TSTP Solution File: LCL902+1 by Drodi---3.6.0

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Drodi---3.6.0
% Problem  : LCL902+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s

% Computer : n029.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 : Tue Apr 30 20:28:21 EDT 2024

% Result   : Theorem 0.21s 0.45s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   10
% Syntax   : Number of formulae    :   55 (  36 unt;   0 def)
%            Number of atoms       :   81 (  26 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   51 (  25   ~;  20   |;   3   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   3 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   :   88 (  87   !;   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(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(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,'1'),'1') = X17,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p') ).

fof(f15,negated_conjecture,
    ~ ! [X17] : '==>'('==>'(X17,'1'),'1') = 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(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(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,'1'),'1') != X17,
    inference(pre_NNF_transformation,[status(esa)],[f15]) ).

fof(f42,plain,
    '==>'('==>'(sk0_0,'1'),'1') != sk0_0,
    inference(skolemization,[status(esa)],[f41]) ).

fof(f43,plain,
    '==>'('==>'(sk0_0,'1'),'1') != sk0_0,
    inference(cnf_transformation,[status(esa)],[f42]) ).

fof(f46,plain,
    ! [X0,X1] : '>='(X0,'==>'(X1,'+'(X1,X0))),
    inference(resolution,[status(thm)],[f19,f27]) ).

fof(f47,plain,
    ! [X0,X1] : '>='('+'(X0,'==>'(X0,X1)),X1),
    inference(resolution,[status(thm)],[f19,f28]) ).

fof(f101,plain,
    ! [X0] : '>='('0','==>'(X0,X0)),
    inference(paramodulation,[status(thm)],[f18,f46]) ).

fof(f104,plain,
    ! [X0] : '1' = '+'('1',X0),
    inference(paramodulation,[status(thm)],[f39,f17]) ).

fof(f113,plain,
    ! [X0,X1,X2] :
      ( ~ '>='('+'(X0,X1),X2)
      | '>='(X0,'==>'(X1,X2)) ),
    inference(paramodulation,[status(thm)],[f17,f27]) ).

fof(f134,plain,
    ! [X0] : '>='('1',X0),
    inference(paramodulation,[status(thm)],[f104,f47]) ).

fof(f144,plain,
    ! [X0,X1] : '>='('==>'(X0,'1'),'==>'(X0,X1)),
    inference(resolution,[status(thm)],[f134,f38]) ).

fof(f198,plain,
    ! [X0] :
      ( ~ '>='('==>'(X0,X0),'0')
      | '0' = '==>'(X0,X0) ),
    inference(resolution,[status(thm)],[f24,f101]) ).

fof(f199,plain,
    ! [X0] : '0' = '==>'(X0,X0),
    inference(forward_subsumption_resolution,[status(thm)],[f198,f29]) ).

fof(f205,plain,
    ! [X0] :
      ( ~ '>='(X0,'1')
      | '1' = X0 ),
    inference(resolution,[status(thm)],[f24,f134]) ).

fof(f223,plain,
    ! [X0,X1] :
      ( '>='('+'(X0,X1),X0)
      | ~ '>='(X1,'0') ),
    inference(paramodulation,[status(thm)],[f199,f28]) ).

fof(f224,plain,
    ! [X0,X1] : '>='('+'(X0,X1),X0),
    inference(forward_subsumption_resolution,[status(thm)],[f223,f29]) ).

fof(f237,plain,
    ! [X0,X1] : '>='('+'(X0,X1),X1),
    inference(paramodulation,[status(thm)],[f17,f224]) ).

fof(f239,plain,
    ! [X0,X1] : '>='(X0,'==>'(X1,X0)),
    inference(resolution,[status(thm)],[f237,f27]) ).

fof(f260,plain,
    ! [X0] : '1' = '+'(X0,'==>'(X0,'1')),
    inference(resolution,[status(thm)],[f205,f47]) ).

fof(f627,plain,
    ! [X0] : '>='('+'('==>'('==>'(X0,'1'),X0),'0'),X0),
    inference(paramodulation,[status(thm)],[f40,f47]) ).

fof(f628,plain,
    ! [X0] : '>='('==>'('==>'(X0,'1'),X0),X0),
    inference(forward_demodulation,[status(thm)],[f18,f627]) ).

fof(f652,plain,
    ! [X0,X1] :
      ( ~ '>='('1',X0)
      | '>='(X1,'==>'('==>'(X1,'1'),X0)) ),
    inference(paramodulation,[status(thm)],[f260,f113]) ).

fof(f653,plain,
    ! [X0,X1] : '>='(X0,'==>'('==>'(X0,'1'),X1)),
    inference(forward_subsumption_resolution,[status(thm)],[f652,f134]) ).

fof(f1119,plain,
    ! [X0] :
      ( ~ '>='(X0,'==>'('==>'(X0,'1'),X0))
      | '==>'('==>'(X0,'1'),X0) = X0 ),
    inference(resolution,[status(thm)],[f628,f24]) ).

fof(f1120,plain,
    ! [X0] : '==>'('==>'(X0,'1'),X0) = X0,
    inference(forward_subsumption_resolution,[status(thm)],[f1119,f239]) ).

fof(f1170,plain,
    ! [X0] : '>='('==>'('==>'(X0,'1'),'1'),X0),
    inference(paramodulation,[status(thm)],[f1120,f144]) ).

fof(f2105,plain,
    ! [X0] :
      ( ~ '>='(X0,'==>'('==>'(X0,'1'),'1'))
      | '==>'('==>'(X0,'1'),'1') = X0 ),
    inference(resolution,[status(thm)],[f1170,f24]) ).

fof(f2106,plain,
    ! [X0] : '==>'('==>'(X0,'1'),'1') = X0,
    inference(forward_subsumption_resolution,[status(thm)],[f2105,f653]) ).

fof(f2130,plain,
    sk0_0 != sk0_0,
    inference(backward_demodulation,[status(thm)],[f2106,f43]) ).

fof(f2131,plain,
    $false,
    inference(trivial_equality_resolution,[status(esa)],[f2130]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.13  % Problem  : LCL902+1 : TPTP v8.1.2. Released v5.5.0.
% 0.08/0.14  % Command  : drodi -learnfrom(drodi.lrn) -timeout(%d) %s
% 0.13/0.35  % Computer : n029.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Mon Apr 29 20:33:35 EDT 2024
% 0.13/0.35  % CPUTime  : 
% 0.13/0.36  % Drodi V3.6.0
% 0.21/0.45  % Refutation found
% 0.21/0.45  % SZS status Theorem for theBenchmark: Theorem is valid
% 0.21/0.45  % SZS output start CNFRefutation for theBenchmark
% See solution above
% 0.21/0.48  % Elapsed time: 0.112470 seconds
% 0.21/0.48  % CPU time: 0.787942 seconds
% 0.21/0.48  % Total memory used: 48.581 MB
% 0.21/0.48  % Net memory used: 47.570 MB
%------------------------------------------------------------------------------