%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU326+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n014.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 02:20:11 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 62 ( 6 unt; 7 def)
% Number of atoms : 155 ( 58 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 167 ( 74 ~; 62 |; 19 &)
% ( 7 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 39 ( 35 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f19,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> element(complements_of_subsets(A,B),powerset(powerset(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> complements_of_subsets(A,complements_of_subsets(A,B)) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,conjecture,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ( ~ ( B = empty_set
& complements_of_subsets(A,B) != empty_set )
& ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ( ~ ( B = empty_set
& complements_of_subsets(A,B) != empty_set )
& ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ) ),
inference(negated_conjecture,[status(cth)],[f29]) ).
fof(f34,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f96,plain,
! [A,B] :
( element(complements_of_subsets(A,B),powerset(powerset(A)))
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f19]) ).
fof(f97,plain,
! [X0,X1] :
( element(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f96]) ).
fof(f107,plain,
! [A,B] :
( complements_of_subsets(A,complements_of_subsets(A,B)) = B
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f24]) ).
fof(f108,plain,
! [X0,X1] :
( complements_of_subsets(X1,complements_of_subsets(X1,X0)) = X0
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f107]) ).
fof(f125,plain,
? [A,B] :
( ( ( B = empty_set
& complements_of_subsets(A,B) != empty_set )
| ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) )
& element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f30]) ).
fof(f126,definition,
! [A,B] :
( sP0_prd(B,A)
<=> ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
introduced(definition,[new_symbols(definition,[sP0_prd])],[]) ).
fof(f127,plain,
? [A,B] :
( ( ( B = empty_set
& complements_of_subsets(A,B) != empty_set )
| sP0_prd(B,A) )
& element(B,powerset(powerset(A))) ),
inference(formula_renaming,[status(thm)],[f125,f126]) ).
fof(f128,plain,
( ( ( sK5_skl = empty_set
& complements_of_subsets(sK4_skl,sK5_skl) != empty_set )
| sP0_prd(sK5_skl,sK4_skl) )
& element(sK5_skl,powerset(powerset(sK4_skl))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK4_skl,sK5_skl]),skolemize(A,sK4_skl),skolemize(B,sK5_skl)],[f127]) ).
fof(f129,plain,
element(sK5_skl,powerset(powerset(sK4_skl))),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f130,plain,
( complements_of_subsets(sK4_skl,sK5_skl) != empty_set
| sP0_prd(sK5_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f131,plain,
( sK5_skl = empty_set
| sP0_prd(sK5_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f140,plain,
! [A,B] :
( complements_of_subsets(A,B) != empty_set
| B = empty_set
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f141,plain,
! [X0,X1] :
( complements_of_subsets(X1,X0) != empty_set
| X0 = empty_set
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f140]) ).
fof(f156,plain,
! [A,B] :
( ( complements_of_subsets(A,B) != empty_set
| B = empty_set
| sP0_prd(B,A) )
& ( ( complements_of_subsets(A,B) = empty_set
& B != empty_set )
| ~ sP0_prd(B,A) ) ),
inference(NNF_transformation,[status(thm)],[f126]) ).
fof(f157,plain,
( ! [A,B] :
( complements_of_subsets(A,B) != empty_set
| B = empty_set
| sP0_prd(B,A) )
& ! [A,B] :
( ( complements_of_subsets(A,B) = empty_set
& B != empty_set )
| ~ sP0_prd(B,A) ) ),
inference(miniscoping,[status(thm)],[f156]) ).
fof(f158,plain,
! [X0,X1] :
( X0 != empty_set
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f159,plain,
! [X0,X1] :
( complements_of_subsets(X1,X0) = empty_set
| ~ sP0_prd(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f157]) ).
fof(f161,definition,
( sQ0_spl
<=> sP0_prd(sK5_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f162,plain,
( ~ sQ0_spl
| sP0_prd(sK5_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f161]) ).
fof(f164,definition,
( sQ1_spl
<=> complements_of_subsets(sK4_skl,sK5_skl) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f166,plain,
( sQ1_spl
| complements_of_subsets(sK4_skl,sK5_skl) != empty_set ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f167,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f130,f161,f164]) ).
fof(f168,definition,
( sQ2_spl
<=> sK5_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f169,plain,
( ~ sQ2_spl
| sK5_skl = empty_set ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f171,plain,
( sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f131,f161,f168]) ).
fof(f172,plain,
! [X0] : ~ sP0_prd(empty_set,X0),
inference(destructive_equality_resolution,[status(thm)],[f158]) ).
fof(f173,plain,
( ~ sQ0_spl
| complements_of_subsets(sK4_skl,sK5_skl) = empty_set ),
inference(resolution,[status(thm)],[f159,f162]) ).
