%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU145+2 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n006.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 02:19:22 PM UTC 2026
% Result : Theorem 72.15s 9.65s
% Output : CNFRefutation 72.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 14
% Syntax : Number of formulae : 85 ( 19 unt; 1 def)
% Number of atoms : 252 ( 74 equ)
% Maximal formula atoms : 14 ( 2 avg)
% Number of connectives : 275 ( 108 ~; 109 |; 43 &)
% ( 9 <=>; 6 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 2 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 5 con; 0-3 aty)
% Number of variables : 177 ( 166 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A,B,C] :
( C = set_difference(A,B)
<=> ! [D] :
( in(D,C)
<=> ( ~ in(D,B)
& in(D,A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,conjecture,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,negated_conjecture,
~ ! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
inference(negated_conjecture,[status(cth)],[f31]) ).
fof(f33,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f47,lemma,
! [A,B,C] :
( subset(A,B)
=> subset(set_difference(A,C),set_difference(B,C)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f48,lemma,
! [A,B] : subset(set_difference(A,B),A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f60,lemma,
! [A,B,C] :
( ( disjoint(B,C)
& subset(A,B) )
=> disjoint(A,C) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f62,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f65,lemma,
! [A,B] :
( disjoint(A,B)
<=> set_difference(A,B) = A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f75,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f6]) ).
fof(f76,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f75]) ).
fof(f77,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f79,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f76]) ).
fof(f80,plain,
! [A,B] :
( ( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ( ! [C] :
( ( C != A
| in(C,B) )
& ( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f81,plain,
( ! [A,B] :
( ? [C] :
( ( C = A
| in(C,B) )
& ( C != A
| ~ in(C,B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(miniscoping,[status(thm)],[f80]) ).
fof(f82,plain,
( ! [A,B] :
( ( ( sK0_skl(B,A) = A
| in(sK0_skl(B,A),B) )
& ( sK0_skl(B,A) != A
| ~ in(sK0_skl(B,A),B) ) )
| B = singleton(A) )
& ! [A,B] :
( ( ! [C] :
( C != A
| in(C,B) )
& ! [C] :
( C = A
| ~ in(C,B) ) )
| B != singleton(A) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(C,sK0_skl(B,A))],[f81]) ).
fof(f84,plain,
! [X0,X1,X2] :
( X2 != X1
| in(X2,X0)
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(thm)],[f82]) ).
fof(f126,plain,
! [A,B,C] :
( ( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ( ! [D] :
( ( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f13]) ).
fof(f127,plain,
( ! [A,B,C] :
( ? [D] :
( ( ( ~ in(D,B)
& in(D,A) )
| in(D,C) )
& ( in(D,B)
| ~ in(D,A)
| ~ in(D,C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(miniscoping,[status(thm)],[f126]) ).
fof(f128,plain,
( ! [A,B,C] :
( ( ( ( ~ in(sK6_skl(C,B,A),B)
& in(sK6_skl(C,B,A),A) )
| in(sK6_skl(C,B,A),C) )
& ( in(sK6_skl(C,B,A),B)
| ~ in(sK6_skl(C,B,A),A)
| ~ in(sK6_skl(C,B,A),C) ) )
| C = set_difference(A,B) )
& ! [A,B,C] :
( ( ! [D] :
( in(D,B)
| ~ in(D,A)
| in(D,C) )
& ! [D] :
( ( ~ in(D,B)
& in(D,A) )
| ~ in(D,C) ) )
| C != set_difference(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK6_skl]),skolemize(D,sK6_skl(C,B,A))],[f127]) ).
fof(f131,plain,
! [X0,X1,X2,X3] :
( in(X3,X2)
| ~ in(X3,X1)
| in(X3,X0)
| X0 != set_difference(X1,X2) ),
inference(cnf_transformation,[status(thm)],[f128]) ).
fof(f158,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(NNF_transformation,[status(thm)],[f29]) ).
fof(f159,plain,
( ! [A,B] :
( ~ in(A,B)
| subset(singleton(A),B) )
& ! [A,B] :
( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(miniscoping,[status(thm)],[f158]) ).
fof(f161,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[status(thm)],[f159]) ).
fof(f162,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f30]) ).
fof(f163,plain,
( ! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ! [A,B] :
( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(miniscoping,[status(thm)],[f162]) ).
fof(f164,plain,
! [X0,X1] :
( subset(X0,X1)
| set_difference(X0,X1) != empty_set ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f165,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f163]) ).
fof(f166,plain,
? [A,B,C] :
( ~ subset(A,set_difference(B,singleton(C)))
& ~ in(C,A)
& subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f32]) ).
