%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET812+4 : TPTP v9.3.1. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n018.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 02:10:40 PM UTC 2026
% Result : Theorem 0.14s 0.39s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 5 unt; 5 def)
% Number of atoms : 196 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 208 ( 76 ~; 80 |; 36 &)
% ( 12 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 11 ( 10 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 3 con; 0-2 aty)
% Number of variables : 87 ( 82 !; 5 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,A] :
( member(X,power_set(A))
<=> subset(X,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,B)
& member(X,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A] :
( member(A,on)
<=> ( ! [X] :
( member(X,A)
=> subset(X,A) )
& strict_well_order(member_predicate,A)
& set(A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,conjecture,
! [A] :
( member(A,on)
=> equal_set(A,intersection(A,power_set(A))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f21,negated_conjecture,
~ ! [A] :
( member(A,on)
=> equal_set(A,intersection(A,power_set(A))) ),
inference(negated_conjecture,[status(cth)],[f20]) ).
fof(f22,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f23,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
( ! [A,B] :
( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f23]) ).
fof(f25,plain,
( ! [A,B] :
( ( ~ member(sK0_skl(B,A),B)
& member(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f24]) ).
fof(f27,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
fof(f29,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f30,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f34,plain,
! [X,A] :
( ( ~ subset(X,A)
| member(X,power_set(A)) )
& ( subset(X,A)
| ~ member(X,power_set(A)) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f35,plain,
( ! [X,A] :
( ~ subset(X,A)
| member(X,power_set(A)) )
& ! [X,A] :
( subset(X,A)
| ~ member(X,power_set(A)) ) ),
inference(miniscoping,[status(thm)],[f34]) ).
fof(f37,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| member(X0,power_set(X1)) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f38,plain,
! [X,A,B] :
( ( ~ member(X,B)
| ~ member(X,A)
| member(X,intersection(A,B)) )
& ( ( member(X,B)
& member(X,A) )
| ~ member(X,intersection(A,B)) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f39,plain,
( ! [X,A,B] :
( ~ member(X,B)
| ~ member(X,A)
| member(X,intersection(A,B)) )
& ! [X,A,B] :
( ( member(X,B)
& member(X,A) )
| ~ member(X,intersection(A,B)) ) ),
inference(miniscoping,[status(thm)],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f76,plain,
! [A] :
( member(A,on)
<=> ( ! [X] :
( subset(X,A)
| ~ member(X,A) )
& strict_well_order(member_predicate,A)
& set(A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f12]) ).
fof(f77,plain,
! [A] :
( ( ? [X] :
( ~ subset(X,A)
& member(X,A) )
| ~ strict_well_order(member_predicate,A)
| ~ set(A)
| member(A,on) )
& ( ( ! [X] :
( subset(X,A)
| ~ member(X,A) )
& strict_well_order(member_predicate,A)
& set(A) )
| ~ member(A,on) ) ),
inference(NNF_transformation,[status(thm)],[f76]) ).
fof(f78,plain,
( ! [A] :
( ? [X] :
( ~ subset(X,A)
& member(X,A) )
| ~ strict_well_order(member_predicate,A)
| ~ set(A)
| member(A,on) )
& ! [A] :
( ( ! [X] :
( subset(X,A)
| ~ member(X,A) )
& strict_well_order(member_predicate,A)
& set(A) )
| ~ member(A,on) ) ),
inference(miniscoping,[status(thm)],[f77]) ).
fof(f79,plain,
( ! [A] :
( ( ~ subset(sK3_skl(A),A)
& member(sK3_skl(A),A) )
| ~ strict_well_order(member_predicate,A)
| ~ set(A)
| member(A,on) )
& ! [A] :
( ( ! [X] :
( subset(X,A)
| ~ member(X,A) )
& strict_well_order(member_predicate,A)
& set(A) )
| ~ member(A,on) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(X,sK3_skl(A))],[f78]) ).
fof(f80,plain,
! [X0] :
( set(X0)
| ~ member(X0,on) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f82,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ member(X1,X0)
| ~ member(X0,on) ),
inference(cnf_transformation,[status(thm)],[f79]) ).
fof(f132,plain,
? [A] :
( ~ equal_set(A,intersection(A,power_set(A)))
& member(A,on) ),
inference(pre_NNF_transformation,[status(thm)],[f21]) ).
fof(f133,plain,
( ~ equal_set(sK13_skl,intersection(sK13_skl,power_set(sK13_skl)))
& member(sK13_skl,on) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK13_skl]),skolemize(A,sK13_skl)],[f132]) ).
fof(f134,plain,
member(sK13_skl,on),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f135,plain,
~ equal_set(sK13_skl,intersection(sK13_skl,power_set(sK13_skl))),
inference(cnf_transformation,[status(thm)],[f133]) ).
fof(f146,plain,
( ~ subset(intersection(sK13_skl,power_set(sK13_skl)),sK13_skl)
| ~ subset(sK13_skl,intersection(sK13_skl,power_set(sK13_skl))) ),
inference(resolution,[status(thm)],[f33,f135]) ).
