TSTP Solution File: SEU219+2 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU219+2 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n002.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 12:36:19 EDT 2023
% Result : Theorem 1.76s 0.60s
% Output : CNFRefutation 1.76s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 39
% Syntax : Number of formulae : 162 ( 46 unt; 0 def)
% Number of atoms : 434 ( 81 equ)
% Maximal formula atoms : 19 ( 2 avg)
% Number of connectives : 416 ( 144 ~; 158 |; 71 &)
% ( 26 <=>; 17 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 31 ( 29 usr; 23 prp; 0-4 aty)
% Number of functors : 16 ( 16 usr; 7 con; 0-2 aty)
% Number of variables : 71 (; 59 !; 12 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f3,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f42,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> function_inverse(A) = relation_inverse(A) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f50,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( relation(function_inverse(A))
& function(function_inverse(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f76,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f86,axiom,
! [A] :
( ( relation(A)
& function(A)
& one_to_one(A) )
=> ( relation(relation_inverse(A))
& function(relation_inverse(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f94,axiom,
! [A] :
( empty(A)
=> ( empty(relation_rng(A))
& relation(relation_rng(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f114,axiom,
? [A] :
( relation(A)
& function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f115,axiom,
? [A] :
( empty(A)
& relation(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f117,axiom,
? [A] : empty(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f118,axiom,
? [A] :
( relation(A)
& empty(A)
& function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f122,axiom,
? [A] :
( relation(A)
& function(A)
& one_to_one(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f174,lemma,
! [A] :
( relation(A)
=> ( relation_rng(A) = relation_dom(relation_inverse(A))
& relation_dom(A) = relation_rng(relation_inverse(A)) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f200,lemma,
! [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(f202,conjecture,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> ( relation_rng(A) = relation_dom(function_inverse(A))
& relation_dom(A) = relation_rng(function_inverse(A)) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f203,negated_conjecture,
~ ! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> ( relation_rng(A) = relation_dom(function_inverse(A))
& relation_dom(A) = relation_rng(function_inverse(A)) ) ) ),
inference(negated_conjecture,[status(cth)],[f202]) ).
fof(f206,lemma,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f213,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f237,plain,
! [A] :
( ~ empty(A)
| function(A) ),
inference(pre_NNF_transformation,[status(esa)],[f3]) ).
fof(f238,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[status(esa)],[f237]) ).
fof(f487,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ~ one_to_one(A)
| function_inverse(A) = relation_inverse(A) ),
inference(pre_NNF_transformation,[status(esa)],[f42]) ).
fof(f488,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ one_to_one(X0)
| function_inverse(X0) = relation_inverse(X0) ),
inference(cnf_transformation,[status(esa)],[f487]) ).
fof(f489,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( relation(function_inverse(A))
& function(function_inverse(A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f50]) ).
fof(f490,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f489]) ).
fof(f523,plain,
relation(empty_set),
inference(cnf_transformation,[status(esa)],[f76]) ).
fof(f542,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ~ one_to_one(A)
| ( relation(relation_inverse(A))
& function(relation_inverse(A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f86]) ).
fof(f544,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ one_to_one(X0)
| function(relation_inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f542]) ).
fof(f560,plain,
! [A] :
( ~ empty(A)
| ( empty(relation_rng(A))
& relation(relation_rng(A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f94]) ).
fof(f561,plain,
! [X0] :
( ~ empty(X0)
| empty(relation_rng(X0)) ),
inference(cnf_transformation,[status(esa)],[f560]) ).
fof(f614,plain,
( relation(sk0_53)
& function(sk0_53) ),
inference(skolemization,[status(esa)],[f114]) ).
fof(f615,plain,
relation(sk0_53),
inference(cnf_transformation,[status(esa)],[f614]) ).
fof(f616,plain,
function(sk0_53),
inference(cnf_transformation,[status(esa)],[f614]) ).
fof(f617,plain,
( empty(sk0_54)
& relation(sk0_54) ),
inference(skolemization,[status(esa)],[f115]) ).
fof(f618,plain,
empty(sk0_54),
inference(cnf_transformation,[status(esa)],[f617]) ).
fof(f619,plain,
relation(sk0_54),
inference(cnf_transformation,[status(esa)],[f617]) ).
fof(f624,plain,
empty(sk0_56),
inference(skolemization,[status(esa)],[f117]) ).
fof(f625,plain,
empty(sk0_56),
inference(cnf_transformation,[status(esa)],[f624]) ).
