%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU320+1 : 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 : n016.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 02:56:50 PM UTC 2026
% Result : Theorem 0.31s 6.09s
% Output : CNFRefutation 0.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 58 ( 14 unt; 3 def)
% Number of atoms : 184 ( 16 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 165 ( 71 ~; 69 |; 12 &)
% ( 4 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 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 : 10 ( 8 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 49 ( 0 sgn 43 !; 6 ?; 17 :)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> element(subset_complement(X0,X1),powerset(X0)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_k3_subset_1) ).
fof(f10,axiom,
! [X0,X1] :
( element(X1,powerset(X0))
=> subset_complement(X0,subset_complement(X0,X1)) = X1 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',involutiveness_k3_subset_1) ).
fof(f12,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t29_tops_1) ).
fof(f13,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( open_subset(X1,X0)
<=> closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t30_tops_1) ).
fof(f14,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( open_subset(X1,X0)
<=> closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(negated_conjecture,[status(cth)],[f13]) ).
fof(f20,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(ennf_transformation,[],[f10]) ).
fof(f22,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(ennf_transformation,[],[f12]) ).
fof(f23,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ( open_subset(X1,X0)
<~> closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(ennf_transformation,[],[f14]) ).
fof(f27,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( ( ~ closed_subset(X1,X0)
| open_subset(subset_complement(the_carrier(X0),X1),X0) )
& ( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f22]) ).
fof(f28,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ( open_subset(X1,X0)
| closed_subset(subset_complement(the_carrier(X0),X1),X0) )
& ( ~ open_subset(X1,X0)
| ~ closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f29,plain,
? [X0] :
( top_str(X0)
& ? [X1] :
( element(X1,powerset(the_carrier(X0)))
& ( open_subset(X1,X0)
| closed_subset(subset_complement(the_carrier(X0),X1),X0) )
& ( ~ open_subset(X1,X0)
| ~ closed_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(flattening,[],[f28]) ).
fof(f30,plain,
( top_str(sK2)
& element(sK3,powerset(the_carrier(sK2)))
& ( open_subset(sK3,sK2)
| closed_subset(subset_complement(the_carrier(sK2),sK3),sK2) )
& ( ~ open_subset(sK3,sK2)
| ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2,sK3]),skolemize(X0,sK2),skolemize(X1,sK3)],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| element(subset_complement(X0,X1),powerset(X0)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f34,plain,
! [X0,X1] :
( ~ element(X1,powerset(X0))
| subset_complement(X0,subset_complement(X0,X1)) = X1 ),
inference(cnf_transformation,[],[f21]) ).
fof(f36,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f37,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| closed_subset(X1,X0) ),
inference(cnf_transformation,[],[f27]) ).
fof(f38,plain,
top_str(sK2),
inference(cnf_transformation,[],[f30]) ).
fof(f39,plain,
element(sK3,powerset(the_carrier(sK2))),
inference(cnf_transformation,[],[f30]) ).
fof(f40,plain,
( open_subset(sK3,sK2)
| closed_subset(subset_complement(the_carrier(sK2),sK3),sK2) ),
inference(cnf_transformation,[],[f30]) ).
fof(f41,plain,
( ~ open_subset(sK3,sK2)
| ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2) ),
inference(cnf_transformation,[],[f30]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( element(subset_complement(X1,X0),powerset(X1))
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f31]) ).
tcf(c_52,plain,
! [X0: $i,X1: $i] :
( ( subset_complement(X1,subset_complement(X1,X0)) = X0 )
| ~ element(X0,powerset(X1)) ),
inference(cnf_transformation,[],[f34]) ).
tcf(c_54,plain,
! [X0: $i,X1: $i] :
( closed_subset(X1,X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(cnf_transformation,[],[f37]) ).
tcf(c_55,plain,
! [X0: $i,X1: $i] :
( open_subset(subset_complement(the_carrier(X1),X0),X1)
| ~ top_str(X1)
| ~ closed_subset(X0,X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f36]) ).
tcf(c_56,negated_conjecture,
( ~ open_subset(sK3,sK2)
| ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_57,negated_conjecture,
( open_subset(sK3,sK2)
| closed_subset(subset_complement(the_carrier(sK2),sK3),sK2) ),
inference(cnf_transformation,[],[f40]) ).
tcf(c_58,negated_conjecture,
element(sK3,powerset(the_carrier(sK2))),
inference(cnf_transformation,[],[f39]) ).
