%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU317+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 : n020.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 02:56:47 PM UTC 2026
% Result : Theorem 97.26s 25.75s
% Output : CNFRefutation 97.26s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 4
% Syntax : Number of formulae : 48 ( 8 unt; 0 def)
% Number of atoms : 190 ( 2 equ)
% Maximal formula atoms : 13 ( 3 avg)
% Number of connectives : 241 ( 99 ~; 102 |; 24 &)
% ( 6 <=>; 10 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 7 ( 5 usr; 1 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 94 ( 0 sgn 88 !; 6 ?; 26 :)
% Comments :
%------------------------------------------------------------------------------
fof(f82,axiom,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( in(X2,X0)
=> in(X2,X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d3_tarski) ).
fof(f443,axiom,
! [X0,X1] :
( element(X0,powerset(X1))
<=> subset(X0,X1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t3_subset) ).
fof(f453,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ! [X2] :
( in(X2,the_carrier(X0))
=> ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( element(X3,powerset(the_carrier(X0)))
=> ( ( subset(X1,X3)
& closed_subset(X3,X0) )
=> in(X2,X3) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t45_pre_topc) ).
fof(f463,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(X1,topstr_closure(X0,X1)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t48_pre_topc) ).
fof(f464,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset(X1,topstr_closure(X0,X1)) ) ),
inference(negated_conjecture,[status(cth)],[f463]) ).
fof(f739,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X2,X3) ) ) ) ) ),
inference(ennf_transformation,[],[f453]) ).
fof(f740,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( in(X2,topstr_closure(X0,X1))
<=> ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X2,X3) ) ) ) ) ),
inference(flattening,[],[f739]) ).
fof(f754,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ~ subset(X1,topstr_closure(X0,X1)) ) ),
inference(ennf_transformation,[],[f464]) ).
fof(f846,plain,
! [X0,X1] :
( subset(X0,X1)
<=> ! [X2] :
( ~ in(X2,X0)
| in(X2,X1) ) ),
inference(ennf_transformation,[],[f82]) ).
fof(f1261,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( ( ~ in(X2,topstr_closure(X0,X1))
| ! [X3] :
( ~ element(X3,powerset(the_carrier(X0)))
| ~ subset(X1,X3)
| ~ closed_subset(X3,X0)
| in(X2,X3) ) )
& ( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& subset(X1,X3)
& closed_subset(X3,X0)
& ~ in(X2,X3) )
| in(X2,topstr_closure(X0,X1)) ) ) ) ) ),
inference(nnf_transformation,[],[f740]) ).
fof(f1262,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( ( ~ in(X2,topstr_closure(X0,X1))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ subset(X1,X4)
| ~ closed_subset(X4,X0)
| in(X2,X4) ) )
& ( ? [X3] :
( element(X3,powerset(the_carrier(X0)))
& subset(X1,X3)
& closed_subset(X3,X0)
& ~ in(X2,X3) )
| in(X2,topstr_closure(X0,X1)) ) ) ) ) ),
inference(rectify,[],[f1261]) ).
fof(f1263,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ! [X2] :
( ~ in(X2,the_carrier(X0))
| ( ( ~ in(X2,topstr_closure(X0,X1))
| ! [X4] :
( ~ element(X4,powerset(the_carrier(X0)))
| ~ subset(X1,X4)
| ~ closed_subset(X4,X0)
| in(X2,X4) ) )
& ( ( element(sK131(X0,X1,X2),powerset(the_carrier(X0)))
& subset(X1,sK131(X0,X1,X2))
& closed_subset(sK131(X0,X1,X2),X0)
& ~ in(X2,sK131(X0,X1,X2)) )
| in(X2,topstr_closure(X0,X1)) ) ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK131]),skolemize(X3,sK131(X0,X1,X2))],[f1262]) ).