fof(f626,plain,
( relation(sk0_57)
& empty(sk0_57)
& function(sk0_57) ),
inference(skolemization,[status(esa)],[f118]) ).
fof(f627,plain,
relation(sk0_57),
inference(cnf_transformation,[status(esa)],[f626]) ).
fof(f628,plain,
empty(sk0_57),
inference(cnf_transformation,[status(esa)],[f626]) ).
fof(f629,plain,
function(sk0_57),
inference(cnf_transformation,[status(esa)],[f626]) ).
fof(f638,plain,
( relation(sk0_61)
& function(sk0_61)
& one_to_one(sk0_61) ),
inference(skolemization,[status(esa)],[f122]) ).
fof(f639,plain,
relation(sk0_61),
inference(cnf_transformation,[status(esa)],[f638]) ).
fof(f640,plain,
function(sk0_61),
inference(cnf_transformation,[status(esa)],[f638]) ).
fof(f641,plain,
one_to_one(sk0_61),
inference(cnf_transformation,[status(esa)],[f638]) ).
fof(f800,plain,
! [A] :
( ~ relation(A)
| ( relation_rng(A) = relation_dom(relation_inverse(A))
& relation_dom(A) = relation_rng(relation_inverse(A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f174]) ).
fof(f802,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) = relation_rng(relation_inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f800]) ).
fof(f870,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)],[f200]) ).
fof(f871,plain,
! [A,B,C,D] :
( pd0_1(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,[f870]) ).
fof(f872,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_1(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)],[f870,f871]) ).
fof(f873,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_1(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_1(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)],[f872]) ).
fof(f874,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_1(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_1(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)],[f873]) ).
fof(f875,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_1(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_1(sk0_71(B,A),sk0_70(B,A),B,A)
| ( in(sk0_73(B,A),relation_dom(A))
& sk0_72(B,A) = apply(A,sk0_73(B,A))
& ( ~ in(sk0_72(B,A),relation_rng(A))
| sk0_73(B,A) != apply(B,sk0_72(B,A)) ) ) ) ) ) ),
inference(skolemization,[status(esa)],[f874]) ).
fof(f876,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)],[f875]) ).
fof(f886,plain,
? [A] :
( relation(A)
& function(A)
& one_to_one(A)
& ( relation_rng(A) != relation_dom(function_inverse(A))
| relation_dom(A) != relation_rng(function_inverse(A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f203]) ).
fof(f887,plain,
( relation(sk0_74)
& function(sk0_74)
& one_to_one(sk0_74)
& ( relation_rng(sk0_74) != relation_dom(function_inverse(sk0_74))
| relation_dom(sk0_74) != relation_rng(function_inverse(sk0_74)) ) ),
inference(skolemization,[status(esa)],[f886]) ).
fof(f888,plain,
relation(sk0_74),
inference(cnf_transformation,[status(esa)],[f887]) ).
fof(f889,plain,
function(sk0_74),
inference(cnf_transformation,[status(esa)],[f887]) ).
fof(f890,plain,
one_to_one(sk0_74),
inference(cnf_transformation,[status(esa)],[f887]) ).
fof(f891,plain,
( relation_rng(sk0_74) != relation_dom(function_inverse(sk0_74))
| relation_dom(sk0_74) != relation_rng(function_inverse(sk0_74)) ),
inference(cnf_transformation,[status(esa)],[f887]) ).
fof(f899,plain,
relation_rng(empty_set) = empty_set,
inference(cnf_transformation,[status(esa)],[f206]) ).
fof(f917,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f213]) ).
fof(f918,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f917]) ).
fof(f997,plain,
( spl0_0
<=> relation_rng(sk0_74) = relation_dom(function_inverse(sk0_74)) ),
introduced(split_symbol_definition) ).
fof(f1000,plain,
( spl0_1
<=> relation_dom(sk0_74) = relation_rng(function_inverse(sk0_74)) ),
introduced(split_symbol_definition) ).
fof(f1002,plain,
( relation_dom(sk0_74) != relation_rng(function_inverse(sk0_74))
| spl0_1 ),
inference(component_clause,[status(thm)],[f1000]) ).
fof(f1003,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f891,f997,f1000]) ).
fof(f1071,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)],[f876]) ).
fof(f1084,plain,
( spl0_3
<=> one_to_one(sk0_74) ),
introduced(split_symbol_definition) ).
fof(f1086,plain,
( ~ one_to_one(sk0_74)
| spl0_3 ),
inference(component_clause,[status(thm)],[f1084]) ).
