TSTP Solution File: SET971+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET971+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n003.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 12:35:38 EDT 2023
% Result : Theorem 0.16s 0.33s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 5
% Syntax : Number of formulae : 27 ( 20 unt; 0 def)
% Number of atoms : 38 ( 24 equ)
% Maximal formula atoms : 3 ( 1 avg)
% Number of connectives : 20 ( 9 ~; 2 |; 6 &)
% ( 0 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 45 (; 41 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : set_intersection2(A,B) = set_intersection2(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [A,B] : set_intersection2(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,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/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [A,B,C,D] :
( ( subset(A,B)
& subset(C,D) )
=> set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A,B,C,D] :
( ( subset(A,B)
& subset(C,D) )
=> set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) = cartesian_product2(A,C) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [A,B] :
( subset(A,B)
=> set_intersection2(A,B) = A ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,plain,
! [X0,X1] : set_intersection2(X0,X1) = set_intersection2(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f11,plain,
! [A] : set_intersection2(A,A) = A,
inference(miniscoping,[status(esa)],[f2]) ).
fof(f12,plain,
! [X0] : set_intersection2(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f19,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)],[f6]) ).
fof(f20,plain,
? [A,B,C,D] :
( subset(A,B)
& subset(C,D)
& set_intersection2(cartesian_product2(A,D),cartesian_product2(B,C)) != cartesian_product2(A,C) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f21,plain,
( subset(sk0_2,sk0_3)
& subset(sk0_4,sk0_5)
& set_intersection2(cartesian_product2(sk0_2,sk0_5),cartesian_product2(sk0_3,sk0_4)) != cartesian_product2(sk0_2,sk0_4) ),
inference(skolemization,[status(esa)],[f20]) ).
fof(f22,plain,
subset(sk0_2,sk0_3),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f23,plain,
subset(sk0_4,sk0_5),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f24,plain,
set_intersection2(cartesian_product2(sk0_2,sk0_5),cartesian_product2(sk0_3,sk0_4)) != cartesian_product2(sk0_2,sk0_4),
inference(cnf_transformation,[status(esa)],[f21]) ).
fof(f25,plain,
! [A,B] :
( ~ subset(A,B)
| set_intersection2(A,B) = A ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f26,plain,
! [X0,X1] :
( ~ subset(X0,X1)
| set_intersection2(X0,X1) = X0 ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f27,plain,
set_intersection2(sk0_4,sk0_5) = sk0_4,
inference(resolution,[status(thm)],[f26,f23]) ).
fof(f28,plain,
set_intersection2(sk0_2,sk0_3) = sk0_2,
inference(resolution,[status(thm)],[f26,f22]) ).
fof(f30,plain,
! [X0,X1] : cartesian_product2(sk0_2,set_intersection2(X0,X1)) = set_intersection2(cartesian_product2(sk0_2,X0),cartesian_product2(sk0_3,X1)),
inference(paramodulation,[status(thm)],[f28,f19]) ).
fof(f36,plain,
! [X0,X1,X2] : cartesian_product2(X0,set_intersection2(X1,X2)) = set_intersection2(cartesian_product2(X0,X1),cartesian_product2(X0,X2)),
inference(paramodulation,[status(thm)],[f12,f19]) ).
fof(f44,plain,
! [X0,X1,X2] : cartesian_product2(X0,set_intersection2(X1,X2)) = set_intersection2(cartesian_product2(X0,X2),cartesian_product2(X0,X1)),
inference(paramodulation,[status(thm)],[f10,f36]) ).
fof(f45,plain,
! [X0,X1,X2] : cartesian_product2(X0,set_intersection2(X1,X2)) = cartesian_product2(X0,set_intersection2(X2,X1)),
inference(forward_demodulation,[status(thm)],[f36,f44]) ).
fof(f220,plain,
cartesian_product2(sk0_2,set_intersection2(sk0_5,sk0_4)) != cartesian_product2(sk0_2,sk0_4),
inference(backward_demodulation,[status(thm)],[f30,f24]) ).
fof(f221,plain,
cartesian_product2(sk0_2,set_intersection2(sk0_4,sk0_5)) != cartesian_product2(sk0_2,sk0_4),
inference(forward_demodulation,[status(thm)],[f45,f220]) ).
fof(f222,plain,
cartesian_product2(sk0_2,sk0_4) != cartesian_product2(sk0_2,sk0_4),
inference(forward_demodulation,[status(thm)],[f27,f221]) ).
fof(f223,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f222]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.10 % Problem : SET971+1 : TPTP v8.1.2. Released v3.2.0.
% 0.08/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.31 % Computer : n003.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 : Tue May 30 10:18:38 EDT 2023
% 0.10/0.31 % CPUTime :
% 0.16/0.32 % Drodi V3.5.1
% 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
% 0.17/0.58 % Elapsed time: 0.039441 seconds
% 0.17/0.58 % CPU time: 0.019036 seconds
% 0.17/0.58 % Memory used: 2.459 MB
%------------------------------------------------------------------------------