TSTP Solution File: KLE148+2 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE148+2 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n025.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 1.89s 0.63s
% Output : CNFRefutation 1.89s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 14
% Syntax : Number of formulae : 59 ( 26 unt; 0 def)
% Number of atoms : 102 ( 49 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 77 ( 34 ~; 30 |; 7 &)
% ( 4 <=>; 2 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 2 avg)
% Number of predicates : 6 ( 4 usr; 4 prp; 0-2 aty)
% Number of functors : 9 ( 9 usr; 6 con; 0-2 aty)
% Number of variables : 67 (; 61 !; 6 ?)
% Comments :
%------------------------------------------------------------------------------
fof(f1,axiom,
! [A,B] : addition(A,B) = addition(B,A),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f2,axiom,
! [C,B,A] : addition(A,addition(B,C)) = addition(addition(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f3,axiom,
! [A] : addition(A,zero) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f5,axiom,
! [A,B,C] : multiplication(A,multiplication(B,C)) = multiplication(multiplication(A,B),C),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f8,axiom,
! [A,B,C] : multiplication(A,addition(B,C)) = addition(multiplication(A,B),multiplication(A,C)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f10,axiom,
! [A] : multiplication(zero,A) = zero,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A] : strong_iteration(A) = addition(multiplication(A,strong_iteration(A)),one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f19,conjecture,
! [X0,X1] :
( ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,strong_iteration(X1)),X0) )
& leq(X0,multiplication(X0,strong_iteration(X1))) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( ( multiplication(X0,X1) = zero
=> leq(multiplication(X0,strong_iteration(X1)),X0) )
& leq(X0,multiplication(X0,strong_iteration(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(f25,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f5]) ).
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(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,X1] :
( ( multiplication(X0,X1) = zero
& ~ leq(multiplication(X0,strong_iteration(X1)),X0) )
| ~ leq(X0,multiplication(X0,strong_iteration(X1))) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f46,plain,
( ? [X0,X1] :
( multiplication(X0,X1) = zero
& ~ leq(multiplication(X0,strong_iteration(X1)),X0) )
| ? [X0,X1] : ~ leq(X0,multiplication(X0,strong_iteration(X1))) ),
inference(miniscoping,[status(esa)],[f45]) ).
fof(f47,plain,
( ( multiplication(sk0_0,sk0_1) = zero
& ~ leq(multiplication(sk0_0,strong_iteration(sk0_1)),sk0_0) )
| ~ leq(sk0_2,multiplication(sk0_2,strong_iteration(sk0_3))) ),
inference(skolemization,[status(esa)],[f46]) ).
fof(f48,plain,
( multiplication(sk0_0,sk0_1) = zero
| ~ leq(sk0_2,multiplication(sk0_2,strong_iteration(sk0_3))) ),
inference(cnf_transformation,[status(esa)],[f47]) ).
fof(f49,plain,
( ~ leq(multiplication(sk0_0,strong_iteration(sk0_1)),sk0_0)
| ~ leq(sk0_2,multiplication(sk0_2,strong_iteration(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,strong_iteration(sk0_3))) ),
introduced(split_symbol_definition) ).
fof(f55,plain,
( ~ leq(sk0_2,multiplication(sk0_2,strong_iteration(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,strong_iteration(sk0_1)),sk0_0) ),
introduced(split_symbol_definition) ).
fof(f59,plain,
( ~ leq(multiplication(sk0_0,strong_iteration(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(f61,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(forward_demodulation,[status(thm)],[f21,f37]) ).
fof(f67,plain,
( addition(sk0_2,multiplication(sk0_2,strong_iteration(sk0_3))) != multiplication(sk0_2,strong_iteration(sk0_3))
| spl0_1 ),
inference(resolution,[status(thm)],[f44,f55]) ).