fof(f1266,plain,
( top_str(sK132)
& element(sK133,powerset(the_carrier(sK132)))
& ~ subset(sK133,topstr_closure(sK132,sK133)) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK132,sK133]),skolemize(X0,sK132),skolemize(X1,sK133)],[f754]) ).
fof(f1351,plain,
! [X0,X1] :
( ( ~ element(X0,powerset(X1))
| subset(X0,X1) )
& ( ~ subset(X0,X1)
| element(X0,powerset(X1)) ) ),
inference(nnf_transformation,[],[f443]) ).
fof(f1352,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,[],[f846]) ).
fof(f1353,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,[],[f1352]) ).
fof(f1354,plain,
! [X0,X1] :
( ( ~ subset(X0,X1)
| ! [X3] :
( ~ in(X3,X0)
| in(X3,X1) ) )
& ( ( in(sK188(X0,X1),X0)
& ~ in(sK188(X0,X1),X1) )
| subset(X0,X1) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK188]),skolemize(X2,sK188(X0,X1))],[f1353]) ).
fof(f1939,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| subset(X1,sK131(X0,X1,X2))
| in(X2,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f1263]) ).
fof(f1941,plain,
! [X2,X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ in(X2,the_carrier(X0))
| ~ in(X2,sK131(X0,X1,X2))
| in(X2,topstr_closure(X0,X1)) ),
inference(cnf_transformation,[],[f1263]) ).
fof(f1952,plain,
top_str(sK132),
inference(cnf_transformation,[],[f1266]) ).
fof(f1953,plain,
element(sK133,powerset(the_carrier(sK132))),
inference(cnf_transformation,[],[f1266]) ).
fof(f1954,plain,
~ subset(sK133,topstr_closure(sK132,sK133)),
inference(cnf_transformation,[],[f1266]) ).
fof(f2161,plain,
! [X0,X1] :
( ~ element(X0,powerset(X1))
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1351]) ).
fof(f2164,plain,
! [X3,X0,X1] :
( ~ subset(X0,X1)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[],[f1354]) ).
fof(f2165,plain,
! [X0,X1] :
( in(sK188(X0,X1),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1354]) ).
fof(f2166,plain,
! [X0,X1] :
( ~ in(sK188(X0,X1),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[],[f1354]) ).
tcf(c_409,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,topstr_closure(X1,X2))
| ~ top_str(X1)
| ~ in(X0,the_carrier(X1))
| ~ element(X2,powerset(the_carrier(X1)))
| ~ in(X0,sK131(X1,X2,X0)) ),
inference(cnf_transformation,[],[f1941]) ).
tcf(c_411,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X1,X0))
| subset(X0,sK131(X1,X0,X2))
| ~ top_str(X1)
| ~ in(X2,the_carrier(X1))
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f1939]) ).
tcf(c_424,negated_conjecture,
~ subset(sK133,topstr_closure(sK132,sK133)),
inference(cnf_transformation,[],[f1954]) ).
tcf(c_425,negated_conjecture,
element(sK133,powerset(the_carrier(sK132))),
inference(cnf_transformation,[],[f1953]) ).
tcf(c_426,negated_conjecture,
top_str(sK132),
inference(cnf_transformation,[],[f1952]) ).
tcf(c_629,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f2161]) ).
tcf(c_631,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| ~ in(sK188(X0,X1),X1) ),
inference(cnf_transformation,[],[f2166]) ).
tcf(c_632,plain,
! [X0: $i,X1: $i] :
( subset(X0,X1)
| in(sK188(X0,X1),X0) ),
inference(cnf_transformation,[],[f2165]) ).
tcf(c_633,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X0,X2)
| ~ subset(X1,X2)
| ~ in(X0,X1) ),
inference(cnf_transformation,[],[f2164]) ).
tcf(c_21634,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X2,topstr_closure(X0,X1))
| subset(X1,sK131(X0,X1,X2))
| ~ in(X2,the_carrier(X0))
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK132 ) ),
inference(resolution_lifted,[status(thm)],[c_411,c_426]) ).
