TSTP Solution File: SET994+1 by Drodi---3.6.0
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : SET994+1 : TPTP v8.1.2. Released v3.2.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n014.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 : Tue Apr 30 20:40:51 EDT 2024
% Result : Theorem 0.17s 0.36s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 15
% Number of leaves : 11
% Syntax : Number of formulae : 64 ( 19 unt; 0 def)
% Number of atoms : 174 ( 69 equ)
% Maximal formula atoms : 8 ( 2 avg)
% Number of connectives : 174 ( 64 ~; 68 |; 28 &)
% ( 2 <=>; 12 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 4 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 3 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 4 con; 0-2 aty)
% Number of variables : 69 ( 63 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f4,axiom,
! [A] :
? [B] : element(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
( empty(empty_set)
& relation(empty_set)
& relation_empty_yielding(empty_set) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,axiom,
! [A] :
? [B] :
( relation(B)
& function(B)
& relation_dom(B) = A
& ! [C] :
( in(C,A)
=> apply(B,C) = n0 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f21,axiom,
! [A] :
? [B] :
( relation(B)
& function(B)
& relation_dom(B) = A
& ! [C] :
( in(C,A)
=> apply(B,C) = n1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f22,axiom,
empty(n0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f23,axiom,
~ empty(n1),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f24,conjecture,
! [A] :
( ! [B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( ( relation_dom(B) = A
& relation_dom(C) = A )
=> B = C ) ) )
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f25,negated_conjecture,
~ ! [A] :
( ! [B] :
( ( relation(B)
& function(B) )
=> ! [C] :
( ( relation(C)
& function(C) )
=> ( ( relation_dom(B) = A
& relation_dom(C) = A )
=> B = C ) ) )
=> A = empty_set ),
inference(negated_conjecture,[status(cth)],[f24]) ).
fof(f27,axiom,
! [A,B] :
( element(A,B)
=> ( empty(B)
| in(A,B) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f31,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f40,plain,
! [A] : element(sk0_0(A),A),
inference(skolemization,[status(esa)],[f4]) ).
fof(f41,plain,
! [X0] : element(sk0_0(X0),X0),
inference(cnf_transformation,[status(esa)],[f40]) ).
fof(f42,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f79,plain,
! [A] :
? [B] :
( relation(B)
& function(B)
& relation_dom(B) = A
& ! [C] :
( ~ in(C,A)
| apply(B,C) = n0 ) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f80,plain,
! [A] :
( relation(sk0_9(A))
& function(sk0_9(A))
& relation_dom(sk0_9(A)) = A
& ! [C] :
( ~ in(C,A)
| apply(sk0_9(A),C) = n0 ) ),
inference(skolemization,[status(esa)],[f79]) ).
fof(f81,plain,
! [X0] : relation(sk0_9(X0)),
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f82,plain,
! [X0] : function(sk0_9(X0)),
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f83,plain,
! [X0] : relation_dom(sk0_9(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f84,plain,
! [X0,X1] :
( ~ in(X0,X1)
| apply(sk0_9(X1),X0) = n0 ),
inference(cnf_transformation,[status(esa)],[f80]) ).
fof(f85,plain,
! [A] :
? [B] :
( relation(B)
& function(B)
& relation_dom(B) = A
& ! [C] :
( ~ in(C,A)
| apply(B,C) = n1 ) ),
inference(pre_NNF_transformation,[status(esa)],[f21]) ).
fof(f86,plain,
! [A] :
( relation(sk0_10(A))
& function(sk0_10(A))
& relation_dom(sk0_10(A)) = A
& ! [C] :
( ~ in(C,A)
| apply(sk0_10(A),C) = n1 ) ),
inference(skolemization,[status(esa)],[f85]) ).
fof(f87,plain,
! [X0] : relation(sk0_10(X0)),
inference(cnf_transformation,[status(esa)],[f86]) ).
fof(f88,plain,
! [X0] : function(sk0_10(X0)),
inference(cnf_transformation,[status(esa)],[f86]) ).
fof(f89,plain,
! [X0] : relation_dom(sk0_10(X0)) = X0,
inference(cnf_transformation,[status(esa)],[f86]) ).
