TSTP Solution File: SET935+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET935+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n007.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 20:40:45 EDT 2024
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 73 ( 18 unt; 0 def)
% Number of atoms : 221 ( 39 equ)
% Maximal formula atoms : 14 ( 3 avg)
% Number of connectives : 239 ( 91 ~; 99 |; 35 &)
% ( 12 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 2 con; 0-3 aty)
% Number of variables : 108 ( 102 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A,B] : set_union2(A,B) = set_union2(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A,B] :
( A = B
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A,B] :
( B = powerset(A)
<=> ! [C] :
( in(C,B)
<=> subset(C,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] :
( C = set_union2(A,B)
<=> ! [D] :
( in(D,C)
<=> ( in(D,A)
| in(D,B) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A,B] :
( inclusion_comparable(A,B)
<=> ( subset(A,B)
| subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B] : set_union2(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B] : subset(A,set_union2(A,B)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,conjecture,
! [A,B] :
( set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B))
=> inclusion_comparable(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,negated_conjecture,
~ ! [A,B] :
( set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B))
=> inclusion_comparable(A,B) ),
inference(negated_conjecture,[status(cth)],[f16]) ).
fof(f20,plain,
! [X0,X1] : set_union2(X0,X1) = set_union2(X1,X0),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f21,plain,
! [A,B] :
( ( A != B
| ( subset(A,B)
& subset(B,A) ) )
& ( A = B
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f22,plain,
( ! [A,B] :
( A != B
| ( subset(A,B)
& subset(B,A) ) )
& ! [A,B] :
( A = B
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(miniscoping,[status(esa)],[f21]) ).
fof(f25,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f26,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)],[f4]) ).
fof(f27,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)],[f26]) ).
fof(f28,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)],[f27]) ).
fof(f29,plain,
! [X0,X1,X2] :
( X0 != powerset(X1)
| ~ in(X2,X0)
| subset(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f30,plain,
! [X0,X1,X2] :
( X0 != powerset(X1)
| in(X2,X0)
| ~ subset(X2,X1) ),
inference(cnf_transformation,[status(esa)],[f28]) ).
fof(f33,plain,
! [A,B,C] :
( ( C != set_union2(A,B)
| ! [D] :
( ( ~ in(D,C)
| in(D,A)
| in(D,B) )
& ( in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) ) ) )
& ( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) )
& ( in(D,C)
| in(D,A)
| in(D,B) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f5]) ).
fof(f34,plain,
( ! [A,B,C] :
( C != set_union2(A,B)
| ( ! [D] :
( ~ in(D,C)
| in(D,A)
| in(D,B) )
& ! [D] :
( in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) ) ) )
& ! [A,B,C] :
( C = set_union2(A,B)
| ? [D] :
( ( ~ in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) )
& ( in(D,C)
| in(D,A)
| in(D,B) ) ) ) ),
inference(miniscoping,[status(esa)],[f33]) ).
fof(f35,plain,
( ! [A,B,C] :
( C != set_union2(A,B)
| ( ! [D] :
( ~ in(D,C)
| in(D,A)
| in(D,B) )
& ! [D] :
( in(D,C)
| ( ~ in(D,A)
& ~ in(D,B) ) ) ) )
& ! [A,B,C] :
( C = set_union2(A,B)
| ( ( ~ in(sk0_1(C,B,A),C)
| ( ~ in(sk0_1(C,B,A),A)
& ~ in(sk0_1(C,B,A),B) ) )
& ( in(sk0_1(C,B,A),C)
| in(sk0_1(C,B,A),A)
| in(sk0_1(C,B,A),B) ) ) ) ),
inference(skolemization,[status(esa)],[f34]) ).
fof(f36,plain,
! [X0,X1,X2,X3] :
( X0 != set_union2(X1,X2)
| ~ in(X3,X0)
| in(X3,X1)
| in(X3,X2) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f42,plain,
! [A,B] :
( ( ~ inclusion_comparable(A,B)
| subset(A,B)
| subset(B,A) )
& ( inclusion_comparable(A,B)
| ( ~ subset(A,B)
& ~ subset(B,A) ) ) ),
inference(NNF_transformation,[status(esa)],[f6]) ).
