TSTP Solution File: SET931+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SET931+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n025.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 12:35:34 EDT 2023
% Result : Theorem 0.13s 0.35s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 9
% Number of leaves : 9
% Syntax : Number of formulae : 63 ( 7 unt; 0 def)
% Number of atoms : 192 ( 102 equ)
% Maximal formula atoms : 10 ( 3 avg)
% Number of connectives : 217 ( 88 ~; 91 |; 27 &)
% ( 10 <=>; 0 =>; 0 <=; 1 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 8 ( 6 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 63 (; 57 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ~ ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,conjecture,
! [A,B,C] :
( set_difference(A,unordered_pair(B,C)) = empty_set
<=> ~ ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,negated_conjecture,
~ ! [A,B,C] :
( set_difference(A,unordered_pair(B,C)) = empty_set
<=> ~ ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ),
inference(negated_conjecture,[status(cth)],[f8]) ).
fof(f12,plain,
! [A,B,C] :
( subset(A,unordered_pair(B,C))
<=> ( A = empty_set
| A = singleton(B)
| A = singleton(C)
| A = unordered_pair(B,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f13,plain,
! [A,B,C] :
( ( ~ subset(A,unordered_pair(B,C))
| A = empty_set
| A = singleton(B)
| A = singleton(C)
| A = unordered_pair(B,C) )
& ( subset(A,unordered_pair(B,C))
| ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f12]) ).
fof(f14,plain,
( ! [A,B,C] :
( ~ subset(A,unordered_pair(B,C))
| A = empty_set
| A = singleton(B)
| A = singleton(C)
| A = unordered_pair(B,C) )
& ! [A,B,C] :
( subset(A,unordered_pair(B,C))
| ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ) ),
inference(miniscoping,[status(esa)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( ~ subset(X0,unordered_pair(X1,X2))
| X0 = empty_set
| X0 = singleton(X1)
| X0 = singleton(X2)
| X0 = unordered_pair(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f16,plain,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
| X0 != empty_set ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f17,plain,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
| X0 != singleton(X1) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f18,plain,
! [X0,X1,X2] :
( subset(X0,unordered_pair(X1,X2))
| X0 != singleton(X2) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f24,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(esa)],[f6]) ).
fof(f25,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
! [A,B] :
( ( set_difference(A,B) != empty_set
| subset(A,B) )
& ( set_difference(A,B) = empty_set
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f7]) ).
fof(f27,plain,
( ! [A,B] :
( set_difference(A,B) != empty_set
| subset(A,B) )
& ! [A,B] :
( set_difference(A,B) = empty_set
| ~ subset(A,B) ) ),
inference(miniscoping,[status(esa)],[f26]) ).
fof(f28,plain,
! [X0,X1] :
( set_difference(X0,X1) != empty_set
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f29,plain,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f27]) ).
fof(f30,plain,
? [A,B,C] :
( set_difference(A,unordered_pair(B,C)) = empty_set
<~> ( A = empty_set
| A = singleton(B)
| A = singleton(C)
| A = unordered_pair(B,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f31,plain,
? [A,B,C] :
( ( set_difference(A,unordered_pair(B,C)) = empty_set
| A = empty_set
| A = singleton(B)
| A = singleton(C)
| A = unordered_pair(B,C) )
& ( set_difference(A,unordered_pair(B,C)) != empty_set
| ( A != empty_set
& A != singleton(B)
& A != singleton(C)
& A != unordered_pair(B,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
( ( set_difference(sk0_2,unordered_pair(sk0_3,sk0_4)) = empty_set
| sk0_2 = empty_set
| sk0_2 = singleton(sk0_3)
| sk0_2 = singleton(sk0_4)
| sk0_2 = unordered_pair(sk0_3,sk0_4) )
& ( set_difference(sk0_2,unordered_pair(sk0_3,sk0_4)) != empty_set
| ( sk0_2 != empty_set
& sk0_2 != singleton(sk0_3)
& sk0_2 != singleton(sk0_4)
& sk0_2 != unordered_pair(sk0_3,sk0_4) ) ) ),
inference(skolemization,[status(esa)],[f31]) ).
fof(f33,plain,
( set_difference(sk0_2,unordered_pair(sk0_3,sk0_4)) = empty_set
| sk0_2 = empty_set
| sk0_2 = singleton(sk0_3)
| sk0_2 = singleton(sk0_4)
| sk0_2 = unordered_pair(sk0_3,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
( set_difference(sk0_2,unordered_pair(sk0_3,sk0_4)) != empty_set
| sk0_2 != empty_set ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f35,plain,
( set_difference(sk0_2,unordered_pair(sk0_3,sk0_4)) != empty_set
| sk0_2 != singleton(sk0_3) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f36,plain,
( set_difference(sk0_2,unordered_pair(sk0_3,sk0_4)) != empty_set
| sk0_2 != singleton(sk0_4) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f37,plain,
( set_difference(sk0_2,unordered_pair(sk0_3,sk0_4)) != empty_set
| sk0_2 != unordered_pair(sk0_3,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f38,plain,
( spl0_0
<=> set_difference(sk0_2,unordered_pair(sk0_3,sk0_4)) = empty_set ),
introduced(split_symbol_definition) ).
