%------------------------------------------------------------------------------
% File : Drodi---4.1.1
% Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% Computer : n017.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 02:10:37 PM UTC 2026
% Result : Theorem 0.16s 0.39s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 50 ( 1 unt; 6 def)
% Number of atoms : 182 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 211 ( 79 ~; 99 |; 16 &)
% ( 14 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 10 ( 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 : 53 ( 45 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,conjecture,
( ! [X,Y] :
( equalish(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [X,Y] :
( equalish(X,Y)
<=> equalish(Y,X) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,negated_conjecture,
~ ( ! [X,Y] :
( equalish(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
=> ! [X,Y] :
( equalish(X,Y)
<=> equalish(Y,X) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
fof(f3,plain,
( ? [X,Y] :
( equalish(X,Y)
<~> equalish(Y,X) )
& ! [X,Y] :
( equalish(X,Y)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) ) ),
inference(pre_NNF_transformation,[status(thm)],[f2]) ).
fof(f4,plain,
( ? [X,Y] :
( ( ~ equalish(Y,X)
| ~ equalish(X,Y) )
& ( equalish(Y,X)
| equalish(X,Y) ) )
& ! [X,Y] :
( ( ? [Z] :
( ( a_member_of(Z,Y)
| a_member_of(Z,X) )
& ( ~ a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| equalish(X,Y) )
& ( ! [Z] :
( ( ~ a_member_of(Z,Y)
| a_member_of(Z,X) )
& ( a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| ~ equalish(X,Y) ) ) ),
inference(NNF_transformation,[status(thm)],[f3]) ).
fof(f5,plain,
( ? [X,Y] :
( ( ~ equalish(Y,X)
| ~ equalish(X,Y) )
& ( equalish(Y,X)
| equalish(X,Y) ) )
& ! [X,Y] :
( ? [Z] :
( ( a_member_of(Z,Y)
| a_member_of(Z,X) )
& ( ~ a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| equalish(X,Y) )
& ! [X,Y] :
( ( ! [Z] :
( ~ a_member_of(Z,Y)
| a_member_of(Z,X) )
& ! [Z] :
( a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| ~ equalish(X,Y) ) ),
inference(miniscoping,[status(thm)],[f4]) ).
fof(f6,plain,
( ( ~ equalish(sK2_skl,sK1_skl)
| ~ equalish(sK1_skl,sK2_skl) )
& ( equalish(sK2_skl,sK1_skl)
| equalish(sK1_skl,sK2_skl) )
& ! [X,Y] :
( ( ( a_member_of(sK0_skl(Y,X),Y)
| a_member_of(sK0_skl(Y,X),X) )
& ( ~ a_member_of(sK0_skl(Y,X),Y)
| ~ a_member_of(sK0_skl(Y,X),X) ) )
| equalish(X,Y) )
& ! [X,Y] :
( ( ! [Z] :
( ~ a_member_of(Z,Y)
| a_member_of(Z,X) )
& ! [Z] :
( a_member_of(Z,Y)
| ~ a_member_of(Z,X) ) )
| ~ equalish(X,Y) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0_skl,sK1_skl,sK2_skl]),skolemize(Z,sK0_skl(Y,X)),skolemize(X,sK1_skl),skolemize(Y,sK2_skl)],[f5]) ).
fof(f7,plain,
! [X0,X1,X2] :
( a_member_of(X2,X1)
| ~ a_member_of(X2,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( ~ a_member_of(X2,X1)
| a_member_of(X2,X0)
| ~ equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f9,plain,
! [X0,X1] :
( ~ a_member_of(sK0_skl(X1,X0),X1)
| ~ a_member_of(sK0_skl(X1,X0),X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f10,plain,
! [X0,X1] :
( a_member_of(sK0_skl(X1,X0),X1)
| a_member_of(sK0_skl(X1,X0),X0)
| equalish(X0,X1) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f11,plain,
( equalish(sK2_skl,sK1_skl)
| equalish(sK1_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f12,plain,
( ~ equalish(sK2_skl,sK1_skl)
| ~ equalish(sK1_skl,sK2_skl) ),
inference(cnf_transformation,[status(thm)],[f6]) ).
