TSTP Solution File: SET983+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET983+1 : TPTP v8.1.2. Released v3.2.0.
% 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 : Wed May 31 12:35:39 EDT 2023
% Result : Theorem 0.07s 0.28s
% Output : CNFRefutation 0.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 3
% Syntax : Number of formulae : 19 ( 8 unt; 0 def)
% Number of atoms : 75 ( 10 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 88 ( 32 ~; 30 |; 22 &)
% ( 2 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 5 con; 0-3 aty)
% Number of variables : 57 (; 50 !; 7 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,C] :
( C = set_intersection2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
& in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B,C,D] : cartesian_product2(set_intersection2(A,B),set_intersection2(C,D)) = set_intersection2(cartesian_product2(A,C),cartesian_product2(B,D)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A,B,C,D,E] :
( ( in(A,cartesian_product2(B,C))
& in(A,cartesian_product2(D,E)) )
=> in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B,C,D,E] :
( ( in(A,cartesian_product2(B,C))
& in(A,cartesian_product2(D,E)) )
=> in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f13,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)],[f3]) ).
fof(f14,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)],[f13]) ).
fof(f15,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_0(C,B,A),C)
| ~ in(sk0_0(C,B,A),A)
| ~ in(sk0_0(C,B,A),B) )
& ( in(sk0_0(C,B,A),C)
| ( in(sk0_0(C,B,A),A)
& in(sk0_0(C,B,A),B) ) ) ) ) ),
inference(skolemization,[status(esa)],[f14]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( X0 != set_intersection2(X1,X2)
| in(X3,X0)
| ~ in(X3,X1)
| ~ in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f28,plain,
! [X0,X1,X2,X3] : cartesian_product2(set_intersection2(X0,X1),set_intersection2(X2,X3)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X1,X3)),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f29,plain,
? [A,B,C,D,E] :
( in(A,cartesian_product2(B,C))
& in(A,cartesian_product2(D,E))
& ~ in(A,cartesian_product2(set_intersection2(B,D),set_intersection2(C,E))) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f30,plain,
( in(sk0_3,cartesian_product2(sk0_4,sk0_5))
& in(sk0_3,cartesian_product2(sk0_6,sk0_7))
& ~ in(sk0_3,cartesian_product2(set_intersection2(sk0_4,sk0_6),set_intersection2(sk0_5,sk0_7))) ),
inference(skolemization,[status(esa)],[f29]) ).
fof(f31,plain,
in(sk0_3,cartesian_product2(sk0_4,sk0_5)),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
in(sk0_3,cartesian_product2(sk0_6,sk0_7)),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f33,plain,
~ in(sk0_3,cartesian_product2(set_intersection2(sk0_4,sk0_6),set_intersection2(sk0_5,sk0_7))),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f36,plain,
! [X0,X1,X2] :
( in(X0,set_intersection2(X1,X2))
| ~ in(X0,X1)
| ~ in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f18]) ).
fof(f43,plain,
! [X0] :
( in(sk0_3,set_intersection2(X0,cartesian_product2(sk0_6,sk0_7)))
| ~ in(sk0_3,X0) ),
inference(resolution,[status(thm)],[f36,f32]) ).
fof(f47,plain,
in(sk0_3,set_intersection2(cartesian_product2(sk0_4,sk0_5),cartesian_product2(sk0_6,sk0_7))),
inference(resolution,[status(thm)],[f43,f31]) ).
fof(f60,plain,
~ in(sk0_3,set_intersection2(cartesian_product2(sk0_4,sk0_5),cartesian_product2(sk0_6,sk0_7))),
inference(backward_demodulation,[status(thm)],[f28,f33]) ).
fof(f61,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f60,f47]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET983+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.07/0.26 % Computer : n018.cluster.edu
% 0.07/0.26 % Model : x86_64 x86_64
% 0.07/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.26 % Memory : 8042.1875MB
% 0.07/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.26 % CPULimit : 300
% 0.07/0.26 % WCLimit : 300
% 0.07/0.26 % DateTime : Tue May 30 10:24:10 EDT 2023
% 0.07/0.26 % CPUTime :
% 0.07/0.27 % Drodi V3.5.1
% 0.07/0.28 % Refutation found
% 0.07/0.28 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.07/0.28 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.07/0.28 % Elapsed time: 0.015040 seconds
% 0.07/0.28 % CPU time: 0.021762 seconds
% 0.07/0.28 % Memory used: 14.311 MB
%------------------------------------------------------------------------------