TSTP Solution File: SEU337+2 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU337+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Thu Aug 31 17:06:15 EDT 2023
% Result : Theorem 17.89s 3.21s
% Output : CNFRefutation 17.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 6
% Syntax : Number of formulae : 37 ( 6 unt; 0 def)
% Number of atoms : 128 ( 5 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 146 ( 55 ~; 54 |; 22 &)
% ( 4 <=>; 10 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 48 ( 0 sgn; 26 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f169,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> element(complements_of_subsets(X0,X1),powerset(powerset(X0))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',dt_k7_setfam_1) ).
fof(f260,axiom,
! [X0,X1] :
( element(X1,powerset(powerset(X0)))
=> complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',involutiveness_k7_setfam_1) ).
fof(f404,axiom,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( closed_subsets(X1,X0)
<=> open_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t16_tops_2) ).
fof(f410,conjecture,
! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( open_subsets(X1,X0)
<=> closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',t17_tops_2) ).
fof(f411,negated_conjecture,
~ ! [X0] :
( top_str(X0)
=> ! [X1] :
( element(X1,powerset(powerset(the_carrier(X0))))
=> ( open_subsets(X1,X0)
<=> closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ) ) ),
inference(negated_conjecture,[],[f410]) ).
fof(f771,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f169]) ).
fof(f857,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(ennf_transformation,[],[f260]) ).
fof(f1027,plain,
! [X0] :
( ! [X1] :
( ( closed_subsets(X1,X0)
<=> open_subsets(complements_of_subsets(the_carrier(X0),X1),X0) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f404]) ).
fof(f1036,plain,
? [X0] :
( ? [X1] :
( ( open_subsets(X1,X0)
<~> closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) )
& element(X1,powerset(powerset(the_carrier(X0)))) )
& top_str(X0) ),
inference(ennf_transformation,[],[f411]) ).
fof(f2121,plain,
! [X0] :
( ! [X1] :
( ( ( closed_subsets(X1,X0)
| ~ open_subsets(complements_of_subsets(the_carrier(X0),X1),X0) )
& ( open_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ closed_subsets(X1,X0) ) )
| ~ element(X1,powerset(powerset(the_carrier(X0)))) )
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f1027]) ).
fof(f2124,plain,
? [X0] :
( ? [X1] :
( ( ~ closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ open_subsets(X1,X0) )
& ( closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| open_subsets(X1,X0) )
& element(X1,powerset(powerset(the_carrier(X0)))) )
& top_str(X0) ),
inference(nnf_transformation,[],[f1036]) ).
fof(f2125,plain,
? [X0] :
( ? [X1] :
( ( ~ closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ open_subsets(X1,X0) )
& ( closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| open_subsets(X1,X0) )
& element(X1,powerset(powerset(the_carrier(X0)))) )
& top_str(X0) ),
inference(flattening,[],[f2124]) ).
fof(f2126,plain,
( ? [X0] :
( ? [X1] :
( ( ~ closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ open_subsets(X1,X0) )
& ( closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| open_subsets(X1,X0) )
& element(X1,powerset(powerset(the_carrier(X0)))) )
& top_str(X0) )
=> ( ? [X1] :
( ( ~ closed_subsets(complements_of_subsets(the_carrier(sK447),X1),sK447)
| ~ open_subsets(X1,sK447) )
& ( closed_subsets(complements_of_subsets(the_carrier(sK447),X1),sK447)
| open_subsets(X1,sK447) )
& element(X1,powerset(powerset(the_carrier(sK447)))) )
& top_str(sK447) ) ),
introduced(choice_axiom,[]) ).
fof(f2127,plain,
( ? [X1] :
( ( ~ closed_subsets(complements_of_subsets(the_carrier(sK447),X1),sK447)
| ~ open_subsets(X1,sK447) )
& ( closed_subsets(complements_of_subsets(the_carrier(sK447),X1),sK447)
| open_subsets(X1,sK447) )
& element(X1,powerset(powerset(the_carrier(sK447)))) )
=> ( ( ~ closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| ~ open_subsets(sK448,sK447) )
& ( closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| open_subsets(sK448,sK447) )
& element(sK448,powerset(powerset(the_carrier(sK447)))) ) ),
introduced(choice_axiom,[]) ).
