%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET595+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 : n001.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 02:10:10 PM UTC 2026
% Result : Theorem 219.91s 28.14s
% Output : CNFRefutation 27.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 7
% Syntax : Number of formulae : 76 ( 19 unt; 1 def)
% Number of atoms : 184 ( 25 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 172 ( 64 ~; 77 |; 22 &)
% ( 6 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 167 ( 163 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C,D] :
( member(D,difference(B,C))
<=> ( ~ member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B,C] :
( subset(B,C)
=> C = union(B,difference(C,B)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B,C] :
( subset(B,C)
=> C = union(B,difference(C,B)) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f16,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)],[f2]) ).
fof(f17,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)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(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(f25,plain,
! [X0,X1,X2] :
( member(X0,X2)
| ~ member(X0,X1)
| member(X0,difference(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f26,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f4]) ).
fof(f27,plain,
! [B,C] :
( ( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f26]) ).
fof(f28,plain,
( ! [B,C] :
( ? [D] :
( ~ member(D,C)
& member(D,B) )
| subset(B,C) )
& ! [B,C] :
( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(miniscoping,[status(thm)],[f27]) ).
fof(f29,plain,
( ! [B,C] :
( ( ~ member(sK1_skl(C,B),C)
& member(sK1_skl(C,B),B) )
| subset(B,C) )
& ! [B,C] :
( ! [D] :
( member(D,C)
| ~ member(D,B) )
| ~ subset(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( member(sK1_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f32,plain,
! [X0,X1] :
( ~ member(sK1_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f29]) ).
fof(f33,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f34,plain,
( ! [B,C] :
( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ! [B,C] :
( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(miniscoping,[status(thm)],[f33]) ).
fof(f37,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f38,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f47,plain,
? [B,C] :
( C != union(B,difference(C,B))
& subset(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f48,plain,
( sK4_skl != union(sK3_skl,difference(sK4_skl,sK3_skl))
& subset(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,
subset(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f50,plain,
sK4_skl != union(sK3_skl,difference(sK4_skl,sK3_skl)),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f53,plain,
sK4_skl != union(difference(sK4_skl,sK3_skl),sK3_skl),
inference(backward_demodulation,[status(thm)],[f38,f50]) ).
fof(f78,plain,
! [X0,X1,X2] :
( member(sK1_skl(X2,union(X0,X1)),X1)
| member(sK1_skl(X2,union(X0,X1)),X0)
| subset(union(X0,X1),X2) ),
inference(resolution,[status(thm)],[f31,f18]) ).
fof(f80,plain,
! [X0,X1,X2] :
( ~ member(sK1_skl(union(X1,X2),X0),X2)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[f32,f20]) ).
fof(f81,plain,
! [X0,X1,X2] :
( ~ member(sK1_skl(union(X1,X2),X0),X1)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[f32,f19]) ).
fof(f115,plain,
! [X0,X1] :
( subset(union(X0,X1),X1)
| member(sK1_skl(X1,union(X0,X1)),X0)
| subset(union(X0,X1),X1) ),
inference(resolution,[status(thm)],[f78,f32]) ).
fof(f121,plain,
! [X0,X1] :
( member(sK1_skl(X1,union(X0,X1)),X0)
| subset(union(X0,X1),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f115]) ).
fof(f167,plain,
! [X0,X1,X2] :
( member(sK1_skl(union(X2,X1),union(X0,X1)),X0)
| subset(union(X0,X1),union(X2,X1))
| subset(union(X0,X1),union(X2,X1)) ),
inference(resolution,[status(thm)],[f80,f78]) ).
fof(f170,plain,
! [X0,X1,X2,X3] :
( member(sK1_skl(union(X1,difference(X2,X3)),X0),X3)
| ~ member(sK1_skl(union(X1,difference(X2,X3)),X0),X2)
| subset(X0,union(X1,difference(X2,X3))) ),
inference(resolution,[status(thm)],[f80,f25]) ).
