%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU382+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n009.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 : Thu Sep 24 02:20:21 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 39 ( 21 unt; 0 def)
% Number of atoms : 75 ( 33 equ)
% Maximal formula atoms : 5 ( 1 avg)
% Number of connectives : 58 ( 22 ~; 17 |; 14 &)
% ( 1 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 1 prp; 0-3 aty)
% Number of functors : 9 ( 9 usr; 1 con; 0-2 aty)
% Number of variables : 65 ( 64 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A] :
( rel_str(A)
=> ( strict_rel_str(A)
=> A = rel_str_of(the_carrier(A),the_InternalRel(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A] : incl_POSet(A) = rel_str_of(A,inclusion_order(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A] :
( relation_of2_as_subset(inclusion_order(A),A,A)
& v1_partfun1(inclusion_order(A),A,A)
& transitive(inclusion_order(A))
& antisymmetric(inclusion_order(A))
& reflexive(inclusion_order(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A] :
( rel_str(boole_POSet(A))
& strict_rel_str(boole_POSet(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f60,axiom,
! [A,B] :
( relation_of2(B,A,A)
=> ! [C,D] :
( rel_str_of(A,B) = rel_str_of(C,D)
=> ( B = D
& A = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f77,axiom,
! [A] : inclusion_order(A) = inclusion_relation(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f78,axiom,
! [A,B,C] :
( relation_of2_as_subset(C,A,B)
<=> relation_of2(C,A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f84,conjecture,
! [A] : the_carrier(boole_POSet(A)) = powerset(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f85,negated_conjecture,
~ ! [A] : the_carrier(boole_POSet(A)) = powerset(A),
inference(negated_conjecture,[status(cth)],[f84]) ).
fof(f86,axiom,
! [A] : boole_POSet(A) = incl_POSet(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f91,plain,
! [A] :
( A = rel_str_of(the_carrier(A),the_InternalRel(A))
| ~ strict_rel_str(A)
| ~ rel_str(A) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f92,plain,
! [X0] :
( X0 = rel_str_of(the_carrier(X0),the_InternalRel(X0))
| ~ strict_rel_str(X0)
| ~ rel_str(X0) ),
inference(cnf_transformation,[status(thm)],[f91]) ).
fof(f219,plain,
! [X0] : incl_POSet(X0) = rel_str_of(X0,inclusion_order(X0)),
inference(cnf_transformation,[status(thm)],[f27]) ).
fof(f224,plain,
( ! [A] : relation_of2_as_subset(inclusion_order(A),A,A)
& ! [A] : v1_partfun1(inclusion_order(A),A,A)
& ! [A] : transitive(inclusion_order(A))
& ! [A] : antisymmetric(inclusion_order(A))
& ! [A] : reflexive(inclusion_order(A)) ),
inference(miniscoping,[status(thm)],[f31]) ).
fof(f229,plain,
! [X0] : relation_of2_as_subset(inclusion_order(X0),X0,X0),
inference(cnf_transformation,[status(thm)],[f224]) ).
fof(f233,plain,
( ! [A] : rel_str(boole_POSet(A))
& ! [A] : strict_rel_str(boole_POSet(A)) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f234,plain,
! [X0] : strict_rel_str(boole_POSet(X0)),
inference(cnf_transformation,[status(thm)],[f233]) ).
fof(f235,plain,
! [X0] : rel_str(boole_POSet(X0)),
inference(cnf_transformation,[status(thm)],[f233]) ).
fof(f323,plain,
! [A,B] :
( ! [C,D] :
( ( B = D
& A = C )
| rel_str_of(A,B) != rel_str_of(C,D) )
| ~ relation_of2(B,A,A) ),
inference(pre_NNF_transformation,[status(thm)],[f60]) ).
fof(f324,plain,
! [X0,X1,X2,X3] :
( X1 = X2
| rel_str_of(X1,X0) != rel_str_of(X2,X3)
| ~ relation_of2(X0,X1,X1) ),
inference(cnf_transformation,[status(thm)],[f323]) ).
fof(f438,plain,
! [X0] : inclusion_order(X0) = inclusion_relation(X0),
inference(cnf_transformation,[status(thm)],[f77]) ).
fof(f439,plain,
! [A,B,C] :
( ( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(NNF_transformation,[status(thm)],[f78]) ).
