TSTP Solution File: KRS131+1 by Drodi---3.6.0
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.6.0
% Problem : KRS131+1 : TPTP v8.1.2. Released v3.1.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n021.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 20:24:51 EDT 2024
% Result : Theorem 0.12s 0.34s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 13
% Syntax : Number of formulae : 76 ( 8 unt; 0 def)
% Number of atoms : 227 ( 0 equ)
% Maximal formula atoms : 7 ( 2 avg)
% Number of connectives : 257 ( 106 ~; 102 |; 27 &)
% ( 13 <=>; 4 =>; 0 <=; 5 <~>)
% Maximal formula depth : 8 ( 4 avg)
% Maximal term depth : 2 ( 1 avg)
% Number of predicates : 16 ( 15 usr; 6 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-1 aty)
% Number of variables : 88 ( 67 !; 21 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] :
( cowlThing(X)
& ~ cowlNothing(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] :
( cA(X)
<=> ? [Y] :
( rq(X,Y)
& cowlThing(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X] :
( cNothing(X)
=> ~ ? [Y] : rp(X,Y) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] :
( cNothing(X)
=> ? [Y0] : rp(X,Y0) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] :
( cnotA(X)
<=> ! [Y] :
( rq(X,Y)
=> cNothing(Y) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,conjecture,
( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( cnotA(X)
<=> ~ cA(X) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
~ ( ! [X] :
( cowlThing(X)
& ~ cowlNothing(X) )
& ! [X] :
( xsd_string(X)
<=> ~ xsd_integer(X) )
& ! [X] :
( cnotA(X)
<=> ~ cA(X) ) ),
inference(negated_conjecture,[status(cth)],[f7]) ).
fof(f9,plain,
( ! [X] : cowlThing(X)
& ! [X] : ~ cowlNothing(X) ),
inference(miniscoping,[status(esa)],[f1]) ).
fof(f10,plain,
! [X0] : cowlThing(X0),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f11,plain,
! [X0] : ~ cowlNothing(X0),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f12,plain,
! [X] :
( ( ~ xsd_string(X)
| ~ xsd_integer(X) )
& ( xsd_string(X)
| xsd_integer(X) ) ),
inference(NNF_transformation,[status(esa)],[f2]) ).
fof(f13,plain,
( ! [X] :
( ~ xsd_string(X)
| ~ xsd_integer(X) )
& ! [X] :
( xsd_string(X)
| xsd_integer(X) ) ),
inference(miniscoping,[status(esa)],[f12]) ).
fof(f14,plain,
! [X0] :
( ~ xsd_string(X0)
| ~ xsd_integer(X0) ),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f15,plain,
! [X0] :
( xsd_string(X0)
| xsd_integer(X0) ),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f16,plain,
! [X] :
( ( ~ cA(X)
| ? [Y] :
( rq(X,Y)
& cowlThing(Y) ) )
& ( cA(X)
| ! [Y] :
( ~ rq(X,Y)
| ~ cowlThing(Y) ) ) ),
inference(NNF_transformation,[status(esa)],[f3]) ).
fof(f17,plain,
( ! [X] :
( ~ cA(X)
| ? [Y] :
( rq(X,Y)
& cowlThing(Y) ) )
& ! [X] :
( cA(X)
| ! [Y] :
( ~ rq(X,Y)
| ~ cowlThing(Y) ) ) ),
inference(miniscoping,[status(esa)],[f16]) ).
fof(f18,plain,
( ! [X] :
( ~ cA(X)
| ( rq(X,sk0_0(X))
& cowlThing(sk0_0(X)) ) )
& ! [X] :
( cA(X)
| ! [Y] :
( ~ rq(X,Y)
| ~ cowlThing(Y) ) ) ),
inference(skolemization,[status(esa)],[f17]) ).
fof(f19,plain,
! [X0] :
( ~ cA(X0)
| rq(X0,sk0_0(X0)) ),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f21,plain,
! [X0,X1] :
( cA(X0)
| ~ rq(X0,X1)
| ~ cowlThing(X1) ),
inference(cnf_transformation,[status(esa)],[f18]) ).
fof(f22,plain,
! [X] :
( ~ cNothing(X)
| ! [Y] : ~ rp(X,Y) ),
inference(pre_NNF_transformation,[status(esa)],[f4]) ).
fof(f23,plain,
! [X0,X1] :
( ~ cNothing(X0)
| ~ rp(X0,X1) ),
inference(cnf_transformation,[status(esa)],[f22]) ).
fof(f24,plain,
! [X] :
( ~ cNothing(X)
| ? [Y0] : rp(X,Y0) ),
inference(pre_NNF_transformation,[status(esa)],[f5]) ).
fof(f25,plain,
! [X] :
( ~ cNothing(X)
| rp(X,sk0_1(X)) ),
inference(skolemization,[status(esa)],[f24]) ).
