TSTP Solution File: KLE039+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : KLE039+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n005.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 12:15:36 EDT 2023

% Result   : Theorem 8.76s 1.50s
% Output   : CNFRefutation 8.76s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   32
%            Number of leaves      :   13
% Syntax   : Number of formulae    :  103 (  88 unt;   0 def)
%            Number of atoms       :  122 (  87 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   39 (  20   ~;  15   |;   2   &)
%                                         (   1 <=>;   1  =>;   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    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  170 (; 169   !;   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(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(f14,axiom,
    ! [A] : leq(addition(one,multiplication(star(A),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(f17,conjecture,
    ! [X0] : star(star(X0)) = star(X0),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f18,negated_conjecture,
    ~ ! [X0] : star(star(X0)) = star(X0),
    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(f35,plain,
    ! [X0] : leq(addition(one,multiplication(star(X0),X0)),star(X0)),
    inference(cnf_transformation,[status(esa)],[f14]) ).

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(f40,plain,
    ? [X0] : star(star(X0)) != star(X0),
    inference(pre_NNF_transformation,[status(esa)],[f18]) ).

fof(f41,plain,
    star(star(sk0_0)) != star(sk0_0),
    inference(skolemization,[status(esa)],[f40]) ).

fof(f42,plain,
    star(star(sk0_0)) != star(sk0_0),
    inference(cnf_transformation,[status(esa)],[f41]) ).

fof(f43,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X0,X1)),
    inference(paramodulation,[status(thm)],[f19,f20]) ).

fof(f49,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X1,X0),X2),
    inference(paramodulation,[status(thm)],[f19,f20]) ).

fof(f50,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X1,addition(X0,X2)),
    inference(forward_demodulation,[status(thm)],[f20,f49]) ).

fof(f53,plain,
    ! [X0,X1] : addition(X0,addition(X0,X1)) = addition(X0,X1),
    inference(paramodulation,[status(thm)],[f22,f20]) ).

fof(f57,plain,
    ! [X0] : leq(X0,X0),
    inference(resolution,[status(thm)],[f33,f22]) ).

fof(f77,plain,
    ! [X0,X1] : addition(X0,addition(X1,X0)) = addition(X0,X1),
    inference(paramodulation,[status(thm)],[f19,f53]) ).

fof(f113,plain,
    ! [X0,X1,X2] : addition(X0,addition(addition(X1,X0),X2)) = addition(addition(X0,X1),X2),
    inference(paramodulation,[status(thm)],[f77,f20]) ).

fof(f114,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(addition(X0,X1),X2),
    inference(forward_demodulation,[status(thm)],[f20,f113]) ).

fof(f115,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X1,X2)),
    inference(forward_demodulation,[status(thm)],[f20,f114]) ).

fof(f141,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(addition(X2,X1),addition(X0,X1)),
    inference(paramodulation,[status(thm)],[f77,f43]) ).

fof(f142,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,addition(X0,X1))),
    inference(forward_demodulation,[status(thm)],[f20,f141]) ).

fof(f143,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X2,addition(X1,X0)),
    inference(forward_demodulation,[status(thm)],[f77,f142]) ).

fof(f185,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,addition(X0,X2))) = addition(X0,addition(X2,X1)),
    inference(paramodulation,[status(thm)],[f43,f53]) ).

fof(f186,plain,
    ! [X0,X1,X2] : addition(X0,addition(X1,X2)) = addition(X0,addition(X2,X1)),
    inference(forward_demodulation,[status(thm)],[f115,f185]) ).

fof(f700,plain,
    ! [X0] : addition(addition(one,multiplication(X0,star(X0))),star(X0)) = star(X0),
    inference(resolution,[status(thm)],[f34,f32]) ).

fof(f701,plain,
    ! [X0] : addition(one,addition(multiplication(X0,star(X0)),star(X0))) = star(X0),
    inference(forward_demodulation,[status(thm)],[f20,f700]) ).