fof(f1089,plain,
( spl0_4
<=> function(sk0_74) ),
introduced(split_symbol_definition) ).
fof(f1091,plain,
( ~ function(sk0_74)
| spl0_4 ),
inference(component_clause,[status(thm)],[f1089]) ).
fof(f1097,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f1091,f889]) ).
fof(f1098,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f1097]) ).
fof(f1392,plain,
( spl0_71
<=> relation(sk0_74) ),
introduced(split_symbol_definition) ).
fof(f1394,plain,
( ~ relation(sk0_74)
| spl0_71 ),
inference(component_clause,[status(thm)],[f1392]) ).
fof(f1400,plain,
( $false
| spl0_71 ),
inference(forward_subsumption_resolution,[status(thm)],[f1394,f888]) ).
fof(f1401,plain,
spl0_71,
inference(contradiction_clause,[status(thm)],[f1400]) ).
fof(f1402,plain,
( spl0_73
<=> function(relation_inverse(sk0_74)) ),
introduced(split_symbol_definition) ).
fof(f1405,plain,
( ~ relation(sk0_74)
| ~ function(sk0_74)
| function(relation_inverse(sk0_74)) ),
inference(resolution,[status(thm)],[f544,f890]) ).
fof(f1406,plain,
( ~ spl0_71
| ~ spl0_4
| spl0_73 ),
inference(split_clause,[status(thm)],[f1405,f1392,f1089,f1402]) ).
fof(f1407,plain,
( spl0_74
<=> function_inverse(sk0_74) = relation_inverse(sk0_74) ),
introduced(split_symbol_definition) ).
fof(f1408,plain,
( function_inverse(sk0_74) = relation_inverse(sk0_74)
| ~ spl0_74 ),
inference(component_clause,[status(thm)],[f1407]) ).
fof(f1410,plain,
( ~ relation(sk0_74)
| ~ function(sk0_74)
| function_inverse(sk0_74) = relation_inverse(sk0_74) ),
inference(resolution,[status(thm)],[f488,f890]) ).
fof(f1411,plain,
( ~ spl0_71
| ~ spl0_4
| spl0_74 ),
inference(split_clause,[status(thm)],[f1410,f1392,f1089,f1407]) ).
fof(f1523,plain,
( spl0_87
<=> empty(empty_set) ),
introduced(split_symbol_definition) ).
fof(f1525,plain,
( ~ empty(empty_set)
| spl0_87 ),
inference(component_clause,[status(thm)],[f1523]) ).
fof(f1526,plain,
( spl0_88
<=> relation(empty_set) ),
introduced(split_symbol_definition) ).
fof(f1528,plain,
( ~ relation(empty_set)
| spl0_88 ),
inference(component_clause,[status(thm)],[f1526]) ).
fof(f1565,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)],[f1071,f490]) ).
fof(f1581,plain,
( ~ relation(sk0_74)
| ~ function(sk0_74)
| ~ one_to_one(sk0_74)
| ~ function(relation_inverse(sk0_74))
| relation_dom(function_inverse(sk0_74)) = relation_rng(sk0_74)
| ~ spl0_74 ),
inference(paramodulation,[status(thm)],[f1408,f1565]) ).
fof(f1582,plain,
( ~ spl0_71
| ~ spl0_4
| ~ spl0_3
| ~ spl0_73
| spl0_0
| ~ spl0_74 ),
inference(split_clause,[status(thm)],[f1581,f1392,f1089,f1084,f1402,f997,f1407]) ).
fof(f1583,plain,
( relation_dom(sk0_74) != relation_rng(relation_inverse(sk0_74))
| ~ spl0_74
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f1408,f1002]) ).
fof(f1584,plain,
( $false
| spl0_3 ),
inference(forward_subsumption_resolution,[status(thm)],[f1086,f890]) ).
fof(f1585,plain,
spl0_3,
inference(contradiction_clause,[status(thm)],[f1584]) ).
fof(f1642,plain,
( $false
| spl0_88 ),
inference(forward_subsumption_resolution,[status(thm)],[f523,f1528]) ).
fof(f1643,plain,
spl0_88,
inference(contradiction_clause,[status(thm)],[f1642]) ).
fof(f1647,plain,
( spl0_108
<=> function(empty_set) ),
introduced(split_symbol_definition) ).
fof(f1649,plain,
( ~ function(empty_set)
| spl0_108 ),
inference(component_clause,[status(thm)],[f1647]) ).
fof(f1667,plain,
( spl0_112
<=> function(sk0_53) ),
introduced(split_symbol_definition) ).
