TSTP Solution File: NUM845+2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM845+2 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n019.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 10:40:58 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   12
% Syntax   : Number of formulae    :   38 (  25 unt;   6 typ;   0 def)
%            Number of atoms       :   39 (  38 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   13 (   6   ~;   0   |;   5   &)
%                                         (   0 <=>;   2  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :   41 (   0 sgn;  22   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    vd411: $i ).

tff(decl_23,type,
    vsucc: $i > $i ).

tff(decl_24,type,
    vmul: ( $i * $i ) > $i ).

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

tff(decl_26,type,
    v1: $i ).

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

fof('qu(ind(267), imp(267))',conjecture,
    ! [X1] :
      ( vmul(vsucc(vd411),X1) = vplus(vmul(vd411,X1),X1)
     => vmul(vsucc(vd411),vsucc(X1)) = vplus(vmul(vd411,vsucc(X1)),vsucc(X1)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(ind(267), imp(267))') ).

fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
    ! [X11,X12] :
      ( vplus(X11,vsucc(X12)) = vsucc(vplus(X11,X12))
      & vplus(X11,v1) = vsucc(X11) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))') ).

fof('ass(cond(43, 0), 0)',axiom,
    ! [X7] : vplus(v1,X7) = vsucc(X7),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(43, 0), 0)') ).

fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
    ! [X3,X4] :
      ( vmul(X3,vsucc(X4)) = vplus(vmul(X3,X4),X3)
      & vmul(X3,v1) = X3 ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))') ).

fof('ass(cond(61, 0), 0)',axiom,
    ! [X5,X6] : vplus(X6,X5) = vplus(X5,X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).

fof('ass(cond(33, 0), 0)',axiom,
    ! [X8,X9,X10] : vplus(vplus(X8,X9),X10) = vplus(X8,vplus(X9,X10)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).

fof(c_0_6,negated_conjecture,
    ~ ! [X1] :
        ( vmul(vsucc(vd411),X1) = vplus(vmul(vd411,X1),X1)
       => vmul(vsucc(vd411),vsucc(X1)) = vplus(vmul(vd411,vsucc(X1)),vsucc(X1)) ),
    inference(assume_negation,[status(cth)],['qu(ind(267), imp(267))']) ).

fof(c_0_7,negated_conjecture,
    ( vmul(vsucc(vd411),esk1_0) = vplus(vmul(vd411,esk1_0),esk1_0)
    & vmul(vsucc(vd411),vsucc(esk1_0)) != vplus(vmul(vd411,vsucc(esk1_0)),vsucc(esk1_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_6])])]) ).

fof(c_0_8,plain,
    ! [X30,X31] :
      ( vplus(X30,vsucc(X31)) = vsucc(vplus(X30,X31))
      & vplus(X30,v1) = vsucc(X30) ),
    inference(variable_rename,[status(thm)],['qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))']) ).

fof(c_0_9,plain,
    ! [X26] : vplus(v1,X26) = vsucc(X26),
    inference(variable_rename,[status(thm)],['ass(cond(43, 0), 0)']) ).

fof(c_0_10,plain,
    ! [X22,X23] :
      ( vmul(X22,vsucc(X23)) = vplus(vmul(X22,X23),X22)
      & vmul(X22,v1) = X22 ),
    inference(variable_rename,[status(thm)],['qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))']) ).

cnf(c_0_11,negated_conjecture,
    vmul(vsucc(vd411),vsucc(esk1_0)) != vplus(vmul(vd411,vsucc(esk1_0)),vsucc(esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_12,plain,
    vplus(X1,v1) = vsucc(X1),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,plain,
    vplus(v1,X1) = vsucc(X1),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

cnf(c_0_14,plain,
    vmul(X1,vsucc(X2)) = vplus(vmul(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

fof(c_0_15,plain,
    ! [X24,X25] : vplus(X25,X24) = vplus(X24,X25),
    inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).

cnf(c_0_16,negated_conjecture,
    vmul(vsucc(vd411),esk1_0) = vplus(vmul(vd411,esk1_0),esk1_0),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_17,negated_conjecture,
    vmul(vplus(vd411,v1),vplus(esk1_0,v1)) != vplus(vmul(vd411,vplus(esk1_0,v1)),vplus(esk1_0,v1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_11,c_0_12]),c_0_12]),c_0_12]),c_0_12]) ).

cnf(c_0_18,plain,
    vplus(v1,X1) = vplus(X1,v1),
    inference(rw,[status(thm)],[c_0_13,c_0_12]) ).

fof(c_0_19,plain,
    ! [X27,X28,X29] : vplus(vplus(X27,X28),X29) = vplus(X27,vplus(X28,X29)),
    inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).

cnf(c_0_20,plain,
    vmul(X1,vplus(X2,v1)) = vplus(vmul(X1,X2),X1),
    inference(rw,[status(thm)],[c_0_14,c_0_12]) ).

cnf(c_0_21,plain,
    vplus(X1,X2) = vplus(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_22,negated_conjecture,
    vplus(vmul(vd411,esk1_0),esk1_0) = vmul(vplus(vd411,v1),esk1_0),
    inference(rw,[status(thm)],[c_0_16,c_0_12]) ).

cnf(c_0_23,negated_conjecture,
    vplus(vmul(vd411,vplus(v1,esk1_0)),vplus(v1,esk1_0)) != vmul(vplus(vd411,v1),vplus(v1,esk1_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_18]),c_0_18]),c_0_18]) ).

cnf(c_0_24,plain,
    vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_19]) ).

cnf(c_0_25,plain,
    vmul(X1,vplus(X2,v1)) = vplus(X1,vmul(X1,X2)),
    inference(rw,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,negated_conjecture,
    vmul(vplus(vd411,v1),esk1_0) = vplus(esk1_0,vmul(vd411,esk1_0)),
    inference(rw,[status(thm)],[c_0_22,c_0_21]) ).

cnf(c_0_27,negated_conjecture,
    vplus(v1,vplus(esk1_0,vmul(vd411,vplus(v1,esk1_0)))) != vmul(vplus(vd411,v1),vplus(v1,esk1_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_21]),c_0_24]) ).

cnf(c_0_28,plain,
    vmul(X1,vplus(v1,X2)) = vplus(X1,vmul(X1,X2)),
    inference(spm,[status(thm)],[c_0_25,c_0_21]) ).

cnf(c_0_29,plain,
    vplus(X1,vplus(X2,X3)) = vplus(X2,vplus(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_21]),c_0_24]) ).

cnf(c_0_30,negated_conjecture,
    vplus(vd411,vplus(v1,vplus(esk1_0,vmul(vd411,esk1_0)))) = vmul(vplus(vd411,v1),vplus(v1,esk1_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_25,c_0_26]),c_0_18]),c_0_24]) ).

cnf(c_0_31,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_29]),c_0_29]),c_0_30])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM845+2 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n019.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Fri Aug 25 14:43:13 EDT 2023
% 0.12/0.34  % 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 : 0.012000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.015000 s
%------------------------------------------------------------------------------