%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET007-1 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% Computer : n016.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 02:08:47 PM UTC 2026
% Result : Unsatisfiable 0.13s 0.41s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 22
% Syntax : Number of formulae : 94 ( 12 unt; 8 def)
% Number of atoms : 240 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 264 ( 118 ~; 138 |; 0 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 12 ( 11 usr; 9 prp; 0-3 aty)
% Number of functors : 8 ( 8 usr; 7 con; 0-3 aty)
% Number of variables : 109 ( 109 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [Set1,Set2,Union,Element] :
( member(Element,Set2)
| member(Element,Set1)
| ~ member(Element,Union)
| ~ union(Set1,Set2,Union) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Set1,Set2,Union,Element] :
( member(Element,Union)
| ~ member(Element,Set1)
| ~ union(Set1,Set2,Union) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Set1,Set2,Union,Element] :
( member(Element,Union)
| ~ member(Element,Set2)
| ~ union(Set1,Set2,Union) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Set1,Set2,Union] :
( member(g(Set1,Set2,Union),Union)
| member(g(Set1,Set2,Union),Set2)
| member(g(Set1,Set2,Union),Set1)
| union(Set1,Set2,Union) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Set1,Set2,Union] :
( union(Set1,Set2,Union)
| ~ member(g(Set1,Set2,Union),Union)
| ~ member(g(Set1,Set2,Union),Set1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Set1,Set2,Union] :
( union(Set1,Set2,Union)
| ~ member(g(Set1,Set2,Union),Union)
| ~ member(g(Set1,Set2,Union),Set2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [Set1,Set2,Intersection,Element] :
( member(Element,Set1)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [Set1,Set2,Intersection,Element] :
( member(Element,Set2)
| ~ member(Element,Intersection)
| ~ intersection(Set1,Set2,Intersection) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [Set1,Set2,Intersection,Element] :
( member(Element,Intersection)
| ~ member(Element,Set1)
| ~ member(Element,Set2)
| ~ intersection(Set1,Set2,Intersection) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,axiom,
union(b,c,bUc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
intersection(a,b,aIb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
intersection(a,c,aIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
intersection(a,bUc,aI_bUc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,negated_conjecture,
~ union(aIb,aIc,aI_bUc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,plain,
! [Set2,Element] :
( member(Element,Set2)
| ! [Set1] :
( member(Element,Set1)
| ! [Union] :
( ~ member(Element,Union)
| ~ union(Set1,Set2,Union) ) ) ),
inference(miniscoping,[status(thm)],[f7]) ).
fof(f32,plain,
! [X0,X1,X2,X3] :
( member(X3,X1)
| member(X3,X0)
| ~ member(X3,X2)
| ~ union(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
! [Union,Element] :
( member(Element,Union)
| ! [Set1] :
( ~ member(Element,Set1)
| ! [Set2] : ~ union(Set1,Set2,Union) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f34,plain,
! [X0,X1,X2,X3] :
( member(X3,X2)
| ~ member(X3,X0)
| ~ union(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f33]) ).
fof(f35,plain,
! [Union,Element] :
( member(Element,Union)
| ! [Set2] :
( ~ member(Element,Set2)
| ! [Set1] : ~ union(Set1,Set2,Union) ) ),
inference(miniscoping,[status(thm)],[f9]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( member(X3,X2)
| ~ member(X3,X1)
| ~ union(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( member(g(X0,X1,X2),X2)
| member(g(X0,X1,X2),X1)
| member(g(X0,X1,X2),X0)
| union(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f38,plain,
! [X0,X1,X2] :
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X0) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f39,plain,
! [X0,X1,X2] :
( union(X0,X1,X2)
| ~ member(g(X0,X1,X2),X2)
| ~ member(g(X0,X1,X2),X1) ),
inference(cnf_transformation,[status(thm)],[f12]) ).
fof(f40,plain,
! [Set1,Element] :
( member(Element,Set1)
| ! [Intersection] :
( ~ member(Element,Intersection)
| ! [Set2] : ~ intersection(Set1,Set2,Intersection) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f41,plain,
! [X0,X1,X2,X3] :
( member(X3,X0)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f40]) ).