fof(f2128,plain,
( ( ~ closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| ~ open_subsets(sK448,sK447) )
& ( closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| open_subsets(sK448,sK447) )
& element(sK448,powerset(powerset(the_carrier(sK447))))
& top_str(sK447) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK447,sK448])],[f2125,f2127,f2126]) ).
fof(f2666,plain,
! [X0,X1] :
( element(complements_of_subsets(X0,X1),powerset(powerset(X0)))
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f771]) ).
fof(f2834,plain,
! [X0,X1] :
( complements_of_subsets(X0,complements_of_subsets(X0,X1)) = X1
| ~ element(X1,powerset(powerset(X0))) ),
inference(cnf_transformation,[],[f857]) ).
fof(f3518,plain,
! [X0,X1] :
( open_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ closed_subsets(X1,X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f2121]) ).
fof(f3519,plain,
! [X0,X1] :
( closed_subsets(X1,X0)
| ~ open_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f2121]) ).
fof(f3527,plain,
top_str(sK447),
inference(cnf_transformation,[],[f2128]) ).
fof(f3528,plain,
element(sK448,powerset(powerset(the_carrier(sK447)))),
inference(cnf_transformation,[],[f2128]) ).
fof(f3529,plain,
( closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| open_subsets(sK448,sK447) ),
inference(cnf_transformation,[],[f2128]) ).
fof(f3530,plain,
( ~ closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| ~ open_subsets(sK448,sK447) ),
inference(cnf_transformation,[],[f2128]) ).
cnf(c_486,plain,
( ~ element(X0,powerset(powerset(X1)))
| element(complements_of_subsets(X1,X0),powerset(powerset(X1))) ),
inference(cnf_transformation,[],[f2666]) ).
cnf(c_654,plain,
( ~ element(X0,powerset(powerset(X1)))
| complements_of_subsets(X1,complements_of_subsets(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f2834]) ).
cnf(c_1338,plain,
( ~ open_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| closed_subsets(X1,X0) ),
inference(cnf_transformation,[],[f3519]) ).
cnf(c_1339,plain,
( ~ element(X0,powerset(powerset(the_carrier(X1))))
| ~ closed_subsets(X0,X1)
| ~ top_str(X1)
| open_subsets(complements_of_subsets(the_carrier(X1),X0),X1) ),
inference(cnf_transformation,[],[f3518]) ).
cnf(c_1347,negated_conjecture,
( ~ closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| ~ open_subsets(sK448,sK447) ),
inference(cnf_transformation,[],[f3530]) ).
cnf(c_1348,negated_conjecture,
( closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| open_subsets(sK448,sK447) ),
inference(cnf_transformation,[],[f3529]) ).
cnf(c_1349,negated_conjecture,
element(sK448,powerset(powerset(the_carrier(sK447)))),
inference(cnf_transformation,[],[f3528]) ).
cnf(c_1350,negated_conjecture,
top_str(sK447),
inference(cnf_transformation,[],[f3527]) ).
cnf(c_46609,plain,
complements_of_subsets(the_carrier(sK447),complements_of_subsets(the_carrier(sK447),sK448)) = sK448,
inference(superposition,[status(thm)],[c_1349,c_654]) ).
cnf(c_46628,plain,
( ~ closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| open_subsets(complements_of_subsets(the_carrier(X0),complements_of_subsets(the_carrier(X0),X1)),X0) ),
inference(superposition,[status(thm)],[c_486,c_1339]) ).
cnf(c_46643,plain,
( ~ open_subsets(complements_of_subsets(the_carrier(X0),complements_of_subsets(the_carrier(X0),X1)),X0)
| ~ element(X1,powerset(powerset(the_carrier(X0))))
| ~ top_str(X0)
| closed_subsets(complements_of_subsets(the_carrier(X0),X1),X0) ),
inference(superposition,[status(thm)],[c_486,c_1338]) ).
