TSTP Solution File: SEU221+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU221+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 12:36:20 EDT 2023
% Result : Theorem 0.09s 0.33s
% Output : CNFRefutation 0.15s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 41
% Syntax : Number of formulae : 194 ( 39 unt; 0 def)
% Number of atoms : 575 ( 94 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 632 ( 251 ~; 253 |; 80 &)
% ( 30 <=>; 18 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 4 avg)
% Maximal term depth : 5 ( 1 avg)
% Number of predicates : 33 ( 31 usr; 25 prp; 0-4 aty)
% Number of functors : 18 ( 18 usr; 7 con; 0-2 aty)
% Number of variables : 103 (; 89 !; 14 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,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(f9,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( relation(function_inverse(A))
& function(function_inverse(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A] :
( empty(A)
=> ( empty(relation_dom(A))
& relation(relation_dom(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A] :
( empty(A)
=> ( empty(relation_rng(A))
& relation(relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,axiom,
? [A] :
( relation(A)
& function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
? [A] :
( empty(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f26,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f27,axiom,
? [A] :
( relation(A)
& empty(A)
& function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f30,axiom,
? [A] :
( relation(A)
& function(A)
& one_to_one(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f34,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> ! [B] :
( ( relation(B)
& function(B) )
=> ( B = function_inverse(A)
<=> ( relation_dom(B) = relation_rng(A)
& ! [C,D] :
( ( ( in(C,relation_rng(A))
& D = apply(B,C) )
=> ( in(D,relation_dom(A))
& C = apply(A,D) ) )
& ( ( in(D,relation_dom(A))
& C = apply(A,D) )
=> ( in(C,relation_rng(A))
& D = apply(B,C) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f35,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ( ( one_to_one(B)
& in(A,relation_rng(B)) )
=> ( A = apply(B,apply(function_inverse(B),A))
& A = apply(relation_composition(function_inverse(B),B),A) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f36,conjecture,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f37,negated_conjecture,
~ ! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
inference(negated_conjecture,[status(cth)],[f36]) ).
fof(f38,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A,B] :
~ ( in(A,B)
& empty(B) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f43,plain,
! [A] :
( ~ empty(A)
| function(A) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f44,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f51,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)],[f5]) ).
fof(f52,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)],[f51]) ).
fof(f53,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_0(A),relation_dom(A))
& in(sk0_1(A),relation_dom(A))
& apply(A,sk0_0(A)) = apply(A,sk0_1(A))
& sk0_0(A) != sk0_1(A) ) ) ) ),
inference(skolemization,[status(esa)],[f52]) ).
fof(f55,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| in(sk0_0(X0),relation_dom(X0)) ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f56,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| in(sk0_1(X0),relation_dom(X0)) ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f57,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| apply(X0,sk0_0(X0)) = apply(X0,sk0_1(X0)) ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f58,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| sk0_0(X0) != sk0_1(X0) ),
inference(cnf_transformation,[status(esa)],[f53]) ).
fof(f59,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( relation(function_inverse(A))
& function(function_inverse(A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f60,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f61,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f59]) ).
fof(f69,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f82,plain,
! [A] :
( ~ empty(A)
| ( empty(relation_dom(A))
& relation(relation_dom(A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f83,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_dom(X0)) ),
inference(cnf_transformation,[status(esa)],[f82]) ).
fof(f85,plain,
! [A] :
( ~ empty(A)
| ( empty(relation_rng(A))
& relation(relation_rng(A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f22]) ).
fof(f86,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_rng(X0)) ),
inference(cnf_transformation,[status(esa)],[f85]) ).
fof(f91,plain,
( relation(sk0_3)
& function(sk0_3) ),
inference(skolemization,[status(esa)],[f24]) ).
fof(f92,plain,
relation(sk0_3),
inference(cnf_transformation,[status(esa)],[f91]) ).
fof(f94,plain,
( empty(sk0_4)
& relation(sk0_4) ),
inference(skolemization,[status(esa)],[f25]) ).
fof(f95,plain,
empty(sk0_4),
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f97,plain,
empty(sk0_5),
inference(skolemization,[status(esa)],[f26]) ).
fof(f98,plain,
empty(sk0_5),
inference(cnf_transformation,[status(esa)],[f97]) ).
