TSTP Solution File: SEU055+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU055+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n001.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 12:35:46 EDT 2023
% Result : Theorem 0.15s 0.51s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 39
% Syntax : Number of formulae : 211 ( 41 unt; 0 def)
% Number of atoms : 477 ( 77 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 446 ( 180 ~; 197 |; 28 &)
% ( 32 <=>; 9 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 37 ( 35 usr; 29 prp; 0-2 aty)
% Number of functors : 13 ( 13 usr; 6 con; 0-2 aty)
% Number of variables : 81 (; 77 !; 4 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
<=> ! [B,C] :
( ( in(B,relation_dom(A))
& in(C,relation_dom(A))
& apply(A,B) = apply(A,C) )
=> B = C ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f16,axiom,
? [A] :
( relation(A)
& function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A,B] : subset(A,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ( in(A,relation_dom(B))
=> relation_image(B,singleton(A)) = singleton(apply(B,A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [A] :
( ( relation(A)
& function(A) )
=> ( ! [B,C] : relation_image(A,set_difference(B,C)) = set_difference(relation_image(A,B),relation_image(A,C))
=> one_to_one(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [A] :
( ( relation(A)
& function(A) )
=> ( ! [B,C] : relation_image(A,set_difference(B,C)) = set_difference(relation_image(A,B),relation_image(A,C))
=> one_to_one(A) ) ),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f31,axiom,
! [A,B] :
( set_difference(singleton(A),singleton(B)) = singleton(A)
<=> A != B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f33,axiom,
! [A,B] :
( set_difference(A,B) = empty_set
<=> subset(A,B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A] : set_difference(A,empty_set) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [A] : set_difference(empty_set,A) = empty_set,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f44,plain,
! [A] :
( ~ empty(A)
| function(A) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f45,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[status(esa)],[f44]) ).
fof(f59,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( one_to_one(A)
<=> ! [B,C] :
( ~ in(B,relation_dom(A))
| ~ in(C,relation_dom(A))
| apply(A,B) != apply(A,C)
| B = C ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f60,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( ( ~ one_to_one(A)
| ! [B,C] :
( ~ in(B,relation_dom(A))
| ~ in(C,relation_dom(A))
| apply(A,B) != apply(A,C)
| B = C ) )
& ( one_to_one(A)
| ? [B,C] :
( in(B,relation_dom(A))
& in(C,relation_dom(A))
& apply(A,B) = apply(A,C)
& B != C ) ) ) ),
inference(NNF_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( ( ~ one_to_one(A)
| ! [B,C] :
( ~ in(B,relation_dom(A))
| ~ in(C,relation_dom(A))
| apply(A,B) != apply(A,C)
| B = C ) )
& ( one_to_one(A)
| ( in(sk0_1(A),relation_dom(A))
& in(sk0_2(A),relation_dom(A))
& apply(A,sk0_1(A)) = apply(A,sk0_2(A))
& sk0_1(A) != sk0_2(A) ) ) ) ),
inference(skolemization,[status(esa)],[f60]) ).
fof(f63,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| in(sk0_1(X0),relation_dom(X0)) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f64,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| in(sk0_2(X0),relation_dom(X0)) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f65,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| apply(X0,sk0_1(X0)) = apply(X0,sk0_2(X0)) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f66,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| sk0_1(X0) != sk0_2(X0) ),
inference(cnf_transformation,[status(esa)],[f61]) ).
fof(f69,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f84,plain,
( relation(sk0_4)
& function(sk0_4) ),
inference(skolemization,[status(esa)],[f16]) ).
fof(f86,plain,
function(sk0_4),
inference(cnf_transformation,[status(esa)],[f84]) ).
fof(f115,plain,
! [A] : subset(A,A),
inference(miniscoping,[status(esa)],[f26]) ).
fof(f116,plain,
! [X0] : subset(X0,X0),
inference(cnf_transformation,[status(esa)],[f115]) ).
fof(f117,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ~ in(A,relation_dom(B))
| relation_image(B,singleton(A)) = singleton(apply(B,A)) ),
inference(pre_NNF_transformation,[status(esa)],[f27]) ).
fof(f118,plain,
! [B] :
( ~ relation(B)
| ~ function(B)
| ! [A] :
( ~ in(A,relation_dom(B))
| relation_image(B,singleton(A)) = singleton(apply(B,A)) ) ),
inference(miniscoping,[status(esa)],[f117]) ).
fof(f119,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| ~ in(X1,relation_dom(X0))
| relation_image(X0,singleton(X1)) = singleton(apply(X0,X1)) ),
inference(cnf_transformation,[status(esa)],[f118]) ).
fof(f120,plain,
? [A] :
( relation(A)
& function(A)
& ! [B,C] : relation_image(A,set_difference(B,C)) = set_difference(relation_image(A,B),relation_image(A,C))
& ~ one_to_one(A) ),
inference(pre_NNF_transformation,[status(esa)],[f29]) ).