tcf(c_59,negated_conjecture,
top_str(sK2),
inference(cnf_transformation,[],[f38]) ).
tcf(c_68,plain,
( ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| ~ open_subset(sK3,sK2) ),
inference(prop_impl_just,[status(thm)],[c_56]) ).
tcf(c_69,plain,
( ~ open_subset(sK3,sK2)
| ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2) ),
inference(renaming,[status(thm)],[c_68]) ).
tcf(c_70,plain,
( closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| open_subset(sK3,sK2) ),
inference(prop_impl_just,[status(thm)],[c_57]) ).
tcf(c_71,plain,
( open_subset(sK3,sK2)
| closed_subset(subset_complement(the_carrier(sK2),sK3),sK2) ),
inference(renaming,[status(thm)],[c_70]) ).
tcf(c_229,plain,
! [X0: $i,X1: $i] :
( closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_54,c_59]) ).
tcf(c_230,plain,
! [X0: $i] :
( closed_subset(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ open_subset(subset_complement(the_carrier(sK2),X0),sK2) ),
inference(unflattening,[status(thm)],[c_229]) ).
tcf(c_241,plain,
! [X0: $i,X1: $i] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK2 ) ),
inference(resolution_lifted,[status(thm)],[c_55,c_59]) ).
tcf(c_242,plain,
! [X0: $i] :
( open_subset(subset_complement(the_carrier(sK2),X0),sK2)
| ~ closed_subset(X0,sK2)
| ~ element(X0,powerset(the_carrier(sK2))) ),
inference(unflattening,[status(thm)],[c_241]) ).
tcf(c_298,plain,
! [X0: $i] :
( open_subset(sK3,sK2)
| open_subset(subset_complement(the_carrier(sK2),X0),sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ( sK2 != sK2 )
| ( subset_complement(the_carrier(sK2),sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_71,c_242]) ).
tcf(c_299,plain,
( open_subset(sK3,sK2)
| open_subset(subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK3)),sK2)
| ~ element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2))) ),
inference(unflattening,[status(thm)],[c_298]) ).
tcf(c_309,plain,
! [X0: $i] :
( ~ open_subset(sK3,sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ open_subset(subset_complement(the_carrier(sK2),X0),sK2)
| ( sK2 != sK2 )
| ( subset_complement(the_carrier(sK2),sK3) != X0 ) ),
inference(resolution_lifted,[status(thm)],[c_69,c_230]) ).
tcf(c_310,plain,
( ~ open_subset(sK3,sK2)
| ~ element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2)))
| ~ open_subset(subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK3)),sK2) ),
inference(unflattening,[status(thm)],[c_309]) ).
tcf(c_507,definition,
iPr_def_13 = powerset(iPr_def_10),
introduced(definition,[new_symbols(definition,[iPr_def_13])],[]) ).
tcf(c_508,definition,
iPr_def_14 = subset_complement(iPr_def_10,sK3),
introduced(definition,[new_symbols(definition,[iPr_def_14])],[]) ).
tcf(c_509,definition,
iPr_def_15 = subset_complement(iPr_def_10,iPr_def_14),
introduced(definition,[new_symbols(definition,[iPr_def_15])],[]) ).
tcf(c_512,plain,
( ~ open_subset(iPr_def_15,sK2)
| ~ open_subset(sK3,sK2)
| ~ element(iPr_def_14,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_310,c_508,c_509]) ).
tcf(c_513,plain,
( open_subset(iPr_def_15,sK2)
| open_subset(sK3,sK2)
| ~ element(iPr_def_14,iPr_def_13) ),
inference(demodulation,[status(thm)],[c_299]) ).
tcf(c_514,negated_conjecture,
element(sK3,iPr_def_13),
inference(demodulation,[status(thm)],[c_58]) ).
tcf(c_791,plain,
( element(iPr_def_14,powerset(iPr_def_10))
| ~ element(sK3,powerset(iPr_def_10)) ),
inference(superposition,[status(thm)],[c_508,c_49]) ).
tcf(c_798,plain,
( element(iPr_def_14,iPr_def_13)
| ~ element(sK3,iPr_def_13) ),
inference(light_normalisation,[status(thm)],[c_791,c_507]) ).
tcf(c_799,plain,
element(iPr_def_14,iPr_def_13),
inference(forward_subsumption_resolution,[status(thm)],[c_798,c_514]) ).
