%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET162+4 : TPTP v9.3.1. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:09:32 PM UTC 2026
% Result : Theorem 0.13s 0.38s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 10
% Syntax : Number of formulae : 51 ( 10 unt; 5 def)
% Number of atoms : 133 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 136 ( 54 ~; 57 |; 15 &)
% ( 9 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 6 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-2 aty)
% Number of variables : 63 ( 60 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X,A,B] :
( member(X,union(A,B))
<=> ( member(X,B)
| member(X,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A] : equal_set(union(A,empty_set),A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A] : equal_set(union(A,empty_set),A),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,B)
| ~ member(X,A) ) ),
inference(pre_NNF_transformation,[status(thm)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ? [X] :
( ~ member(X,B)
& member(X,A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(miniscoping,[status(thm)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ( ~ member(sK0_skl(B,A),B)
& member(sK0_skl(B,A),A) )
| subset(A,B) )
& ! [A,B] :
( ! [X] :
( member(X,B)
| ~ member(X,A) )
| ~ subset(A,B) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(X,sK0_skl(B,A))],[f16]) ).
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,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f22,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| equal_set(A,B) )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| ~ equal_set(A,B) ) ),
inference(miniscoping,[status(thm)],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f35,plain,
! [X,A,B] :
( ( ( ~ member(X,B)
& ~ member(X,A) )
| member(X,union(A,B)) )
& ( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(NNF_transformation,[status(thm)],[f5]) ).
fof(f36,plain,
( ! [X,A,B] :
( ( ~ member(X,B)
& ~ member(X,A) )
| member(X,union(A,B)) )
& ! [X,A,B] :
( member(X,B)
| member(X,A)
| ~ member(X,union(A,B)) ) ),
inference(miniscoping,[status(thm)],[f35]) ).
fof(f37,plain,
! [X0,X1,X2] :
( member(X0,X2)
| member(X0,X1)
| ~ member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f38,plain,
! [X0,X1,X2] :
( ~ member(X0,X1)
| member(X0,union(X1,X2)) ),
inference(cnf_transformation,[status(thm)],[f36]) ).
fof(f40,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f68,plain,
? [A] : ~ equal_set(union(A,empty_set),A),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
~ equal_set(union(sK3_skl,empty_set),sK3_skl),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(A,sK3_skl)],[f68]) ).
fof(f70,plain,
~ equal_set(union(sK3_skl,empty_set),sK3_skl),
inference(cnf_transformation,[status(thm)],[f69]) ).
fof(f76,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,f37]) ).
fof(f79,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| equal_set(X0,X1)
| ~ member(sK0_skl(X0,X1),X0) ),
inference(resolution,[status(thm)],[f20,f25]) ).
fof(f88,plain,
( ~ subset(union(sK3_skl,empty_set),sK3_skl)
| ~ member(sK0_skl(union(sK3_skl,empty_set),sK3_skl),union(sK3_skl,empty_set)) ),
inference(resolution,[status(thm)],[f79,f70]) ).
fof(f91,definition,
( sQ0_spl
<=> member(sK0_skl(union(sK3_skl,empty_set),sK3_skl),union(sK3_skl,empty_set)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f93,plain,
( sQ0_spl
| ~ member(sK0_skl(union(sK3_skl,empty_set),sK3_skl),union(sK3_skl,empty_set)) ),
inference(component_clause,[status(thm)],[f91]) ).
fof(f94,definition,
( sQ1_spl
<=> subset(union(sK3_skl,empty_set),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( sQ1_spl
| ~ subset(union(sK3_skl,empty_set),sK3_skl) ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f97,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f88,f91,f94]) ).
fof(f101,plain,
( sQ0_spl
| ~ member(sK0_skl(union(sK3_skl,empty_set),sK3_skl),sK3_skl) ),
inference(resolution,[status(thm)],[f93,f38]) ).
fof(f107,plain,
( sQ0_spl
| subset(sK3_skl,union(sK3_skl,empty_set)) ),
inference(resolution,[status(thm)],[f101,f19]) ).
fof(f113,plain,
( sQ0_spl
| ~ subset(union(sK3_skl,empty_set),sK3_skl)
| equal_set(union(sK3_skl,empty_set),sK3_skl) ),
inference(resolution,[status(thm)],[f107,f25]) ).
fof(f114,definition,
( sQ2_spl
<=> equal_set(union(sK3_skl,empty_set),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f115,plain,
( ~ sQ2_spl
| equal_set(union(sK3_skl,empty_set),sK3_skl) ),
inference(component_clause,[status(thm)],[f114]) ).
fof(f117,plain,
( sQ0_spl
| ~ sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f113,f114,f94,f91]) ).
fof(f119,plain,
( sQ1_spl
| member(sK0_skl(sK3_skl,union(sK3_skl,empty_set)),empty_set)
| member(sK0_skl(sK3_skl,union(sK3_skl,empty_set)),sK3_skl) ),
inference(resolution,[status(thm)],[f96,f76]) ).
fof(f120,plain,
( sQ1_spl
| ~ member(sK0_skl(sK3_skl,union(sK3_skl,empty_set)),sK3_skl) ),
inference(resolution,[status(thm)],[f96,f20]) ).
fof(f122,definition,
( sQ3_spl
<=> member(sK0_skl(sK3_skl,union(sK3_skl,empty_set)),sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f123,plain,
( ~ sQ3_spl
| member(sK0_skl(sK3_skl,union(sK3_skl,empty_set)),sK3_skl) ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,definition,
( sQ4_spl
<=> member(sK0_skl(sK3_skl,union(sK3_skl,empty_set)),empty_set) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f126,plain,
( ~ sQ4_spl
| member(sK0_skl(sK3_skl,union(sK3_skl,empty_set)),empty_set) ),
inference(component_clause,[status(thm)],[f125]) ).
fof(f128,plain,
( sQ1_spl
| sQ4_spl
| sQ3_spl ),
inference(split_clause,[status(thm)],[f119,f122,f125,f94]) ).
fof(f139,plain,
( ~ sQ3_spl
| sQ1_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f123,f120]) ).
fof(f140,plain,
( ~ sQ3_spl
| sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f139]) ).
fof(f141,plain,
( ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f115,f70]) ).
fof(f142,plain,
~ sQ2_spl,
inference(contradiction_clause,[status(thm)],[f141]) ).
fof(f143,plain,
( ~ sQ4_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f126,f40]) ).
fof(f144,plain,
~ sQ4_spl,
inference(contradiction_clause,[status(thm)],[f143]) ).
fof(f145,plain,
$false,
inference(sat_refutation,[status(thm)],[f97,f117,f128,f140,f142,f144]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET162+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.07/0.35 % Computer : n001.cluster.edu
% 0.07/0.35 % Model : x86_64 x86_64
% 0.07/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.35 % Memory : 8046.5625MB
% 0.07/0.35 % OS : Linux 6.8.0-71-generic
% 0.07/0.35 % CPULimit : 300
% 0.07/0.35 % WCLimit : 300
% 0.07/0.35 % DateTime : Mon Sep 21 05:03:00 UTC 2026
% 0.07/0.35 % CPUTime :
% 0.07/0.36 % Drodi V4.1.1
% 0.13/0.38 % Refutation found
% 0.13/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.40 % Elapsed time: 0.046991 seconds
% 0.13/0.40 % CPU time: 0.152421 seconds
% 0.13/0.40 % Total memory used: 81.162 MB
% 0.13/0.40 % Net memory used: 80.837 MB
%------------------------------------------------------------------------------