%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SEU146+1 : TPTP v9.3.1. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n010.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 02:19:23 PM UTC 2026
% Result : Theorem 0.13s 0.39s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 14
% Syntax : Number of formulae : 69 ( 6 unt; 7 def)
% Number of atoms : 179 ( 46 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 179 ( 69 ~; 82 |; 13 &)
% ( 12 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 65 ( 61 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( A = B
<=> ( subset(B,A)
& subset(A,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] :
( subset(A,B)
=> ( subset(A,set_difference(B,singleton(C)))
| in(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( A = singleton(B)
| A = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f14,axiom,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,plain,
! [A,B] :
( ( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(NNF_transformation,[status(thm)],[f2]) ).
fof(f20,plain,
( ! [A,B] :
( ~ subset(B,A)
| ~ subset(A,B)
| A = B )
& ! [A,B] :
( ( subset(B,A)
& subset(A,B) )
| A != B ) ),
inference(miniscoping,[status(thm)],[f19]) ).
fof(f21,plain,
! [X0,X1] :
( subset(X0,X1)
| X0 != X1 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f23,plain,
! [X0,X1] :
( ~ subset(X1,X0)
| ~ subset(X0,X1)
| X0 = X1 ),
inference(cnf_transformation,[status(thm)],[f20]) ).
fof(f25,plain,
! [A,B] :
( ( ~ in(A,B)
| subset(singleton(A),B) )
& ( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(NNF_transformation,[status(thm)],[f7]) ).
fof(f26,plain,
( ! [A,B] :
( ~ in(A,B)
| subset(singleton(A),B) )
& ! [A,B] :
( in(A,B)
| ~ subset(singleton(A),B) ) ),
inference(miniscoping,[status(thm)],[f25]) ).
fof(f28,plain,
! [X0,X1] :
( ~ in(X0,X1)
| subset(singleton(X0),X1) ),
inference(cnf_transformation,[status(thm)],[f26]) ).
fof(f29,plain,
! [A,B,C] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A)
| ~ subset(A,B) ),
inference(pre_NNF_transformation,[status(thm)],[f8]) ).
fof(f30,plain,
! [A,B] :
( ! [C] :
( subset(A,set_difference(B,singleton(C)))
| in(C,A) )
| ~ subset(A,B) ),
inference(miniscoping,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0,X1,X2] :
( subset(X0,set_difference(X1,singleton(X2)))
| in(X2,X0)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f30]) ).
fof(f32,plain,
? [A,B] :
( subset(A,singleton(B))
<~> ( A = singleton(B)
| A = empty_set ) ),
inference(pre_NNF_transformation,[status(thm)],[f10]) ).
fof(f33,plain,
? [A,B] :
( ( ( A != singleton(B)
& A != empty_set )
| ~ subset(A,singleton(B)) )
& ( A = singleton(B)
| A = empty_set
| subset(A,singleton(B)) ) ),
inference(NNF_transformation,[status(thm)],[f32]) ).
fof(f34,plain,
( ( ( sK0_skl != singleton(sK1_skl)
& sK0_skl != empty_set )
| ~ subset(sK0_skl,singleton(sK1_skl)) )
& ( sK0_skl = singleton(sK1_skl)
| sK0_skl = empty_set
| subset(sK0_skl,singleton(sK1_skl)) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl]),skolemize(A,sK0_skl),skolemize(B,sK1_skl)],[f33]) ).
fof(f35,plain,
( sK0_skl = singleton(sK1_skl)
| sK0_skl = empty_set
| subset(sK0_skl,singleton(sK1_skl)) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f36,plain,
( sK0_skl != empty_set
| ~ subset(sK0_skl,singleton(sK1_skl)) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f37,plain,
( sK0_skl != singleton(sK1_skl)
| ~ subset(sK0_skl,singleton(sK1_skl)) ),
inference(cnf_transformation,[status(thm)],[f34]) ).
fof(f44,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(thm)],[f14]) ).
fof(f45,plain,
! [A,B] :
( ( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(NNF_transformation,[status(thm)],[f15]) ).
fof(f46,plain,
( ! [A,B] :
( ~ subset(A,B)
| set_difference(A,B) = empty_set )
& ! [A,B] :
( subset(A,B)
| set_difference(A,B) != empty_set ) ),
inference(miniscoping,[status(thm)],[f45]) ).
fof(f47,plain,
! [X0,X1] :
( subset(X0,X1)
| set_difference(X0,X1) != empty_set ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f48,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_difference(X0,X1) = empty_set ),
inference(cnf_transformation,[status(thm)],[f46]) ).
fof(f49,plain,
! [A] :
( A = empty_set
| ~ subset(A,empty_set) ),
inference(pre_NNF_transformation,[status(thm)],[f16]) ).
fof(f50,plain,
! [X0] :
( X0 = empty_set
| ~ subset(X0,empty_set) ),
inference(cnf_transformation,[status(thm)],[f49]) ).
fof(f51,definition,
( sQ0_spl
<=> subset(sK0_skl,singleton(sK1_skl)) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f52,plain,
( ~ sQ0_spl
| subset(sK0_skl,singleton(sK1_skl)) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f53,plain,
( sQ0_spl
| ~ subset(sK0_skl,singleton(sK1_skl)) ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,definition,
( sQ1_spl
<=> sK0_skl = empty_set ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f55,plain,
( ~ sQ1_spl
| sK0_skl = empty_set ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,definition,
( sQ2_spl
<=> sK0_skl = singleton(sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f58,plain,
( ~ sQ2_spl
| sK0_skl = singleton(sK1_skl) ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( sQ2_spl
| sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f35,f51,f54,f57]) ).
