TSTP Solution File: ALG177+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : ALG177+1 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %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 Aug 30 16:05:50 EDT 2023

% Result   : Theorem 0.19s 0.63s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   51 (   3 unt;   8 typ;   0 def)
%            Number of atoms       :  142 (  37 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  172 (  73   ~;  60   |;  17   &)
%                                         (   0 <=>;  22  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   16 (   4 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   7   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   1 con; 0-2 aty)
%            Number of variables   :   79 (   0 sgn;  32   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    sorti1: $i > $o ).

tff(decl_23,type,
    op1: ( $i * $i ) > $i ).

tff(decl_24,type,
    sorti2: $i > $o ).

tff(decl_25,type,
    op2: ( $i * $i ) > $i ).

tff(decl_26,type,
    h: $i > $i ).

tff(decl_27,type,
    j: $i > $i ).

tff(decl_28,type,
    esk1_0: $i ).

tff(decl_29,type,
    esk2_1: $i > $i ).

fof(co1,conjecture,
    ( ( ! [X1] :
          ( sorti1(X1)
         => sorti2(h(X1)) )
      & ! [X2] :
          ( sorti2(X2)
         => sorti1(j(X2)) ) )
   => ~ ( ! [X3] :
            ( sorti1(X3)
           => ! [X4] :
                ( sorti1(X4)
               => h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
        & ! [X5] :
            ( sorti2(X5)
           => ! [X6] :
                ( sorti2(X6)
               => j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
        & ! [X7] :
            ( sorti2(X7)
           => h(j(X7)) = X7 )
        & ! [X8] :
            ( sorti1(X8)
           => j(h(X8)) = X8 ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

fof(ax1,axiom,
    ! [X1] :
      ( sorti1(X1)
     => ! [X2] :
          ( sorti1(X2)
         => sorti1(op1(X1,X2)) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax1) ).

fof(ax4,axiom,
    ~ ? [X1] :
        ( sorti2(X1)
        & ! [X2] :
            ( sorti2(X2)
           => op2(X1,X2) != X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax4) ).

fof(ax3,axiom,
    ? [X1] :
      ( sorti1(X1)
      & ! [X2] :
          ( sorti1(X2)
         => op1(X1,X2) != X2 ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ax3) ).

fof(c_0_4,negated_conjecture,
    ~ ( ( ! [X1] :
            ( sorti1(X1)
           => sorti2(h(X1)) )
        & ! [X2] :
            ( sorti2(X2)
           => sorti1(j(X2)) ) )
     => ~ ( ! [X3] :
              ( sorti1(X3)
             => ! [X4] :
                  ( sorti1(X4)
                 => h(op1(X3,X4)) = op2(h(X3),h(X4)) ) )
          & ! [X5] :
              ( sorti2(X5)
             => ! [X6] :
                  ( sorti2(X6)
                 => j(op2(X5,X6)) = op1(j(X5),j(X6)) ) )
          & ! [X7] :
              ( sorti2(X7)
             => h(j(X7)) = X7 )
          & ! [X8] :
              ( sorti1(X8)
             => j(h(X8)) = X8 ) ) ),
    inference(assume_negation,[status(cth)],[co1]) ).

fof(c_0_5,negated_conjecture,
    ! [X17,X18,X19,X20,X21,X22,X23,X24] :
      ( ( ~ sorti1(X17)
        | sorti2(h(X17)) )
      & ( ~ sorti2(X18)
        | sorti1(j(X18)) )
      & ( ~ sorti1(X19)
        | ~ sorti1(X20)
        | h(op1(X19,X20)) = op2(h(X19),h(X20)) )
      & ( ~ sorti2(X21)
        | ~ sorti2(X22)
        | j(op2(X21,X22)) = op1(j(X21),j(X22)) )
      & ( ~ sorti2(X23)
        | h(j(X23)) = X23 )
      & ( ~ sorti1(X24)
        | j(h(X24)) = X24 ) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_4])])]) ).

fof(c_0_6,plain,
    ! [X9,X10] :
      ( ~ sorti1(X9)
      | ~ sorti1(X10)
      | sorti1(op1(X9,X10)) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax1])])]) ).

cnf(c_0_7,negated_conjecture,
    ( j(op2(X1,X2)) = op1(j(X1),j(X2))
    | ~ sorti2(X1)
    | ~ sorti2(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_8,negated_conjecture,
    ( j(h(X1)) = X1
    | ~ sorti1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_9,negated_conjecture,
    ( sorti2(h(X1))
    | ~ sorti1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_10,plain,
    ( sorti1(op1(X1,X2))
    | ~ sorti1(X1)
    | ~ sorti1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_11,negated_conjecture,
    ( sorti1(j(X1))
    | ~ sorti2(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_12,negated_conjecture,
    ( h(op1(X1,X2)) = op2(h(X1),h(X2))
    | ~ sorti1(X1)
    | ~ sorti1(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_13,negated_conjecture,
    ( h(j(X1)) = X1
    | ~ sorti2(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_5]) ).

cnf(c_0_14,negated_conjecture,
    ( j(op2(X1,h(X2))) = op1(j(X1),X2)
    | ~ sorti2(X1)
    | ~ sorti1(X2) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).

cnf(c_0_15,negated_conjecture,
    ( sorti1(j(op2(X1,X2)))
    | ~ sorti2(X2)
    | ~ sorti2(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_7]),c_0_11]),c_0_11]) ).

cnf(c_0_16,negated_conjecture,
    ( h(op1(X1,j(X2))) = op2(h(X1),X2)
    | ~ sorti2(X2)
    | ~ sorti1(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_13]),c_0_11]) ).

