
( ( in(X3,X2)
| in(X3,X1)
| in(X3,X0) )
& ( ~ in(X3,X2)
| ( ~ in(X3,X1)
& ~ in(X3,X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(rectify,[],[f187]) ).
fof(f189,plain,
! [X0,X1,X2] :
( ( set_union2(X0,X1) != X2
| ! [X4] :
( ( ~ in(X4,X2)
| in(X4,X1)
| in(X4,X0) )
& ( ( ~ in(X4,X1)
& ~ in(X4,X0) )
| in(X4,X2) ) ) )
& ( ( ( in(sK4(X0,X1,X2),X2)
| in(sK4(X0,X1,X2),X1)
| in(sK4(X0,X1,X2),X0) )
& ( ~ in(sK4(X0,X1,X2),X2)
| ( ~ in(sK4(X0,X1,X2),X1)
& ~ in(sK4(X0,X1,X2),X0) ) ) )
| X2 = set_union2(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4]),skolemize(X3,sK4(X0,X1,X2))],[f188]) ).
fof(f211,plain,
( element(sK18,powerset(sK17))
& in(sK19,sK18)
& ~ in(sK19,sK17) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18,sK19]),skolemize(X0,sK17),skolemize(X1,sK18),skolemize(X2,sK19)],[f129]) ).
fof(f238,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f4]) ).
fof(f249,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ in(X3,X1)
| subset(X3,X0) ),
inference(cnf_transformation,[],[f180]) ).
fof(f255,plain,
! [X0,X1] :
( empty(X0)
| ~ element(X1,X0)
| in(X1,X0) ),
inference(cnf_transformation,[],[f181]) ).
fof(f264,plain,
! [X2,X0,X1,X4] :
( set_union2(X0,X1) != X2
| ~ in(X4,X1)
| in(X4,X2) ),
inference(cnf_transformation,[],[f189]) ).
fof(f303,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f33]) ).
fof(f319,plain,
element(sK18,powerset(sK17)),
inference(cnf_transformation,[],[f211]) ).
fof(f320,plain,
in(sK19,sK18),
inference(cnf_transformation,[],[f211]) ).
fof(f321,plain,
~ in(sK19,sK17),
inference(cnf_transformation,[],[f211]) ).
fof(f343,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_union2(X0,X1) = X1 ),
inference(cnf_transformation,[],[f139]) ).
fof(f470,plain,
! [X3,X0] :
( ~ in(X3,powerset(X0))
| subset(X3,X0) ),
inference(equality_resolution,[],[f249]) ).
fof(f477,plain,
! [X0,X1,X4] :
( ~ in(X4,X1)
| in(X4,set_union2(X0,X1)) ),
inference(equality_resolution,[],[f264]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[],[f238]) ).
tcf(c_66,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f470]) ).
tcf(c_68,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ~ element(X0,X1) ),
inference(cnf_transformation,[],[f255]) ).
tcf(c_81,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,set_union2(X2,X1))
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f477]) ).
tcf(c_116,plain,
! [X0: $i] : ~ empty(powerset(X0)),
inference(cnf_transformation,[],[f303]) ).
tcf(c_132,negated_conjecture,
~ in(sK19,sK17),
inference(cnf_transformation,[],[f321]) ).
tcf(c_133,negated_conjecture,
in(sK19,sK18),
inference(cnf_transformation,[],[f320]) ).
tcf(c_134,negated_conjecture,
element(sK18,powerset(sK17)),
inference(cnf_transformation,[],[f319]) ).
tcf(c_156,plain,
! [X0: $i,X1: $i] :
( ( set_union2(X0,X1) = X1 )
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f343]) ).
tcf(c_2005,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| in(X0,X1)
| ( X0 != sK18 )
| ( powerset(sK17) != X1 ) ),
inference(resolution_lifted,[status(thm)],[c_68,c_134]) ).
tcf(c_2006,plain,
( empty(powerset(sK17))
| in(sK18,powerset(sK17)) ),
inference(unflattening,[status(thm)],[c_2005]) ).
tcf(c_2011,plain,
in(sK18,powerset(sK17)),
inference(forward_subsumption_resolution,[status(thm)],[c_2006,c_116]) ).
