TSTP Solution File: SEU189+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : SEU189+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n018.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 12:36:11 EDT 2023
% Result : Theorem 0.13s 0.36s
% Output : CNFRefutation 0.13s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 15
% Syntax : Number of formulae : 66 ( 7 unt; 0 def)
% Number of atoms : 161 ( 46 equ)
% Maximal formula atoms : 5 ( 2 avg)
% Number of connectives : 161 ( 66 ~; 65 |; 12 &)
% ( 9 <=>; 8 =>; 0 <=; 1 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 11 ( 9 usr; 8 prp; 0-2 aty)
% Number of functors : 4 ( 4 usr; 2 con; 0-1 aty)
% Number of variables : 19 (; 17 !; 2 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f9,axiom,
! [A] :
( ( ~ empty(A)
& relation(A) )
=> ~ empty(relation_dom(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] :
( ( ~ empty(A)
& relation(A) )
=> ~ empty(relation_rng(A)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] :
( empty(A)
=> ( empty(relation_dom(A))
& relation(relation_dom(A)) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,axiom,
( empty(empty_set)
& relation(empty_set) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f22,axiom,
! [A] :
( empty(A)
=> A = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f23,conjecture,
! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f24,negated_conjecture,
~ ! [A] :
( relation(A)
=> ( relation_dom(A) = empty_set
<=> relation_rng(A) = empty_set ) ),
inference(negated_conjecture,[status(cth)],[f23]) ).
fof(f25,axiom,
( relation_dom(empty_set) = empty_set
& relation_rng(empty_set) = empty_set ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f26,axiom,
! [A] :
( relation(A)
=> ( ( relation_dom(A) = empty_set
| relation_rng(A) = empty_set )
=> A = empty_set ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f43,plain,
! [A] :
( empty(A)
| ~ relation(A)
| ~ empty(relation_dom(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f9]) ).
fof(f44,plain,
! [X0] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_dom(X0)) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f45,plain,
! [A] :
( empty(A)
| ~ relation(A)
| ~ empty(relation_rng(A)) ),
inference(pre_NNF_transformation,[status(esa)],[f10]) ).
fof(f46,plain,
! [X0] :
( empty(X0)
| ~ relation(X0)
| ~ empty(relation_rng(X0)) ),
inference(cnf_transformation,[status(esa)],[f45]) ).
fof(f47,plain,
! [A] :
( ~ empty(A)
| ( empty(relation_dom(A))
& relation(relation_dom(A)) ) ),
inference(pre_NNF_transformation,[status(esa)],[f11]) ).
fof(f49,plain,
! [X0] :
( ~ empty(X0)
| relation(relation_dom(X0)) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f63,plain,
empty(empty_set),
inference(cnf_transformation,[status(esa)],[f20]) ).
fof(f66,plain,
! [A] :
( ~ empty(A)
| A = empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f22]) ).
fof(f67,plain,
! [X0] :
( ~ empty(X0)
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f66]) ).
fof(f68,plain,
? [A] :
( relation(A)
& ( relation_dom(A) = empty_set
<~> relation_rng(A) = empty_set ) ),
inference(pre_NNF_transformation,[status(esa)],[f24]) ).
fof(f69,plain,
? [A] :
( relation(A)
& ( relation_dom(A) = empty_set
| relation_rng(A) = empty_set )
& ( relation_dom(A) != empty_set
| relation_rng(A) != empty_set ) ),
inference(NNF_transformation,[status(esa)],[f68]) ).
fof(f70,plain,
( relation(sk0_5)
& ( relation_dom(sk0_5) = empty_set
| relation_rng(sk0_5) = empty_set )
& ( relation_dom(sk0_5) != empty_set
| relation_rng(sk0_5) != empty_set ) ),
inference(skolemization,[status(esa)],[f69]) ).
fof(f71,plain,
relation(sk0_5),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f72,plain,
( relation_dom(sk0_5) = empty_set
| relation_rng(sk0_5) = empty_set ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f73,plain,
( relation_dom(sk0_5) != empty_set
| relation_rng(sk0_5) != empty_set ),
inference(cnf_transformation,[status(esa)],[f70]) ).
fof(f74,plain,
relation_dom(empty_set) = empty_set,
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f75,plain,
relation_rng(empty_set) = empty_set,
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f76,plain,
! [A] :
( ~ relation(A)
| ( relation_dom(A) != empty_set
& relation_rng(A) != empty_set )
| A = empty_set ),
inference(pre_NNF_transformation,[status(esa)],[f26]) ).
fof(f77,plain,
! [X0] :
( ~ relation(X0)
| relation_dom(X0) != empty_set
| X0 = empty_set ),
inference(cnf_transformation,[status(esa)],[f76]) ).
fof(f79,plain,
( spl0_0
<=> relation_dom(sk0_5) = empty_set ),
introduced(split_symbol_definition) ).
fof(f80,plain,
( relation_dom(sk0_5) = empty_set
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f81,plain,
( relation_dom(sk0_5) != empty_set
| spl0_0 ),
inference(component_clause,[status(thm)],[f79]) ).
fof(f82,plain,
( spl0_1
<=> relation_rng(sk0_5) = empty_set ),
introduced(split_symbol_definition) ).