fof(f702,plain,
    ! [X0] : addition(one,addition(star(X0),multiplication(X0,star(X0)))) = star(X0),
    inference(forward_demodulation,[status(thm)],[f186,f701]) ).

fof(f705,plain,
    ! [X0] : addition(addition(one,multiplication(star(X0),X0)),star(X0)) = star(X0),
    inference(resolution,[status(thm)],[f35,f32]) ).

fof(f706,plain,
    ! [X0] : addition(one,addition(multiplication(star(X0),X0),star(X0))) = star(X0),
    inference(forward_demodulation,[status(thm)],[f20,f705]) ).

fof(f707,plain,
    ! [X0] : addition(one,addition(star(X0),multiplication(star(X0),X0))) = star(X0),
    inference(forward_demodulation,[status(thm)],[f186,f706]) ).

fof(f709,plain,
    ! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = addition(multiplication(X0,X2),multiplication(X0,X1)),
    inference(paramodulation,[status(thm)],[f19,f26]) ).

fof(f710,plain,
    ! [X0,X1,X2] : multiplication(X0,addition(X1,X2)) = multiplication(X0,addition(X2,X1)),
    inference(forward_demodulation,[status(thm)],[f26,f709]) ).

fof(f727,plain,
    ! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(multiplication(X0,X1),X0),
    inference(paramodulation,[status(thm)],[f24,f26]) ).

fof(f728,plain,
    ! [X0,X1] : multiplication(X0,addition(X1,one)) = addition(X0,multiplication(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f19,f727]) ).

fof(f979,plain,
    ! [X0,X1] : multiplication(addition(one,X0),X1) = addition(X1,multiplication(X0,X1)),
    inference(paramodulation,[status(thm)],[f25,f27]) ).

fof(f989,plain,
    ! [X0,X1] : multiplication(addition(X0,one),X1) = addition(multiplication(X0,X1),X1),
    inference(paramodulation,[status(thm)],[f25,f27]) ).

fof(f990,plain,
    ! [X0,X1] : multiplication(addition(X0,one),X1) = addition(X1,multiplication(X0,X1)),
    inference(forward_demodulation,[status(thm)],[f19,f989]) ).

fof(f1442,plain,
    ! [X0] : addition(addition(star(X0),multiplication(X0,star(X0))),star(X0)) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
    inference(paramodulation,[status(thm)],[f702,f77]) ).

fof(f1443,plain,
    ! [X0] : addition(star(X0),addition(multiplication(X0,star(X0)),star(X0))) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
    inference(forward_demodulation,[status(thm)],[f20,f1442]) ).

fof(f1444,plain,
    ! [X0] : addition(star(X0),addition(star(X0),multiplication(X0,star(X0)))) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
    inference(forward_demodulation,[status(thm)],[f186,f1443]) ).

fof(f1445,plain,
    ! [X0] : addition(star(X0),multiplication(X0,star(X0))) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
    inference(forward_demodulation,[status(thm)],[f53,f1444]) ).

fof(f1446,plain,
    ! [X0] : multiplication(addition(X0,one),star(X0)) = addition(addition(star(X0),multiplication(X0,star(X0))),one),
    inference(forward_demodulation,[status(thm)],[f990,f1445]) ).

fof(f1447,plain,
    ! [X0] : multiplication(addition(X0,one),star(X0)) = addition(star(X0),addition(multiplication(X0,star(X0)),one)),
    inference(forward_demodulation,[status(thm)],[f20,f1446]) ).

fof(f1448,plain,
    ! [X0] : multiplication(addition(X0,one),star(X0)) = addition(star(X0),addition(one,multiplication(X0,star(X0)))),
    inference(forward_demodulation,[status(thm)],[f186,f1447]) ).

fof(f1449,plain,
    ! [X0] : multiplication(addition(X0,one),star(X0)) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
    inference(forward_demodulation,[status(thm)],[f50,f1448]) ).

fof(f1450,plain,
    ! [X0] : multiplication(addition(X0,one),star(X0)) = star(X0),
    inference(forward_demodulation,[status(thm)],[f702,f1449]) ).

