%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET047+1 : TPTP v9.3.1. Released v2.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n004.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 02:09:03 PM UTC 2026
% Result : Theorem 0.11s 0.40s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 8
% Syntax : Number of formulae : 49 ( 1 unt; 6 def)
% Number of atoms : 149 ( 0 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 168 ( 68 ~; 78 |; 11 &)
% ( 10 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 2 con; 0-2 aty)
% Number of variables : 42 ( 36 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y] :
( set_equal(X,Y)
<=> ! [Z] :
( element(Z,X)
<=> element(Z,Y) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,conjecture,
! [X,Y] :
( set_equal(X,Y)
<=> set_equal(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,negated_conjecture,
~ ! [X,Y] :
( set_equal(X,Y)
<=> set_equal(Y,X) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
fof(f4,plain,
! [X,Y] :
( ( ? [Z] :
( ( element(Z,Y)
| element(Z,X) )
& ( ~ element(Z,Y)
| ~ element(Z,X) ) )
| set_equal(X,Y) )
& ( ! [Z] :
( ( ~ element(Z,Y)
| element(Z,X) )
& ( element(Z,Y)
| ~ element(Z,X) ) )
| ~ set_equal(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f1]) ).
fof(f5,plain,
( ! [X,Y] :
( ? [Z] :
( ( element(Z,Y)
| element(Z,X) )
& ( ~ element(Z,Y)
| ~ element(Z,X) ) )
| set_equal(X,Y) )
& ! [X,Y] :
( ( ! [Z] :
( ~ element(Z,Y)
| element(Z,X) )
& ! [Z] :
( element(Z,Y)
| ~ element(Z,X) ) )
| ~ set_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f6,plain,
( ! [X,Y] :
( ( ( element(sK0_skl(Y,X),Y)
| element(sK0_skl(Y,X),X) )
& ( ~ element(sK0_skl(Y,X),Y)
| ~ element(sK0_skl(Y,X),X) ) )
| set_equal(X,Y) )
& ! [X,Y] :
( ( ! [Z] :
( ~ element(Z,Y)
| element(Z,X) )
& ! [Z] :
( element(Z,Y)
| ~ element(Z,X) ) )
| ~ set_equal(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl]),skolemize(Z,sK0_skl(Y,X))],[f5]) ).
fof(f7,plain,
! [X0,X1,X2] :
( element(X2,X1)
| ~ element(X2,X0)
| ~ set_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( ~ element(X2,X1)
| element(X2,X0)
| ~ set_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X0,X1] :
( ~ element(sK0_skl(X1,X0),X1)
| ~ element(sK0_skl(X1,X0),X0)
| set_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
! [X0,X1] :
( element(sK0_skl(X1,X0),X1)
| element(sK0_skl(X1,X0),X0)
| set_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,plain,
? [X,Y] :
( set_equal(X,Y)
<~> set_equal(Y,X) ),
inference(pre_NNF_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
? [X,Y] :
( ( ~ set_equal(Y,X)
| ~ set_equal(X,Y) )
& ( set_equal(Y,X)
| set_equal(X,Y) ) ),
inference(NNF_transformation,[status(thm)],[f11]) ).
fof(f13,plain,
( ( ~ set_equal(sK2_skl,sK1_skl)
| ~ set_equal(sK1_skl,sK2_skl) )
& ( set_equal(sK2_skl,sK1_skl)
| set_equal(sK1_skl,sK2_skl) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK1_skl,sK2_skl]),skolemize(X,sK1_skl),skolemize(Y,sK2_skl)],[f12]) ).
fof(f14,plain,
( set_equal(sK2_skl,sK1_skl)
| set_equal(sK1_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f15,plain,
( ~ set_equal(sK2_skl,sK1_skl)
| ~ set_equal(sK1_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
fof(f16,definition,
( sQ0_spl
<=> set_equal(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f17,plain,
( ~ sQ0_spl
| set_equal(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f16]) ).
fof(f18,plain,
( sQ0_spl
| ~ set_equal(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f16]) ).
fof(f19,definition,
( sQ1_spl
<=> set_equal(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f20,plain,
( ~ sQ1_spl
| set_equal(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f19]) ).
fof(f21,plain,
( sQ1_spl
| ~ set_equal(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f19]) ).
fof(f22,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f14,f16,f19]) ).
fof(f23,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f15,f16,f19]) ).
fof(f24,plain,
( sQ0_spl
| ~ element(sK0_skl(sK2_skl,sK1_skl),sK2_skl)
| ~ element(sK0_skl(sK2_skl,sK1_skl),sK1_skl) ),
inference(resolution,[status(thm)],[f9,f18]) ).
