%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET606+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n026.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 02:10:13 PM UTC 2026
% Result : Theorem 0.14s 0.40s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 10
% Syntax : Number of formulae : 58 ( 7 unt; 6 def)
% Number of atoms : 150 ( 14 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 160 ( 68 ~; 69 |; 12 &)
% ( 9 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 62 ( 58 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] :
( ! [D] :
( member(D,B)
<=> member(D,C) )
=> B = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B,C] : difference(B,intersection(B,C)) = difference(B,C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B,C] : difference(B,intersection(B,C)) = difference(B,C),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [B,C] :
( B = C
| ? [D] :
( member(D,B)
<~> member(D,C) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f12,plain,
! [B,C] :
( B = C
| ? [D] :
( ( ~ member(D,C)
| ~ member(D,B) )
& ( member(D,C)
| member(D,B) ) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
! [B,C] :
( B = C
| ( ( ~ member(sK0_skl(C,B),C)
| ~ member(sK0_skl(C,B),B) )
& ( member(sK0_skl(C,B),C)
| member(sK0_skl(C,B),B) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f12]) ).
fof(f14,plain,
! [X0,X1] :
( X1 = X0
| member(sK0_skl(X0,X1),X0)
| member(sK0_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
! [X0,X1] :
( X1 = X0
| ~ member(sK0_skl(X0,X1),X0)
| ~ member(sK0_skl(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f17,plain,
( ! [B,C,D] :
( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ! [B,C,D] :
( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(miniscoping,[status(thm)],[f16]) ).
fof(f19,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [B,C,D] :
( ( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f22,plain,
( ! [B,C,D] :
( member(D,C)
| ~ member(D,B)
| member(D,difference(B,C)) )
& ! [B,C,D] :
( ( ~ member(D,C)
& member(D,B) )
| ~ member(D,difference(B,C)) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f23,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f47,plain,
? [B,C] : difference(B,intersection(B,C)) != difference(B,C),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f48,plain,
difference(sK3_skl,intersection(sK3_skl,sK4_skl)) != difference(sK3_skl,sK4_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl]),skolemize(B,sK3_skl),skolemize(C,sK4_skl)],[f47]) ).
fof(f49,plain,
difference(sK3_skl,intersection(sK3_skl,sK4_skl)) != difference(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f72,plain,
( ~ member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),difference(sK3_skl,intersection(sK3_skl,sK4_skl)))
| ~ member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f15,f49]) ).
fof(f80,definition,
( sQ4_spl
<=> member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f81,plain,
( ~ sQ4_spl
| member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f82,plain,
( sQ4_spl
| ~ member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,definition,
( sQ5_spl
<=> member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),difference(sK3_skl,intersection(sK3_skl,sK4_skl))) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f84,plain,
( ~ sQ5_spl
| member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),difference(sK3_skl,intersection(sK3_skl,sK4_skl))) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f85,plain,
( sQ5_spl
| ~ member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),difference(sK3_skl,intersection(sK3_skl,sK4_skl))) ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f72,f80,f83]) ).
fof(f110,plain,
( sQ4_spl
| difference(sK3_skl,sK4_skl) = difference(sK3_skl,intersection(sK3_skl,sK4_skl))
| member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),difference(sK3_skl,intersection(sK3_skl,sK4_skl))) ),
inference(resolution,[status(thm)],[f82,f14]) ).
fof(f111,plain,
( sQ4_spl
| member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),sK4_skl)
| ~ member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f82,f25]) ).
fof(f116,definition,
( sQ10_spl
<=> difference(sK3_skl,sK4_skl) = difference(sK3_skl,intersection(sK3_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f117,plain,
( ~ sQ10_spl
| difference(sK3_skl,sK4_skl) = difference(sK3_skl,intersection(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f116]) ).
fof(f119,plain,
( sQ4_spl
| sQ10_spl
| sQ5_spl ),
inference(split_clause,[status(thm)],[f110,f83,f116,f80]) ).
fof(f120,definition,
( sQ11_spl
<=> member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( sQ11_spl
| ~ member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),sK3_skl) ),
inference(component_clause,[status(thm)],[f120]) ).
fof(f123,definition,
( sQ12_spl
<=> member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ12_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( sQ4_spl
| sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f111,f120,f123,f80]) ).
fof(f127,plain,
( ~ sQ10_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f117,f49]) ).
fof(f128,plain,
~ sQ10_spl,
inference(contradiction_clause,[status(thm)],[f127]) ).
fof(f143,plain,
( ~ sQ4_spl
| ~ member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),sK4_skl) ),
inference(resolution,[status(thm)],[f81,f24]) ).
fof(f146,plain,
! [X0] :
( ~ sQ4_spl
| ~ member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),intersection(X0,sK4_skl)) ),
inference(resolution,[status(thm)],[f143,f19]) ).
fof(f158,plain,
! [X0] :
( sQ11_spl
| ~ member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),difference(sK3_skl,X0)) ),
inference(resolution,[status(thm)],[f122,f23]) ).
fof(f161,plain,
( ~ sQ5_spl
| sQ11_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f84,f158]) ).
fof(f162,plain,
( ~ sQ5_spl
| sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f161]) ).
fof(f211,plain,
( ~ sQ5_spl
| ~ member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),intersection(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f84,f24]) ).
fof(f254,plain,
( ~ sQ5_spl
| ~ member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),sK4_skl)
| ~ member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f211,f20]) ).
fof(f259,plain,
( ~ sQ5_spl
| ~ sQ12_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f254,f120,f123,f83]) ).
fof(f311,plain,
( sQ5_spl
| member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),intersection(sK3_skl,sK4_skl))
| ~ member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),sK3_skl) ),
inference(resolution,[status(thm)],[f85,f25]) ).
fof(f317,definition,
( sQ24_spl
<=> member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),intersection(sK3_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ24_spl])],[split_symbol_definition]) ).
fof(f318,plain,
( ~ sQ24_spl
| member(sK0_skl(difference(sK3_skl,intersection(sK3_skl,sK4_skl)),difference(sK3_skl,sK4_skl)),intersection(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f317]) ).
fof(f320,plain,
( sQ5_spl
| sQ24_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f311,f120,f317,f83]) ).
fof(f321,plain,
( ~ sQ4_spl
| sQ11_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f81,f158]) ).
fof(f322,plain,
( ~ sQ4_spl
| sQ11_spl ),
inference(contradiction_clause,[status(thm)],[f321]) ).
fof(f323,plain,
( ~ sQ24_spl
| ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f318,f146]) ).
fof(f324,plain,
( ~ sQ24_spl
| ~ sQ4_spl ),
inference(contradiction_clause,[status(thm)],[f323]) ).
fof(f325,plain,
$false,
inference(sat_refutation,[status(thm)],[f86,f119,f126,f128,f162,f259,f320,f322,f324]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET606+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n026.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:31:21 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.14/0.40 % Refutation found
% 0.14/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.43 % Elapsed time: 0.063806 seconds
% 0.14/0.43 % CPU time: 0.205441 seconds
% 0.14/0.43 % Total memory used: 103.063 MB
% 0.14/0.43 % Net memory used: 102.539 MB
%------------------------------------------------------------------------------