%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU174+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n003.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 02:19:32 PM UTC 2026
% Result : Theorem 0.15s 0.39s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 8
% Syntax : Number of formulae : 56 ( 18 unt; 0 def)
% Number of atoms : 152 ( 41 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 172 ( 76 ~; 64 |; 18 &)
% ( 5 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 1 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-3 aty)
% Number of variables : 83 ( 77 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A,B] :
( element(B,powerset(powerset(A)))
=> ! [C] :
( element(C,powerset(powerset(A)))
=> ( C = complements_of_subsets(A,B)
<=> ! [D] :
( element(D,powerset(A))
=> ( in(D,C)
<=> in(subset_complement(A,D),B) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f34,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(f45,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(f60,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f98,conjecture,
! [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(f99,negated_conjecture,
~ ! [A,B] :
( element(B,powerset(powerset(A)))
=> ~ ( complements_of_subsets(A,B) = empty_set
& B != empty_set ) ),
inference(negated_conjecture,[status(cth)],[f98]) ).
fof(f103,axiom,
! [A,B,C] :
( ( element(B,powerset(C))
& in(A,B) )
=> element(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f112,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f143,plain,
! [A] :
( ( ? [B] : in(B,A)
| A = empty_set )
& ( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f144,plain,
( ! [A] :
( ? [B] : in(B,A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(miniscoping,[status(thm)],[f143]) ).
fof(f145,plain,
( ! [A] :
( in(sK1_skl(A),A)
| A = empty_set )
& ! [A] :
( ! [B] : ~ in(B,A)
| A != empty_set ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(B,sK1_skl(A))],[f144]) ).
fof(f146,plain,
! [X0,X1] :
( ~ in(X1,X0)
| X0 != empty_set ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f147,plain,
! [X0] :
( in(sK1_skl(X0),X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(thm)],[f145]) ).
fof(f230,plain,
! [A,B] :
( ! [C] :
( ( C = complements_of_subsets(A,B)
<=> ! [D] :
( ( in(D,C)
<=> in(subset_complement(A,D),B) )
| ~ element(D,powerset(A)) ) )
| ~ element(C,powerset(powerset(A))) )
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f231,plain,
! [A,B] :
( ! [C] :
( ( ( ? [D] :
( ( in(subset_complement(A,D),B)
| in(D,C) )
& ( ~ in(subset_complement(A,D),B)
| ~ in(D,C) )
& element(D,powerset(A)) )
| C = complements_of_subsets(A,B) )
& ( ! [D] :
( ( ( ~ in(subset_complement(A,D),B)
| in(D,C) )
& ( in(subset_complement(A,D),B)
| ~ in(D,C) ) )
| ~ element(D,powerset(A)) )
| C != complements_of_subsets(A,B) ) )
| ~ element(C,powerset(powerset(A))) )
| ~ element(B,powerset(powerset(A))) ),
inference(NNF_transformation,[status(thm)],[f230]) ).
fof(f232,plain,
! [A,B] :
( ! [C] :
( ( ( ( ( in(subset_complement(A,sK16_skl(C,B,A)),B)
| in(sK16_skl(C,B,A),C) )
& ( ~ in(subset_complement(A,sK16_skl(C,B,A)),B)
| ~ in(sK16_skl(C,B,A),C) )
& element(sK16_skl(C,B,A),powerset(A)) )
| C = complements_of_subsets(A,B) )
& ( ! [D] :
( ( ( ~ in(subset_complement(A,D),B)
| in(D,C) )
& ( in(subset_complement(A,D),B)
| ~ in(D,C) ) )
| ~ element(D,powerset(A)) )
| C != complements_of_subsets(A,B) ) )
| ~ element(C,powerset(powerset(A))) )
| ~ element(B,powerset(powerset(A))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK16_skl]),skolemize(D,sK16_skl(C,B,A))],[f231]) ).
