TSTP Solution File: SEU032+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU032+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n011.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 12:35:43 EDT 2023
% Result : Theorem 0.19s 0.38s
% Output : CNFRefutation 0.19s
% Verified :
% SZS Type : Refutation
% Derivation depth : 7
% Number of leaves : 17
% Syntax : Number of formulae : 73 ( 9 unt; 0 def)
% Number of atoms : 223 ( 41 equ)
% Maximal formula atoms : 8 ( 3 avg)
% Number of connectives : 254 ( 104 ~; 103 |; 22 &)
% ( 11 <=>; 14 =>; 0 <=; 0 <~>)
% Maximal formula depth : 11 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 16 ( 14 usr; 12 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 1 con; 0-2 aty)
% Number of variables : 23 (; 22 !; 1 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f5,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( relation(function_inverse(A))
& function(function_inverse(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f36,axiom,
! [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/sandbox/benchmark/theBenchmark.p') ).
fof(f38,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> ( relation_composition(A,function_inverse(A)) = identity_relation(relation_dom(A))
& relation_composition(function_inverse(A),A) = identity_relation(relation_rng(A)) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f39,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> one_to_one(function_inverse(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f40,axiom,
! [A] :
( ( relation(A)
& function(A) )
=> ! [B] :
( ( relation(B)
& function(B) )
=> ( ( one_to_one(A)
& relation_rng(A) = relation_dom(B)
& relation_composition(A,B) = identity_relation(relation_dom(A)) )
=> B = function_inverse(A) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f41,conjecture,
! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> function_inverse(function_inverse(A)) = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f42,negated_conjecture,
~ ! [A] :
( ( relation(A)
& function(A) )
=> ( one_to_one(A)
=> function_inverse(function_inverse(A)) = A ) ),
inference(negated_conjecture,[status(cth)],[f41]) ).
fof(f56,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ( relation(function_inverse(A))
& function(function_inverse(A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f57,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| relation(function_inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f58,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| function(function_inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f137,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)],[f36]) ).
fof(f138,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ one_to_one(X0)
| relation_rng(X0) = relation_dom(function_inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f137]) ).
fof(f139,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ one_to_one(X0)
| relation_dom(X0) = relation_rng(function_inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f137]) ).
fof(f143,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ~ one_to_one(A)
| ( relation_composition(A,function_inverse(A)) = identity_relation(relation_dom(A))
& relation_composition(function_inverse(A),A) = identity_relation(relation_rng(A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f38]) ).
fof(f145,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ one_to_one(X0)
| relation_composition(function_inverse(X0),X0) = identity_relation(relation_rng(X0)) ),
inference(cnf_transformation,[status(esa)],[f143]) ).
fof(f146,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ~ one_to_one(A)
| one_to_one(function_inverse(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f39]) ).
fof(f147,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| ~ one_to_one(X0)
| one_to_one(function_inverse(X0)) ),
inference(cnf_transformation,[status(esa)],[f146]) ).
fof(f148,plain,
! [A] :
( ~ relation(A)
| ~ function(A)
| ! [B] :
( ~ relation(B)
| ~ function(B)
| ~ one_to_one(A)
| relation_rng(A) != relation_dom(B)
| relation_composition(A,B) != identity_relation(relation_dom(A))
| B = function_inverse(A) ) ),
inference(pre_NNF_transformation,[status(esa)],[f40]) ).
fof(f149,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1)
| ~ one_to_one(X0)
| relation_rng(X0) != relation_dom(X1)
| relation_composition(X0,X1) != identity_relation(relation_dom(X0))
| X1 = function_inverse(X0) ),
inference(cnf_transformation,[status(esa)],[f148]) ).
fof(f150,plain,
? [A] :
( relation(A)
& function(A)
& one_to_one(A)
& function_inverse(function_inverse(A)) != A ),
inference(pre_NNF_transformation,[status(esa)],[f42]) ).
fof(f151,plain,
( relation(sk0_11)
& function(sk0_11)
& one_to_one(sk0_11)
& function_inverse(function_inverse(sk0_11)) != sk0_11 ),
inference(skolemization,[status(esa)],[f150]) ).
fof(f152,plain,
relation(sk0_11),
inference(cnf_transformation,[status(esa)],[f151]) ).
fof(f153,plain,
function(sk0_11),
inference(cnf_transformation,[status(esa)],[f151]) ).
fof(f154,plain,
one_to_one(sk0_11),
inference(cnf_transformation,[status(esa)],[f151]) ).
fof(f155,plain,
function_inverse(function_inverse(sk0_11)) != sk0_11,
inference(cnf_transformation,[status(esa)],[f151]) ).
