%------------------------------------------------------------------------------
% File : iProver---3.9.4
% Problem : SEU319+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 : n018.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 2.00s 1.29s
% Output : CNFRefutation 2.00s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 6
% Syntax : Number of formulae : 60 ( 13 unt; 2 def)
% Number of atoms : 181 ( 19 equ)
% Maximal formula atoms : 6 ( 3 avg)
% Number of connectives : 177 ( 77 ~; 74 |; 12 &)
% ( 4 <=>; 9 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 2 avg)
% Number of types : 1 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of predicates : 12 ( 10 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 2 con; 0-3 aty)
% Number of variables : 50 ( 0 sgn 44 !; 6 ?; 21 :)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> ( closed_subset(X1,X0)
<=> open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',d6_pre_topc) ).
fof(f7,axiom,
! [X0] :
( top_str(X0)
=> one_sorted_str(X0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',dt_l1_pre_topc) ).
fof(f17,axiom,
! [X0] :
( one_sorted_str(X0)
=> ! [X1] :
( element(X1,powerset(the_carrier(X0)))
=> subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',t17_pre_topc) ).
fof(f18,conjecture,
! [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(f19,negated_conjecture,
~ ! [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(negated_conjecture,[status(cth)],[f18]) ).
fof(f23,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( closed_subset(X1,X0)
<=> open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) ) ) ),
inference(ennf_transformation,[],[f1]) ).
fof(f28,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(ennf_transformation,[],[f7]) ).
fof(f32,plain,
! [X0] :
( ~ one_sorted_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| subset_complement(the_carrier(X0),X1) = subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) ) ),
inference(ennf_transformation,[],[f17]) ).
fof(f33,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,[],[f19]) ).
fof(f35,plain,
! [X0] :
( ~ top_str(X0)
| ! [X1] :
( ~ element(X1,powerset(the_carrier(X0)))
| ( ( ~ closed_subset(X1,X0)
| open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) )
& ( ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| closed_subset(X1,X0) ) ) ) ),
inference(nnf_transformation,[],[f23]) ).
fof(f39,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) )
& ( ~ closed_subset(X1,X0)
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(nnf_transformation,[],[f33]) ).
fof(f40,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) )
& ( ~ closed_subset(X1,X0)
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0) ) ) ),
inference(flattening,[],[f39]) ).
fof(f41,plain,
( top_str(sK3)
& element(sK4,powerset(the_carrier(sK3)))
& ( closed_subset(sK4,sK3)
| open_subset(subset_complement(the_carrier(sK3),sK4),sK3) )
& ( ~ closed_subset(sK4,sK3)
| ~ open_subset(subset_complement(the_carrier(sK3),sK4),sK3) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3,sK4]),skolemize(X0,sK3),skolemize(X1,sK4)],[f40]) ).
fof(f42,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f43,plain,
! [X0,X1] :
( ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| closed_subset(X1,X0) ),
inference(cnf_transformation,[],[f35]) ).
fof(f47,plain,
! [X0] :
( ~ top_str(X0)
| one_sorted_str(X0) ),
inference(cnf_transformation,[],[f28]) ).
fof(f54,plain,
! [X0,X1] :
( ~ one_sorted_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1) ),
inference(cnf_transformation,[],[f32]) ).
fof(f55,plain,
top_str(sK3),
inference(cnf_transformation,[],[f41]) ).
fof(f56,plain,
element(sK4,powerset(the_carrier(sK3))),
inference(cnf_transformation,[],[f41]) ).
fof(f57,plain,
( closed_subset(sK4,sK3)
| open_subset(subset_complement(the_carrier(sK3),sK4),sK3) ),
inference(cnf_transformation,[],[f41]) ).
fof(f58,plain,
( ~ closed_subset(sK4,sK3)
| ~ open_subset(subset_complement(the_carrier(sK3),sK4),sK3) ),
inference(cnf_transformation,[],[f41]) ).
