TSTP Solution File: SEU019+1 by Drodi---3.5.1
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU019+1 : TPTP v8.1.2. Released v3.2.0.
% 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 12:35:42 EDT 2023
% Result : Theorem 0.09s 0.31s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 19
% Syntax : Number of formulae : 104 ( 23 unt; 0 def)
% Number of atoms : 283 ( 58 equ)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 300 ( 121 ~; 131 |; 29 &)
% ( 14 <=>; 5 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 18 ( 16 usr; 11 prp; 0-2 aty)
% Number of functors : 10 ( 10 usr; 3 con; 0-2 aty)
% Number of variables : 72 (; 66 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f2,axiom,
! [A] :
( empty(A)
=> function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,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(f5,axiom,
! [A] : relation(identity_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A] : ~ empty(powerset(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] :
( relation(identity_relation(A))
& function(identity_relation(A)) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
? [A] :
( relation(A)
& function(A) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,axiom,
! [A,B] :
( ( relation(B)
& function(B) )
=> ( B = identity_relation(A)
<=> ( relation_dom(B) = A
& ! [C] :
( in(C,A)
=> apply(B,C) = C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f28,conjecture,
! [A] : one_to_one(identity_relation(A)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f29,negated_conjecture,
~ ! [A] : one_to_one(identity_relation(A)),
inference(negated_conjecture,[status(cth)],[f28]) ).
fof(f36,plain,
! [A] :
( ~ empty(A)
| function(A) ),
inference(pre_NNF_transformation,[status(esa)],[f2]) ).
fof(f37,plain,
! [X0] :
( ~ empty(X0)
| function(X0) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f40,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)],[f4]) ).
fof(f41,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)],[f40]) ).
fof(f42,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)],[f41]) ).
fof(f44,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| in(sk0_0(X0),relation_dom(X0)) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f45,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| in(sk0_1(X0),relation_dom(X0)) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f46,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)],[f42]) ).
fof(f47,plain,
! [X0] :
( ~ relation(X0)
| ~ function(X0)
| one_to_one(X0)
| sk0_0(X0) != sk0_1(X0) ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f48,plain,
! [X0] : relation(identity_relation(X0)),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f51,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f52,plain,
relation(empty_set),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f54,plain,
! [X0] : ~ empty(powerset(X0)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f56,plain,
( ! [A] : relation(identity_relation(A))
& ! [A] : function(identity_relation(A)) ),
inference(miniscoping,[status(esa)],[f10]) ).
fof(f58,plain,
! [X0] : function(identity_relation(X0)),
inference(cnf_transformation,[status(esa)],[f56]) ).
fof(f66,plain,
( relation(sk0_3)
& function(sk0_3) ),
inference(skolemization,[status(esa)],[f14]) ).
fof(f67,plain,
relation(sk0_3),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f95,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ( B = identity_relation(A)
<=> ( relation_dom(B) = A
& ! [C] :
( ~ in(C,A)
| apply(B,C) = C ) ) ) ),
inference(pre_NNF_transformation,[status(esa)],[f25]) ).
fof(f96,plain,
! [A,B] :
( ~ relation(B)
| ~ function(B)
| ( ( B != identity_relation(A)
| ( relation_dom(B) = A
& ! [C] :
( ~ in(C,A)
| apply(B,C) = C ) ) )
& ( B = identity_relation(A)
| relation_dom(B) != A
| ? [C] :
( in(C,A)
& apply(B,C) != C ) ) ) ),
inference(NNF_transformation,[status(esa)],[f95]) ).
fof(f97,plain,
! [B] :
( ~ relation(B)
| ~ function(B)
| ( ! [A] :
( B != identity_relation(A)
| ( relation_dom(B) = A
& ! [C] :
( ~ in(C,A)
| apply(B,C) = C ) ) )
& ! [A] :
( B = identity_relation(A)
| relation_dom(B) != A
| ? [C] :
( in(C,A)
& apply(B,C) != C ) ) ) ),
inference(miniscoping,[status(esa)],[f96]) ).
