TSTP Solution File: NUM016-2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : NUM016-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n006.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 12:24:20 EDT 2023
% Result : Unsatisfiable 0.12s 0.35s
% Output : CNFRefutation 0.12s
% Verified :
% SZS Type : Refutation
% Derivation depth : 6
% Number of leaves : 14
% Syntax : Number of formulae : 48 ( 7 unt; 0 def)
% Number of atoms : 100 ( 0 equ)
% Maximal formula atoms : 3 ( 2 avg)
% Number of connectives : 88 ( 36 ~; 46 |; 0 &)
% ( 6 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 5 ( 3 avg)
% Maximal term depth : 3 ( 1 avg)
% Number of predicates : 10 ( 9 usr; 7 prp; 0-2 aty)
% Number of functors : 3 ( 3 usr; 1 con; 0-1 aty)
% Number of variables : 24 (; 24 !; 0 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [X] : ~ less(X,X),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [X,Y] :
( ~ less(X,Y)
| ~ less(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [X] : less(X,factorial_plus_one(X)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [X,Y] :
( ~ divides(X,factorial_plus_one(Y))
| less(Y,X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [X] :
( prime(X)
| divides(prime_divisor(X),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [X] :
( prime(X)
| prime(prime_divisor(X)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [X] :
( prime(X)
| less(prime_divisor(X),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,negated_conjecture,
! [X] :
( ~ prime(X)
| ~ less(a,X)
| less(factorial_plus_one(a),X) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f9,plain,
! [X0] : ~ less(X0,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f10,plain,
! [X0,X1] :
( ~ less(X0,X1)
| ~ less(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f11,plain,
! [X0] : less(X0,factorial_plus_one(X0)),
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f12,plain,
! [X0,X1] :
( ~ divides(X0,factorial_plus_one(X1))
| less(X1,X0) ),
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f13,plain,
! [X0] :
( prime(X0)
| divides(prime_divisor(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f14,plain,
! [X0] :
( prime(X0)
| prime(prime_divisor(X0)) ),
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f15,plain,
! [X0] :
( prime(X0)
| less(prime_divisor(X0),X0) ),
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f16,plain,
! [X0] :
( ~ prime(X0)
| ~ less(a,X0)
| less(factorial_plus_one(a),X0) ),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f18,plain,
! [X0] :
( prime(X0)
| ~ less(a,prime_divisor(X0))
| less(factorial_plus_one(a),prime_divisor(X0)) ),
inference(resolution,[status(thm)],[f14,f16]) ).
fof(f19,plain,
! [X0] :
( divides(prime_divisor(X0),X0)
| ~ less(a,X0)
| less(factorial_plus_one(a),X0) ),
inference(resolution,[status(thm)],[f13,f16]) ).
fof(f20,plain,
! [X0] :
( ~ less(a,factorial_plus_one(X0))
| less(factorial_plus_one(a),factorial_plus_one(X0))
| less(X0,prime_divisor(factorial_plus_one(X0))) ),
inference(resolution,[status(thm)],[f19,f12]) ).
fof(f21,plain,
( spl0_0
<=> less(factorial_plus_one(a),factorial_plus_one(a)) ),
introduced(split_symbol_definition) ).
fof(f22,plain,
( less(factorial_plus_one(a),factorial_plus_one(a))
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f21]) ).
fof(f24,plain,
( spl0_1
<=> less(a,prime_divisor(factorial_plus_one(a))) ),
introduced(split_symbol_definition) ).
fof(f25,plain,
( less(a,prime_divisor(factorial_plus_one(a)))
| ~ spl0_1 ),
inference(component_clause,[status(thm)],[f24]) ).
fof(f27,plain,
( less(factorial_plus_one(a),factorial_plus_one(a))
| less(a,prime_divisor(factorial_plus_one(a))) ),
inference(resolution,[status(thm)],[f20,f11]) ).
fof(f28,plain,
( spl0_0
| spl0_1 ),
inference(split_clause,[status(thm)],[f27,f21,f24]) ).
