%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET047-5 : TPTP v9.3.1. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox2/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 02:09:03 PM UTC 2026
% Result : Unsatisfiable 0.11s 0.39s
% Output : CNFRefutation 0.11s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 12
% Syntax : Number of formulae : 48 ( 1 unt; 6 def)
% Number of atoms : 124 ( 0 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 136 ( 60 ~; 70 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 7 ( 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 : 30 ( 30 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X,Y,Z] :
( element(Z,Y)
| ~ element(Z,X)
| ~ set_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y,Z] :
( element(Z,X)
| ~ element(Z,Y)
| ~ set_equal(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X,Y] :
( set_equal(X,Y)
| element(f(X,Y),Y)
| element(f(X,Y),X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( set_equal(X,Y)
| ~ element(f(X,Y),X)
| ~ element(f(X,Y),Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,negated_conjecture,
( set_equal(b,a)
| set_equal(a,b) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,negated_conjecture,
( ~ set_equal(a,b)
| ~ set_equal(b,a) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,plain,
! [Y,Z] :
( element(Z,Y)
| ! [X] :
( ~ element(Z,X)
| ~ set_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f1]) ).
fof(f8,plain,
! [X0,X1,X2] :
( element(X2,X1)
| ~ element(X2,X0)
| ~ set_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f7]) ).
fof(f9,plain,
! [X,Z] :
( element(Z,X)
| ! [Y] :
( ~ element(Z,Y)
| ~ set_equal(X,Y) ) ),
inference(miniscoping,[status(thm)],[f2]) ).
fof(f10,plain,
! [X0,X1,X2] :
( element(X2,X0)
| ~ element(X2,X1)
| ~ set_equal(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f9]) ).
fof(f11,plain,
! [X0,X1] :
( set_equal(X0,X1)
| element(f(X0,X1),X1)
| element(f(X0,X1),X0) ),
inference(cnf_transformation,[status(thm)],[f3]) ).
fof(f12,plain,
! [X0,X1] :
( set_equal(X0,X1)
| ~ element(f(X0,X1),X0)
| ~ element(f(X0,X1),X1) ),
inference(cnf_transformation,[status(thm)],[f4]) ).
fof(f13,plain,
( set_equal(b,a)
| set_equal(a,b) ),
inference(cnf_transformation,[status(thm)],[f5]) ).
fof(f14,plain,
( ~ set_equal(a,b)
| ~ set_equal(b,a) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f15,definition,
( sQ0_spl
<=> set_equal(a,b) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f16,plain,
( ~ sQ0_spl
| set_equal(a,b) ),
inference(component_clause,[status(thm)],[f15]) ).
fof(f17,plain,
( sQ0_spl
| ~ set_equal(a,b) ),
inference(component_clause,[status(thm)],[f15]) ).
fof(f18,definition,
( sQ1_spl
<=> set_equal(b,a) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f19,plain,
( ~ sQ1_spl
| set_equal(b,a) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f20,plain,
( sQ1_spl
| ~ set_equal(b,a) ),
inference(component_clause,[status(thm)],[f18]) ).
fof(f21,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f13,f15,f18]) ).
fof(f22,plain,
( ~ sQ0_spl
| ~ sQ1_spl ),
inference(split_clause,[status(thm)],[f14,f18,f15]) ).
fof(f23,plain,
( sQ1_spl
| ~ element(f(b,a),b)
| ~ element(f(b,a),a) ),
inference(resolution,[status(thm)],[f12,f20]) ).
fof(f24,definition,
( sQ2_spl
<=> element(f(b,a),a) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f26,plain,
( sQ2_spl
| ~ element(f(b,a),a) ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f27,definition,
( sQ3_spl
<=> element(f(b,a),b) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f29,plain,
( sQ3_spl
| ~ element(f(b,a),b) ),
inference(component_clause,[status(thm)],[f27]) ).
fof(f30,plain,
( sQ1_spl
| ~ sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f23,f24,f27,f18]) ).
fof(f31,plain,
( sQ0_spl
| ~ element(f(a,b),a)
| ~ element(f(a,b),b) ),
inference(resolution,[status(thm)],[f17,f12]) ).
