%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET624+3 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n009.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 02:10:16 PM UTC 2026
% Result : Theorem 0.08s 0.39s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 11
% Syntax : Number of formulae : 67 ( 1 unt; 7 def)
% Number of atoms : 187 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 205 ( 85 ~; 92 |; 15 &)
% ( 11 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 73 ( 64 !; 9 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,conjecture,
! [B,C,D] :
( intersect(B,union(C,D))
<=> ( intersect(B,D)
| intersect(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,negated_conjecture,
~ ! [B,C,D] :
( intersect(B,union(C,D))
<=> ( intersect(B,D)
| intersect(B,C) ) ),
inference(negated_conjecture,[status(cth)],[f6]) ).
fof(f8,plain,
! [B,C,D] :
( ( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f9,plain,
( ! [B,C,D] :
( ( ~ member(D,C)
& ~ member(D,B) )
| member(D,union(B,C)) )
& ! [B,C,D] :
( member(D,C)
| member(D,B)
| ~ member(D,union(B,C)) ) ),
inference(miniscoping,[status(thm)],[f8]) ).
fof(f10,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f13,plain,
! [B,C] :
( ( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f14,plain,
( ! [B,C] :
( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ! [B,C] :
( ? [D] :
( member(D,C)
& member(D,B) )
| ~ intersect(B,C) ) ),
inference(miniscoping,[status(thm)],[f13]) ).
fof(f15,plain,
( ! [B,C] :
( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ! [B,C] :
( ( member(sK0_skl(C,B),C)
& member(sK0_skl(C,B),B) )
| ~ intersect(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f17,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X1)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
fof(f20,plain,
! [B,C] :
( intersect(C,B)
| ~ intersect(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f21,plain,
! [X0,X1] :
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f29,plain,
? [B,C,D] :
( intersect(B,union(C,D))
<~> ( intersect(B,D)
| intersect(B,C) ) ),
inference(pre_NNF_transformation,[status(thm)],[f7]) ).
fof(f30,plain,
? [B,C,D] :
( ( ( ~ intersect(B,D)
& ~ intersect(B,C) )
| ~ intersect(B,union(C,D)) )
& ( intersect(B,D)
| intersect(B,C)
| intersect(B,union(C,D)) ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
( ( ( ~ intersect(sK2_skl,sK4_skl)
& ~ intersect(sK2_skl,sK3_skl) )
| ~ intersect(sK2_skl,union(sK3_skl,sK4_skl)) )
& ( intersect(sK2_skl,sK4_skl)
| intersect(sK2_skl,sK3_skl)
| intersect(sK2_skl,union(sK3_skl,sK4_skl)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl,sK4_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl),skolemize(D,sK4_skl)],[f30]) ).
fof(f32,plain,
( intersect(sK2_skl,sK4_skl)
| intersect(sK2_skl,sK3_skl)
| intersect(sK2_skl,union(sK3_skl,sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f33,plain,
( ~ intersect(sK2_skl,sK3_skl)
| ~ intersect(sK2_skl,union(sK3_skl,sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f34,plain,
( ~ intersect(sK2_skl,sK4_skl)
| ~ intersect(sK2_skl,union(sK3_skl,sK4_skl)) ),
inference(cnf_transformation,[status(thm)],[f31]) ).
fof(f35,definition,
( sQ0_spl
<=> intersect(sK2_skl,union(sK3_skl,sK4_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f36,plain,
( ~ sQ0_spl
| intersect(sK2_skl,union(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f37,plain,
( sQ0_spl
| ~ intersect(sK2_skl,union(sK3_skl,sK4_skl)) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,definition,
( sQ1_spl
<=> intersect(sK2_skl,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f40,plain,
( sQ1_spl
| ~ intersect(sK2_skl,sK3_skl) ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,definition,
( sQ2_spl
<=> intersect(sK2_skl,sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f43,plain,
( sQ2_spl
| ~ intersect(sK2_skl,sK4_skl) ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f32,f35,f38,f41]) ).
fof(f45,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f33,f35,f38]) ).
fof(f46,plain,
( ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f34,f35,f41]) ).
fof(f53,plain,
( sQ0_spl
| ~ intersect(union(sK3_skl,sK4_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f21,f37]) ).
fof(f61,plain,
! [X0] :
( sQ0_spl
| ~ member(X0,sK2_skl)
| ~ member(X0,union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f18,f53]) ).
