TSTP Solution File: SET903+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET903+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 12:35:30 EDT 2023
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 47 ( 7 unt; 0 def)
% Number of atoms : 123 ( 69 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 129 ( 53 ~; 40 |; 29 &)
% ( 5 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 6 prp; 0-3 aty)
% Number of functors : 6 ( 6 usr; 4 con; 0-2 aty)
% Number of variables : 51 (; 45 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f8,axiom,
! [A,B,C] :
~ ( singleton(A) = set_union2(B,C)
& ~ ( B = singleton(A)
& C = singleton(A) )
& ~ ( B = empty_set
& C = singleton(A) )
& ~ ( B = singleton(A)
& C = empty_set ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,conjecture,
! [A,B,C] :
~ ( singleton(A) = set_union2(B,C)
& B != C
& B != empty_set
& C != empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,negated_conjecture,
~ ! [A,B,C] :
~ ( singleton(A) = set_union2(B,C)
& B != C
& B != empty_set
& C != empty_set ),
inference(negated_conjecture,[status(cth)],[f9]) ).
fof(f25,plain,
! [A,B,C] :
( singleton(A) != set_union2(B,C)
| ( B = singleton(A)
& C = singleton(A) )
| ( B = empty_set
& C = singleton(A) )
| ( B = singleton(A)
& C = empty_set ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f26,plain,
! [A,B,C] :
( pd0_0(C,B,A)
=> ( B = singleton(A)
& C = singleton(A) ) ),
introduced(predicate_definition,[f25]) ).
fof(f27,plain,
! [A,B,C] :
( pd0_1(C,B,A)
=> ( B = empty_set
& C = singleton(A) ) ),
introduced(predicate_definition,[f25]) ).
fof(f28,plain,
! [A,B,C] :
( singleton(A) != set_union2(B,C)
| pd0_0(C,B,A)
| pd0_1(C,B,A)
| ( B = singleton(A)
& C = empty_set ) ),
inference(formula_renaming,[status(thm)],[f25,f27,f26]) ).
fof(f29,plain,
! [X0,X1,X2] :
( singleton(X0) != set_union2(X1,X2)
| pd0_0(X2,X1,X0)
| pd0_1(X2,X1,X0)
| X1 = singleton(X0) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( singleton(X0) != set_union2(X1,X2)
| pd0_0(X2,X1,X0)
| pd0_1(X2,X1,X0)
| X2 = empty_set ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f31,plain,
? [A,B,C] :
( singleton(A) = set_union2(B,C)
& B != C
& B != empty_set
& C != empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f32,plain,
? [C] :
( ? [B] :
( ? [A] : singleton(A) = set_union2(B,C)
& B != C
& B != empty_set )
& C != empty_set ),
inference(miniscoping,[status(esa)],[f31]) ).
fof(f33,plain,
( singleton(sk0_4) = set_union2(sk0_3,sk0_2)
& sk0_3 != sk0_2
& sk0_3 != empty_set
& sk0_2 != empty_set ),
inference(skolemization,[status(esa)],[f32]) ).
fof(f34,plain,
singleton(sk0_4) = set_union2(sk0_3,sk0_2),
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f35,plain,
sk0_3 != sk0_2,
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f36,plain,
sk0_3 != empty_set,
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f37,plain,
sk0_2 != empty_set,
inference(cnf_transformation,[status(esa)],[f33]) ).
fof(f38,plain,
! [A,B,C] :
( ~ pd0_0(C,B,A)
| ( B = singleton(A)
& C = singleton(A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f26]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1,X2)
| X1 = singleton(X2) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1,X2)
| X0 = singleton(X2) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f41,plain,
! [A,B,C] :
( ~ pd0_1(C,B,A)
| ( B = empty_set
& C = singleton(A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f27]) ).
fof(f42,plain,
! [X0,X1,X2] :
( ~ pd0_1(X0,X1,X2)
| X1 = empty_set ),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f75,plain,
( spl0_5
<=> sk0_3 = empty_set ),
introduced(split_symbol_definition) ).
fof(f76,plain,
( sk0_3 = empty_set
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f80,plain,
( spl0_6
<=> pd0_0(sk0_2,sk0_3,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f81,plain,
( pd0_0(sk0_2,sk0_3,sk0_4)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f80]) ).
fof(f83,plain,
( spl0_7
<=> pd0_1(sk0_2,sk0_3,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f84,plain,
( pd0_1(sk0_2,sk0_3,sk0_4)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f83]) ).
fof(f86,plain,
( spl0_8
<=> sk0_2 = empty_set ),
introduced(split_symbol_definition) ).
fof(f87,plain,
( sk0_2 = empty_set
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f86]) ).
fof(f89,plain,
( pd0_0(sk0_2,sk0_3,sk0_4)
| pd0_1(sk0_2,sk0_3,sk0_4)
| sk0_2 = empty_set ),
inference(resolution,[status(thm)],[f30,f34]) ).
fof(f90,plain,
( spl0_6
| spl0_7
| spl0_8 ),
inference(split_clause,[status(thm)],[f89,f80,f83,f86]) ).
fof(f108,plain,
( $false
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f87,f37]) ).
fof(f109,plain,
~ spl0_8,
inference(contradiction_clause,[status(thm)],[f108]) ).
fof(f110,plain,
( $false
| ~ spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f76,f36]) ).
fof(f111,plain,
~ spl0_5,
inference(contradiction_clause,[status(thm)],[f110]) ).
fof(f125,plain,
! [X0,X1,X2] :
( singleton(X0) != set_union2(X1,X2)
| pd0_1(X2,X1,X0)
| X1 = singleton(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f29,f39]) ).
fof(f131,plain,
( spl0_12
<=> sk0_3 = singleton(sk0_4) ),
introduced(split_symbol_definition) ).
fof(f132,plain,
( sk0_3 = singleton(sk0_4)
| ~ spl0_12 ),
inference(component_clause,[status(thm)],[f131]) ).
fof(f134,plain,
( pd0_1(sk0_2,sk0_3,sk0_4)
| sk0_3 = singleton(sk0_4) ),
inference(resolution,[status(thm)],[f125,f34]) ).
fof(f135,plain,
( spl0_7
| spl0_12 ),
inference(split_clause,[status(thm)],[f134,f83,f131]) ).
fof(f155,plain,
( sk0_3 = empty_set
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f84,f42]) ).
fof(f156,plain,
( spl0_5
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f155,f75,f83]) ).
fof(f157,plain,
( sk0_2 = singleton(sk0_4)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f81,f40]) ).
fof(f184,plain,
( sk0_2 = sk0_3
| ~ spl0_12
| ~ spl0_6 ),
inference(forward_demodulation,[status(thm)],[f132,f157]) ).
fof(f185,plain,
( $false
| ~ spl0_12
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f184,f35]) ).
fof(f186,plain,
( ~ spl0_12
| ~ spl0_6 ),
inference(contradiction_clause,[status(thm)],[f185]) ).
fof(f187,plain,
$false,
inference(sat_refutation,[status(thm)],[f90,f109,f111,f135,f156,f186]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SET903+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n017.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.34 % DateTime : Tue May 30 09:39:25 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.13/0.36 % Refutation found
% 0.13/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.22/0.58 % Elapsed time: 0.017792 seconds
% 0.22/0.58 % CPU time: 0.019143 seconds
% 0.22/0.58 % Memory used: 3.638 MB
%------------------------------------------------------------------------------