fof(f29,plain,
( $false
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f22,f9]) ).
fof(f30,plain,
~ spl0_0,
inference(contradiction_clause,[status(thm)],[f29]) ).
fof(f31,plain,
! [X0] :
( less(prime_divisor(X0),X0)
| ~ less(a,X0)
| less(factorial_plus_one(a),X0) ),
inference(resolution,[status(thm)],[f15,f16]) ).
fof(f32,plain,
( spl0_2
<=> less(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a)) ),
introduced(split_symbol_definition) ).
fof(f33,plain,
( less(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a))
| ~ spl0_2 ),
inference(component_clause,[status(thm)],[f32]) ).
fof(f35,plain,
( less(prime_divisor(factorial_plus_one(a)),factorial_plus_one(a))
| less(factorial_plus_one(a),factorial_plus_one(a)) ),
inference(resolution,[status(thm)],[f31,f11]) ).
fof(f36,plain,
( spl0_2
| spl0_0 ),
inference(split_clause,[status(thm)],[f35,f32,f21]) ).
fof(f37,plain,
( spl0_3
<=> prime(factorial_plus_one(a)) ),
introduced(split_symbol_definition) ).
fof(f38,plain,
( prime(factorial_plus_one(a))
| ~ spl0_3 ),
inference(component_clause,[status(thm)],[f37]) ).
fof(f40,plain,
( spl0_4
<=> less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a))) ),
introduced(split_symbol_definition) ).
fof(f41,plain,
( less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
| ~ spl0_4 ),
inference(component_clause,[status(thm)],[f40]) ).
fof(f43,plain,
( prime(factorial_plus_one(a))
| less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
| ~ spl0_1 ),
inference(resolution,[status(thm)],[f25,f18]) ).
fof(f44,plain,
( spl0_3
| spl0_4
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f43,f37,f40,f24]) ).
fof(f51,plain,
( ~ less(factorial_plus_one(a),prime_divisor(factorial_plus_one(a)))
| ~ spl0_2 ),
inference(resolution,[status(thm)],[f33,f10]) ).
fof(f52,plain,
( $false
| ~ spl0_4
| ~ spl0_2 ),
inference(forward_subsumption_resolution,[status(thm)],[f51,f41]) ).
fof(f53,plain,
( ~ spl0_4
| ~ spl0_2 ),
inference(contradiction_clause,[status(thm)],[f52]) ).
fof(f54,plain,
( spl0_6
<=> less(a,factorial_plus_one(a)) ),
introduced(split_symbol_definition) ).
fof(f56,plain,
( ~ less(a,factorial_plus_one(a))
| spl0_6 ),
inference(component_clause,[status(thm)],[f54]) ).
fof(f57,plain,
( ~ less(a,factorial_plus_one(a))
| less(factorial_plus_one(a),factorial_plus_one(a))
| ~ spl0_3 ),
inference(resolution,[status(thm)],[f38,f16]) ).
fof(f58,plain,
( ~ spl0_6
| spl0_0
| ~ spl0_3 ),
inference(split_clause,[status(thm)],[f57,f54,f21,f37]) ).
fof(f59,plain,
( $false
| spl0_6 ),
inference(forward_subsumption_resolution,[status(thm)],[f56,f11]) ).
fof(f60,plain,
spl0_6,
inference(contradiction_clause,[status(thm)],[f59]) ).
fof(f61,plain,
$false,
inference(sat_refutation,[status(thm)],[f28,f30,f36,f44,f53,f58,f60]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12 % Problem : NUM016-2 : TPTP v8.1.2. Released v1.0.0.
% 0.04/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n006.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 09:51:47 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 0.12/0.35 % Refutation found
% 0.12/0.35 % SZS status Unsatisfiable for theBenchmark: Theory is unsatisfiable
% 0.12/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.27/0.57 % Elapsed time: 0.017994 seconds
% 0.27/0.57 % CPU time: 0.029010 seconds
% 0.27/0.57 % Memory used: 1.844 MB
%------------------------------------------------------------------------------