TSTP Solution File: SET788+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET788+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n031.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Tue Apr 30 20:40:21 EDT 2024
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 7
% Syntax : Number of formulae : 43 ( 1 unt; 0 def)
% Number of atoms : 154 ( 0 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 173 ( 62 ~; 78 |; 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 : 52 ( 44 !; 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/sandbox2/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)
<=> ! [Z] :
( a_member_of(Z,X)
<=> a_member_of(Z,Y) ) )
& ? [X,Y] :
( equalish(X,Y)
<~> equalish(Y,X) ) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f4,plain,
( ! [X,Y] :
( ( ~ equalish(X,Y)
| ! [Z] :
( ( ~ a_member_of(Z,X)
| a_member_of(Z,Y) )
& ( a_member_of(Z,X)
| ~ a_member_of(Z,Y) ) ) )
& ( equalish(X,Y)
| ? [Z] :
( ( ~ a_member_of(Z,X)
| ~ a_member_of(Z,Y) )
& ( a_member_of(Z,X)
| a_member_of(Z,Y) ) ) ) )
& ? [X,Y] :
( ( equalish(X,Y)
| equalish(Y,X) )
& ( ~ equalish(X,Y)
| ~ equalish(Y,X) ) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f5,plain,
( ! [X,Y] :
( ~ equalish(X,Y)
| ( ! [Z] :
( ~ a_member_of(Z,X)
| a_member_of(Z,Y) )
& ! [Z] :
( a_member_of(Z,X)
| ~ a_member_of(Z,Y) ) ) )
& ! [X,Y] :
( equalish(X,Y)
| ? [Z] :
( ( ~ a_member_of(Z,X)
| ~ a_member_of(Z,Y) )
& ( a_member_of(Z,X)
| a_member_of(Z,Y) ) ) )
& ? [X,Y] :
( ( equalish(X,Y)
| equalish(Y,X) )
& ( ~ equalish(X,Y)
| ~ equalish(Y,X) ) ) ),
inference(miniscoping,[status(esa)],[f4]) ).
fof(f6,plain,
( ! [X,Y] :
( ~ equalish(X,Y)
| ( ! [Z] :
( ~ a_member_of(Z,X)
| a_member_of(Z,Y) )
& ! [Z] :
( a_member_of(Z,X)
| ~ a_member_of(Z,Y) ) ) )
& ! [X,Y] :
( equalish(X,Y)
| ( ( ~ a_member_of(sk0_0(Y,X),X)
| ~ a_member_of(sk0_0(Y,X),Y) )
& ( a_member_of(sk0_0(Y,X),X)
| a_member_of(sk0_0(Y,X),Y) ) ) )
& ( equalish(sk0_1,sk0_2)
| equalish(sk0_2,sk0_1) )
& ( ~ equalish(sk0_1,sk0_2)
| ~ equalish(sk0_2,sk0_1) ) ),
inference(skolemization,[status(esa)],[f5]) ).
fof(f7,plain,
! [X0,X1,X2] :
( ~ equalish(X0,X1)
| ~ a_member_of(X2,X0)
| a_member_of(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f8,plain,
! [X0,X1,X2] :
( ~ equalish(X0,X1)
| a_member_of(X2,X0)
| ~ a_member_of(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f9,plain,
! [X0,X1] :
( equalish(X0,X1)
| ~ a_member_of(sk0_0(X1,X0),X0)
| ~ a_member_of(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f10,plain,
! [X0,X1] :
( equalish(X0,X1)
| a_member_of(sk0_0(X1,X0),X0)
| a_member_of(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f11,plain,
( equalish(sk0_1,sk0_2)
| equalish(sk0_2,sk0_1) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f12,plain,
( ~ equalish(sk0_1,sk0_2)
| ~ equalish(sk0_2,sk0_1) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f13,plain,
( spl0_0
<=> equalish(sk0_1,sk0_2) ),
introduced(split_symbol_definition) ).
fof(f14,plain,
( equalish(sk0_1,sk0_2)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f13]) ).
fof(f16,plain,
( spl0_1
<=> equalish(sk0_2,sk0_1) ),
introduced(split_symbol_definition) ).
fof(f17,plain,
( equalish(sk0_2,sk0_1)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f16]) ).
fof(f19,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f11,f13,f16]) ).
fof(f20,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f12,f13,f16]) ).
