TSTP Solution File: SET916+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET916+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n016.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 12:35:31 EDT 2023
% Result : Theorem 0.09s 0.34s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 9
% Syntax : Number of formulae : 52 ( 7 unt; 0 def)
% Number of atoms : 195 ( 55 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 237 ( 94 ~; 89 |; 45 &)
% ( 9 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 3 con; 0-3 aty)
% Number of variables : 110 (; 100 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,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(f5,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,axiom,
! [A,B] :
( ~ ( ~ disjoint(A,B)
& ! [C] : ~ in(C,set_intersection2(A,B)) )
& ~ ( ? [C] : in(C,set_intersection2(A,B))
& disjoint(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A,B,C] :
~ ( ~ in(A,B)
& ~ in(C,B)
& ~ disjoint(unordered_pair(A,C),B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A,B,C] :
~ ( ~ in(A,B)
& ~ in(C,B)
& ~ disjoint(unordered_pair(A,C),B) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f17,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)],[f4]) ).
fof(f18,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)],[f17]) ).
fof(f19,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_0(C,B,A),C)
| ( sk0_0(C,B,A) != A
& sk0_0(C,B,A) != B ) )
& ( in(sk0_0(C,B,A),C)
| sk0_0(C,B,A) = A
| sk0_0(C,B,A) = B ) ) ) ),
inference(skolemization,[status(esa)],[f18]) ).
fof(f20,plain,
! [X0,X1,X2,X3] :
( X0 != unordered_pair(X1,X2)
| ~ in(X3,X0)
| X3 = X1
| X3 = X2 ),
inference(cnf_transformation,[status(esa)],[f19]) ).
fof(f26,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)],[f5]) ).
fof(f27,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)],[f26]) ).
fof(f28,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_1(C,B,A),C)
| ~ in(sk0_1(C,B,A),A)
| ~ in(sk0_1(C,B,A),B) )
& ( in(sk0_1(C,B,A),C)
| ( in(sk0_1(C,B,A),A)
& in(sk0_1(C,B,A),B) ) ) ) ) ),
inference(skolemization,[status(esa)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( X0 != set_intersection2(X1,X2)
| ~ in(X3,X0)
| in(X3,X1) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2,X3] :
( X0 != set_intersection2(X1,X2)
| ~ in(X3,X0)
| in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f43,plain,
! [A,B] :
( ( disjoint(A,B)
| ? [C] : in(C,set_intersection2(A,B)) )
& ( ! [C] : ~ in(C,set_intersection2(A,B))
| ~ disjoint(A,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f44,plain,
( ! [A,B] :
( disjoint(A,B)
| ? [C] : in(C,set_intersection2(A,B)) )
& ! [A,B] :
( ! [C] : ~ in(C,set_intersection2(A,B))
| ~ disjoint(A,B) ) ),
inference(miniscoping,[status(esa)],[f43]) ).
fof(f45,plain,
( ! [A,B] :
( disjoint(A,B)
| in(sk0_4(B,A),set_intersection2(A,B)) )
& ! [A,B] :
( ! [C] : ~ in(C,set_intersection2(A,B))
| ~ disjoint(A,B) ) ),
inference(skolemization,[status(esa)],[f44]) ).
fof(f46,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sk0_4(X1,X0),set_intersection2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f48,plain,
? [A,B,C] :
( ~ in(A,B)
& ~ in(C,B)
& ~ disjoint(unordered_pair(A,C),B) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f49,plain,
( ~ in(sk0_5,sk0_6)
& ~ in(sk0_7,sk0_6)
& ~ disjoint(unordered_pair(sk0_5,sk0_7),sk0_6) ),
inference(skolemization,[status(esa)],[f48]) ).
fof(f50,plain,
~ in(sk0_5,sk0_6),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f51,plain,
~ in(sk0_7,sk0_6),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f52,plain,
~ disjoint(unordered_pair(sk0_5,sk0_7),sk0_6),
inference(cnf_transformation,[status(esa)],[f49]) ).
fof(f53,plain,
! [X0,X1,X2] :
( ~ in(X0,unordered_pair(X1,X2))
| X0 = X1
| X0 = X2 ),
inference(destructive_equality_resolution,[status(esa)],[f20]) ).
fof(f56,plain,
! [X0,X1,X2] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f29]) ).
