TSTP Solution File: KLE167+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE167+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n013.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 12:15:58 EDT 2023
% Result : Theorem 0.17s 0.47s
% Output : CNFRefutation 0.17s
% Verified :
% SZS Type : Refutation
% Derivation depth : 11
% Number of leaves : 17
% Syntax : Number of formulae : 71 ( 30 unt; 0 def)
% Number of atoms : 124 ( 32 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 88 ( 35 ~; 35 |; 7 &)
% ( 8 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 10 ( 8 usr; 8 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 73 (; 67 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f11,axiom,
! [A] : addition(one,multiplication(A,star(A))) = star(A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f14,axiom,
! [A,B,C] :
( leq(addition(multiplication(C,A),B),C)
=> leq(multiplication(B,star(A)),C) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0,X1] :
( ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,star(X1)),X0) )
& leq(X0,multiplication(X0,star(X1))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,star(X1)),X0) )
& leq(X0,multiplication(X0,star(X1))) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f22,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f23,plain,
! [X0] : addition(X0,zero) = X0,
inference(cnf_transformation,[status(esa)],[f3]) ).
fof(f24,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f26,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f31,plain,
! [X0] : addition(one,multiplication(X0,star(X0))) = star(X0),
inference(cnf_transformation,[status(esa)],[f11]) ).
fof(f35,plain,
! [A,B,C] :
( ~ leq(addition(multiplication(C,A),B),C)
| leq(multiplication(B,star(A)),C) ),
inference(pre_NNF_transformation,[status(esa)],[f14]) ).
fof(f36,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(cnf_transformation,[status(esa)],[f35]) ).
fof(f41,plain,
! [A,B] :
( ( ~ leq(A,B)
| addition(A,B) = B )
& ( leq(A,B)
| addition(A,B) != B ) ),
inference(NNF_transformation,[status(esa)],[f18]) ).
fof(f42,plain,
( ! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B )
& ! [A,B] :
( leq(A,B)
| addition(A,B) != B ) ),
inference(miniscoping,[status(esa)],[f41]) ).
fof(f43,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f44,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f45,plain,
? [X0,X1] :
( ( multiplication(X0,X1) = zero
& ~ leq(multiplication(X0,star(X1)),X0) )
| ~ leq(X0,multiplication(X0,star(X1))) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f46,plain,
( ? [X0,X1] :
( multiplication(X0,X1) = zero
& ~ leq(multiplication(X0,star(X1)),X0) )
| ? [X0,X1] : ~ leq(X0,multiplication(X0,star(X1))) ),
inference(miniscoping,[status(esa)],[f45]) ).
fof(f47,plain,
( ( multiplication(sk0_0,sk0_1) = zero
& ~ leq(multiplication(sk0_0,star(sk0_1)),sk0_0) )
| ~ leq(sk0_2,multiplication(sk0_2,star(sk0_3))) ),
inference(skolemization,[status(esa)],[f46]) ).
fof(f48,plain,
( multiplication(sk0_0,sk0_1) = zero
| ~ leq(sk0_2,multiplication(sk0_2,star(sk0_3))) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
( ~ leq(multiplication(sk0_0,star(sk0_1)),sk0_0)
| ~ leq(sk0_2,multiplication(sk0_2,star(sk0_3))) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f50,plain,
( spl0_0
<=> multiplication(sk0_0,sk0_1) = zero ),
introduced(split_symbol_definition) ).
fof(f51,plain,
( multiplication(sk0_0,sk0_1) = zero
| ~ spl0_0 ),
inference(component_clause,[status(thm)],[f50]) ).
fof(f53,plain,
( spl0_1
<=> leq(sk0_2,multiplication(sk0_2,star(sk0_3))) ),
introduced(split_symbol_definition) ).
fof(f55,plain,
( ~ leq(sk0_2,multiplication(sk0_2,star(sk0_3)))
| spl0_1 ),
inference(component_clause,[status(thm)],[f53]) ).
fof(f56,plain,
( spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f48,f50,f53]) ).
fof(f57,plain,
( spl0_2
<=> leq(multiplication(sk0_0,star(sk0_1)),sk0_0) ),
introduced(split_symbol_definition) ).
fof(f59,plain,
( ~ leq(multiplication(sk0_0,star(sk0_1)),sk0_0)
| spl0_2 ),
inference(component_clause,[status(thm)],[f57]) ).
fof(f60,plain,
( ~ spl0_2
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f49,f57,f53]) ).
fof(f103,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f24,f44]) ).
fof(f121,plain,
! [X0] : X0 = addition(zero,X0),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f131,plain,
! [X0] : leq(zero,X0),
inference(resolution,[status(thm)],[f121,f44]) ).
fof(f167,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f465,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f167,f44]) ).
fof(f503,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(X0,addition(X1,X2))),
inference(paramodulation,[status(thm)],[f28,f465]) ).
