TSTP Solution File: LCL903+1 by Drodi---3.5.1

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.5.1
% Problem  : LCL903+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n025.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 12:20:49 EDT 2023

% Result   : Theorem 14.84s 2.30s
% Output   : CNFRefutation 15.55s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   13
% Syntax   : Number of formulae    :   89 (  41 unt;   0 def)
%            Number of atoms       :  152 (  46 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :  121 (  58   ~;  53   |;   4   &)
%                                         (   1 <=>;   5  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of predicates  :    3 (   1 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   3 con; 0-2 aty)
%            Number of variables   :  166 (; 165   !;   1   ?)

% Comments : 
%------------------------------------------------------------------------------
fof(f2,axiom,
    ! [A,B] : '+'(A,B) = '+'(B,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f3,axiom,
    ! [A] : '+'(A,'0') = A,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f4,axiom,
    ! [A] : '>='(A,A),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f5,axiom,
    ! [X0,X1,X2] :
      ( ( '>='(X0,X1)
        & '>='(X1,X2) )
     => '>='(X0,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f6,axiom,
    ! [X3,X4] :
      ( ( '>='(X3,X4)
        & '>='(X4,X3) )
     => X3 = X4 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f7,axiom,
    ! [X5,X6,X7] :
      ( '>='('+'(X5,X6),X7)
    <=> '>='(X6,'==>'(X5,X7)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f8,axiom,
    ! [A] : '>='(A,'0'),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f9,axiom,
    ! [X8,X9,X10] :
      ( '>='(X8,X9)
     => '>='('+'(X8,X10),'+'(X9,X10)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f10,axiom,
    ! [X11,X12,X13] :
      ( '>='(X11,X12)
     => '>='('==>'(X12,X13),'==>'(X11,X13)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f11,axiom,
    ! [X14,X15,X16] :
      ( '>='(X14,X15)
     => '>='('==>'(X16,X14),'==>'(X16,X15)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f12,axiom,
    ! [A] : '+'(A,'1') = '1',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f13,axiom,
    ! [A] : '==>'('==>'('==>'(A,'1'),A),A) = '0',
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f14,conjecture,
    ! [X17] : '+'(X17,X17) = X17,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,negated_conjecture,
    ~ ! [X17] : '+'(X17,X17) = X17,
    inference(negated_conjecture,[status(cth)],[f14]) ).

fof(f17,plain,
    ! [X0,X1] : '+'(X0,X1) = '+'(X1,X0),
    inference(cnf_transformation,[status(esa)],[f2]) ).

fof(f18,plain,
    ! [X0] : '+'(X0,'0') = X0,
    inference(cnf_transformation,[status(esa)],[f3]) ).

fof(f19,plain,
    ! [X0] : '>='(X0,X0),
    inference(cnf_transformation,[status(esa)],[f4]) ).

fof(f20,plain,
    ! [X0,X1,X2] :
      ( ~ '>='(X0,X1)
      | ~ '>='(X1,X2)
      | '>='(X0,X2) ),
    inference(pre_NNF_transformation,[status(esa)],[f5]) ).

fof(f21,plain,
    ! [X0,X2] :
      ( ! [X1] :
          ( ~ '>='(X0,X1)
          | ~ '>='(X1,X2) )
      | '>='(X0,X2) ),
    inference(miniscoping,[status(esa)],[f20]) ).

fof(f22,plain,
    ! [X0,X1,X2] :
      ( ~ '>='(X0,X1)
      | ~ '>='(X1,X2)
      | '>='(X0,X2) ),
    inference(cnf_transformation,[status(esa)],[f21]) ).

fof(f23,plain,
    ! [X3,X4] :
      ( ~ '>='(X3,X4)
      | ~ '>='(X4,X3)
      | X3 = X4 ),
    inference(pre_NNF_transformation,[status(esa)],[f6]) ).