fof(f42,plain,
! [Set2,Element] :
( member(Element,Set2)
| ! [Intersection] :
( ~ member(Element,Intersection)
| ! [Set1] : ~ intersection(Set1,Set2,Intersection) ) ),
inference(miniscoping,[status(thm)],[f14]) ).
fof(f43,plain,
! [X0,X1,X2,X3] :
( member(X3,X1)
| ~ member(X3,X2)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f42]) ).
fof(f44,plain,
! [Intersection,Element] :
( member(Element,Intersection)
| ! [Set1] :
( ~ member(Element,Set1)
| ! [Set2] :
( ~ member(Element,Set2)
| ~ intersection(Set1,Set2,Intersection) ) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f45,plain,
! [X0,X1,X2,X3] :
( member(X3,X2)
| ~ member(X3,X0)
| ~ member(X3,X1)
| ~ intersection(X0,X1,X2) ),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f49,plain,
union(b,c,bUc),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f50,plain,
intersection(a,b,aIb),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f51,plain,
intersection(a,c,aIc),
inference(cnf_transformation,[status(thm)],[f21]) ).
fof(f52,plain,
intersection(a,bUc,aI_bUc),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f53,plain,
~ union(aIb,aIc,aI_bUc),
inference(cnf_transformation,[status(thm)],[f23]) ).
fof(f59,plain,
( ~ member(g(aIb,aIc,aI_bUc),aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),aIb) ),
inference(resolution,[status(thm)],[f38,f53]) ).
fof(f60,definition,
( sQ0_spl
<=> member(g(aIb,aIc,aI_bUc),aIb) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f62,plain,
( sQ0_spl
| ~ member(g(aIb,aIc,aI_bUc),aIb) ),
inference(component_clause,[status(thm)],[f60]) ).
fof(f63,definition,
( sQ1_spl
<=> member(g(aIb,aIc,aI_bUc),aI_bUc) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( ~ sQ1_spl
| member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f65,plain,
( sQ1_spl
| ~ member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(component_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f59,f60,f63]) ).
fof(f67,plain,
! [X0,X1] :
( sQ0_spl
| ~ member(g(aIb,aIc,aI_bUc),X0)
| ~ member(g(aIb,aIc,aI_bUc),X1)
| ~ intersection(X0,X1,aIb) ),
inference(resolution,[status(thm)],[f62,f45]) ).
fof(f73,plain,
( sQ0_spl
| ~ member(g(aIb,aIc,aI_bUc),a)
| ~ member(g(aIb,aIc,aI_bUc),b) ),
inference(resolution,[status(thm)],[f67,f50]) ).
fof(f74,definition,
( sQ2_spl
<=> member(g(aIb,aIc,aI_bUc),b) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f77,definition,
( sQ3_spl
<=> member(g(aIb,aIc,aI_bUc),a) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f79,plain,
( sQ3_spl
| ~ member(g(aIb,aIc,aI_bUc),a) ),
inference(component_clause,[status(thm)],[f77]) ).
fof(f80,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f73,f74,f77,f60]) ).
fof(f81,plain,
! [X0,X1] :
( sQ1_spl
| ~ member(g(aIb,aIc,aI_bUc),X0)
| ~ member(g(aIb,aIc,aI_bUc),X1)
| ~ intersection(X0,X1,aI_bUc) ),
inference(resolution,[status(thm)],[f65,f45]) ).
fof(f90,plain,
! [X0,X1] :
( sQ3_spl
| ~ member(g(aIb,aIc,aI_bUc),X1)
| ~ intersection(a,X0,X1) ),
inference(resolution,[status(thm)],[f79,f41]) ).
fof(f95,plain,
( sQ3_spl
| ~ member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(resolution,[status(thm)],[f90,f52]) ).
fof(f96,plain,
( sQ3_spl
| ~ member(g(aIb,aIc,aI_bUc),aIc) ),
inference(resolution,[status(thm)],[f90,f51]) ).
