TSTP Solution File: SET005-1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET005-1 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n004.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 20:38:34 EDT 2024
% Result : Unsatisfiable 0.17s 0.43s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 15
% Syntax : Number of formulae : 70 ( 10 unt; 0 def)
% Number of atoms : 179 ( 0 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 201 ( 92 ~; 104 |; 0 &)
% ( 5 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 8 ( 7 usr; 6 prp; 0-3 aty)
% Number of functors : 7 ( 7 usr; 6 con; 0-3 aty)
% Number of variables : 73 ( 73 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f7,axiom,
! [Set1,Set2,Intersection,Element] :
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection)
| member(Element,Set1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [Set1,Set2,Intersection,Element] :
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection)
| member(Element,Set2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [Set1,Set2,Intersection,Element] :
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Set2)
| ~ member(Element,Set1)
| member(Element,Intersection) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [Set1,Set2,Intersection] :
( member(h(Set1,Set2,Intersection),Intersection)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Set1) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [Set1,Set2,Intersection] :
( member(h(Set1,Set2,Intersection),Intersection)
| intersection(Set1,Set2,Intersection)
| member(h(Set1,Set2,Intersection),Set2) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [Set1,Set2,Intersection] :
( ~ member(h(Set1,Set2,Intersection),Intersection)
| ~ member(h(Set1,Set2,Intersection),Set2)
| ~ member(h(Set1,Set2,Intersection),Set1)
| intersection(Set1,Set2,Intersection) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
intersection(a,b,aIb),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
intersection(b,c,bIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
intersection(a,bIc,aIbIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,negated_conjecture,
~ intersection(aIb,c,aIbIc),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,plain,
! [Set1,Element] :
( ! [Intersection] :
( ! [Set2] : ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection) )
| member(Element,Set1) ),
inference(miniscoping,[status(esa)],[f7]) ).
fof(f25,plain,
! [X0,X1,X2,X3] :
( ~ intersection(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X0) ),
inference(cnf_transformation,[status(esa)],[f24]) ).
fof(f26,plain,
! [Set2,Element] :
( ! [Intersection] :
( ! [Set1] : ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Intersection) )
| member(Element,Set2) ),
inference(miniscoping,[status(esa)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2,X3] :
( ~ intersection(X0,X1,X2)
| ~ member(X3,X2)
| member(X3,X1) ),
inference(cnf_transformation,[status(esa)],[f26]) ).
fof(f28,plain,
! [Intersection,Element] :
( ! [Set1] :
( ! [Set2] :
( ~ intersection(Set1,Set2,Intersection)
| ~ member(Element,Set2) )
| ~ member(Element,Set1) )
| member(Element,Intersection) ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f29,plain,
! [X0,X1,X2,X3] :
( ~ intersection(X0,X1,X2)
| ~ member(X3,X1)
| ~ member(X3,X0)
| member(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( member(h(X0,X1,X2),X2)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X0) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f31,plain,
! [X0,X1,X2] :
( member(h(X0,X1,X2),X2)
| intersection(X0,X1,X2)
| member(h(X0,X1,X2),X1) ),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f32,plain,
! [X0,X1,X2] :
( ~ member(h(X0,X1,X2),X2)
| ~ member(h(X0,X1,X2),X1)
| ~ member(h(X0,X1,X2),X0)
| intersection(X0,X1,X2) ),
inference(cnf_transformation,[status(esa)],[f12]) ).
fof(f33,plain,
intersection(a,b,aIb),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f34,plain,
intersection(b,c,bIc),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f35,plain,
intersection(a,bIc,aIbIc),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f36,plain,
~ intersection(aIb,c,aIbIc),
inference(cnf_transformation,[status(esa)],[f16]) ).
fof(f41,plain,
( spl0_0
<=> member(h(aIb,c,aIbIc),aIbIc) ),
introduced(split_symbol_definition) ).
fof(f42,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f41]) ).
fof(f44,plain,
( spl0_1
<=> member(h(aIb,c,aIbIc),aIb) ),
introduced(split_symbol_definition) ).
fof(f45,plain,
( member(h(aIb,c,aIbIc),aIb)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f44]) ).
fof(f47,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| member(h(aIb,c,aIbIc),aIb) ),
inference(resolution,[status(thm)],[f30,f36]) ).
fof(f48,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f47,f41,f44]) ).
fof(f49,plain,
( spl0_2
<=> member(h(aIb,c,aIbIc),c) ),
introduced(split_symbol_definition) ).
fof(f50,plain,
( member(h(aIb,c,aIbIc),c)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f51,plain,
( ~ member(h(aIb,c,aIbIc),c)
| spl0_2 ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( member(h(aIb,c,aIbIc),aIbIc)
| member(h(aIb,c,aIbIc),c) ),
inference(resolution,[status(thm)],[f31,f36]) ).
fof(f53,plain,
( spl0_0
| spl0_2 ),
inference(split_clause,[status(thm)],[f52,f41,f49]) ).
fof(f54,plain,
( spl0_3
<=> intersection(aIb,c,aIbIc) ),
introduced(split_symbol_definition) ).
fof(f55,plain,
( intersection(aIb,c,aIbIc)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( ~ member(h(aIb,c,aIbIc),c)
| ~ member(h(aIb,c,aIbIc),aIb)
| intersection(aIb,c,aIbIc)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f42,f32]) ).