fof(f99,plain,
( relation(sk0_6)
& empty(sk0_6)
& function(sk0_6) ),
inference(skolemization,[status(esa)],[f27]) ).
fof(f100,plain,
relation(sk0_6),
inference(cnf_transformation,[status(esa)],[f99]) ).
fof(f101,plain,
empty(sk0_6),
inference(cnf_transformation,[status(esa)],[f99]) ).
fof(f102,plain,
function(sk0_6),
inference(cnf_transformation,[status(esa)],[f99]) ).
fof(f108,plain,
( relation(sk0_9)
& function(sk0_9)
& one_to_one(sk0_9) ),
inference(skolemization,[status(esa)],[f30]) ).
fof(f109,plain,
relation(sk0_9),
inference(cnf_transformation,[status(esa)],[f108]) ).
fof(f110,plain,
function(sk0_9),
inference(cnf_transformation,[status(esa)],[f108]) ).
fof(f119,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ~ one_to_one(A)
| ! [B] :
( ~ relation(B)
| ~ function(B)
| ( B = function_inverse(A)
<=> ( relation_dom(B) = relation_rng(A)
& ! [C,D] :
( ( ~ in(C,relation_rng(A))
| D != apply(B,C)
| ( in(D,relation_dom(A))
& C = apply(A,D) ) )
& ( ~ in(D,relation_dom(A))
| C != apply(A,D)
| ( in(C,relation_rng(A))
& D = apply(B,C) ) ) ) ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f34]) ).
fof(f120,plain,
! [A,B,C,D] :
( pd0_0(D,C,B,A)
<=> ( ~ in(C,relation_rng(A))
| D != apply(B,C)
| ( in(D,relation_dom(A))
& C = apply(A,D) ) ) ),
introduced(predicate_definition,[f119]) ).
fof(f121,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ~ one_to_one(A)
| ! [B] :
( ~ relation(B)
| ~ function(B)
| ( B = function_inverse(A)
<=> ( relation_dom(B) = relation_rng(A)
& ! [C,D] :
( pd0_0(D,C,B,A)
& ( ~ in(D,relation_dom(A))
| C != apply(A,D)
| ( in(C,relation_rng(A))
& D = apply(B,C) ) ) ) ) ) ) ),
inference(formula_renaming,[status(thm)],[f119,f120]) ).
fof(f122,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ~ one_to_one(A)
| ! [B] :
( ~ relation(B)
| ~ function(B)
| ( ( B != function_inverse(A)
| ( relation_dom(B) = relation_rng(A)
& ! [C,D] :
( pd0_0(D,C,B,A)
& ( ~ in(D,relation_dom(A))
| C != apply(A,D)
| ( in(C,relation_rng(A))
& D = apply(B,C) ) ) ) ) )
& ( B = function_inverse(A)
| relation_dom(B) != relation_rng(A)
| ? [C,D] :
( ~ pd0_0(D,C,B,A)
| ( in(D,relation_dom(A))
& C = apply(A,D)
& ( ~ in(C,relation_rng(A))
| D != apply(B,C) ) ) ) ) ) ) ),
inference(NNF_transformation,[status(esa)],[f121]) ).
fof(f123,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ~ one_to_one(A)
| ! [B] :
( ~ relation(B)
| ~ function(B)
| ( ( B != function_inverse(A)
| ( relation_dom(B) = relation_rng(A)
& ! [C,D] : pd0_0(D,C,B,A)
& ! [C,D] :
( ~ in(D,relation_dom(A))
| C != apply(A,D)
| ( in(C,relation_rng(A))
& D = apply(B,C) ) ) ) )
& ( B = function_inverse(A)
| relation_dom(B) != relation_rng(A)
| ? [C,D] : ~ pd0_0(D,C,B,A)
| ? [C,D] :
( in(D,relation_dom(A))
& C = apply(A,D)
& ( ~ in(C,relation_rng(A))
| D != apply(B,C) ) ) ) ) ) ),
inference(miniscoping,[status(esa)],[f122]) ).
