%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET699+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n017.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 02:10:28 PM UTC 2026
% Result : Theorem 3.85s 0.92s
% Output : CNFRefutation 3.85s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 15
% Syntax : Number of formulae : 96 ( 5 unt; 10 def)
% Number of atoms : 265 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 277 ( 108 ~; 117 |; 31 &)
% ( 17 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 14 ( 13 usr; 11 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 117 ( 109 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,A,B] :
( member(X,intersection(A,B))
<=> ( member(X,B)
& member(X,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( ~ member(B,A)
& member(B,E) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B,E] :
( ( subset(B,E)
& subset(A,E) )
=> ( subset(A,B)
<=> subset(intersection(A,difference(E,B)),difference(E,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B,E] :
( ( subset(B,E)
& subset(A,E) )
=> ( subset(A,B)
<=> subset(intersection(A,difference(E,B)),difference(E,A)) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f15,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)],[f14]) ).
fof(f16,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)],[f15]) ).
fof(f17,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))],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,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(f22,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)],[f21]) ).
fof(f23,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X1,X0)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f30,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(f31,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)],[f30]) ).
fof(f32,plain,
! [X0,X1,X2] :
( member(X0,X1)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f41,plain,
! [B,A,E] :
( ( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f42,plain,
( ! [B,A,E] :
( member(B,A)
| ~ member(B,E)
| member(B,difference(E,A)) )
& ! [B,A,E] :
( ( ~ member(B,A)
& member(B,E) )
| ~ member(B,difference(E,A)) ) ),
inference(miniscoping,[status(thm)],[f41]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f45,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f68,plain,
? [A,B,E] :
( ( subset(A,B)
<~> subset(intersection(A,difference(E,B)),difference(E,A)) )
& subset(B,E)
& subset(A,E) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
? [A,B,E] :
( ( ~ subset(intersection(A,difference(E,B)),difference(E,A))
| ~ subset(A,B) )
& ( subset(intersection(A,difference(E,B)),difference(E,A))
| subset(A,B) )
& subset(B,E)
& subset(A,E) ),
inference(NNF_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
( ( ~ subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),difference(sK5_skl,sK3_skl))
| ~ subset(sK3_skl,sK4_skl) )
& ( subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),difference(sK5_skl,sK3_skl))
| subset(sK3_skl,sK4_skl) )
& subset(sK4_skl,sK5_skl)
& subset(sK3_skl,sK5_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(A,sK3_skl),skolemize(B,sK4_skl),skolemize(E,sK5_skl)],[f69]) ).
fof(f71,plain,
subset(sK3_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
subset(sK4_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,plain,
( subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),difference(sK5_skl,sK3_skl))
| subset(sK3_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f74,plain,
( ~ subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),difference(sK5_skl,sK3_skl))
| ~ subset(sK3_skl,sK4_skl) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f75,definition,
( sQ0_spl
<=> subset(sK3_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ0_spl
| subset(sK3_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,definition,
( sQ1_spl
<=> subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),difference(sK5_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( ~ sQ1_spl
| subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),difference(sK5_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f80,plain,
( sQ1_spl
| ~ subset(intersection(sK3_skl,difference(sK5_skl,sK4_skl)),difference(sK5_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f73,f75,f78]) ).
fof(f82,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f74,f75,f78]) ).
fof(f86,plain,
! [X0] :
( ~ sQ1_spl
| member(X0,difference(sK5_skl,sK3_skl))
| ~ member(X0,intersection(sK3_skl,difference(sK5_skl,sK4_skl))) ),
inference(resolution,[status(thm)],[f18,f79]) ).
fof(f88,plain,
! [X0] :
( member(X0,sK5_skl)
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f18,f71]) ).
fof(f93,plain,
! [X0] :
( ~ sQ1_spl
| ~ member(X0,difference(sK5_skl,sK4_skl))
| ~ member(X0,sK3_skl)
| member(X0,difference(sK5_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f86,f34]) ).
fof(f94,plain,
! [X0] :
( ~ sQ1_spl
| ~ member(X0,difference(sK5_skl,sK4_skl))
| ~ member(X0,sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f93,f44]) ).
fof(f95,plain,
! [X0] :
( ~ sQ1_spl
| member(X0,sK4_skl)
| ~ member(X0,sK5_skl)
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f94,f45]) ).
fof(f96,plain,
! [X0] :
( ~ sQ1_spl
| member(X0,sK4_skl)
| ~ member(X0,sK3_skl) ),
inference(forward_subsumption_resolution,[status(thm)],[f95,f88]) ).
fof(f101,plain,
! [X0] :
( ~ sQ1_spl
| member(sK0_skl(X0,sK3_skl),sK4_skl)
| subset(sK3_skl,X0) ),
inference(resolution,[status(thm)],[f19,f96]) ).
fof(f105,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,intersection(X0,X1)),X1)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f19,f33]) ).
fof(f106,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,intersection(X0,X1)),X0)
| subset(intersection(X0,X1),X2) ),
inference(resolution,[status(thm)],[f19,f32]) ).
fof(f130,plain,
( ~ subset(sK5_skl,sK4_skl)
| equal_set(sK5_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f25,f72]) ).
fof(f131,plain,
( ~ subset(sK5_skl,sK3_skl)
| equal_set(sK5_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f25,f71]) ).
fof(f140,definition,
( sQ4_spl
<=> equal_set(sK5_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f141,plain,
( ~ sQ4_spl
| equal_set(sK5_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f140]) ).
fof(f143,definition,
( sQ5_spl
<=> subset(sK5_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f145,plain,
( sQ5_spl
| ~ subset(sK5_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f146,plain,
( ~ sQ5_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f130,f140,f143]) ).