fof(f1451,plain,
    ! [X0] : addition(one,star(X0)) = addition(one,addition(star(X0),multiplication(X0,star(X0)))),
    inference(paramodulation,[status(thm)],[f702,f53]) ).

fof(f1452,plain,
    ! [X0] : addition(one,star(X0)) = star(X0),
    inference(forward_demodulation,[status(thm)],[f702,f1451]) ).

fof(f1475,plain,
    ! [X0,X1] : multiplication(star(X0),X1) = addition(X1,multiplication(star(X0),X1)),
    inference(paramodulation,[status(thm)],[f1452,f979]) ).

fof(f1477,plain,
    ! [X0,X1] : addition(star(X0),addition(one,X1)) = addition(X1,star(X0)),
    inference(paramodulation,[status(thm)],[f1452,f143]) ).

fof(f1478,plain,
    ! [X0,X1] : addition(one,addition(star(X0),X1)) = addition(X1,star(X0)),
    inference(forward_demodulation,[status(thm)],[f50,f1477]) ).

fof(f1497,plain,
    ! [X0] : addition(multiplication(star(X0),X0),star(X0)) = star(X0),
    inference(backward_demodulation,[status(thm)],[f1478,f707]) ).

fof(f1498,plain,
    ! [X0] : addition(star(X0),multiplication(star(X0),X0)) = star(X0),
    inference(forward_demodulation,[status(thm)],[f19,f1497]) ).

fof(f1499,plain,
    ! [X0] : multiplication(star(X0),addition(X0,one)) = star(X0),
    inference(forward_demodulation,[status(thm)],[f728,f1498]) ).

fof(f1522,plain,
    ! [X0] : multiplication(addition(X0,one),addition(star(X0),one)) = addition(addition(X0,one),star(X0)),
    inference(paramodulation,[status(thm)],[f1450,f728]) ).

fof(f1523,plain,
    ! [X0] : multiplication(addition(X0,one),addition(one,star(X0))) = addition(addition(X0,one),star(X0)),
    inference(forward_demodulation,[status(thm)],[f710,f1522]) ).

fof(f1524,plain,
    ! [X0] : multiplication(addition(X0,one),star(X0)) = addition(addition(X0,one),star(X0)),
    inference(forward_demodulation,[status(thm)],[f1452,f1523]) ).

fof(f1525,plain,
    ! [X0] : star(X0) = addition(addition(X0,one),star(X0)),
    inference(forward_demodulation,[status(thm)],[f1450,f1524]) ).

fof(f1526,plain,
    ! [X0] : star(X0) = addition(X0,addition(one,star(X0))),
    inference(forward_demodulation,[status(thm)],[f20,f1525]) ).

fof(f1527,plain,
    ! [X0] : star(X0) = addition(X0,star(X0)),
    inference(forward_demodulation,[status(thm)],[f1452,f1526]) ).

fof(f1611,plain,
    ! [X0,X1,X2] :
      ( ~ leq(multiplication(addition(X0,X1),X2),X2)
      | leq(multiplication(star(X0),multiplication(X1,X2)),X2) ),
    inference(paramodulation,[status(thm)],[f27,f37]) ).

fof(f1635,plain,
    ! [X0,X1] :
      ( ~ leq(multiplication(X0,X1),X1)
      | leq(multiplication(star(X0),multiplication(X0,X1)),X1) ),
    inference(paramodulation,[status(thm)],[f22,f37]) ).

fof(f1683,plain,
    ! [X0] : multiplication(star(X0),addition(one,X0)) = star(X0),
    inference(paramodulation,[status(thm)],[f710,f1499]) ).

fof(f1832,plain,
    ! [X0] : multiplication(star(star(X0)),star(X0)) = star(star(X0)),
    inference(paramodulation,[status(thm)],[f1452,f1683]) ).

fof(f3854,plain,
    ! [X0,X1] : multiplication(star(star(X0)),multiplication(star(X0),X1)) = multiplication(star(star(X0)),X1),
    inference(paramodulation,[status(thm)],[f1832,f23]) ).