fof(f57,plain,
! [X0,X1,X2] :
( ~ in(X0,set_intersection2(X1,X2))
| in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f30]) ).
fof(f78,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sk0_4(X1,X0),X1) ),
inference(resolution,[status(thm)],[f46,f57]) ).
fof(f79,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sk0_4(X1,X0),X0) ),
inference(resolution,[status(thm)],[f46,f56]) ).
fof(f92,plain,
! [X0,X1,X2] :
( disjoint(unordered_pair(X0,X1),X2)
| sk0_4(X2,unordered_pair(X0,X1)) = X0
| sk0_4(X2,unordered_pair(X0,X1)) = X1 ),
inference(resolution,[status(thm)],[f79,f53]) ).
fof(f119,plain,
( spl0_0
<=> sk0_4(sk0_6,unordered_pair(sk0_5,sk0_7)) = sk0_5 ),
introduced(split_symbol_definition) ).
fof(f120,plain,
( sk0_4(sk0_6,unordered_pair(sk0_5,sk0_7)) = sk0_5
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f119]) ).
fof(f122,plain,
( spl0_1
<=> sk0_4(sk0_6,unordered_pair(sk0_5,sk0_7)) = sk0_7 ),
introduced(split_symbol_definition) ).
fof(f123,plain,
( sk0_4(sk0_6,unordered_pair(sk0_5,sk0_7)) = sk0_7
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f122]) ).
fof(f125,plain,
( sk0_4(sk0_6,unordered_pair(sk0_5,sk0_7)) = sk0_5
| sk0_4(sk0_6,unordered_pair(sk0_5,sk0_7)) = sk0_7 ),
inference(resolution,[status(thm)],[f92,f52]) ).
fof(f126,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f125,f119,f122]) ).
fof(f134,plain,
( spl0_2
<=> disjoint(unordered_pair(sk0_5,sk0_7),sk0_6) ),
introduced(split_symbol_definition) ).
fof(f135,plain,
( disjoint(unordered_pair(sk0_5,sk0_7),sk0_6)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f134]) ).
fof(f167,plain,
( spl0_9
<=> in(sk0_5,sk0_6) ),
introduced(split_symbol_definition) ).
fof(f168,plain,
( in(sk0_5,sk0_6)
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,plain,
( disjoint(unordered_pair(sk0_5,sk0_7),sk0_6)
| in(sk0_5,sk0_6)
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f120,f78]) ).
fof(f171,plain,
( spl0_2
| spl0_9
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f170,f134,f167,f119]) ).
fof(f177,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f135,f52]) ).
fof(f178,plain,
~ spl0_2,
inference(contradiction_clause,[status(thm)],[f177]) ).
fof(f209,plain,
( spl0_17
<=> in(sk0_7,sk0_6) ),
introduced(split_symbol_definition) ).
fof(f210,plain,
( in(sk0_7,sk0_6)
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f209]) ).
fof(f212,plain,
( disjoint(unordered_pair(sk0_5,sk0_7),sk0_6)
| in(sk0_7,sk0_6)
| ~ spl0_1 ),
inference(paramodulation,[status(thm)],[f123,f78]) ).
fof(f213,plain,
( spl0_2
| spl0_17
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f212,f134,f209,f122]) ).
fof(f220,plain,
( $false
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f210,f51]) ).
fof(f221,plain,
~ spl0_17,
inference(contradiction_clause,[status(thm)],[f220]) ).
fof(f223,plain,
( $false
| ~ spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f168,f50]) ).
fof(f224,plain,
~ spl0_9,
inference(contradiction_clause,[status(thm)],[f223]) ).
fof(f225,plain,
$false,
inference(sat_refutation,[status(thm)],[f126,f171,f178,f213,f221,f224]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SET916+1 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.33 % Computer : n016.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8042.1875MB
% 0.09/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.33 % CPULimit : 300
% 0.09/0.33 % WCLimit : 300
% 0.09/0.33 % DateTime : Tue May 30 10:49:14 EDT 2023
% 0.09/0.33 % CPUTime :
% 0.09/0.34 % Drodi V3.5.1
% 0.09/0.34 % Refutation found
% 0.09/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.56 % Elapsed time: 0.014549 seconds
% 0.16/0.56 % CPU time: 0.015201 seconds
% 0.16/0.56 % Memory used: 3.692 MB
%------------------------------------------------------------------------------