TSTP Solution File: SEU371+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU371+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n031.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 : Tue Apr 30 20:42:06 EDT 2024
% Result : Theorem 0.11s 0.38s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 9
% Syntax : Number of formulae : 46 ( 20 unt; 0 def)
% Number of atoms : 144 ( 37 equ)
% Maximal formula atoms : 17 ( 3 avg)
% Number of connectives : 141 ( 43 ~; 40 |; 55 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 22 ( 20 usr; 1 prp; 0-2 aty)
% Number of functors : 11 ( 11 usr; 2 con; 0-2 aty)
% Number of variables : 71 ( 70 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [A] :
( rel_str(A)
=> bottom_of_relstr(A) = join_on_relstr(A,empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A] : boole_POSet(A) = poset_of_lattice(boole_lattice(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A] :
( strict_latt_str(boole_lattice(A))
& latt_str(boole_lattice(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A] :
( strict_rel_str(boole_POSet(A))
& rel_str(boole_POSet(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f59,axiom,
! [A] :
( ~ empty_carrier(boole_lattice(A))
& strict_latt_str(boole_lattice(A))
& join_commutative(boole_lattice(A))
& join_associative(boole_lattice(A))
& meet_commutative(boole_lattice(A))
& meet_associative(boole_lattice(A))
& meet_absorbing(boole_lattice(A))
& join_absorbing(boole_lattice(A))
& lattice(boole_lattice(A))
& distributive_lattstr(boole_lattice(A))
& modular_lattstr(boole_lattice(A))
& lower_bounded_semilattstr(boole_lattice(A))
& upper_bounded_semilattstr(boole_lattice(A))
& bounded_lattstr(boole_lattice(A))
& complemented_lattstr(boole_lattice(A))
& boolean_lattstr(boole_lattice(A))
& complete_latt_str(boole_lattice(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f103,conjecture,
! [A] : bottom_of_relstr(boole_POSet(A)) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f104,negated_conjecture,
~ ! [A] : bottom_of_relstr(boole_POSet(A)) = empty_set,
inference(negated_conjecture,[status(cth)],[f103]) ).
fof(f106,axiom,
! [A] :
( ( ~ empty_carrier(A)
& lattice(A)
& complete_latt_str(A)
& latt_str(A) )
=> ! [B] :
( join_of_latt_set(A,B) = join_on_relstr(poset_of_lattice(A),B)
& meet_of_latt_set(A,B) = meet_on_relstr(poset_of_lattice(A),B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f109,axiom,
! [A] :
( lower_bounded_semilattstr(boole_lattice(A))
& bottom_of_semilattstr(boole_lattice(A)) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f112,axiom,
! [A] :
( ( ~ empty_carrier(A)
& lattice(A)
& complete_latt_str(A)
& latt_str(A) )
=> ( ~ empty_carrier(A)
& lattice(A)
& lower_bounded_semilattstr(A)
& latt_str(A)
& bottom_of_semilattstr(A) = join_of_latt_set(A,empty_set) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f192,plain,
! [A] :
( ~ rel_str(A)
| bottom_of_relstr(A) = join_on_relstr(A,empty_set) ),
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f193,plain,
! [X0] :
( ~ rel_str(X0)
| bottom_of_relstr(X0) = join_on_relstr(X0,empty_set) ),
inference(cnf_transformation,[status(esa)],[f192]) ).
fof(f198,plain,
! [X0] : boole_POSet(X0) = poset_of_lattice(boole_lattice(X0)),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f211,plain,
( ! [A] : strict_latt_str(boole_lattice(A))
& ! [A] : latt_str(boole_lattice(A)) ),
inference(miniscoping,[status(esa)],[f27]) ).
fof(f213,plain,
! [X0] : latt_str(boole_lattice(X0)),
inference(cnf_transformation,[status(esa)],[f211]) ).
fof(f234,plain,
( ! [A] : strict_rel_str(boole_POSet(A))
& ! [A] : rel_str(boole_POSet(A)) ),
inference(miniscoping,[status(esa)],[f36]) ).
fof(f236,plain,
! [X0] : rel_str(boole_POSet(X0)),
inference(cnf_transformation,[status(esa)],[f234]) ).
