TSTP Solution File: SET578+3 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET578+3 : TPTP v8.1.2. Released v2.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n019.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 0.19s 0.41s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 12
% Syntax : Number of formulae : 74 ( 4 unt; 0 def)
% Number of atoms : 211 ( 14 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 219 ( 82 ~; 90 |; 29 &)
% ( 15 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 12 ( 10 usr; 9 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 3 con; 0-2 aty)
% Number of variables : 91 ( 80 !; 11 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [B,C,D] :
( member(D,intersection(B,C))
<=> ( member(D,B)
& member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [B,C] :
( B = C
<=> ( subset(B,C)
& subset(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [B,C] :
( subset(B,C)
<=> ! [D] :
( member(D,B)
=> member(D,C) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,C)
& member(E,D) ) )
=> B = intersection(C,D) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [B,C,D] :
( ! [E] :
( member(E,B)
<=> ( member(E,C)
& member(E,D) ) )
=> B = intersection(C,D) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
! [B,C,D] :
( ( ~ member(D,intersection(B,C))
| ( member(D,B)
& member(D,C) ) )
& ( member(D,intersection(B,C))
| ~ member(D,B)
| ~ member(D,C) ) ),
inference(NNF_transformation,[status(esa)],[f1]) ).
fof(f10,plain,
( ! [B,C,D] :
( ~ member(D,intersection(B,C))
| ( member(D,B)
& member(D,C) ) )
& ! [B,C,D] :
( member(D,intersection(B,C))
| ~ member(D,B)
| ~ member(D,C) ) ),
inference(miniscoping,[status(esa)],[f9]) ).
fof(f11,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f12,plain,
! [X0,X1,X2] :
( ~ member(X0,intersection(X1,X2))
| member(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f13,plain,
! [X0,X1,X2] :
( member(X0,intersection(X1,X2))
| ~ member(X0,X1)
| ~ 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(f16,plain,
! [X0,X1] :
( X0 != X1
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f18,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f15]) ).
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 != intersection(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 != intersection(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 != intersection(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 != intersection(sk0_3,sk0_4) ),
inference(skolemization,[status(esa)],[f37]) ).
fof(f39,plain,
! [X0] :
( ~ member(X0,sk0_2)
| member(X0,sk0_3) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
! [X0] :
( ~ member(X0,sk0_2)
| member(X0,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f41,plain,
! [X0] :
( member(X0,sk0_2)
| ~ member(X0,sk0_3)
| ~ member(X0,sk0_4) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f42,plain,
sk0_2 != intersection(sk0_3,sk0_4),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f43,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f16]) ).
fof(f47,plain,
( spl0_0
<=> subset(sk0_2,intersection(sk0_3,sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f49,plain,
( ~ subset(sk0_2,intersection(sk0_3,sk0_4))
| spl0_0 ),
inference(component_clause,[status(thm)],[f47]) ).
fof(f50,plain,
( spl0_1
<=> subset(intersection(sk0_3,sk0_4),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f52,plain,
( ~ subset(intersection(sk0_3,sk0_4),sk0_2)
| spl0_1 ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
( ~ subset(sk0_2,intersection(sk0_3,sk0_4))
| ~ subset(intersection(sk0_3,sk0_4),sk0_2) ),
inference(resolution,[status(thm)],[f18,f42]) ).
fof(f54,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f53,f47,f50]) ).
fof(f57,plain,
( ~ member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),intersection(sk0_3,sk0_4))
| spl0_0 ),
inference(resolution,[status(thm)],[f26,f49]) ).
fof(f58,plain,
( spl0_2
<=> member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f60,plain,
( ~ member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),sk0_3)
| spl0_2 ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,plain,
( spl0_3
<=> member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f63,plain,
( ~ member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),sk0_4)
| spl0_3 ),
inference(component_clause,[status(thm)],[f61]) ).
fof(f64,plain,
( ~ member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),sk0_3)
| ~ member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),sk0_4)
| spl0_0 ),
inference(resolution,[status(thm)],[f57,f13]) ).
fof(f65,plain,
( ~ spl0_2
| ~ spl0_3
| spl0_0 ),
inference(split_clause,[status(thm)],[f64,f58,f61,f47]) ).
fof(f69,plain,
( ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_2)
| spl0_1 ),
inference(resolution,[status(thm)],[f52,f26]) ).
fof(f70,plain,
( spl0_4
<=> member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_3) ),
introduced(split_symbol_definition) ).
fof(f72,plain,
( ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_3)
| spl0_4 ),
inference(component_clause,[status(thm)],[f70]) ).
fof(f73,plain,
( spl0_5
<=> member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_4) ),
introduced(split_symbol_definition) ).