tcf(c_3652,definition,
iPr_def_10 = powerset(sK17),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3653,plain,
in(sK18,iPr_def_10),
inference(demodulation,[status(thm)],[c_2011,c_3652]) ).
tcf(c_3654,negated_conjecture,
in(sK19,sK18),
inference(demodulation,[status(thm)],[c_133]) ).
tcf(c_3655,negated_conjecture,
~ in(sK19,sK17),
inference(demodulation,[status(thm)],[c_132]) ).
tcf(c_6152,plain,
! [X0: $i] :
( subset(X0,sK17)
| ~ in(X0,iPr_def_10) ),
inference(superposition,[status(thm)],[c_3652,c_66]) ).
tcf(c_6439,plain,
subset(sK18,sK17),
inference(superposition,[status(thm)],[c_3653,c_6152]) ).
tcf(c_6936,plain,
set_union2(sK18,sK17) = sK17,
inference(superposition,[status(thm)],[c_6439,c_156]) ).
tcf(c_6982,plain,
set_union2(sK17,sK18) = sK17,
inference(demodulation,[status(thm)],[c_6936,c_52]) ).
tcf(c_6995,plain,
! [X0: $i] :
( in(X0,sK17)
| ~ in(X0,sK18) ),
inference(superposition,[status(thm)],[c_6982,c_81]) ).
tcf(c_7050,plain,
in(sK19,sK17),
inference(superposition,[status(thm)],[c_3654,c_6995]) ).
tcf(c_7054,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7050,c_3655]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU169+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.11/0.36 % Computer : n017.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Thu Sep 24 12:57:01 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.36 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.14/0.39 Running first-order theorem proving
% 0.14/0.40 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
% 0.14/0.41
% 0.14/0.41 % ======== iProver multi-core TPTP/SMT =========
% 0.14/0.41
% 0.14/0.41 % Detected problem language: tptp
% 0.14/0.42 % Proving...
% 2.72/1.27 % SZS status Started for theBenchmark.p
% 2.72/1.27 % SZS status Theorem for theBenchmark.p
% 2.72/1.27
% 2.72/1.27 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.72/1.27
% 2.72/1.27 % ------ iProver source info
% 2.72/1.27
% 2.72/1.27 % git: date: 2026-07-19 20:42:38 +0200
% 2.72/1.27 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.72/1.27 % git: non_committed_changes: false
% 2.72/1.27
% 2.72/1.27 % ------ Parsing...
% 2.72/1.27 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.72/1.27
% 2.72/1.27 % ------ Preprocessing... sup_sim: 5 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe_e sup_sim: 0 sf_s rm: 2 0s sf_e pe_s pe_e %
% 2.72/1.27
% 2.72/1.27 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.72/1.27
% 2.72/1.27 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.72/1.27 % ------ Proving...
% 2.72/1.27 % ------ Problem Properties
% 2.72/1.27
% 2.72/1.27 %
% 2.72/1.27 % clauses 143
% 2.72/1.27 % conjectures 2
% 2.72/1.27 % EPR 24
% 2.72/1.27 % Horn 112
% 2.72/1.27 % unary 32
% 2.72/1.27 % binary 63
% 2.72/1.27 % lits 309
% 2.72/1.27 % lits eq 82
% 2.72/1.27 % fd_pure 0
% 2.72/1.27 % fd_pseudo 0
% 2.72/1.27 % fd_cond 3
% 2.72/1.27 % fd_pseudo_cond 35
% 2.72/1.27 % AC symbols 0
% 2.72/1.27
% 2.72/1.27 % ------ Schedule dynamic 5 is on
% 2.72/1.27
% 2.72/1.27 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.72/1.27
% 2.72/1.27
% 2.72/1.27 % ------
% 2.72/1.27 % Current options:
% 2.72/1.27 % ------
% 2.72/1.27
% 2.72/1.27
% 2.72/1.27 %
% 2.72/1.27
% 2.72/1.27 % ------ Proving...
% 2.72/1.27 %
% 2.72/1.27
% 2.72/1.27 % SZS status Theorem for theBenchmark.p
% 2.72/1.27
% 2.72/1.27 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.72/1.27
% 2.72/1.27
%------------------------------------------------------------------------------