TSTP Solution File: SET577+3 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET577+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n016.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 20:39:51 EDT 2024
% Result : Theorem 0.20s 0.57s
% Output : CNFRefutation 1.58s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 77 ( 11 unt; 0 def)
% Number of atoms : 218 ( 21 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 218 ( 77 ~; 100 |; 25 &)
% ( 13 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 5 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 7 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 122 ( 111 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,union(B,C))
<=> ( member(D,B)
| member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [B,C] : union(B,C) = union(C,B),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,C)
| member(E,D) ) )
=> B = union(C,D) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,C)
| member(E,D) ) )
=> B = union(C,D) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [B,C,D] :
( ( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) )
& ( member(D,union(B,C))
| ( ~ member(D,B)
& ~ member(D,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f1]) ).
fof(f10,plain,
( ! [B,C,D] :
( ~ member(D,union(B,C))
| member(D,B)
| member(D,C) )
& ! [B,C,D] :
( member(D,union(B,C))
| ( ~ member(D,B)
& ~ member(D,C) ) ) ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ~ member(X0,union(X1,X2))
| member(X0,X1)
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f12,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( member(X0,union(X1,X2))
| ~ member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f14,plain,
! [B,C] :
( ( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f15,plain,
( ! [B,C] :
( B != C
| ( subset(B,C)
& subset(C,B) ) )
& ! [B,C] :
( B = C
| ~ subset(B,C)
| ~ subset(C,B) ) ),
inference(miniscoping,[status(esa)],[f14]) ).
fof(f18,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f19,plain,
! [X0,X1] : union(X0,X1) = union(X1,X0),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f20,plain,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( ~ member(D,B)
| member(D,C) ) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f21,plain,
! [B,C] :
( ( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ( subset(B,C)
| ? [D] :
( member(D,B)
& ~ member(D,C) ) ) ),
inference(NNF_transformation,[status(esa)],[f20]) ).
fof(f22,plain,
( ! [B,C] :
( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ! [B,C] :
( subset(B,C)
| ? [D] :
( member(D,B)
& ~ member(D,C) ) ) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f23,plain,
( ! [B,C] :
( ~ subset(B,C)
| ! [D] :
( ~ member(D,B)
| member(D,C) ) )
& ! [B,C] :
( subset(B,C)
| ( member(sk0_0(C,B),B)
& ~ member(sk0_0(C,B),C) ) ) ),
inference(skolemization,[status(esa)],[f22]) ).
fof(f24,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| ~ member(X2,X0)
| member(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
| member(sk0_0(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f26,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ member(sk0_0(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f35,plain,
? [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,C)
| member(E,D) ) )
& B != union(C,D) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f36,plain,
? [B,C,D] :
( ! [E] :
( ( ~ member(E,B)
| member(E,C)
| member(E,D) )
& ( member(E,B)
| ( ~ member(E,C)
& ~ member(E,D) ) ) )
& B != union(C,D) ),
inference(NNF_transformation,[status(esa)],[f35]) ).
fof(f37,plain,
? [B,C,D] :
( ! [E] :
( ~ member(E,B)
| member(E,C)
| member(E,D) )
& ! [E] :
( member(E,B)
| ( ~ member(E,C)
& ~ member(E,D) ) )
& B != union(C,D) ),
inference(miniscoping,[status(esa)],[f36]) ).
fof(f38,plain,
( ! [E] :
( ~ member(E,sk0_2)
| member(E,sk0_3)
| member(E,sk0_4) )
& ! [E] :
( member(E,sk0_2)
| ( ~ member(E,sk0_3)
& ~ member(E,sk0_4) ) )
& sk0_2 != union(sk0_3,sk0_4) ),
inference(skolemization,[status(esa)],[f37]) ).
fof(f39,plain,
! [X0] :
( ~ member(X0,sk0_2)
| member(X0,sk0_3)
| member(X0,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
! [X0] :
( member(X0,sk0_2)
| ~ member(X0,sk0_3) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f41,plain,
! [X0] :
( member(X0,sk0_2)
| ~ member(X0,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f42,plain,
sk0_2 != union(sk0_3,sk0_4),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f51,plain,
! [X0,X1,X2] :
( subset(union(X0,X1),X2)
| member(sk0_0(X2,union(X0,X1)),X0)
| member(sk0_0(X2,union(X0,X1)),X1) ),
inference(resolution,[status(thm)],[f25,f11]) ).
fof(f52,plain,
! [X0] :
( subset(sk0_2,X0)
| member(sk0_0(X0,sk0_2),sk0_3)
| member(sk0_0(X0,sk0_2),sk0_4) ),
inference(resolution,[status(thm)],[f25,f39]) ).