tcf(c_49,plain,
! [X0: $i,X1: $i] :
( closed_subset(X1,X0)
| ~ top_str(X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0) ),
inference(cnf_transformation,[],[f43]) ).
tcf(c_50,plain,
! [X0: $i,X1: $i] :
( open_subset(subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X0),X1)
| ~ top_str(X1)
| ~ closed_subset(X0,X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f42]) ).
tcf(c_54,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f47]) ).
tcf(c_61,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X1),cast_as_carrier_subset(X1),X0) = subset_complement(the_carrier(X1),X0) )
| ~ one_sorted_str(X1)
| ~ element(X0,powerset(the_carrier(X1))) ),
inference(cnf_transformation,[],[f54]) ).
tcf(c_62,negated_conjecture,
( ~ closed_subset(sK4,sK3)
| ~ open_subset(subset_complement(the_carrier(sK3),sK4),sK3) ),
inference(cnf_transformation,[],[f58]) ).
tcf(c_63,negated_conjecture,
( closed_subset(sK4,sK3)
| open_subset(subset_complement(the_carrier(sK3),sK4),sK3) ),
inference(cnf_transformation,[],[f57]) ).
tcf(c_64,negated_conjecture,
element(sK4,powerset(the_carrier(sK3))),
inference(cnf_transformation,[],[f56]) ).
tcf(c_65,negated_conjecture,
top_str(sK3),
inference(cnf_transformation,[],[f55]) ).
tcf(c_79,plain,
( ~ open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| ~ closed_subset(sK4,sK3) ),
inference(prop_impl_just,[status(thm)],[c_62]) ).
tcf(c_80,plain,
( ~ closed_subset(sK4,sK3)
| ~ open_subset(subset_complement(the_carrier(sK3),sK4),sK3) ),
inference(renaming,[status(thm)],[c_79]) ).
tcf(c_81,plain,
( open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| closed_subset(sK4,sK3) ),
inference(prop_impl_just,[status(thm)],[c_63]) ).
tcf(c_82,plain,
( closed_subset(sK4,sK3)
| open_subset(subset_complement(the_carrier(sK3),sK4),sK3) ),
inference(renaming,[status(thm)],[c_81]) ).
tcf(c_83,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ~ top_str(X0) ),
inference(prop_impl_just,[status(thm)],[c_54]) ).
tcf(c_344,plain,
! [X0: $i,X1: $i] :
( open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_50,c_65]) ).
tcf(c_345,plain,
! [X0: $i] :
( open_subset(subset_difference(the_carrier(sK3),cast_as_carrier_subset(sK3),X0),sK3)
| ~ closed_subset(X0,sK3)
| ~ element(X0,powerset(the_carrier(sK3))) ),
inference(unflattening,[status(thm)],[c_344]) ).
tcf(c_373,plain,
! [X0: $i] :
( one_sorted_str(X0)
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_83,c_65]) ).
tcf(c_374,plain,
one_sorted_str(sK3),
inference(unflattening,[status(thm)],[c_373]) ).
tcf(c_378,plain,
! [X0: $i,X1: $i] :
( closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ open_subset(subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1),X0)
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_49,c_65]) ).
tcf(c_379,plain,
! [X0: $i] :
( closed_subset(X0,sK3)
| ~ element(X0,powerset(the_carrier(sK3)))
| ~ open_subset(subset_difference(the_carrier(sK3),cast_as_carrier_subset(sK3),X0),sK3) ),
inference(unflattening,[status(thm)],[c_378]) ).
tcf(c_412,plain,
! [X0: $i,X1: $i] :
( ( subset_difference(the_carrier(X0),cast_as_carrier_subset(X0),X1) = subset_complement(the_carrier(X0),X1) )
| ~ element(X1,powerset(the_carrier(X0)))
| ( X0 != sK3 ) ),
inference(resolution_lifted,[status(thm)],[c_61,c_374]) ).