fof(f43,plain,
( ! [A,B] :
( ~ inclusion_comparable(A,B)
| subset(A,B)
| subset(B,A) )
& ! [A,B] :
( inclusion_comparable(A,B)
| ( ~ subset(A,B)
& ~ subset(B,A) ) ) ),
inference(miniscoping,[status(esa)],[f42]) ).
fof(f45,plain,
! [X0,X1] :
( inclusion_comparable(X0,X1)
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f46,plain,
! [X0,X1] :
( inclusion_comparable(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f53,plain,
! [A] : set_union2(A,A) = A,
inference(miniscoping,[status(esa)],[f9]) ).
fof(f54,plain,
! [X0] : set_union2(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f65,plain,
! [X0,X1] : subset(X0,set_union2(X0,X1)),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f66,plain,
? [A,B] :
( set_union2(powerset(A),powerset(B)) = powerset(set_union2(A,B))
& ~ inclusion_comparable(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f17]) ).
fof(f67,plain,
( set_union2(powerset(sk0_4),powerset(sk0_5)) = powerset(set_union2(sk0_4,sk0_5))
& ~ inclusion_comparable(sk0_4,sk0_5) ),
inference(skolemization,[status(esa)],[f66]) ).
fof(f68,plain,
set_union2(powerset(sk0_4),powerset(sk0_5)) = powerset(set_union2(sk0_4,sk0_5)),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f69,plain,
~ inclusion_comparable(sk0_4,sk0_5),
inference(cnf_transformation,[status(esa)],[f67]) ).
fof(f72,plain,
! [X0,X1] :
( ~ in(X0,powerset(X1))
| subset(X0,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f29]) ).
fof(f73,plain,
! [X0,X1] :
( in(X0,powerset(X1))
| ~ subset(X0,X1) ),
inference(destructive_equality_resolution,[status(esa)],[f30]) ).
fof(f74,plain,
! [X0,X1,X2] :
( ~ in(X0,set_union2(X1,X2))
| in(X0,X1)
| in(X0,X2) ),
inference(destructive_equality_resolution,[status(esa)],[f36]) ).
fof(f78,plain,
! [X0] : subset(X0,X0),
inference(paramodulation,[status(thm)],[f54,f65]) ).
fof(f79,plain,
! [X0,X1] : subset(X0,set_union2(X1,X0)),
inference(paramodulation,[status(thm)],[f20,f65]) ).
fof(f85,plain,
~ subset(sk0_4,sk0_5),
inference(resolution,[status(thm)],[f45,f69]) ).
fof(f86,plain,
~ subset(sk0_5,sk0_4),
inference(resolution,[status(thm)],[f46,f69]) ).
fof(f131,plain,
! [X0] :
( ~ in(X0,powerset(set_union2(sk0_4,sk0_5)))
| in(X0,powerset(sk0_4))
| in(X0,powerset(sk0_5)) ),
inference(paramodulation,[status(thm)],[f68,f74]) ).
fof(f143,plain,
! [X0] :
( in(X0,powerset(sk0_4))
| in(X0,powerset(sk0_5))
| ~ subset(X0,set_union2(sk0_4,sk0_5)) ),
inference(resolution,[status(thm)],[f131,f73]) ).
fof(f179,plain,
( spl0_14
<=> in(set_union2(sk0_4,sk0_5),powerset(sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f180,plain,
( in(set_union2(sk0_4,sk0_5),powerset(sk0_4))
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f179]) ).
fof(f182,plain,
( spl0_15
<=> in(set_union2(sk0_4,sk0_5),powerset(sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f183,plain,
( in(set_union2(sk0_4,sk0_5),powerset(sk0_5))
| ~ spl0_15 ),
inference(component_clause,[status(thm)],[f182]) ).
fof(f185,plain,
( in(set_union2(sk0_4,sk0_5),powerset(sk0_4))
| in(set_union2(sk0_4,sk0_5),powerset(sk0_5)) ),
inference(resolution,[status(thm)],[f143,f78]) ).
fof(f186,plain,
( spl0_14
| spl0_15 ),
inference(split_clause,[status(thm)],[f185,f179,f182]) ).
