TSTP Solution File: SEU165+3 by Drodi---3.6.0
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%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SEU165+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 20:41:19 EDT 2024
% Result : Theorem 0.10s 0.35s
% Output : CNFRefutation 0.10s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 5
% Syntax : Number of formulae : 33 ( 1 unt; 0 def)
% Number of atoms : 92 ( 0 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 97 ( 38 ~; 40 |; 12 &)
% ( 6 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 5 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 46 ( 38 !; 8 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,plain,
? [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<~> ( in(A,C)
& in(B,D) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f20,plain,
? [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ( in(A,C)
& in(B,D) ) )
& ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ) ),
inference(NNF_transformation,[status(esa)],[f19]) ).
fof(f21,plain,
( ( in(ordered_pair(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5))
| ( in(sk0_2,sk0_4)
& in(sk0_3,sk0_5) ) )
& ( ~ in(ordered_pair(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5))
| ~ in(sk0_2,sk0_4)
| ~ in(sk0_3,sk0_5) ) ),
inference(skolemization,[status(esa)],[f20]) ).
fof(f22,plain,
( in(ordered_pair(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5))
| in(sk0_2,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f23,plain,
( in(ordered_pair(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5))
| in(sk0_3,sk0_5) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f24,plain,
( ~ in(ordered_pair(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5))
| ~ in(sk0_2,sk0_4)
| ~ in(sk0_3,sk0_5) ),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f25,plain,
! [A,B,C,D] :
( ( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| ( in(A,C)
& in(B,D) ) )
& ( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ) ),
inference(NNF_transformation,[status(esa)],[f9]) ).
fof(f26,plain,
( ! [A,B,C,D] :
( ~ in(ordered_pair(A,B),cartesian_product2(C,D))
| ( in(A,C)
& in(B,D) ) )
& ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
| ~ in(A,C)
| ~ in(B,D) ) ),
inference(miniscoping,[status(esa)],[f25]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f28,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| ~ in(X0,X2)
| ~ in(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f30,plain,
( spl0_0
<=> in(ordered_pair(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f31,plain,
( in(ordered_pair(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f30]) ).
fof(f33,plain,
( spl0_1
<=> in(sk0_2,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f34,plain,
( in(sk0_2,sk0_4)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f35,plain,
( ~ in(sk0_2,sk0_4)
| spl0_1 ),
inference(component_clause,[status(thm)],[f33]) ).
fof(f36,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f22,f30,f33]) ).
fof(f37,plain,
( spl0_2
<=> in(sk0_3,sk0_5) ),
introduced(split_symbol_definition) ).
fof(f38,plain,
( in(sk0_3,sk0_5)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f37]) ).
fof(f40,plain,
( spl0_0
| spl0_2 ),
inference(split_clause,[status(thm)],[f23,f30,f37]) ).
fof(f41,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f24,f30,f33,f37]) ).
fof(f43,plain,
( in(sk0_2,sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f27,f31]) ).
fof(f44,plain,
( $false
| spl0_1
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f43,f35]) ).
fof(f45,plain,
( spl0_1
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f44]) ).
fof(f48,plain,
! [X0,X1] :
( in(ordered_pair(X0,sk0_3),cartesian_product2(X1,sk0_5))
| ~ in(X0,X1)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f29,f38]) ).
fof(f51,plain,
( in(ordered_pair(sk0_2,sk0_3),cartesian_product2(sk0_4,sk0_5))
| ~ spl0_2
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f48,f34]) ).
fof(f52,plain,
( spl0_0
| ~ spl0_2
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f51,f30,f37,f33]) ).
fof(f53,plain,
( in(sk0_3,sk0_5)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f31,f28]) ).
fof(f54,plain,
( spl0_2
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f53,f37,f30]) ).
fof(f57,plain,
$false,
inference(sat_refutation,[status(thm)],[f36,f40,f41,f45,f52,f54]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU165+3 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.33 % Computer : n007.cluster.edu
% 0.10/0.33 % Model : x86_64 x86_64
% 0.10/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.33 % Memory : 8042.1875MB
% 0.10/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.33 % CPULimit : 300
% 0.10/0.33 % WCLimit : 300
% 0.10/0.33 % DateTime : Mon Apr 29 19:41:32 EDT 2024
% 0.10/0.33 % CPUTime :
% 0.10/0.34 % Drodi V3.6.0
% 0.10/0.35 % Refutation found
% 0.10/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.10/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.16/0.37 % Elapsed time: 0.022594 seconds
% 0.16/0.37 % CPU time: 0.030330 seconds
% 0.16/0.37 % Total memory used: 12.994 MB
% 0.16/0.37 % Net memory used: 12.938 MB
%------------------------------------------------------------------------------