fof(f182,plain,
complements_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,sK5_skl)) = sK5_skl,
inference(resolution,[status(thm)],[f108,f129]) ).
fof(f185,definition,
( sQ4_spl
<=> sP0_prd(empty_set,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f186,plain,
( ~ sQ4_spl
| sP0_prd(empty_set,sK4_skl) ),
inference(component_clause,[status(thm)],[f185]) ).
fof(f189,plain,
( complements_of_subsets(sK4_skl,sK5_skl) != empty_set
| sK5_skl = empty_set ),
inference(resolution,[status(thm)],[f141,f129]) ).
fof(f190,plain,
( ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f189,f168,f164]) ).
fof(f191,plain,
( sQ1_spl
| ~ sQ0_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f173,f166]) ).
fof(f192,plain,
( sQ1_spl
| ~ sQ0_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f191]) ).
fof(f193,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f192]) ).
fof(f194,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f186,f172]) ).
fof(f195,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f194]) ).
fof(f196,plain,
element(complements_of_subsets(sK4_skl,sK5_skl),powerset(powerset(sK4_skl))),
inference(resolution,[status(thm)],[f97,f129]) ).
fof(f200,plain,
( sQ1_spl
| ~ sQ2_spl
| complements_of_subsets(sK4_skl,empty_set) != empty_set ),
inference(forward_demodulation,[status(thm)],[f169,f166]) ).
fof(f204,definition,
( sQ5_spl
<=> complements_of_subsets(sK4_skl,empty_set) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f205,plain,
( ~ sQ5_spl
| complements_of_subsets(sK4_skl,empty_set) = empty_set ),
inference(component_clause,[status(thm)],[f204]) ).
fof(f208,plain,
( ~ sQ2_spl
| complements_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,empty_set)) = sK5_skl ),
inference(forward_demodulation,[status(thm)],[f169,f182]) ).
fof(f209,plain,
( ~ sQ2_spl
| complements_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,empty_set)) = empty_set ),
inference(forward_demodulation,[status(thm)],[f169,f208]) ).
fof(f217,plain,
( ~ sQ2_spl
| element(complements_of_subsets(sK4_skl,empty_set),powerset(powerset(sK4_skl))) ),
inference(forward_demodulation,[status(thm)],[f169,f196]) ).
fof(f219,plain,
( ~ sQ2_spl
| complements_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,empty_set)) != empty_set
| complements_of_subsets(sK4_skl,empty_set) = empty_set ),
inference(resolution,[status(thm)],[f217,f141]) ).
fof(f222,definition,
( sQ7_spl
<=> complements_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,empty_set)) = empty_set ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f224,plain,
( sQ7_spl
| complements_of_subsets(sK4_skl,complements_of_subsets(sK4_skl,empty_set)) != empty_set ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f225,plain,
( ~ sQ2_spl
| ~ sQ7_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f219,f204,f222,f168]) ).
fof(f226,plain,
( ~ sQ5_spl
| sQ1_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f205,f200]) ).
fof(f227,plain,
( ~ sQ5_spl
| sQ1_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f226]) ).
fof(f228,plain,
( sQ7_spl
| ~ sQ2_spl
| empty_set != empty_set ),
inference(forward_demodulation,[status(thm)],[f209,f224]) ).
fof(f229,plain,
( sQ7_spl
| ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f228]) ).
fof(f230,plain,
( sQ7_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f229]) ).
fof(f231,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| sP0_prd(empty_set,sK4_skl) ),
inference(forward_demodulation,[status(thm)],[f169,f162]) ).
fof(f232,plain,
( ~ sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f231,f172]) ).
fof(f233,plain,
( ~ sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f232]) ).
fof(f234,plain,
$false,
inference(sat_refutation,[status(thm)],[f167,f171,f190,f193,f195,f225,f227,f230,f233]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU326+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n014.cluster.edu
% 0.08/0.35 % Model : x86_64 x86_64
% 0.08/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.35 % Memory : 8046.5625MB
% 0.08/0.35 % OS : Linux 6.8.0-71-generic
% 0.08/0.35 % CPULimit : 300
% 0.08/0.35 % WCLimit : 300
% 0.08/0.35 % DateTime : Mon Sep 21 06:11:49 UTC 2026
% 0.08/0.35 % CPUTime :
% 0.13/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.41 % Elapsed time: 0.044405 seconds
% 0.13/0.41 % CPU time: 0.129999 seconds
% 0.13/0.41 % Total memory used: 64.360 MB
% 0.13/0.41 % Net memory used: 64.317 MB
%------------------------------------------------------------------------------