fof(f578,plain,
! [X0] : leq(one,star(X0)),
inference(paramodulation,[status(thm)],[f31,f465]) ).
fof(f649,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(resolution,[status(thm)],[f578,f43]) ).
fof(f2245,plain,
! [X0,X1] : leq(multiplication(X0,one),multiplication(X0,star(X1))),
inference(paramodulation,[status(thm)],[f649,f503]) ).
fof(f2246,plain,
! [X0,X1] : leq(X0,multiplication(X0,star(X1))),
inference(forward_demodulation,[status(thm)],[f26,f2245]) ).
fof(f2275,plain,
( $false
| spl0_1 ),
inference(backward_subsumption_resolution,[status(thm)],[f55,f2246]) ).
fof(f2276,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f2275]) ).
fof(f2293,plain,
( spl0_34
<=> leq(zero,sk0_1) ),
introduced(split_symbol_definition) ).
fof(f2295,plain,
( ~ leq(zero,sk0_1)
| spl0_34 ),
inference(component_clause,[status(thm)],[f2293]) ).
fof(f2301,plain,
( spl0_36
<=> leq(zero,sk0_0) ),
introduced(split_symbol_definition) ).
fof(f2303,plain,
( ~ leq(zero,sk0_0)
| spl0_36 ),
inference(component_clause,[status(thm)],[f2301]) ).
fof(f2321,plain,
! [X0] :
( ~ leq(addition(zero,X0),sk0_0)
| leq(multiplication(X0,star(sk0_1)),sk0_0)
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f51,f36]) ).
fof(f2322,plain,
! [X0] :
( ~ leq(X0,sk0_0)
| leq(multiplication(X0,star(sk0_1)),sk0_0)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f121,f2321]) ).
fof(f2332,plain,
( $false
| spl0_36 ),
inference(forward_subsumption_resolution,[status(thm)],[f2303,f131]) ).
fof(f2333,plain,
spl0_36,
inference(contradiction_clause,[status(thm)],[f2332]) ).
fof(f2334,plain,
( $false
| spl0_34 ),
inference(forward_subsumption_resolution,[status(thm)],[f2295,f131]) ).
fof(f2335,plain,
spl0_34,
inference(contradiction_clause,[status(thm)],[f2334]) ).
fof(f2808,plain,
( spl0_44
<=> leq(zero,star(sk0_0)) ),
introduced(split_symbol_definition) ).
fof(f2810,plain,
( ~ leq(zero,star(sk0_0))
| spl0_44 ),
inference(component_clause,[status(thm)],[f2808]) ).
fof(f2846,plain,
( $false
| spl0_44 ),
inference(forward_subsumption_resolution,[status(thm)],[f2810,f131]) ).
fof(f2847,plain,
spl0_44,
inference(contradiction_clause,[status(thm)],[f2846]) ).
fof(f4719,plain,
( spl0_48
<=> leq(zero,star(star(sk0_0))) ),
introduced(split_symbol_definition) ).
fof(f4721,plain,
( ~ leq(zero,star(star(sk0_0)))
| spl0_48 ),
inference(component_clause,[status(thm)],[f4719]) ).
fof(f4757,plain,
( $false
| spl0_48 ),
inference(forward_subsumption_resolution,[status(thm)],[f4721,f131]) ).
fof(f4758,plain,
spl0_48,
inference(contradiction_clause,[status(thm)],[f4757]) ).
fof(f4769,plain,
( leq(multiplication(sk0_0,star(sk0_1)),sk0_0)
| ~ spl0_0 ),
inference(resolution,[status(thm)],[f2322,f103]) ).
fof(f4770,plain,
( $false
| spl0_2
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f4769,f59]) ).
fof(f4771,plain,
( spl0_2
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f4770]) ).
fof(f4772,plain,
$false,
inference(sat_refutation,[status(thm)],[f56,f60,f2276,f2333,f2335,f2847,f4758,f4771]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.10/0.13 % Problem : KLE167+1 : TPTP v8.1.2. Released v4.0.0.
% 0.10/0.14 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.11/0.34 % Computer : n013.cluster.edu
% 0.11/0.34 % Model : x86_64 x86_64
% 0.11/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.34 % Memory : 8042.1875MB
% 0.11/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.34 % CPULimit : 300
% 0.11/0.34 % WCLimit : 300
% 0.11/0.34 % DateTime : Tue May 30 11:42:50 EDT 2023
% 0.17/0.34 % CPUTime :
% 0.17/0.35 % Drodi V3.5.1
% 0.17/0.47 % Refutation found
% 0.17/0.47 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.17/0.47 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.17/0.49 % Elapsed time: 0.147002 seconds
% 0.17/0.49 % CPU time: 0.756983 seconds
% 0.17/0.49 % Memory used: 48.848 MB
%------------------------------------------------------------------------------