fof(f1669,plain,
( ~ function(sk0_53)
| spl0_112 ),
inference(component_clause,[status(thm)],[f1667]) ).
fof(f1689,plain,
empty(relation_rng(sk0_54)),
inference(resolution,[status(thm)],[f618,f561]) ).
fof(f1690,plain,
function(sk0_54),
inference(resolution,[status(thm)],[f618,f238]) ).
fof(f1693,plain,
( spl0_117
<=> function(sk0_54) ),
introduced(split_symbol_definition) ).
fof(f1695,plain,
( ~ function(sk0_54)
| spl0_117 ),
inference(component_clause,[status(thm)],[f1693]) ).
fof(f1706,plain,
( spl0_120
<=> empty(sk0_54) ),
introduced(split_symbol_definition) ).
fof(f1708,plain,
( ~ empty(sk0_54)
| spl0_120 ),
inference(component_clause,[status(thm)],[f1706]) ).
fof(f1714,plain,
( $false
| spl0_120 ),
inference(forward_subsumption_resolution,[status(thm)],[f1708,f618]) ).
fof(f1715,plain,
spl0_120,
inference(contradiction_clause,[status(thm)],[f1714]) ).
fof(f1718,plain,
function(sk0_56),
inference(resolution,[status(thm)],[f625,f238]) ).
fof(f1721,plain,
( spl0_122
<=> function(sk0_57) ),
introduced(split_symbol_definition) ).
fof(f1723,plain,
( ~ function(sk0_57)
| spl0_122 ),
inference(component_clause,[status(thm)],[f1721]) ).
fof(f1734,plain,
( spl0_125
<=> empty(sk0_57) ),
introduced(split_symbol_definition) ).
fof(f1736,plain,
( ~ empty(sk0_57)
| spl0_125 ),
inference(component_clause,[status(thm)],[f1734]) ).
fof(f1770,plain,
( spl0_132
<=> function(sk0_61) ),
introduced(split_symbol_definition) ).
fof(f1772,plain,
( ~ function(sk0_61)
| spl0_132 ),
inference(component_clause,[status(thm)],[f1770]) ).
fof(f1786,plain,
( spl0_136
<=> one_to_one(sk0_61) ),
introduced(split_symbol_definition) ).
fof(f1788,plain,
( ~ one_to_one(sk0_61)
| spl0_136 ),
inference(component_clause,[status(thm)],[f1786]) ).
fof(f1791,plain,
( spl0_137
<=> relation(sk0_61) ),
introduced(split_symbol_definition) ).
fof(f1793,plain,
( ~ relation(sk0_61)
| spl0_137 ),
inference(component_clause,[status(thm)],[f1791]) ).
fof(f1832,plain,
( $false
| spl0_112 ),
inference(forward_subsumption_resolution,[status(thm)],[f1669,f616]) ).
fof(f1833,plain,
spl0_112,
inference(contradiction_clause,[status(thm)],[f1832]) ).
fof(f1834,plain,
( $false
| spl0_117 ),
inference(forward_subsumption_resolution,[status(thm)],[f1695,f1690]) ).
fof(f1835,plain,
spl0_117,
inference(contradiction_clause,[status(thm)],[f1834]) ).
fof(f1836,plain,
( spl0_146
<=> relation(sk0_54) ),
introduced(split_symbol_definition) ).
fof(f1838,plain,
( ~ relation(sk0_54)
| spl0_146 ),
inference(component_clause,[status(thm)],[f1836]) ).
fof(f1854,plain,
( $false
| spl0_146 ),
inference(forward_subsumption_resolution,[status(thm)],[f1838,f619]) ).
fof(f1855,plain,
spl0_146,
inference(contradiction_clause,[status(thm)],[f1854]) ).
fof(f1856,plain,
( $false
| spl0_125 ),
inference(forward_subsumption_resolution,[status(thm)],[f1736,f628]) ).
fof(f1857,plain,
spl0_125,
inference(contradiction_clause,[status(thm)],[f1856]) ).
fof(f1858,plain,
( $false
| spl0_122 ),
inference(forward_subsumption_resolution,[status(thm)],[f1723,f629]) ).
fof(f1859,plain,
spl0_122,
inference(contradiction_clause,[status(thm)],[f1858]) ).
fof(f1860,plain,
( $false
| spl0_132 ),
inference(forward_subsumption_resolution,[status(thm)],[f1772,f640]) ).
