TSTP Solution File: KLE150+2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE150+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n023.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 12:15:55 EDT 2023
% Result : Theorem 2.30s 0.77s
% Output : CNFRefutation 2.30s
% Verified :
% SZS Type : Refutation
% Derivation depth : 8
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 17 unt; 0 def)
% Number of atoms : 59 ( 19 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 43 ( 20 ~; 16 |; 4 &)
% ( 3 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 6 ( 2 avg)
% Number of predicates : 5 ( 3 usr; 3 prp; 0-2 aty)
% Number of functors : 7 ( 7 usr; 4 con; 0-2 aty)
% Number of variables : 36 (; 33 !; 3 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
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] :
( leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))
& leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0] :
( leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))
& leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))) ),
inference(negated_conjecture,[status(cth)],[f19]) ).
fof(f21,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f24,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f25,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f30,plain,
! [X0] : multiplication(zero,X0) = zero,
inference(cnf_transformation,[status(esa)],[f10]) ).
fof(f37,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[status(esa)],[f15]) ).
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(f44,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f42]) ).
fof(f45,plain,
? [X0] :
( ~ leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))
| ~ leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f46,plain,
( ? [X0] : ~ leq(strong_iteration(multiplication(X0,zero)),addition(one,multiplication(X0,zero)))
| ? [X0] : ~ leq(addition(one,multiplication(X0,zero)),strong_iteration(multiplication(X0,zero))) ),
inference(miniscoping,[status(esa)],[f45]) ).
fof(f47,plain,
( ~ leq(strong_iteration(multiplication(sk0_0,zero)),addition(one,multiplication(sk0_0,zero)))
| ~ leq(addition(one,multiplication(sk0_1,zero)),strong_iteration(multiplication(sk0_1,zero))) ),
inference(skolemization,[status(esa)],[f46]) ).
fof(f48,plain,
( ~ leq(strong_iteration(multiplication(sk0_0,zero)),addition(one,multiplication(sk0_0,zero)))
| ~ leq(addition(one,multiplication(sk0_1,zero)),strong_iteration(multiplication(sk0_1,zero))) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
( spl0_0
<=> leq(strong_iteration(multiplication(sk0_0,zero)),addition(one,multiplication(sk0_0,zero))) ),
introduced(split_symbol_definition) ).
fof(f51,plain,
( ~ leq(strong_iteration(multiplication(sk0_0,zero)),addition(one,multiplication(sk0_0,zero)))
| spl0_0 ),
inference(component_clause,[status(thm)],[f49]) ).
fof(f52,plain,
( spl0_1
<=> leq(addition(one,multiplication(sk0_1,zero)),strong_iteration(multiplication(sk0_1,zero))) ),
introduced(split_symbol_definition) ).
fof(f54,plain,
( ~ leq(addition(one,multiplication(sk0_1,zero)),strong_iteration(multiplication(sk0_1,zero)))
| spl0_1 ),
inference(component_clause,[status(thm)],[f52]) ).
fof(f55,plain,
( ~ spl0_0
| ~ spl0_1 ),
inference(split_clause,[status(thm)],[f48,f49,f52]) ).
fof(f56,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(forward_demodulation,[status(thm)],[f21,f37]) ).
fof(f66,plain,
! [X0] : leq(X0,X0),
inference(resolution,[status(thm)],[f44,f24]) ).
fof(f148,plain,
! [X0,X1] : strong_iteration(multiplication(X0,X1)) = addition(one,multiplication(X0,multiplication(X1,strong_iteration(multiplication(X0,X1))))),
inference(paramodulation,[status(thm)],[f25,f56]) ).
fof(f4002,plain,
! [X0] : strong_iteration(multiplication(X0,zero)) = addition(one,multiplication(X0,zero)),
inference(paramodulation,[status(thm)],[f30,f148]) ).
fof(f4093,plain,
( ~ leq(strong_iteration(multiplication(sk0_0,zero)),strong_iteration(multiplication(sk0_0,zero)))
| spl0_0 ),
inference(backward_demodulation,[status(thm)],[f4002,f51]) ).
fof(f4094,plain,
( $false
| spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f4093,f66]) ).
fof(f4095,plain,
spl0_0,
inference(contradiction_clause,[status(thm)],[f4094]) ).
fof(f4096,plain,
( ~ leq(strong_iteration(multiplication(sk0_1,zero)),strong_iteration(multiplication(sk0_1,zero)))
| spl0_1 ),
inference(forward_demodulation,[status(thm)],[f4002,f54]) ).
fof(f4097,plain,
( $false
| spl0_1 ),
inference(forward_subsumption_resolution,[status(thm)],[f4096,f66]) ).
fof(f4098,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f4097]) ).
fof(f4099,plain,
$false,
inference(sat_refutation,[status(thm)],[f55,f4095,f4098]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.09 % Problem : KLE150+2 : TPTP v8.1.2. Released v4.0.0.
% 0.04/0.10 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.30 % Computer : n023.cluster.edu
% 0.09/0.30 % Model : x86_64 x86_64
% 0.09/0.30 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.30 % Memory : 8042.1875MB
% 0.09/0.30 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.30 % CPULimit : 300
% 0.09/0.30 % WCLimit : 300
% 0.09/0.30 % DateTime : Tue May 30 12:04:23 EDT 2023
% 0.09/0.30 % CPUTime :
% 0.09/0.31 % Drodi V3.5.1
% 2.30/0.77 % Refutation found
% 2.30/0.77 % SZS status Theorem for theBenchmark: Theorem is valid
% 2.30/0.77 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.30/0.79 % Elapsed time: 0.482317 seconds
% 2.30/0.79 % CPU time: 2.593244 seconds
% 2.30/0.79 % Memory used: 68.263 MB
%------------------------------------------------------------------------------