fof(c_0_17,plain,
    ! [X15] :
      ( ( sorti2(esk2_1(X15))
        | ~ sorti2(X15) )
      & ( op2(X15,esk2_1(X15)) = esk2_1(X15)
        | ~ sorti2(X15) ) ),
    inference(distribute,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax4])])])]) ).

cnf(c_0_18,negated_conjecture,
    ( j(h(op1(X1,X2))) = op1(j(h(X1)),X2)
    | ~ sorti1(X2)
    | ~ sorti1(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_12]),c_0_9]) ).

cnf(c_0_19,negated_conjecture,
    ( j(op2(h(X1),X2)) = op1(X1,j(X2))
    | ~ sorti2(X2)
    | ~ sorti1(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_8]),c_0_9]) ).

cnf(c_0_20,negated_conjecture,
    ( sorti1(j(h(op1(X1,X2))))
    | ~ sorti1(X2)
    | ~ sorti1(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_12]),c_0_9]),c_0_9]) ).

cnf(c_0_21,negated_conjecture,
    ( h(j(op2(X1,X2))) = op2(h(j(X1)),X2)
    | ~ sorti2(X2)
    | ~ sorti2(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_7]),c_0_11]) ).

cnf(c_0_22,plain,
    ( op2(X1,esk2_1(X1)) = esk2_1(X1)
    | ~ sorti2(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,plain,
    ( sorti2(esk2_1(X1))
    | ~ sorti2(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

fof(c_0_24,plain,
    ! [X14] :
      ( sorti1(esk1_0)
      & ( ~ sorti1(X14)
        | op1(esk1_0,X14) != X14 ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax3])])])]) ).

cnf(c_0_25,negated_conjecture,
    ( op1(j(h(X1)),X2) = op1(X1,X2)
    | ~ sorti1(X2)
    | ~ sorti1(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_18]),c_0_10]) ).

cnf(c_0_26,negated_conjecture,
    ( op1(j(h(X1)),X2) = op1(X1,j(h(X2)))
    | ~ sorti1(X2)
    | ~ sorti1(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_19]),c_0_9]),c_0_9]) ).

cnf(c_0_27,negated_conjecture,
    ( sorti1(j(op2(h(X1),X2)))
    | ~ sorti2(X2)
    | ~ sorti1(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_16]),c_0_11]) ).

cnf(c_0_28,negated_conjecture,
    ( op2(h(j(X1)),esk2_1(X1)) = h(j(esk2_1(X1)))
    | ~ sorti2(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]) ).

cnf(c_0_29,plain,
    ( ~ sorti1(X1)
    | op1(esk1_0,X1) != X1 ),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_30,negated_conjecture,
    ( op1(X1,j(h(X2))) = op1(X1,X2)
    | ~ sorti1(X2)
    | ~ sorti1(X1) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_31,plain,
    sorti1(esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_32,negated_conjecture,
    ( sorti1(j(h(j(esk2_1(X1)))))
    | ~ sorti2(X1) ),
    inference(csr,[status(thm)],[inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_11]),c_0_23]) ).

cnf(c_0_33,negated_conjecture,
    ( op2(X1,esk2_1(X1)) = h(j(esk2_1(X1)))
    | ~ sorti2(X1) ),
    inference(spm,[status(thm)],[c_0_28,c_0_13]) ).

cnf(c_0_34,negated_conjecture,
    ( j(h(X1)) != op1(esk1_0,X1)
    | ~ sorti1(j(h(X1)))
    | ~ sorti1(X1) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31])]) ).

cnf(c_0_35,negated_conjecture,
    ( sorti1(j(op2(X1,esk2_1(X1))))
    | ~ sorti2(X1) ),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_36,negated_conjecture,
    ( j(h(X1)) != op1(esk1_0,X1)
    | ~ sorti1(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_11]),c_0_9]) ).

cnf(c_0_37,negated_conjecture,
    ( sorti1(j(esk2_1(X1)))
    | ~ sorti2(X1) ),
    inference(spm,[status(thm)],[c_0_35,c_0_22]) ).

cnf(c_0_38,negated_conjecture,
    ( j(op2(X1,esk2_1(X1))) != op1(esk1_0,j(esk2_1(X1)))
    | ~ sorti2(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_33]),c_0_37]) ).

cnf(c_0_39,negated_conjecture,
    ( op1(esk1_0,j(esk2_1(X1))) != j(esk2_1(X1))
    | ~ sorti2(X1) ),
    inference(spm,[status(thm)],[c_0_38,c_0_22]) ).

cnf(c_0_40,negated_conjecture,
    ( op1(X1,j(esk2_1(h(X1)))) = j(esk2_1(h(X1)))
    | ~ sorti2(esk2_1(h(X1)))
    | ~ sorti1(X1) ),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_22]),c_0_9]) ).

cnf(c_0_41,negated_conjecture,
    ~ sorti2(h(esk1_0)),
    inference(csr,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_40]),c_0_31])]),c_0_23]) ).

cnf(c_0_42,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_9]),c_0_31])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : ALG177+1 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n026.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   : Mon Aug 28 05:52:19 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.19/0.63  % Version  : CSE_E---1.5
% 0.19/0.63  % Problem  : theBenchmark.p
% 0.19/0.63  % Proof found
% 0.19/0.63  % SZS status Theorem for theBenchmark.p
% 0.19/0.63  % SZS output start Proof
% See solution above
% 0.19/0.63  % Total time : 0.049000 s
% 0.19/0.63  % SZS output end Proof
% 0.19/0.63  % Total time : 0.052000 s
%------------------------------------------------------------------------------