%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET632+3 : 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 02:10:18 PM UTC 2026
% Result : Theorem 0.08s 0.40s
% Output : CNFRefutation 0.08s
% Verified :
% SZS Type : Refutation
% Derivation depth : 12
% Number of leaves : 11
% Syntax : Number of formulae : 66 ( 10 unt; 3 def)
% Number of atoms : 185 ( 15 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 197 ( 78 ~; 70 |; 36 &)
% ( 9 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 4 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 110 ( 97 !; 13 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] :
( intersect(B,C)
<=> ? [D] :
( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B] : ~ member(B,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( disjoint(B,C)
<=> ~ intersect(B,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [B,C] :
( intersect(B,C)
=> intersect(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [B] :
( empty(B)
<=> ! [C] : ~ member(C,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [B,C,D] :
( ( disjoint(C,D)
& subset(B,D)
& subset(B,C) )
=> B = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [B,C,D] :
( ( disjoint(C,D)
& subset(B,D)
& subset(B,C) )
=> B = empty_set ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f11,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f12,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)],[f11]) ).
fof(f13,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)],[f12]) ).
fof(f14,plain,
( ! [B,C] :
( ( ~ member(sK0_skl(C,B),C)
& member(sK0_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,[sK0_skl]),skolemize(D,sK0_skl(C,B))],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f18,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(f19,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)],[f18]) ).
fof(f20,plain,
( ! [B,C] :
( ! [D] :
( ~ member(D,C)
| ~ member(D,B) )
| intersect(B,C) )
& ! [B,C] :
( ( member(sK1_skl(C,B),C)
& member(sK1_skl(C,B),B) )
| ~ intersect(B,C) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl]),skolemize(D,sK1_skl(C,B))],[f19]) ).
fof(f23,plain,
! [X0,X1,X2] :
( ~ member(X2,X1)
| ~ member(X2,X0)
| intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f24,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f25,plain,
! [B,C] :
( ( intersect(B,C)
| disjoint(B,C) )
& ( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f26,plain,
( ! [B,C] :
( intersect(B,C)
| disjoint(B,C) )
& ! [B,C] :
( ~ intersect(B,C)
| ~ disjoint(B,C) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f27,plain,
! [X0,X1] :
( ~ intersect(X0,X1)
| ~ disjoint(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f29,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(f30,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)],[f29]) ).
fof(f33,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f34,plain,
! [B,C] :
( intersect(C,B)
| ~ intersect(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f6]) ).
fof(f35,plain,
! [X0,X1] :
( intersect(X1,X0)
| ~ intersect(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
! [B] :
( ( ? [C] : member(C,B)
| empty(B) )
& ( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(NNF_transformation,[status(thm)],[f8]) ).
fof(f38,plain,
( ! [B] :
( ? [C] : member(C,B)
| empty(B) )
& ! [B] :
( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(miniscoping,[status(thm)],[f37]) ).
fof(f39,plain,
( ! [B] :
( member(sK2_skl(B),B)
| empty(B) )
& ! [B] :
( ! [C] : ~ member(C,B)
| ~ empty(B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl]),skolemize(C,sK2_skl(B))],[f38]) ).
fof(f40,plain,
! [X0,X1] :
( ~ member(X1,X0)
| ~ empty(X0) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f41,plain,
! [X0] :
( member(sK2_skl(X0),X0)
| empty(X0) ),
inference(cnf_transformation,[status(thm)],[f39]) ).
fof(f42,plain,
? [B,C,D] :
( B != empty_set
& disjoint(C,D)
& subset(B,D)
& subset(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f43,plain,
? [B] :
( B != empty_set
& ? [C,D] :
( disjoint(C,D)
& subset(B,D)
& subset(B,C) ) ),
inference(miniscoping,[status(thm)],[f42]) ).
fof(f44,plain,
( sK3_skl != empty_set
& disjoint(sK4_skl,sK5_skl)
& subset(sK3_skl,sK5_skl)
& subset(sK3_skl,sK4_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl,sK4_skl,sK5_skl]),skolemize(B,sK3_skl),skolemize(C,sK4_skl),skolemize(D,sK5_skl)],[f43]) ).
fof(f45,plain,
subset(sK3_skl,sK4_skl),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f46,plain,
subset(sK3_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f47,plain,
disjoint(sK4_skl,sK5_skl),
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f48,plain,
sK3_skl != empty_set,
inference(cnf_transformation,[status(thm)],[f44]) ).
fof(f52,plain,
! [X0] :
( member(X0,sK4_skl)
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f15,f45]) ).