fof(f167,plain,
? [A,B] :
( ? [C] :
( ~ subset(A,set_difference(B,singleton(C)))
& ~ in(C,A) )
& subset(A,B) ),
inference(miniscoping,[status(thm)],[f166]) ).
fof(f168,plain,
( ~ subset(sK7_skl,set_difference(sK8_skl,singleton(sK9_skl)))
& ~ in(sK9_skl,sK7_skl)
& subset(sK7_skl,sK8_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK7_skl,sK8_skl,sK9_skl]),skolemize(A,sK7_skl),skolemize(B,sK8_skl),skolemize(C,sK9_skl)],[f167]) ).
fof(f169,plain,
subset(sK7_skl,sK8_skl),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f170,plain,
~ in(sK9_skl,sK7_skl),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f171,plain,
~ subset(sK7_skl,set_difference(sK8_skl,singleton(sK9_skl))),
inference(cnf_transformation,[status(thm)],[f168]) ).
fof(f172,plain,
empty(sK10_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK10_skl]),skolemize(A,sK10_skl)],[f33]) ).
fof(f173,plain,
empty(sK10_skl),
inference(cnf_transformation,[status(thm)],[f172]) ).
fof(f178,plain,
! [A,B] :
( disjoint(B,A)
| ~ disjoint(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f36]) ).
fof(f179,plain,
! [X0,X1] :
( disjoint(X1,X0)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f178]) ).
fof(f201,plain,
! [A,B,C] :
( subset(set_difference(A,C),set_difference(B,C))
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f47]) ).
fof(f202,plain,
! [A,B] :
( ! [C] : subset(set_difference(A,C),set_difference(B,C))
| ~ subset(A,B) ),
inference(miniscoping,[status(thm)],[f201]) ).
fof(f203,plain,
! [X0,X1,X2] :
( subset(set_difference(X0,X2),set_difference(X1,X2))
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f202]) ).
fof(f204,plain,
! [X0,X1] : subset(set_difference(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f48]) ).
fof(f231,plain,
! [A,B,C] :
( disjoint(A,C)
| ~ disjoint(B,C)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f60]) ).
fof(f232,plain,
! [A,C] :
( disjoint(A,C)
| ! [B] :
( ~ disjoint(B,C)
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f231]) ).
fof(f233,plain,
! [X0,X1,X2] :
( disjoint(X0,X2)
| ~ disjoint(X1,X2)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f232]) ).
fof(f235,plain,
! [A] :
( A = empty_set
| ~ empty(A) ),
inference(pre_NNF_transformation,[status(thm)],[f62]) ).
fof(f236,plain,
! [X0] :
( X0 = empty_set
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f235]) ).
fof(f241,plain,
! [A,B] :
( ( set_difference(A,B) != A
| disjoint(A,B) )
& ( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f65]) ).
fof(f242,plain,
( ! [A,B] :
( set_difference(A,B) != A
| disjoint(A,B) )
& ! [A,B] :
( set_difference(A,B) = A
| ~ disjoint(A,B) ) ),
inference(miniscoping,[status(thm)],[f241]) ).
fof(f243,plain,
! [X0,X1] :
( set_difference(X0,X1) = X0
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f242]) ).
fof(f244,plain,
! [X0,X1] :
( set_difference(X0,X1) != X0
| disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f242]) ).
fof(f250,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f77]) ).
fof(f253,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(thm)],[f84]) ).
fof(f266,plain,
! [X0,X1,X2] :
( in(X0,X2)
| ~ in(X0,X1)
| in(X0,set_difference(X1,X2)) ),
inference(destructive_equality_resolution,[status(thm)],[f131]) ).
fof(f298,plain,
! [X0,X1] :
( ~ subset(X0,set_difference(X0,X1))
| X0 = set_difference(X0,X1) ),
inference(resolution,[status(thm)],[f204,f79]) ).
fof(f302,plain,
! [X0,X1] :
( in(X0,X1)
| in(X0,set_difference(singleton(X0),X1)) ),
inference(resolution,[status(thm)],[f266,f253]) ).
fof(f415,plain,
! [X0,X1] :
( subset(singleton(X0),set_difference(singleton(X0),X1))
| in(X0,X1) ),
inference(resolution,[status(thm)],[f302,f161]) ).
fof(f1192,plain,
set_difference(sK7_skl,set_difference(sK8_skl,singleton(sK9_skl))) != empty_set,
inference(resolution,[status(thm)],[f171,f164]) ).
fof(f1209,plain,
! [X0] : subset(set_difference(sK7_skl,X0),set_difference(sK8_skl,X0)),
inference(resolution,[status(thm)],[f169,f203]) ).
fof(f1441,plain,
sK10_skl = empty_set,
inference(resolution,[status(thm)],[f236,f173]) ).
