TSTP Solution File: SEU320+1 by iProver---3.8
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%------------------------------------------------------------------------------
% File : iProver---3.8
% Problem : SEU320+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : run_iprover %s %d THM
% Computer : n029.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 17:05:46 EDT 2023
% Result : Theorem 1.76s 1.15s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 6
% Syntax : Number of formulae : 49 ( 8 unt; 0 def)
% Number of atoms : 156 ( 11 equ)
% Maximal formula atoms : 12 ( 3 avg)
% Number of connectives : 181 ( 74 ~; 70 |; 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 : 52 ( 0 sgn; 26 !; 10 ?)
% 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,[],[f13]) ).
fof(f20,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f2]) ).
fof(f21,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(ennf_transformation,[],[f10]) ).
fof(f22,plain,
! [X0] :
( ! [X1] :
( ( closed_subset(X1,X0)
<=> open_subset(subset_complement(the_carrier(X0),X1),X0) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(ennf_transformation,[],[f12]) ).
fof(f23,plain,
? [X0] :
( ? [X1] :
( ( open_subset(X1,X0)
<~> closed_subset(subset_complement(the_carrier(X0),X1),X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(ennf_transformation,[],[f14]) ).
fof(f29,plain,
! [X0] :
( ! [X1] :
( ( ( 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) ) )
| ~ element(X1,powerset(the_carrier(X0))) )
| ~ top_str(X0) ),
inference(nnf_transformation,[],[f22]) ).
fof(f30,plain,
? [X0] :
( ? [X1] :
( ( ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ open_subset(X1,X0) )
& ( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| open_subset(X1,X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(nnf_transformation,[],[f23]) ).
fof(f31,plain,
? [X0] :
( ? [X1] :
( ( ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ open_subset(X1,X0) )
& ( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| open_subset(X1,X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) ),
inference(flattening,[],[f30]) ).
fof(f32,plain,
( ? [X0] :
( ? [X1] :
( ( ~ closed_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ open_subset(X1,X0) )
& ( closed_subset(subset_complement(the_carrier(X0),X1),X0)
| open_subset(X1,X0) )
& element(X1,powerset(the_carrier(X0))) )
& top_str(X0) )
=> ( ? [X1] :
( ( ~ closed_subset(subset_complement(the_carrier(sK2),X1),sK2)
| ~ open_subset(X1,sK2) )
& ( closed_subset(subset_complement(the_carrier(sK2),X1),sK2)
| open_subset(X1,sK2) )
& element(X1,powerset(the_carrier(sK2))) )
& top_str(sK2) ) ),
introduced(choice_axiom,[]) ).
fof(f33,plain,
( ? [X1] :
( ( ~ closed_subset(subset_complement(the_carrier(sK2),X1),sK2)
| ~ open_subset(X1,sK2) )
& ( closed_subset(subset_complement(the_carrier(sK2),X1),sK2)
| open_subset(X1,sK2) )
& element(X1,powerset(the_carrier(sK2))) )
=> ( ( ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| ~ open_subset(sK3,sK2) )
& ( closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| open_subset(sK3,sK2) )
& element(sK3,powerset(the_carrier(sK2))) ) ),
introduced(choice_axiom,[]) ).
fof(f34,plain,
( ( ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| ~ open_subset(sK3,sK2) )
& ( closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| open_subset(sK3,sK2) )
& element(sK3,powerset(the_carrier(sK2)))
& top_str(sK2) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f31,f33,f32]) ).
fof(f35,plain,
! [X0,X1] :
( element(subset_complement(X0,X1),powerset(X0))
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f20]) ).
fof(f38,plain,
! [X0,X1] :
( subset_complement(X0,subset_complement(X0,X1)) = X1
| ~ element(X1,powerset(X0)) ),
inference(cnf_transformation,[],[f21]) ).
fof(f40,plain,
! [X0,X1] :
( open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ closed_subset(X1,X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f41,plain,
! [X0,X1] :
( closed_subset(X1,X0)
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0) ),
inference(cnf_transformation,[],[f29]) ).
fof(f42,plain,
top_str(sK2),
inference(cnf_transformation,[],[f34]) ).
fof(f43,plain,
element(sK3,powerset(the_carrier(sK2))),
inference(cnf_transformation,[],[f34]) ).
fof(f44,plain,
( closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| open_subset(sK3,sK2) ),
inference(cnf_transformation,[],[f34]) ).