fof(f147,definition,
( sQ0_spl
<=> subset(sK13_skl,intersection(sK13_skl,power_set(sK13_skl))) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f149,plain,
( sQ0_spl
| ~ subset(sK13_skl,intersection(sK13_skl,power_set(sK13_skl))) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,definition,
( sQ1_spl
<=> subset(intersection(sK13_skl,power_set(sK13_skl)),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( sQ1_spl
| ~ subset(intersection(sK13_skl,power_set(sK13_skl)),sK13_skl) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f146,f147,f150]) ).
fof(f159,plain,
! [X0] :
( subset(X0,sK13_skl)
| ~ member(X0,sK13_skl) ),
inference(resolution,[status(thm)],[f82,f134]) ).
fof(f168,plain,
( sQ0_spl
| member(sK0_skl(intersection(sK13_skl,power_set(sK13_skl)),sK13_skl),sK13_skl) ),
inference(resolution,[status(thm)],[f27,f149]) ).
fof(f170,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(intersection(X1,X2),X0),X2)
| ~ member(sK0_skl(intersection(X1,X2),X0),X1)
| subset(X0,intersection(X1,X2)) ),
inference(resolution,[status(thm)],[f28,f42]) ).
fof(f191,plain,
( sQ0_spl
| ~ member(sK0_skl(intersection(sK13_skl,power_set(sK13_skl)),sK13_skl),power_set(sK13_skl))
| ~ member(sK0_skl(intersection(sK13_skl,power_set(sK13_skl)),sK13_skl),sK13_skl) ),
inference(resolution,[status(thm)],[f170,f149]) ).
fof(f193,definition,
( sQ2_spl
<=> member(sK0_skl(intersection(sK13_skl,power_set(sK13_skl)),sK13_skl),sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f195,plain,
( sQ2_spl
| ~ member(sK0_skl(intersection(sK13_skl,power_set(sK13_skl)),sK13_skl),sK13_skl) ),
inference(component_clause,[status(thm)],[f193]) ).
fof(f196,definition,
( sQ3_spl
<=> member(sK0_skl(intersection(sK13_skl,power_set(sK13_skl)),sK13_skl),power_set(sK13_skl)) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f198,plain,
( sQ3_spl
| ~ member(sK0_skl(intersection(sK13_skl,power_set(sK13_skl)),sK13_skl),power_set(sK13_skl)) ),
inference(component_clause,[status(thm)],[f196]) ).
fof(f199,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f191,f193,f196,f147]) ).
fof(f202,plain,
( sQ1_spl
| member(sK0_skl(sK13_skl,intersection(sK13_skl,power_set(sK13_skl))),intersection(sK13_skl,power_set(sK13_skl))) ),
inference(resolution,[status(thm)],[f152,f27]) ).
fof(f218,plain,
( sQ3_spl
| ~ subset(sK0_skl(intersection(sK13_skl,power_set(sK13_skl)),sK13_skl),sK13_skl) ),
inference(resolution,[status(thm)],[f198,f37]) ).
fof(f219,plain,
( sQ3_spl
| ~ member(sK0_skl(intersection(sK13_skl,power_set(sK13_skl)),sK13_skl),sK13_skl) ),
inference(resolution,[status(thm)],[f218,f159]) ).
fof(f225,plain,
( sQ1_spl
| member(sK0_skl(sK13_skl,intersection(sK13_skl,power_set(sK13_skl))),sK13_skl) ),
inference(resolution,[status(thm)],[f202,f40]) ).
fof(f234,plain,
( sQ1_spl
| subset(intersection(sK13_skl,power_set(sK13_skl)),sK13_skl) ),
inference(resolution,[status(thm)],[f225,f28]) ).
fof(f236,plain,
( sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f234,f152]) ).
fof(f237,plain,
sQ1_spl,
inference(contradiction_clause,[status(thm)],[f236]) ).
fof(f270,definition,
( sQ7_spl
<=> set(sK13_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f272,plain,
( sQ7_spl
| ~ set(sK13_skl) ),
inference(component_clause,[status(thm)],[f270]) ).
fof(f284,plain,
( sQ7_spl
| ~ member(sK13_skl,on) ),
inference(resolution,[status(thm)],[f272,f80]) ).
fof(f285,plain,
( sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f284,f134]) ).
fof(f286,plain,
sQ7_spl,
inference(contradiction_clause,[status(thm)],[f285]) ).
fof(f295,plain,
( sQ0_spl
| sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f195]) ).
fof(f296,plain,
( sQ0_spl
| sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f295]) ).
fof(f297,plain,
( sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f219,f193,f196]) ).
fof(f298,plain,
$false,
inference(sat_refutation,[status(thm)],[f153,f199,f237,f286,f296,f297]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET812+4 : TPTP v9.3.1. Released v3.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n018.cluster.edu
% 0.10/0.36 % Model : x86_64 x86_64
% 0.10/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.36 % Memory : 8046.5625MB
% 0.10/0.36 % OS : Linux 6.8.0-71-generic
% 0.10/0.36 % CPULimit : 300
% 0.10/0.36 % WCLimit : 300
% 0.10/0.36 % DateTime : Mon Sep 21 05:41:14 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.39 % Refutation found
% 0.14/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.41 % Elapsed time: 0.051540 seconds
% 0.14/0.41 % CPU time: 0.159530 seconds
% 0.14/0.41 % Total memory used: 82.975 MB
% 0.14/0.41 % Net memory used: 82.818 MB
%------------------------------------------------------------------------------