TSTP Solution File: SEU168+3 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU168+3 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n031.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 12:36:06 EDT 2023
% Result : Theorem 0.15s 0.33s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 8
% Syntax : Number of formulae : 67 ( 5 unt; 0 def)
% Number of atoms : 261 ( 8 equ)
% Maximal formula atoms : 11 ( 3 avg)
% Number of connectives : 315 ( 121 ~; 117 |; 62 &)
% ( 6 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 14 ( 6 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 9 ( 7 usr; 3 prp; 0-3 aty)
% Number of functors : 10 ( 10 usr; 1 con; 0-2 aty)
% Number of variables : 168 (; 147 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( in(C,A)
=> in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
! [A] :
? [B] :
( in(A,B)
& ! [C,D] :
( ( in(C,B)
& subset(D,C) )
=> in(D,B) )
& ! [C] :
( in(C,B)
=> in(powerset(C),B) )
& ! [C] :
~ ( subset(C,B)
& ~ are_equipotent(C,B)
& ~ in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ! [A] :
? [B] :
( in(A,B)
& ! [C,D] :
( ( in(C,B)
& subset(D,C) )
=> in(D,B) )
& ! [C] :
( in(C,B)
=> in(powerset(C),B) )
& ! [C] :
~ ( subset(C,B)
& ~ are_equipotent(C,B)
& ~ in(C,B) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,axiom,
! [A] :
? [B] :
( in(A,B)
& ! [C,D] :
( ( in(C,B)
& subset(D,C) )
=> in(D,B) )
& ! [C] :
~ ( in(C,B)
& ! [D] :
~ ( in(D,B)
& ! [E] :
( subset(E,C)
=> in(E,D) ) ) )
& ! [C] :
~ ( subset(C,B)
& ~ are_equipotent(C,B)
& ~ in(C,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,plain,
! [A,B] :
( ( B != powerset(A)
| ! [C] :
( ( ~ in(C,B)
| subset(C,A) )
& ( in(C,B)
| ~ subset(C,A) ) ) )
& ( B = powerset(A)
| ? [C] :
( ( ~ in(C,B)
| ~ subset(C,A) )
& ( in(C,B)
| subset(C,A) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f13,plain,
( ! [A,B] :
( B != powerset(A)
| ( ! [C] :
( ~ in(C,B)
| subset(C,A) )
& ! [C] :
( in(C,B)
| ~ subset(C,A) ) ) )
& ! [A,B] :
( B = powerset(A)
| ? [C] :
( ( ~ in(C,B)
| ~ subset(C,A) )
& ( in(C,B)
| subset(C,A) ) ) ) ),
inference(miniscoping,[status(esa)],[f12]) ).
fof(f14,plain,
( ! [A,B] :
( B != powerset(A)
| ( ! [C] :
( ~ in(C,B)
| subset(C,A) )
& ! [C] :
( in(C,B)
| ~ subset(C,A) ) ) )
& ! [A,B] :
( B = powerset(A)
| ( ( ~ in(sk0_0(B,A),B)
| ~ subset(sk0_0(B,A),A) )
& ( in(sk0_0(B,A),B)
| subset(sk0_0(B,A),A) ) ) ) ),
inference(skolemization,[status(esa)],[f13]) ).
fof(f15,plain,
! [X0,X1,X2] :
( X0 != powerset(X1)
| ~ in(X2,X0)
| subset(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f14]) ).
fof(f19,plain,
! [A,B] :
( subset(A,B)
<=> ! [C] :
( ~ in(C,A)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f20,plain,
! [A,B] :
( ( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(NNF_transformation,[status(esa)],[f19]) ).
fof(f21,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ? [C] :
( in(C,A)
& ~ in(C,B) ) ) ),
inference(miniscoping,[status(esa)],[f20]) ).
fof(f22,plain,
( ! [A,B] :
( ~ subset(A,B)
| ! [C] :
( ~ in(C,A)
| in(C,B) ) )
& ! [A,B] :
( subset(A,B)
| ( in(sk0_1(B,A),A)
& ~ in(sk0_1(B,A),B) ) ) ),
inference(skolemization,[status(esa)],[f21]) ).
