TSTP Solution File: SEU146+2 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU146+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n017.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 12:35:58 EDT 2023
% Result : Theorem 0.14s 0.36s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 75 ( 6 unt; 0 def)
% Number of atoms : 196 ( 49 equ)
% Maximal formula atoms : 6 ( 2 avg)
% Number of connectives : 202 ( 81 ~; 89 |; 16 &)
% ( 13 <=>; 2 =>; 0 <=; 1 <~>)
% Maximal formula depth : 7 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 74 (; 68 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f6,axiom,
! [A,B] :
( A = B
<=> ( subset(A,B)
& subset(B,A) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] :
( A = empty_set
<=> ! [B] : ~ in(B,A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f29,lemma,
! [A,B] :
( subset(singleton(A),B)
<=> in(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f30,lemma,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f31,lemma,
! [A,B,C] :
( subset(A,B)
=> ( in(C,A)
| subset(A,set_difference(B,singleton(C))) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f32,conjecture,
! [A,B] :
( subset(A,singleton(B))
<=> ( A = empty_set
| A = singleton(B) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f33,negated_conjecture,
~ ! [A,B] :
( subset(A,singleton(B))
<=> ( A = empty_set
| A = singleton(B) ) ),
inference(negated_conjecture,[status(cth)],[f32]) ).
fof(f47,lemma,
! [A] : subset(empty_set,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f54,lemma,
! [A] :
( subset(A,empty_set)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f76,plain,
! [A,B] :
( ( A != B
| ( subset(A,B)
& subset(B,A) ) )
& ( A = B
| ~ subset(A,B)
| ~ subset(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f6]) ).
fof(f77,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)],[f76]) ).
fof(f78,plain,
! [X0,X1] :
( X0 != X1
| subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f77]) ).
fof(f80,plain,
! [X0,X1] :
( X0 = X1
| ~ subset(X0,X1)
| ~ subset(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f77]) ).
fof(f88,plain,
! [A] :
( ( A != empty_set
| ! [B] : ~ in(B,A) )
& ( A = empty_set
| ? [B] : in(B,A) ) ),
inference(NNF_transformation,[status(esa)],[f8]) ).
fof(f89,plain,
( ! [A] :
( A != empty_set
| ! [B] : ~ in(B,A) )
& ! [A] :
( A = empty_set
| ? [B] : in(B,A) ) ),
inference(miniscoping,[status(esa)],[f88]) ).
fof(f90,plain,
( ! [A] :
( A != empty_set
| ! [B] : ~ in(B,A) )
& ! [A] :
( A = empty_set
| in(sk0_1(A),A) ) ),
inference(skolemization,[status(esa)],[f89]) ).
fof(f91,plain,
! [X0,X1] :
( X0 != empty_set
| ~ in(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f90]) ).
fof(f159,plain,
! [A,B] :
( ( ~ subset(singleton(A),B)
| in(A,B) )
& ( subset(singleton(A),B)
| ~ in(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f29]) ).
fof(f160,plain,
( ! [A,B] :
( ~ subset(singleton(A),B)
| in(A,B) )
& ! [A,B] :
( subset(singleton(A),B)
| ~ in(A,B) ) ),
inference(miniscoping,[status(esa)],[f159]) ).
fof(f162,plain,
! [X0,X1] :
( subset(singleton(X0),X1)
| ~ in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f160]) ).
fof(f163,plain,
! [A,B] :
( ( set_difference(A,B) != empty_set
| subset(A,B) )
& ( set_difference(A,B) = empty_set
| ~ subset(A,B) ) ),
inference(NNF_transformation,[status(esa)],[f30]) ).
fof(f164,plain,
( ! [A,B] :
( set_difference(A,B) != empty_set
| subset(A,B) )
& ! [A,B] :
( set_difference(A,B) = empty_set
| ~ subset(A,B) ) ),
inference(miniscoping,[status(esa)],[f163]) ).
fof(f166,plain,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f164]) ).