fof(f90,plain,
! [X0,X1] :
( ~ in(X0,X1)
| apply(sk0_10(X1),X0) = n1 ),
inference(cnf_transformation,[status(esa)],[f86]) ).
fof(f91,plain,
empty(n0),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f92,plain,
~ empty(n1),
inference(cnf_transformation,[status(esa)],[f23]) ).
fof(f93,plain,
? [A] :
( ! [B] :
( ~ relation(B)
| ~ function(B)
| ! [C] :
( ~ relation(C)
| ~ function(C)
| relation_dom(B) != A
| relation_dom(C) != A
| B = C ) )
& A != empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f25]) ).
fof(f94,plain,
( ! [B] :
( ~ relation(B)
| ~ function(B)
| ! [C] :
( ~ relation(C)
| ~ function(C)
| relation_dom(B) != sk0_11
| relation_dom(C) != sk0_11
| B = C ) )
& sk0_11 != empty_set ),
inference(skolemization,[status(esa)],[f93]) ).
fof(f95,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| ~ relation(X1)
| ~ function(X1)
| relation_dom(X0) != sk0_11
| relation_dom(X1) != sk0_11
| X0 = X1 ),
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f96,plain,
sk0_11 != empty_set,
inference(cnf_transformation,[status(esa)],[f94]) ).
fof(f99,plain,
! [A,B] :
( ~ element(A,B)
| empty(B)
| in(A,B) ),
inference(pre_NNF_transformation,[status(esa)],[f27]) ).
fof(f100,plain,
! [X0,X1] :
( ~ element(X0,X1)
| empty(X1)
| in(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f99]) ).
fof(f111,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f31]) ).
fof(f112,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f111]) ).
fof(f253,plain,
n0 = empty_set,
inference(resolution,[status(thm)],[f91,f112]) ).
fof(f275,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| ~ function(sk0_9(X1))
| relation_dom(X0) != sk0_11
| relation_dom(sk0_9(X1)) != sk0_11
| X0 = sk0_9(X1) ),
inference(resolution,[status(thm)],[f81,f95]) ).
fof(f277,plain,
! [X0,X1] :
( ~ relation(X0)
| ~ function(X0)
| relation_dom(X0) != sk0_11
| relation_dom(sk0_9(X1)) != sk0_11
| X0 = sk0_9(X1) ),
inference(backward_subsumption_resolution,[status(thm)],[f275,f82]) ).
fof(f296,plain,
! [X0,X1] :
( ~ relation(sk0_10(X0))
| relation_dom(sk0_10(X0)) != sk0_11
| relation_dom(sk0_9(X1)) != sk0_11
| sk0_10(X0) = sk0_9(X1) ),
inference(resolution,[status(thm)],[f88,f277]) ).
fof(f297,plain,
! [X0,X1] :
( relation_dom(sk0_10(X0)) != sk0_11
| relation_dom(sk0_9(X1)) != sk0_11
| sk0_10(X0) = sk0_9(X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f296,f87]) ).
fof(f314,plain,
! [X0,X1] :
( relation_dom(sk0_10(X0)) != sk0_11
| X1 != sk0_11
| sk0_10(X0) = sk0_9(X1) ),
inference(backward_demodulation,[status(thm)],[f83,f297]) ).
fof(f315,plain,
! [X0] :
( relation_dom(sk0_10(X0)) != sk0_11
| sk0_10(X0) = sk0_9(sk0_11) ),
inference(destructive_equality_resolution,[status(esa)],[f314]) ).
fof(f372,plain,
! [X0] :
( X0 != sk0_11
| sk0_10(X0) = sk0_9(sk0_11) ),
inference(backward_demodulation,[status(thm)],[f89,f315]) ).
fof(f373,plain,
sk0_10(sk0_11) = sk0_9(sk0_11),
inference(destructive_equality_resolution,[status(esa)],[f372]) ).
fof(f433,plain,
! [X0,X1] :
( ~ in(X0,X1)
| apply(sk0_9(X1),X0) = empty_set ),
inference(forward_demodulation,[status(thm)],[f253,f84]) ).