fof(f233,plain,
! [X0,X1,X2,X3] :
( in(subset_complement(X1,X3),X0)
| ~ in(X3,X2)
| ~ element(X3,powerset(X1))
| X2 != complements_of_subsets(X1,X0)
| ~ element(X2,powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f232]) ).
fof(f245,plain,
! [A,B] :
( element(complements_of_subsets(A,B),powerset(powerset(A)))
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f34]) ).
fof(f246,plain,
! [X0,X1] :
( element(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f245]) ).
fof(f264,plain,
! [A,B] :
( complements_of_subsets(A,complements_of_subsets(A,B)) = B
| ~ element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f45]) ).
fof(f265,plain,
! [X0,X1] :
( complements_of_subsets(X1,complements_of_subsets(X1,X0)) = X0
| ~ element(X0,powerset(powerset(X1))) ),
inference(cnf_transformation,[status(thm)],[f264]) ).
fof(f308,plain,
empty(sK20_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK20_skl]),skolemize(A,sK20_skl)],[f60]) ).
fof(f309,plain,
empty(sK20_skl),
inference(cnf_transformation,[status(thm)],[f308]) ).
fof(f412,plain,
? [A,B] :
( complements_of_subsets(A,B) = empty_set
& B != empty_set
& element(B,powerset(powerset(A))) ),
inference(pre_NNF_transformation,[status(thm)],[f99]) ).
fof(f413,plain,
( complements_of_subsets(sK26_skl,sK27_skl) = empty_set
& sK27_skl != empty_set
& element(sK27_skl,powerset(powerset(sK26_skl))) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK26_skl,sK27_skl]),skolemize(A,sK26_skl),skolemize(B,sK27_skl)],[f412]) ).
fof(f414,plain,
element(sK27_skl,powerset(powerset(sK26_skl))),
inference(cnf_transformation,[status(thm)],[f413]) ).
fof(f415,plain,
sK27_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f413]) ).
fof(f416,plain,
complements_of_subsets(sK26_skl,sK27_skl) = empty_set,
inference(cnf_transformation,[status(thm)],[f413]) ).
fof(f421,plain,
! [A,B,C] :
( element(A,C)
| ~ element(B,powerset(C))
| ~ in(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f103]) ).
fof(f422,plain,
! [A,C] :
( element(A,C)
| ! [B] :
( ~ element(B,powerset(C))
| ~ in(A,B) ) ),
inference(miniscoping,[status(thm)],[f421]) ).
fof(f423,plain,
! [X0,X1,X2] :
( element(X0,X2)
| ~ element(X1,powerset(X2))
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f422]) ).
fof(f447,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f112]) ).
fof(f448,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f447]) ).
fof(f491,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(thm)],[f146]) ).
fof(f511,plain,
! [X0,X1,X2] :
( in(subset_complement(X1,X2),X0)
| ~ in(X2,complements_of_subsets(X1,X0))
| ~ element(X2,powerset(X1))
| ~ element(complements_of_subsets(X1,X0),powerset(powerset(X1)))
| ~ element(X0,powerset(powerset(X1))) ),
inference(destructive_equality_resolution,[status(thm)],[f233]) ).
fof(f536,plain,
! [X0,X1,X2] :
( in(subset_complement(X1,X2),X0)
| ~ in(X2,complements_of_subsets(X1,X0))
| ~ element(X2,powerset(X1))
| ~ element(X0,powerset(powerset(X1))) ),
inference(backward_subsumption_resolution,[status(thm)],[f511,f246]) ).
fof(f537,plain,
( element(empty_set,powerset(powerset(sK26_skl)))
| ~ element(sK27_skl,powerset(powerset(sK26_skl))) ),
inference(paramodulation,[status(thm)],[f416,f246]) ).
fof(f539,plain,
element(empty_set,powerset(powerset(sK26_skl))),
inference(forward_subsumption_resolution,[status(thm)],[f537,f414]) ).