fof(f168,plain,
( spl0_1
<=> one_to_one(sk0_11) ),
introduced(split_symbol_definition) ).
fof(f170,plain,
( ~ one_to_one(sk0_11)
| spl0_1 ),
inference(component_clause,[status(thm)],[f168]) ).
fof(f529,plain,
( spl0_15
<=> relation(sk0_11) ),
introduced(split_symbol_definition) ).
fof(f531,plain,
( ~ relation(sk0_11)
| spl0_15 ),
inference(component_clause,[status(thm)],[f529]) ).
fof(f532,plain,
( spl0_16
<=> function(sk0_11) ),
introduced(split_symbol_definition) ).
fof(f534,plain,
( ~ function(sk0_11)
| spl0_16 ),
inference(component_clause,[status(thm)],[f532]) ).
fof(f535,plain,
( spl0_17
<=> relation_rng(sk0_11) = relation_dom(function_inverse(sk0_11)) ),
introduced(split_symbol_definition) ).
fof(f536,plain,
( relation_rng(sk0_11) = relation_dom(function_inverse(sk0_11))
| ~ spl0_17 ),
inference(component_clause,[status(thm)],[f535]) ).
fof(f538,plain,
( ~ relation(sk0_11)
| ~ function(sk0_11)
| relation_rng(sk0_11) = relation_dom(function_inverse(sk0_11)) ),
inference(resolution,[status(thm)],[f138,f154]) ).
fof(f539,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_17 ),
inference(split_clause,[status(thm)],[f538,f529,f532,f535]) ).
fof(f542,plain,
( $false
| spl0_16 ),
inference(forward_subsumption_resolution,[status(thm)],[f534,f153]) ).
fof(f543,plain,
spl0_16,
inference(contradiction_clause,[status(thm)],[f542]) ).
fof(f544,plain,
( $false
| spl0_15 ),
inference(forward_subsumption_resolution,[status(thm)],[f531,f152]) ).
fof(f545,plain,
spl0_15,
inference(contradiction_clause,[status(thm)],[f544]) ).
fof(f565,plain,
( spl0_21
<=> relation(function_inverse(sk0_11)) ),
introduced(split_symbol_definition) ).
fof(f567,plain,
( ~ relation(function_inverse(sk0_11))
| spl0_21 ),
inference(component_clause,[status(thm)],[f565]) ).
fof(f570,plain,
( ~ relation(sk0_11)
| ~ function(sk0_11)
| spl0_21 ),
inference(resolution,[status(thm)],[f567,f57]) ).
fof(f571,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_21 ),
inference(split_clause,[status(thm)],[f570,f529,f532,f565]) ).
fof(f1214,plain,
( spl0_55
<=> relation_dom(sk0_11) = relation_rng(function_inverse(sk0_11)) ),
introduced(split_symbol_definition) ).
fof(f1215,plain,
( relation_dom(sk0_11) = relation_rng(function_inverse(sk0_11))
| ~ spl0_55 ),
inference(component_clause,[status(thm)],[f1214]) ).
fof(f1217,plain,
( ~ relation(sk0_11)
| ~ function(sk0_11)
| relation_dom(sk0_11) = relation_rng(function_inverse(sk0_11)) ),
inference(resolution,[status(thm)],[f139,f154]) ).
fof(f1218,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_55 ),
inference(split_clause,[status(thm)],[f1217,f529,f532,f1214]) ).
fof(f1469,plain,
( spl0_77
<=> function(function_inverse(sk0_11)) ),
introduced(split_symbol_definition) ).
fof(f1471,plain,
( ~ function(function_inverse(sk0_11))
| spl0_77 ),
inference(component_clause,[status(thm)],[f1469]) ).
fof(f1484,plain,
( ~ relation(sk0_11)
| ~ function(sk0_11)
| spl0_77 ),
inference(resolution,[status(thm)],[f1471,f58]) ).
fof(f1485,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_77 ),
inference(split_clause,[status(thm)],[f1484,f529,f532,f1469]) ).
fof(f2136,plain,
( spl0_97
<=> relation_composition(function_inverse(sk0_11),sk0_11) = identity_relation(relation_rng(sk0_11)) ),
introduced(split_symbol_definition) ).
fof(f2137,plain,
( relation_composition(function_inverse(sk0_11),sk0_11) = identity_relation(relation_rng(sk0_11))
| ~ spl0_97 ),
inference(component_clause,[status(thm)],[f2136]) ).
fof(f2139,plain,
( ~ relation(sk0_11)
| ~ function(sk0_11)
| relation_composition(function_inverse(sk0_11),sk0_11) = identity_relation(relation_rng(sk0_11)) ),
inference(resolution,[status(thm)],[f145,f154]) ).