tcf(c_413,plain,
! [X0: $i] :
( ( subset_difference(the_carrier(sK3),cast_as_carrier_subset(sK3),X0) = subset_complement(the_carrier(sK3),X0) )
| ~ element(X0,powerset(the_carrier(sK3))) ),
inference(unflattening,[status(thm)],[c_412]) ).
tcf(c_487,plain,
! [X0: $i] :
( open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| open_subset(subset_difference(the_carrier(sK3),cast_as_carrier_subset(sK3),X0),sK3)
| ~ element(X0,powerset(the_carrier(sK3)))
| ( sK3 != sK3 )
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_82,c_345]) ).
tcf(c_488,plain,
( open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| open_subset(subset_difference(the_carrier(sK3),cast_as_carrier_subset(sK3),sK4),sK3)
| ~ element(sK4,powerset(the_carrier(sK3))) ),
inference(unflattening,[status(thm)],[c_487]) ).
tcf(c_489,plain,
( open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| open_subset(subset_difference(the_carrier(sK3),cast_as_carrier_subset(sK3),sK4),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_488,c_64,c_488]) ).
tcf(c_497,plain,
! [X0: $i] :
( ~ element(X0,powerset(the_carrier(sK3)))
| ~ open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| ~ open_subset(subset_difference(the_carrier(sK3),cast_as_carrier_subset(sK3),X0),sK3)
| ( sK3 != sK3 )
| ( X0 != sK4 ) ),
inference(resolution_lifted,[status(thm)],[c_80,c_379]) ).
tcf(c_498,plain,
( ~ element(sK4,powerset(the_carrier(sK3)))
| ~ open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| ~ open_subset(subset_difference(the_carrier(sK3),cast_as_carrier_subset(sK3),sK4),sK3) ),
inference(unflattening,[status(thm)],[c_497]) ).
tcf(c_499,plain,
( ~ open_subset(subset_difference(the_carrier(sK3),cast_as_carrier_subset(sK3),sK4),sK3)
| ~ open_subset(subset_complement(the_carrier(sK3),sK4),sK3) ),
inference(global_subsumption_just,[status(thm)],[c_498,c_64,c_498]) ).
tcf(c_500,plain,
( ~ open_subset(subset_complement(the_carrier(sK3),sK4),sK3)
| ~ open_subset(subset_difference(the_carrier(sK3),cast_as_carrier_subset(sK3),sK4),sK3) ),
inference(renaming,[status(thm)],[c_499]) ).
tcf(c_571,definition,
iPr_def_16 = subset_difference(iPr_def_10,iPr_def_11,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_16])],[]) ).
tcf(c_572,definition,
iPr_def_17 = subset_complement(iPr_def_10,sK4),
introduced(definition,[new_symbols(definition,[iPr_def_17])],[]) ).
tcf(c_575,plain,
( ~ open_subset(iPr_def_17,sK3)
| ~ open_subset(iPr_def_16,sK3) ),
inference(demodulation,[status(thm)],[c_500,c_572,c_571]) ).
tcf(c_576,plain,
( open_subset(iPr_def_17,sK3)
| open_subset(iPr_def_16,sK3) ),
inference(demodulation,[status(thm)],[c_489]) ).
tcf(c_578,plain,
! [X0: $i] :
( ( subset_difference(iPr_def_10,iPr_def_11,X0) = subset_complement(iPr_def_10,X0) )
| ~ element(X0,iPr_def_14) ),
inference(demodulation,[status(thm)],[c_413]) ).
tcf(c_579,negated_conjecture,
element(sK4,iPr_def_14),
inference(demodulation,[status(thm)],[c_64]) ).
tcf(c_1110,plain,
subset_difference(iPr_def_10,iPr_def_11,sK4) = subset_complement(iPr_def_10,sK4),
inference(superposition,[status(thm)],[c_579,c_578]) ).
tcf(c_1111,plain,
iPr_def_16 = iPr_def_17,
inference(light_normalisation,[status(thm)],[c_1110,c_571,c_572]) ).