fof(f98,plain,
! [B] :
( ~ relation(B)
| ~ function(B)
| ( ! [A] :
( B != identity_relation(A)
| ( relation_dom(B) = A
& ! [C] :
( ~ in(C,A)
| apply(B,C) = C ) ) )
& ! [A] :
( B = identity_relation(A)
| relation_dom(B) != A
| ( in(sk0_11(A,B),A)
& apply(B,sk0_11(A,B)) != sk0_11(A,B) ) ) ) ),
inference(skolemization,[status(esa)],[f97]) ).
fof(f99,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| X0 != identity_relation(X1)
| relation_dom(X0) = X1 ),
inference(cnf_transformation,[status(esa)],[f98]) ).
fof(f100,plain,
! [X0,X1,X2] :
( ~ relation(X0)
| ~ function(X0)
| X0 != identity_relation(X1)
| ~ in(X2,X1)
| apply(X0,X2) = X2 ),
inference(cnf_transformation,[status(esa)],[f98]) ).
fof(f110,plain,
? [A] : ~ one_to_one(identity_relation(A)),
inference(pre_NNF_transformation,[status(esa)],[f29]) ).
fof(f111,plain,
~ one_to_one(identity_relation(sk0_12)),
inference(skolemization,[status(esa)],[f110]) ).
fof(f112,plain,
~ one_to_one(identity_relation(sk0_12)),
inference(cnf_transformation,[status(esa)],[f111]) ).
fof(f124,plain,
! [X0] :
( ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(destructive_equality_resolution,[status(esa)],[f99]) ).
fof(f125,plain,
! [X0,X1] :
( ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0))
| ~ in(X1,X0)
| apply(identity_relation(X0),X1) = X1 ),
inference(destructive_equality_resolution,[status(esa)],[f100]) ).
fof(f128,plain,
! [X0] :
( ~ function(identity_relation(X0))
| relation_dom(identity_relation(X0)) = X0 ),
inference(forward_subsumption_resolution,[status(thm)],[f124,f48]) ).
fof(f129,plain,
! [X0] : relation_dom(identity_relation(X0)) = X0,
inference(resolution,[status(thm)],[f128,f58]) ).
fof(f137,plain,
! [X0] :
( ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0))
| one_to_one(identity_relation(X0))
| in(sk0_0(identity_relation(X0)),X0) ),
inference(paramodulation,[status(thm)],[f129,f44]) ).
fof(f138,plain,
! [X0] :
( ~ function(identity_relation(X0))
| one_to_one(identity_relation(X0))
| in(sk0_0(identity_relation(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f137,f48]) ).
fof(f140,plain,
! [X0] :
( ~ relation(identity_relation(X0))
| ~ function(identity_relation(X0))
| one_to_one(identity_relation(X0))
| in(sk0_1(identity_relation(X0)),X0) ),
inference(paramodulation,[status(thm)],[f129,f45]) ).
fof(f141,plain,
! [X0] :
( ~ function(identity_relation(X0))
| one_to_one(identity_relation(X0))
| in(sk0_1(identity_relation(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f140,f48]) ).
fof(f142,plain,
( spl0_0
<=> relation(identity_relation(sk0_12)) ),
introduced(split_symbol_definition) ).
fof(f144,plain,
( ~ relation(identity_relation(sk0_12))
| spl0_0 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f145,plain,
( spl0_1
<=> function(identity_relation(sk0_12)) ),
introduced(split_symbol_definition) ).
fof(f147,plain,
( ~ function(identity_relation(sk0_12))
| spl0_1 ),
inference(component_clause,[status(thm)],[f145]) ).
fof(f148,plain,
( spl0_2
<=> apply(identity_relation(sk0_12),sk0_0(identity_relation(sk0_12))) = apply(identity_relation(sk0_12),sk0_1(identity_relation(sk0_12))) ),
introduced(split_symbol_definition) ).
fof(f149,plain,
( apply(identity_relation(sk0_12),sk0_0(identity_relation(sk0_12))) = apply(identity_relation(sk0_12),sk0_1(identity_relation(sk0_12)))
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f148]) ).
fof(f151,plain,
( ~ relation(identity_relation(sk0_12))
| ~ function(identity_relation(sk0_12))
| apply(identity_relation(sk0_12),sk0_0(identity_relation(sk0_12))) = apply(identity_relation(sk0_12),sk0_1(identity_relation(sk0_12))) ),
inference(resolution,[status(thm)],[f46,f112]) ).
