%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET185+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 : n012.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 02:09:35 PM UTC 2026
% Result : Theorem 0.07s 5.40s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 5
% Syntax : Number of formulae : 40 ( 6 unt; 1 def)
% Number of atoms : 111 ( 13 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 112 ( 41 ~; 46 |; 17 &)
% ( 5 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 2 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 80 ( 76 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,C)
| member(D,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [B,C] :
( subset(B,C)
=> union(B,C) = C ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B,C] :
( subset(B,C)
=> union(B,C) = C ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,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(f10,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)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f10]) ).
fof(f14,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f15,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)],[f14]) ).
fof(f16,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)],[f15]) ).
fof(f17,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))],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
fof(f21,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f22,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)],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f35,plain,
? [B,C] :
( union(B,C) != C
& subset(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f36,plain,
( union(sK2_skl,sK3_skl) != sK3_skl
& subset(sK2_skl,sK3_skl) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK2_skl,sK3_skl]),skolemize(B,sK2_skl),skolemize(C,sK3_skl)],[f35]) ).
fof(f37,plain,
subset(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
union(sK2_skl,sK3_skl) != sK3_skl,
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f62,plain,
! [X0] :
( member(X0,sK3_skl)
| ~ member(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f18,f37]) ).
fof(f64,plain,
! [X0,X1,X2] :
( member(sK0_skl(X2,union(X0,X1)),X1)
| member(sK0_skl(X2,union(X0,X1)),X0)
| subset(union(X0,X1),X2) ),
inference(resolution,[status(thm)],[f19,f11]) ).
fof(f71,plain,
! [X0,X1] :
( member(sK0_skl(X1,union(X0,X1)),X0)
| subset(union(X0,X1),X1)
| subset(union(X0,X1),X1) ),
inference(resolution,[status(thm)],[f20,f64]) ).
fof(f73,plain,
! [X0,X1,X2] :
( ~ member(sK0_skl(union(X1,X2),X0),X2)
| subset(X0,union(X1,X2)) ),
inference(resolution,[status(thm)],[f20,f13]) ).
fof(f75,plain,
! [X0,X1] :
( member(sK0_skl(X1,union(X0,X1)),X0)
| subset(union(X0,X1),X1) ),
inference(duplicate_literals_removal,[status(thm)],[f71]) ).
fof(f82,plain,
! [X0,X1] :
( subset(X0,union(X1,X0))
| subset(X0,union(X1,X0)) ),
inference(resolution,[status(thm)],[f73,f19]) ).
fof(f88,plain,
! [X0,X1] : subset(X0,union(X1,X0)),
inference(duplicate_literals_removal,[status(thm)],[f82]) ).
fof(f102,plain,
! [X0,X1] :
( ~ subset(union(X0,X1),X1)
| union(X0,X1) = X1 ),
inference(resolution,[status(thm)],[f88,f25]) ).
fof(f265,plain,
! [X0] :
( subset(X0,sK3_skl)
| ~ member(sK0_skl(sK3_skl,X0),sK2_skl) ),
inference(resolution,[status(thm)],[f62,f20]) ).
fof(f304,plain,
( subset(union(sK2_skl,sK3_skl),sK3_skl)
| subset(union(sK2_skl,sK3_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f265,f75]) ).
fof(f318,definition,
( sQ2_spl
<=> subset(union(sK2_skl,sK3_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f319,plain,
( ~ sQ2_spl
| subset(union(sK2_skl,sK3_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f318]) ).
fof(f321,plain,
sQ2_spl,
inference(split_clause,[status(thm)],[f304,f318]) ).
fof(f398,plain,
( ~ sQ2_spl
| union(sK2_skl,sK3_skl) = sK3_skl ),
inference(resolution,[status(thm)],[f319,f102]) ).
fof(f401,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f398,f38]) ).
fof(f402,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f401]) ).
fof(f403,plain,
$false,
inference(sat_refutation,[status(thm)],[f321,f402]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET185+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/5.35 % Computer : n012.cluster.edu
% 0.07/5.35 % Model : x86_64 x86_64
% 0.07/5.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/5.35 % Memory : 8046.5625MB
% 0.07/5.35 % OS : Linux 6.8.0-71-generic
% 0.07/5.35 % CPULimit : 300
% 0.07/5.35 % WCLimit : 300
% 0.07/5.35 % DateTime : Mon Sep 21 04:59:27 UTC 2026
% 0.07/5.35 % CPUTime :
% 0.07/5.36 % Drodi V4.1.1
% 0.07/5.40 % Refutation found
% 0.07/5.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/5.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/5.42 % Elapsed time: 0.058547 seconds
% 0.12/5.42 % CPU time: 0.255559 seconds
% 0.12/5.42 % Total memory used: 104.731 MB
% 0.12/5.42 % Net memory used: 103.841 MB
%------------------------------------------------------------------------------