fof(f64,plain,
! [X0,X1,X2] :
( member(sK0_skl(union(X1,X2),X0),X2)
| member(sK0_skl(union(X1,X2),X0),X1)
| ~ intersect(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[f17,f10]) ).
fof(f65,plain,
! [X0] :
( sQ0_spl
| ~ intersect(X0,sK2_skl)
| ~ member(sK0_skl(sK2_skl,X0),union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f61,f17]) ).
fof(f77,plain,
! [X0] :
( sQ0_spl
| ~ member(sK0_skl(sK2_skl,X0),sK4_skl)
| ~ intersect(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f65,f12]) ).
fof(f78,plain,
! [X0] :
( sQ0_spl
| ~ member(sK0_skl(sK2_skl,X0),sK3_skl)
| ~ intersect(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f65,f11]) ).
fof(f83,plain,
( sQ0_spl
| ~ intersect(sK4_skl,sK2_skl)
| ~ intersect(sK4_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f77,f16]) ).
fof(f84,definition,
( sQ4_spl
<=> intersect(sK4_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f86,plain,
( sQ4_spl
| ~ intersect(sK4_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f84]) ).
fof(f87,plain,
( sQ0_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f83,f84,f35]) ).
fof(f107,plain,
( sQ0_spl
| ~ intersect(sK3_skl,sK2_skl)
| ~ intersect(sK3_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f78,f16]) ).
fof(f108,definition,
( sQ5_spl
<=> intersect(sK3_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f110,plain,
( sQ5_spl
| ~ intersect(sK3_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f108]) ).
fof(f111,plain,
( sQ0_spl
| ~ sQ5_spl ),
inference(split_clause,[status(thm)],[f107,f108,f35]) ).
fof(f112,plain,
! [X0] :
( sQ1_spl
| ~ member(X0,sK3_skl)
| ~ member(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f40,f18]) ).
fof(f114,plain,
! [X0] :
( sQ2_spl
| ~ member(X0,sK4_skl)
| ~ member(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f43,f18]) ).
fof(f120,plain,
( ~ sQ0_spl
| member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),sK4_skl)
| member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f36,f64]) ).
fof(f121,definition,
( sQ6_spl
<=> member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f122,plain,
( ~ sQ6_spl
| member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f121]) ).
fof(f124,definition,
( sQ7_spl
<=> member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f125,plain,
( ~ sQ7_spl
| member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f124]) ).
fof(f127,plain,
( ~ sQ0_spl
| sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f120,f121,f124,f35]) ).
fof(f135,plain,
( sQ4_spl
| ~ intersect(sK2_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f86,f21]) ).
fof(f141,plain,
( sQ5_spl
| ~ intersect(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f110,f21]) ).
fof(f142,plain,
( sQ5_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f141,f38,f108]) ).
fof(f151,plain,
( sQ4_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f135,f41,f84]) ).
fof(f185,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f122,f112]) ).
fof(f224,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ intersect(sK2_skl,union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f185,f16]) ).
fof(f225,plain,
( sQ1_spl
| ~ sQ6_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f224,f35,f121,f38]) ).
fof(f240,plain,
( sQ2_spl
| ~ sQ7_spl
| ~ member(sK0_skl(union(sK3_skl,sK4_skl),sK2_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f125,f114]) ).
fof(f245,plain,
( sQ2_spl
| ~ sQ7_spl
| ~ intersect(sK2_skl,union(sK3_skl,sK4_skl)) ),
inference(resolution,[status(thm)],[f240,f16]) ).
fof(f246,plain,
( sQ2_spl
| ~ sQ7_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f245,f35,f124,f41]) ).
fof(f247,plain,
$false,
inference(sat_refutation,[status(thm)],[f44,f45,f46,f87,f111,f127,f142,f151,f225,f246]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET624+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.35 % Computer : n009.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 05:29:58 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.36 % Drodi V4.1.1
% 0.08/0.39 % Refutation found
% 0.08/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.43 % Elapsed time: 0.054058 seconds
% 0.08/0.43 % CPU time: 0.248871 seconds
% 0.08/0.43 % Total memory used: 104.264 MB
% 0.08/0.43 % Net memory used: 103.582 MB
%------------------------------------------------------------------------------