fof(f24,plain,
! [X0,X1] :
( subset(X0,X1)
| in(sk0_1(X1,X0),X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f25,plain,
! [X0,X1] :
( subset(X0,X1)
| ~ in(sk0_1(X1,X0),X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f32,plain,
? [A] :
! [B] :
( ~ in(A,B)
| ? [C,D] :
( in(C,B)
& subset(D,C)
& ~ in(D,B) )
| ? [C] :
( in(C,B)
& ~ in(powerset(C),B) )
| ? [C] :
( subset(C,B)
& ~ are_equipotent(C,B)
& ~ in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f33,plain,
! [B,C,D] :
( pd0_0(D,C,B)
=> ( in(C,B)
& subset(D,C)
& ~ in(D,B) ) ),
introduced(predicate_definition,[f32]) ).
fof(f34,plain,
! [B,C] :
( pd0_1(C,B)
=> ( in(C,B)
& ~ in(powerset(C),B) ) ),
introduced(predicate_definition,[f32]) ).
fof(f35,plain,
? [A] :
! [B] :
( ~ in(A,B)
| ? [C,D] : pd0_0(D,C,B)
| ? [C] : pd0_1(C,B)
| ? [C] :
( subset(C,B)
& ~ are_equipotent(C,B)
& ~ in(C,B) ) ),
inference(formula_renaming,[status(thm)],[f32,f34,f33]) ).
fof(f36,plain,
! [B] :
( ~ in(sk0_4,B)
| pd0_0(sk0_6(B),sk0_5(B),B)
| pd0_1(sk0_7(B),B)
| ( subset(sk0_8(B),B)
& ~ are_equipotent(sk0_8(B),B)
& ~ in(sk0_8(B),B) ) ),
inference(skolemization,[status(esa)],[f35]) ).
fof(f37,plain,
! [X0] :
( ~ in(sk0_4,X0)
| pd0_0(sk0_6(X0),sk0_5(X0),X0)
| pd0_1(sk0_7(X0),X0)
| subset(sk0_8(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [X0] :
( ~ in(sk0_4,X0)
| pd0_0(sk0_6(X0),sk0_5(X0),X0)
| pd0_1(sk0_7(X0),X0)
| ~ are_equipotent(sk0_8(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f39,plain,
! [X0] :
( ~ in(sk0_4,X0)
| pd0_0(sk0_6(X0),sk0_5(X0),X0)
| pd0_1(sk0_7(X0),X0)
| ~ in(sk0_8(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f40,plain,
! [A] :
? [B] :
( in(A,B)
& ! [C,D] :
( ~ in(C,B)
| ~ subset(D,C)
| in(D,B) )
& ! [C] :
( ~ in(C,B)
| ? [D] :
( in(D,B)
& ! [E] :
( ~ subset(E,C)
| in(E,D) ) ) )
& ! [C] :
( ~ subset(C,B)
| are_equipotent(C,B)
| in(C,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f41,plain,
! [A] :
? [B] :
( in(A,B)
& ! [D] :
( ! [C] :
( ~ in(C,B)
| ~ subset(D,C) )
| in(D,B) )
& ! [C] :
( ~ in(C,B)
| ? [D] :
( in(D,B)
& ! [E] :
( ~ subset(E,C)
| in(E,D) ) ) )
& ! [C] :
( ~ subset(C,B)
| are_equipotent(C,B)
| in(C,B) ) ),
inference(miniscoping,[status(esa)],[f40]) ).
fof(f42,plain,
! [A] :
( in(A,sk0_9(A))
& ! [D] :
( ! [C] :
( ~ in(C,sk0_9(A))
| ~ subset(D,C) )
| in(D,sk0_9(A)) )
& ! [C] :
( ~ in(C,sk0_9(A))
| ( in(sk0_10(C,A),sk0_9(A))
& ! [E] :
( ~ subset(E,C)
| in(E,sk0_10(C,A)) ) ) )
& ! [C] :
( ~ subset(C,sk0_9(A))
| are_equipotent(C,sk0_9(A))
| in(C,sk0_9(A)) ) ),
inference(skolemization,[status(esa)],[f41]) ).