fof(f147,definition,
( sQ6_spl
<=> equal_set(sK5_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( ~ sQ6_spl
| equal_set(sK5_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,definition,
( sQ7_spl
<=> subset(sK5_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f152,plain,
( sQ7_spl
| ~ subset(sK5_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f153,plain,
( ~ sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f131,f147,f150]) ).
fof(f158,plain,
( ~ sQ6_spl
| subset(sK5_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f148,f23]) ).
fof(f160,plain,
( ~ sQ4_spl
| subset(sK5_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f141,f23]) ).
fof(f161,plain,
( ~ sQ6_spl
| ~ subset(sK3_skl,sK5_skl)
| equal_set(sK3_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f158,f25]) ).
fof(f163,definition,
( sQ8_spl
<=> equal_set(sK3_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ8_spl])],[split_symbol_definition]) ).
fof(f164,plain,
( ~ sQ8_spl
| equal_set(sK3_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,definition,
( sQ9_spl
<=> subset(sK3_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f168,plain,
( sQ9_spl
| ~ subset(sK3_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f169,plain,
( ~ sQ6_spl
| ~ sQ9_spl
| sQ8_spl ),
inference(split_clause,[status(thm)],[f161,f163,f166,f147]) ).
fof(f170,plain,
( sQ9_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f71]) ).
fof(f171,plain,
sQ9_spl,
inference(contradiction_clause,[status(thm)],[f170]) ).
fof(f172,plain,
( ~ sQ4_spl
| ~ subset(sK4_skl,sK5_skl)
| equal_set(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f160,f25]) ).
fof(f174,definition,
( sQ10_spl
<=> equal_set(sK4_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f175,plain,
( ~ sQ10_spl
| equal_set(sK4_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f174]) ).
fof(f177,definition,
( sQ11_spl
<=> subset(sK4_skl,sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f179,plain,
( sQ11_spl
| ~ subset(sK4_skl,sK5_skl) ),
inference(component_clause,[status(thm)],[f177]) ).
fof(f180,plain,
( ~ sQ4_spl
| ~ sQ11_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f172,f174,f177,f140]) ).
fof(f181,plain,
( sQ11_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f179,f72]) ).
fof(f182,plain,
sQ11_spl,
inference(contradiction_clause,[status(thm)],[f181]) ).
fof(f200,plain,
( ~ sQ8_spl
| subset(sK5_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f164,f24]) ).
fof(f202,plain,
( ~ sQ8_spl
| sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f200,f152]) ).
fof(f203,plain,
( ~ sQ8_spl
| sQ7_spl ),
inference(contradiction_clause,[status(thm)],[f202]) ).
fof(f204,plain,
( ~ sQ10_spl
| subset(sK5_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f175,f24]) ).
fof(f206,plain,
( ~ sQ10_spl
| sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f145]) ).
fof(f207,plain,
( ~ sQ10_spl
| sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f206]) ).
fof(f224,plain,
( ~ sQ1_spl
| subset(sK3_skl,sK4_skl)
| subset(sK3_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f101,f20]) ).
fof(f226,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f224,f75,f78]) ).
fof(f228,plain,
! [X0] :
( ~ sQ0_spl
| member(X0,sK4_skl)
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f76,f18]) ).
fof(f377,plain,
! [X0,X1,X2,X3] :
( ~ member(sK0_skl(X3,intersection(X0,difference(X1,X2))),X2)
| subset(intersection(X0,difference(X1,X2)),X3) ),
inference(resolution,[status(thm)],[f105,f44]) ).
fof(f399,plain,
! [X0,X1] :
( ~ sQ0_spl
| member(sK0_skl(X1,intersection(sK3_skl,X0)),sK4_skl)
| subset(intersection(sK3_skl,X0),X1) ),
inference(resolution,[status(thm)],[f106,f228]) ).
fof(f4039,plain,
! [X0,X1] :
( ~ sQ0_spl
| subset(intersection(sK3_skl,difference(X0,sK4_skl)),X1)
| subset(intersection(sK3_skl,difference(X0,sK4_skl)),X1) ),
inference(resolution,[status(thm)],[f377,f399]) ).
fof(f4079,plain,
! [X0,X1] :
( ~ sQ0_spl
| subset(intersection(sK3_skl,difference(X0,sK4_skl)),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f4039]) ).
fof(f4221,plain,
( sQ1_spl
| ~ sQ0_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f80,f4079]) ).
fof(f4226,plain,
( sQ1_spl
| ~ sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f4221]) ).
fof(f4227,plain,
$false,
inference(sat_refutation,[status(thm)],[f81,f82,f146,f153,f169,f171,f180,f182,f203,f207,f226,f4226]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET699+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.09/0.36 % Computer : n017.cluster.edu
% 0.09/0.36 % Model : x86_64 x86_64
% 0.09/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.36 % Memory : 8046.5625MB
% 0.09/0.36 % OS : Linux 6.8.0-71-generic
% 0.09/0.36 % CPULimit : 300
% 0.09/0.36 % WCLimit : 300
% 0.09/0.36 % DateTime : Mon Sep 21 05:28:12 UTC 2026
% 0.09/0.36 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 3.85/0.92 % Refutation found
% 3.85/0.92 % SZS status Theorem for theBenchmark: Theorem is valid
% 3.85/0.92 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 3.85/0.96 % Elapsed time: 0.575767 seconds
% 3.85/0.96 % CPU time: 4.195268 seconds
% 3.85/0.96 % Total memory used: 129.786 MB
% 3.85/0.96 % Net memory used: 122.011 MB
%------------------------------------------------------------------------------