fof(f440,plain,
( ! [A,B,C] :
( ~ relation_of2(C,A,B)
| relation_of2_as_subset(C,A,B) )
& ! [A,B,C] :
( relation_of2(C,A,B)
| ~ relation_of2_as_subset(C,A,B) ) ),
inference(miniscoping,[status(thm)],[f439]) ).
fof(f441,plain,
! [X0,X1,X2] :
( relation_of2(X0,X1,X2)
| ~ relation_of2_as_subset(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f440]) ).
fof(f456,plain,
? [A] : the_carrier(boole_POSet(A)) != powerset(A),
inference(pre_NNF_transformation,[status(thm)],[f85]) ).
fof(f457,plain,
the_carrier(boole_POSet(sK21_skl)) != powerset(sK21_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK21_skl]),skolemize(A,sK21_skl)],[f456]) ).
fof(f458,plain,
the_carrier(boole_POSet(sK21_skl)) != powerset(sK21_skl),
inference(cnf_transformation,[status(thm)],[f457]) ).
fof(f459,plain,
! [X0] : boole_POSet(X0) = incl_POSet(powerset(X0)),
inference(cnf_transformation,[status(thm)],[f86]) ).
fof(f490,plain,
! [X0] :
( boole_POSet(X0) = rel_str_of(the_carrier(boole_POSet(X0)),the_InternalRel(boole_POSet(X0)))
| ~ rel_str(boole_POSet(X0)) ),
inference(resolution,[status(thm)],[f234,f92]) ).
fof(f491,plain,
! [X0] : boole_POSet(X0) = rel_str_of(the_carrier(boole_POSet(X0)),the_InternalRel(boole_POSet(X0))),
inference(forward_subsumption_resolution,[status(thm)],[f490,f235]) ).
fof(f498,plain,
! [X0] : incl_POSet(X0) = rel_str_of(X0,inclusion_relation(X0)),
inference(backward_demodulation,[status(thm)],[f438,f219]) ).
fof(f502,plain,
! [X0] : relation_of2_as_subset(inclusion_relation(X0),X0,X0),
inference(forward_demodulation,[status(thm)],[f438,f229]) ).
fof(f527,plain,
! [X0] : relation_of2(inclusion_relation(X0),X0,X0),
inference(resolution,[status(thm)],[f441,f502]) ).
fof(f529,plain,
! [X0,X1,X2] :
( X0 = X1
| rel_str_of(X0,inclusion_relation(X0)) != rel_str_of(X1,X2) ),
inference(resolution,[status(thm)],[f527,f324]) ).
fof(f533,plain,
! [X0,X1,X2] :
( X0 = X1
| incl_POSet(X0) != rel_str_of(X1,X2) ),
inference(forward_demodulation,[status(thm)],[f498,f529]) ).
fof(f542,plain,
! [X0,X1] :
( X0 = the_carrier(boole_POSet(X1))
| incl_POSet(X0) != boole_POSet(X1) ),
inference(paramodulation,[status(thm)],[f491,f533]) ).
fof(f544,plain,
! [X0] : powerset(X0) = the_carrier(boole_POSet(X0)),
inference(resolution,[status(thm)],[f542,f459]) ).
fof(f546,plain,
powerset(sK21_skl) != powerset(sK21_skl),
inference(backward_demodulation,[status(thm)],[f544,f458]) ).
fof(f553,plain,
$false,
inference(trivial_equality_resolution,[status(thm)],[f546]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU382+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.35 % Computer : n009.cluster.edu
% 0.09/0.35 % Model : x86_64 x86_64
% 0.09/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.35 % Memory : 8046.5625MB
% 0.09/0.35 % OS : Linux 6.8.0-71-generic
% 0.09/0.35 % CPULimit : 300
% 0.09/0.35 % WCLimit : 300
% 0.09/0.35 % DateTime : Mon Sep 21 06:17:28 UTC 2026
% 0.09/0.35 % CPUTime :
% 0.09/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.064715 seconds
% 0.13/0.42 % CPU time: 0.189449 seconds
% 0.13/0.42 % Total memory used: 114.183 MB
% 0.13/0.42 % Net memory used: 114.044 MB
%------------------------------------------------------------------------------