%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET691+4 : 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 02:10:27 PM UTC 2026
% Result : Theorem 0.12s 0.36s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 43 ( 4 unt; 4 def)
% Number of atoms : 115 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 119 ( 47 ~; 48 |; 13 &)
% ( 9 <=>; 1 =>; 0 <=; 1 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 5 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 41 ( 37 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] :
( equal_set(A,B)
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] : ~ member(X,empty_set),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A] :
( subset(A,empty_set)
<=> equal_set(A,empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A] :
( subset(A,empty_set)
<=> equal_set(A,empty_set) ),
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(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(f23,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| equal_set(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f22]) ).
fof(f40,plain,
! [X0] : ~ member(X0,empty_set),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f68,plain,
? [A] :
( subset(A,empty_set)
<~> equal_set(A,empty_set) ),
inference(pre_NNF_transformation,[status(thm)],[f13]) ).
fof(f69,plain,
? [A] :
( ( ~ equal_set(A,empty_set)
| ~ subset(A,empty_set) )
& ( equal_set(A,empty_set)
| subset(A,empty_set) ) ),
inference(NNF_transformation,[status(thm)],[f68]) ).
fof(f70,plain,
( ( ~ equal_set(sK3_skl,empty_set)
| ~ subset(sK3_skl,empty_set) )
& ( equal_set(sK3_skl,empty_set)
| subset(sK3_skl,empty_set) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK3_skl]),skolemize(A,sK3_skl)],[f69]) ).
fof(f71,plain,
( equal_set(sK3_skl,empty_set)
| subset(sK3_skl,empty_set) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f72,plain,
( ~ equal_set(sK3_skl,empty_set)
| ~ subset(sK3_skl,empty_set) ),
inference(cnf_transformation,[status(thm)],[f70]) ).
fof(f73,definition,
( sQ0_spl
<=> subset(sK3_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f74,plain,
( ~ sQ0_spl
| subset(sK3_skl,empty_set) ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f75,plain,
( sQ0_spl
| ~ subset(sK3_skl,empty_set) ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,definition,
( sQ1_spl
<=> equal_set(sK3_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f77,plain,
( ~ sQ1_spl
| equal_set(sK3_skl,empty_set) ),
inference(component_clause,[status(thm)],[f76]) ).
fof(f79,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f71,f73,f76]) ).
fof(f80,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f72,f73,f76]) ).
fof(f84,plain,
( ~ sQ1_spl
| subset(sK3_skl,empty_set) ),
inference(resolution,[status(thm)],[f23,f77]) ).
fof(f85,plain,
( ~ sQ1_spl
| sQ0_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f84,f75]) ).
fof(f86,plain,
( ~ sQ1_spl
| sQ0_spl ),
inference(contradiction_clause,[status(thm)],[f85]) ).
fof(f89,plain,
( ~ sQ0_spl
| ~ subset(empty_set,sK3_skl)
| equal_set(empty_set,sK3_skl) ),
inference(resolution,[status(thm)],[f25,f74]) ).
fof(f90,definition,
( sQ2_spl
<=> equal_set(empty_set,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f91,plain,
( ~ sQ2_spl
| equal_set(empty_set,sK3_skl) ),
inference(component_clause,[status(thm)],[f90]) ).
fof(f93,definition,
( sQ3_spl
<=> subset(empty_set,sK3_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f95,plain,
( sQ3_spl
| ~ subset(empty_set,sK3_skl) ),
inference(component_clause,[status(thm)],[f93]) ).
fof(f96,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f89,f90,f93,f73]) ).
fof(f98,plain,
( ~ sQ2_spl
| subset(empty_set,sK3_skl) ),
inference(resolution,[status(thm)],[f91,f23]) ).
fof(f99,plain,
( ~ sQ2_spl
| ~ subset(sK3_skl,empty_set)
| equal_set(sK3_skl,empty_set) ),
inference(resolution,[status(thm)],[f98,f25]) ).
fof(f101,plain,
( ~ sQ2_spl
| ~ sQ0_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f99,f76,f73,f90]) ).
fof(f104,plain,
( sQ3_spl
| member(sK0_skl(sK3_skl,empty_set),empty_set) ),
inference(resolution,[status(thm)],[f19,f95]) ).
fof(f107,plain,
( sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f104,f40]) ).
fof(f108,plain,
sQ3_spl,
inference(contradiction_clause,[status(thm)],[f107]) ).
fof(f109,plain,
$false,
inference(sat_refutation,[status(thm)],[f79,f80,f86,f96,f101,f108]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SET691+4 : TPTP v9.3.1. Released v2.2.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.08/0.34 % Computer : n014.cluster.edu
% 0.08/0.34 % Model : x86_64 x86_64
% 0.08/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.34 % Memory : 8046.5625MB
% 0.08/0.34 % OS : Linux 6.8.0-71-generic
% 0.08/0.34 % CPULimit : 300
% 0.08/0.34 % WCLimit : 300
% 0.08/0.34 % DateTime : Mon Sep 21 05:32:19 UTC 2026
% 0.08/0.34 % CPUTime :
% 0.08/0.35 % Drodi V4.1.1
% 0.12/0.36 % Refutation found
% 0.12/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.38 % Elapsed time: 0.035298 seconds
% 0.12/0.38 % CPU time: 0.105910 seconds
% 0.12/0.38 % Total memory used: 47.866 MB
% 0.12/0.38 % Net memory used: 47.723 MB
%------------------------------------------------------------------------------