fof(f121,plain,
( relation(sk0_14)
& function(sk0_14)
& ! [B,C] : relation_image(sk0_14,set_difference(B,C)) = set_difference(relation_image(sk0_14,B),relation_image(sk0_14,C))
& ~ one_to_one(sk0_14) ),
inference(skolemization,[status(esa)],[f120]) ).
fof(f122,plain,
relation(sk0_14),
inference(cnf_transformation,[status(esa)],[f121]) ).
fof(f123,plain,
function(sk0_14),
inference(cnf_transformation,[status(esa)],[f121]) ).
fof(f124,plain,
! [X0,X1] : relation_image(sk0_14,set_difference(X0,X1)) = set_difference(relation_image(sk0_14,X0),relation_image(sk0_14,X1)),
inference(cnf_transformation,[status(esa)],[f121]) ).
fof(f125,plain,
~ one_to_one(sk0_14),
inference(cnf_transformation,[status(esa)],[f121]) ).
fof(f128,plain,
! [A,B] :
( ( set_difference(singleton(A),singleton(B)) != singleton(A)
| A != B )
& ( set_difference(singleton(A),singleton(B)) = singleton(A)
| A = B ) ),
inference(NNF_transformation,[status(esa)],[f31]) ).
fof(f129,plain,
( ! [A,B] :
( set_difference(singleton(A),singleton(B)) != singleton(A)
| A != B )
& ! [A,B] :
( set_difference(singleton(A),singleton(B)) = singleton(A)
| A = B ) ),
inference(miniscoping,[status(esa)],[f128]) ).
fof(f130,plain,
! [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) != singleton(X0)
| X0 != X1 ),
inference(cnf_transformation,[status(esa)],[f129]) ).
fof(f131,plain,
! [X0,X1] :
( set_difference(singleton(X0),singleton(X1)) = singleton(X0)
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f129]) ).
fof(f134,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)],[f33]) ).
fof(f135,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)],[f134]) ).
fof(f137,plain,
! [X0,X1] :
( set_difference(X0,X1) = empty_set
| ~ subset(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f135]) ).
fof(f138,plain,
! [X0] : set_difference(X0,empty_set) = X0,
inference(cnf_transformation,[status(esa)],[f34]) ).
fof(f143,plain,
! [X0] : set_difference(empty_set,X0) = empty_set,
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f159,plain,
! [X0] : set_difference(singleton(X0),singleton(X0)) != singleton(X0),
inference(destructive_equality_resolution,[status(esa)],[f130]) ).
fof(f164,plain,
( spl0_1
<=> one_to_one(sk0_14) ),
introduced(split_symbol_definition) ).
fof(f165,plain,
( one_to_one(sk0_14)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f164]) ).
fof(f169,plain,
( spl0_2
<=> function(sk0_14) ),
introduced(split_symbol_definition) ).
fof(f171,plain,
( ~ function(sk0_14)
| spl0_2 ),
inference(component_clause,[status(thm)],[f169]) ).
fof(f174,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f171,f123]) ).
fof(f175,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f174]) ).
fof(f189,plain,
function(empty_set),
inference(resolution,[status(thm)],[f69,f45]) ).
fof(f1709,plain,
( spl0_35
<=> function(set_difference(sk0_4,set_difference(sk0_14,sk0_14))) ),
introduced(split_symbol_definition) ).
fof(f1711,plain,
( ~ function(set_difference(sk0_4,set_difference(sk0_14,sk0_14)))
| spl0_35 ),
inference(component_clause,[status(thm)],[f1709]) ).
fof(f1797,plain,
( spl0_59
<=> function(set_difference(set_difference(sk0_14,sk0_14),sk0_13)) ),
introduced(split_symbol_definition) ).
fof(f1799,plain,
( ~ function(set_difference(set_difference(sk0_14,sk0_14),sk0_13))
| spl0_59 ),
inference(component_clause,[status(thm)],[f1797]) ).
fof(f1808,plain,
( spl0_62
<=> function(set_difference(set_difference(sk0_14,sk0_14),sk0_12)) ),
introduced(split_symbol_definition) ).
fof(f1810,plain,
( ~ function(set_difference(set_difference(sk0_14,sk0_14),sk0_12))
| spl0_62 ),
inference(component_clause,[status(thm)],[f1808]) ).
fof(f1819,plain,
( spl0_65
<=> function(set_difference(set_difference(sk0_14,sk0_14),sk0_9)) ),
introduced(split_symbol_definition) ).
fof(f1821,plain,
( ~ function(set_difference(set_difference(sk0_14,sk0_14),sk0_9))
| spl0_65 ),
inference(component_clause,[status(thm)],[f1819]) ).