fof(f124,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ~ one_to_one(A)
| ! [B] :
( ~ relation(B)
| ~ function(B)
| ( ( B != function_inverse(A)
| ( relation_dom(B) = relation_rng(A)
& ! [C,D] : pd0_0(D,C,B,A)
& ! [C,D] :
( ~ in(D,relation_dom(A))
| C != apply(A,D)
| ( in(C,relation_rng(A))
& D = apply(B,C) ) ) ) )
& ( B = function_inverse(A)
| relation_dom(B) != relation_rng(A)
| ~ pd0_0(sk0_12(B,A),sk0_11(B,A),B,A)
| ( in(sk0_14(B,A),relation_dom(A))
& sk0_13(B,A) = apply(A,sk0_14(B,A))
& ( ~ in(sk0_13(B,A),relation_rng(A))
| sk0_14(B,A) != apply(B,sk0_13(B,A)) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f123]) ).
fof(f125,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| ~ one_to_one(X0)
| ~ relation(X1)
| ~ function(X1)
| X1 != function_inverse(X0)
| relation_dom(X1) = relation_rng(X0) ),
inference(cnf_transformation,[status(esa)],[f124]) ).
fof(f132,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ~ one_to_one(B)
| ~ in(A,relation_rng(B))
| ( A = apply(B,apply(function_inverse(B),A))
& A = apply(relation_composition(function_inverse(B),B),A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f35]) ).
fof(f133,plain,
! [B] :
( ~ relation(B)
| ~ function(B)
| ! [A] :
( ~ one_to_one(B)
| ~ in(A,relation_rng(B))
| ( A = apply(B,apply(function_inverse(B),A))
& A = apply(relation_composition(function_inverse(B),B),A) ) ) ),
inference(miniscoping,[status(esa)],[f132]) ).
fof(f134,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| ~ one_to_one(X0)
| ~ in(X1,relation_rng(X0))
| X1 = apply(X0,apply(function_inverse(X0),X1)) ),
inference(cnf_transformation,[status(esa)],[f133]) ).
fof(f136,plain,
? [A] :
( relation(A)
& function(A)
& one_to_one(A)
& ~ one_to_one(function_inverse(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f37]) ).
fof(f137,plain,
( relation(sk0_15)
& function(sk0_15)
& one_to_one(sk0_15)
& ~ one_to_one(function_inverse(sk0_15)) ),
inference(skolemization,[status(esa)],[f136]) ).
fof(f138,plain,
relation(sk0_15),
inference(cnf_transformation,[status(esa)],[f137]) ).
fof(f139,plain,
function(sk0_15),
inference(cnf_transformation,[status(esa)],[f137]) ).
fof(f140,plain,
one_to_one(sk0_15),
inference(cnf_transformation,[status(esa)],[f137]) ).
fof(f141,plain,
~ one_to_one(function_inverse(sk0_15)),
inference(cnf_transformation,[status(esa)],[f137]) ).
fof(f142,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f38]) ).
fof(f143,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f142]) ).
fof(f144,plain,
! [A,B] :
( ~ in(A,B)
| ~ empty(B) ),
inference(pre_NNF_transformation,[status(esa)],[f39]) ).
fof(f145,plain,
! [B] :
( ! [A] : ~ in(A,B)
| ~ empty(B) ),
inference(miniscoping,[status(esa)],[f144]) ).
fof(f146,plain,
! [X0,X1] :
( ~ in(X0,X1)
| ~ empty(X1) ),
inference(cnf_transformation,[status(esa)],[f145]) ).
fof(f157,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ one_to_one(X0)
| ~ relation(function_inverse(X0))
| ~ function(function_inverse(X0))
| relation_dom(function_inverse(X0)) = relation_rng(X0) ),
inference(destructive_equality_resolution,[status(esa)],[f125]) ).
fof(f164,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ one_to_one(X0)
| ~ function(function_inverse(X0))
| relation_dom(function_inverse(X0)) = relation_rng(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f157,f60]) ).
fof(f165,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ one_to_one(X0)
| relation_dom(function_inverse(X0)) = relation_rng(X0)
| ~ relation(X0)
| ~ function(X0) ),
inference(resolution,[status(thm)],[f164,f61]) ).
fof(f166,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ one_to_one(X0)
| relation_dom(function_inverse(X0)) = relation_rng(X0) ),
inference(duplicate_literals_removal,[status(esa)],[f165]) ).
fof(f167,plain,
( spl0_0
<=> relation(sk0_15) ),
introduced(split_symbol_definition) ).
fof(f169,plain,
( ~ relation(sk0_15)
| spl0_0 ),
inference(component_clause,[status(thm)],[f167]) ).