fof(f53,plain,
! [X0] :
( subset(sk0_4,X0)
| member(sk0_0(X0,sk0_4),sk0_2) ),
inference(resolution,[status(thm)],[f25,f41]) ).
fof(f71,plain,
! [X0,X1] :
( subset(union(X0,X1),X1)
| subset(union(X0,X1),X1)
| member(sk0_0(X1,union(X0,X1)),X0) ),
inference(resolution,[status(thm)],[f26,f51]) ).
fof(f72,plain,
! [X0,X1] :
( subset(union(X0,X1),X1)
| member(sk0_0(X1,union(X0,X1)),X0) ),
inference(duplicate_literals_removal,[status(esa)],[f71]) ).
fof(f73,plain,
( spl0_2
<=> subset(sk0_4,sk0_2) ),
introduced(split_symbol_definition) ).
fof(f74,plain,
( subset(sk0_4,sk0_2)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( subset(sk0_4,sk0_2)
| subset(sk0_4,sk0_2) ),
inference(resolution,[status(thm)],[f26,f53]) ).
fof(f77,plain,
spl0_2,
inference(split_clause,[status(thm)],[f76,f73]) ).
fof(f80,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
| ~ member(sk0_0(union(X1,X2),X0),X2) ),
inference(resolution,[status(thm)],[f26,f13]) ).
fof(f81,plain,
! [X0,X1,X2] :
( subset(X0,union(X1,X2))
| ~ member(sk0_0(union(X1,X2),X0),X1) ),
inference(resolution,[status(thm)],[f26,f12]) ).
fof(f99,plain,
! [X0] :
( subset(union(sk0_3,X0),X0)
| member(sk0_0(X0,union(sk0_3,X0)),sk0_2) ),
inference(resolution,[status(thm)],[f72,f40]) ).
fof(f110,plain,
! [X0] :
( subset(sk0_2,union(X0,sk0_4))
| subset(sk0_2,union(X0,sk0_4))
| member(sk0_0(union(X0,sk0_4),sk0_2),sk0_3) ),
inference(resolution,[status(thm)],[f80,f52]) ).
fof(f111,plain,
! [X0] :
( subset(sk0_2,union(X0,sk0_4))
| member(sk0_0(union(X0,sk0_4),sk0_2),sk0_3) ),
inference(duplicate_literals_removal,[status(esa)],[f110]) ).
fof(f118,plain,
! [X0,X1] :
( subset(X0,union(X1,X0))
| subset(X0,union(X1,X0)) ),
inference(resolution,[status(thm)],[f80,f25]) ).
fof(f119,plain,
! [X0,X1] : subset(X0,union(X1,X0)),
inference(duplicate_literals_removal,[status(esa)],[f118]) ).
fof(f127,plain,
! [X0,X1] : subset(X0,union(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f119]) ).
fof(f260,plain,
( spl0_8
<=> subset(union(sk0_3,sk0_2),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f261,plain,
( subset(union(sk0_3,sk0_2),sk0_2)
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,plain,
( subset(union(sk0_3,sk0_2),sk0_2)
| subset(union(sk0_3,sk0_2),sk0_2) ),
inference(resolution,[status(thm)],[f99,f26]) ).
fof(f264,plain,
spl0_8,
inference(split_clause,[status(thm)],[f263,f260]) ).
fof(f275,plain,
( subset(union(sk0_2,sk0_3),sk0_2)
| ~ spl0_8 ),
inference(forward_demodulation,[status(thm)],[f19,f261]) ).
fof(f278,plain,
( spl0_11
<=> sk0_2 = union(sk0_2,sk0_3) ),
introduced(split_symbol_definition) ).
fof(f279,plain,
( sk0_2 = union(sk0_2,sk0_3)
| ~ spl0_11 ),
inference(component_clause,[status(thm)],[f278]) ).
fof(f281,plain,
( spl0_12
<=> subset(sk0_2,union(sk0_2,sk0_3)) ),
introduced(split_symbol_definition) ).
fof(f283,plain,
( ~ subset(sk0_2,union(sk0_2,sk0_3))
| spl0_12 ),
inference(component_clause,[status(thm)],[f281]) ).
fof(f284,plain,
( sk0_2 = union(sk0_2,sk0_3)
| ~ subset(sk0_2,union(sk0_2,sk0_3))
| ~ spl0_8 ),
inference(resolution,[status(thm)],[f275,f18]) ).