fof(f1830,plain,
( spl0_68
<=> function(set_difference(set_difference(sk0_14,sk0_14),set_difference(sk0_14,set_difference(sk0_14,sk0_4)))) ),
introduced(split_symbol_definition) ).
fof(f1832,plain,
( ~ function(set_difference(set_difference(sk0_14,sk0_14),set_difference(sk0_14,set_difference(sk0_14,sk0_4))))
| spl0_68 ),
inference(component_clause,[status(thm)],[f1830]) ).
fof(f1841,plain,
( spl0_71
<=> function(set_difference(set_difference(sk0_14,sk0_14),set_difference(sk0_14,set_difference(sk0_14,sk0_14)))) ),
introduced(split_symbol_definition) ).
fof(f1843,plain,
( ~ function(set_difference(set_difference(sk0_14,sk0_14),set_difference(sk0_14,set_difference(sk0_14,sk0_14))))
| spl0_71 ),
inference(component_clause,[status(thm)],[f1841]) ).
fof(f1852,plain,
( spl0_74
<=> function(set_difference(set_difference(sk0_14,sk0_14),set_difference(sk0_14,sk0_4))) ),
introduced(split_symbol_definition) ).
fof(f1854,plain,
( ~ function(set_difference(set_difference(sk0_14,sk0_14),set_difference(sk0_14,sk0_4)))
| spl0_74 ),
inference(component_clause,[status(thm)],[f1852]) ).
fof(f1874,plain,
( spl0_80
<=> function(set_difference(set_difference(sk0_14,sk0_14),sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f1876,plain,
( ~ function(set_difference(set_difference(sk0_14,sk0_14),sk0_4))
| spl0_80 ),
inference(component_clause,[status(thm)],[f1874]) ).
fof(f1885,plain,
( spl0_83
<=> function(set_difference(set_difference(sk0_14,sk0_14),sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f1887,plain,
( ~ function(set_difference(set_difference(sk0_14,sk0_14),sk0_14))
| spl0_83 ),
inference(component_clause,[status(thm)],[f1885]) ).
fof(f1951,plain,
( spl0_101
<=> function(set_difference(sk0_14,set_difference(set_difference(sk0_14,sk0_14),sk0_4))) ),
introduced(split_symbol_definition) ).
fof(f1953,plain,
( ~ function(set_difference(sk0_14,set_difference(set_difference(sk0_14,sk0_14),sk0_4)))
| spl0_101 ),
inference(component_clause,[status(thm)],[f1951]) ).
fof(f1954,plain,
( spl0_102
<=> one_to_one(set_difference(sk0_14,set_difference(set_difference(sk0_14,sk0_14),sk0_4))) ),
introduced(split_symbol_definition) ).
fof(f1955,plain,
( one_to_one(set_difference(sk0_14,set_difference(set_difference(sk0_14,sk0_14),sk0_4)))
| ~ spl0_102 ),
inference(component_clause,[status(thm)],[f1954]) ).
fof(f1962,plain,
( spl0_104
<=> function(set_difference(sk0_14,set_difference(set_difference(sk0_14,sk0_14),sk0_14))) ),
introduced(split_symbol_definition) ).
fof(f1964,plain,
( ~ function(set_difference(sk0_14,set_difference(set_difference(sk0_14,sk0_14),sk0_14)))
| spl0_104 ),
inference(component_clause,[status(thm)],[f1962]) ).
fof(f1965,plain,
( spl0_105
<=> one_to_one(set_difference(sk0_14,set_difference(set_difference(sk0_14,sk0_14),sk0_14))) ),
introduced(split_symbol_definition) ).
fof(f1966,plain,
( one_to_one(set_difference(sk0_14,set_difference(set_difference(sk0_14,sk0_14),sk0_14)))
| ~ spl0_105 ),
inference(component_clause,[status(thm)],[f1965]) ).
fof(f1995,plain,
( spl0_113
<=> function(set_difference(sk0_14,set_difference(sk0_14,set_difference(sk0_14,sk0_14)))) ),
introduced(split_symbol_definition) ).
fof(f1997,plain,
( ~ function(set_difference(sk0_14,set_difference(sk0_14,set_difference(sk0_14,sk0_14))))
| spl0_113 ),
inference(component_clause,[status(thm)],[f1995]) ).
fof(f2006,plain,
( spl0_116
<=> function(set_difference(sk0_14,set_difference(sk0_14,sk0_14))) ),
introduced(split_symbol_definition) ).
fof(f2008,plain,
( ~ function(set_difference(sk0_14,set_difference(sk0_14,sk0_14)))
| spl0_116 ),
inference(component_clause,[status(thm)],[f2006]) ).
fof(f2009,plain,
( spl0_117
<=> one_to_one(set_difference(sk0_14,set_difference(sk0_14,sk0_14))) ),
introduced(split_symbol_definition) ).