fof(f170,plain,
( spl0_1
<=> function(sk0_15) ),
introduced(split_symbol_definition) ).
fof(f172,plain,
( ~ function(sk0_15)
| spl0_1 ),
inference(component_clause,[status(thm)],[f170]) ).
fof(f173,plain,
( spl0_2
<=> relation_dom(function_inverse(sk0_15)) = relation_rng(sk0_15) ),
introduced(split_symbol_definition) ).
fof(f174,plain,
( relation_dom(function_inverse(sk0_15)) = relation_rng(sk0_15)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f173]) ).
fof(f176,plain,
( ~ relation(sk0_15)
| ~ function(sk0_15)
| relation_dom(function_inverse(sk0_15)) = relation_rng(sk0_15) ),
inference(resolution,[status(thm)],[f166,f140]) ).
fof(f177,plain,
( ~ spl0_0
| ~ spl0_1
| spl0_2 ),
inference(split_clause,[status(thm)],[f176,f167,f170,f173]) ).
fof(f178,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f172,f139]) ).
fof(f179,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f178]) ).
fof(f180,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f169,f138]) ).
fof(f181,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f180]) ).
fof(f187,plain,
( spl0_4
<=> function(empty_set) ),
introduced(split_symbol_definition) ).
fof(f189,plain,
( ~ function(empty_set)
| spl0_4 ),
inference(component_clause,[status(thm)],[f187]) ).
fof(f197,plain,
( spl0_6
<=> relation(function_inverse(sk0_15)) ),
introduced(split_symbol_definition) ).
fof(f199,plain,
( ~ relation(function_inverse(sk0_15))
| spl0_6 ),
inference(component_clause,[status(thm)],[f197]) ).
fof(f200,plain,
( spl0_7
<=> function(function_inverse(sk0_15)) ),
introduced(split_symbol_definition) ).
fof(f202,plain,
( ~ function(function_inverse(sk0_15))
| spl0_7 ),
inference(component_clause,[status(thm)],[f200]) ).
fof(f203,plain,
( spl0_8
<=> one_to_one(function_inverse(sk0_15)) ),
introduced(split_symbol_definition) ).
fof(f204,plain,
( one_to_one(function_inverse(sk0_15))
| ~ spl0_8 ),
inference(component_clause,[status(thm)],[f203]) ).
fof(f206,plain,
( spl0_9
<=> in(sk0_0(function_inverse(sk0_15)),relation_rng(sk0_15)) ),
introduced(split_symbol_definition) ).
fof(f207,plain,
( in(sk0_0(function_inverse(sk0_15)),relation_rng(sk0_15))
| ~ spl0_9 ),
inference(component_clause,[status(thm)],[f206]) ).
fof(f209,plain,
( ~ relation(function_inverse(sk0_15))
| ~ function(function_inverse(sk0_15))
| one_to_one(function_inverse(sk0_15))
| in(sk0_0(function_inverse(sk0_15)),relation_rng(sk0_15))
| ~ spl0_2 ),
inference(paramodulation,[status(thm)],[f174,f55]) ).
fof(f210,plain,
( ~ spl0_6
| ~ spl0_7
| spl0_8
| spl0_9
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f209,f197,f200,f203,f206,f173]) ).
fof(f226,plain,
( ~ relation(sk0_15)
| ~ function(sk0_15)
| spl0_7 ),
inference(resolution,[status(thm)],[f202,f61]) ).
fof(f227,plain,
( ~ spl0_0
| ~ spl0_1
| spl0_7 ),
inference(split_clause,[status(thm)],[f226,f167,f170,f200]) ).
fof(f229,plain,
( ~ relation(sk0_15)
| ~ function(sk0_15)
| spl0_6 ),
inference(resolution,[status(thm)],[f199,f60]) ).
fof(f230,plain,
( ~ spl0_0
| ~ spl0_1
| spl0_6 ),
inference(split_clause,[status(thm)],[f229,f167,f170,f197]) ).
fof(f232,plain,
( $false
| ~ spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f204,f141]) ).
fof(f233,plain,
~ spl0_8,
inference(contradiction_clause,[status(thm)],[f232]) ).
fof(f234,plain,
( spl0_13
<=> one_to_one(sk0_15) ),
introduced(split_symbol_definition) ).
