%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET183+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 : n014.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 02:09:34 PM UTC 2026
% Result : Theorem 0.09s 0.41s
% Output : CNFRefutation 0.09s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 48 ( 6 unt; 4 def)
% Number of atoms : 131 ( 11 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 136 ( 53 ~; 54 |; 18 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 64 ( 60 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,C)
& member(D,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] : subset(intersection(B,C),B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( B = C
<=> ( subset(C,B)
& subset(B,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [B,C] :
( subset(B,C)
=> intersection(B,C) = B ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f10,plain,
! [B,C,D] :
( ( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f11,plain,
( ! [B,C,D] :
( ~ member(D,C)
| ~ member(D,B)
| member(D,intersection(B,C)) )
& ! [B,C,D] :
( ( member(D,C)
& member(D,B) )
| ~ member(D,intersection(B,C)) ) ),
inference(miniscoping,[status(thm)],[f10]) ).
fof(f14,plain,
! [X0,X1,X2] :
( ~ member(X0,X2)
| ~ member(X0,X1)
| member(X0,intersection(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f11]) ).
fof(f15,plain,
! [X0,X1] : subset(intersection(X0,X1),X0),
inference(cnf_transformation,[status(thm)],[f2]) ).
fof(f16,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,C)
| ~ member(D,B) ) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f17,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)],[f16]) ).
fof(f18,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)],[f17]) ).
fof(f19,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))],[f18]) ).
fof(f20,plain,
! [X0,X1,X2] :
( member(X2,X1)
| ~ member(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( member(sK0_skl(X1,X0),X0)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f22,plain,
! [X0,X1] :
( ~ member(sK0_skl(X1,X0),X1)
| subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
fof(f23,plain,
! [B,C] :
( ( ~ subset(C,B)
| ~ subset(B,C)
| B = C )
& ( ( subset(C,B)
& subset(B,C) )
| B != C ) ),
inference(NNF_transformation,[status(thm)],[f4]) ).
fof(f24,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)],[f23]) ).
fof(f27,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f24]) ).
fof(f37,plain,
? [B,C] :
( intersection(B,C) != B
& subset(B,C) ),
inference(pre_NNF_transformation,[status(thm)],[f9]) ).
fof(f38,plain,
( intersection(sK2_skl,sK3_skl) != sK2_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)],[f37]) ).
fof(f39,plain,
subset(sK2_skl,sK3_skl),
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f40,plain,
intersection(sK2_skl,sK3_skl) != sK2_skl,
inference(cnf_transformation,[status(thm)],[f38]) ).
fof(f51,plain,
( ~ subset(sK2_skl,intersection(sK2_skl,sK3_skl))
| ~ subset(intersection(sK2_skl,sK3_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f27,f40]) ).
fof(f53,definition,
( sQ0_spl
<=> subset(intersection(sK2_skl,sK3_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( sQ0_spl
| ~ subset(intersection(sK2_skl,sK3_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,definition,
( sQ1_spl
<=> subset(sK2_skl,intersection(sK2_skl,sK3_skl)) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( sQ1_spl
| ~ subset(sK2_skl,intersection(sK2_skl,sK3_skl)) ),
inference(component_clause,[status(thm)],[f56]) ).
fof(f59,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f51,f53,f56]) ).
fof(f61,plain,
( sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f15]) ).
fof(f62,plain,
sQ0_spl,
inference(contradiction_clause,[status(thm)],[f61]) ).
fof(f65,plain,
( sQ1_spl
| ~ member(sK0_skl(intersection(sK2_skl,sK3_skl),sK2_skl),intersection(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f58,f22]) ).
fof(f66,plain,
( sQ1_spl
| ~ member(sK0_skl(intersection(sK2_skl,sK3_skl),sK2_skl),sK3_skl)
| ~ member(sK0_skl(intersection(sK2_skl,sK3_skl),sK2_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f65,f14]) ).
fof(f70,definition,
( sQ2_spl
<=> member(sK0_skl(intersection(sK2_skl,sK3_skl),sK2_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f71,plain,
( ~ sQ2_spl
| member(sK0_skl(intersection(sK2_skl,sK3_skl),sK2_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f72,plain,
( sQ2_spl
| ~ member(sK0_skl(intersection(sK2_skl,sK3_skl),sK2_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ3_spl
<=> member(sK0_skl(intersection(sK2_skl,sK3_skl),sK2_skl),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f75,plain,
( sQ3_spl
| ~ member(sK0_skl(intersection(sK2_skl,sK3_skl),sK2_skl),sK3_skl) ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f66,f70,f73,f56]) ).
fof(f110,plain,
( sQ2_spl
| subset(sK2_skl,intersection(sK2_skl,sK3_skl)) ),
inference(resolution,[status(thm)],[f72,f21]) ).
fof(f114,plain,
( sQ2_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f110,f58]) ).
fof(f115,plain,
( sQ2_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f114]) ).
fof(f116,plain,
! [X0] :
( sQ3_spl
| ~ member(sK0_skl(intersection(sK2_skl,sK3_skl),sK2_skl),X0)
| ~ subset(X0,sK3_skl) ),
inference(resolution,[status(thm)],[f75,f20]) ).
fof(f133,plain,
( ~ sQ2_spl
| sQ3_spl
| ~ subset(sK2_skl,sK3_skl) ),
inference(resolution,[status(thm)],[f116,f71]) ).
fof(f139,plain,
( ~ sQ2_spl
| sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f39]) ).
fof(f140,plain,
( ~ sQ2_spl
| sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f139]) ).
fof(f141,plain,
$false,
inference(sat_refutation,[status(thm)],[f59,f62,f76,f115,f140]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET183+3 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.09/0.37 % Computer : n014.cluster.edu
% 0.09/0.37 % Model : x86_64 x86_64
% 0.09/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.37 % Memory : 8046.5625MB
% 0.09/0.37 % OS : Linux 6.8.0-71-generic
% 0.09/0.37 % CPULimit : 300
% 0.09/0.37 % WCLimit : 300
% 0.09/0.37 % DateTime : Mon Sep 21 04:59:04 UTC 2026
% 0.09/0.37 % CPUTime :
% 0.09/0.38 % Drodi V4.1.1
% 0.09/0.41 % Refutation found
% 0.09/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.09/0.43 % Elapsed time: 0.055843 seconds
% 0.09/0.43 % CPU time: 0.155000 seconds
% 0.09/0.43 % Total memory used: 101.733 MB
% 0.09/0.43 % Net memory used: 101.304 MB
%------------------------------------------------------------------------------