fof(f2010,plain,
( one_to_one(set_difference(sk0_14,set_difference(sk0_14,sk0_14)))
| ~ spl0_117 ),
inference(component_clause,[status(thm)],[f2009]) ).
fof(f2028,plain,
( spl0_122
<=> in(sk0_1(sk0_14),relation_dom(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f2029,plain,
( in(sk0_1(sk0_14),relation_dom(sk0_14))
| ~ spl0_122 ),
inference(component_clause,[status(thm)],[f2028]) ).
fof(f2031,plain,
( ~ function(sk0_14)
| one_to_one(sk0_14)
| in(sk0_1(sk0_14),relation_dom(sk0_14)) ),
inference(resolution,[status(thm)],[f63,f122]) ).
fof(f2032,plain,
( ~ spl0_2
| spl0_1
| spl0_122 ),
inference(split_clause,[status(thm)],[f2031,f169,f164,f2028]) ).
fof(f2037,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f165,f125]) ).
fof(f2038,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f2037]) ).
fof(f2219,plain,
( spl0_159
<=> in(sk0_2(sk0_14),relation_dom(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f2220,plain,
( in(sk0_2(sk0_14),relation_dom(sk0_14))
| ~ spl0_159 ),
inference(component_clause,[status(thm)],[f2219]) ).
fof(f2222,plain,
( ~ function(sk0_14)
| one_to_one(sk0_14)
| in(sk0_2(sk0_14),relation_dom(sk0_14)) ),
inference(resolution,[status(thm)],[f64,f122]) ).
fof(f2223,plain,
( ~ spl0_2
| spl0_1
| spl0_159 ),
inference(split_clause,[status(thm)],[f2222,f169,f164,f2219]) ).
fof(f2404,plain,
( spl0_196
<=> apply(sk0_14,sk0_1(sk0_14)) = apply(sk0_14,sk0_2(sk0_14)) ),
introduced(split_symbol_definition) ).
fof(f2405,plain,
( apply(sk0_14,sk0_1(sk0_14)) = apply(sk0_14,sk0_2(sk0_14))
| ~ spl0_196 ),
inference(component_clause,[status(thm)],[f2404]) ).
fof(f2407,plain,
( ~ function(sk0_14)
| one_to_one(sk0_14)
| apply(sk0_14,sk0_1(sk0_14)) = apply(sk0_14,sk0_2(sk0_14)) ),
inference(resolution,[status(thm)],[f65,f122]) ).
fof(f2408,plain,
( ~ spl0_2
| spl0_1
| spl0_196 ),
inference(split_clause,[status(thm)],[f2407,f169,f164,f2404]) ).
fof(f2409,plain,
( spl0_197
<=> relation(sk0_14) ),
introduced(split_symbol_definition) ).
fof(f2411,plain,
( ~ relation(sk0_14)
| spl0_197 ),
inference(component_clause,[status(thm)],[f2409]) ).
fof(f2412,plain,
( spl0_198
<=> relation_image(sk0_14,singleton(sk0_1(sk0_14))) = singleton(apply(sk0_14,sk0_1(sk0_14))) ),
introduced(split_symbol_definition) ).
fof(f2413,plain,
( relation_image(sk0_14,singleton(sk0_1(sk0_14))) = singleton(apply(sk0_14,sk0_1(sk0_14)))
| ~ spl0_198 ),
inference(component_clause,[status(thm)],[f2412]) ).
fof(f2415,plain,
( ~ relation(sk0_14)
| ~ function(sk0_14)
| relation_image(sk0_14,singleton(sk0_1(sk0_14))) = singleton(apply(sk0_14,sk0_1(sk0_14)))
| ~ spl0_122 ),
inference(resolution,[status(thm)],[f2029,f119]) ).
fof(f2416,plain,
( ~ spl0_197
| ~ spl0_2
| spl0_198
| ~ spl0_122 ),
inference(split_clause,[status(thm)],[f2415,f2409,f169,f2412,f2028]) ).
fof(f2420,plain,
( $false
| spl0_197 ),
inference(forward_subsumption_resolution,[status(thm)],[f2411,f122]) ).
fof(f2421,plain,
spl0_197,
inference(contradiction_clause,[status(thm)],[f2420]) ).
fof(f2422,plain,
( spl0_199
<=> relation_image(sk0_14,singleton(sk0_2(sk0_14))) = singleton(apply(sk0_14,sk0_2(sk0_14))) ),
introduced(split_symbol_definition) ).
fof(f2423,plain,
( relation_image(sk0_14,singleton(sk0_2(sk0_14))) = singleton(apply(sk0_14,sk0_2(sk0_14)))
| ~ spl0_199 ),
inference(component_clause,[status(thm)],[f2422]) ).
fof(f2425,plain,
( ~ relation(sk0_14)
| ~ function(sk0_14)
| relation_image(sk0_14,singleton(sk0_2(sk0_14))) = singleton(apply(sk0_14,sk0_2(sk0_14)))
| ~ spl0_159 ),
inference(resolution,[status(thm)],[f2220,f119]) ).
