TSTP Solution File: LCL899+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : LCL899+1 : TPTP v8.1.2. Released v5.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n014.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 : Thu Aug 31 07:00:08 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    9
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   52 (  35 unt;   6 typ;   0 def)
%            Number of atoms       :   62 (  28 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   32 (  16   ~;  11   |;   2   &)
%                                         (   1 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    7 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            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   :   69 (  13 sgn;  32   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    '+': ( $i * $i ) > $i ).

tff(decl_23,type,
    '0': $i ).

tff(decl_24,type,
    '>=': ( $i * $i ) > $o ).

tff(decl_25,type,
    '==>': ( $i * $i ) > $i ).

tff(decl_26,type,
    '1': $i ).

tff(decl_27,type,
    esk1_0: $i ).

fof(sos_03,axiom,
    ! [X1] : '+'(X1,'0') = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_03) ).

fof(sos_02,axiom,
    ! [X1,X2] : '+'(X1,X2) = '+'(X2,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_02) ).

fof(sos_06,axiom,
    ! [X7,X8] :
      ( ( '>='(X7,X8)
        & '>='(X8,X7) )
     => X7 = X8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_06) ).

fof(sos_08,axiom,
    ! [X1] : '>='(X1,'0'),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_08) ).

fof(sos_07,axiom,
    ! [X9,X10,X11] :
      ( '>='('+'(X9,X10),X11)
    <=> '>='(X10,'==>'(X9,X11)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_07) ).

fof(sos_09,axiom,
    ! [X12,X13,X14] :
      ( '>='(X12,X13)
     => '>='('+'(X12,X14),'+'(X13,X14)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_09) ).

fof(sos_12,axiom,
    ! [X1] : '+'(X1,'1') = '1',
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_12) ).

fof(sos_13,axiom,
    ! [X1,X2] : '==>'('==>'(X1,X2),X2) = '==>'('==>'(X2,X1),X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',sos_13) ).

fof(goals_14,conjecture,
    ! [X21] : '==>'('==>'(X21,'1'),'1') = X21,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals_14) ).

fof(c_0_9,plain,
    ! [X27] : '+'(X27,'0') = X27,
    inference(variable_rename,[status(thm)],[sos_03]) ).

fof(c_0_10,plain,
    ! [X25,X26] : '+'(X25,X26) = '+'(X26,X25),
    inference(variable_rename,[status(thm)],[sos_02]) ).

fof(c_0_11,plain,
    ! [X32,X33] :
      ( ~ '>='(X32,X33)
      | ~ '>='(X33,X32)
      | X32 = X33 ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_06])]) ).

fof(c_0_12,plain,
    ! [X37] : '>='(X37,'0'),
    inference(variable_rename,[status(thm)],[sos_08]) ).

fof(c_0_13,plain,
    ! [X34,X35,X36] :
      ( ( ~ '>='('+'(X34,X35),X36)
        | '>='(X35,'==>'(X34,X36)) )
      & ( ~ '>='(X35,'==>'(X34,X36))
        | '>='('+'(X34,X35),X36) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_07])]) ).

fof(c_0_14,plain,
    ! [X38,X39,X40] :
      ( ~ '>='(X38,X39)
      | '>='('+'(X38,X40),'+'(X39,X40)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[sos_09])]) ).

cnf(c_0_15,plain,
    '+'(X1,'0') = X1,
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_16,plain,
    '+'(X1,X2) = '+'(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_17,plain,
    ! [X47] : '+'(X47,'1') = '1',
    inference(variable_rename,[status(thm)],[sos_12]) ).

cnf(c_0_18,plain,
    ( X1 = X2
    | ~ '>='(X1,X2)
    | ~ '>='(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,plain,
    '>='(X1,'0'),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_20,plain,
    ( '>='(X2,'==>'(X1,X3))
    | ~ '>='('+'(X1,X2),X3) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,plain,
    ( '>='('+'(X1,X3),'+'(X2,X3))
    | ~ '>='(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,plain,
    '+'('0',X1) = X1,
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_23,plain,
    '+'(X1,'1') = '1',
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_24,plain,
    ! [X48,X49] : '==>'('==>'(X48,X49),X49) = '==>'('==>'(X49,X48),X48),
    inference(variable_rename,[status(thm)],[sos_13]) ).

cnf(c_0_25,plain,
    ( '0' = X1
    | ~ '>='('0',X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_26,plain,
    '>='(X1,'==>'(X2,'0')),
    inference(spm,[status(thm)],[c_0_20,c_0_19]) ).

fof(c_0_27,negated_conjecture,
    ~ ! [X21] : '==>'('==>'(X21,'1'),'1') = X21,
    inference(assume_negation,[status(cth)],[goals_14]) ).

cnf(c_0_28,plain,
    '>='('+'(X1,X2),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_19]),c_0_22]) ).

cnf(c_0_29,plain,
    '+'('1',X1) = '1',
    inference(spm,[status(thm)],[c_0_23,c_0_16]) ).

cnf(c_0_30,plain,
    '==>'('==>'(X1,X2),X2) = '==>'('==>'(X2,X1),X1),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_31,plain,
    '==>'(X1,'0') = '0',
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

fof(c_0_32,negated_conjecture,
    '==>'('==>'(esk1_0,'1'),'1') != esk1_0,
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_27])])]) ).

cnf(c_0_33,plain,
    '>='('1',X1),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_34,plain,
    ( '>='('+'(X2,X1),X3)
    | ~ '>='(X1,'==>'(X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_35,plain,
    '==>'('==>'('0',X1),X1) = '0',
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_36,negated_conjecture,
    '==>'('==>'(esk1_0,'1'),'1') != esk1_0,
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_37,plain,
    '>='(X1,'==>'('1',X2)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_29]),c_0_33])]) ).

cnf(c_0_38,plain,
    '>='('+'('==>'('0',X1),X2),X1),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_19])]) ).

cnf(c_0_39,negated_conjecture,
    '==>'('==>'('1',esk1_0),esk1_0) != esk1_0,
    inference(rw,[status(thm)],[c_0_36,c_0_30]) ).

cnf(c_0_40,plain,
    '==>'('1',X1) = '0',
    inference(spm,[status(thm)],[c_0_25,c_0_37]) ).

cnf(c_0_41,plain,
    '>='('==>'('0',X1),X1),
    inference(spm,[status(thm)],[c_0_38,c_0_15]) ).

cnf(c_0_42,plain,
    '>='(X1,'==>'(X2,X1)),
    inference(spm,[status(thm)],[c_0_20,c_0_28]) ).

cnf(c_0_43,negated_conjecture,
    '==>'('0',esk1_0) != esk1_0,
    inference(rw,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_44,plain,
    '==>'('0',X1) = X1,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_41]),c_0_42])]) ).

cnf(c_0_45,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : LCL899+1 : TPTP v8.1.2. Released v5.5.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n014.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   : Fri Aug 25 00:27:03 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.57  start to proof: theBenchmark
% 0.20/0.59  % Version  : CSE_E---1.5
% 0.20/0.59  % Problem  : theBenchmark.p
% 0.20/0.59  % Proof found
% 0.20/0.59  % SZS status Theorem for theBenchmark.p
% 0.20/0.59  % SZS output start Proof
% See solution above
% 0.20/0.59  % Total time : 0.013000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.016000 s
%------------------------------------------------------------------------------