fof(f13,definition,
( sQ0_spl
<=> equalish(sK1_skl,sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ0_spl])],[split_symbol_definition]) ).
fof(f14,plain,
( ~ sQ0_spl
| equalish(sK1_skl,sK2_skl) ),
inference(component_clause,[status(thm)],[f13]) ).
fof(f16,definition,
( sQ1_spl
<=> equalish(sK2_skl,sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ1_spl])],[split_symbol_definition]) ).
fof(f17,plain,
( ~ sQ1_spl
| equalish(sK2_skl,sK1_skl) ),
inference(component_clause,[status(thm)],[f16]) ).
fof(f19,plain,
( sQ1_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f11,f13,f16]) ).
fof(f20,plain,
( ~ sQ1_spl
| ~ sQ0_spl ),
inference(split_clause,[status(thm)],[f12,f13,f16]) ).
fof(f21,plain,
! [X0,X1,X2] :
( ~ a_member_of(sK0_skl(X1,X0),X2)
| ~ equalish(X1,X2)
| ~ a_member_of(sK0_skl(X1,X0),X0)
| equalish(X0,X1) ),
inference(resolution,[status(thm)],[f9,f8]) ).
fof(f39,plain,
! [X0] :
( ~ sQ1_spl
| ~ a_member_of(sK0_skl(sK2_skl,X0),sK1_skl)
| ~ a_member_of(sK0_skl(sK2_skl,X0),X0)
| equalish(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f21,f17]) ).
fof(f43,plain,
( ~ sQ1_spl
| a_member_of(sK0_skl(sK2_skl,sK1_skl),sK2_skl)
| equalish(sK1_skl,sK2_skl)
| ~ a_member_of(sK0_skl(sK2_skl,sK1_skl),sK1_skl)
| equalish(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f39,f10]) ).
fof(f46,definition,
( sQ2_spl
<=> a_member_of(sK0_skl(sK2_skl,sK1_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ2_spl])],[split_symbol_definition]) ).
fof(f48,plain,
( sQ2_spl
| ~ a_member_of(sK0_skl(sK2_skl,sK1_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,definition,
( sQ3_spl
<=> a_member_of(sK0_skl(sK2_skl,sK1_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ3_spl])],[split_symbol_definition]) ).
fof(f50,plain,
( ~ sQ3_spl
| a_member_of(sK0_skl(sK2_skl,sK1_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( ~ sQ1_spl
| sQ3_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f43,f13,f46,f49,f16]) ).
fof(f54,plain,
! [X0] :
( ~ sQ0_spl
| ~ a_member_of(sK0_skl(sK1_skl,X0),sK2_skl)
| ~ a_member_of(sK0_skl(sK1_skl,X0),X0)
| equalish(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f14,f21]) ).
fof(f59,plain,
( ~ sQ0_spl
| a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl)
| equalish(sK2_skl,sK1_skl)
| ~ a_member_of(sK0_skl(sK1_skl,sK2_skl),sK2_skl)
| equalish(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f54,f10]) ).
fof(f62,definition,
( sQ4_spl
<=> a_member_of(sK0_skl(sK1_skl,sK2_skl),sK2_skl) ),
introduced(definition,[new_symbols(definition,[sQ4_spl])],[split_symbol_definition]) ).
fof(f64,plain,
( sQ4_spl
| ~ a_member_of(sK0_skl(sK1_skl,sK2_skl),sK2_skl) ),
inference(component_clause,[status(thm)],[f62]) ).
fof(f65,definition,
( sQ5_spl
<=> a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl) ),
introduced(definition,[new_symbols(definition,[sQ5_spl])],[split_symbol_definition]) ).
fof(f66,plain,
( ~ sQ5_spl
| a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl) ),
inference(component_clause,[status(thm)],[f65]) ).
fof(f68,plain,
( ~ sQ0_spl
| sQ5_spl
| ~ sQ4_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f59,f16,f62,f65,f13]) ).