fof(f2426,plain,
( ~ spl0_197
| ~ spl0_2
| spl0_199
| ~ spl0_159 ),
inference(split_clause,[status(thm)],[f2425,f2409,f169,f2422,f2219]) ).
fof(f2429,plain,
( spl0_200
<=> sk0_1(sk0_14) = sk0_2(sk0_14) ),
introduced(split_symbol_definition) ).
fof(f2430,plain,
( sk0_1(sk0_14) = sk0_2(sk0_14)
| ~ spl0_200 ),
inference(component_clause,[status(thm)],[f2429]) ).
fof(f2445,plain,
! [X0] :
( relation_image(sk0_14,set_difference(X0,singleton(sk0_1(sk0_14)))) = set_difference(relation_image(sk0_14,X0),singleton(apply(sk0_14,sk0_1(sk0_14))))
| ~ spl0_198 ),
inference(paramodulation,[status(thm)],[f2413,f124]) ).
fof(f2447,plain,
( relation_image(sk0_14,singleton(sk0_2(sk0_14))) = singleton(apply(sk0_14,sk0_1(sk0_14)))
| ~ spl0_196
| ~ spl0_199 ),
inference(forward_demodulation,[status(thm)],[f2405,f2423]) ).
fof(f2450,plain,
! [X0] :
( relation_image(sk0_14,set_difference(X0,singleton(sk0_2(sk0_14)))) = set_difference(relation_image(sk0_14,X0),singleton(apply(sk0_14,sk0_1(sk0_14))))
| ~ spl0_196
| ~ spl0_199 ),
inference(paramodulation,[status(thm)],[f2447,f124]) ).
fof(f2948,plain,
! [X0] :
( relation_image(sk0_14,set_difference(X0,singleton(sk0_2(sk0_14)))) = relation_image(sk0_14,set_difference(X0,singleton(sk0_1(sk0_14))))
| ~ spl0_196
| ~ spl0_199
| ~ spl0_198 ),
inference(paramodulation,[status(thm)],[f2445,f2450]) ).
fof(f2952,plain,
! [X0] :
( relation_image(sk0_14,singleton(X0)) = relation_image(sk0_14,set_difference(singleton(X0),singleton(sk0_1(sk0_14))))
| X0 = sk0_2(sk0_14)
| ~ spl0_196
| ~ spl0_199
| ~ spl0_198 ),
inference(paramodulation,[status(thm)],[f131,f2948]) ).
fof(f3288,plain,
( spl0_290
<=> function(set_difference(sk0_13,sk0_13)) ),
introduced(split_symbol_definition) ).
fof(f3290,plain,
( ~ function(set_difference(sk0_13,sk0_13))
| spl0_290 ),
inference(component_clause,[status(thm)],[f3288]) ).
fof(f3758,plain,
( spl0_375
<=> empty_set = empty_set ),
introduced(split_symbol_definition) ).
fof(f3760,plain,
( empty_set != empty_set
| spl0_375 ),
inference(component_clause,[status(thm)],[f3758]) ).
fof(f3771,plain,
( $false
| spl0_375 ),
inference(trivial_equality_resolution,[status(esa)],[f3760]) ).
fof(f3772,plain,
spl0_375,
inference(contradiction_clause,[status(thm)],[f3771]) ).
fof(f3789,plain,
! [X0] : set_difference(X0,X0) = empty_set,
inference(resolution,[status(thm)],[f137,f116]) ).
fof(f3803,plain,
( ~ function(set_difference(empty_set,set_difference(sk0_14,set_difference(sk0_14,sk0_4))))
| spl0_68 ),
inference(backward_demodulation,[status(thm)],[f3789,f1832]) ).
fof(f3804,plain,
( ~ function(empty_set)
| spl0_68 ),
inference(forward_demodulation,[status(thm)],[f143,f3803]) ).
fof(f3805,plain,
( $false
| spl0_68 ),
inference(forward_subsumption_resolution,[status(thm)],[f3804,f189]) ).
fof(f3806,plain,
spl0_68,
inference(contradiction_clause,[status(thm)],[f3805]) ).
fof(f3807,plain,
( ~ function(set_difference(set_difference(sk0_14,sk0_14),set_difference(sk0_14,empty_set)))
| spl0_71 ),
inference(backward_demodulation,[status(thm)],[f3789,f1843]) ).
fof(f3808,plain,
( ~ function(set_difference(empty_set,set_difference(sk0_14,empty_set)))
| spl0_71 ),
inference(forward_demodulation,[status(thm)],[f3789,f3807]) ).
fof(f3809,plain,
( ~ function(empty_set)
| spl0_71 ),
inference(forward_demodulation,[status(thm)],[f143,f3808]) ).