fof(f24,plain,
    ! [X0,X1] :
      ( ~ '>='(X0,X1)
      | ~ '>='(X1,X0)
      | X0 = X1 ),
    inference(cnf_transformation,[status(esa)],[f23]) ).

fof(f25,plain,
    ! [X5,X6,X7] :
      ( ( ~ '>='('+'(X5,X6),X7)
        | '>='(X6,'==>'(X5,X7)) )
      & ( '>='('+'(X5,X6),X7)
        | ~ '>='(X6,'==>'(X5,X7)) ) ),
    inference(NNF_transformation,[status(esa)],[f7]) ).

fof(f26,plain,
    ( ! [X5,X6,X7] :
        ( ~ '>='('+'(X5,X6),X7)
        | '>='(X6,'==>'(X5,X7)) )
    & ! [X5,X6,X7] :
        ( '>='('+'(X5,X6),X7)
        | ~ '>='(X6,'==>'(X5,X7)) ) ),
    inference(miniscoping,[status(esa)],[f25]) ).

fof(f27,plain,
    ! [X0,X1,X2] :
      ( ~ '>='('+'(X0,X1),X2)
      | '>='(X1,'==>'(X0,X2)) ),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f28,plain,
    ! [X0,X1,X2] :
      ( '>='('+'(X0,X1),X2)
      | ~ '>='(X1,'==>'(X0,X2)) ),
    inference(cnf_transformation,[status(esa)],[f26]) ).

fof(f29,plain,
    ! [X0] : '>='(X0,'0'),
    inference(cnf_transformation,[status(esa)],[f8]) ).

fof(f30,plain,
    ! [X8,X9,X10] :
      ( ~ '>='(X8,X9)
      | '>='('+'(X8,X10),'+'(X9,X10)) ),
    inference(pre_NNF_transformation,[status(esa)],[f9]) ).

fof(f31,plain,
    ! [X8,X9] :
      ( ~ '>='(X8,X9)
      | ! [X10] : '>='('+'(X8,X10),'+'(X9,X10)) ),
    inference(miniscoping,[status(esa)],[f30]) ).

fof(f32,plain,
    ! [X0,X1,X2] :
      ( ~ '>='(X0,X1)
      | '>='('+'(X0,X2),'+'(X1,X2)) ),
    inference(cnf_transformation,[status(esa)],[f31]) ).

fof(f33,plain,
    ! [X11,X12,X13] :
      ( ~ '>='(X11,X12)
      | '>='('==>'(X12,X13),'==>'(X11,X13)) ),
    inference(pre_NNF_transformation,[status(esa)],[f10]) ).

fof(f34,plain,
    ! [X11,X12] :
      ( ~ '>='(X11,X12)
      | ! [X13] : '>='('==>'(X12,X13),'==>'(X11,X13)) ),
    inference(miniscoping,[status(esa)],[f33]) ).

fof(f35,plain,
    ! [X0,X1,X2] :
      ( ~ '>='(X0,X1)
      | '>='('==>'(X1,X2),'==>'(X0,X2)) ),
    inference(cnf_transformation,[status(esa)],[f34]) ).

fof(f36,plain,
    ! [X14,X15,X16] :
      ( ~ '>='(X14,X15)
      | '>='('==>'(X16,X14),'==>'(X16,X15)) ),
    inference(pre_NNF_transformation,[status(esa)],[f11]) ).

fof(f37,plain,
    ! [X14,X15] :
      ( ~ '>='(X14,X15)
      | ! [X16] : '>='('==>'(X16,X14),'==>'(X16,X15)) ),
    inference(miniscoping,[status(esa)],[f36]) ).

fof(f38,plain,
    ! [X0,X1,X2] :
      ( ~ '>='(X0,X1)
      | '>='('==>'(X2,X0),'==>'(X2,X1)) ),
    inference(cnf_transformation,[status(esa)],[f37]) ).