fof(f438,plain,
! [X0] :
( empty(X0)
| in(sk0_0(X0),X0) ),
inference(resolution,[status(thm)],[f100,f41]) ).
fof(f444,plain,
! [X0] :
( empty(X0)
| apply(sk0_10(X0),sk0_0(X0)) = n1 ),
inference(resolution,[status(thm)],[f438,f90]) ).
fof(f445,plain,
! [X0] :
( empty(X0)
| apply(sk0_9(X0),sk0_0(X0)) = empty_set ),
inference(resolution,[status(thm)],[f438,f433]) ).
fof(f541,plain,
( spl0_48
<=> empty(sk0_11) ),
introduced(split_symbol_definition) ).
fof(f542,plain,
( empty(sk0_11)
| ~ spl0_48 ),
inference(component_clause,[status(thm)],[f541]) ).
fof(f543,plain,
( ~ empty(sk0_11)
| spl0_48 ),
inference(component_clause,[status(thm)],[f541]) ).
fof(f544,plain,
( spl0_49
<=> apply(sk0_9(sk0_11),sk0_0(sk0_11)) = n1 ),
introduced(split_symbol_definition) ).
fof(f545,plain,
( apply(sk0_9(sk0_11),sk0_0(sk0_11)) = n1
| ~ spl0_49 ),
inference(component_clause,[status(thm)],[f544]) ).
fof(f547,plain,
( empty(sk0_11)
| apply(sk0_9(sk0_11),sk0_0(sk0_11)) = n1 ),
inference(paramodulation,[status(thm)],[f373,f444]) ).
fof(f548,plain,
( spl0_48
| spl0_49 ),
inference(split_clause,[status(thm)],[f547,f541,f544]) ).
fof(f617,plain,
( sk0_11 = empty_set
| ~ spl0_48 ),
inference(resolution,[status(thm)],[f542,f112]) ).
fof(f618,plain,
( $false
| ~ spl0_48 ),
inference(forward_subsumption_resolution,[status(thm)],[f617,f96]) ).
fof(f619,plain,
~ spl0_48,
inference(contradiction_clause,[status(thm)],[f618]) ).
fof(f621,plain,
( apply(sk0_9(sk0_11),sk0_0(sk0_11)) = empty_set
| spl0_48 ),
inference(resolution,[status(thm)],[f543,f445]) ).
fof(f627,plain,
( n1 = empty_set
| ~ spl0_49
| spl0_48 ),
inference(forward_demodulation,[status(thm)],[f545,f621]) ).
fof(f635,plain,
( ~ empty(empty_set)
| ~ spl0_49
| spl0_48 ),
inference(backward_demodulation,[status(thm)],[f627,f92]) ).
fof(f636,plain,
( $false
| ~ spl0_49
| spl0_48 ),
inference(forward_subsumption_resolution,[status(thm)],[f635,f42]) ).
fof(f637,plain,
( ~ spl0_49
| spl0_48 ),
inference(contradiction_clause,[status(thm)],[f636]) ).
fof(f638,plain,
$false,
inference(sat_refutation,[status(thm)],[f548,f619,f637]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SET994+1 : TPTP v8.1.2. Released v3.2.0.
% 0.10/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.32 % Computer : n014.cluster.edu
% 0.11/0.32 % Model : x86_64 x86_64
% 0.11/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.32 % Memory : 8042.1875MB
% 0.11/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.32 % CPULimit : 300
% 0.11/0.32 % WCLimit : 300
% 0.11/0.32 % DateTime : Mon Apr 29 21:22:19 EDT 2024
% 0.11/0.32 % CPUTime :
% 0.17/0.33 % Drodi V3.6.0
% 0.17/0.36 % Refutation found
% 0.17/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.37 % Elapsed time: 0.045248 seconds
% 0.17/0.37 % CPU time: 0.254076 seconds
% 0.17/0.37 % Total memory used: 56.309 MB
% 0.17/0.37 % Net memory used: 55.992 MB
%------------------------------------------------------------------------------