fof(f214,plain,
( subset(set_union2(sk0_4,sk0_5),sk0_4)
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f180,f72]) ).
fof(f218,plain,
( subset(set_union2(sk0_4,sk0_5),sk0_5)
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f183,f72]) ).
fof(f222,plain,
( spl0_17
<=> sk0_4 = set_union2(sk0_4,sk0_5) ),
introduced(split_symbol_definition) ).
fof(f223,plain,
( sk0_4 = set_union2(sk0_4,sk0_5)
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f222]) ).
fof(f225,plain,
( spl0_18
<=> subset(sk0_4,set_union2(sk0_4,sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f227,plain,
( ~ subset(sk0_4,set_union2(sk0_4,sk0_5))
| spl0_18 ),
inference(component_clause,[status(thm)],[f225]) ).
fof(f228,plain,
( sk0_4 = set_union2(sk0_4,sk0_5)
| ~ subset(sk0_4,set_union2(sk0_4,sk0_5))
| ~ spl0_14 ),
inference(resolution,[status(thm)],[f214,f25]) ).
fof(f229,plain,
( spl0_17
| ~ spl0_18
| ~ spl0_14 ),
inference(split_clause,[status(thm)],[f228,f222,f225,f179]) ).
fof(f230,plain,
( $false
| spl0_18 ),
inference(forward_subsumption_resolution,[status(thm)],[f227,f65]) ).
fof(f231,plain,
spl0_18,
inference(contradiction_clause,[status(thm)],[f230]) ).
fof(f244,plain,
( spl0_19
<=> sk0_5 = set_union2(sk0_4,sk0_5) ),
introduced(split_symbol_definition) ).
fof(f245,plain,
( sk0_5 = set_union2(sk0_4,sk0_5)
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f244]) ).
fof(f247,plain,
( spl0_20
<=> subset(sk0_5,set_union2(sk0_4,sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f249,plain,
( ~ subset(sk0_5,set_union2(sk0_4,sk0_5))
| spl0_20 ),
inference(component_clause,[status(thm)],[f247]) ).
fof(f250,plain,
( sk0_5 = set_union2(sk0_4,sk0_5)
| ~ subset(sk0_5,set_union2(sk0_4,sk0_5))
| ~ spl0_15 ),
inference(resolution,[status(thm)],[f218,f25]) ).
fof(f251,plain,
( spl0_19
| ~ spl0_20
| ~ spl0_15 ),
inference(split_clause,[status(thm)],[f250,f244,f247,f182]) ).
fof(f252,plain,
( $false
| spl0_20 ),
inference(forward_subsumption_resolution,[status(thm)],[f249,f79]) ).
fof(f253,plain,
spl0_20,
inference(contradiction_clause,[status(thm)],[f252]) ).
fof(f267,plain,
( subset(sk0_4,sk0_5)
| ~ spl0_19 ),
inference(paramodulation,[status(thm)],[f245,f65]) ).
fof(f268,plain,
( $false
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f267,f85]) ).
fof(f269,plain,
~ spl0_19,
inference(contradiction_clause,[status(thm)],[f268]) ).
fof(f277,plain,
( subset(sk0_5,sk0_4)
| ~ spl0_17 ),
inference(paramodulation,[status(thm)],[f223,f79]) ).
fof(f278,plain,
( $false
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f277,f86]) ).
fof(f279,plain,
~ spl0_17,
inference(contradiction_clause,[status(thm)],[f278]) ).
fof(f280,plain,
$false,
inference(sat_refutation,[status(thm)],[f186,f229,f231,f251,f253,f269,f279]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SET935+1 : TPTP v8.1.2. Released v3.2.0.
% 0.12/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35 % Computer : n007.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 21:21:47 EDT 2024
% 0.13/0.35 % CPUTime :
% 0.13/0.36 % Drodi V3.6.0
% 0.13/0.36 % Refutation found
% 0.13/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.38 % Elapsed time: 0.022533 seconds
% 0.13/0.38 % CPU time: 0.050138 seconds
% 0.13/0.38 % Total memory used: 15.053 MB
% 0.13/0.38 % Net memory used: 14.990 MB
%------------------------------------------------------------------------------