fof(f43,plain,
! [X0] : in(X0,sk0_9(X0)),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [X0,X1,X2] :
( ~ in(X0,sk0_9(X1))
| ~ subset(X2,X0)
| in(X2,sk0_9(X1)) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f45,plain,
! [X0,X1] :
( ~ in(X0,sk0_9(X1))
| in(sk0_10(X0,X1),sk0_9(X1)) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f46,plain,
! [X0,X1,X2] :
( ~ in(X0,sk0_9(X1))
| ~ subset(X2,X0)
| in(X2,sk0_10(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f47,plain,
! [X0,X1] :
( ~ subset(X0,sk0_9(X1))
| are_equipotent(X0,sk0_9(X1))
| in(X0,sk0_9(X1)) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f48,plain,
! [B,C,D] :
( ~ pd0_0(D,C,B)
| ( in(C,B)
& subset(D,C)
& ~ in(D,B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f33]) ).
fof(f49,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1,X2)
| in(X1,X2) ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f50,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1,X2)
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f51,plain,
! [X0,X1,X2] :
( ~ pd0_0(X0,X1,X2)
| ~ in(X0,X2) ),
inference(cnf_transformation,[status(esa)],[f48]) ).
fof(f52,plain,
! [B,C] :
( ~ pd0_1(C,B)
| ( in(C,B)
& ~ in(powerset(C),B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f34]) ).
fof(f53,plain,
! [X0,X1] :
( ~ pd0_1(X0,X1)
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f54,plain,
! [X0,X1] :
( ~ pd0_1(X0,X1)
| ~ in(powerset(X0),X1) ),
inference(cnf_transformation,[status(esa)],[f52]) ).
fof(f55,plain,
! [X0,X1] :
( ~ in(X0,powerset(X1))
| subset(X0,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f15]) ).
fof(f73,plain,
! [X0] :
( ~ in(sk0_4,sk0_9(X0))
| pd0_0(sk0_6(sk0_9(X0)),sk0_5(sk0_9(X0)),sk0_9(X0))
| pd0_1(sk0_7(sk0_9(X0)),sk0_9(X0))
| ~ subset(sk0_8(sk0_9(X0)),sk0_9(X0))
| in(sk0_8(sk0_9(X0)),sk0_9(X0)) ),
inference(resolution,[status(thm)],[f38,f47]) ).
fof(f74,plain,
! [X0] :
( ~ in(sk0_4,sk0_9(X0))
| pd0_0(sk0_6(sk0_9(X0)),sk0_5(sk0_9(X0)),sk0_9(X0))
| pd0_1(sk0_7(sk0_9(X0)),sk0_9(X0))
| in(sk0_8(sk0_9(X0)),sk0_9(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f73,f37]) ).
fof(f75,plain,
( spl0_3
<=> pd0_0(sk0_6(sk0_9(sk0_4)),sk0_5(sk0_9(sk0_4)),sk0_9(sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f76,plain,
( pd0_0(sk0_6(sk0_9(sk0_4)),sk0_5(sk0_9(sk0_4)),sk0_9(sk0_4))
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f75]) ).
fof(f78,plain,
( spl0_4
<=> pd0_1(sk0_7(sk0_9(sk0_4)),sk0_9(sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f79,plain,
( pd0_1(sk0_7(sk0_9(sk0_4)),sk0_9(sk0_4))
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f78]) ).
fof(f89,plain,
! [X0,X1] :
( subset(powerset(X0),X1)
| subset(sk0_1(X1,powerset(X0)),X0) ),
inference(resolution,[status(thm)],[f24,f55]) ).
fof(f106,plain,
! [X0,X1,X2] :
( ~ in(X0,sk0_9(X1))
| in(sk0_1(X2,powerset(X0)),sk0_10(X0,X1))
| subset(powerset(X0),X2) ),
inference(resolution,[status(thm)],[f46,f89]) ).
fof(f119,plain,
( subset(sk0_6(sk0_9(sk0_4)),sk0_5(sk0_9(sk0_4)))
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f76,f50]) ).
fof(f120,plain,
( in(sk0_5(sk0_9(sk0_4)),sk0_9(sk0_4))
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f76,f49]) ).
fof(f130,plain,
! [X0] :
( ~ in(sk0_5(sk0_9(sk0_4)),sk0_9(X0))
| in(sk0_6(sk0_9(sk0_4)),sk0_9(X0))
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f119,f44]) ).