fof(f1633,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = sK10_skl ),
inference(backward_demodulation,[status(thm)],[f1441,f165]) ).
fof(f1672,plain,
! [X0,X1,X2] :
( disjoint(X2,X1)
| ~ subset(X2,X0)
| set_difference(X0,X1) != X0 ),
inference(resolution,[status(thm)],[f244,f233]) ).
fof(f4185,plain,
! [X0,X1,X2] :
( disjoint(X1,X2)
| ~ subset(X2,X0)
| set_difference(X0,X1) != X0 ),
inference(resolution,[status(thm)],[f1672,f179]) ).
fof(f4519,plain,
set_difference(sK7_skl,set_difference(sK8_skl,singleton(sK9_skl))) != sK10_skl,
inference(forward_demodulation,[status(thm)],[f1441,f1192]) ).
fof(f5243,plain,
! [X0] : set_difference(set_difference(sK7_skl,X0),set_difference(sK8_skl,X0)) = sK10_skl,
inference(resolution,[status(thm)],[f1209,f1633]) ).
fof(f8555,plain,
! [X0,X1,X2] :
( set_difference(X1,X2) = X1
| ~ subset(X2,X0)
| set_difference(X0,X1) != X0 ),
inference(resolution,[status(thm)],[f4185,f243]) ).
fof(f10335,plain,
! [X0,X1] :
( set_difference(X1,X0) = X1
| set_difference(X0,X1) != X0 ),
inference(resolution,[status(thm)],[f8555,f250]) ).
fof(f17279,plain,
! [X0,X1] :
( singleton(X0) = set_difference(singleton(X0),X1)
| in(X0,X1) ),
inference(resolution,[status(thm)],[f415,f298]) ).
fof(f17437,plain,
singleton(sK9_skl) = set_difference(singleton(sK9_skl),sK7_skl),
inference(resolution,[status(thm)],[f17279,f170]) ).
fof(f17605,definition,
( sQ154_spl
<=> set_difference(sK7_skl,singleton(sK9_skl)) = sK7_skl ),
introduced(definition,[new_symbols(definition,[sQ154_spl])],[split_symbol_definition]) ).
fof(f17606,plain,
( ~ sQ154_spl
| set_difference(sK7_skl,singleton(sK9_skl)) = sK7_skl ),
inference(component_clause,[status(thm)],[f17605]) ).
fof(f17607,plain,
( sQ154_spl
| set_difference(sK7_skl,singleton(sK9_skl)) != sK7_skl ),
inference(component_clause,[status(thm)],[f17605]) ).
fof(f17807,plain,
( sQ154_spl
| set_difference(singleton(sK9_skl),sK7_skl) != singleton(sK9_skl) ),
inference(resolution,[status(thm)],[f17607,f10335]) ).
fof(f17810,plain,
( sQ154_spl
| singleton(sK9_skl) != singleton(sK9_skl) ),
inference(forward_demodulation,[status(thm)],[f17437,f17807]) ).
fof(f17811,plain,
( sQ154_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f17810]) ).
fof(f17812,plain,
sQ154_spl,
inference(contradiction_clause,[status(thm)],[f17811]) ).
fof(f17935,plain,
( ~ sQ154_spl
| set_difference(sK7_skl,set_difference(sK8_skl,singleton(sK9_skl))) = sK10_skl ),
inference(paramodulation,[status(thm)],[f17606,f5243]) ).
fof(f18012,plain,
( ~ sQ154_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f17935,f4519]) ).
fof(f18013,plain,
~ sQ154_spl,
inference(contradiction_clause,[status(thm)],[f18012]) ).
fof(f18014,plain,
$false,
inference(sat_refutation,[status(thm)],[f17812,f18013]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.05 % Problem : SEU145+2 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.06 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.16/0.44 % Computer : n006.cluster.edu
% 0.16/0.44 % Model : x86_64 x86_64
% 0.16/0.44 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.44 % Memory : 8046.5625MB
% 0.16/0.44 % OS : Linux 6.8.0-71-generic
% 0.16/0.45 % CPULimit : 300
% 0.16/0.45 % WCLimit : 300
% 0.16/0.45 % DateTime : Mon Sep 21 05:52:42 UTC 2026
% 0.16/0.45 % CPUTime :
% 0.16/0.46 % Drodi V4.1.1
% 72.15/9.65 % Refutation found
% 72.15/9.65 % SZS status Theorem for theBenchmark: Theorem is valid
% 72.15/9.65 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 5.04/9.91 % Elapsed time: 9.445519 seconds
% 5.04/9.91 % CPU time: 73.019860 seconds
% 5.04/9.91 % Total memory used: 413.102 MB
% 5.04/9.91 % Net memory used: 364.395 MB
%------------------------------------------------------------------------------