fof(f39,plain,
    ! [X0] : '+'(X0,'1') = '1',
    inference(cnf_transformation,[status(esa)],[f12]) ).

fof(f40,plain,
    ! [X0] : '==>'('==>'('==>'(X0,'1'),X0),X0) = '0',
    inference(cnf_transformation,[status(esa)],[f13]) ).

fof(f41,plain,
    ? [X17] : '+'(X17,X17) != X17,
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f42,plain,
    '+'(sk0_0,sk0_0) != sk0_0,
    inference(skolemization,[status(esa)],[f41]) ).

fof(f43,plain,
    '+'(sk0_0,sk0_0) != sk0_0,
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f848,plain,
    ! [X0,X1] : '>='('+'(X0,X1),'+'('0',X1)),
    inference(resolution,[status(thm)],[f29,f32]) ).

fof(f850,plain,
    ! [X0] : '+'('0',X0) = X0,
    inference(paramodulation,[status(thm)],[f17,f18]) ).

fof(f945,plain,
    ! [X0] : '+'('1',X0) = '1',
    inference(paramodulation,[status(thm)],[f17,f39]) ).

fof(f1086,plain,
    ! [X0] :
      ( ~ '>='('0',X0)
      | '0' = X0 ),
    inference(resolution,[status(thm)],[f24,f29]) ).

fof(f1092,plain,
    ! [X0,X1,X2] :
      ( ~ '>='('+'(X0,X1),X2)
      | ~ '>='('==>'(X0,X2),X1)
      | '==>'(X0,X2) = X1 ),
    inference(resolution,[status(thm)],[f27,f24]) ).

fof(f1093,plain,
    ! [X0,X1,X2,X3] :
      ( ~ '>='('+'(X0,X1),X2)
      | '>='('+'(X1,X3),'+'('==>'(X0,X2),X3)) ),
    inference(resolution,[status(thm)],[f27,f32]) ).

fof(f1094,plain,
    ! [X0,X1] : '>='('+'(X0,'==>'(X0,X1)),X1),
    inference(resolution,[status(thm)],[f28,f19]) ).

fof(f1097,plain,
    ! [X0,X1] : '>='('+'(X0,X1),X1),
    inference(forward_demodulation,[status(thm)],[f850,f848]) ).

fof(f1103,plain,
    ! [X0] : '>='('1',X0),
    inference(paramodulation,[status(thm)],[f945,f1097]) ).

fof(f1120,plain,
    ! [X0,X1] : '>='('+'(X0,X1),X0),
    inference(paramodulation,[status(thm)],[f17,f1097]) ).

fof(f1125,plain,
    ! [X0] :
      ( ~ '>='(X0,'1')
      | X0 = '1' ),
    inference(resolution,[status(thm)],[f1103,f24]) ).

fof(f1129,plain,
    ! [X0,X1,X2] :
      ( ~ '>='(X0,'+'(X1,X2))
      | '>='(X0,X1) ),
    inference(resolution,[status(thm)],[f1120,f22]) ).

fof(f1130,plain,
    ! [X0,X1] :
      ( ~ '>='(X0,'+'(X0,X1))
      | X0 = '+'(X0,X1) ),
    inference(resolution,[status(thm)],[f1120,f24]) ).

fof(f1273,plain,
    ! [X0,X1] :
      ( ~ '>='('0','+'(X0,X1))
      | '0' = X0 ),
    inference(resolution,[status(thm)],[f1129,f1086]) ).

fof(f1340,plain,
    ! [X0] :
      ( ~ '>='('0',X0)
      | '0' = X0 ),
    inference(paramodulation,[status(thm)],[f18,f1273]) ).

fof(f1365,plain,
    ! [X0,X1,X2] : '>='('+'(X0,X1),'+'('==>'(X2,'+'(X2,X0)),X1)),
    inference(resolution,[status(thm)],[f1093,f19]) ).