fof(f3810,plain,
( $false
| spl0_71 ),
inference(forward_subsumption_resolution,[status(thm)],[f3809,f189]) ).
fof(f3811,plain,
spl0_71,
inference(contradiction_clause,[status(thm)],[f3810]) ).
fof(f3812,plain,
( ~ function(set_difference(empty_set,set_difference(sk0_14,sk0_4)))
| spl0_74 ),
inference(backward_demodulation,[status(thm)],[f3789,f1854]) ).
fof(f3813,plain,
( ~ function(empty_set)
| spl0_74 ),
inference(forward_demodulation,[status(thm)],[f143,f3812]) ).
fof(f3814,plain,
( $false
| spl0_74 ),
inference(forward_subsumption_resolution,[status(thm)],[f3813,f189]) ).
fof(f3815,plain,
spl0_74,
inference(contradiction_clause,[status(thm)],[f3814]) ).
fof(f3816,plain,
( ~ function(set_difference(sk0_14,set_difference(empty_set,sk0_4)))
| spl0_101 ),
inference(backward_demodulation,[status(thm)],[f3789,f1953]) ).
fof(f3817,plain,
( ~ function(set_difference(sk0_14,empty_set))
| spl0_101 ),
inference(forward_demodulation,[status(thm)],[f143,f3816]) ).
fof(f3818,plain,
( ~ function(sk0_14)
| spl0_101 ),
inference(forward_demodulation,[status(thm)],[f138,f3817]) ).
fof(f3819,plain,
( $false
| spl0_101 ),
inference(forward_subsumption_resolution,[status(thm)],[f3818,f123]) ).
fof(f3820,plain,
spl0_101,
inference(contradiction_clause,[status(thm)],[f3819]) ).
fof(f3821,plain,
( ~ function(set_difference(sk0_14,set_difference(empty_set,sk0_14)))
| spl0_104 ),
inference(backward_demodulation,[status(thm)],[f3789,f1964]) ).
fof(f3822,plain,
( ~ function(set_difference(sk0_14,empty_set))
| spl0_104 ),
inference(forward_demodulation,[status(thm)],[f143,f3821]) ).
fof(f3823,plain,
( ~ function(sk0_14)
| spl0_104 ),
inference(forward_demodulation,[status(thm)],[f138,f3822]) ).
fof(f3824,plain,
( $false
| spl0_104 ),
inference(forward_subsumption_resolution,[status(thm)],[f3823,f123]) ).
fof(f3825,plain,
spl0_104,
inference(contradiction_clause,[status(thm)],[f3824]) ).
fof(f3826,plain,
( ~ function(set_difference(sk0_14,set_difference(sk0_14,empty_set)))
| spl0_113 ),
inference(backward_demodulation,[status(thm)],[f3789,f1997]) ).
fof(f3827,plain,
( ~ function(set_difference(sk0_14,sk0_14))
| spl0_113 ),
inference(forward_demodulation,[status(thm)],[f138,f3826]) ).
fof(f3828,plain,
( ~ function(empty_set)
| spl0_113 ),
inference(forward_demodulation,[status(thm)],[f3789,f3827]) ).
fof(f3829,plain,
( $false
| spl0_113 ),
inference(forward_subsumption_resolution,[status(thm)],[f3828,f189]) ).
fof(f3830,plain,
spl0_113,
inference(contradiction_clause,[status(thm)],[f3829]) ).
fof(f3831,plain,
( ~ function(set_difference(sk0_4,empty_set))
| spl0_35 ),
inference(backward_demodulation,[status(thm)],[f3789,f1711]) ).
fof(f3832,plain,
( ~ function(sk0_4)
| spl0_35 ),
inference(forward_demodulation,[status(thm)],[f138,f3831]) ).
fof(f3833,plain,
( $false
| spl0_35 ),
inference(forward_subsumption_resolution,[status(thm)],[f3832,f86]) ).
fof(f3834,plain,
spl0_35,
inference(contradiction_clause,[status(thm)],[f3833]) ).
fof(f3835,plain,
( ~ function(set_difference(empty_set,sk0_13))
| spl0_59 ),
inference(backward_demodulation,[status(thm)],[f3789,f1799]) ).
fof(f3836,plain,
( ~ function(empty_set)
| spl0_59 ),
inference(forward_demodulation,[status(thm)],[f143,f3835]) ).
fof(f3837,plain,
( $false
| spl0_59 ),
inference(forward_subsumption_resolution,[status(thm)],[f3836,f189]) ).
fof(f3838,plain,
spl0_59,
inference(contradiction_clause,[status(thm)],[f3837]) ).
fof(f3839,plain,
( ~ function(set_difference(empty_set,sk0_12))
| spl0_62 ),
inference(backward_demodulation,[status(thm)],[f3789,f1810]) ).
