TSTP Solution File: SET695+4 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET695+4 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n018.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 20:40:12 EDT 2024
% Result : Theorem 0.15s 0.61s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 7
% Syntax : Number of formulae : 56 ( 5 unt; 0 def)
% Number of atoms : 160 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 153 ( 49 ~; 70 |; 21 &)
% ( 9 <=>; 3 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 6 usr; 5 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 100 ( 92 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( member(X,A)
=> member(X,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [B,A,E] :
( member(B,difference(E,A))
<=> ( member(B,E)
& ~ member(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f12,conjecture,
! [A,B,E] :
( ( subset(A,E)
& subset(B,E) )
=> ( subset(A,B)
<=> subset(difference(E,B),difference(E,A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,negated_conjecture,
~ ! [A,B,E] :
( ( subset(A,E)
& subset(B,E) )
=> ( subset(A,B)
<=> subset(difference(E,B),difference(E,A)) ) ),
inference(negated_conjecture,[status(cth)],[f12]) ).
fof(f14,plain,
! [A,B] :
( subset(A,B)
<=> ! [X] :
( ~ member(X,A)
| member(X,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f1]) ).
fof(f15,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [X] :
( member(X,A)
& ~ member(X,B) ) ) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f17,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [X] :
( ~ member(X,A)
| member(X,B) ) )
& ! [A,B] :
( subset(A,B)
| ( member(sk0_0(B,A),A)
& ~ member(sk0_0(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f19,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f20,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f41,plain,
! [B,A,E] :
( ( ~ member(B,difference(E,A))
| ( member(B,E)
& ~ member(B,A) ) )
& ( member(B,difference(E,A))
| ~ member(B,E)
| member(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f42,plain,
( ! [B,A,E] :
( ~ member(B,difference(E,A))
| ( member(B,E)
& ~ member(B,A) ) )
& ! [B,A,E] :
( member(B,difference(E,A))
| ~ member(B,E)
| member(B,A) ) ),
inference(miniscoping,[status(esa)],[f41]) ).
fof(f43,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ member(X0,difference(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f45,plain,
! [X0,X1,X2] :
( member(X0,difference(X1,X2))
| ~ member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f68,plain,
? [A,B,E] :
( subset(A,E)
& subset(B,E)
& ( subset(A,B)
<~> subset(difference(E,B),difference(E,A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f13]) ).
fof(f69,plain,
? [A,B,E] :
( subset(A,E)
& subset(B,E)
& ( subset(A,B)
| subset(difference(E,B),difference(E,A)) )
& ( ~ subset(A,B)
| ~ subset(difference(E,B),difference(E,A)) ) ),
inference(NNF_transformation,[status(esa)],[f68]) ).
fof(f70,plain,
( subset(sk0_3,sk0_5)
& subset(sk0_4,sk0_5)
& ( subset(sk0_3,sk0_4)
| subset(difference(sk0_5,sk0_4),difference(sk0_5,sk0_3)) )
& ( ~ subset(sk0_3,sk0_4)
| ~ subset(difference(sk0_5,sk0_4),difference(sk0_5,sk0_3)) ) ),
inference(skolemization,[status(esa)],[f69]) ).
fof(f71,plain,
subset(sk0_3,sk0_5),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f72,plain,
subset(sk0_4,sk0_5),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f73,plain,
( subset(sk0_3,sk0_4)
| subset(difference(sk0_5,sk0_4),difference(sk0_5,sk0_3)) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f74,plain,
( ~ subset(sk0_3,sk0_4)
| ~ subset(difference(sk0_5,sk0_4),difference(sk0_5,sk0_3)) ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f75,plain,
( spl0_0
<=> subset(sk0_3,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f78,plain,
( spl0_1
<=> subset(difference(sk0_5,sk0_4),difference(sk0_5,sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f79,plain,
( subset(difference(sk0_5,sk0_4),difference(sk0_5,sk0_3))
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f80,plain,
( ~ subset(difference(sk0_5,sk0_4),difference(sk0_5,sk0_3))
| spl0_1 ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f81,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f73,f75,f78]) ).
fof(f82,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f74,f75,f78]) ).
fof(f83,plain,
! [X0,X1,X2] :
( subset(difference(X0,X1),X2)
| ~ member(sk0_0(X2,difference(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f19,f44]) ).
fof(f84,plain,
! [X0,X1,X2] :
( subset(difference(X0,X1),X2)
| member(sk0_0(X2,difference(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f19,f43]) ).
fof(f86,plain,
! [X0,X1,X2] :
( subset(X0,X1)
| ~ subset(X0,X2)
| member(sk0_0(X1,X0),X2) ),
inference(resolution,[status(thm)],[f19,f18]) ).
fof(f88,plain,
! [X0] :
( subset(sk0_4,X0)
| member(sk0_0(X0,sk0_4),sk0_5) ),
inference(resolution,[status(thm)],[f86,f72]) ).
fof(f89,plain,
! [X0] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),sk0_5) ),
inference(resolution,[status(thm)],[f86,f71]) ).
