TSTP Solution File: KLE140+1 by Drodi---3.5.1
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%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE140+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n010.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 119.03s 15.42s
% Output : CNFRefutation 120.82s
% Verified :
% SZS Type : Refutation
% Derivation depth : 10
% Number of leaves : 10
% Syntax : Number of formulae : 49 ( 35 unt; 0 def)
% Number of atoms : 67 ( 38 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 37 ( 19 ~; 10 |; 4 &)
% ( 1 <=>; 3 =>; 0 <=; 0 <~>)
% Maximal formula depth : 6 ( 3 avg)
% Maximal term depth : 5 ( 2 avg)
% Number of predicates : 3 ( 1 usr; 1 prp; 0-2 aty)
% Number of functors : 6 ( 6 usr; 3 con; 0-2 aty)
% Number of variables : 76 (; 74 !; 2 ?)
% 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(f9,axiom,
! [A,B,C] : multiplication(addition(A,B),C) = addition(multiplication(A,C),multiplication(B,C)),
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(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,X1] :
( leq(X0,X1)
=> leq(strong_iteration(X0),strong_iteration(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f20,negated_conjecture,
~ ! [X0,X1] :
( leq(X0,X1)
=> leq(strong_iteration(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(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(f29,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f37,plain,
! [X0] : strong_iteration(X0) = addition(multiplication(X0,strong_iteration(X0)),one),
inference(cnf_transformation,[status(esa)],[f15]) ).
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,X1] :
( leq(X0,X1)
& ~ leq(strong_iteration(X0),strong_iteration(X1)) ),
inference(pre_NNF_transformation,[status(esa)],[f20]) ).
fof(f46,plain,
( leq(sk0_0,sk0_1)
& ~ leq(strong_iteration(sk0_0),strong_iteration(sk0_1)) ),
inference(skolemization,[status(esa)],[f45]) ).
fof(f47,plain,
leq(sk0_0,sk0_1),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f48,plain,
~ leq(strong_iteration(sk0_0),strong_iteration(sk0_1)),
inference(cnf_transformation,[status(esa)],[f46]) ).
fof(f49,plain,
addition(sk0_0,sk0_1) = sk0_1,
inference(resolution,[status(thm)],[f43,f47]) ).
fof(f67,plain,
! [X0,X1] :
( ~ leq(X0,addition(multiplication(X1,X0),one))
| leq(X0,strong_iteration(X1)) ),
inference(paramodulation,[status(thm)],[f26,f39]) ).
fof(f159,plain,
! [X0] : strong_iteration(X0) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(forward_demodulation,[status(thm)],[f21,f37]) ).
fof(f177,plain,
! [X0,X1] : addition(one,addition(multiplication(X0,strong_iteration(X0)),X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f159,f22]) ).
fof(f181,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f21,f22]) ).
fof(f182,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f22,f181]) ).
fof(f185,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f24,f22]) ).
fof(f208,plain,
! [X0] : addition(one,strong_iteration(X0)) = addition(one,multiplication(X0,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f159,f185]) ).
fof(f209,plain,
! [X0] : addition(one,strong_iteration(X0)) = strong_iteration(X0),
inference(forward_demodulation,[status(thm)],[f159,f208]) ).
fof(f225,plain,
! [X0,X1] : addition(one,addition(strong_iteration(X0),X1)) = addition(strong_iteration(X0),X1),
inference(paramodulation,[status(thm)],[f209,f22]) ).
fof(f353,plain,
! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f27,f29]) ).
fof(f2967,plain,
! [X0,X1] :
( ~ leq(X0,addition(one,multiplication(X1,X0)))
| leq(X0,strong_iteration(X1)) ),
inference(forward_demodulation,[status(thm)],[f21,f67]) ).
fof(f2968,plain,
~ leq(strong_iteration(sk0_0),addition(one,multiplication(sk0_1,strong_iteration(sk0_0)))),
inference(resolution,[status(thm)],[f2967,f48]) ).
fof(f7632,plain,
! [X0,X1] : addition(one,multiplication(addition(X0,X1),strong_iteration(X0))) = addition(strong_iteration(X0),multiplication(X1,strong_iteration(X0))),
inference(paramodulation,[status(thm)],[f29,f177]) ).
fof(f9305,plain,
addition(strong_iteration(sk0_0),addition(one,multiplication(sk0_1,strong_iteration(sk0_0)))) != addition(one,multiplication(sk0_1,strong_iteration(sk0_0))),
inference(resolution,[status(thm)],[f2968,f44]) ).
fof(f9306,plain,
addition(one,addition(strong_iteration(sk0_0),multiplication(sk0_1,strong_iteration(sk0_0)))) != addition(one,multiplication(sk0_1,strong_iteration(sk0_0))),
inference(forward_demodulation,[status(thm)],[f182,f9305]) ).
fof(f19290,plain,
addition(strong_iteration(sk0_0),multiplication(sk0_1,strong_iteration(sk0_0))) != addition(one,multiplication(sk0_1,strong_iteration(sk0_0))),
inference(forward_demodulation,[status(thm)],[f225,f9306]) ).
fof(f19291,plain,
multiplication(addition(one,sk0_1),strong_iteration(sk0_0)) != addition(one,multiplication(sk0_1,strong_iteration(sk0_0))),
inference(forward_demodulation,[status(thm)],[f353,f19290]) ).
fof(f79774,plain,
! [X0,X1] : addition(one,multiplication(addition(X0,X1),strong_iteration(X0))) = multiplication(addition(one,X1),strong_iteration(X0)),
inference(forward_demodulation,[status(thm)],[f353,f7632]) ).
fof(f80114,plain,
addition(one,multiplication(sk0_1,strong_iteration(sk0_0))) = multiplication(addition(one,sk0_1),strong_iteration(sk0_0)),
inference(paramodulation,[status(thm)],[f49,f79774]) ).
fof(f80115,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f80114,f19291]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE140+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.12/0.34 % Computer : n010.cluster.edu
% 0.12/0.34 % Model : x86_64 x86_64
% 0.12/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34 % Memory : 8042.1875MB
% 0.12/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34 % CPULimit : 300
% 0.12/0.34 % WCLimit : 300
% 0.12/0.34 % DateTime : Tue May 30 11:37:22 EDT 2023
% 0.12/0.34 % CPUTime :
% 0.12/0.35 % Drodi V3.5.1
% 119.03/15.42 % Refutation found
% 119.03/15.42 % SZS status Theorem for theBenchmark: Theorem is valid
% 119.03/15.42 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 122.14/15.77 % Elapsed time: 15.401806 seconds
% 122.14/15.77 % CPU time: 121.130658 seconds
% 122.14/15.77 % Memory used: 946.774 MB
%------------------------------------------------------------------------------