fof(f4969,plain,
    ! [X0] :
      ( ~ leq(star(X0),star(X0))
      | leq(multiplication(star(X0),multiplication(one,star(X0))),star(X0)) ),
    inference(paramodulation,[status(thm)],[f1450,f1611]) ).

fof(f4970,plain,
    ! [X0] :
      ( ~ leq(star(X0),star(X0))
      | leq(multiplication(star(X0),star(X0)),star(X0)) ),
    inference(forward_demodulation,[status(thm)],[f25,f4969]) ).

fof(f4971,plain,
    ! [X0] : leq(multiplication(star(X0),star(X0)),star(X0)),
    inference(forward_subsumption_resolution,[status(thm)],[f4970,f57]) ).

fof(f5157,plain,
    ! [X0] : addition(multiplication(star(X0),star(X0)),star(X0)) = star(X0),
    inference(resolution,[status(thm)],[f4971,f32]) ).

fof(f5158,plain,
    ! [X0] : addition(star(X0),multiplication(star(X0),star(X0))) = star(X0),
    inference(forward_demodulation,[status(thm)],[f19,f5157]) ).

fof(f5159,plain,
    ! [X0] : multiplication(star(X0),star(X0)) = star(X0),
    inference(forward_demodulation,[status(thm)],[f1475,f5158]) ).

fof(f5287,plain,
    ! [X0] :
      ( ~ leq(star(X0),star(X0))
      | leq(multiplication(star(star(X0)),multiplication(star(X0),star(X0))),star(X0)) ),
    inference(paramodulation,[status(thm)],[f5159,f1635]) ).

fof(f5288,plain,
    ! [X0] :
      ( ~ leq(star(X0),star(X0))
      | leq(multiplication(star(star(X0)),star(X0)),star(X0)) ),
    inference(forward_demodulation,[status(thm)],[f3854,f5287]) ).

fof(f5289,plain,
    ! [X0] :
      ( ~ leq(star(X0),star(X0))
      | leq(star(star(X0)),star(X0)) ),
    inference(forward_demodulation,[status(thm)],[f1832,f5288]) ).

fof(f5290,plain,
    ! [X0] : leq(star(star(X0)),star(X0)),
    inference(forward_subsumption_resolution,[status(thm)],[f5289,f57]) ).

fof(f5329,plain,
    ! [X0] : addition(star(star(X0)),star(X0)) = star(X0),
    inference(resolution,[status(thm)],[f5290,f32]) ).

fof(f5330,plain,
    ! [X0] : addition(star(X0),star(star(X0))) = star(X0),
    inference(forward_demodulation,[status(thm)],[f19,f5329]) ).

fof(f5331,plain,
    ! [X0] : star(star(X0)) = star(X0),
    inference(forward_demodulation,[status(thm)],[f1527,f5330]) ).

fof(f5334,plain,
    star(sk0_0) != star(sk0_0),
    inference(backward_demodulation,[status(thm)],[f5331,f42]) ).

fof(f5335,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f5334]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.11  % Problem  : KLE039+1 : TPTP v8.1.2. Released v4.0.0.
% 0.03/0.11  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.10/0.32  % Computer : n005.cluster.edu
% 0.10/0.32  % Model    : x86_64 x86_64
% 0.10/0.32  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.32  % Memory   : 8042.1875MB
% 0.10/0.32  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.32  % CPULimit : 300
% 0.10/0.32  % WCLimit  : 300
% 0.10/0.32  % DateTime : Tue May 30 11:45:36 EDT 2023
% 0.10/0.32  % CPUTime  : 
% 0.10/0.32  % Drodi V3.5.1
% 8.76/1.50  % Refutation found
% 8.76/1.50  % SZS status Theorem for theBenchmark: Theorem is valid
% 8.76/1.50  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 8.76/1.56  % Elapsed time: 1.222447 seconds
% 8.76/1.56  % CPU time: 9.269671 seconds
% 8.76/1.56  % Memory used: 114.911 MB
%------------------------------------------------------------------------------