fof(f45,plain,
( ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| ~ open_subset(sK3,sK2) ),
inference(cnf_transformation,[],[f34]) ).
cnf(c_49,plain,
( ~ element(X0,powerset(X1))
| element(subset_complement(X1,X0),powerset(X1)) ),
inference(cnf_transformation,[],[f35]) ).
cnf(c_52,plain,
( ~ element(X0,powerset(X1))
| subset_complement(X1,subset_complement(X1,X0)) = X0 ),
inference(cnf_transformation,[],[f38]) ).
cnf(c_54,plain,
( ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| ~ top_str(X0)
| closed_subset(X1,X0) ),
inference(cnf_transformation,[],[f41]) ).
cnf(c_55,plain,
( ~ element(X0,powerset(the_carrier(X1)))
| ~ closed_subset(X0,X1)
| ~ top_str(X1)
| open_subset(subset_complement(the_carrier(X1),X0),X1) ),
inference(cnf_transformation,[],[f40]) ).
cnf(c_56,negated_conjecture,
( ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| ~ open_subset(sK3,sK2) ),
inference(cnf_transformation,[],[f45]) ).
cnf(c_57,negated_conjecture,
( closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| open_subset(sK3,sK2) ),
inference(cnf_transformation,[],[f44]) ).
cnf(c_58,negated_conjecture,
element(sK3,powerset(the_carrier(sK2))),
inference(cnf_transformation,[],[f43]) ).
cnf(c_59,negated_conjecture,
top_str(sK2),
inference(cnf_transformation,[],[f42]) ).
cnf(c_68,plain,
( ~ open_subset(sK3,sK2)
| ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2) ),
inference(prop_impl_just,[status(thm)],[c_56]) ).
cnf(c_69,plain,
( ~ closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| ~ open_subset(sK3,sK2) ),
inference(renaming,[status(thm)],[c_68]) ).
cnf(c_70,plain,
( open_subset(sK3,sK2)
| closed_subset(subset_complement(the_carrier(sK2),sK3),sK2) ),
inference(prop_impl_just,[status(thm)],[c_57]) ).
cnf(c_71,plain,
( closed_subset(subset_complement(the_carrier(sK2),sK3),sK2)
| open_subset(sK3,sK2) ),
inference(renaming,[status(thm)],[c_70]) ).
cnf(c_229,plain,
( X0 != sK2
| ~ open_subset(subset_complement(the_carrier(X0),X1),X0)
| ~ element(X1,powerset(the_carrier(X0)))
| closed_subset(X1,X0) ),
inference(resolution_lifted,[status(thm)],[c_54,c_59]) ).
cnf(c_230,plain,
( ~ open_subset(subset_complement(the_carrier(sK2),X0),sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| closed_subset(X0,sK2) ),
inference(unflattening,[status(thm)],[c_229]) ).
cnf(c_241,plain,
( X0 != sK2
| ~ element(X1,powerset(the_carrier(X0)))
| ~ closed_subset(X1,X0)
| open_subset(subset_complement(the_carrier(X0),X1),X0) ),
inference(resolution_lifted,[status(thm)],[c_55,c_59]) ).
cnf(c_242,plain,
( ~ element(X0,powerset(the_carrier(sK2)))
| ~ closed_subset(X0,sK2)
| open_subset(subset_complement(the_carrier(sK2),X0),sK2) ),
inference(unflattening,[status(thm)],[c_241]) ).
cnf(c_298,plain,
( subset_complement(the_carrier(sK2),sK3) != X0
| sK2 != sK2
| ~ element(X0,powerset(the_carrier(sK2)))
| open_subset(subset_complement(the_carrier(sK2),X0),sK2)
| open_subset(sK3,sK2) ),
inference(resolution_lifted,[status(thm)],[c_71,c_242]) ).
cnf(c_299,plain,
( ~ 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)
| open_subset(sK3,sK2) ),
inference(unflattening,[status(thm)],[c_298]) ).
cnf(c_309,plain,
( subset_complement(the_carrier(sK2),sK3) != X0
| sK2 != sK2
| ~ open_subset(subset_complement(the_carrier(sK2),X0),sK2)
| ~ element(X0,powerset(the_carrier(sK2)))
| ~ open_subset(sK3,sK2) ),
inference(resolution_lifted,[status(thm)],[c_69,c_230]) ).
