%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU173+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 : 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 02:55:45 PM UTC 2026
% Result : Theorem 6.61s 2.00s
% Output : CNFRefutation 6.61s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 6
% Syntax : Number of formulae : 45 ( 8 unt; 1 def)
% Number of atoms : 149 ( 9 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 161 ( 62 ~; 61 |; 23 &)
% ( 8 <=>; 7 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 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 : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 85 ( 0 sgn 79 !; 6 ?; 20 :)
% Comments :
%------------------------------------------------------------------------------
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(f14,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f55,conjecture,
! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l71_subset_1) ).
fof(f56,negated_conjecture,
~ ! [X0,X1] :
( ! [X2] :
( in(X2,X0)
=> in(X2,X1) )
=> element(X0,powerset(X1)) ),
inference(negated_conjecture,[status(cth)],[f55]) ).
fof(f105,axiom,
! [X0,X1] :
~ ( empty(X1)
& in(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t7_boole) ).
fof(f128,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] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f144,plain,
? [X0,X1] :
( ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) )
& ~ element(X0,powerset(X1)) ),
inference(ennf_transformation,[],[f56]) ).
fof(f178,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(ennf_transformation,[],[f105]) ).
fof(f195,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(f196,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,[],[f195]) ).
fof(f197,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))],[f196]) ).
fof(f198,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,[],[f128]) ).
fof(f210,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(nnf_transformation,[],[f129]) ).
fof(f211,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ? [X2] :
( in(X2,X0)
& ~ in(X2,X1) )
| subset(X0,X1) ) ),
inference(rectify,[],[f210]) ).
fof(f212,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK10(X0,X1),X0)
& ~ in(sK10(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10]),skolemize(X2,sK10(X0,X1))],[f211]) ).
fof(f232,plain,
( ! [X2] :
( ~ in(X2,sK17)
| in(X2,sK18) )
& ~ element(sK17,powerset(sK18)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK17,sK18]),skolemize(X0,sK17),skolemize(X1,sK18)],[f144]) ).
fof(f269,plain,
! [X3,X0,X1] :
( powerset(X0) != X1
| ~ subset(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f197]) ).
fof(f275,plain,
! [X0,X1] :
( empty(X0)
| ~ in(X1,X0)
| element(X1,X0) ),
inference(cnf_transformation,[],[f198]) ).
fof(f297,plain,
! [X0,X1] :
( in(sK10(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f212]) ).
fof(f298,plain,
! [X0,X1] :
( ~ in(sK10(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f212]) ).
fof(f350,plain,
! [X2] :
( ~ in(X2,sK17)
| in(X2,sK18) ),
inference(cnf_transformation,[],[f232]) ).
fof(f351,plain,
~ element(sK17,powerset(sK18)),
inference(cnf_transformation,[],[f232]) ).
fof(f420,plain,
! [X0,X1] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f178]) ).
fof(f497,plain,
! [X3,X0] :
( ~ subset(X3,X0)
| in(X3,powerset(X0)) ),
inference(equality_resolution,[],[f269]) ).
tcf(c_65,plain,
! [X0: $i,X1: $i] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[],[f497]) ).
tcf(c_67,plain,
! [X0: $i,X1: $i] :
( empty(X1)
| element(X0,X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f275]) ).
tcf(c_91,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK10(X0,X1),X1) ),
inference(cnf_transformation,[],[f298]) ).
tcf(c_92,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK10(X0,X1),X0) ),
inference(cnf_transformation,[],[f297]) ).
tcf(c_144,negated_conjecture,
~ element(sK17,powerset(sK18)),
inference(cnf_transformation,[],[f351]) ).
tcf(c_145,negated_conjecture,
! [X0: $i] :
( in(X0,sK18)
| ~ in(X0,sK17) ),
inference(cnf_transformation,[],[f350]) ).
tcf(c_212,plain,
! [X0: $i,X1: $i] :
( ~ empty(X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f420]) ).
tcf(c_310,plain,
! [X0: $i,X1: $i] :
( ~ in(X0,X1)
| element(X0,X1) ),
inference(global_subsumption_just,[status(thm)],[c_67,c_212,c_67]) ).
tcf(c_311,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(renaming,[status(thm)],[c_310]) ).
tcf(c_2162,plain,
! [X0: $i,X1: $i] :
( element(X0,X1)
| ~ in(X0,X1) ),
inference(prop_impl_just,[status(thm)],[c_311]) ).