fof(f167,plain,
! [A,B,C] :
( ~ subset(A,B)
| in(C,A)
| subset(A,set_difference(B,singleton(C))) ),
inference(pre_NNF_transformation,[status(esa)],[f31]) ).
fof(f168,plain,
! [A,B] :
( ~ subset(A,B)
| ! [C] :
( in(C,A)
| subset(A,set_difference(B,singleton(C))) ) ),
inference(miniscoping,[status(esa)],[f167]) ).
fof(f169,plain,
! [X0,X1,X2] :
( ~ subset(X0,X1)
| in(X2,X0)
| subset(X0,set_difference(X1,singleton(X2))) ),
inference(cnf_transformation,[status(esa)],[f168]) ).
fof(f170,plain,
? [A,B] :
( subset(A,singleton(B))
<~> ( A = empty_set
| A = singleton(B) ) ),
inference(pre_NNF_transformation,[status(esa)],[f33]) ).
fof(f171,plain,
? [A,B] :
( ( subset(A,singleton(B))
| A = empty_set
| A = singleton(B) )
& ( ~ subset(A,singleton(B))
| ( A != empty_set
& A != singleton(B) ) ) ),
inference(NNF_transformation,[status(esa)],[f170]) ).
fof(f172,plain,
( ( subset(sk0_7,singleton(sk0_8))
| sk0_7 = empty_set
| sk0_7 = singleton(sk0_8) )
& ( ~ subset(sk0_7,singleton(sk0_8))
| ( sk0_7 != empty_set
& sk0_7 != singleton(sk0_8) ) ) ),
inference(skolemization,[status(esa)],[f171]) ).
fof(f173,plain,
( subset(sk0_7,singleton(sk0_8))
| sk0_7 = empty_set
| sk0_7 = singleton(sk0_8) ),
inference(cnf_transformation,[status(esa)],[f172]) ).
fof(f174,plain,
( ~ subset(sk0_7,singleton(sk0_8))
| sk0_7 != empty_set ),
inference(cnf_transformation,[status(esa)],[f172]) ).
fof(f175,plain,
( ~ subset(sk0_7,singleton(sk0_8))
| sk0_7 != singleton(sk0_8) ),
inference(cnf_transformation,[status(esa)],[f172]) ).
fof(f204,plain,
! [X0] : subset(empty_set,X0),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f221,plain,
! [A] :
( ~ subset(A,empty_set)
| A = empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f54]) ).
fof(f222,plain,
! [X0] :
( ~ subset(X0,empty_set)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f221]) ).
fof(f254,plain,
( spl0_0
<=> subset(sk0_7,singleton(sk0_8)) ),
introduced(split_symbol_definition) ).
fof(f255,plain,
( subset(sk0_7,singleton(sk0_8))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f256,plain,
( ~ subset(sk0_7,singleton(sk0_8))
| spl0_0 ),
inference(component_clause,[status(thm)],[f254]) ).
fof(f257,plain,
( spl0_1
<=> sk0_7 = empty_set ),
introduced(split_symbol_definition) ).
fof(f258,plain,
( sk0_7 = empty_set
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f257]) ).
fof(f260,plain,
( spl0_2
<=> sk0_7 = singleton(sk0_8) ),
introduced(split_symbol_definition) ).
fof(f261,plain,
( sk0_7 = singleton(sk0_8)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f260]) ).
fof(f263,plain,
( spl0_0
| spl0_1
| spl0_2 ),
inference(split_clause,[status(thm)],[f173,f254,f257,f260]) ).
fof(f264,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f174,f254,f257]) ).
fof(f265,plain,
( ~ spl0_0
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f175,f254,f260]) ).
fof(f266,plain,
! [X0] : subset(X0,X0),
inference(destructive_equality_resolution,[status(esa)],[f78]) ).
fof(f270,plain,
! [X0] : ~ in(X0,empty_set),
inference(destructive_equality_resolution,[status(esa)],[f91]) ).