fof(f61,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f36,f51,f54]) ).
fof(f62,plain,
( ~ sQ2_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f37,f51,f57]) ).
fof(f63,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(thm)],[f21]) ).
fof(f65,plain,
( sQ0_spl
| ~ sQ1_spl
| ~ subset(empty_set,singleton(sK1_skl)) ),
inference(forward_demodulation,[status(thm)],[f55,f53]) ).
fof(f67,plain,
( sQ0_spl
| ~ sQ1_spl
| $false ),
inference(backward_subsumption_resolution,[status(thm)],[f65,f44]) ).
fof(f69,plain,
( sQ0_spl
| ~ sQ1_spl ),
inference(contradiction_clause,[status(thm)],[f67]) ).
fof(f72,plain,
( ~ sQ0_spl
| ~ subset(singleton(sK1_skl),sK0_skl)
| singleton(sK1_skl) = sK0_skl ),
inference(resolution,[status(thm)],[f52,f23]) ).
fof(f73,definition,
( sQ3_spl
<=> subset(singleton(sK1_skl),sK0_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f76,plain,
( ~ sQ0_spl
| ~ sQ3_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f72,f57,f73,f51]) ).
fof(f77,plain,
( sQ0_spl
| ~ sQ2_spl
| ~ subset(sK0_skl,sK0_skl) ),
inference(forward_demodulation,[status(thm)],[f58,f53]) ).
fof(f78,plain,
( sQ0_spl
| ~ sQ2_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f77,f63]) ).
fof(f79,plain,
( sQ0_spl
| ~ sQ2_spl ),
inference(contradiction_clause,[status(thm)],[f78]) ).
fof(f85,plain,
( ~ sQ0_spl
| set_difference(sK0_skl,singleton(sK1_skl)) = empty_set ),
inference(resolution,[status(thm)],[f48,f52]) ).
fof(f86,plain,
! [X0] : set_difference(empty_set,X0) = empty_set,
inference(resolution,[status(thm)],[f48,f44]) ).
fof(f92,plain,
! [X0] :
( ~ sQ0_spl
| subset(X0,empty_set)
| in(sK1_skl,X0)
| ~ subset(X0,sK0_skl) ),
inference(paramodulation,[status(thm)],[f85,f31]) ).
fof(f94,definition,
( sQ4_spl
<=> empty_set = empty_set ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f96,plain,
( sQ4_spl
| empty_set != empty_set ),
inference(component_clause,[status(thm)],[f94]) ).
fof(f100,plain,
! [X0] :
( subset(empty_set,X0)
| empty_set != empty_set ),
inference(paramodulation,[status(thm)],[f86,f47]) ).
fof(f101,definition,
! [X0] :
( sQ5_spl
<=> subset(empty_set,X0) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f104,plain,
( sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f100,f94,f101]) ).
fof(f105,plain,
( sQ4_spl
| $false ),
inference(trivial_equality_resolution,[status(thm)],[f96]) ).
fof(f106,plain,
sQ4_spl,
inference(contradiction_clause,[status(thm)],[f105]) ).
fof(f107,plain,
! [X0] :
( ~ sQ0_spl
| subset(singleton(sK1_skl),X0)
| subset(X0,empty_set)
| ~ subset(X0,sK0_skl) ),
inference(resolution,[status(thm)],[f92,f28]) ).
fof(f118,plain,
( ~ sQ0_spl
| subset(singleton(sK1_skl),sK0_skl)
| subset(sK0_skl,empty_set) ),
inference(resolution,[status(thm)],[f107,f63]) ).
fof(f126,definition,
( sQ10_spl
<=> subset(sK0_skl,empty_set) ),
introduced(definition,[new_symbols(definition,[sQ10_spl])],[split_symbol_definition]) ).
fof(f127,plain,
( ~ sQ10_spl
| subset(sK0_skl,empty_set) ),
inference(component_clause,[status(thm)],[f126]) ).
fof(f129,plain,
( ~ sQ0_spl
| sQ3_spl
| sQ10_spl ),
inference(split_clause,[status(thm)],[f118,f126,f73,f51]) ).
fof(f130,plain,
( ~ sQ10_spl
| sK0_skl = empty_set ),
inference(resolution,[status(thm)],[f127,f50]) ).
fof(f133,plain,
( ~ sQ10_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f130,f54,f126]) ).
fof(f138,plain,
$false,
inference(sat_refutation,[status(thm)],[f60,f61,f62,f69,f76,f79,f104,f106,f129,f133]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SEU146+1 : TPTP v9.3.1. Released v3.3.0.
% 0.00/0.03 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.10/0.35 % Computer : n010.cluster.edu
% 0.10/0.35 % Model : x86_64 x86_64
% 0.10/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.35 % Memory : 8046.5625MB
% 0.10/0.35 % OS : Linux 6.8.0-71-generic
% 0.10/0.35 % CPULimit : 300
% 0.10/0.35 % WCLimit : 300
% 0.10/0.35 % DateTime : Mon Sep 21 05:53:10 UTC 2026
% 0.10/0.36 % CPUTime :
% 0.10/0.37 % Drodi V4.1.1
% 0.13/0.39 % Refutation found
% 0.13/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.42 % Elapsed time: 0.046016 seconds
% 0.13/0.42 % CPU time: 0.137692 seconds
% 0.13/0.42 % Total memory used: 80.478 MB
% 0.13/0.42 % Net memory used: 80.102 MB
%------------------------------------------------------------------------------