fof(f25,plain,
! [X0] :
( a_member_of(X0,sk0_2)
| ~ a_member_of(X0,sk0_1)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f17,f8]) ).
fof(f26,plain,
! [X0] :
( ~ a_member_of(X0,sk0_2)
| a_member_of(X0,sk0_1)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f17,f7]) ).
fof(f38,plain,
! [X0] :
( a_member_of(sk0_0(X0,sk0_1),sk0_2)
| equalish(sk0_1,X0)
| a_member_of(sk0_0(X0,sk0_1),X0)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f25,f10]) ).
fof(f46,plain,
( spl0_5
<=> a_member_of(sk0_0(sk0_2,sk0_1),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f49,plain,
( a_member_of(sk0_0(sk0_2,sk0_1),sk0_2)
| equalish(sk0_1,sk0_2)
| ~ spl0_1 ),
inference(factoring,[status(esa)],[f38]) ).
fof(f50,plain,
( spl0_5
| spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f49,f46,f13,f16]) ).
fof(f51,plain,
( spl0_6
<=> a_member_of(sk0_0(sk0_2,sk0_1),sk0_1) ),
introduced(split_symbol_definition) ).
fof(f52,plain,
( a_member_of(sk0_0(sk0_2,sk0_1),sk0_1)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f51]) ).
fof(f54,plain,
( a_member_of(sk0_0(sk0_2,sk0_1),sk0_1)
| equalish(sk0_1,sk0_2)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f26,f38]) ).
fof(f55,plain,
( spl0_6
| spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f54,f51,f13,f16]) ).
fof(f73,plain,
( spl0_9
<=> a_member_of(sk0_0(sk0_1,sk0_2),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f74,plain,
( a_member_of(sk0_0(sk0_1,sk0_2),sk0_2)
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f86,plain,
( spl0_11
<=> a_member_of(sk0_0(sk0_1,sk0_2),sk0_1) ),
introduced(split_symbol_definition) ).
fof(f94,plain,
( equalish(sk0_1,sk0_2)
| ~ a_member_of(sk0_0(sk0_2,sk0_1),sk0_2)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f52,f9]) ).
fof(f95,plain,
( spl0_0
| ~ spl0_5
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f94,f13,f46,f51]) ).
fof(f96,plain,
! [X0] :
( a_member_of(X0,sk0_1)
| ~ a_member_of(X0,sk0_2)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f14,f8]) ).
fof(f97,plain,
! [X0] :
( ~ a_member_of(X0,sk0_1)
| a_member_of(X0,sk0_2)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f14,f7]) ).
fof(f103,plain,
! [X0] :
( a_member_of(sk0_0(X0,sk0_2),sk0_1)
| equalish(sk0_2,X0)
| a_member_of(sk0_0(X0,sk0_2),X0)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f96,f10]) ).
fof(f110,plain,
( equalish(sk0_2,sk0_1)
| a_member_of(sk0_0(sk0_1,sk0_2),sk0_2)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f103,f97]) ).
fof(f111,plain,
( spl0_1
| spl0_9
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f110,f16,f73,f13]) ).
fof(f119,plain,
( a_member_of(sk0_0(sk0_1,sk0_2),sk0_1)
| equalish(sk0_2,sk0_1)
| ~ spl0_0 ),
inference(factoring,[status(esa)],[f103]) ).
fof(f120,plain,
( spl0_11
| spl0_1
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f119,f86,f16,f13]) ).
fof(f134,plain,
( equalish(sk0_2,sk0_1)
| ~ a_member_of(sk0_0(sk0_1,sk0_2),sk0_1)
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f74,f9]) ).
fof(f135,plain,
( spl0_1
| ~ spl0_11
| ~ spl0_9 ),
inference(split_clause,[status(thm)],[f134,f16,f86,f73]) ).
fof(f136,plain,
$false,
inference(sat_refutation,[status(thm)],[f19,f20,f50,f55,f95,f111,f120,f135]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET788+1 : TPTP v8.1.2. Released v3.1.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n031.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Mon Apr 29 22:22:58 EDT 2024
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.6.0
% 0.13/0.36 % Refutation found
% 0.13/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.20/0.38 % Elapsed time: 0.024452 seconds
% 0.20/0.38 % CPU time: 0.064756 seconds
% 0.20/0.38 % Total memory used: 2.450 MB
% 0.20/0.38 % Net memory used: 2.400 MB
%------------------------------------------------------------------------------