fof(f152,plain,
( ~ spl0_0
| ~ spl0_1
| spl0_2 ),
inference(split_clause,[status(thm)],[f151,f142,f145,f148]) ).
fof(f153,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f147,f58]) ).
fof(f154,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f153]) ).
fof(f155,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f48]) ).
fof(f156,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f155]) ).
fof(f160,plain,
( spl0_4
<=> in(sk0_0(identity_relation(sk0_12)),relation_dom(identity_relation(sk0_12))) ),
introduced(split_symbol_definition) ).
fof(f161,plain,
( in(sk0_0(identity_relation(sk0_12)),relation_dom(identity_relation(sk0_12)))
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f162,plain,
( ~ in(sk0_0(identity_relation(sk0_12)),relation_dom(identity_relation(sk0_12)))
| spl0_4 ),
inference(component_clause,[status(thm)],[f160]) ).
fof(f163,plain,
( spl0_5
<=> in(sk0_1(identity_relation(sk0_12)),relation_dom(identity_relation(sk0_12))) ),
introduced(split_symbol_definition) ).
fof(f164,plain,
( in(sk0_1(identity_relation(sk0_12)),relation_dom(identity_relation(sk0_12)))
| ~ spl0_5 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f165,plain,
( ~ in(sk0_1(identity_relation(sk0_12)),relation_dom(identity_relation(sk0_12)))
| spl0_5 ),
inference(component_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( spl0_6
<=> sk0_0(identity_relation(sk0_12)) = sk0_1(identity_relation(sk0_12)) ),
introduced(split_symbol_definition) ).
fof(f168,plain,
( sk0_0(identity_relation(sk0_12)) != sk0_1(identity_relation(sk0_12))
| spl0_6 ),
inference(component_clause,[status(thm)],[f166]) ).
fof(f180,plain,
( ~ in(sk0_0(identity_relation(sk0_12)),sk0_12)
| spl0_4 ),
inference(forward_demodulation,[status(thm)],[f129,f162]) ).
fof(f181,plain,
( ~ in(sk0_1(identity_relation(sk0_12)),sk0_12)
| spl0_5 ),
inference(forward_demodulation,[status(thm)],[f129,f165]) ).
fof(f182,plain,
! [X0] :
( one_to_one(identity_relation(X0))
| in(sk0_0(identity_relation(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f138,f58]) ).
fof(f183,plain,
( one_to_one(identity_relation(sk0_12))
| spl0_4 ),
inference(resolution,[status(thm)],[f182,f180]) ).
fof(f184,plain,
( $false
| spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f183,f112]) ).
fof(f185,plain,
spl0_4,
inference(contradiction_clause,[status(thm)],[f184]) ).
fof(f187,plain,
( in(sk0_0(identity_relation(sk0_12)),sk0_12)
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f129,f161]) ).
fof(f189,plain,
! [X0] :
( one_to_one(identity_relation(X0))
| in(sk0_1(identity_relation(X0)),X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f141,f58]) ).
fof(f190,plain,
( one_to_one(identity_relation(sk0_12))
| spl0_5 ),
inference(resolution,[status(thm)],[f189,f181]) ).
fof(f191,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f190,f112]) ).
fof(f192,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f191]) ).
fof(f194,plain,
( in(sk0_1(identity_relation(sk0_12)),sk0_12)
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f129,f164]) ).
fof(f200,plain,
( ~ relation(identity_relation(sk0_12))
| ~ function(identity_relation(sk0_12))
| sk0_0(identity_relation(sk0_12)) != sk0_1(identity_relation(sk0_12)) ),
inference(resolution,[status(thm)],[f47,f112]) ).
fof(f201,plain,
( ~ spl0_0
| ~ spl0_1
| ~ spl0_6 ),
inference(split_clause,[status(thm)],[f200,f142,f145,f166]) ).
fof(f207,plain,
( spl0_8
<=> relation(empty_set) ),
introduced(split_symbol_definition) ).
fof(f209,plain,
( ~ relation(empty_set)
| spl0_8 ),
inference(component_clause,[status(thm)],[f207]) ).