fof(f68,plain,
( addition(multiplication(sk0_0,strong_iteration(sk0_1)),sk0_0) != sk0_0
| spl0_2 ),
inference(resolution,[status(thm)],[f44,f59]) ).
fof(f69,plain,
( addition(sk0_0,multiplication(sk0_0,strong_iteration(sk0_1))) != sk0_0
| spl0_2 ),
inference(forward_demodulation,[status(thm)],[f21,f68]) ).
fof(f283,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f297,plain,
! [X0] : addition(one,strong_iteration(X0)) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f61,f283]) ).
fof(f298,plain,
! [X0] : addition(one,strong_iteration(X0)) = strong_iteration(X0),
inference(forward_demodulation,[status(thm)],[f61,f297]) ).
fof(f614,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f26,f28]) ).
fof(f2005,plain,
! [X0,X1] : multiplication(X0,strong_iteration(X1)) = addition(X0,multiplication(X0,strong_iteration(X1))),
inference(paramodulation,[status(thm)],[f298,f614]) ).
fof(f2139,plain,
( multiplication(sk0_2,strong_iteration(sk0_3)) != multiplication(sk0_2,strong_iteration(sk0_3))
| spl0_1 ),
inference(backward_demodulation,[status(thm)],[f2005,f67]) ).
fof(f2140,plain,
( $false
| spl0_1 ),
inference(trivial_equality_resolution,[status(esa)],[f2139]) ).
fof(f2141,plain,
spl0_1,
inference(contradiction_clause,[status(thm)],[f2140]) ).
fof(f2142,plain,
( multiplication(sk0_0,strong_iteration(sk0_1)) != sk0_0
| spl0_2 ),
inference(backward_demodulation,[status(thm)],[f2005,f69]) ).
fof(f2191,plain,
! [X0] :
( multiplication(sk0_0,multiplication(sk0_1,X0)) = multiplication(zero,X0)
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f51,f25]) ).
fof(f2192,plain,
! [X0] :
( multiplication(sk0_0,multiplication(sk0_1,X0)) = zero
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f30,f2191]) ).
fof(f2238,plain,
! [X0,X1] :
( multiplication(sk0_0,addition(X0,multiplication(sk0_1,X1))) = addition(multiplication(sk0_0,X0),zero)
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f2192,f28]) ).
fof(f2239,plain,
! [X0,X1] :
( multiplication(sk0_0,addition(X0,multiplication(sk0_1,X1))) = multiplication(sk0_0,X0)
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f23,f2238]) ).
fof(f2622,plain,
( multiplication(sk0_0,strong_iteration(sk0_1)) = multiplication(sk0_0,one)
| ~ spl0_0 ),
inference(paramodulation,[status(thm)],[f61,f2239]) ).
fof(f2623,plain,
( multiplication(sk0_0,strong_iteration(sk0_1)) = sk0_0
| ~ spl0_0 ),
inference(forward_demodulation,[status(thm)],[f26,f2622]) ).
fof(f2624,plain,
( $false
| spl0_2
| ~ spl0_0 ),
inference(forward_subsumption_resolution,[status(thm)],[f2623,f2142]) ).
fof(f2625,plain,
( spl0_2
| ~ spl0_0 ),
inference(contradiction_clause,[status(thm)],[f2624]) ).
fof(f2626,plain,
$false,
inference(sat_refutation,[status(thm)],[f56,f60,f2141,f2625]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : KLE148+2 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34 % Computer : n025.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
% 0.13/0.34 % DateTime : Tue May 30 11:58:42 EDT 2023
% 0.13/0.34 % CPUTime :
% 0.13/0.35 % Drodi V3.5.1
% 1.89/0.63 % Refutation found
% 1.89/0.63 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.89/0.63 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 2.33/0.66 % Elapsed time: 0.312093 seconds
% 2.33/0.66 % CPU time: 2.314864 seconds
% 2.33/0.66 % Memory used: 70.700 MB
%------------------------------------------------------------------------------