TSTP Solution File: SET918+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET918+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n025.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 : Wed May 31 12:35:32 EDT 2023
% Result : Theorem 0.14s 0.31s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 6
% Syntax : Number of formulae : 39 ( 7 unt; 0 def)
% Number of atoms : 183 ( 79 equ)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 229 ( 85 ~; 86 |; 50 &)
% ( 8 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 3 con; 0-3 aty)
% Number of variables : 103 (; 91 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( C = unordered_pair(A,B)
<=> ! [D] :
( in(D,C)
<=> ( D = A
| D = B ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,conjecture,
! [A,B,C] :
~ ( set_intersection2(unordered_pair(A,B),C) = singleton(A)
& in(B,C)
& A != B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,negated_conjecture,
~ ! [A,B,C] :
~ ( set_intersection2(unordered_pair(A,B),C) = singleton(A)
& in(B,C)
& A != B ),
inference(negated_conjecture,[status(cth)],[f10]) ).
fof(f16,plain,
! [A,B] :
( ( B != singleton(A)
| ! [C] :
( ( ~ in(C,B)
| C = A )
& ( in(C,B)
| C != A ) ) )
& ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(NNF_transformation,[status(esa)],[f4]) ).
fof(f17,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f18,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ( ( ~ in(sk0_0(B,A),B)
| sk0_0(B,A) != A )
& ( in(sk0_0(B,A),B)
| sk0_0(B,A) = A ) ) ) ),
inference(skolemization,[status(esa)],[f17]) ).
fof(f19,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| ~ in(X2,X0)
| X2 = X1 ),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f23,plain,
! [A,B,C] :
( ( C != unordered_pair(A,B)
| ! [D] :
( ( ~ in(D,C)
| D = A
| D = B )
& ( in(D,C)
| ( D != A
& D != B ) ) ) )
& ( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( D != A
& D != B ) )
& ( in(D,C)
| D = A
| D = B ) ) ) ),
inference(NNF_transformation,[status(esa)],[f5]) ).
fof(f24,plain,
( ! [A,B,C] :
( C != unordered_pair(A,B)
| ( ! [D] :
( ~ in(D,C)
| D = A
| D = B )
& ! [D] :
( in(D,C)
| ( D != A
& D != B ) ) ) )
& ! [A,B,C] :
( C = unordered_pair(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( D != A
& D != B ) )
& ( in(D,C)
| D = A
| D = B ) ) ) ),
inference(miniscoping,[status(esa)],[f23]) ).
fof(f25,plain,
( ! [A,B,C] :
( C != unordered_pair(A,B)
| ( ! [D] :
( ~ in(D,C)
| D = A
| D = B )
& ! [D] :
( in(D,C)
| ( D != A
& D != B ) ) ) )
& ! [A,B,C] :
( C = unordered_pair(A,B)
| ( ( ~ in(sk0_1(C,B,A),C)
| ( sk0_1(C,B,A) != A
& sk0_1(C,B,A) != B ) )
& ( in(sk0_1(C,B,A),C)
| sk0_1(C,B,A) = A
| sk0_1(C,B,A) = B ) ) ) ),
inference(skolemization,[status(esa)],[f24]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( X0 != unordered_pair(X1,X2)
| in(X3,X0)
| X3 != X2 ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f32,plain,
! [A,B,C] :
( ( C != set_intersection2(A,B)
| ! [D] :
( ( ~ in(D,C)
| ( in(D,A)
& in(D,B) ) )
& ( in(D,C)
| ~ in(D,A)
| ~ in(D,B) ) ) )
& ( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ~ in(D,A)
| ~ in(D,B) )
& ( in(D,C)
| ( in(D,A)
& in(D,B) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f6]) ).