fof(f92,plain,
! [X0,X1] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),difference(sk0_5,X1))
| member(sk0_0(X0,sk0_3),X1) ),
inference(resolution,[status(thm)],[f89,f45]) ).
fof(f103,plain,
! [X0,X1,X2] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),X1)
| ~ subset(difference(sk0_5,X1),X2)
| member(sk0_0(X0,sk0_3),X2) ),
inference(resolution,[status(thm)],[f92,f18]) ).
fof(f105,plain,
! [X0] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),sk0_4)
| member(sk0_0(X0,sk0_3),difference(sk0_5,sk0_3))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f103,f79]) ).
fof(f106,plain,
! [X0] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),sk0_4)
| ~ member(sk0_0(X0,sk0_3),sk0_3)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f105,f44]) ).
fof(f107,plain,
! [X0] :
( subset(sk0_3,X0)
| member(sk0_0(X0,sk0_3),sk0_4)
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f106,f19]) ).
fof(f172,plain,
! [X0,X1,X2,X3] :
( subset(difference(X0,X1),X2)
| member(sk0_0(X2,difference(X0,X1)),difference(X0,X3))
| member(sk0_0(X2,difference(X0,X1)),X3) ),
inference(resolution,[status(thm)],[f84,f45]) ).
fof(f524,plain,
! [X0,X1,X2] :
( subset(difference(X0,X1),difference(X0,X2))
| subset(difference(X0,X1),difference(X0,X2))
| member(sk0_0(difference(X0,X2),difference(X0,X1)),X2) ),
inference(resolution,[status(thm)],[f20,f172]) ).
fof(f525,plain,
! [X0,X1,X2] :
( subset(difference(X0,X1),difference(X0,X2))
| member(sk0_0(difference(X0,X2),difference(X0,X1)),X2) ),
inference(duplicate_literals_removal,[status(esa)],[f524]) ).
fof(f528,plain,
( subset(sk0_3,sk0_4)
| subset(sk0_3,sk0_4)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f20,f107]) ).
fof(f529,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f528,f75,f78]) ).
fof(f550,plain,
( spl0_2
<=> subset(sk0_3,sk0_5) ),
introduced(split_symbol_definition) ).
fof(f553,plain,
( subset(sk0_3,sk0_5)
| subset(sk0_3,sk0_5) ),
inference(resolution,[status(thm)],[f20,f89]) ).
fof(f554,plain,
spl0_2,
inference(split_clause,[status(thm)],[f553,f550]) ).
fof(f565,plain,
( spl0_3
<=> subset(sk0_4,sk0_5) ),
introduced(split_symbol_definition) ).
fof(f568,plain,
( subset(sk0_4,sk0_5)
| subset(sk0_4,sk0_5) ),
inference(resolution,[status(thm)],[f20,f88]) ).
fof(f569,plain,
spl0_3,
inference(split_clause,[status(thm)],[f568,f565]) ).
fof(f717,plain,
! [X0,X1,X2,X3] :
( subset(difference(X0,X1),difference(X0,X2))
| ~ subset(X2,X3)
| member(sk0_0(difference(X0,X2),difference(X0,X1)),X3) ),
inference(resolution,[status(thm)],[f525,f18]) ).
fof(f927,plain,
! [X0,X1,X2] :
( subset(difference(X0,X1),difference(X0,X2))
| ~ subset(X2,X1)
| subset(difference(X0,X1),difference(X0,X2)) ),
inference(resolution,[status(thm)],[f717,f83]) ).
fof(f928,plain,
! [X0,X1,X2] :
( subset(difference(X0,X1),difference(X0,X2))
| ~ subset(X2,X1) ),
inference(duplicate_literals_removal,[status(esa)],[f927]) ).
fof(f943,plain,
( ~ subset(sk0_3,sk0_4)
| spl0_1 ),
inference(resolution,[status(thm)],[f928,f80]) ).
fof(f944,plain,
( ~ spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f943,f75,f78]) ).
fof(f950,plain,
$false,
inference(sat_refutation,[status(thm)],[f81,f82,f529,f554,f569,f944]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET695+4 : TPTP v8.1.2. Released v2.2.0.
% 0.10/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.31 % Computer : n018.cluster.edu
% 0.11/0.31 % Model : x86_64 x86_64
% 0.11/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.31 % Memory : 8042.1875MB
% 0.11/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.31 % CPULimit : 300
% 0.11/0.31 % WCLimit : 300
% 0.11/0.31 % DateTime : Mon Apr 29 21:43:28 EDT 2024
% 0.11/0.31 % CPUTime :
% 0.15/0.32 % Drodi V3.6.0
% 0.15/0.61 % Refutation found
% 0.15/0.61 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.61 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.22/0.64 % Elapsed time: 0.308512 seconds
% 2.22/0.64 % CPU time: 2.323302 seconds
% 2.22/0.64 % Total memory used: 73.733 MB
% 2.22/0.64 % Net memory used: 72.070 MB
%------------------------------------------------------------------------------