TSTP Solution File: KLE052+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE052+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n032.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 12:15:40 EDT 2023
% Result : Theorem 1.44s 0.58s
% Output : CNFRefutation 1.44s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 9
% Syntax : Number of formulae : 36 ( 31 unt; 0 def)
% Number of atoms : 45 ( 32 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 20 ( 11 ~; 6 |; 2 &)
% ( 1 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 4 ( 1 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 5 ( 5 usr; 2 con; 0-2 aty)
% Number of variables : 58 (; 57 !; 1 ?)
% 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(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [X0] : addition(domain(X0),one) = one,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f18,conjecture,
! [X0] : multiplication(domain(X0),X0) = X0,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p') ).
fof(f19,negated_conjecture,
~ ! [X0] : multiplication(domain(X0),X0) = X0,
inference(negated_conjecture,[status(cth)],[f18]) ).
fof(f20,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f21,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,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f26,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f28,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f31,plain,
! [A,B] :
( ( ~ leq(A,B)
| addition(A,B) = B )
& ( leq(A,B)
| addition(A,B) != B ) ),
inference(NNF_transformation,[status(esa)],[f12]) ).
fof(f32,plain,
( ! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B )
& ! [A,B] :
( leq(A,B)
| addition(A,B) != B ) ),
inference(miniscoping,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f34,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f32]) ).
fof(f35,plain,
! [X0] : addition(X0,multiplication(domain(X0),X0)) = multiplication(domain(X0),X0),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f37,plain,
! [X0] : addition(domain(X0),one) = one,
inference(cnf_transformation,[status(esa)],[f15]) ).
fof(f40,plain,
? [X0] : multiplication(domain(X0),X0) != X0,
inference(pre_NNF_transformation,[status(esa)],[f19]) ).
fof(f41,plain,
multiplication(domain(sk0_0),sk0_0) != sk0_0,
inference(skolemization,[status(esa)],[f40]) ).
fof(f42,plain,
multiplication(domain(sk0_0),sk0_0) != sk0_0,
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f771,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f23,f21]) ).
fof(f1328,plain,
! [X0] : addition(one,domain(X0)) = one,
inference(forward_demodulation,[status(thm)],[f20,f37]) ).
fof(f2607,plain,
! [X0,X1] : leq(X0,addition(X0,X1)),
inference(resolution,[status(thm)],[f771,f34]) ).
fof(f2714,plain,
! [X0,X1] : leq(X0,addition(X1,X0)),
inference(paramodulation,[status(thm)],[f20,f2607]) ).
fof(f2722,plain,
! [X0,X1,X2] : leq(multiplication(X0,X1),multiplication(addition(X2,X0),X1)),
inference(paramodulation,[status(thm)],[f28,f2714]) ).
fof(f9183,plain,
! [X0,X1] : leq(multiplication(domain(X0),X1),multiplication(one,X1)),
inference(paramodulation,[status(thm)],[f1328,f2722]) ).
fof(f9184,plain,
! [X0,X1] : leq(multiplication(domain(X0),X1),X1),
inference(forward_demodulation,[status(thm)],[f26,f9183]) ).
fof(f9229,plain,
! [X0,X1] : addition(multiplication(domain(X0),X1),X1) = X1,
inference(resolution,[status(thm)],[f9184,f33]) ).
fof(f9230,plain,
! [X0,X1] : addition(X0,multiplication(domain(X1),X0)) = X0,
inference(forward_demodulation,[status(thm)],[f20,f9229]) ).
fof(f9272,plain,
! [X0] : X0 = multiplication(domain(X0),X0),
inference(backward_demodulation,[status(thm)],[f9230,f35]) ).
fof(f9465,plain,
sk0_0 != sk0_0,
inference(backward_demodulation,[status(thm)],[f9272,f42]) ).
fof(f9466,plain,
$false,
inference(trivial_equality_resolution,[status(esa)],[f9465]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.02/0.12 % Problem : KLE052+1 : TPTP v8.1.2. Released v4.0.0.
% 0.02/0.12 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.33 % Computer : n032.cluster.edu
% 0.09/0.33 % Model : x86_64 x86_64
% 0.09/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.33 % Memory : 8042.1875MB
% 0.09/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.33 % CPULimit : 300
% 0.09/0.33 % WCLimit : 300
% 0.09/0.33 % DateTime : Tue May 30 11:48:31 EDT 2023
% 0.09/0.33 % CPUTime :
% 0.09/0.33 % Drodi V3.5.1
% 1.44/0.58 % Refutation found
% 1.44/0.58 % SZS status Theorem for theBenchmark: Theorem is valid
% 1.44/0.58 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 1.44/0.62 % Elapsed time: 0.274508 seconds
% 1.44/0.62 % CPU time: 1.791390 seconds
% 1.44/0.62 % Memory used: 74.599 MB
%------------------------------------------------------------------------------