fof(f236,plain,
( ~ one_to_one(sk0_15)
| spl0_13 ),
inference(component_clause,[status(thm)],[f234]) ).
fof(f237,plain,
( spl0_14
<=> sk0_0(function_inverse(sk0_15)) = apply(sk0_15,apply(function_inverse(sk0_15),sk0_0(function_inverse(sk0_15)))) ),
introduced(split_symbol_definition) ).
fof(f238,plain,
( sk0_0(function_inverse(sk0_15)) = apply(sk0_15,apply(function_inverse(sk0_15),sk0_0(function_inverse(sk0_15))))
| ~ spl0_14 ),
inference(component_clause,[status(thm)],[f237]) ).
fof(f240,plain,
( ~ relation(sk0_15)
| ~ function(sk0_15)
| ~ one_to_one(sk0_15)
| sk0_0(function_inverse(sk0_15)) = apply(sk0_15,apply(function_inverse(sk0_15),sk0_0(function_inverse(sk0_15))))
| ~ spl0_9 ),
inference(resolution,[status(thm)],[f207,f134]) ).
fof(f241,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_13
| spl0_14
| ~ spl0_9 ),
inference(split_clause,[status(thm)],[f240,f167,f170,f234,f237,f206]) ).
fof(f243,plain,
( $false
| spl0_13 ),
inference(forward_subsumption_resolution,[status(thm)],[f236,f140]) ).
fof(f244,plain,
spl0_13,
inference(contradiction_clause,[status(thm)],[f243]) ).
fof(f245,plain,
( ~ empty(empty_set)
| spl0_4 ),
inference(resolution,[status(thm)],[f189,f44]) ).
fof(f246,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f245,f69]) ).
fof(f247,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f246]) ).
fof(f357,plain,
( spl0_36
<=> relation(sk0_6) ),
introduced(split_symbol_definition) ).
fof(f359,plain,
( ~ relation(sk0_6)
| spl0_36 ),
inference(component_clause,[status(thm)],[f357]) ).
fof(f360,plain,
( spl0_37
<=> function(sk0_6) ),
introduced(split_symbol_definition) ).
fof(f362,plain,
( ~ function(sk0_6)
| spl0_37 ),
inference(component_clause,[status(thm)],[f360]) ).
fof(f366,plain,
( $false
| spl0_37 ),
inference(forward_subsumption_resolution,[status(thm)],[f362,f102]) ).
fof(f367,plain,
spl0_37,
inference(contradiction_clause,[status(thm)],[f366]) ).
fof(f368,plain,
( $false
| spl0_36 ),
inference(forward_subsumption_resolution,[status(thm)],[f359,f100]) ).
fof(f369,plain,
spl0_36,
inference(contradiction_clause,[status(thm)],[f368]) ).
fof(f394,plain,
( spl0_43
<=> in(sk0_0(function_inverse(sk0_5)),relation_rng(sk0_5)) ),
introduced(split_symbol_definition) ).
fof(f395,plain,
( in(sk0_0(function_inverse(sk0_5)),relation_rng(sk0_5))
| ~ spl0_43 ),
inference(component_clause,[status(thm)],[f394]) ).
fof(f421,plain,
( spl0_50
<=> in(sk0_0(function_inverse(sk0_4)),relation_rng(sk0_4)) ),
introduced(split_symbol_definition) ).
fof(f422,plain,
( in(sk0_0(function_inverse(sk0_4)),relation_rng(sk0_4))
| ~ spl0_50 ),
inference(component_clause,[status(thm)],[f421]) ).
fof(f439,plain,
( spl0_54
<=> relation(sk0_9) ),
introduced(split_symbol_definition) ).
fof(f441,plain,
( ~ relation(sk0_9)
| spl0_54 ),
inference(component_clause,[status(thm)],[f439]) ).
fof(f442,plain,
( spl0_55
<=> function(sk0_9) ),
introduced(split_symbol_definition) ).
fof(f444,plain,
( ~ function(sk0_9)
| spl0_55 ),
inference(component_clause,[status(thm)],[f442]) ).
fof(f450,plain,
( $false
| spl0_55 ),
inference(forward_subsumption_resolution,[status(thm)],[f444,f110]) ).
fof(f451,plain,
spl0_55,
inference(contradiction_clause,[status(thm)],[f450]) ).