fof(f3840,plain,
( ~ function(empty_set)
| spl0_62 ),
inference(forward_demodulation,[status(thm)],[f143,f3839]) ).
fof(f3841,plain,
( $false
| spl0_62 ),
inference(forward_subsumption_resolution,[status(thm)],[f3840,f189]) ).
fof(f3842,plain,
spl0_62,
inference(contradiction_clause,[status(thm)],[f3841]) ).
fof(f3843,plain,
( ~ function(set_difference(empty_set,sk0_9))
| spl0_65 ),
inference(backward_demodulation,[status(thm)],[f3789,f1821]) ).
fof(f3844,plain,
( ~ function(empty_set)
| spl0_65 ),
inference(forward_demodulation,[status(thm)],[f143,f3843]) ).
fof(f3845,plain,
( $false
| spl0_65 ),
inference(forward_subsumption_resolution,[status(thm)],[f3844,f189]) ).
fof(f3846,plain,
spl0_65,
inference(contradiction_clause,[status(thm)],[f3845]) ).
fof(f3847,plain,
( ~ function(set_difference(empty_set,sk0_4))
| spl0_80 ),
inference(backward_demodulation,[status(thm)],[f3789,f1876]) ).
fof(f3848,plain,
( ~ function(empty_set)
| spl0_80 ),
inference(forward_demodulation,[status(thm)],[f143,f3847]) ).
fof(f3849,plain,
( $false
| spl0_80 ),
inference(forward_subsumption_resolution,[status(thm)],[f3848,f189]) ).
fof(f3850,plain,
spl0_80,
inference(contradiction_clause,[status(thm)],[f3849]) ).
fof(f3851,plain,
( ~ function(set_difference(empty_set,sk0_14))
| spl0_83 ),
inference(backward_demodulation,[status(thm)],[f3789,f1887]) ).
fof(f3852,plain,
( ~ function(empty_set)
| spl0_83 ),
inference(forward_demodulation,[status(thm)],[f143,f3851]) ).
fof(f3853,plain,
( $false
| spl0_83 ),
inference(forward_subsumption_resolution,[status(thm)],[f3852,f189]) ).
fof(f3854,plain,
spl0_83,
inference(contradiction_clause,[status(thm)],[f3853]) ).
fof(f3855,plain,
( ~ function(set_difference(sk0_14,empty_set))
| spl0_116 ),
inference(backward_demodulation,[status(thm)],[f3789,f2008]) ).
fof(f3856,plain,
( ~ function(sk0_14)
| spl0_116 ),
inference(forward_demodulation,[status(thm)],[f138,f3855]) ).
fof(f3857,plain,
( $false
| spl0_116 ),
inference(forward_subsumption_resolution,[status(thm)],[f3856,f123]) ).
fof(f3858,plain,
spl0_116,
inference(contradiction_clause,[status(thm)],[f3857]) ).
fof(f3900,plain,
! [X0] : relation_image(sk0_14,set_difference(X0,X0)) = empty_set,
inference(paramodulation,[status(thm)],[f124,f3789]) ).
fof(f3901,plain,
relation_image(sk0_14,empty_set) = empty_set,
inference(forward_demodulation,[status(thm)],[f3789,f3900]) ).
fof(f3903,plain,
( spl0_377
<=> relation_image(sk0_14,singleton(sk0_1(sk0_14))) = relation_image(sk0_14,empty_set) ),
introduced(split_symbol_definition) ).
fof(f3904,plain,
( relation_image(sk0_14,singleton(sk0_1(sk0_14))) = relation_image(sk0_14,empty_set)
| ~ spl0_377 ),
inference(component_clause,[status(thm)],[f3903]) ).
fof(f3906,plain,
( relation_image(sk0_14,singleton(sk0_1(sk0_14))) = relation_image(sk0_14,empty_set)
| sk0_1(sk0_14) = sk0_2(sk0_14)
| ~ spl0_196
| ~ spl0_199
| ~ spl0_198 ),
inference(paramodulation,[status(thm)],[f3789,f2952]) ).
fof(f3907,plain,
( spl0_377
| spl0_200
| ~ spl0_196
| ~ spl0_199
| ~ spl0_198 ),
inference(split_clause,[status(thm)],[f3906,f3903,f2429,f2404,f2422,f2412]) ).
fof(f3908,plain,
! [X0] : empty_set != singleton(X0),
inference(paramodulation,[status(thm)],[f3789,f159]) ).
fof(f4011,plain,
( one_to_one(set_difference(sk0_14,set_difference(empty_set,sk0_4)))
| ~ spl0_102 ),
inference(forward_demodulation,[status(thm)],[f3789,f1955]) ).
fof(f4012,plain,
( one_to_one(set_difference(sk0_14,empty_set))
| ~ spl0_102 ),
inference(forward_demodulation,[status(thm)],[f143,f4011]) ).