fof(f311,plain,
( ~ subset(empty_set,singleton(sk0_8))
| ~ spl0_1
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f258,f256]) ).
fof(f312,plain,
( $false
| ~ spl0_1
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f311,f204]) ).
fof(f313,plain,
( ~ spl0_1
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f312]) ).
fof(f314,plain,
( set_difference(sk0_7,singleton(sk0_8)) = empty_set
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f255,f166]) ).
fof(f315,plain,
( spl0_3
<=> subset(singleton(sk0_8),sk0_7) ),
introduced(split_symbol_definition) ).
fof(f317,plain,
( ~ subset(singleton(sk0_8),sk0_7)
| spl0_3 ),
inference(component_clause,[status(thm)],[f315]) ).
fof(f318,plain,
( singleton(sk0_8) = sk0_7
| ~ subset(singleton(sk0_8),sk0_7)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f255,f80]) ).
fof(f319,plain,
( spl0_2
| ~ spl0_3
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f318,f260,f315,f254]) ).
fof(f321,plain,
( ~ subset(sk0_7,sk0_7)
| ~ spl0_2
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f261,f256]) ).
fof(f322,plain,
( $false
| ~ spl0_2
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f321,f266]) ).
fof(f323,plain,
( ~ spl0_2
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f322]) ).
fof(f337,plain,
! [X0] :
( ~ subset(X0,sk0_7)
| in(sk0_8,X0)
| subset(X0,empty_set)
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f314,f169]) ).
fof(f340,plain,
( spl0_4
<=> in(sk0_8,empty_set) ),
introduced(split_symbol_definition) ).
fof(f341,plain,
( in(sk0_8,empty_set)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f340]) ).
fof(f349,plain,
( spl0_6
<=> in(sk0_8,sk0_7) ),
introduced(split_symbol_definition) ).
fof(f350,plain,
( in(sk0_8,sk0_7)
| ~ spl0_6 ),
inference(component_clause,[status(thm)],[f349]) ).
fof(f352,plain,
( spl0_7
<=> subset(sk0_7,empty_set) ),
introduced(split_symbol_definition) ).
fof(f353,plain,
( subset(sk0_7,empty_set)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f355,plain,
( in(sk0_8,sk0_7)
| subset(sk0_7,empty_set)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f337,f266]) ).
fof(f356,plain,
( spl0_6
| spl0_7
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f355,f349,f352,f254]) ).
fof(f357,plain,
( $false
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f341,f270]) ).
fof(f358,plain,
~ spl0_4,
inference(contradiction_clause,[status(thm)],[f357]) ).
fof(f361,plain,
( subset(singleton(sk0_8),sk0_7)
| ~ spl0_6 ),
inference(resolution,[status(thm)],[f350,f162]) ).
fof(f362,plain,
( $false
| spl0_3
| ~ spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f361,f317]) ).
fof(f363,plain,
( spl0_3
| ~ spl0_6 ),
inference(contradiction_clause,[status(thm)],[f362]) ).
fof(f364,plain,
( sk0_7 = empty_set
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f353,f222]) ).
fof(f365,plain,
( spl0_1
| ~ spl0_7 ),
inference(split_clause,[status(thm)],[f364,f257,f352]) ).
fof(f370,plain,
$false,
inference(sat_refutation,[status(thm)],[f263,f264,f265,f313,f319,f323,f356,f358,f363,f365]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12 % Problem : SEU146+2 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.33 % Computer : n017.cluster.edu
% 0.14/0.33 % Model : x86_64 x86_64
% 0.14/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.33 % Memory : 8042.1875MB
% 0.14/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.33 % CPULimit : 300
% 0.14/0.33 % WCLimit : 300
% 0.14/0.33 % DateTime : Tue May 30 08:36:10 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.5.1
% 0.14/0.36 % Refutation found
% 0.14/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.57 % Elapsed time: 0.016588 seconds
% 0.19/0.57 % CPU time: 0.043556 seconds
% 0.19/0.57 % Memory used: 15.221 MB
%------------------------------------------------------------------------------