TSTP Solution File: KLE041+1 by Drodi---3.5.1
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- Process Solution
%------------------------------------------------------------------------------
% File : Drodi---3.5.1
% Problem : KLE041+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% Computer : n026.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 12:15:37 EDT 2023
% Result : Theorem 7.87s 1.36s
% Output : CNFRefutation 7.87s
% Verified :
% SZS Type : Refutation
% Derivation depth : 35
% Number of leaves : 13
% Syntax : Number of formulae : 102 ( 73 unt; 0 def)
% Number of atoms : 135 ( 72 equ)
% Maximal formula atoms : 4 ( 1 avg)
% Number of connectives : 77 ( 44 ~; 24 |; 4 &)
% ( 1 <=>; 4 =>; 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 : 164 (; 162 !; 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(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(f7,axiom,
! [A] : multiplication(one,A) = 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(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(f12,axiom,
! [A,B] :
( leq(A,B)
<=> addition(A,B) = B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f13,axiom,
! [A] : leq(addition(one,multiplication(A,star(A))),star(A)),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f15,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),B)
=> leq(multiplication(star(A),C),B) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f16,axiom,
! [A,B,C] :
( leq(addition(multiplication(A,B),C),A)
=> leq(multiplication(C,star(B)),A) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f17,conjecture,
! [X0,X1] :
( leq(X0,X1)
=> leq(star(X0),star(X1)) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).
fof(f18,negated_conjecture,
~ ! [X0,X1] :
( leq(X0,X1)
=> leq(star(X0),star(X1)) ),
inference(negated_conjecture,[status(cth)],[f17]) ).
fof(f19,plain,
! [X0,X1] : addition(X0,X1) = addition(X1,X0),
inference(cnf_transformation,[status(esa)],[f1]) ).
fof(f20,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f2]) ).
fof(f22,plain,
! [X0] : addition(X0,X0) = X0,
inference(cnf_transformation,[status(esa)],[f4]) ).
fof(f23,plain,
! [X0,X1,X2] : multiplication(X0,multiplication(X1,X2)) = multiplication(multiplication(X0,X1),X2),
inference(cnf_transformation,[status(esa)],[f5]) ).
fof(f24,plain,
! [X0] : multiplication(X0,one) = X0,
inference(cnf_transformation,[status(esa)],[f6]) ).
fof(f25,plain,
! [X0] : multiplication(one,X0) = X0,
inference(cnf_transformation,[status(esa)],[f7]) ).
fof(f26,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X1),multiplication(X0,X2)),
inference(cnf_transformation,[status(esa)],[f8]) ).
fof(f27,plain,
! [X0,X1,X2] : multiplication(addition(X0,X1),X2) = addition(multiplication(X0,X2),multiplication(X1,X2)),
inference(cnf_transformation,[status(esa)],[f9]) ).
fof(f30,plain,
! [A,B] :
( ( ~ leq(A,B)
| addition(A,B) = B )
& ( leq(A,B)
| addition(A,B) != B ) ),
inference(NNF_transformation,[status(esa)],[f12]) ).
fof(f31,plain,
( ! [A,B] :
( ~ leq(A,B)
| addition(A,B) = B )
& ! [A,B] :
( leq(A,B)
| addition(A,B) != B ) ),
inference(miniscoping,[status(esa)],[f30]) ).
fof(f32,plain,
! [X0,X1] :
( ~ leq(X0,X1)
| addition(X0,X1) = X1 ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f33,plain,
! [X0,X1] :
( leq(X0,X1)
| addition(X0,X1) != X1 ),
inference(cnf_transformation,[status(esa)],[f31]) ).
fof(f34,plain,
! [X0] : leq(addition(one,multiplication(X0,star(X0))),star(X0)),
inference(cnf_transformation,[status(esa)],[f13]) ).
fof(f36,plain,
! [A,B,C] :
( ~ leq(addition(multiplication(A,B),C),B)
| leq(multiplication(star(A),C),B) ),
inference(pre_NNF_transformation,[status(esa)],[f15]) ).
fof(f37,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X1)
| leq(multiplication(star(X0),X2),X1) ),
inference(cnf_transformation,[status(esa)],[f36]) ).
fof(f38,plain,
! [A,B,C] :
( ~ leq(addition(multiplication(A,B),C),A)
| leq(multiplication(C,star(B)),A) ),
inference(pre_NNF_transformation,[status(esa)],[f16]) ).