fof(f26,plain,
! [X0] :
( ~ cNothing(X0)
| rp(X0,sk0_1(X0)) ),
inference(cnf_transformation,[status(esa)],[f25]) ).
fof(f27,plain,
! [X] :
( cnotA(X)
<=> ! [Y] :
( ~ rq(X,Y)
| cNothing(Y) ) ),
inference(pre_NNF_transformation,[status(esa)],[f6]) ).
fof(f28,plain,
! [X] :
( ( ~ cnotA(X)
| ! [Y] :
( ~ rq(X,Y)
| cNothing(Y) ) )
& ( cnotA(X)
| ? [Y] :
( rq(X,Y)
& ~ cNothing(Y) ) ) ),
inference(NNF_transformation,[status(esa)],[f27]) ).
fof(f29,plain,
( ! [X] :
( ~ cnotA(X)
| ! [Y] :
( ~ rq(X,Y)
| cNothing(Y) ) )
& ! [X] :
( cnotA(X)
| ? [Y] :
( rq(X,Y)
& ~ cNothing(Y) ) ) ),
inference(miniscoping,[status(esa)],[f28]) ).
fof(f30,plain,
( ! [X] :
( ~ cnotA(X)
| ! [Y] :
( ~ rq(X,Y)
| cNothing(Y) ) )
& ! [X] :
( cnotA(X)
| ( rq(X,sk0_2(X))
& ~ cNothing(sk0_2(X)) ) ) ),
inference(skolemization,[status(esa)],[f29]) ).
fof(f31,plain,
! [X0,X1] :
( ~ cnotA(X0)
| ~ rq(X0,X1)
| cNothing(X1) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f32,plain,
! [X0] :
( cnotA(X0)
| rq(X0,sk0_2(X0)) ),
inference(cnf_transformation,[status(esa)],[f30]) ).
fof(f34,plain,
( ? [X] :
( ~ cowlThing(X)
| cowlNothing(X) )
| ? [X] :
( xsd_string(X)
<~> ~ xsd_integer(X) )
| ? [X] :
( cnotA(X)
<~> ~ cA(X) ) ),
inference(pre_NNF_transformation,[status(esa)],[f8]) ).
fof(f35,plain,
! [X] :
( pd0_0(X)
=> ( xsd_string(X)
<~> ~ xsd_integer(X) ) ),
introduced(predicate_definition,[f34]) ).
fof(f36,plain,
( ? [X] :
( ~ cowlThing(X)
| cowlNothing(X) )
| ? [X] : pd0_0(X)
| ? [X] :
( cnotA(X)
<~> ~ cA(X) ) ),
inference(formula_renaming,[status(thm)],[f34,f35]) ).
fof(f37,plain,
( ? [X] :
( ~ cowlThing(X)
| cowlNothing(X) )
| ? [X] : pd0_0(X)
| ? [X] :
( ( cnotA(X)
| ~ cA(X) )
& ( ~ cnotA(X)
| cA(X) ) ) ),
inference(NNF_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
( ? [X] : ~ cowlThing(X)
| ? [X] : cowlNothing(X)
| ? [X] : pd0_0(X)
| ? [X] :
( ( cnotA(X)
| ~ cA(X) )
& ( ~ cnotA(X)
| cA(X) ) ) ),
inference(miniscoping,[status(esa)],[f37]) ).
fof(f39,plain,
( ~ cowlThing(sk0_3)
| cowlNothing(sk0_4)
| pd0_0(sk0_5)
| ( ( cnotA(sk0_6)
| ~ cA(sk0_6) )
& ( ~ cnotA(sk0_6)
| cA(sk0_6) ) ) ),
inference(skolemization,[status(esa)],[f38]) ).
fof(f40,plain,
( ~ cowlThing(sk0_3)
| cowlNothing(sk0_4)
| pd0_0(sk0_5)
| cnotA(sk0_6)
| ~ cA(sk0_6) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f41,plain,
( ~ cowlThing(sk0_3)
| cowlNothing(sk0_4)
| pd0_0(sk0_5)
| ~ cnotA(sk0_6)
| cA(sk0_6) ),
inference(cnf_transformation,[status(esa)],[f39]) ).
fof(f42,plain,
! [X] :
( ~ pd0_0(X)
| ( xsd_string(X)
<~> ~ xsd_integer(X) ) ),
inference(pre_NNF_transformation,[status(esa)],[f35]) ).
fof(f43,plain,
! [X] :
( ~ pd0_0(X)
| ( ( xsd_string(X)
| ~ xsd_integer(X) )
& ( ~ xsd_string(X)
| xsd_integer(X) ) ) ),
inference(NNF_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [X0] :
( ~ pd0_0(X0)
| xsd_string(X0)
| ~ xsd_integer(X0) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f45,plain,
! [X0] :
( ~ pd0_0(X0)
| ~ xsd_string(X0)
| xsd_integer(X0) ),
inference(cnf_transformation,[status(esa)],[f43]) ).