fof(f278,plain,
( ! [A] : ~ empty_carrier(boole_lattice(A))
& ! [A] : strict_latt_str(boole_lattice(A))
& ! [A] : join_commutative(boole_lattice(A))
& ! [A] : join_associative(boole_lattice(A))
& ! [A] : meet_commutative(boole_lattice(A))
& ! [A] : meet_associative(boole_lattice(A))
& ! [A] : meet_absorbing(boole_lattice(A))
& ! [A] : join_absorbing(boole_lattice(A))
& ! [A] : lattice(boole_lattice(A))
& ! [A] : distributive_lattstr(boole_lattice(A))
& ! [A] : modular_lattstr(boole_lattice(A))
& ! [A] : lower_bounded_semilattstr(boole_lattice(A))
& ! [A] : upper_bounded_semilattstr(boole_lattice(A))
& ! [A] : bounded_lattstr(boole_lattice(A))
& ! [A] : complemented_lattstr(boole_lattice(A))
& ! [A] : boolean_lattstr(boole_lattice(A))
& ! [A] : complete_latt_str(boole_lattice(A)) ),
inference(miniscoping,[status(esa)],[f59]) ).
fof(f279,plain,
! [X0] : ~ empty_carrier(boole_lattice(X0)),
inference(cnf_transformation,[status(esa)],[f278]) ).
fof(f287,plain,
! [X0] : lattice(boole_lattice(X0)),
inference(cnf_transformation,[status(esa)],[f278]) ).
fof(f295,plain,
! [X0] : complete_latt_str(boole_lattice(X0)),
inference(cnf_transformation,[status(esa)],[f278]) ).
fof(f575,plain,
? [A] : bottom_of_relstr(boole_POSet(A)) != empty_set,
inference(pre_NNF_transformation,[status(esa)],[f104]) ).
fof(f576,plain,
bottom_of_relstr(boole_POSet(sk0_28)) != empty_set,
inference(skolemization,[status(esa)],[f575]) ).
fof(f577,plain,
bottom_of_relstr(boole_POSet(sk0_28)) != empty_set,
inference(cnf_transformation,[status(esa)],[f576]) ).
fof(f580,plain,
! [A] :
( empty_carrier(A)
| ~ lattice(A)
| ~ complete_latt_str(A)
| ~ latt_str(A)
| ! [B] :
( join_of_latt_set(A,B) = join_on_relstr(poset_of_lattice(A),B)
& meet_of_latt_set(A,B) = meet_on_relstr(poset_of_lattice(A),B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f106]) ).
fof(f581,plain,
! [A] :
( empty_carrier(A)
| ~ lattice(A)
| ~ complete_latt_str(A)
| ~ latt_str(A)
| ( ! [B] : join_of_latt_set(A,B) = join_on_relstr(poset_of_lattice(A),B)
& ! [B] : meet_of_latt_set(A,B) = meet_on_relstr(poset_of_lattice(A),B) ) ),
inference(miniscoping,[status(esa)],[f580]) ).
fof(f582,plain,
! [X0,X1] :
( empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0)
| join_of_latt_set(X0,X1) = join_on_relstr(poset_of_lattice(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f581]) ).
fof(f591,plain,
( ! [A] : lower_bounded_semilattstr(boole_lattice(A))
& ! [A] : bottom_of_semilattstr(boole_lattice(A)) = empty_set ),
inference(miniscoping,[status(esa)],[f109]) ).
fof(f593,plain,
! [X0] : bottom_of_semilattstr(boole_lattice(X0)) = empty_set,
inference(cnf_transformation,[status(esa)],[f591]) ).
fof(f601,plain,
! [A] :
( empty_carrier(A)
| ~ lattice(A)
| ~ complete_latt_str(A)
| ~ latt_str(A)
| ( ~ empty_carrier(A)
& lattice(A)
& lower_bounded_semilattstr(A)
& latt_str(A)
& bottom_of_semilattstr(A) = join_of_latt_set(A,empty_set) ) ),
inference(pre_NNF_transformation,[status(esa)],[f112]) ).
fof(f606,plain,
! [X0] :
( empty_carrier(X0)
| ~ lattice(X0)
| ~ complete_latt_str(X0)
| ~ latt_str(X0)
| bottom_of_semilattstr(X0) = join_of_latt_set(X0,empty_set) ),
inference(cnf_transformation,[status(esa)],[f601]) ).