fof(f75,plain,
( ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_4)
| spl0_5 ),
inference(component_clause,[status(thm)],[f73]) ).
fof(f76,plain,
( ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_3)
| ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_4)
| spl0_1 ),
inference(resolution,[status(thm)],[f69,f41]) ).
fof(f77,plain,
( ~ spl0_4
| ~ spl0_5
| spl0_1 ),
inference(split_clause,[status(thm)],[f76,f70,f73,f50]) ).
fof(f82,plain,
( ~ member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),sk0_2)
| spl0_2 ),
inference(resolution,[status(thm)],[f60,f39]) ).
fof(f88,plain,
! [X0] :
( ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),intersection(X0,sk0_4))
| spl0_5 ),
inference(resolution,[status(thm)],[f75,f12]) ).
fof(f90,plain,
( subset(sk0_2,intersection(sk0_3,sk0_4))
| spl0_2 ),
inference(resolution,[status(thm)],[f82,f25]) ).
fof(f91,plain,
( $false
| spl0_0
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f90,f49]) ).
fof(f92,plain,
( spl0_0
| spl0_2 ),
inference(contradiction_clause,[status(thm)],[f91]) ).
fof(f94,plain,
! [X0] :
( ~ subset(X0,sk0_3)
| ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),X0)
| spl0_4 ),
inference(resolution,[status(thm)],[f72,f24]) ).
fof(f96,plain,
! [X0] :
( ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),intersection(sk0_3,X0))
| spl0_4 ),
inference(resolution,[status(thm)],[f72,f11]) ).
fof(f104,plain,
( ~ member(sk0_0(intersection(sk0_3,sk0_4),sk0_2),sk0_2)
| spl0_3 ),
inference(resolution,[status(thm)],[f63,f40]) ).
fof(f113,plain,
( subset(sk0_2,intersection(sk0_3,sk0_4))
| spl0_3 ),
inference(resolution,[status(thm)],[f104,f25]) ).
fof(f114,plain,
( spl0_0
| spl0_3 ),
inference(split_clause,[status(thm)],[f113,f47,f61]) ).
fof(f144,plain,
( spl0_10
<=> member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_2) ),
introduced(split_symbol_definition) ).
fof(f149,plain,
( spl0_11
<=> subset(sk0_3,sk0_3) ),
introduced(split_symbol_definition) ).
fof(f151,plain,
( ~ subset(sk0_3,sk0_3)
| spl0_11 ),
inference(component_clause,[status(thm)],[f149]) ).
fof(f152,plain,
( ~ subset(sk0_3,sk0_3)
| ~ member(sk0_0(sk0_2,intersection(sk0_3,sk0_4)),sk0_2)
| spl0_4 ),
inference(resolution,[status(thm)],[f94,f39]) ).
fof(f153,plain,
( ~ spl0_11
| ~ spl0_10
| spl0_4 ),
inference(split_clause,[status(thm)],[f152,f149,f144,f70]) ).
fof(f157,plain,
( $false
| spl0_11 ),
inference(forward_subsumption_resolution,[status(thm)],[f151,f43]) ).
fof(f158,plain,
spl0_11,
inference(contradiction_clause,[status(thm)],[f157]) ).
fof(f197,plain,
( subset(intersection(sk0_3,sk0_4),sk0_2)
| spl0_5 ),
inference(resolution,[status(thm)],[f88,f25]) ).
fof(f198,plain,
( $false
| spl0_1
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f197,f52]) ).
fof(f199,plain,
( spl0_1
| spl0_5 ),
inference(contradiction_clause,[status(thm)],[f198]) ).
fof(f218,plain,
( subset(intersection(sk0_3,sk0_4),sk0_2)
| spl0_4 ),
inference(resolution,[status(thm)],[f96,f25]) ).
fof(f219,plain,
( $false
| spl0_1
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f218,f52]) ).
fof(f220,plain,
( spl0_1
| spl0_4 ),
inference(contradiction_clause,[status(thm)],[f219]) ).
fof(f221,plain,
$false,
inference(sat_refutation,[status(thm)],[f54,f65,f77,f92,f114,f153,f158,f199,f220]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SET578+3 : TPTP v8.1.2. Released v2.2.0.
% 0.06/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n019.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Mon Apr 29 21:33:29 EDT 2024
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.6.0
% 0.19/0.41 % Refutation found
% 0.19/0.41 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.41 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.42 % Elapsed time: 0.076865 seconds
% 0.19/0.42 % CPU time: 0.503173 seconds
% 0.19/0.42 % Total memory used: 66.086 MB
% 0.19/0.42 % Net memory used: 65.539 MB
%------------------------------------------------------------------------------