fof(f2239,plain,
    ! [X0,X1] :
      ( '0' = '==>'(X0,X1)
      | ~ '>='('+'(X0,'0'),X1) ),
    inference(resolution,[status(thm)],[f1340,f27]) ).

fof(f2240,plain,
    ! [X0,X1] :
      ( '0' = '==>'(X0,X1)
      | ~ '>='(X0,X1) ),
    inference(forward_demodulation,[status(thm)],[f18,f2239]) ).

fof(f2813,plain,
    ! [X0] : '+'(X0,'==>'(X0,'1')) = '1',
    inference(resolution,[status(thm)],[f1094,f1125]) ).

fof(f2820,plain,
    ! [X0] : '>='('==>'('0',X0),X0),
    inference(paramodulation,[status(thm)],[f850,f1094]) ).

fof(f2948,plain,
    ! [X0,X1] :
      ( ~ '>='(X0,'+'(X1,X0))
      | X0 = '+'(X0,X1) ),
    inference(paramodulation,[status(thm)],[f17,f1130]) ).

fof(f3084,plain,
    ! [X0,X1,X2] :
      ( ~ '>='(X0,X1)
      | ~ '>='('==>'(X0,X2),'==>'(X1,X2))
      | '==>'(X0,X2) = '==>'(X1,X2) ),
    inference(resolution,[status(thm)],[f35,f24]) ).

fof(f3103,plain,
    ! [X0] : '>='('+'('==>'('==>'(X0,'1'),X0),'0'),X0),
    inference(paramodulation,[status(thm)],[f40,f1094]) ).

fof(f3104,plain,
    ! [X0] : '>='('==>'('==>'(X0,'1'),X0),X0),
    inference(forward_demodulation,[status(thm)],[f18,f3103]) ).

fof(f5293,plain,
    ! [X0] :
      ( ~ '>='('+'('==>'(X0,'1'),X0),X0)
      | '==>'('==>'(X0,'1'),X0) = X0 ),
    inference(resolution,[status(thm)],[f1092,f3104]) ).

fof(f5294,plain,
    ! [X0] :
      ( ~ '>='('+'(X0,'==>'(X0,'1')),X0)
      | '==>'('==>'(X0,'1'),X0) = X0 ),
    inference(forward_demodulation,[status(thm)],[f17,f5293]) ).

fof(f5295,plain,
    ! [X0] :
      ( ~ '>='('1',X0)
      | '==>'('==>'(X0,'1'),X0) = X0 ),
    inference(forward_demodulation,[status(thm)],[f2813,f5294]) ).

fof(f5296,plain,
    ! [X0] : '==>'('==>'(X0,'1'),X0) = X0,
    inference(forward_subsumption_resolution,[status(thm)],[f5295,f1103]) ).

fof(f5301,plain,
    ! [X0] :
      ( ~ '>='('+'('0',X0),X0)
      | '==>'('0',X0) = X0 ),
    inference(resolution,[status(thm)],[f1092,f2820]) ).

fof(f5302,plain,
    ! [X0] :
      ( ~ '>='(X0,X0)
      | '==>'('0',X0) = X0 ),
    inference(forward_demodulation,[status(thm)],[f850,f5301]) ).

fof(f5303,plain,
    ! [X0] : '==>'('0',X0) = X0,
    inference(forward_subsumption_resolution,[status(thm)],[f5302,f19]) ).

fof(f5384,plain,
    ! [X0,X1] :
      ( ~ '>='(X0,'0')
      | '>='(X1,'==>'(X0,X1)) ),
    inference(paramodulation,[status(thm)],[f5303,f35]) ).

fof(f5385,plain,
    ! [X0,X1] : '>='(X0,'==>'(X1,X0)),
    inference(forward_subsumption_resolution,[status(thm)],[f5384,f29]) ).

