TSTP Solution File: SET974+1 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET974+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n021.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 20:40:49 EDT 2024
% Result : Theorem 0.16s 0.33s
% Output : CNFRefutation 0.16s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 7
% Syntax : Number of formulae : 42 ( 8 unt; 0 def)
% Number of atoms : 96 ( 6 equ)
% Maximal formula atoms : 4 ( 2 avg)
% Number of connectives : 95 ( 41 ~; 32 |; 17 &)
% ( 2 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 13 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 6 ( 4 usr; 3 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 4 con; 0-5 aty)
% Number of variables : 102 ( 91 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] :
( disjoint(A,B)
=> disjoint(B,A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A,B,C,D,E] :
~ ( in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
& ! [F,G] :
~ ( A = ordered_pair(F,G)
& in(F,set_intersection2(B,D))
& in(G,set_intersection2(C,E)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,conjecture,
! [A,B,C,D] :
( ( disjoint(A,B)
| disjoint(C,D) )
=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,negated_conjecture,
~ ! [A,B,C,D] :
( ( disjoint(A,B)
| disjoint(C,D) )
=> disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(negated_conjecture,[status(cth)],[f11]) ).
fof(f13,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(f17,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f26,plain,
! [A,B] :
( ~ disjoint(A,B)
| disjoint(B,A) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f27,plain,
! [X0,X1] :
( ~ disjoint(X0,X1)
| disjoint(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f28,plain,
! [A,B,C,D,E] :
( ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
| ? [F,G] :
( A = ordered_pair(F,G)
& in(F,set_intersection2(B,D))
& in(G,set_intersection2(C,E)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f29,plain,
! [A,B,C,D,E] :
( ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
| ? [G] :
( ? [F] :
( A = ordered_pair(F,G)
& in(F,set_intersection2(B,D)) )
& in(G,set_intersection2(C,E)) ) ),
inference(miniscoping,[status(esa)],[f28]) ).
fof(f30,plain,
! [A,B,C,D,E] :
( ~ in(A,set_intersection2(cartesian_product2(B,C),cartesian_product2(D,E)))
| ( A = ordered_pair(sk0_3(E,D,C,B,A),sk0_2(E,D,C,B,A))
& in(sk0_3(E,D,C,B,A),set_intersection2(B,D))
& in(sk0_2(E,D,C,B,A),set_intersection2(C,E)) ) ),
inference(skolemization,[status(esa)],[f29]) ).
fof(f32,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
| in(sk0_3(X4,X3,X2,X1,X0),set_intersection2(X1,X3)) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f33,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
| in(sk0_2(X4,X3,X2,X1,X0),set_intersection2(X2,X4)) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f34,plain,
? [A,B,C,D] :
( ( disjoint(A,B)
| disjoint(C,D) )
& ~ disjoint(cartesian_product2(A,C),cartesian_product2(B,D)) ),
inference(pre_NNF_transformation,[status(esa)],[f12]) ).
fof(f35,plain,
( ( disjoint(sk0_4,sk0_5)
| disjoint(sk0_6,sk0_7) )
& ~ disjoint(cartesian_product2(sk0_4,sk0_6),cartesian_product2(sk0_5,sk0_7)) ),
inference(skolemization,[status(esa)],[f34]) ).
fof(f36,plain,
( disjoint(sk0_4,sk0_5)
| disjoint(sk0_6,sk0_7) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f37,plain,
~ disjoint(cartesian_product2(sk0_4,sk0_6),cartesian_product2(sk0_5,sk0_7)),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f38,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)],[f13]) ).
fof(f39,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)],[f38]) ).
fof(f40,plain,
( ! [A,B] :
( disjoint(A,B)
| in(sk0_8(B,A),set_intersection2(A,B)) )
& ! [A,B] :
( ! [C] : ~ in(C,set_intersection2(A,B))
| ~ disjoint(A,B) ) ),
inference(skolemization,[status(esa)],[f39]) ).
fof(f41,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sk0_8(X1,X0),set_intersection2(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ in(X0,set_intersection2(X1,X2))
| ~ disjoint(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f43,plain,
( spl0_0
<=> disjoint(sk0_4,sk0_5) ),
introduced(split_symbol_definition) ).
fof(f44,plain,
( disjoint(sk0_4,sk0_5)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f43]) ).
fof(f46,plain,
( spl0_1
<=> disjoint(sk0_6,sk0_7) ),
introduced(split_symbol_definition) ).
fof(f47,plain,
( disjoint(sk0_6,sk0_7)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f36,f43,f46]) ).
fof(f68,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
| ~ disjoint(X1,X3) ),
inference(resolution,[status(thm)],[f32,f42]) ).
fof(f75,plain,
! [X0,X1] :
( disjoint(X0,X1)
| in(sk0_8(X1,X0),set_intersection2(X1,X0)) ),
inference(paramodulation,[status(thm)],[f17,f41]) ).
fof(f127,plain,
! [X0,X1,X2,X3,X4] :
( ~ in(X0,set_intersection2(cartesian_product2(X1,X2),cartesian_product2(X3,X4)))
| ~ disjoint(X2,X4) ),
inference(resolution,[status(thm)],[f33,f42]) ).
fof(f140,plain,
! [X0,X1,X2,X3] :
( ~ disjoint(X0,X1)
| disjoint(cartesian_product2(X1,X2),cartesian_product2(X0,X3)) ),
inference(resolution,[status(thm)],[f68,f75]) ).
fof(f147,plain,
( disjoint(sk0_5,sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f44,f27]) ).
fof(f151,plain,
! [X0,X1,X2,X3] :
( ~ disjoint(X0,X1)
| disjoint(cartesian_product2(X2,X1),cartesian_product2(X3,X0)) ),
inference(resolution,[status(thm)],[f127,f75]) ).
fof(f159,plain,
~ disjoint(sk0_5,sk0_4),
inference(resolution,[status(thm)],[f140,f37]) ).
fof(f160,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f159,f147]) ).
fof(f161,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f160]) ).
fof(f164,plain,
( disjoint(sk0_7,sk0_6)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f47,f27]) ).
fof(f184,plain,
~ disjoint(sk0_7,sk0_6),
inference(resolution,[status(thm)],[f151,f37]) ).
fof(f185,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f164]) ).
fof(f186,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f185]) ).
fof(f187,plain,
$false,
inference(sat_refutation,[status(thm)],[f49,f161,f186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.10 % Problem : SET974+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n021.cluster.edu
% 0.10/0.31 % Model : x86_64 x86_64
% 0.10/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.31 % Memory : 8042.1875MB
% 0.10/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.31 % CPULimit : 300
% 0.10/0.31 % WCLimit : 300
% 0.10/0.31 % DateTime : Mon Apr 29 21:44:25 EDT 2024
% 0.15/0.31 % CPUTime :
% 0.15/0.32 % Drodi V3.6.0
% 0.16/0.33 % Refutation found
% 0.16/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.16/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.34 % Elapsed time: 0.019082 seconds
% 0.16/0.34 % CPU time: 0.043403 seconds
% 0.16/0.34 % Total memory used: 15.182 MB
% 0.16/0.34 % Net memory used: 15.131 MB
%------------------------------------------------------------------------------