fof(f39,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| leq(multiplication(X2,star(X1)),X0) ),
inference(cnf_transformation,[status(esa)],[f38]) ).
fof(f40,plain,
? [X0,X1] :
( leq(X0,X1)
& ~ leq(star(X0),star(X1)) ),
inference(pre_NNF_transformation,[status(esa)],[f18]) ).
fof(f41,plain,
( leq(sk0_0,sk0_1)
& ~ leq(star(sk0_0),star(sk0_1)) ),
inference(skolemization,[status(esa)],[f40]) ).
fof(f42,plain,
leq(sk0_0,sk0_1),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f43,plain,
~ leq(star(sk0_0),star(sk0_1)),
inference(cnf_transformation,[status(esa)],[f41]) ).
fof(f44,plain,
addition(sk0_0,sk0_1) = sk0_1,
inference(resolution,[status(thm)],[f32,f42]) ).
fof(f47,plain,
! [X0,X1,X2] :
( ~ leq(addition(multiplication(X0,X1),X2),X0)
| addition(multiplication(X2,star(X1)),X0) = X0 ),
inference(resolution,[status(thm)],[f39,f32]) ).
fof(f52,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X0)
| addition(multiplication(multiplication(X0,X1),star(X1)),X0) = X0 ),
inference(paramodulation,[status(thm)],[f22,f47]) ).
fof(f53,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X0)
| addition(X0,multiplication(multiplication(X0,X1),star(X1))) = X0 ),
inference(forward_demodulation,[status(thm)],[f19,f52]) ).
fof(f54,plain,
! [X0,X1] :
( ~ leq(multiplication(X0,X1),X0)
| addition(X0,multiplication(X0,multiplication(X1,star(X1)))) = X0 ),
inference(forward_demodulation,[status(thm)],[f23,f53]) ).
fof(f60,plain,
! [X0,X1] :
( addition(X0,multiplication(X0,multiplication(X1,star(X1)))) = X0
| addition(multiplication(X0,X1),X0) != X0 ),
inference(resolution,[status(thm)],[f54,f33]) ).
fof(f61,plain,
! [X0,X1] :
( addition(X0,multiplication(X0,multiplication(X1,star(X1)))) = X0
| addition(X0,multiplication(X0,X1)) != X0 ),
inference(forward_demodulation,[status(thm)],[f19,f60]) ).
fof(f94,plain,
! [X0] :
( addition(X0,multiplication(X0,multiplication(one,star(one)))) = X0
| addition(X0,X0) != X0 ),
inference(paramodulation,[status(thm)],[f24,f61]) ).
fof(f95,plain,
! [X0] :
( addition(X0,multiplication(X0,star(one))) = X0
| addition(X0,X0) != X0 ),
inference(forward_demodulation,[status(thm)],[f25,f94]) ).
fof(f96,plain,
! [X0] :
( addition(X0,multiplication(X0,star(one))) = X0
| X0 != X0 ),
inference(forward_demodulation,[status(thm)],[f22,f95]) ).
fof(f97,plain,
! [X0] : addition(X0,multiplication(X0,star(one))) = X0,
inference(trivial_equality_resolution,[status(esa)],[f96]) ).
fof(f109,plain,
! [X0,X1] :
( ~ leq(addition(multiplication(X0,X1),one),X0)
| leq(star(X1),X0) ),
inference(paramodulation,[status(thm)],[f25,f39]) ).
fof(f110,plain,
! [X0,X1] :
( ~ leq(addition(one,multiplication(X0,X1)),X0)
| leq(star(X1),X0) ),
inference(forward_demodulation,[status(thm)],[f19,f109]) ).
fof(f215,plain,
addition(one,star(one)) = one,
inference(paramodulation,[status(thm)],[f25,f97]) ).
fof(f245,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f253,plain,
! [X0] : addition(sk0_0,addition(sk0_1,X0)) = addition(sk0_1,X0),
inference(paramodulation,[status(thm)],[f44,f20]) ).
fof(f256,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
inference(paramodulation,[status(thm)],[f19,f20]) ).
fof(f257,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
inference(forward_demodulation,[status(thm)],[f20,f256]) ).
fof(f260,plain,
! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f22,f20]) ).
fof(f283,plain,
! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
inference(paramodulation,[status(thm)],[f19,f260]) ).