fof(f69,plain,
( sQ4_spl
| a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl)
| equalish(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f64,f10]) ).
fof(f71,plain,
! [X0] :
( sQ4_spl
| ~ a_member_of(sK0_skl(sK1_skl,sK2_skl),X0)
| ~ equalish(X0,sK2_skl) ),
inference(resolution,[status(thm)],[f64,f7]) ).
fof(f72,plain,
( sQ4_spl
| sQ5_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f69,f16,f65,f62]) ).
fof(f79,plain,
( sQ2_spl
| a_member_of(sK0_skl(sK2_skl,sK1_skl),sK2_skl)
| equalish(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f48,f10]) ).
fof(f81,plain,
! [X0] :
( sQ2_spl
| ~ a_member_of(sK0_skl(sK2_skl,sK1_skl),X0)
| ~ equalish(X0,sK1_skl) ),
inference(resolution,[status(thm)],[f48,f7]) ).
fof(f82,plain,
( sQ2_spl
| sQ3_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f79,f13,f49,f46]) ).
fof(f89,plain,
( ~ sQ5_spl
| ~ a_member_of(sK0_skl(sK1_skl,sK2_skl),sK2_skl)
| equalish(sK2_skl,sK1_skl) ),
inference(resolution,[status(thm)],[f66,f9]) ).
fof(f90,plain,
( ~ sQ5_spl
| ~ sQ4_spl
| sQ1_spl ),
inference(split_clause,[status(thm)],[f89,f16,f62,f65]) ).
fof(f93,plain,
( ~ sQ3_spl
| ~ a_member_of(sK0_skl(sK2_skl,sK1_skl),sK1_skl)
| equalish(sK1_skl,sK2_skl) ),
inference(resolution,[status(thm)],[f50,f9]) ).
fof(f94,plain,
( ~ sQ3_spl
| ~ sQ2_spl
| sQ0_spl ),
inference(split_clause,[status(thm)],[f93,f13,f46,f49]) ).
fof(f112,plain,
( ~ sQ0_spl
| sQ4_spl
| ~ a_member_of(sK0_skl(sK1_skl,sK2_skl),sK1_skl) ),
inference(resolution,[status(thm)],[f71,f14]) ).
fof(f114,plain,
( ~ sQ0_spl
| sQ4_spl
| ~ sQ5_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f112,f66]) ).
fof(f115,plain,
( ~ sQ0_spl
| sQ4_spl
| ~ sQ5_spl ),
inference(contradiction_clause,[status(thm)],[f114]) ).
fof(f133,plain,
( ~ sQ1_spl
| sQ2_spl
| ~ a_member_of(sK0_skl(sK2_skl,sK1_skl),sK2_skl) ),
inference(resolution,[status(thm)],[f81,f17]) ).
fof(f135,plain,
( ~ sQ1_spl
| sQ2_spl
| ~ sQ3_spl
| $false ),
inference(forward_subsumption_resolution,[status(thm)],[f133,f50]) ).
fof(f136,plain,
( ~ sQ1_spl
| sQ2_spl
| ~ sQ3_spl ),
inference(contradiction_clause,[status(thm)],[f135]) ).
fof(f137,plain,
$false,
inference(sat_refutation,[status(thm)],[f19,f20,f52,f68,f72,f82,f90,f94,f115,f136]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SET788+1 : TPTP v9.3.1. Released v3.1.0.
% 0.00/0.04 % Command : drodi -timeout(300) /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.11/0.37 % Computer : n017.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 05:33:26 UTC 2026
% 0.11/0.37 % CPUTime :
% 0.11/0.38 % Drodi V4.1.1
% 0.16/0.39 % Refutation found
% 0.16/0.39 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.39 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.42 % Elapsed time: 0.042512 seconds
% 0.16/0.42 % CPU time: 0.127236 seconds
% 0.16/0.42 % Total memory used: 15.844 MB
% 0.16/0.42 % Net memory used: 15.378 MB
%------------------------------------------------------------------------------