tcf(c_21635,plain,
! [X0: $i,X1: $i] :
( in(X1,topstr_closure(sK132,X0))
| subset(X0,sK131(sK132,X0,X1))
| ~ in(X1,the_carrier(sK132))
| ~ element(X0,powerset(the_carrier(sK132))) ),
inference(unflattening,[status(thm)],[c_21634]) ).
tcf(c_21664,plain,
! [X0: $i,X1: $i,X2: $i] :
( in(X1,topstr_closure(X0,X2))
| ~ in(X1,the_carrier(X0))
| ~ element(X2,powerset(the_carrier(X0)))
| ~ in(X1,sK131(X0,X2,X1))
| ( X0 != sK132 ) ),
inference(resolution_lifted,[status(thm)],[c_409,c_426]) ).
tcf(c_21665,plain,
! [X0: $i,X1: $i] :
( in(X0,topstr_closure(sK132,X1))
| ~ in(X0,the_carrier(sK132))
| ~ element(X1,powerset(the_carrier(sK132)))
| ~ in(X0,sK131(sK132,X1,X0)) ),
inference(unflattening,[status(thm)],[c_21664]) ).
tcf(c_140882,plain,
subset(sK133,the_carrier(sK132)),
inference(superposition,[status(thm)],[c_425,c_629]) ).
tcf(c_145551,plain,
( subset(sK133,topstr_closure(sK132,sK133))
| ~ in(sK188(sK133,topstr_closure(sK132,sK133)),topstr_closure(sK132,sK133)) ),
inference(instantiation,[status(thm)],[c_631]) ).
tcf(c_145554,plain,
( subset(sK133,topstr_closure(sK132,sK133))
| in(sK188(sK133,topstr_closure(sK132,sK133)),sK133) ),
inference(instantiation,[status(thm)],[c_632]) ).
tcf(c_157630,plain,
! [X0: $i] :
( in(sK188(sK133,topstr_closure(sK132,sK133)),X0)
| ~ subset(sK133,X0)
| ~ in(sK188(sK133,topstr_closure(sK132,sK133)),sK133) ),
inference(instantiation,[status(thm)],[c_633]) ).
tcf(c_190230,plain,
( in(sK188(sK133,topstr_closure(sK132,sK133)),topstr_closure(sK132,sK133))
| subset(sK133,sK131(sK132,sK133,sK188(sK133,topstr_closure(sK132,sK133))))
| ~ element(sK133,powerset(the_carrier(sK132)))
| ~ in(sK188(sK133,topstr_closure(sK132,sK133)),the_carrier(sK132)) ),
inference(instantiation,[status(thm)],[c_21635]) ).
tcf(c_190267,plain,
( in(sK188(sK133,topstr_closure(sK132,sK133)),topstr_closure(sK132,sK133))
| ~ element(sK133,powerset(the_carrier(sK132)))
| ~ in(sK188(sK133,topstr_closure(sK132,sK133)),the_carrier(sK132))
| ~ in(sK188(sK133,topstr_closure(sK132,sK133)),sK131(sK132,sK133,sK188(sK133,topstr_closure(sK132,sK133)))) ),
inference(instantiation,[status(thm)],[c_21665]) ).
tcf(c_191332,plain,
( in(sK188(sK133,topstr_closure(sK132,sK133)),the_carrier(sK132))
| ~ subset(sK133,the_carrier(sK132))
| ~ in(sK188(sK133,topstr_closure(sK132,sK133)),sK133) ),
inference(instantiation,[status(thm)],[c_157630]) ).
tcf(c_191751,plain,
( in(sK188(sK133,topstr_closure(sK132,sK133)),sK131(sK132,sK133,sK188(sK133,topstr_closure(sK132,sK133))))
| ~ in(sK188(sK133,topstr_closure(sK132,sK133)),sK133)
| ~ subset(sK133,sK131(sK132,sK133,sK188(sK133,topstr_closure(sK132,sK133)))) ),
inference(instantiation,[status(thm)],[c_157630]) ).