fof(f380,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f19,f26]) ).
fof(f381,plain,
! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
inference(forward_demodulation,[status(thm)],[f26,f380]) ).
fof(f396,plain,
! [X0,X1] : multiplication(X0,addition(one,X1)) = addition(X0,multiplication(X0,X1)),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f408,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
inference(paramodulation,[status(thm)],[f24,f26]) ).
fof(f409,plain,
! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f408]) ).
fof(f457,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
inference(paramodulation,[status(thm)],[f25,f27]) ).
fof(f458,plain,
! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
inference(forward_demodulation,[status(thm)],[f19,f457]) ).
fof(f504,plain,
! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
inference(resolution,[status(thm)],[f34,f32]) ).
fof(f505,plain,
! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f20,f504]) ).
fof(f506,plain,
! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
inference(forward_demodulation,[status(thm)],[f19,f505]) ).
fof(f507,plain,
! [X0] : addition(one,multiplication(addition(X0,one),star(X0))) = star(X0),
inference(forward_demodulation,[status(thm)],[f458,f506]) ).
fof(f508,plain,
leq(one,star(one)),
inference(paramodulation,[status(thm)],[f97,f34]) ).
fof(f885,plain,
addition(one,star(one)) = star(one),
inference(resolution,[status(thm)],[f508,f32]) ).
fof(f886,plain,
one = star(one),
inference(forward_demodulation,[status(thm)],[f215,f885]) ).
fof(f965,plain,
! [X0,X1] :
( ~ leq(addition(multiplication(X0,one),X1),X0)
| leq(multiplication(X1,one),X0) ),
inference(paramodulation,[status(thm)],[f886,f39]) ).
fof(f966,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| leq(multiplication(X1,one),X0) ),
inference(forward_demodulation,[status(thm)],[f24,f965]) ).
fof(f967,plain,
! [X0,X1] :
( ~ leq(addition(X0,X1),X0)
| leq(X1,X0) ),
inference(forward_demodulation,[status(thm)],[f24,f966]) ).
fof(f1202,plain,
~ leq(addition(one,multiplication(star(sk0_1),sk0_0)),star(sk0_1)),
inference(resolution,[status(thm)],[f110,f43]) ).
fof(f1289,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(X1,X3),addition(X0,multiplication(X1,X2))),
inference(paramodulation,[status(thm)],[f26,f245]) ).
fof(f1319,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X1)),
inference(paramodulation,[status(thm)],[f283,f245]) ).
fof(f1320,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X1))),
inference(forward_demodulation,[status(thm)],[f20,f1319]) ).
fof(f1321,plain,
! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
inference(forward_demodulation,[status(thm)],[f283,f1320]) ).
fof(f1560,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(multiplication(X1,X2),addition(X0,multiplication(X1,X3))),
inference(paramodulation,[status(thm)],[f26,f257]) ).
fof(f1561,plain,
! [X0,X1,X2,X3] : addition(X0,multiplication(X1,addition(X2,X3))) = addition(X0,multiplication(X1,addition(X3,X2))),
inference(forward_demodulation,[status(thm)],[f1289,f1560]) ).
fof(f3652,plain,
~ leq(addition(star(sk0_1),addition(one,multiplication(star(sk0_1),sk0_0))),star(sk0_1)),
inference(resolution,[status(thm)],[f1202,f967]) ).
fof(f3653,plain,
~ leq(addition(one,addition(star(sk0_1),multiplication(star(sk0_1),sk0_0))),star(sk0_1)),
inference(forward_demodulation,[status(thm)],[f257,f3652]) ).
fof(f3654,plain,
~ leq(addition(one,multiplication(star(sk0_1),addition(sk0_0,one))),star(sk0_1)),
inference(forward_demodulation,[status(thm)],[f409,f3653]) ).
fof(f3655,plain,
~ leq(addition(one,multiplication(star(sk0_1),addition(one,sk0_0))),star(sk0_1)),
inference(forward_demodulation,[status(thm)],[f1561,f3654]) ).
fof(f3745,plain,
! [X0] : addition(one,star(X0)) = addition(one,multiplication(addition(X0,one),star(X0))),
inference(paramodulation,[status(thm)],[f507,f260]) ).
fof(f3746,plain,
! [X0] : addition(one,star(X0)) = star(X0),
inference(forward_demodulation,[status(thm)],[f507,f3745]) ).