fof(f452,plain,
( $false
| spl0_54 ),
inference(forward_subsumption_resolution,[status(thm)],[f441,f109]) ).
fof(f453,plain,
spl0_54,
inference(contradiction_clause,[status(thm)],[f452]) ).
fof(f465,plain,
( spl0_59
<=> in(sk0_1(function_inverse(sk0_6)),relation_rng(sk0_6)) ),
introduced(split_symbol_definition) ).
fof(f466,plain,
( in(sk0_1(function_inverse(sk0_6)),relation_rng(sk0_6))
| ~ spl0_59 ),
inference(component_clause,[status(thm)],[f465]) ).
fof(f475,plain,
( spl0_61
<=> in(sk0_1(function_inverse(sk0_15)),relation_rng(sk0_15)) ),
introduced(split_symbol_definition) ).
fof(f476,plain,
( in(sk0_1(function_inverse(sk0_15)),relation_rng(sk0_15))
| ~ spl0_61 ),
inference(component_clause,[status(thm)],[f475]) ).
fof(f478,plain,
( ~ relation(function_inverse(sk0_15))
| ~ function(function_inverse(sk0_15))
| one_to_one(function_inverse(sk0_15))
| in(sk0_1(function_inverse(sk0_15)),relation_rng(sk0_15))
| ~ spl0_2 ),
inference(paramodulation,[status(thm)],[f174,f56]) ).
fof(f479,plain,
( ~ spl0_6
| ~ spl0_7
| spl0_8
| spl0_61
| ~ spl0_2 ),
inference(split_clause,[status(thm)],[f478,f197,f200,f203,f475,f173]) ).
fof(f480,plain,
sk0_6 = empty_set,
inference(resolution,[status(thm)],[f143,f101]) ).
fof(f481,plain,
sk0_5 = empty_set,
inference(resolution,[status(thm)],[f143,f98]) ).
fof(f482,plain,
sk0_4 = empty_set,
inference(resolution,[status(thm)],[f143,f95]) ).
fof(f494,plain,
! [X0] : ~ in(X0,empty_set),
inference(resolution,[status(thm)],[f146,f69]) ).
fof(f495,plain,
empty(relation_dom(empty_set)),
inference(resolution,[status(thm)],[f83,f69]) ).
fof(f498,plain,
relation_dom(empty_set) = empty_set,
inference(resolution,[status(thm)],[f495,f143]) ).
fof(f509,plain,
( spl0_65
<=> in(sk0_1(function_inverse(relation_dom(empty_set))),relation_rng(relation_dom(empty_set))) ),
introduced(split_symbol_definition) ).
fof(f510,plain,
( in(sk0_1(function_inverse(relation_dom(empty_set))),relation_rng(relation_dom(empty_set)))
| ~ spl0_65 ),
inference(component_clause,[status(thm)],[f509]) ).
fof(f537,plain,
( spl0_71
<=> apply(function_inverse(sk0_15),sk0_0(function_inverse(sk0_15))) = apply(function_inverse(sk0_15),sk0_1(function_inverse(sk0_15))) ),
introduced(split_symbol_definition) ).
fof(f538,plain,
( apply(function_inverse(sk0_15),sk0_0(function_inverse(sk0_15))) = apply(function_inverse(sk0_15),sk0_1(function_inverse(sk0_15)))
| ~ spl0_71 ),
inference(component_clause,[status(thm)],[f537]) ).
fof(f540,plain,
( ~ relation(function_inverse(sk0_15))
| ~ function(function_inverse(sk0_15))
| apply(function_inverse(sk0_15),sk0_0(function_inverse(sk0_15))) = apply(function_inverse(sk0_15),sk0_1(function_inverse(sk0_15))) ),
inference(resolution,[status(thm)],[f57,f141]) ).
fof(f541,plain,
( ~ spl0_6
| ~ spl0_7
| spl0_71 ),
inference(split_clause,[status(thm)],[f540,f197,f200,f537]) ).
fof(f554,plain,
( spl0_74
<=> relation(sk0_3) ),
introduced(split_symbol_definition) ).
fof(f556,plain,
( ~ relation(sk0_3)
| spl0_74 ),
inference(component_clause,[status(thm)],[f554]) ).