fof(f25,definition,
( sQ2_spl
<=> element(sK0_skl(sK2_skl,sK1_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f27,plain,
( sQ2_spl
| ~ element(sK0_skl(sK2_skl,sK1_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f25]) ).
fof(f28,definition,
( sQ3_spl
<=> element(sK0_skl(sK2_skl,sK1_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f30,plain,
( sQ3_spl
| ~ element(sK0_skl(sK2_skl,sK1_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f28]) ).
fof(f31,plain,
( sQ0_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f24,f25,f28,f16]) ).
fof(f32,plain,
( sQ1_spl
| ~ element(sK0_skl(sK1_skl,sK2_skl),sK1_skl)
| ~ element(sK0_skl(sK1_skl,sK2_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f21,f9]) ).
fof(f33,definition,
( sQ4_spl
<=> element(sK0_skl(sK1_skl,sK2_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f35,plain,
( sQ4_spl
| ~ element(sK0_skl(sK1_skl,sK2_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,definition,
( sQ5_spl
<=> element(sK0_skl(sK1_skl,sK2_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f38,plain,
( sQ5_spl
| ~ element(sK0_skl(sK1_skl,sK2_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f36]) ).
fof(f39,plain,
( sQ1_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f32,f33,f36,f19]) ).
fof(f41,plain,
! [X0] :
( sQ4_spl
| ~ element(sK0_skl(sK1_skl,sK2_skl),X0)
| ~ set_equal(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f35,f7]) ).
fof(f45,plain,
( sQ4_spl
| ~ set_equal(sK1_skl,sK2_skl)
| element(sK0_skl(sK1_skl,sK2_skl),sK2_skl)
| set_equal(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f10,f41]) ).
fof(f46,plain,
( ~ sQ0_spl
| sQ4_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f45,f19,f33,f16]) ).
fof(f50,plain,
! [X0] :
( sQ2_spl
| ~ element(sK0_skl(sK2_skl,sK1_skl),X0)
| ~ set_equal(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f27,f7]) ).
fof(f52,plain,
( ~ sQ1_spl
| sQ2_spl
| ~ element(sK0_skl(sK2_skl,sK1_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f50,f20]) ).
fof(f64,plain,
( ~ sQ1_spl
| sQ2_spl
| element(sK0_skl(sK2_skl,sK1_skl),sK1_skl)
| set_equal(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f52,f10]) ).
fof(f67,plain,
( ~ sQ1_spl
| sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f64,f16,f25,f19]) ).
fof(f71,plain,
! [X0] :
( sQ5_spl
| ~ element(sK0_skl(sK1_skl,sK2_skl),X0)
| ~ set_equal(sK1_skl,X0) ),
inference(resolution,[status(thm)],[f38,f8]) ).
fof(f77,plain,
! [X0] :
( sQ3_spl
| ~ element(sK0_skl(sK2_skl,sK1_skl),X0)
| ~ set_equal(sK2_skl,X0) ),
inference(resolution,[status(thm)],[f30,f8]) ).
fof(f86,plain,
( ~ sQ0_spl
| sQ5_spl
| ~ element(sK0_skl(sK1_skl,sK2_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f71,f17]) ).
fof(f88,plain,
( ~ sQ0_spl
| sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f86,f33,f36,f16]) ).
fof(f95,plain,
( ~ sQ1_spl
| sQ3_spl
| ~ element(sK0_skl(sK2_skl,sK1_skl),sK1_skl) ),
inference(resolution,[status(thm)],[f77,f20]) ).
fof(f97,plain,
( ~ sQ1_spl
| sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f95,f25,f28,f19]) ).
fof(f98,plain,
$false,
inference(sat_refutation,[status(thm)],[f22,f23,f31,f39,f46,f67,f88,f97]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET047+1 : TPTP v9.3.1. Released v2.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n004.cluster.edu
% 0.11/0.37 % Model : x86_64 x86_64
% 0.11/0.37 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.37 % Memory : 8046.5625MB
% 0.11/0.37 % OS : Linux 6.8.0-71-generic
% 0.11/0.37 % CPULimit : 300
% 0.11/0.37 % WCLimit : 300
% 0.11/0.37 % DateTime : Mon Sep 21 04:47:34 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.11/0.40 % Refutation found
% 0.11/0.40 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.11/0.40 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.43 % Elapsed time: 0.052440 seconds
% 0.11/0.43 % CPU time: 0.137882 seconds
% 0.11/0.43 % Total memory used: 17.076 MB
% 0.11/0.43 % Net memory used: 16.509 MB
%------------------------------------------------------------------------------