fof(f33,plain,
( ! [A,B,C] :
( C != set_intersection2(A,B)
| ( ! [D] :
( ~ in(D,C)
| ( in(D,A)
& in(D,B) ) )
& ! [D] :
( in(D,C)
| ~ in(D,A)
| ~ in(D,B) ) ) )
& ! [A,B,C] :
( C = set_intersection2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ~ in(D,A)
| ~ in(D,B) )
& ( in(D,C)
| ( in(D,A)
& in(D,B) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f32]) ).
fof(f34,plain,
( ! [A,B,C] :
( C != set_intersection2(A,B)
| ( ! [D] :
( ~ in(D,C)
| ( in(D,A)
& in(D,B) ) )
& ! [D] :
( in(D,C)
| ~ in(D,A)
| ~ in(D,B) ) ) )
& ! [A,B,C] :
( C = set_intersection2(A,B)
| ( ( ~ in(sk0_2(C,B,A),C)
| ~ in(sk0_2(C,B,A),A)
| ~ in(sk0_2(C,B,A),B) )
& ( in(sk0_2(C,B,A),C)
| ( in(sk0_2(C,B,A),A)
& in(sk0_2(C,B,A),B) ) ) ) ) ),
inference(skolemization,[status(esa)],[f33]) ).
fof(f37,plain,
! [X0,X1,X2,X3] :
( X0 != set_intersection2(X1,X2)
| in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f47,plain,
? [A,B,C] :
( set_intersection2(unordered_pair(A,B),C) = singleton(A)
& in(B,C)
& A != B ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f48,plain,
? [A,B] :
( ? [C] :
( set_intersection2(unordered_pair(A,B),C) = singleton(A)
& in(B,C) )
& A != B ),
inference(miniscoping,[status(esa)],[f47]) ).
fof(f49,plain,
( set_intersection2(unordered_pair(sk0_5,sk0_6),sk0_7) = singleton(sk0_5)
& in(sk0_6,sk0_7)
& sk0_5 != sk0_6 ),
inference(skolemization,[status(esa)],[f48]) ).
fof(f50,plain,
set_intersection2(unordered_pair(sk0_5,sk0_6),sk0_7) = singleton(sk0_5),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f51,plain,
in(sk0_6,sk0_7),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f52,plain,
sk0_5 != sk0_6,
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f53,plain,
! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(destructive_equality_resolution,[status(esa)],[f19]) ).
fof(f57,plain,
! [X0,X1] : in(X0,unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(esa)],[f28]) ).
fof(f60,plain,
! [X0,X1,X2] :
( in(X0,set_intersection2(X1,X2))
| ~ in(X0,X1)
| ~ in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f37]) ).
fof(f94,plain,
! [X0] :
( in(X0,singleton(sk0_5))
| ~ in(X0,unordered_pair(sk0_5,sk0_6))
| ~ in(X0,sk0_7) ),
inference(paramodulation,[status(thm)],[f50,f60]) ).
fof(f131,plain,
( spl0_0
<=> in(sk0_6,singleton(sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f132,plain,
( in(sk0_6,singleton(sk0_5))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,plain,
( spl0_1
<=> in(sk0_6,sk0_7) ),
introduced(split_symbol_definition) ).
fof(f136,plain,
( ~ in(sk0_6,sk0_7)
| spl0_1 ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f137,plain,
( in(sk0_6,singleton(sk0_5))
| ~ in(sk0_6,sk0_7) ),
inference(resolution,[status(thm)],[f94,f57]) ).
fof(f138,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f137,f131,f134]) ).
fof(f149,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f136,f51]) ).
fof(f150,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( sk0_6 = sk0_5
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f132,f53]) ).
fof(f153,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f152,f52]) ).
fof(f154,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f153]) ).
fof(f155,plain,
$false,
inference(sat_refutation,[status(thm)],[f138,f150,f154]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SET918+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n025.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 10:30:42 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 0.14/0.31 % Refutation found
% 0.14/0.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.53 % Elapsed time: 0.012489 seconds
% 0.14/0.53 % CPU time: 0.014424 seconds
% 0.14/0.53 % Memory used: 3.713 MB
%------------------------------------------------------------------------------