TSTP Solution File: KLE141+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE141+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n022.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 12:15:52 EDT 2023
% Result : Theorem 0.14s 0.35s
% Output : CNFRefutation 0.14s
% Verified :
% SZS Type : Refutation
% Derivation depth : 13
% Number of leaves : 8
% Syntax : Number of formulae : 39 ( 24 unt; 0 def)
% Number of atoms : 58 ( 31 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 40 ( 21 ~; 15 |; 2 &)
% ( 1 <=>; 1 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 3 ( 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/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(f4,axiom,
! [A] : addition(A,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f6,axiom,
! [A] : multiplication(A,one) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f7,axiom,
! [A] : multiplication(one,A) = A,
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( leq(C,addition(multiplication(A,C),B))
=> leq(C,multiplication(strong_iteration(A),B)) ),
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] : multiplication(strong_iteration(one),X0) = strong_iteration(one),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0] : multiplication(strong_iteration(one),X0) = strong_iteration(one),
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(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(f27,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f38,plain,
! [A,B,C] :
( ~ leq(C,addition(multiplication(A,C),B))
| leq(C,multiplication(strong_iteration(A),B)) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ leq(X0,addition(multiplication(X1,X0),X2))
| leq(X0,multiplication(strong_iteration(X1),X2)) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
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] : multiplication(strong_iteration(one),X0) != strong_iteration(one),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f46,plain,
multiplication(strong_iteration(one),sk0_0) != strong_iteration(one),
inference(skolemization,[status(esa)],[f45]) ).
fof(f47,plain,
multiplication(strong_iteration(one),sk0_0) != strong_iteration(one),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f62,plain,
! [X0,X1] :
( ~ leq(X0,addition(X0,X1))
| leq(X0,multiplication(strong_iteration(one),X1)) ),
inference(paramodulation,[status(thm)],[f27,f39]) ).
fof(f85,plain,
! [X0] :
( ~ leq(X0,addition(X0,one))
| leq(X0,strong_iteration(one)) ),
inference(paramodulation,[status(thm)],[f26,f62]) ).
fof(f308,plain,
! [X0] :
( addition(X0,addition(X0,one)) != addition(X0,one)
| leq(X0,strong_iteration(one)) ),
inference(resolution,[status(thm)],[f44,f85]) ).
fof(f309,plain,
! [X0,X1] :
( addition(X0,addition(X0,X1)) != addition(X0,X1)
| leq(X0,multiplication(strong_iteration(one),X1)) ),
inference(resolution,[status(thm)],[f44,f62]) ).
fof(f386,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f395,plain,
! [X0] :
( addition(X0,one) != addition(X0,one)
| leq(X0,strong_iteration(one)) ),
inference(backward_demodulation,[status(thm)],[f386,f308]) ).
fof(f396,plain,
! [X0] : leq(X0,strong_iteration(one)),
inference(trivial_equality_resolution,[status(esa)],[f395]) ).
fof(f397,plain,
! [X0,X1] :
( addition(X0,X1) != addition(X0,X1)
| leq(X0,multiplication(strong_iteration(one),X1)) ),
inference(backward_demodulation,[status(thm)],[f386,f309]) ).
fof(f398,plain,
! [X0,X1] : leq(X0,multiplication(strong_iteration(one),X1)),
inference(trivial_equality_resolution,[status(esa)],[f397]) ).
fof(f465,plain,
! [X0] : addition(X0,strong_iteration(one)) = strong_iteration(one),
inference(resolution,[status(thm)],[f396,f43]) ).
fof(f493,plain,
! [X0] : addition(strong_iteration(one),X0) = strong_iteration(one),
inference(paramodulation,[status(thm)],[f21,f465]) ).
fof(f559,plain,
! [X0] :
( ~ leq(strong_iteration(one),X0)
| strong_iteration(one) = X0 ),
inference(paramodulation,[status(thm)],[f493,f43]) ).
fof(f575,plain,
! [X0] : strong_iteration(one) = multiplication(strong_iteration(one),X0),
inference(resolution,[status(thm)],[f559,f398]) ).
fof(f581,plain,
~ leq(strong_iteration(one),multiplication(strong_iteration(one),sk0_0)),
inference(resolution,[status(thm)],[f559,f47]) ).
fof(f582,plain,
~ leq(strong_iteration(one),strong_iteration(one)),
inference(forward_demodulation,[status(thm)],[f575,f581]) ).
fof(f583,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f582,f396]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.09 % Problem : KLE141+1 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.09 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.09/0.29 % Computer : n022.cluster.edu
% 0.09/0.29 % Model : x86_64 x86_64
% 0.09/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.29 % Memory : 8042.1875MB
% 0.09/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.09/0.29 % CPULimit : 300
% 0.09/0.29 % WCLimit : 300
% 0.09/0.29 % DateTime : Tue May 30 11:45:57 EDT 2023
% 0.09/0.29 % CPUTime :
% 0.09/0.30 % Drodi V3.5.1
% 0.14/0.35 % Refutation found
% 0.14/0.35 % SZS status Theorem for theBenchmark: Theorem is valid
% 0.14/0.35 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.14/0.37 % Elapsed time: 0.073019 seconds
% 0.14/0.37 % CPU time: 0.177609 seconds
% 0.14/0.37 % Memory used: 23.350 MB
%------------------------------------------------------------------------------