fof(f7421,plain,
    ! [X0,X1] :
      ( ~ '>='('==>'(X0,'1'),X1)
      | ~ '>='(X0,'==>'(X1,X0))
      | '==>'('==>'(X0,'1'),X0) = '==>'(X1,X0) ),
    inference(paramodulation,[status(thm)],[f5296,f3084]) ).

fof(f7422,plain,
    ! [X0,X1] :
      ( ~ '>='('==>'(X0,'1'),X1)
      | ~ '>='(X0,'==>'(X1,X0))
      | X0 = '==>'(X1,X0) ),
    inference(forward_demodulation,[status(thm)],[f5296,f7421]) ).

fof(f7423,plain,
    ! [X0,X1] :
      ( ~ '>='('==>'(X0,'1'),X1)
      | X0 = '==>'(X1,X0) ),
    inference(forward_subsumption_resolution,[status(thm)],[f7422,f5385]) ).

fof(f9088,plain,
    ! [X0,X1] :
      ( X0 = '==>'('==>'(X0,X1),X0)
      | ~ '>='('1',X1) ),
    inference(resolution,[status(thm)],[f7423,f38]) ).

fof(f9089,plain,
    ! [X0,X1] : X0 = '==>'('==>'(X0,X1),X0),
    inference(forward_subsumption_resolution,[status(thm)],[f9088,f1103]) ).

fof(f9191,plain,
    ! [X0,X1] :
      ( '0' = X0
      | ~ '>='('==>'(X0,X1),X0) ),
    inference(paramodulation,[status(thm)],[f9089,f2240]) ).

fof(f9194,plain,
    ! [X0,X1] :
      ( '0' = '==>'(X0,X1)
      | ~ '>='(X0,'==>'(X0,X1)) ),
    inference(resolution,[status(thm)],[f9191,f35]) ).

fof(f11514,plain,
    ! [X0,X1] : '>='(X0,'+'('==>'(X1,'+'(X1,X0)),'0')),
    inference(paramodulation,[status(thm)],[f18,f1365]) ).

fof(f11515,plain,
    ! [X0,X1] : '>='(X0,'==>'(X1,'+'(X1,X0))),
    inference(forward_demodulation,[status(thm)],[f18,f11514]) ).

fof(f11695,plain,
    ! [X0] : '0' = '==>'(X0,'+'(X0,X0)),
    inference(resolution,[status(thm)],[f11515,f9194]) ).

fof(f11885,plain,
    ! [X0] : '>='('+'(X0,'0'),'+'(X0,X0)),
    inference(paramodulation,[status(thm)],[f11695,f1094]) ).

fof(f11886,plain,
    ! [X0] : '>='(X0,'+'(X0,X0)),
    inference(forward_demodulation,[status(thm)],[f18,f11885]) ).

fof(f11927,plain,
    ! [X0] : X0 = '+'(X0,X0),
    inference(resolution,[status(thm)],[f11886,f2948]) ).

fof(f11994,plain,
    sk0_0 != sk0_0,
    inference(backward_demodulation,[status(thm)],[f11927,f43]) ).

fof(f11995,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f11994]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.04/0.12  % Problem  : LCL903+1 : TPTP v8.1.2. Released v5.5.0.
% 0.04/0.13  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.34  % Computer : n025.cluster.edu
% 0.13/0.34  % Model    : x86_64 x86_64
% 0.13/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.34  % Memory   : 8042.1875MB
% 0.13/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.34  % CPULimit : 300
% 0.13/0.34  % WCLimit  : 300
% 0.13/0.34  % DateTime : Tue May 30 09:57:27 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.13/0.35  % Drodi V3.5.1
% 14.84/2.30  % Refutation found
% 14.84/2.30  % SZS status Theorem for theBenchmark: Theorem is valid
% 14.84/2.30  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 15.55/2.35  % Elapsed time: 1.985784 seconds
% 15.55/2.35  % CPU time: 15.572081 seconds
% 15.55/2.35  % Memory used: 102.012 MB
%------------------------------------------------------------------------------