fof(f58,plain,
( ~ spl0_2
| ~ spl0_1
| spl0_3
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f57,f49,f44,f54,f41]) ).
fof(f61,plain,
! [X0,X1] :
( ~ intersection(X0,X1,aIbIc)
| member(h(aIb,c,aIbIc),X1)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f42,f27]) ).
fof(f62,plain,
! [X0,X1] :
( ~ intersection(X0,X1,aIbIc)
| member(h(aIb,c,aIbIc),X0)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f42,f25]) ).
fof(f63,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f55,f36]) ).
fof(f64,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f63]) ).
fof(f66,plain,
( member(h(aIb,c,aIbIc),bIc)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f61,f35]) ).
fof(f71,plain,
! [X0,X1] :
( ~ intersection(X0,X1,bIc)
| member(h(aIb,c,aIbIc),X1)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f66,f27]) ).
fof(f72,plain,
! [X0,X1] :
( ~ intersection(X0,X1,bIc)
| member(h(aIb,c,aIbIc),X0)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f66,f25]) ).
fof(f74,plain,
( member(h(aIb,c,aIbIc),a)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f62,f35]) ).
fof(f82,plain,
( member(h(aIb,c,aIbIc),c)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f71,f34]) ).
fof(f83,plain,
( $false
| spl0_2
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f82,f51]) ).
fof(f84,plain,
( spl0_2
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f83]) ).
fof(f92,plain,
( member(h(aIb,c,aIbIc),b)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f72,f34]) ).
fof(f111,plain,
! [X0,X1] :
( ~ intersection(X0,b,X1)
| ~ member(h(aIb,c,aIbIc),X0)
| member(h(aIb,c,aIbIc),X1)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f92,f29]) ).
fof(f143,plain,
( spl0_7
<=> member(h(aIb,c,aIbIc),a) ),
introduced(split_symbol_definition) ).
fof(f145,plain,
( ~ member(h(aIb,c,aIbIc),a)
| spl0_7 ),
inference(component_clause,[status(thm)],[f143]) ).
fof(f325,plain,
( ~ member(h(aIb,c,aIbIc),a)
| member(h(aIb,c,aIbIc),aIb)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f111,f33]) ).
fof(f326,plain,
( ~ spl0_7
| spl0_1
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f325,f143,f44,f41]) ).
fof(f329,plain,
( $false
| ~ spl0_0
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f145,f74]) ).
fof(f330,plain,
( ~ spl0_0
| spl0_7 ),
inference(contradiction_clause,[status(thm)],[f329]) ).
fof(f332,plain,
! [X0,X1] :
( ~ intersection(X0,c,X1)
| ~ member(h(aIb,c,aIbIc),X0)
| member(h(aIb,c,aIbIc),X1)
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f50,f29]) ).
fof(f337,plain,
! [X0,X1] :
( ~ intersection(X0,X1,aIb)
| member(h(aIb,c,aIbIc),X1)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f45,f27]) ).
fof(f338,plain,
! [X0,X1] :
( ~ intersection(X0,X1,aIb)
| member(h(aIb,c,aIbIc),X0)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f45,f25]) ).
fof(f349,plain,
( member(h(aIb,c,aIbIc),b)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f337,f33]) ).
fof(f353,plain,
! [X0] :
( ~ intersection(b,c,X0)
| member(h(aIb,c,aIbIc),X0)
| ~ spl0_1
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f349,f332]) ).
fof(f359,plain,
( member(h(aIb,c,aIbIc),a)
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f338,f33]) ).
fof(f393,plain,
( member(h(aIb,c,aIbIc),bIc)
| ~ spl0_1
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f353,f34]) ).
fof(f412,plain,
! [X0,X1] :
( ~ intersection(X0,bIc,X1)
| ~ member(h(aIb,c,aIbIc),X0)
| member(h(aIb,c,aIbIc),X1)
| ~ spl0_1
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f393,f29]) ).
fof(f557,plain,
( ~ member(h(aIb,c,aIbIc),a)
| member(h(aIb,c,aIbIc),aIbIc)
| ~ spl0_1
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f412,f35]) ).
fof(f558,plain,
( ~ spl0_7
| spl0_0
| ~ spl0_1
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f557,f143,f41,f44,f49]) ).
fof(f561,plain,
( $false
| ~ spl0_1
| spl0_7 ),
inference(forward_subsumption_resolution,[status(thm)],[f145,f359]) ).
fof(f562,plain,
( ~ spl0_1
| spl0_7 ),
inference(contradiction_clause,[status(thm)],[f561]) ).
fof(f563,plain,
$false,
inference(sat_refutation,[status(thm)],[f48,f53,f58,f64,f84,f326,f330,f558,f562]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.11 % Problem : SET005-1 : TPTP v8.1.2. Released v1.0.0.
% 0.05/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n004.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Apr 29 21:32:03 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.11/0.33 % Drodi V3.6.0
% 0.17/0.43 % Refutation found
% 0.17/0.43 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.17/0.43 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.44 % Elapsed time: 0.117852 seconds
% 0.17/0.44 % CPU time: 0.853855 seconds
% 0.17/0.44 % Total memory used: 17.458 MB
% 0.17/0.44 % Net memory used: 16.610 MB
%------------------------------------------------------------------------------