fof(f97,plain,
( sQ3_spl
| ~ member(g(aIb,aIc,aI_bUc),aIb) ),
inference(resolution,[status(thm)],[f90,f50]) ).
fof(f129,plain,
! [X0] :
( member(X0,c)
| member(X0,b)
| ~ member(X0,bUc) ),
inference(resolution,[status(thm)],[f32,f49]) ).
fof(f147,definition,
( sQ5_spl
<=> member(g(aIb,aIc,aI_bUc),aIc) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f148,plain,
( ~ sQ5_spl
| member(g(aIb,aIc,aI_bUc),aIc) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f149,plain,
( sQ5_spl
| ~ member(g(aIb,aIc,aI_bUc),aIc) ),
inference(component_clause,[status(thm)],[f147]) ).
fof(f150,definition,
( sQ6_spl
<=> union(aIb,aIc,aI_bUc) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f151,plain,
( ~ sQ6_spl
| union(aIb,aIc,aI_bUc) ),
inference(component_clause,[status(thm)],[f150]) ).
fof(f167,plain,
( ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f53]) ).
fof(f168,plain,
~ sQ6_spl,
inference(contradiction_clause,[status(thm)],[f167]) ).
fof(f174,plain,
( sQ3_spl
| member(g(aIb,aIc,aI_bUc),aIc)
| member(g(aIb,aIc,aI_bUc),aIb)
| union(aIb,aIc,aI_bUc) ),
inference(resolution,[status(thm)],[f95,f37]) ).
fof(f183,plain,
( sQ3_spl
| sQ5_spl
| sQ0_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f174,f150,f60,f147,f77]) ).
fof(f185,plain,
( ~ sQ5_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f148,f96]) ).
fof(f186,plain,
( ~ sQ5_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f185]) ).
fof(f201,plain,
! [X0,X1] :
( sQ5_spl
| ~ member(g(aIb,aIc,aI_bUc),X0)
| ~ member(g(aIb,aIc,aI_bUc),X1)
| ~ intersection(X0,X1,aIc) ),
inference(resolution,[status(thm)],[f149,f45]) ).
fof(f208,plain,
( sQ1_spl
| member(g(aIb,aIc,aI_bUc),aIc)
| member(g(aIb,aIc,aI_bUc),aIb)
| union(aIb,aIc,aI_bUc) ),
inference(resolution,[status(thm)],[f65,f37]) ).
fof(f217,plain,
( sQ1_spl
| sQ5_spl
| sQ0_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f208,f150,f60,f147,f63]) ).
fof(f222,plain,
( sQ1_spl
| ~ member(g(aIb,aIc,aI_bUc),a)
| ~ member(g(aIb,aIc,aI_bUc),bUc) ),
inference(resolution,[status(thm)],[f81,f52]) ).
fof(f223,definition,
( sQ11_spl
<=> member(g(aIb,aIc,aI_bUc),bUc) ),
introduced(definition,[new_symbols(definition,[sQ11_spl])],[split_symbol_definition]) ).
fof(f225,plain,
( sQ11_spl
| ~ member(g(aIb,aIc,aI_bUc),bUc) ),
inference(component_clause,[status(thm)],[f223]) ).
fof(f226,plain,
( sQ1_spl
| ~ sQ3_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f222,f223,f77,f63]) ).
fof(f248,plain,
! [X0,X1] :
( sQ11_spl
| ~ member(g(aIb,aIc,aI_bUc),X1)
| ~ intersection(X0,bUc,X1) ),
inference(resolution,[status(thm)],[f225,f43]) ).
fof(f250,plain,
! [X0,X1] :
( sQ11_spl
| ~ member(g(aIb,aIc,aI_bUc),X1)
| ~ union(X0,X1,bUc) ),
inference(resolution,[status(thm)],[f225,f36]) ).
fof(f251,plain,
! [X0,X1] :
( sQ11_spl
| ~ member(g(aIb,aIc,aI_bUc),X0)
| ~ union(X0,X1,bUc) ),
inference(resolution,[status(thm)],[f225,f34]) ).