fof(f2140,plain,
( ~ spl0_15
| ~ spl0_16
| spl0_97 ),
inference(split_clause,[status(thm)],[f2139,f529,f532,f2136]) ).
fof(f2273,plain,
( spl0_130
<=> one_to_one(function_inverse(sk0_11)) ),
introduced(split_symbol_definition) ).
fof(f2275,plain,
( ~ one_to_one(function_inverse(sk0_11))
| spl0_130 ),
inference(component_clause,[status(thm)],[f2273]) ).
fof(f2276,plain,
( spl0_131
<=> relation_composition(function_inverse(sk0_11),sk0_11) = identity_relation(relation_dom(function_inverse(sk0_11))) ),
introduced(split_symbol_definition) ).
fof(f2278,plain,
( relation_composition(function_inverse(sk0_11),sk0_11) != identity_relation(relation_dom(function_inverse(sk0_11)))
| spl0_131 ),
inference(component_clause,[status(thm)],[f2276]) ).
fof(f2279,plain,
( spl0_132
<=> sk0_11 = function_inverse(function_inverse(sk0_11)) ),
introduced(split_symbol_definition) ).
fof(f2280,plain,
( sk0_11 = function_inverse(function_inverse(sk0_11))
| ~ spl0_132 ),
inference(component_clause,[status(thm)],[f2279]) ).
fof(f2282,plain,
( ~ relation(function_inverse(sk0_11))
| ~ function(function_inverse(sk0_11))
| ~ relation(sk0_11)
| ~ function(sk0_11)
| ~ one_to_one(function_inverse(sk0_11))
| relation_composition(function_inverse(sk0_11),sk0_11) != identity_relation(relation_dom(function_inverse(sk0_11)))
| sk0_11 = function_inverse(function_inverse(sk0_11))
| ~ spl0_55 ),
inference(resolution,[status(thm)],[f149,f1215]) ).
fof(f2283,plain,
( ~ spl0_21
| ~ spl0_77
| ~ spl0_15
| ~ spl0_16
| ~ spl0_130
| ~ spl0_131
| spl0_132
| ~ spl0_55 ),
inference(split_clause,[status(thm)],[f2282,f565,f1469,f529,f532,f2273,f2276,f2279,f1214]) ).
fof(f2510,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f170,f154]) ).
fof(f2511,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f2510]) ).
fof(f2536,plain,
( ~ relation(sk0_11)
| ~ function(sk0_11)
| ~ one_to_one(sk0_11)
| spl0_130 ),
inference(resolution,[status(thm)],[f2275,f147]) ).
fof(f2537,plain,
( ~ spl0_15
| ~ spl0_16
| ~ spl0_1
| spl0_130 ),
inference(split_clause,[status(thm)],[f2536,f529,f532,f168,f2273]) ).
fof(f2718,plain,
( relation_composition(function_inverse(sk0_11),sk0_11) != identity_relation(relation_rng(sk0_11))
| spl0_131
| ~ spl0_17 ),
inference(paramodulation,[status(thm)],[f536,f2278]) ).
fof(f2719,plain,
( $false
| ~ spl0_97
| spl0_131
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[status(thm)],[f2718,f2137]) ).
fof(f2720,plain,
( ~ spl0_97
| spl0_131
| ~ spl0_17 ),
inference(contradiction_clause,[status(thm)],[f2719]) ).
fof(f2721,plain,
( $false
| ~ spl0_132 ),
inference(forward_subsumption_resolution,[status(thm)],[f2280,f155]) ).
fof(f2722,plain,
~ spl0_132,
inference(contradiction_clause,[status(thm)],[f2721]) ).
fof(f2723,plain,
$false,
inference(sat_refutation,[status(thm)],[f539,f543,f545,f571,f1218,f1485,f2140,f2283,f2511,f2537,f2720,f2722]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SEU032+1 : TPTP v8.1.2. Released v3.2.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n011.cluster.edu
% 0.12/0.33 % Model : x86_64 x86_64
% 0.12/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33 % Memory : 8042.1875MB
% 0.12/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33 % CPULimit : 300
% 0.12/0.33 % WCLimit : 300
% 0.12/0.33 % DateTime : Tue May 30 09:08:12 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.34 % Drodi V3.5.1
% 0.19/0.38 % Refutation found
% 0.19/0.38 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.19/0.38 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.19/0.39 % Elapsed time: 0.049876 seconds
% 0.19/0.39 % CPU time: 0.245617 seconds
% 0.19/0.39 % Memory used: 20.744 MB
%------------------------------------------------------------------------------