cnf(c_46826,plain,
( ~ element(sK448,powerset(powerset(the_carrier(sK447))))
| ~ closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447)
| ~ top_str(sK447)
| open_subsets(sK448,sK447) ),
inference(superposition,[status(thm)],[c_46609,c_46628]) ).
cnf(c_46878,plain,
( ~ element(sK448,powerset(powerset(the_carrier(sK447))))
| ~ open_subsets(sK448,sK447)
| ~ top_str(sK447)
| closed_subsets(complements_of_subsets(the_carrier(sK447),sK448),sK447) ),
inference(superposition,[status(thm)],[c_46609,c_46643]) ).
cnf(c_47057,plain,
$false,
inference(prop_impl_just,[status(thm)],[c_46878,c_46826,c_1347,c_1348,c_1349,c_1350]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14 % Problem : SEU337+2 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.15 % Command : run_iprover %s %d THM
% 0.14/0.37 % Computer : n002.cluster.edu
% 0.14/0.37 % Model : x86_64 x86_64
% 0.14/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37 % Memory : 8042.1875MB
% 0.14/0.37 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37 % CPULimit : 300
% 0.14/0.37 % WCLimit : 300
% 0.14/0.37 % DateTime : Wed Aug 23 21:02:01 EDT 2023
% 0.14/0.37 % CPUTime :
% 0.21/0.48 Running first-order theorem proving
% 0.21/0.48 Running: /export/starexec/sandbox/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 17.89/3.21 % SZS status Started for theBenchmark.p
% 17.89/3.21 % SZS status Theorem for theBenchmark.p
% 17.89/3.21
% 17.89/3.21 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 17.89/3.21
% 17.89/3.21 ------ iProver source info
% 17.89/3.21
% 17.89/3.21 git: date: 2023-05-31 18:12:56 +0000
% 17.89/3.21 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 17.89/3.21 git: non_committed_changes: false
% 17.89/3.21 git: last_make_outside_of_git: false
% 17.89/3.21
% 17.89/3.21 ------ Parsing...
% 17.89/3.21 ------ Clausification by vclausify_rel & Parsing by iProver...
% 17.89/3.21
% 17.89/3.21 ------ Preprocessing... sup_sim: 103 sf_s rm: 96 0s sf_e pe_s pe:1:0s pe:2:0s pe:4:0s pe:8:0s pe_e
% 17.89/3.21
% 17.89/3.21 ------ Preprocessing... gs_s sp: 19 0s gs_e snvd_s sp: 0 0s snvd_e
% 17.89/3.21
% 17.89/3.21 ------ Preprocessing... sf_s rm: 5 0s sf_e
% 17.89/3.21 ------ Proving...
% 17.89/3.21 ------ Problem Properties
% 17.89/3.21
% 17.89/3.21
% 17.89/3.21 clauses 1348
% 17.89/3.21 conjectures 4
% 17.89/3.21 EPR 184
% 17.89/3.21 Horn 972
% 17.89/3.21 unary 154
% 17.89/3.21 binary 375
% 17.89/3.21 lits 4245
% 17.89/3.21 lits eq 576
% 17.89/3.21 fd_pure 0
% 17.89/3.21 fd_pseudo 0
% 17.89/3.21 fd_cond 46
% 17.89/3.21 fd_pseudo_cond 118
% 17.89/3.21 AC symbols 0
% 17.89/3.21
% 17.89/3.21 ------ Input Options Time Limit: Unbounded
% 17.89/3.21
% 17.89/3.21
% 17.89/3.21 ------
% 17.89/3.21 Current options:
% 17.89/3.21 ------
% 17.89/3.21
% 17.89/3.21
% 17.89/3.21
% 17.89/3.21
% 17.89/3.21 ------ Proving...
% 17.89/3.21
% 17.89/3.21
% 17.89/3.21 % SZS status Theorem for theBenchmark.p
% 17.89/3.21
% 17.89/3.21 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 17.89/3.21
% 17.89/3.21
%------------------------------------------------------------------------------