fof(f257,plain,
( sQ11_spl
| ~ member(g(aIb,aIc,aI_bUc),aI_bUc) ),
inference(resolution,[status(thm)],[f248,f52]) ).
fof(f258,plain,
( sQ11_spl
| ~ member(g(aIb,aIc,aI_bUc),c) ),
inference(resolution,[status(thm)],[f250,f49]) ).
fof(f266,plain,
! [X0,X1] :
( sQ11_spl
| ~ member(g(aIb,aIc,aI_bUc),X1)
| ~ intersection(X0,c,X1) ),
inference(resolution,[status(thm)],[f258,f43]) ).
fof(f275,plain,
( sQ11_spl
| ~ member(g(aIb,aIc,aI_bUc),b) ),
inference(resolution,[status(thm)],[f251,f49]) ).
fof(f282,plain,
! [X0,X1] :
( sQ11_spl
| ~ member(g(aIb,aIc,aI_bUc),X1)
| ~ intersection(X0,b,X1) ),
inference(resolution,[status(thm)],[f275,f43]) ).
fof(f287,plain,
( sQ11_spl
| ~ member(g(aIb,aIc,aI_bUc),aIc) ),
inference(resolution,[status(thm)],[f266,f51]) ).
fof(f290,plain,
( sQ11_spl
| ~ member(g(aIb,aIc,aI_bUc),aIb) ),
inference(resolution,[status(thm)],[f282,f50]) ).
fof(f291,plain,
( sQ11_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f290,f60,f223]) ).
fof(f292,plain,
( sQ3_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f97,f60,f77]) ).
fof(f293,plain,
( ~ sQ1_spl
| union(aIb,aIc,aI_bUc)
| ~ member(g(aIb,aIc,aI_bUc),aIc) ),
inference(resolution,[status(thm)],[f64,f39]) ).
fof(f294,plain,
( ~ sQ1_spl
| sQ6_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f293,f147,f150,f63]) ).
fof(f295,plain,
( sQ11_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f257,f63,f223]) ).
fof(f422,plain,
( sQ5_spl
| ~ member(g(aIb,aIc,aI_bUc),a)
| ~ member(g(aIb,aIc,aI_bUc),c) ),
inference(resolution,[status(thm)],[f201,f51]) ).
fof(f423,definition,
( sQ21_spl
<=> member(g(aIb,aIc,aI_bUc),c) ),
introduced(definition,[new_symbols(definition,[sQ21_spl])],[split_symbol_definition]) ).
fof(f425,plain,
( sQ21_spl
| ~ member(g(aIb,aIc,aI_bUc),c) ),
inference(component_clause,[status(thm)],[f423]) ).
fof(f426,plain,
( sQ5_spl
| ~ sQ3_spl
| ~ sQ21_spl ),
inference(split_clause,[status(thm)],[f422,f423,f77,f147]) ).
fof(f429,plain,
( sQ21_spl
| member(g(aIb,aIc,aI_bUc),b)
| ~ member(g(aIb,aIc,aI_bUc),bUc) ),
inference(resolution,[status(thm)],[f425,f129]) ).
fof(f438,plain,
( sQ21_spl
| sQ2_spl
| ~ sQ11_spl ),
inference(split_clause,[status(thm)],[f429,f223,f74,f423]) ).
fof(f439,plain,
( sQ11_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f287,f147,f223]) ).
fof(f440,plain,
$false,
inference(sat_refutation,[status(thm)],[f66,f80,f168,f183,f186,f217,f226,f291,f292,f294,f295,f426,f438,f439]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET007-1 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n016.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 04:46:09 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.13/0.41 % Refutation found
% 0.13/0.41 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.13/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.44 % Elapsed time: 0.068673 seconds
% 0.13/0.44 % CPU time: 0.320936 seconds
% 0.13/0.44 % Total memory used: 20.494 MB
% 0.13/0.44 % Net memory used: 20.002 MB
%------------------------------------------------------------------------------