tcf(c_807,plain,
( open_subset(iPr_def_15,sK2)
| open_subset(sK3,sK2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_513,c_799]) ).
tcf(c_808,plain,
( ~ open_subset(iPr_def_15,sK2)
| ~ open_subset(sK3,sK2) ),
inference(backward_subsumption_resolution,[status(thm)],[c_512,c_799]) ).
tcf(c_842,plain,
! [X0: $i] :
( ( subset_complement(iPr_def_10,subset_complement(iPr_def_10,X0)) = X0 )
| ~ element(X0,iPr_def_13) ),
inference(superposition,[status(thm)],[c_507,c_52]) ).
tcf(c_886,plain,
subset_complement(iPr_def_10,subset_complement(iPr_def_10,sK3)) = sK3,
inference(superposition,[status(thm)],[c_514,c_842]) ).
tcf(c_890,plain,
sK3 = iPr_def_15,
inference(light_normalisation,[status(thm)],[c_886,c_508,c_509]) ).
tcf(c_894,plain,
~ open_subset(iPr_def_15,sK2),
inference(demodulation,[status(thm)],[c_808,c_890]) ).
tcf(c_895,plain,
open_subset(iPr_def_15,sK2),
inference(demodulation,[status(thm)],[c_807,c_890]) ).
tcf(c_898,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_894,c_895]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU320+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/5.38 % Computer : n016.cluster.edu
% 0.10/5.38 % Model : x86_64 x86_64
% 0.10/5.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/5.38 % Memory : 8046.5625MB
% 0.10/5.38 % OS : Linux 6.8.0-71-generic
% 0.10/5.38 % CPULimit : 300
% 0.10/5.38 % WCLimit : 300
% 0.10/5.38 % DateTime : Thu Sep 24 13:46:18 UTC 2026
% 0.10/5.39 % CPUTime :
% 0.10/5.39 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.17/5.43 Running first-order theorem proving
% 0.17/5.43 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
% 0.17/5.44
% 0.17/5.44 % ======== iProver multi-core TPTP/SMT =========
% 0.17/5.44
% 0.17/5.44 % Detected problem language: tptp
% 0.17/5.45 % Proving...
% 0.31/6.09 % SZS status Started for theBenchmark.p
% 0.31/6.09 % SZS status Theorem for theBenchmark.p
% 0.31/6.09
% 0.31/6.09 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 0.31/6.09
% 0.31/6.09 % ------ iProver source info
% 0.31/6.09
% 0.31/6.09 % git: date: 2026-07-19 20:42:38 +0200
% 0.31/6.09 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 0.31/6.09 % git: non_committed_changes: false
% 0.31/6.09
% 0.31/6.09 % ------ Parsing...
% 0.31/6.09 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 0.31/6.09
% 0.31/6.09 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe_e sup_sim: 0 sf_s rm: 3 0s sf_e pe_s pe_e %
% 0.31/6.09
% 0.31/6.09 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 0.31/6.09
% 0.31/6.09 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 0.31/6.09 % ------ Proving...
% 0.31/6.09 % ------ Problem Properties
% 0.31/6.09
% 0.31/6.09 %
% 0.31/6.09 % clauses 17
% 0.31/6.09 % conjectures 1
% 0.31/6.09 % EPR 3
% 0.31/6.09 % Horn 15
% 0.31/6.09 % unary 9
% 0.31/6.09 % binary 2
% 0.31/6.09 % lits 37
% 0.31/6.09 % lits eq 11
% 0.31/6.09 % fd_pure 0
% 0.31/6.09 % fd_pseudo 0
% 0.31/6.09 % fd_cond 0
% 0.31/6.09 % fd_pseudo_cond 0
% 0.31/6.09 % AC symbols 0
% 0.31/6.09
% 0.31/6.09 % ------ Schedule dynamic 5 is on
% 0.31/6.09
% 0.31/6.09 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 0.31/6.09
% 0.31/6.09
% 0.31/6.09 % ------
% 0.31/6.09 % Current options:
% 0.31/6.09 % ------
% 0.31/6.09
% 0.31/6.09
% 0.31/6.09 %
% 0.31/6.09
% 0.31/6.09 % ------ Proving...
% 0.31/6.09 %
% 0.31/6.09
% 0.31/6.09 % SZS status Theorem for theBenchmark.p
% 0.31/6.09
% 0.31/6.09 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 0.31/6.09
% 0.31/6.09
%------------------------------------------------------------------------------