fof(f591,plain,
( $false
| spl0_74 ),
inference(forward_subsumption_resolution,[status(thm)],[f556,f92]) ).
fof(f592,plain,
spl0_74,
inference(contradiction_clause,[status(thm)],[f591]) ).
fof(f620,plain,
empty(relation_rng(empty_set)),
inference(resolution,[status(thm)],[f86,f69]) ).
fof(f625,plain,
relation_rng(empty_set) = empty_set,
inference(resolution,[status(thm)],[f620,f143]) ).
fof(f635,plain,
( spl0_87
<=> empty(empty_set) ),
introduced(split_symbol_definition) ).
fof(f637,plain,
( ~ empty(empty_set)
| spl0_87 ),
inference(component_clause,[status(thm)],[f635]) ).
fof(f640,plain,
( $false
| spl0_87 ),
inference(forward_subsumption_resolution,[status(thm)],[f637,f69]) ).
fof(f641,plain,
spl0_87,
inference(contradiction_clause,[status(thm)],[f640]) ).
fof(f661,plain,
( spl0_90
<=> sk0_0(function_inverse(sk0_15)) = sk0_1(function_inverse(sk0_15)) ),
introduced(split_symbol_definition) ).
fof(f663,plain,
( sk0_0(function_inverse(sk0_15)) != sk0_1(function_inverse(sk0_15))
| spl0_90 ),
inference(component_clause,[status(thm)],[f661]) ).
fof(f664,plain,
( ~ relation(function_inverse(sk0_15))
| ~ function(function_inverse(sk0_15))
| sk0_0(function_inverse(sk0_15)) != sk0_1(function_inverse(sk0_15)) ),
inference(resolution,[status(thm)],[f58,f141]) ).
fof(f665,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_90 ),
inference(split_clause,[status(thm)],[f664,f197,f200,f661]) ).
fof(f723,plain,
( in(sk0_0(function_inverse(empty_set)),relation_rng(sk0_4))
| ~ spl0_50 ),
inference(forward_demodulation,[status(thm)],[f482,f422]) ).
fof(f724,plain,
( in(sk0_0(function_inverse(empty_set)),relation_rng(empty_set))
| ~ spl0_50 ),
inference(forward_demodulation,[status(thm)],[f482,f723]) ).
fof(f725,plain,
( in(sk0_0(function_inverse(empty_set)),empty_set)
| ~ spl0_50 ),
inference(forward_demodulation,[status(thm)],[f625,f724]) ).
fof(f726,plain,
( $false
| ~ spl0_50 ),
inference(forward_subsumption_resolution,[status(thm)],[f725,f494]) ).
fof(f727,plain,
~ spl0_50,
inference(contradiction_clause,[status(thm)],[f726]) ).
fof(f735,plain,
( in(sk0_0(function_inverse(empty_set)),relation_rng(sk0_5))
| ~ spl0_43 ),
inference(forward_demodulation,[status(thm)],[f481,f395]) ).
fof(f736,plain,
( in(sk0_0(function_inverse(empty_set)),relation_rng(empty_set))
| ~ spl0_43 ),
inference(forward_demodulation,[status(thm)],[f481,f735]) ).
fof(f737,plain,
( in(sk0_0(function_inverse(empty_set)),empty_set)
| ~ spl0_43 ),
inference(forward_demodulation,[status(thm)],[f625,f736]) ).
fof(f738,plain,
( $false
| ~ spl0_43 ),
inference(forward_subsumption_resolution,[status(thm)],[f737,f494]) ).
fof(f739,plain,
~ spl0_43,
inference(contradiction_clause,[status(thm)],[f738]) ).
fof(f747,plain,
( in(sk0_1(function_inverse(empty_set)),relation_rng(sk0_6))
| ~ spl0_59 ),
inference(forward_demodulation,[status(thm)],[f480,f466]) ).
fof(f748,plain,
( in(sk0_1(function_inverse(empty_set)),relation_rng(empty_set))
| ~ spl0_59 ),
inference(forward_demodulation,[status(thm)],[f480,f747]) ).
fof(f749,plain,
( in(sk0_1(function_inverse(empty_set)),empty_set)
| ~ spl0_59 ),
inference(forward_demodulation,[status(thm)],[f625,f748]) ).