fof(f46,plain,
( spl0_0
<=> cowlThing(sk0_3) ),
introduced(split_symbol_definition) ).
fof(f48,plain,
( ~ cowlThing(sk0_3)
| spl0_0 ),
inference(component_clause,[status(thm)],[f46]) ).
fof(f49,plain,
( spl0_1
<=> cowlNothing(sk0_4) ),
introduced(split_symbol_definition) ).
fof(f50,plain,
( cowlNothing(sk0_4)
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( spl0_2
<=> pd0_0(sk0_5) ),
introduced(split_symbol_definition) ).
fof(f53,plain,
( pd0_0(sk0_5)
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,plain,
( spl0_3
<=> cnotA(sk0_6) ),
introduced(split_symbol_definition) ).
fof(f56,plain,
( cnotA(sk0_6)
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f57,plain,
( ~ cnotA(sk0_6)
| spl0_3 ),
inference(component_clause,[status(thm)],[f55]) ).
fof(f58,plain,
( spl0_4
<=> cA(sk0_6) ),
introduced(split_symbol_definition) ).
fof(f59,plain,
( cA(sk0_6)
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f58]) ).
fof(f61,plain,
( ~ spl0_0
| spl0_1
| spl0_2
| spl0_3
| ~ spl0_4 ),
inference(split_clause,[status(thm)],[f40,f46,f49,f52,f55,f58]) ).
fof(f62,plain,
( ~ spl0_0
| spl0_1
| spl0_2
| ~ spl0_3
| spl0_4 ),
inference(split_clause,[status(thm)],[f41,f46,f49,f52,f55,f58]) ).
fof(f63,plain,
! [X0,X1] :
( cA(X0)
| ~ rq(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f21,f10]) ).
fof(f64,plain,
! [X0] : ~ cNothing(X0),
inference(forward_subsumption_resolution,[status(thm)],[f26,f23]) ).
fof(f65,plain,
! [X0,X1] :
( ~ cnotA(X0)
| ~ rq(X0,X1) ),
inference(forward_subsumption_resolution,[status(thm)],[f31,f64]) ).
fof(f66,plain,
! [X0] :
( ~ pd0_0(X0)
| ~ xsd_integer(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f44,f14]) ).
fof(f67,plain,
! [X0] :
( ~ pd0_0(X0)
| xsd_integer(X0) ),
inference(forward_subsumption_resolution,[status(thm)],[f45,f15]) ).
fof(f68,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f48,f10]) ).
fof(f69,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f68]) ).
fof(f70,plain,
! [X0] : ~ pd0_0(X0),
inference(backward_subsumption_resolution,[status(thm)],[f66,f67]) ).
fof(f71,plain,
( $false
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f53,f70]) ).
fof(f72,plain,
~ spl0_2,
inference(contradiction_clause,[status(thm)],[f71]) ).
fof(f73,plain,
( $false
| ~ spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f50,f11]) ).
fof(f74,plain,
~ spl0_1,
inference(contradiction_clause,[status(thm)],[f73]) ).
fof(f75,plain,
! [X0] :
( cnotA(X0)
| cA(X0) ),
inference(resolution,[status(thm)],[f32,f63]) ).
fof(f76,plain,
( rq(sk0_6,sk0_0(sk0_6))
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f59,f19]) ).
fof(f77,plain,
( ~ cnotA(sk0_6)
| ~ spl0_4 ),
inference(resolution,[status(thm)],[f76,f65]) ).
fof(f78,plain,
( $false
| ~ spl0_3
| ~ spl0_4 ),
inference(forward_subsumption_resolution,[status(thm)],[f77,f56]) ).
fof(f79,plain,
( ~ spl0_3
| ~ spl0_4 ),
inference(contradiction_clause,[status(thm)],[f78]) ).
fof(f80,plain,
( cA(sk0_6)
| spl0_3 ),
inference(resolution,[status(thm)],[f57,f75]) ).
fof(f81,plain,
( spl0_4
| spl0_3 ),
inference(split_clause,[status(thm)],[f80,f58,f55]) ).
fof(f82,plain,
$false,
inference(sat_refutation,[status(thm)],[f61,f62,f69,f72,f74,f79,f81]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.12 % Problem : KRS131+1 : TPTP v8.1.2. Released v3.1.0.
% 0.09/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.33 % Computer : n021.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 : Mon Apr 29 23:28:40 EDT 2024
% 0.12/0.33 % CPUTime :
% 0.12/0.34 % Drodi V3.6.0
% 0.12/0.34 % Refutation found
% 0.12/0.34 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.12/0.34 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.12/0.35 % Elapsed time: 0.015300 seconds
% 0.12/0.35 % CPU time: 0.029021 seconds
% 0.12/0.35 % Total memory used: 1.987 MB
% 0.12/0.35 % Net memory used: 1.964 MB
%------------------------------------------------------------------------------