tcf(c_191753,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_191751,c_191332,c_190267,c_190230,c_145554,c_145551,c_140882,c_424,c_425]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU317+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.07 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/10.45 % Computer : n020.cluster.edu
% 0.17/10.45 % Model : x86_64 x86_64
% 0.17/10.45 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/10.45 % Memory : 8046.5625MB
% 0.17/10.45 % OS : Linux 6.8.0-71-generic
% 0.17/10.45 % CPULimit : 300
% 0.17/10.45 % WCLimit : 300
% 0.17/10.45 % DateTime : Thu Sep 24 13:41:30 UTC 2026
% 0.17/10.45 % CPUTime :
% 0.17/10.45 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.22/10.51 Running first-order theorem proving
% 0.22/10.51 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
% 0.22/10.53
% 0.22/10.53 % ======== iProver multi-core TPTP/SMT =========
% 0.22/10.53
% 0.22/10.53 % Detected problem language: tptp
% 0.22/10.55 % Proving...
% 97.26/25.75 % SZS status Started for theBenchmark.p
% 97.26/25.75 % SZS status Theorem for theBenchmark.p
% 97.26/25.75
% 97.26/25.75 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 97.26/25.75
% 97.26/25.75 % ------ iProver source info
% 97.26/25.75
% 97.26/25.75 % git: date: 2026-07-19 20:42:38 +0200
% 97.26/25.75 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 97.26/25.75 % git: non_committed_changes: false
% 97.26/25.75
% 97.26/25.75 % ------ Parsing...
% 97.26/25.75 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 97.26/25.75
% 97.26/25.75 % ------ Preprocessing... sup_sim: 96 sf_s rm: 76 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e sup_sim: 28 sf_s rm: 19 0s sf_e pe_s pe_e sup_sim: 0 sf_s rm: 19 0s sf_e pe_s pe_e %
% 97.26/25.75
% 97.26/25.75 % ------ Preprocessing... gs_s sp: 15 0s gs_e snvd_s sp: 0 0s snvd_e %
% 97.26/25.75
% 97.26/25.75 % ------ Preprocessing... sf_s rm: 3 0s sf_e sf_s rm: 0 0s sf_e
% 97.26/25.75 % ------ Proving...
% 97.26/25.75 % ------ Problem Properties
% 97.26/25.75
% 97.26/25.75 %
% 97.26/25.75 % clauses 1079
% 97.26/25.75 % conjectures 2
% 97.26/25.75 % EPR 163
% 97.26/25.75 % Horn 808
% 97.26/25.75 % unary 133
% 97.26/25.75 % binary 343
% 97.26/25.75 % lits 3223
% 97.26/25.75 % lits eq 481
% 97.26/25.75 % fd_pure 0
% 97.26/25.75 % fd_pseudo 0
% 97.26/25.75 % fd_cond 41
% 97.26/25.75 % fd_pseudo_cond 108
% 97.26/25.75 % AC symbols 0
% 97.26/25.75
% 97.26/25.75 % ------ Schedule dynamic 5 is on
% 97.26/25.75
% 97.26/25.75 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 97.26/25.75
% 97.26/25.75
% 97.26/25.75 % ------
% 97.26/25.75 % Current options:
% 97.26/25.75 % ------
% 97.26/25.75
% 97.26/25.75
% 97.26/25.75 %
% 97.26/25.75
% 97.26/25.75 % ------ Proving...
% 97.26/25.75 %
% 97.26/25.75
% 97.26/25.75 % SZS status Theorem for theBenchmark.p
% 97.26/25.75
% 97.26/25.75 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 97.26/25.75
% 97.26/25.75
%------------------------------------------------------------------------------