fof(f750,plain,
( $false
| ~ spl0_59 ),
inference(forward_subsumption_resolution,[status(thm)],[f749,f494]) ).
fof(f751,plain,
~ spl0_59,
inference(contradiction_clause,[status(thm)],[f750]) ).
fof(f847,plain,
( in(sk0_1(function_inverse(empty_set)),relation_rng(relation_dom(empty_set)))
| ~ spl0_65 ),
inference(forward_demodulation,[status(thm)],[f498,f510]) ).
fof(f848,plain,
( in(sk0_1(function_inverse(empty_set)),relation_rng(empty_set))
| ~ spl0_65 ),
inference(forward_demodulation,[status(thm)],[f498,f847]) ).
fof(f849,plain,
( in(sk0_1(function_inverse(empty_set)),empty_set)
| ~ spl0_65 ),
inference(forward_demodulation,[status(thm)],[f625,f848]) ).
fof(f850,plain,
( $false
| ~ spl0_65 ),
inference(forward_subsumption_resolution,[status(thm)],[f849,f494]) ).
fof(f851,plain,
~ spl0_65,
inference(contradiction_clause,[status(thm)],[f850]) ).
fof(f910,plain,
( spl0_114
<=> sk0_1(function_inverse(sk0_15)) = apply(sk0_15,apply(function_inverse(sk0_15),sk0_1(function_inverse(sk0_15)))) ),
introduced(split_symbol_definition) ).
fof(f911,plain,
( sk0_1(function_inverse(sk0_15)) = apply(sk0_15,apply(function_inverse(sk0_15),sk0_1(function_inverse(sk0_15))))
| ~ spl0_114 ),
inference(component_clause,[status(thm)],[f910]) ).
fof(f913,plain,
( ~ relation(sk0_15)
| ~ function(sk0_15)
| ~ one_to_one(sk0_15)
| sk0_1(function_inverse(sk0_15)) = apply(sk0_15,apply(function_inverse(sk0_15),sk0_1(function_inverse(sk0_15))))
| ~ spl0_61 ),
inference(resolution,[status(thm)],[f476,f134]) ).
fof(f914,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_13
| spl0_114
| ~ spl0_61 ),
inference(split_clause,[status(thm)],[f913,f167,f170,f234,f910,f475]) ).
fof(f916,plain,
( sk0_1(function_inverse(sk0_15)) = apply(sk0_15,apply(function_inverse(sk0_15),sk0_0(function_inverse(sk0_15))))
| ~ spl0_71
| ~ spl0_114 ),
inference(forward_demodulation,[status(thm)],[f538,f911]) ).
fof(f917,plain,
( sk0_1(function_inverse(sk0_15)) = sk0_0(function_inverse(sk0_15))
| ~ spl0_14
| ~ spl0_71
| ~ spl0_114 ),
inference(forward_demodulation,[status(thm)],[f238,f916]) ).
fof(f918,plain,
( $false
| spl0_90
| ~ spl0_14
| ~ spl0_71
| ~ spl0_114 ),
inference(forward_subsumption_resolution,[status(thm)],[f917,f663]) ).
fof(f919,plain,
( spl0_90
| ~ spl0_14
| ~ spl0_71
| ~ spl0_114 ),
inference(contradiction_clause,[status(thm)],[f918]) ).
fof(f920,plain,
$false,
inference(sat_refutation,[status(thm)],[f177,f179,f181,f210,f227,f230,f233,f241,f244,f247,f367,f369,f451,f453,f479,f541,f592,f641,f665,f727,f739,f751,f851,f914,f919]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEU221+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.11 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.32 % Computer : n032.cluster.edu
% 0.09/0.32 % Model : x86_64 x86_64
% 0.09/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.32 % Memory : 8042.1875MB
% 0.09/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.32 % CPULimit : 300
% 0.09/0.32 % WCLimit : 300
% 0.09/0.32 % DateTime : Tue May 30 09:16:01 EDT 2023
% 0.09/0.32 % CPUTime :
% 0.09/0.32 % Drodi V3.5.1
% 0.09/0.33 % Refutation found
% 0.09/0.33 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.33 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.15/0.55 % Elapsed time: 0.018267 seconds
% 0.15/0.55 % CPU time: 0.022612 seconds
% 0.15/0.55 % Memory used: 3.256 MB
%------------------------------------------------------------------------------