TSTP Solution File: SET949+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET949+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n029.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 12:35:35 EDT 2023
% Result : Theorem 0.06s 0.27s
% Output : CNFRefutation 0.06s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 3
% Syntax : Number of formulae : 21 ( 4 unt; 0 def)
% Number of atoms : 81 ( 23 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 98 ( 38 ~; 31 |; 24 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 8 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 4 ( 2 usr; 1 prp; 0-5 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-4 aty)
% Number of variables : 115 (; 95 !; 20 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] :
( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A,B,C] :
~ ( in(A,cartesian_product2(B,C))
& ! [D,E] : ordered_pair(D,E) != A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B,C] :
~ ( in(A,cartesian_product2(B,C))
& ! [D,E] : ordered_pair(D,E) != A ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f13,plain,
! [A,B,D,E,F] :
( pd0_0(F,E,D,B,A)
<=> ( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) ),
introduced(predicate_definition,[f3]) ).
fof(f14,plain,
! [A,B,C] :
( C = cartesian_product2(A,B)
<=> ! [D] :
( in(D,C)
<=> ? [E,F] : pd0_0(F,E,D,B,A) ) ),
inference(formula_renaming,[status(thm)],[f3,f13]) ).
fof(f15,plain,
! [A,B,C] :
( ( C != cartesian_product2(A,B)
| ! [D] :
( ( ~ in(D,C)
| ? [E,F] : pd0_0(F,E,D,B,A) )
& ( in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) ) ) )
& ( C = cartesian_product2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) )
& ( in(D,C)
| ? [E,F] : pd0_0(F,E,D,B,A) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
( ! [A,B,C] :
( C != cartesian_product2(A,B)
| ( ! [D] :
( ~ in(D,C)
| ? [E,F] : pd0_0(F,E,D,B,A) )
& ! [D] :
( in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) ) ) )
& ! [A,B,C] :
( C = cartesian_product2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) )
& ( in(D,C)
| ? [E,F] : pd0_0(F,E,D,B,A) ) ) ) ),
inference(miniscoping,[status(esa)],[f15]) ).
fof(f17,plain,
( ! [A,B,C] :
( C != cartesian_product2(A,B)
| ( ! [D] :
( ~ in(D,C)
| pd0_0(sk0_1(D,C,B,A),sk0_0(D,C,B,A),D,B,A) )
& ! [D] :
( in(D,C)
| ! [E,F] : ~ pd0_0(F,E,D,B,A) ) ) )
& ! [A,B,C] :
( C = cartesian_product2(A,B)
| ( ( ~ in(sk0_2(C,B,A),C)
| ! [E,F] : ~ pd0_0(F,E,sk0_2(C,B,A),B,A) )
& ( in(sk0_2(C,B,A),C)
| pd0_0(sk0_4(C,B,A),sk0_3(C,B,A),sk0_2(C,B,A),B,A) ) ) ) ),
inference(skolemization,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2,X3] :
( X0 != cartesian_product2(X1,X2)
| ~ in(X3,X0)
| pd0_0(sk0_1(X3,X0,X2,X1),sk0_0(X3,X0,X2,X1),X3,X2,X1) ),
inference(cnf_transformation,[status(esa)],[f17]) ).
fof(f28,plain,
? [A,B,C] :
( in(A,cartesian_product2(B,C))
& ! [D,E] : ordered_pair(D,E) != A ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f29,plain,
? [A] :
( ? [B,C] : in(A,cartesian_product2(B,C))
& ! [D,E] : ordered_pair(D,E) != A ),
inference(miniscoping,[status(esa)],[f28]) ).
fof(f30,plain,
( in(sk0_7,cartesian_product2(sk0_8,sk0_9))
& ! [D,E] : ordered_pair(D,E) != sk0_7 ),
inference(skolemization,[status(esa)],[f29]) ).
fof(f31,plain,
in(sk0_7,cartesian_product2(sk0_8,sk0_9)),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
! [X0,X1] : ordered_pair(X0,X1) != sk0_7,
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f33,plain,
! [A,B,D,E,F] :
( ( ~ pd0_0(F,E,D,B,A)
| ( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) )
& ( pd0_0(F,E,D,B,A)
| ~ in(E,A)
| ~ in(F,B)
| D != ordered_pair(E,F) ) ),
inference(NNF_transformation,[status(esa)],[f13]) ).
fof(f34,plain,
( ! [A,B,D,E,F] :
( ~ pd0_0(F,E,D,B,A)
| ( in(E,A)
& in(F,B)
& D = ordered_pair(E,F) ) )
& ! [A,B,D,E,F] :
( pd0_0(F,E,D,B,A)
| ~ in(E,A)
| ~ in(F,B)
| D != ordered_pair(E,F) ) ),
inference(miniscoping,[status(esa)],[f33]) ).
fof(f37,plain,
! [X0,X1,X2,X3,X4] :
( ~ pd0_0(X0,X1,X2,X3,X4)
| X2 = ordered_pair(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ in(X0,cartesian_product2(X1,X2))
| pd0_0(sk0_1(X0,cartesian_product2(X1,X2),X2,X1),sk0_0(X0,cartesian_product2(X1,X2),X2,X1),X0,X2,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f18]) ).
fof(f61,plain,
! [X0,X1,X2] :
( ~ in(X0,cartesian_product2(X1,X2))
| X0 = ordered_pair(sk0_0(X0,cartesian_product2(X1,X2),X2,X1),sk0_1(X0,cartesian_product2(X1,X2),X2,X1)) ),
inference(resolution,[status(thm)],[f39,f37]) ).
fof(f62,plain,
! [X0,X1] : ~ in(sk0_7,cartesian_product2(X0,X1)),
inference(resolution,[status(thm)],[f61,f32]) ).
fof(f63,plain,
$false,
inference(backward_subsumption_resolution,[status(thm)],[f31,f62]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.07 % Problem : SET949+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.07 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.06/0.26 % Computer : n029.cluster.edu
% 0.06/0.26 % Model : x86_64 x86_64
% 0.06/0.26 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.06/0.26 % Memory : 8042.1875MB
% 0.06/0.26 % OS : Linux 3.10.0-693.el7.x86_64
% 0.06/0.26 % CPULimit : 300
% 0.06/0.26 % WCLimit : 300
% 0.06/0.26 % DateTime : Tue May 30 10:32:06 EDT 2023
% 0.06/0.26 % CPUTime :
% 0.06/0.26 % Drodi V3.5.1
% 0.06/0.27 % Refutation found
% 0.06/0.27 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.06/0.27 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.06/0.28 % Elapsed time: 0.013571 seconds
% 0.06/0.28 % CPU time: 0.019461 seconds
% 0.06/0.28 % Memory used: 14.319 MB
%------------------------------------------------------------------------------