TSTP Solution File: SET976+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET976+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n012.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 0.15s 0.31s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 7
% Syntax : Number of formulae : 46 ( 3 unt; 0 def)
% Number of atoms : 145 ( 37 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 161 ( 62 ~; 68 |; 21 &)
% ( 9 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 9 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 7 ( 5 usr; 5 prp; 0-2 aty)
% Number of functors : 8 ( 8 usr; 4 con; 0-2 aty)
% Number of variables : 73 ( 63 !; 10 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B] :
( B = singleton(A)
<=> ! [C] :
( in(C,B)
<=> C = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,D))
<=> ( in(A,C)
& in(B,D) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
<=> ( in(A,C)
& B = D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
<=> ( in(A,C)
& B = D ) ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f14,plain,
! [A,B] :
( ( B != singleton(A)
| ! [C] :
( ( ~ in(C,B)
| C = A )
& ( in(C,B)
| C != A ) ) )
& ( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f15,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ? [C] :
( ( ~ in(C,B)
| C != A )
& ( in(C,B)
| C = A ) ) ) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f16,plain,
( ! [A,B] :
( B != singleton(A)
| ( ! [C] :
( ~ in(C,B)
| C = A )
& ! [C] :
( in(C,B)
| C != A ) ) )
& ! [A,B] :
( B = singleton(A)
| ( ( ~ in(sk0_0(B,A),B)
| sk0_0(B,A) != A )
& ( in(sk0_0(B,A),B)
| sk0_0(B,A) = A ) ) ) ),
inference(skolemization,[status(esa)],[f15]) ).
fof(f17,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| ~ in(X2,X0)
| X2 = X1 ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f18,plain,
! [X0,X1,X2] :
( X0 != singleton(X1)
| in(X2,X0)
| X2 != X1 ),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f23,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)],[f6]) ).
fof(f24,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)],[f23]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
! [X0,X1,X2,X3] :
( ~ in(ordered_pair(X0,X1),cartesian_product2(X2,X3))
| in(X1,X3) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f27,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)],[f24]) ).
fof(f32,plain,
? [A,B,C,D] :
( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
<~> ( in(A,C)
& B = D ) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f33,plain,
? [A,B,C,D] :
( ( in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
| ( in(A,C)
& B = D ) )
& ( ~ in(ordered_pair(A,B),cartesian_product2(C,singleton(D)))
| ~ in(A,C)
| B != D ) ),
inference(NNF_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
( ( in(ordered_pair(sk0_3,sk0_4),cartesian_product2(sk0_5,singleton(sk0_6)))
| ( in(sk0_3,sk0_5)
& sk0_4 = sk0_6 ) )
& ( ~ in(ordered_pair(sk0_3,sk0_4),cartesian_product2(sk0_5,singleton(sk0_6)))
| ~ in(sk0_3,sk0_5)
| sk0_4 != sk0_6 ) ),
inference(skolemization,[status(esa)],[f33]) ).
fof(f35,plain,
( in(ordered_pair(sk0_3,sk0_4),cartesian_product2(sk0_5,singleton(sk0_6)))
| in(sk0_3,sk0_5) ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f36,plain,
( in(ordered_pair(sk0_3,sk0_4),cartesian_product2(sk0_5,singleton(sk0_6)))
| sk0_4 = sk0_6 ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f37,plain,
( ~ in(ordered_pair(sk0_3,sk0_4),cartesian_product2(sk0_5,singleton(sk0_6)))
| ~ in(sk0_3,sk0_5)
| sk0_4 != sk0_6 ),
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f38,plain,
( spl0_0
<=> in(ordered_pair(sk0_3,sk0_4),cartesian_product2(sk0_5,singleton(sk0_6))) ),
introduced(split_symbol_definition) ).
fof(f39,plain,
( in(ordered_pair(sk0_3,sk0_4),cartesian_product2(sk0_5,singleton(sk0_6)))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f40,plain,
( ~ in(ordered_pair(sk0_3,sk0_4),cartesian_product2(sk0_5,singleton(sk0_6)))
| spl0_0 ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( spl0_1
<=> in(sk0_3,sk0_5) ),
introduced(split_symbol_definition) ).
fof(f43,plain,
( ~ in(sk0_3,sk0_5)
| spl0_1 ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f35,f38,f41]) ).
fof(f45,plain,
( spl0_2
<=> sk0_4 = sk0_6 ),
introduced(split_symbol_definition) ).
fof(f46,plain,
( sk0_4 = sk0_6
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f45]) ).
fof(f48,plain,
( spl0_0
| spl0_2 ),
inference(split_clause,[status(thm)],[f36,f38,f45]) ).
fof(f49,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f37,f38,f41,f45]) ).
fof(f50,plain,
! [X0,X1] :
( ~ in(X0,singleton(X1))
| X0 = X1 ),
inference(destructive_equality_resolution,[status(esa)],[f17]) ).
fof(f51,plain,
! [X0] : in(X0,singleton(X0)),
inference(destructive_equality_resolution,[status(esa)],[f18]) ).
fof(f54,plain,
( in(sk0_3,sk0_5)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f25,f39]) ).
fof(f55,plain,
( $false
| spl0_1
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f54,f43]) ).
fof(f56,plain,
( spl0_1
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( ~ in(ordered_pair(sk0_3,sk0_4),cartesian_product2(sk0_5,singleton(sk0_4)))
| ~ spl0_2
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f46,f40]) ).
fof(f59,plain,
( spl0_3
<=> in(sk0_4,singleton(sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f61,plain,
( ~ in(sk0_4,singleton(sk0_4))
| spl0_3 ),
inference(component_clause,[status(thm)],[f59]) ).
fof(f62,plain,
( ~ in(sk0_3,sk0_5)
| ~ in(sk0_4,singleton(sk0_4))
| ~ spl0_2
| spl0_0 ),
inference(resolution,[status(thm)],[f27,f58]) ).
fof(f63,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_2
| spl0_0 ),
inference(split_clause,[status(thm)],[f62,f41,f59,f45,f38]) ).
fof(f75,plain,
( in(sk0_4,singleton(sk0_6))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f39,f26]) ).
fof(f77,plain,
( sk0_4 = sk0_6
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f75,f50]) ).
fof(f78,plain,
( spl0_2
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f77,f45,f38]) ).
fof(f80,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f61,f51]) ).
fof(f81,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f80]) ).
fof(f82,plain,
$false,
inference(sat_refutation,[status(thm)],[f44,f48,f49,f56,f63,f78,f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09 % Problem : SET976+1 : TPTP v8.1.2. Released v3.2.0.
% 0.09/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n012.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Mon Apr 29 21:43:56 EDT 2024
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.6.0
% 0.15/0.31 % Refutation found
% 0.15/0.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.34 % Elapsed time: 0.020286 seconds
% 0.15/0.34 % CPU time: 0.033081 seconds
% 0.15/0.34 % Total memory used: 15.033 MB
% 0.15/0.34 % Net memory used: 14.990 MB
%------------------------------------------------------------------------------