fof(f285,plain,
( spl0_11
| ~ spl0_12
| ~ spl0_8 ),
inference(split_clause,[status(thm)],[f284,f278,f281,f260]) ).
fof(f286,plain,
( $false
| spl0_12 ),
inference(forward_subsumption_resolution,[status(thm)],[f283,f127]) ).
fof(f287,plain,
spl0_12,
inference(contradiction_clause,[status(thm)],[f286]) ).
fof(f290,plain,
! [X0] :
( ~ member(X0,sk0_4)
| member(X0,sk0_2)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f74,f24]) ).
fof(f334,plain,
! [X0,X1] :
( member(sk0_0(X0,union(X1,sk0_4)),sk0_2)
| subset(union(X1,sk0_4),X0)
| member(sk0_0(X0,union(X1,sk0_4)),X1)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f290,f51]) ).
fof(f785,plain,
! [X0,X1] :
( subset(union(X0,sk0_4),union(sk0_2,X1))
| member(sk0_0(union(sk0_2,X1),union(X0,sk0_4)),X0)
| subset(union(X0,sk0_4),union(sk0_2,X1))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f334,f81]) ).
fof(f786,plain,
! [X0,X1] :
( subset(union(X0,sk0_4),union(sk0_2,X1))
| member(sk0_0(union(sk0_2,X1),union(X0,sk0_4)),X0)
| ~ spl0_2 ),
inference(duplicate_literals_removal,[status(esa)],[f785]) ).
fof(f2318,plain,
! [X0] :
( subset(union(X0,sk0_4),union(sk0_2,X0))
| subset(union(X0,sk0_4),union(sk0_2,X0))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f786,f80]) ).
fof(f2319,plain,
! [X0] :
( subset(union(X0,sk0_4),union(sk0_2,X0))
| ~ spl0_2 ),
inference(duplicate_literals_removal,[status(esa)],[f2318]) ).
fof(f2371,plain,
( subset(union(sk0_3,sk0_4),sk0_2)
| ~ spl0_2
| ~ spl0_11 ),
inference(paramodulation,[status(thm)],[f279,f2319]) ).
fof(f2383,plain,
( spl0_43
<=> sk0_2 = union(sk0_3,sk0_4) ),
introduced(split_symbol_definition) ).
fof(f2384,plain,
( sk0_2 = union(sk0_3,sk0_4)
| ~ spl0_43 ),
inference(component_clause,[status(thm)],[f2383]) ).
fof(f2386,plain,
( spl0_44
<=> subset(sk0_2,union(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f2389,plain,
( sk0_2 = union(sk0_3,sk0_4)
| ~ subset(sk0_2,union(sk0_3,sk0_4))
| ~ spl0_2
| ~ spl0_11 ),
inference(resolution,[status(thm)],[f2371,f18]) ).
fof(f2390,plain,
( spl0_43
| ~ spl0_44
| ~ spl0_2
| ~ spl0_11 ),
inference(split_clause,[status(thm)],[f2389,f2383,f2386,f73,f278]) ).
fof(f2391,plain,
( $false
| ~ spl0_43 ),
inference(forward_subsumption_resolution,[status(thm)],[f2384,f42]) ).
fof(f2392,plain,
~ spl0_43,
inference(contradiction_clause,[status(thm)],[f2391]) ).
fof(f2702,plain,
( subset(sk0_2,union(sk0_3,sk0_4))
| subset(sk0_2,union(sk0_3,sk0_4)) ),
inference(resolution,[status(thm)],[f111,f81]) ).
fof(f2703,plain,
spl0_44,
inference(split_clause,[status(thm)],[f2702,f2386]) ).
fof(f2714,plain,
$false,
inference(sat_refutation,[status(thm)],[f77,f264,f285,f287,f2390,f2392,f2703]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.13 % Problem : SET577+3 : TPTP v8.1.2. Released v2.2.0.
% 0.04/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n016.cluster.edu
% 0.13/0.35 % Model : x86_64 x86_64
% 0.13/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35 % Memory : 8042.1875MB
% 0.13/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35 % CPULimit : 300
% 0.13/0.35 % WCLimit : 300
% 0.13/0.35 % DateTime : Mon Apr 29 22:07:10 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 0.20/0.57 % Refutation found
% 0.20/0.57 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.20/0.57 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.58/0.58 % Elapsed time: 0.226956 seconds
% 1.58/0.58 % CPU time: 1.668662 seconds
% 1.58/0.58 % Total memory used: 74.910 MB
% 1.58/0.58 % Net memory used: 74.214 MB
%------------------------------------------------------------------------------