fof(f32,definition,
( sQ4_spl
<=> element(f(a,b),b) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f34,plain,
( sQ4_spl
| ~ element(f(a,b),b) ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f35,definition,
( sQ5_spl
<=> element(f(a,b),a) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f37,plain,
( sQ5_spl
| ~ element(f(a,b),a) ),
inference(component_clause,[status(thm)],[f35]) ).
fof(f38,plain,
( sQ0_spl
| ~ sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f31,f32,f35,f15]) ).
fof(f41,plain,
! [X0] :
( sQ2_spl
| ~ element(f(b,a),X0)
| ~ set_equal(a,X0) ),
inference(resolution,[status(thm)],[f26,f10]) ).
fof(f46,plain,
( sQ2_spl
| ~ set_equal(a,b)
| set_equal(b,a)
| element(f(b,a),a) ),
inference(resolution,[status(thm)],[f11,f41]) ).
fof(f47,plain,
( ~ sQ0_spl
| sQ1_spl
| sQ2_spl ),
inference(split_clause,[status(thm)],[f46,f24,f18,f15]) ).
fof(f50,plain,
! [X0] :
( sQ4_spl
| ~ element(f(a,b),X0)
| ~ set_equal(b,X0) ),
inference(resolution,[status(thm)],[f34,f10]) ).
fof(f52,plain,
( ~ sQ1_spl
| sQ4_spl
| ~ element(f(a,b),a) ),
inference(resolution,[status(thm)],[f50,f19]) ).
fof(f55,plain,
( ~ sQ1_spl
| sQ4_spl
| set_equal(a,b)
| element(f(a,b),b) ),
inference(resolution,[status(thm)],[f52,f11]) ).
fof(f58,plain,
( ~ sQ1_spl
| sQ0_spl
| sQ4_spl ),
inference(split_clause,[status(thm)],[f55,f32,f15,f18]) ).
fof(f63,plain,
! [X0] :
( sQ3_spl
| ~ element(f(b,a),X0)
| ~ set_equal(X0,b) ),
inference(resolution,[status(thm)],[f29,f8]) ).
fof(f69,plain,
! [X0] :
( sQ5_spl
| ~ element(f(a,b),X0)
| ~ set_equal(X0,a) ),
inference(resolution,[status(thm)],[f37,f8]) ).
fof(f78,plain,
( ~ sQ0_spl
| sQ3_spl
| ~ element(f(b,a),a) ),
inference(resolution,[status(thm)],[f63,f16]) ).
fof(f80,plain,
( ~ sQ0_spl
| sQ3_spl
| ~ sQ2_spl ),
inference(split_clause,[status(thm)],[f78,f24,f27,f15]) ).
fof(f88,plain,
( ~ sQ1_spl
| sQ5_spl
| ~ element(f(a,b),b) ),
inference(resolution,[status(thm)],[f69,f19]) ).
fof(f90,plain,
( ~ sQ1_spl
| sQ5_spl
| ~ sQ4_spl ),
inference(split_clause,[status(thm)],[f88,f32,f35,f18]) ).
fof(f91,plain,
$false,
inference(sat_refutation,[status(thm)],[f21,f22,f30,f38,f47,f58,f80,f90]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET047-5 : TPTP v9.3.1. Released v1.0.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.11/0.36 % Computer : n014.cluster.edu
% 0.11/0.36 % Model : x86_64 x86_64
% 0.11/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.36 % Memory : 8046.5625MB
% 0.11/0.36 % OS : Linux 6.8.0-71-generic
% 0.11/0.36 % CPULimit : 300
% 0.11/0.36 % WCLimit : 300
% 0.11/0.36 % DateTime : Mon Sep 21 04:47:51 UTC 2026
% 0.11/0.36 % CPUTime :
% 0.11/0.37 % Drodi V4.1.1
% 0.11/0.39 % Refutation found
% 0.11/0.39 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.11/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.11/0.41 % Elapsed time: 0.037995 seconds
% 0.11/0.41 % CPU time: 0.116317 seconds
% 0.11/0.41 % Total memory used: 14.198 MB
% 0.11/0.41 % Net memory used: 13.780 MB
%------------------------------------------------------------------------------