fof(f175,plain,
! [X0,X1,X2] :
( member(sK1_skl(union(X2,X1),union(X0,X1)),X0)
| subset(union(X0,X1),union(X2,X1)) ),
inference(duplicate_literals_removal,[status(thm)],[f167]) ).
fof(f178,plain,
! [X0,X1,X2] :
( member(sK1_skl(union(X1,X2),union(X0,X1)),X0)
| subset(union(X0,X1),union(X1,X2))
| subset(union(X0,X1),union(X1,X2)) ),
inference(resolution,[status(thm)],[f81,f78]) ).
fof(f180,plain,
! [X0,X1] :
( subset(X0,union(X0,X1))
| subset(X0,union(X0,X1)) ),
inference(resolution,[status(thm)],[f81,f31]) ).
fof(f182,plain,
! [X0,X1,X2,X3] :
( ~ member(sK1_skl(union(union(X1,X2),X3),X0),X2)
| subset(X0,union(union(X1,X2),X3)) ),
inference(resolution,[status(thm)],[f81,f20]) ).
fof(f186,plain,
! [X0,X1,X2] :
( member(sK1_skl(union(X1,X2),union(X0,X1)),X0)
| subset(union(X0,X1),union(X1,X2)) ),
inference(duplicate_literals_removal,[status(thm)],[f178]) ).
fof(f188,plain,
! [X0,X1] : subset(X0,union(X0,X1)),
inference(duplicate_literals_removal,[status(thm)],[f180]) ).
fof(f194,plain,
! [X0,X1] :
( ~ subset(union(X0,X1),X0)
| union(X0,X1) = X0 ),
inference(resolution,[status(thm)],[f188,f37]) ).
fof(f418,plain,
! [X0,X1] :
( ~ subset(union(X1,X0),X0)
| union(X0,X1) = X0 ),
inference(paramodulation,[status(thm)],[f38,f194]) ).
fof(f1754,plain,
! [X0,X1,X2] :
( member(sK1_skl(X2,union(difference(X0,X1),X2)),X0)
| subset(union(difference(X0,X1),X2),X2) ),
inference(resolution,[status(thm)],[f121,f23]) ).
fof(f2070,plain,
! [X0] :
( member(X0,sK4_skl)
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f49,f30]) ).
fof(f2090,plain,
! [X0] :
( subset(X0,sK4_skl)
| ~ member(sK1_skl(sK4_skl,X0),sK3_skl) ),
inference(resolution,[status(thm)],[f2070,f32]) ).
fof(f2091,plain,
( subset(union(sK3_skl,sK4_skl),sK4_skl)
| subset(union(sK3_skl,sK4_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f2090,f121]) ).
fof(f2098,definition,
( sQ2_spl
<=> subset(union(sK3_skl,sK4_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f2099,plain,
( ~ sQ2_spl
| subset(union(sK3_skl,sK4_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f2098]) ).
fof(f2101,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f2091,f2098]) ).
fof(f2347,plain,
( ~ sQ2_spl
| union(sK4_skl,sK3_skl) = sK4_skl ),
inference(resolution,[status(thm)],[f2099,f418]) ).
fof(f2351,plain,
( ~ sQ2_spl
| union(sK3_skl,sK4_skl) = sK4_skl ),
inference(forward_demodulation,[status(thm)],[f38,f2347]) ).
fof(f2935,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,difference(X2,X1)))
| ~ member(sK1_skl(union(X1,difference(X2,X1)),X0),X2)
| subset(X0,union(X1,difference(X2,X1))) ),
inference(resolution,[status(thm)],[f170,f81]) ).
fof(f2954,plain,
! [X0,X1,X2] :
( ~ member(sK1_skl(union(X1,difference(X2,X1)),X0),X2)
| subset(X0,union(X1,difference(X2,X1))) ),
inference(duplicate_literals_removal,[status(thm)],[f2935]) ).