tcf(c_1112,plain,
~ open_subset(iPr_def_16,sK3),
inference(demodulation,[status(thm)],[c_575,c_1111]) ).
tcf(c_1113,plain,
open_subset(iPr_def_16,sK3),
inference(demodulation,[status(thm)],[c_576,c_1111]) ).
tcf(c_1114,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_1112,c_1113]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU319+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.38 % Computer : n018.cluster.edu
% 0.10/0.38 % Model : x86_64 x86_64
% 0.10/0.38 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.38 % Memory : 8046.5625MB
% 0.10/0.38 % OS : Linux 6.8.0-71-generic
% 0.10/0.38 % CPULimit : 300
% 0.10/0.38 % WCLimit : 300
% 0.10/0.38 % DateTime : Thu Sep 24 13:42:49 UTC 2026
% 0.10/0.38 % CPUTime :
% 0.10/0.38 Running run_iprover 300 /export/starexec/sandbox2/benchmark/theBenchmark.p THM
% 0.10/0.42 Running first-order theorem proving
% 0.10/0.42 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
% 0.10/0.43
% 0.10/0.43 % ======== iProver multi-core TPTP/SMT =========
% 0.10/0.43
% 0.10/0.43 % Detected problem language: tptp
% 0.10/0.44 % Proving...
% 2.00/1.29 % SZS status Started for theBenchmark.p
% 2.00/1.29 % SZS status Theorem for theBenchmark.p
% 2.00/1.29
% 2.00/1.29 %---------------- iProver v3.9.4 (pre CASC 2026/SMT-COMP 2026) ----------------%
% 2.00/1.29
% 2.00/1.29 % ------ iProver source info
% 2.00/1.29
% 2.00/1.29 % git: date: 2026-07-19 20:42:38 +0200
% 2.00/1.29 % git: sha1: 804e7d636a263075307957e923b7a22a4035de61
% 2.00/1.29 % git: non_committed_changes: false
% 2.00/1.29
% 2.00/1.29 % ------ Parsing...
% 2.00/1.29 % ------ Clausification by vclausify_rel & Parsing by iProver...%
% 2.00/1.29
% 2.00/1.29 % ------ Preprocessing... sup_sim: 0 sf_s rm: 1 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe_e %
% 2.00/1.29
% 2.00/1.29 % ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e %
% 2.00/1.29
% 2.00/1.29 % ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 2.00/1.29 % ------ Proving...
% 2.00/1.29 % ------ Problem Properties
% 2.00/1.29
% 2.00/1.29 %
% 2.00/1.29 % clauses 27
% 2.00/1.29 % conjectures 1
% 2.00/1.29 % EPR 4
% 2.00/1.29 % Horn 25
% 2.00/1.29 % unary 14
% 2.00/1.29 % binary 7
% 2.00/1.29 % lits 52
% 2.00/1.29 % lits eq 17
% 2.00/1.29 % fd_pure 0
% 2.00/1.29 % fd_pseudo 0
% 2.00/1.29 % fd_cond 0
% 2.00/1.29 % fd_pseudo_cond 0
% 2.00/1.29 % AC symbols 0
% 2.00/1.29
% 2.00/1.29 % ------ Schedule dynamic 5 is on
% 2.00/1.29
% 2.00/1.29 % ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 2.00/1.29
% 2.00/1.29
% 2.00/1.29 % ------
% 2.00/1.29 % Current options:
% 2.00/1.29 % ------
% 2.00/1.29
% 2.00/1.29
% 2.00/1.29 %
% 2.00/1.29
% 2.00/1.29 % ------ Proving...
% 2.00/1.29 %
% 2.00/1.29
% 2.00/1.29 % SZS status Theorem for theBenchmark.p
% 2.00/1.29
% 2.00/1.29 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 2.00/1.29
% 2.00/1.29
%------------------------------------------------------------------------------