tcf(c_3924,definition,
iPr_def_10 = powerset(sK18),
introduced(definition,[new_symbols(definition,[iPr_def_10])],[]) ).
tcf(c_3925,negated_conjecture,
! [X0: $i] :
( in(X0,sK18)
| ~ in(X0,sK17) ),
inference(demodulation,[status(thm)],[c_145]) ).
tcf(c_3926,negated_conjecture,
~ element(sK17,iPr_def_10),
inference(demodulation,[status(thm)],[c_144,c_3924]) ).
tcf(c_6611,plain,
! [X0: $i] :
( in(X0,iPr_def_10)
| ~ subset(X0,sK18) ),
inference(superposition,[status(thm)],[c_3924,c_65]) ).
tcf(c_6707,plain,
! [X0: $i] :
( subset(sK17,X0)
| in(sK10(sK17,X0),sK18) ),
inference(superposition,[status(thm)],[c_92,c_3925]) ).
tcf(c_7134,plain,
subset(sK17,sK18),
inference(superposition,[status(thm)],[c_6707,c_91]) ).
tcf(c_7170,plain,
in(sK17,iPr_def_10),
inference(superposition,[status(thm)],[c_7134,c_6611]) ).
tcf(c_7173,plain,
element(sK17,iPr_def_10),
inference(superposition,[status(thm)],[c_7170,c_2162]) ).
tcf(c_7174,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_7173,c_3926]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU173+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.19/0.45 % Computer : n008.cluster.edu
% 0.19/0.45 % Model : x86_64 x86_64
% 0.19/0.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.45 % Memory : 8046.5625MB
% 0.19/0.45 % OS : Linux 6.8.0-71-generic
% 0.19/0.45 % CPULimit : 300
% 0.19/0.45 % WCLimit : 300
% 0.19/0.45 % DateTime : Thu Sep 24 13:03:54 UTC 2026
% 0.19/0.45 % CPUTime :
% 0.19/0.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.23/0.51 Running first-order theorem proving
% 0.23/0.51 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
% 0.23/0.53
% 0.23/0.53 % ======== iProver multi-core TPTP/SMT =========
% 0.23/0.53
% 0.23/0.53 % Detected problem language: tptp
% 0.23/0.55 % Proving...
% 6.61/2.00 % SZS status Started for theBenchmark.p
% 6.61/2.00 % SZS status Theorem for theBenchmark.p
% 6.61/2.00
% 6.61/2.00 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 6.61/2.00
% 6.61/2.00 % ------ iProver source info
% 6.61/2.00
% 6.61/2.00 % git: date: 2026-07-19 20:42:38 +0200
% 6.61/2.00 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 6.61/2.00 % git: non_committed_changes: false
% 6.61/2.00
% 6.61/2.00 % ------ Parsing...
% 6.61/2.00 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 6.61/2.00
% 6.61/2.00 % ------ Preprocessing... sup_sim: 5 sf_s rm: 1 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe_e %
% 6.61/2.00
% 6.61/2.00 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 6.61/2.00
% 6.61/2.00 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 6.61/2.00 % ------ Proving...
% 6.61/2.00 % ------ Problem Properties
% 6.61/2.00
% 6.61/2.00 %
% 6.61/2.00 % clauses 155
% 6.61/2.00 % conjectures 2
% 6.61/2.00 % EPR 27
% 6.61/2.00 % Horn 123
% 6.61/2.00 % unary 33
% 6.61/2.00 % binary 66
% 6.61/2.00 % lits 344
% 6.61/2.00 % lits eq 85
% 6.61/2.00 % fd_pure 0
% 6.61/2.00 % fd_pseudo 0
% 6.61/2.00 % fd_cond 4
% 6.61/2.00 % fd_pseudo_cond 35
% 6.61/2.00 % AC symbols 0
% 6.61/2.00
% 6.61/2.00 % ------ Schedule dynamic 5 is on
% 6.61/2.00
% 6.61/2.00 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 6.61/2.00
% 6.61/2.00
% 6.61/2.00 % ------
% 6.61/2.00 % Current options:
% 6.61/2.00 % ------
% 6.61/2.00
% 6.61/2.00
% 6.61/2.00 %
% 6.61/2.00
% 6.61/2.00 % ------ Proving...
% 6.61/2.00 %
% 6.61/2.00
% 6.61/2.00 % SZS status Theorem for theBenchmark.p
% 6.61/2.00
% 6.61/2.00 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 6.61/2.00
% 6.61/2.00
%------------------------------------------------------------------------------