fof(f4012,plain,
! [X0,X1,X2] :
( subset(union(X0,X1),union(union(X2,X0),X1))
| subset(union(X0,X1),union(union(X2,X0),X1)) ),
inference(resolution,[status(thm)],[f182,f175]) ).
fof(f4040,plain,
! [X0,X1,X2] : subset(union(X0,X1),union(union(X2,X0),X1)),
inference(duplicate_literals_removal,[status(thm)],[f4012]) ).
fof(f14477,plain,
! [X0,X1,X2] : subset(union(X0,X1),union(union(X2,X1),X0)),
inference(paramodulation,[status(thm)],[f38,f4040]) ).
fof(f32376,plain,
! [X0,X1] :
( subset(union(difference(X0,X1),X0),X0)
| subset(union(difference(X0,X1),X0),X0) ),
inference(resolution,[status(thm)],[f1754,f32]) ).
fof(f32439,plain,
! [X0,X1] : subset(union(difference(X0,X1),X0),X0),
inference(duplicate_literals_removal,[status(thm)],[f32376]) ).
fof(f32498,plain,
! [X0,X1] : union(X0,difference(X0,X1)) = X0,
inference(resolution,[status(thm)],[f32439,f418]) ).
fof(f32694,plain,
! [X0,X1,X2] : subset(union(X0,difference(X1,X2)),union(X1,X0)),
inference(paramodulation,[status(thm)],[f32498,f14477]) ).
fof(f64141,plain,
! [X0,X1] :
( subset(union(X0,X1),union(X1,difference(X0,X1)))
| subset(union(X0,X1),union(X1,difference(X0,X1))) ),
inference(resolution,[status(thm)],[f2954,f186]) ).
fof(f64280,plain,
! [X0,X1] : subset(union(X0,X1),union(X1,difference(X0,X1))),
inference(duplicate_literals_removal,[status(thm)],[f64141]) ).
fof(f139797,plain,
! [X0,X1] :
( ~ subset(union(X0,difference(X1,X0)),union(X1,X0))
| union(X0,difference(X1,X0)) = union(X1,X0) ),
inference(resolution,[status(thm)],[f64280,f37]) ).
fof(f139853,plain,
! [X0,X1] : union(X0,difference(X1,X0)) = union(X1,X0),
inference(forward_subsumption_resolution,[status(thm)],[f139797,f32694]) ).
fof(f139940,plain,
! [X0,X1] : union(difference(X0,X1),X1) = union(X0,X1),
inference(paramodulation,[status(thm)],[f38,f139853]) ).
fof(f141369,plain,
sK4_skl != union(sK4_skl,sK3_skl),
inference(backward_demodulation,[status(thm)],[f139940,f53]) ).
fof(f142009,plain,
sK4_skl != union(sK3_skl,sK4_skl),
inference(forward_demodulation,[status(thm)],[f38,f141369]) ).
fof(f142010,plain,
( ~ sQ2_spl
| sK4_skl != sK4_skl ),
inference(forward_demodulation,[status(thm)],[f2351,f142009]) ).
fof(f142011,plain,
( ~ sQ2_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f142010]) ).
fof(f142012,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f142011]) ).
fof(f142013,plain,
$false,
inference(sat_refutation,[status(thm)],[f2101,f142012]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET595+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.36 % Computer : n001.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 05:33:29 UTC 2026
% 0.10/0.37 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 219.91/28.14 % Refutation found
% 219.91/28.14 % SZS status Theorem for theBenchmark: Theorem is valid
% 219.91/28.14 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 27.67/28.26 % Elapsed time: 27.865013 seconds
% 27.67/28.26 % CPU time: 220.725912 seconds
% 27.67/28.26 % Total memory used: 857.963 MB
% 27.67/28.26 % Net memory used: 793.316 MB
%------------------------------------------------------------------------------