fof(f619,plain,
! [X0] : bottom_of_relstr(boole_POSet(X0)) = join_on_relstr(boole_POSet(X0),empty_set),
inference(resolution,[status(thm)],[f193,f236]) ).
fof(f676,plain,
! [X0] :
( empty_carrier(boole_lattice(X0))
| ~ complete_latt_str(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0))
| bottom_of_semilattstr(boole_lattice(X0)) = join_of_latt_set(boole_lattice(X0),empty_set) ),
inference(resolution,[status(thm)],[f606,f287]) ).
fof(f677,plain,
! [X0] :
( empty_carrier(boole_lattice(X0))
| ~ complete_latt_str(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0))
| empty_set = join_of_latt_set(boole_lattice(X0),empty_set) ),
inference(forward_demodulation,[status(thm)],[f593,f676]) ).
fof(f678,plain,
! [X0] :
( ~ complete_latt_str(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0))
| empty_set = join_of_latt_set(boole_lattice(X0),empty_set) ),
inference(forward_subsumption_resolution,[status(thm)],[f677,f279]) ).
fof(f682,plain,
! [X0] :
( ~ latt_str(boole_lattice(X0))
| empty_set = join_of_latt_set(boole_lattice(X0),empty_set) ),
inference(resolution,[status(thm)],[f678,f295]) ).
fof(f683,plain,
! [X0] : empty_set = join_of_latt_set(boole_lattice(X0),empty_set),
inference(forward_subsumption_resolution,[status(thm)],[f682,f213]) ).
fof(f697,plain,
! [X0,X1] :
( empty_carrier(boole_lattice(X0))
| ~ complete_latt_str(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0))
| join_of_latt_set(boole_lattice(X0),X1) = join_on_relstr(poset_of_lattice(boole_lattice(X0)),X1) ),
inference(resolution,[status(thm)],[f582,f287]) ).
fof(f698,plain,
! [X0,X1] :
( empty_carrier(boole_lattice(X0))
| ~ complete_latt_str(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0))
| join_of_latt_set(boole_lattice(X0),X1) = join_on_relstr(boole_POSet(X0),X1) ),
inference(forward_demodulation,[status(thm)],[f198,f697]) ).
fof(f699,plain,
! [X0,X1] :
( ~ complete_latt_str(boole_lattice(X0))
| ~ latt_str(boole_lattice(X0))
| join_of_latt_set(boole_lattice(X0),X1) = join_on_relstr(boole_POSet(X0),X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f698,f279]) ).
fof(f703,plain,
! [X0,X1] :
( ~ latt_str(boole_lattice(X0))
| join_of_latt_set(boole_lattice(X0),X1) = join_on_relstr(boole_POSet(X0),X1) ),
inference(resolution,[status(thm)],[f699,f295]) ).
fof(f704,plain,
! [X0,X1] : join_of_latt_set(boole_lattice(X0),X1) = join_on_relstr(boole_POSet(X0),X1),
inference(forward_subsumption_resolution,[status(thm)],[f703,f213]) ).
fof(f705,plain,
! [X0] : empty_set = join_on_relstr(boole_POSet(X0),empty_set),
inference(backward_demodulation,[status(thm)],[f704,f683]) ).
fof(f706,plain,
! [X0] : empty_set = bottom_of_relstr(boole_POSet(X0)),
inference(forward_demodulation,[status(thm)],[f619,f705]) ).
fof(f707,plain,
empty_set != empty_set,
inference(backward_demodulation,[status(thm)],[f706,f577]) ).
fof(f708,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f707]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.07 % Problem : SEU371+1 : TPTP v8.1.2. Released v3.3.0.
% 0.02/0.08 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26 % Computer : n031.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Mon Apr 29 20:17:43 EDT 2024
% 0.07/0.26 % CPUTime :
% 0.11/0.27 % Drodi V3.6.0
% 0.11/0.38 % Refutation found
% 0.11/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.40 % Elapsed time: 0.130646 seconds
% 0.11/0.40 % CPU time: 0.909192 seconds
% 0.11/0.40 % Total memory used: 85.807 MB
% 0.11/0.40 % Net memory used: 85.207 MB
%------------------------------------------------------------------------------