fof(f555,plain,
complements_of_subsets(sK26_skl,complements_of_subsets(sK26_skl,sK27_skl)) = sK27_skl,
inference(resolution,[status(thm)],[f265,f414]) ).
fof(f559,plain,
complements_of_subsets(sK26_skl,empty_set) = sK27_skl,
inference(forward_demodulation,[status(thm)],[f416,f555]) ).
fof(f609,plain,
sK20_skl = empty_set,
inference(resolution,[status(thm)],[f448,f309]) ).
fof(f619,plain,
complements_of_subsets(sK26_skl,sK20_skl) = sK27_skl,
inference(backward_demodulation,[status(thm)],[f609,f559]) ).
fof(f621,plain,
element(sK20_skl,powerset(powerset(sK26_skl))),
inference(backward_demodulation,[status(thm)],[f609,f539]) ).
fof(f627,plain,
! [X0] : ~ in(X0,sK20_skl),
inference(backward_demodulation,[status(thm)],[f609,f491]) ).
fof(f629,plain,
sK27_skl != sK20_skl,
inference(backward_demodulation,[status(thm)],[f609,f415]) ).
fof(f638,plain,
! [X0] :
( in(sK1_skl(X0),X0)
| X0 = sK20_skl ),
inference(forward_demodulation,[status(thm)],[f609,f147]) ).
fof(f662,plain,
! [X0] :
( in(subset_complement(sK26_skl,X0),sK20_skl)
| ~ in(X0,sK27_skl)
| ~ element(X0,powerset(sK26_skl))
| ~ element(sK20_skl,powerset(powerset(sK26_skl))) ),
inference(paramodulation,[status(thm)],[f619,f536]) ).
fof(f663,plain,
! [X0] :
( in(subset_complement(sK26_skl,X0),sK20_skl)
| ~ in(X0,sK27_skl)
| ~ element(X0,powerset(sK26_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f662,f621]) ).
fof(f688,plain,
! [X0] :
( ~ in(X0,sK27_skl)
| ~ element(X0,powerset(sK26_skl)) ),
inference(forward_subsumption_resolution,[status(thm)],[f663,f627]) ).
fof(f689,plain,
( sK27_skl = sK20_skl
| ~ element(sK1_skl(sK27_skl),powerset(sK26_skl)) ),
inference(resolution,[status(thm)],[f688,f638]) ).
fof(f691,plain,
~ element(sK1_skl(sK27_skl),powerset(sK26_skl)),
inference(forward_subsumption_resolution,[status(thm)],[f689,f629]) ).
fof(f693,plain,
! [X0] :
( ~ element(X0,powerset(powerset(sK26_skl)))
| ~ in(sK1_skl(sK27_skl),X0) ),
inference(resolution,[status(thm)],[f691,f423]) ).
fof(f787,plain,
( sK27_skl = sK20_skl
| ~ element(sK27_skl,powerset(powerset(sK26_skl))) ),
inference(resolution,[status(thm)],[f693,f638]) ).
fof(f794,plain,
sK27_skl = sK20_skl,
inference(forward_subsumption_resolution,[status(thm)],[f787,f414]) ).
fof(f795,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f794,f629]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEU174+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.07/0.34 % Computer : n003.cluster.edu
% 0.07/0.34 % Model : x86_64 x86_64
% 0.07/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.34 % Memory : 8046.5625MB
% 0.07/0.34 % OS : Linux 6.8.0-71-generic
% 0.07/0.34 % CPULimit : 300
% 0.07/0.34 % WCLimit : 300
% 0.07/0.34 % DateTime : Mon Sep 21 05:56:30 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.15/0.39 % Refutation found
% 0.15/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.43 % Elapsed time: 0.065929 seconds
% 0.15/0.43 % CPU time: 0.208137 seconds
% 0.15/0.43 % Total memory used: 110.721 MB
% 0.15/0.43 % Net memory used: 110.455 MB
%------------------------------------------------------------------------------