cnf(c_310,plain,
( ~ 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)))
| ~ open_subset(sK3,sK2) ),
inference(unflattening,[status(thm)],[c_309]) ).
cnf(c_759,plain,
subset_complement(the_carrier(sK2),subset_complement(the_carrier(sK2),sK3)) = sK3,
inference(superposition,[status(thm)],[c_58,c_52]) ).
cnf(c_763,plain,
( ~ element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2)))
| ~ open_subset(sK3,sK2) ),
inference(demodulation,[status(thm)],[c_310,c_759]) ).
cnf(c_764,plain,
( ~ element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2)))
| open_subset(sK3,sK2) ),
inference(demodulation,[status(thm)],[c_299,c_759]) ).
cnf(c_769,plain,
~ element(subset_complement(the_carrier(sK2),sK3),powerset(the_carrier(sK2))),
inference(backward_subsumption_resolution,[status(thm)],[c_764,c_763]) ).
cnf(c_790,plain,
~ element(sK3,powerset(the_carrier(sK2))),
inference(superposition,[status(thm)],[c_49,c_769]) ).
cnf(c_791,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[c_790,c_58]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU320+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13 % Command : run_iprover %s %d THM
% 0.16/0.34 % Computer : n029.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Thu Aug 24 01:00:53 EDT 2023
% 0.16/0.34 % CPUTime :
% 0.20/0.47 Running first-order theorem proving
% 0.20/0.47 Running: /export/starexec/sandbox2/solver/bin/run_problem --schedule fof_schedule --no_cores 8 /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 1.76/1.15 % SZS status Started for theBenchmark.p
% 1.76/1.15 % SZS status Theorem for theBenchmark.p
% 1.76/1.15
% 1.76/1.15 %---------------- iProver v3.8 (pre SMT-COMP 2023/CASC 2023) ----------------%
% 1.76/1.15
% 1.76/1.15 ------ iProver source info
% 1.76/1.15
% 1.76/1.15 git: date: 2023-05-31 18:12:56 +0000
% 1.76/1.15 git: sha1: 8abddc1f627fd3ce0bcb8b4cbf113b3cc443d7b6
% 1.76/1.15 git: non_committed_changes: false
% 1.76/1.15 git: last_make_outside_of_git: false
% 1.76/1.15
% 1.76/1.15 ------ Parsing...
% 1.76/1.15 ------ Clausification by vclausify_rel & Parsing by iProver...
% 1.76/1.15
% 1.76/1.15 ------ 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
% 1.76/1.15
% 1.76/1.15 ------ Preprocessing... gs_s sp: 0 0s gs_e snvd_s sp: 0 0s snvd_e
% 1.76/1.15
% 1.76/1.15 ------ Preprocessing... sf_s rm: 1 0s sf_e sf_s rm: 0 0s sf_e
% 1.76/1.15 ------ Proving...
% 1.76/1.15 ------ Problem Properties
% 1.76/1.15
% 1.76/1.15
% 1.76/1.15 clauses 11
% 1.76/1.15 conjectures 1
% 1.76/1.15 EPR 0
% 1.76/1.15 Horn 9
% 1.76/1.15 unary 3
% 1.76/1.15 binary 2
% 1.76/1.15 lits 31
% 1.76/1.15 lits eq 5
% 1.76/1.15 fd_pure 0
% 1.76/1.15 fd_pseudo 0
% 1.76/1.15 fd_cond 0
% 1.76/1.15 fd_pseudo_cond 0
% 1.76/1.15 AC symbols 0
% 1.76/1.15
% 1.76/1.15 ------ Schedule dynamic 5 is on
% 1.76/1.15
% 1.76/1.15 ------ Input Options "--resolution_flag false --inst_lit_sel_side none" Time Limit: 10.
% 1.76/1.15
% 1.76/1.15
% 1.76/1.15 ------
% 1.76/1.15 Current options:
% 1.76/1.15 ------
% 1.76/1.15
% 1.76/1.15
% 1.76/1.15
% 1.76/1.15
% 1.76/1.15 ------ Proving...
% 1.76/1.15
% 1.76/1.15
% 1.76/1.15 % SZS status Theorem for theBenchmark.p
% 1.76/1.15
% 1.76/1.15 % SZS output start CNFRefutation for theBenchmark.p
% See solution above
% 1.76/1.15
% 1.76/1.15
%------------------------------------------------------------------------------