fof(f3753,plain,
! [X0,X1] : multiplication(X0,star(X1)) = addition(X0,multiplication(X0,star(X1))),
inference(paramodulation,[status(thm)],[f3746,f396]) ).
fof(f3754,plain,
! [X0,X1] : addition(star(X0),addition(one,X1)) = addition(X1,star(X0)),
inference(paramodulation,[status(thm)],[f3746,f1321]) ).
fof(f3755,plain,
! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(X1,star(X0)),
inference(forward_demodulation,[status(thm)],[f257,f3754]) ).
fof(f4571,plain,
! [X0] : addition(sk0_0,multiplication(sk0_1,star(X0))) = addition(sk0_1,multiplication(sk0_1,star(X0))),
inference(paramodulation,[status(thm)],[f3753,f253]) ).
fof(f4572,plain,
! [X0] : addition(sk0_0,multiplication(sk0_1,star(X0))) = multiplication(sk0_1,star(X0)),
inference(forward_demodulation,[status(thm)],[f3753,f4571]) ).
fof(f6331,plain,
~ leq(addition(star(sk0_1),addition(one,multiplication(star(sk0_1),addition(one,sk0_0)))),star(sk0_1)),
inference(resolution,[status(thm)],[f3655,f967]) ).
fof(f6332,plain,
~ leq(addition(one,addition(star(sk0_1),multiplication(star(sk0_1),addition(one,sk0_0)))),star(sk0_1)),
inference(forward_demodulation,[status(thm)],[f257,f6331]) ).
fof(f6333,plain,
~ leq(addition(multiplication(star(sk0_1),addition(one,sk0_0)),star(sk0_1)),star(sk0_1)),
inference(forward_demodulation,[status(thm)],[f3755,f6332]) ).
fof(f6334,plain,
~ leq(addition(star(sk0_1),multiplication(star(sk0_1),addition(one,sk0_0))),star(sk0_1)),
inference(forward_demodulation,[status(thm)],[f19,f6333]) ).
fof(f6335,plain,
~ leq(multiplication(star(sk0_1),addition(addition(one,sk0_0),one)),star(sk0_1)),
inference(forward_demodulation,[status(thm)],[f409,f6334]) ).
fof(f6336,plain,
~ leq(multiplication(star(sk0_1),addition(one,addition(one,sk0_0))),star(sk0_1)),
inference(forward_demodulation,[status(thm)],[f381,f6335]) ).
fof(f6337,plain,
~ leq(multiplication(star(sk0_1),addition(one,sk0_0)),star(sk0_1)),
inference(forward_demodulation,[status(thm)],[f260,f6336]) ).
fof(f6346,plain,
~ leq(addition(multiplication(sk0_1,star(sk0_1)),addition(one,sk0_0)),star(sk0_1)),
inference(resolution,[status(thm)],[f6337,f37]) ).
fof(f6347,plain,
~ leq(addition(sk0_0,addition(one,multiplication(sk0_1,star(sk0_1)))),star(sk0_1)),
inference(forward_demodulation,[status(thm)],[f1321,f6346]) ).
fof(f6348,plain,
~ leq(addition(one,addition(sk0_0,multiplication(sk0_1,star(sk0_1)))),star(sk0_1)),
inference(forward_demodulation,[status(thm)],[f257,f6347]) ).
fof(f6349,plain,
~ leq(addition(one,multiplication(sk0_1,star(sk0_1))),star(sk0_1)),
inference(forward_demodulation,[status(thm)],[f4572,f6348]) ).
fof(f6350,plain,
$false,
inference(forward_subsumption_resolution,[status(thm)],[f6349,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.12 % Problem : KLE041+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13 % Command : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.14/0.34 % Computer : n026.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue May 30 12:03:58 EDT 2023
% 0.14/0.34 % CPUTime :
% 0.14/0.35 % Drodi V3.5.1
% 7.87/1.36 % Refutation found
% 7.87/1.36 % SZS status Theorem for theBenchmark: Theorem is valid
% 7.87/1.36 % SZS output start CNFRefutation for theBenchmark
% See solution above
% 7.87/1.40 % Elapsed time: 1.058692 seconds
% 7.87/1.40 % CPU time: 8.155017 seconds
% 7.87/1.40 % Memory used: 109.809 MB
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