fof(f80,plain,
! [X0] : subset(empty_set,X0),
inference(resolution,[status(thm)],[f16,f24]) ).
fof(f81,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f80,f33]) ).
fof(f83,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ empty(X0) ),
inference(resolution,[status(thm)],[f40,f16]) ).
fof(f87,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(resolution,[status(thm)],[f81,f83]) ).
fof(f131,plain,
! [X0] :
( member(X0,sK5_skl)
| ~ member(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f46,f15]) ).
fof(f152,plain,
( empty(sK3_skl)
| member(sK2_skl(sK3_skl),sK4_skl) ),
inference(resolution,[status(thm)],[f52,f41]) ).
fof(f154,definition,
( sQ6_spl
<=> member(sK2_skl(sK3_skl),sK4_skl) ),
introduced(definition,[new_symbols(definition,[sQ6_spl])],[split_symbol_definition]) ).
fof(f155,plain,
( ~ sQ6_spl
| member(sK2_skl(sK3_skl),sK4_skl) ),
inference(component_clause,[status(thm)],[f154]) ).
fof(f157,definition,
( sQ7_spl
<=> empty(sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ7_spl])],[split_symbol_definition]) ).
fof(f158,plain,
( ~ sQ7_spl
| empty(sK3_skl) ),
inference(component_clause,[status(thm)],[f157]) ).
fof(f160,plain,
( sQ7_spl
| sQ6_spl ),
inference(split_clause,[status(thm)],[f152,f154,f157]) ).
fof(f162,plain,
! [X0] :
( ~ sQ6_spl
| ~ member(sK2_skl(sK3_skl),X0)
| intersect(X0,sK4_skl) ),
inference(resolution,[status(thm)],[f155,f23]) ).
fof(f171,plain,
~ intersect(sK4_skl,sK5_skl),
inference(resolution,[status(thm)],[f47,f27]) ).
fof(f177,plain,
( ~ sQ7_spl
| sK3_skl = empty_set ),
inference(resolution,[status(thm)],[f158,f87]) ).
fof(f178,plain,
( ~ sQ7_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f177,f48]) ).
fof(f179,plain,
~ sQ7_spl,
inference(contradiction_clause,[status(thm)],[f178]) ).
fof(f198,plain,
( empty(sK3_skl)
| member(sK2_skl(sK3_skl),sK5_skl) ),
inference(resolution,[status(thm)],[f131,f41]) ).
fof(f200,definition,
( sQ9_spl
<=> member(sK2_skl(sK3_skl),sK5_skl) ),
introduced(definition,[new_symbols(definition,[sQ9_spl])],[split_symbol_definition]) ).
fof(f201,plain,
( ~ sQ9_spl
| member(sK2_skl(sK3_skl),sK5_skl) ),
inference(component_clause,[status(thm)],[f200]) ).
fof(f203,plain,
( sQ7_spl
| sQ9_spl ),
inference(split_clause,[status(thm)],[f198,f200,f157]) ).
fof(f281,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| intersect(sK5_skl,sK4_skl) ),
inference(resolution,[status(thm)],[f162,f201]) ).
fof(f291,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| intersect(sK4_skl,sK5_skl) ),
inference(resolution,[status(thm)],[f281,f35]) ).
fof(f292,plain,
( ~ sQ9_spl
| ~ sQ6_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f291,f171]) ).
fof(f293,plain,
( ~ sQ9_spl
| ~ sQ6_spl ),
inference(contradiction_clause,[status(thm)],[f292]) ).
fof(f294,plain,
$false,
inference(sat_refutation,[status(thm)],[f160,f179,f203,f293]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET632+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.08/0.36 % Computer : n017.cluster.edu
% 0.08/0.36 % Model : x86_64 x86_64
% 0.08/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.36 % Memory : 8046.5625MB
% 0.08/0.36 % OS : Linux 6.8.0-71-generic
% 0.08/0.36 % CPULimit : 300
% 0.08/0.36 % WCLimit : 300
% 0.08/0.36 % DateTime : Mon Sep 21 05:25:42 UTC 2026
% 0.08/0.36 % CPUTime :
% 0.08/0.37 % Drodi V4.1.1
% 0.08/0.40 % Refutation found
% 0.08/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.08/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.08/0.42 % Elapsed time: 0.057470 seconds
% 0.08/0.42 % CPU time: 0.167932 seconds
% 0.08/0.42 % Total memory used: 80.822 MB
% 0.08/0.42 % Net memory used: 80.409 MB
%------------------------------------------------------------------------------