fof(f39,plain,
( set_difference(sk0_2,unordered_pair(sk0_3,sk0_4)) = empty_set
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f40,plain,
( set_difference(sk0_2,unordered_pair(sk0_3,sk0_4)) != empty_set
| spl0_0 ),
inference(component_clause,[status(thm)],[f38]) ).
fof(f41,plain,
( spl0_1
<=> sk0_2 = empty_set ),
introduced(split_symbol_definition) ).
fof(f42,plain,
( sk0_2 = empty_set
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( spl0_2
<=> sk0_2 = singleton(sk0_3) ),
introduced(split_symbol_definition) ).
fof(f45,plain,
( sk0_2 = singleton(sk0_3)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,plain,
( spl0_3
<=> sk0_2 = singleton(sk0_4) ),
introduced(split_symbol_definition) ).
fof(f48,plain,
( sk0_2 = singleton(sk0_4)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( spl0_4
<=> sk0_2 = unordered_pair(sk0_3,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f51,plain,
( sk0_2 = unordered_pair(sk0_3,sk0_4)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
( spl0_0
| spl0_1
| spl0_2
| spl0_3
| spl0_4 ),
inference(split_clause,[status(thm)],[f33,f38,f41,f44,f47,f50]) ).
fof(f54,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f34,f38,f41]) ).
fof(f55,plain,
( ~ spl0_0
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f35,f38,f44]) ).
fof(f56,plain,
( ~ spl0_0
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f36,f38,f47]) ).
fof(f57,plain,
( ~ spl0_0
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f37,f38,f50]) ).
fof(f58,plain,
! [X0,X1] : subset(empty_set,unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(esa)],[f16]) ).
fof(f59,plain,
! [X0,X1] : subset(singleton(X0),unordered_pair(X0,X1)),
inference(destructive_equality_resolution,[status(esa)],[f17]) ).
fof(f60,plain,
! [X0,X1] : subset(singleton(X0),unordered_pair(X1,X0)),
inference(destructive_equality_resolution,[status(esa)],[f18]) ).
fof(f83,plain,
( ~ subset(sk0_2,unordered_pair(sk0_3,sk0_4))
| spl0_0 ),
inference(resolution,[status(thm)],[f40,f29]) ).
fof(f84,plain,
( set_difference(sk0_2,sk0_2) != empty_set
| ~ spl0_4
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f51,f40]) ).
fof(f93,plain,
( ~ subset(sk0_2,sk0_2)
| ~ spl0_4
| spl0_0 ),
inference(resolution,[status(thm)],[f84,f29]) ).
fof(f94,plain,
( $false
| ~ spl0_4
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f93,f25]) ).
fof(f95,plain,
( ~ spl0_4
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f94]) ).
fof(f96,plain,
! [X0] :
( subset(sk0_2,unordered_pair(X0,sk0_4))
| ~ spl0_3 ),
inference(paramodulation,[status(thm)],[f48,f60]) ).
fof(f116,plain,
( $false
| ~ spl0_3
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f83,f96]) ).
fof(f117,plain,
( ~ spl0_3
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f116]) ).
fof(f120,plain,
( ~ subset(empty_set,unordered_pair(sk0_3,sk0_4))
| ~ spl0_1
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f42,f83]) ).
fof(f121,plain,
( $false
| ~ spl0_1
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f120,f58]) ).
fof(f122,plain,
( ~ spl0_1
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f121]) ).
fof(f125,plain,
! [X0] :
( subset(sk0_2,unordered_pair(sk0_3,X0))
| ~ spl0_2 ),
inference(paramodulation,[status(thm)],[f45,f59]) ).
fof(f144,plain,
( $false
| ~ spl0_2
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f83,f125]) ).
fof(f145,plain,
( ~ spl0_2
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f144]) ).
fof(f146,plain,
( subset(sk0_2,unordered_pair(sk0_3,sk0_4))
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f39,f28]) ).
fof(f159,plain,
( sk0_2 = empty_set
| sk0_2 = singleton(sk0_3)
| sk0_2 = singleton(sk0_4)
| sk0_2 = unordered_pair(sk0_3,sk0_4)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f146,f15]) ).
fof(f160,plain,
( spl0_1
| spl0_2
| spl0_3
| spl0_4
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f159,f41,f44,f47,f50,f38]) ).
fof(f161,plain,
$false,
inference(sat_refutation,[status(thm)],[f53,f54,f55,f56,f57,f95,f117,f122,f145,f160]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : SET931+1 : TPTP v8.1.2. Released v3.2.0.
% 0.07/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.33 % Computer : n025.cluster.edu
% 0.13/0.33 % Model : x86_64 x86_64
% 0.13/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.33 % Memory : 8042.1875MB
% 0.13/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.33 % CPULimit : 300
% 0.13/0.33 % WCLimit : 300
% 0.13/0.33 % DateTime : Tue May 30 10:31:27 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.34 % Drodi V3.5.1
% 0.13/0.35 % Refutation found
% 0.13/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.57 % Elapsed time: 0.013263 seconds
% 0.19/0.57 % CPU time: 0.035004 seconds
% 0.19/0.57 % Memory used: 14.385 MB
%------------------------------------------------------------------------------