fof(f4013,plain,
( one_to_one(sk0_14)
| ~ spl0_102 ),
inference(forward_demodulation,[status(thm)],[f138,f4012]) ).
fof(f4014,plain,
( $false
| ~ spl0_102 ),
inference(forward_subsumption_resolution,[status(thm)],[f4013,f125]) ).
fof(f4015,plain,
~ spl0_102,
inference(contradiction_clause,[status(thm)],[f4014]) ).
fof(f4037,plain,
( one_to_one(set_difference(sk0_14,set_difference(empty_set,sk0_14)))
| ~ spl0_105 ),
inference(forward_demodulation,[status(thm)],[f3789,f1966]) ).
fof(f4038,plain,
( one_to_one(set_difference(sk0_14,empty_set))
| ~ spl0_105 ),
inference(forward_demodulation,[status(thm)],[f143,f4037]) ).
fof(f4039,plain,
( one_to_one(sk0_14)
| ~ spl0_105 ),
inference(forward_demodulation,[status(thm)],[f138,f4038]) ).
fof(f4040,plain,
( $false
| ~ spl0_105 ),
inference(forward_subsumption_resolution,[status(thm)],[f4039,f125]) ).
fof(f4041,plain,
~ spl0_105,
inference(contradiction_clause,[status(thm)],[f4040]) ).
fof(f4194,plain,
( one_to_one(set_difference(sk0_14,empty_set))
| ~ spl0_117 ),
inference(forward_demodulation,[status(thm)],[f3789,f2010]) ).
fof(f4195,plain,
( one_to_one(sk0_14)
| ~ spl0_117 ),
inference(forward_demodulation,[status(thm)],[f138,f4194]) ).
fof(f4196,plain,
( $false
| ~ spl0_117 ),
inference(forward_subsumption_resolution,[status(thm)],[f4195,f125]) ).
fof(f4197,plain,
~ spl0_117,
inference(contradiction_clause,[status(thm)],[f4196]) ).
fof(f4362,plain,
( ~ relation(sk0_14)
| ~ function(sk0_14)
| one_to_one(sk0_14)
| ~ spl0_200 ),
inference(resolution,[status(thm)],[f2430,f66]) ).
fof(f4363,plain,
( ~ spl0_197
| ~ spl0_2
| spl0_1
| ~ spl0_200 ),
inference(split_clause,[status(thm)],[f4362,f2409,f169,f164,f2429]) ).
fof(f4366,plain,
( relation_image(sk0_14,singleton(sk0_1(sk0_14))) = empty_set
| ~ spl0_377 ),
inference(forward_demodulation,[status(thm)],[f3901,f3904]) ).
fof(f4377,plain,
( ~ function(empty_set)
| spl0_290 ),
inference(forward_demodulation,[status(thm)],[f3789,f3290]) ).
fof(f4378,plain,
( $false
| spl0_290 ),
inference(forward_subsumption_resolution,[status(thm)],[f4377,f189]) ).
fof(f4379,plain,
spl0_290,
inference(contradiction_clause,[status(thm)],[f4378]) ).
fof(f4413,plain,
( empty_set = singleton(apply(sk0_14,sk0_1(sk0_14)))
| ~ spl0_377
| ~ spl0_198 ),
inference(backward_demodulation,[status(thm)],[f4366,f2413]) ).
fof(f4414,plain,
( $false
| ~ spl0_377
| ~ spl0_198 ),
inference(forward_subsumption_resolution,[status(thm)],[f4413,f3908]) ).
fof(f4415,plain,
( ~ spl0_377
| ~ spl0_198 ),
inference(contradiction_clause,[status(thm)],[f4414]) ).
fof(f4416,plain,
$false,
inference(sat_refutation,[status(thm)],[f175,f2032,f2038,f2223,f2408,f2416,f2421,f2426,f3772,f3806,f3811,f3815,f3820,f3825,f3830,f3834,f3838,f3842,f3846,f3850,f3854,f3858,f3907,f4015,f4041,f4197,f4363,f4379,f4415]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.05/0.12 % Problem : SEU055+1 : TPTP v8.1.2. Released v3.2.0.
% 0.05/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32 % Computer : n001.cluster.edu
% 0.10/0.32 % Model : x86_64 x86_64
% 0.10/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32 % Memory : 8042.1875MB
% 0.10/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32 % CPULimit : 300
% 0.10/0.32 % WCLimit : 300
% 0.10/0.32 % DateTime : Tue May 30 09:46:30 EDT 2023
% 0.10/0.33 % CPUTime :
% 0.10/0.33 % Drodi V3.5.1
% 0.15/0.51 % Refutation found
% 0.15/0.51 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.15/0.51 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.54 % Elapsed time: 0.196654 seconds
% 0.15/0.54 % CPU time: 1.039623 seconds
% 0.15/0.54 % Memory used: 78.579 MB
%------------------------------------------------------------------------------