fof(f1861,plain,
spl0_132,
inference(contradiction_clause,[status(thm)],[f1860]) ).
fof(f1862,plain,
( $false
| spl0_137 ),
inference(forward_subsumption_resolution,[status(thm)],[f1793,f639]) ).
fof(f1863,plain,
spl0_137,
inference(contradiction_clause,[status(thm)],[f1862]) ).
fof(f1864,plain,
( spl0_150
<=> relation(sk0_57) ),
introduced(split_symbol_definition) ).
fof(f1866,plain,
( ~ relation(sk0_57)
| spl0_150 ),
inference(component_clause,[status(thm)],[f1864]) ).
fof(f1882,plain,
( $false
| spl0_150 ),
inference(forward_subsumption_resolution,[status(thm)],[f1866,f627]) ).
fof(f1883,plain,
spl0_150,
inference(contradiction_clause,[status(thm)],[f1882]) ).
fof(f1895,plain,
( spl0_154
<=> function(sk0_56) ),
introduced(split_symbol_definition) ).
fof(f1897,plain,
( ~ function(sk0_56)
| spl0_154 ),
inference(component_clause,[status(thm)],[f1895]) ).
fof(f1908,plain,
( $false
| spl0_154 ),
inference(forward_subsumption_resolution,[status(thm)],[f1897,f1718]) ).
fof(f1909,plain,
spl0_154,
inference(contradiction_clause,[status(thm)],[f1908]) ).
fof(f1910,plain,
sk0_57 = empty_set,
inference(resolution,[status(thm)],[f918,f628]) ).
fof(f1912,plain,
sk0_54 = empty_set,
inference(resolution,[status(thm)],[f918,f618]) ).
fof(f1914,plain,
function(empty_set),
inference(backward_demodulation,[status(thm)],[f1910,f629]) ).
fof(f2227,plain,
empty(relation_rng(empty_set)),
inference(forward_demodulation,[status(thm)],[f1912,f1689]) ).
fof(f2228,plain,
empty(empty_set),
inference(forward_demodulation,[status(thm)],[f899,f2227]) ).
fof(f2243,plain,
( spl0_199
<=> relation(sk0_53) ),
introduced(split_symbol_definition) ).
fof(f2245,plain,
( ~ relation(sk0_53)
| spl0_199 ),
inference(component_clause,[status(thm)],[f2243]) ).
fof(f2261,plain,
( $false
| spl0_199 ),
inference(forward_subsumption_resolution,[status(thm)],[f2245,f615]) ).
fof(f2262,plain,
spl0_199,
inference(contradiction_clause,[status(thm)],[f2261]) ).
fof(f2325,plain,
( $false
| spl0_136 ),
inference(forward_subsumption_resolution,[status(thm)],[f1788,f641]) ).
fof(f2326,plain,
spl0_136,
inference(contradiction_clause,[status(thm)],[f2325]) ).
fof(f2375,plain,
( $false
| spl0_87 ),
inference(forward_subsumption_resolution,[status(thm)],[f1525,f2228]) ).
fof(f2376,plain,
spl0_87,
inference(contradiction_clause,[status(thm)],[f2375]) ).
fof(f2377,plain,
( $false
| spl0_108 ),
inference(forward_subsumption_resolution,[status(thm)],[f1649,f1914]) ).
fof(f2378,plain,
spl0_108,
inference(contradiction_clause,[status(thm)],[f2377]) ).
fof(f2715,plain,
relation_dom(sk0_74) = relation_rng(relation_inverse(sk0_74)),
inference(resolution,[status(thm)],[f802,f888]) ).
fof(f2716,plain,
( $false
| ~ spl0_74
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f2715,f1583]) ).
fof(f2717,plain,
( ~ spl0_74
| spl0_1 ),
inference(contradiction_clause,[status(thm)],[f2716]) ).
fof(f2718,plain,
$false,
inference(sat_refutation,[status(thm)],[f1003,f1098,f1401,f1406,f1411,f1582,f1585,f1643,f1715,f1833,f1835,f1855,f1857,f1859,f1861,f1863,f1883,f1909,f2262,f2326,f2376,f2378,f2717]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : SEU219+2 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n002.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 30 09:28:58 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.37 % Drodi V3.5.1
% 1.76/0.60 % Refutation found
% 1.76/0.60 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.76/0.60 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.76/0.62 % Elapsed time: 0.271888 seconds
% 1.76/0.62 % CPU time: 1.924324 seconds
% 1.76/0.62 % Memory used: 91.406 MB
%------------------------------------------------------------------------------