fof(f155,plain,
! [X0,X1] :
( ~ in(sk0_5(sk0_9(sk0_4)),sk0_9(X0))
| ~ pd0_0(sk0_6(sk0_9(sk0_4)),X1,sk0_9(X0))
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f130,f51]) ).
fof(f156,plain,
! [X0] :
( ~ in(sk0_4,sk0_9(X0))
| pd0_0(sk0_6(sk0_9(X0)),sk0_5(sk0_9(X0)),sk0_9(X0))
| pd0_1(sk0_7(sk0_9(X0)),sk0_9(X0)) ),
inference(forward_subsumption_resolution,[status(thm)],[f74,f39]) ).
fof(f157,plain,
( pd0_0(sk0_6(sk0_9(sk0_4)),sk0_5(sk0_9(sk0_4)),sk0_9(sk0_4))
| pd0_1(sk0_7(sk0_9(sk0_4)),sk0_9(sk0_4)) ),
inference(resolution,[status(thm)],[f156,f43]) ).
fof(f158,plain,
( spl0_3
| spl0_4 ),
inference(split_clause,[status(thm)],[f157,f75,f78]) ).
fof(f234,plain,
! [X0,X1] :
( ~ in(X0,sk0_9(X1))
| subset(powerset(X0),sk0_10(X0,X1))
| subset(powerset(X0),sk0_10(X0,X1)) ),
inference(resolution,[status(thm)],[f106,f25]) ).
fof(f235,plain,
! [X0,X1] :
( ~ in(X0,sk0_9(X1))
| subset(powerset(X0),sk0_10(X0,X1)) ),
inference(duplicate_literals_removal,[status(esa)],[f234]) ).
fof(f239,plain,
! [X0,X1,X2] :
( ~ in(X0,sk0_9(X1))
| ~ in(sk0_10(X0,X1),sk0_9(X2))
| in(powerset(X0),sk0_9(X2)) ),
inference(resolution,[status(thm)],[f235,f44]) ).
fof(f326,plain,
( ~ in(sk0_5(sk0_9(sk0_4)),sk0_9(sk0_4))
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f155,f76]) ).
fof(f327,plain,
( $false
| ~ spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f326,f120]) ).
fof(f328,plain,
~ spl0_3,
inference(contradiction_clause,[status(thm)],[f327]) ).
fof(f441,plain,
! [X0,X1] :
( ~ in(X0,sk0_9(X1))
| in(powerset(X0),sk0_9(X1))
| ~ in(X0,sk0_9(X1)) ),
inference(resolution,[status(thm)],[f239,f45]) ).
fof(f442,plain,
! [X0,X1] :
( ~ in(X0,sk0_9(X1))
| in(powerset(X0),sk0_9(X1)) ),
inference(duplicate_literals_removal,[status(esa)],[f441]) ).
fof(f445,plain,
! [X0,X1] :
( ~ in(X0,sk0_9(X1))
| ~ pd0_1(X0,sk0_9(X1)) ),
inference(resolution,[status(thm)],[f442,f54]) ).
fof(f446,plain,
! [X0,X1] : ~ pd0_1(X0,sk0_9(X1)),
inference(forward_subsumption_resolution,[status(thm)],[f445,f53]) ).
fof(f452,plain,
( $false
| ~ spl0_4 ),
inference(backward_subsumption_resolution,[status(thm)],[f79,f446]) ).
fof(f453,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f452]) ).
fof(f454,plain,
$false,
inference(sat_refutation,[status(thm)],[f158,f328,f453]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.10 % Problem : SEU168+3 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.31 % Computer : n031.cluster.edu
% 0.09/0.31 % Model : x86_64 x86_64
% 0.09/0.31 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.31 % Memory : 8042.1875MB
% 0.09/0.31 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.31 % CPULimit : 300
% 0.09/0.31 % WCLimit : 300
% 0.09/0.31 % DateTime : Tue May 30 09:35:07 EDT 2023
% 0.09/0.31 % CPUTime :
% 0.15/0.32 % Drodi V3.5.1
% 0.15/0.33 % Refutation found
% 0.15/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.56 % Elapsed time: 0.028607 seconds
% 0.15/0.56 % CPU time: 0.034344 seconds
% 0.15/0.56 % Memory used: 3.220 MB
%------------------------------------------------------------------------------