fof(f83,plain,
( relation_rng(sk0_5) = empty_set
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f84,plain,
( relation_rng(sk0_5) != empty_set
| spl0_1 ),
inference(component_clause,[status(thm)],[f82]) ).
fof(f85,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f72,f79,f82]) ).
fof(f86,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f73,f79,f82]) ).
fof(f88,plain,
( spl0_2
<=> empty(empty_set) ),
introduced(split_symbol_definition) ).
fof(f90,plain,
( ~ empty(empty_set)
| spl0_2 ),
inference(component_clause,[status(thm)],[f88]) ).
fof(f91,plain,
( spl0_3
<=> relation(empty_set) ),
introduced(split_symbol_definition) ).
fof(f100,plain,
( ~ empty(empty_set)
| relation(empty_set) ),
inference(paramodulation,[status(thm)],[f74,f49]) ).
fof(f101,plain,
( ~ spl0_2
| spl0_3 ),
inference(split_clause,[status(thm)],[f100,f88,f91]) ).
fof(f102,plain,
( $false
| spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f90,f63]) ).
fof(f103,plain,
spl0_2,
inference(contradiction_clause,[status(thm)],[f102]) ).
fof(f110,plain,
( spl0_4
<=> empty_set = empty_set ),
introduced(split_symbol_definition) ).
fof(f119,plain,
( ~ relation(empty_set)
| empty_set = empty_set ),
inference(resolution,[status(thm)],[f77,f74]) ).
fof(f120,plain,
( ~ spl0_3
| spl0_4 ),
inference(split_clause,[status(thm)],[f119,f91,f110]) ).
fof(f142,plain,
( spl0_5
<=> relation(sk0_5) ),
introduced(split_symbol_definition) ).
fof(f144,plain,
( ~ relation(sk0_5)
| spl0_5 ),
inference(component_clause,[status(thm)],[f142]) ).
fof(f152,plain,
( spl0_7
<=> empty(sk0_5) ),
introduced(split_symbol_definition) ).
fof(f153,plain,
( empty(sk0_5)
| ~ spl0_7 ),
inference(component_clause,[status(thm)],[f152]) ).
fof(f161,plain,
( empty(sk0_5)
| ~ relation(sk0_5)
| ~ empty(empty_set)
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f80,f44]) ).
fof(f162,plain,
( spl0_7
| ~ spl0_5
| ~ spl0_2
| ~ spl0_0 ),
inference(split_clause,[status(thm)],[f161,f152,f142,f88,f79]) ).
fof(f163,plain,
( $false
| spl0_5 ),
inference(forward_subsumption_resolution,[status(thm)],[f144,f71]) ).
fof(f164,plain,
spl0_5,
inference(contradiction_clause,[status(thm)],[f163]) ).
fof(f166,plain,
( sk0_5 = empty_set
| ~ spl0_7 ),
inference(resolution,[status(thm)],[f153,f67]) ).
fof(f170,plain,
( relation_dom(empty_set) != empty_set
| ~ spl0_7
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f166,f81]) ).
fof(f171,plain,
( empty_set != empty_set
| ~ spl0_7
| spl0_0 ),
inference(forward_demodulation,[status(thm)],[f74,f170]) ).
fof(f172,plain,
( $false
| ~ spl0_7
| spl0_0 ),
inference(trivial_equality_resolution,[status(esa)],[f171]) ).
fof(f173,plain,
( ~ spl0_7
| spl0_0 ),
inference(contradiction_clause,[status(thm)],[f172]) ).
fof(f175,plain,
( relation_rng(empty_set) != empty_set
| ~ spl0_7
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f166,f84]) ).
fof(f176,plain,
( empty_set != empty_set
| ~ spl0_7
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f75,f175]) ).
fof(f177,plain,
( $false
| ~ spl0_7
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f176]) ).
fof(f178,plain,
( ~ spl0_7
| spl0_1 ),
inference(contradiction_clause,[status(thm)],[f177]) ).
fof(f183,plain,
( empty(sk0_5)
| ~ relation(sk0_5)
| ~ empty(empty_set)
| ~ spl0_1 ),
inference(paramodulation,[status(thm)],[f83,f46]) ).
fof(f184,plain,
( spl0_7
| ~ spl0_5
| ~ spl0_2
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f183,f152,f142,f88,f82]) ).
fof(f191,plain,
$false,
inference(sat_refutation,[status(thm)],[f85,f86,f101,f103,f120,f162,f164,f173,f178,f184]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13 % Problem : SEU189+1 : TPTP v8.1.2. Released v3.3.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n018.cluster.edu
% 0.13/0.34 % Model : x86_64 x86_64
% 0.13/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34 % Memory : 8042.1875MB
% 0.13/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34 % CPULimit : 300
% 0.13/0.34 % WCLimit : 300
% 0.13/0.35 % DateTime : Tue May 30 09:25:40 EDT 2023
% 0.13/0.35 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 0.13/0.36 % Refutation found
% 0.13/0.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.13/0.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.13/0.37 % Elapsed time: 0.020193 seconds
% 0.13/0.37 % CPU time: 0.034575 seconds
% 0.13/0.37 % Memory used: 14.450 MB
%------------------------------------------------------------------------------