fof(f210,plain,
( spl0_9
<=> function(empty_set) ),
introduced(split_symbol_definition) ).
fof(f212,plain,
( ~ function(empty_set)
| spl0_9 ),
inference(component_clause,[status(thm)],[f210]) ).
fof(f226,plain,
( ~ empty(empty_set)
| spl0_9 ),
inference(resolution,[status(thm)],[f212,f37]) ).
fof(f227,plain,
( $false
| spl0_9 ),
inference(forward_subsumption_resolution,[status(thm)],[f226,f51]) ).
fof(f228,plain,
spl0_9,
inference(contradiction_clause,[status(thm)],[f227]) ).
fof(f229,plain,
( $false
| spl0_8 ),
inference(forward_subsumption_resolution,[status(thm)],[f209,f52]) ).
fof(f230,plain,
spl0_8,
inference(contradiction_clause,[status(thm)],[f229]) ).
fof(f297,plain,
! [X0,X1] :
( ~ function(identity_relation(X0))
| ~ in(X1,X0)
| apply(identity_relation(X0),X1) = X1 ),
inference(forward_subsumption_resolution,[status(thm)],[f125,f48]) ).
fof(f298,plain,
! [X0,X1] :
( ~ in(X0,X1)
| apply(identity_relation(X1),X0) = X0 ),
inference(resolution,[status(thm)],[f297,f58]) ).
fof(f308,plain,
( apply(identity_relation(sk0_12),sk0_1(identity_relation(sk0_12))) = sk0_1(identity_relation(sk0_12))
| ~ spl0_5 ),
inference(resolution,[status(thm)],[f298,f194]) ).
fof(f309,plain,
( apply(identity_relation(sk0_12),sk0_0(identity_relation(sk0_12))) = sk0_1(identity_relation(sk0_12))
| ~ spl0_2
| ~ spl0_5 ),
inference(forward_demodulation,[status(thm)],[f149,f308]) ).
fof(f312,plain,
( apply(identity_relation(sk0_12),sk0_0(identity_relation(sk0_12))) = sk0_0(identity_relation(sk0_12))
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f298,f187]) ).
fof(f352,plain,
( spl0_19
<=> empty(powerset(empty_set)) ),
introduced(split_symbol_definition) ).
fof(f353,plain,
( empty(powerset(empty_set))
| ~ spl0_19 ),
inference(component_clause,[status(thm)],[f352]) ).
fof(f366,plain,
( $false
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[status(thm)],[f353,f54]) ).
fof(f367,plain,
~ spl0_19,
inference(contradiction_clause,[status(thm)],[f366]) ).
fof(f399,plain,
( spl0_27
<=> relation(sk0_3) ),
introduced(split_symbol_definition) ).
fof(f401,plain,
( ~ relation(sk0_3)
| spl0_27 ),
inference(component_clause,[status(thm)],[f399]) ).
fof(f413,plain,
( $false
| spl0_27 ),
inference(forward_subsumption_resolution,[status(thm)],[f401,f67]) ).
fof(f414,plain,
spl0_27,
inference(contradiction_clause,[status(thm)],[f413]) ).
fof(f441,plain,
( sk0_1(identity_relation(sk0_12)) = sk0_0(identity_relation(sk0_12))
| ~ spl0_2
| ~ spl0_5
| ~ spl0_4 ),
inference(forward_demodulation,[status(thm)],[f309,f312]) ).
fof(f442,plain,
( $false
| spl0_6
| ~ spl0_2
| ~ spl0_5
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f441,f168]) ).
fof(f443,plain,
( spl0_6
| ~ spl0_2
| ~ spl0_5
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f442]) ).
fof(f444,plain,
$false,
inference(sat_refutation,[status(thm)],[f152,f154,f156,f185,f192,f201,f228,f230,f367,f414,f443]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SEU019+1 : TPTP v8.1.2. Released v3.2.0.
% 0.00/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.29 % Computer : n032.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue May 30 09:14:16 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 0.09/0.31 % Refutation found
% 0.09/0.31 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.09/0.31 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.54 % Elapsed time: 0.034668 seconds
% 0.14/0.54 % CPU time: 0.017004 seconds
% 0.14/0.54 % Memory used: 3.064 MB
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