TSTP Solution File: NUM849+2 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM849+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 : n027.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 10:41:01 EDT 2023

% Result   : Theorem 0.20s 0.59s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   40 (  22 unt;   7 typ;   0 def)
%            Number of atoms       :   44 (  43 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   19 (   8   ~;   3   |;   5   &)
%                                         (   0 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    4 (   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    :    7 (   7 usr;   4 con; 0-2 aty)
%            Number of variables   :   43 (   0 sgn;  24   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    vd448: $i ).

tff(decl_23,type,
    vd449: $i ).

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

tff(decl_25,type,
    vsucc: $i > $i ).

tff(decl_26,type,
    vplus: ( $i * $i ) > $i ).

tff(decl_27,type,
    v1: $i ).

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

fof('ass(cond(261, 0), 0)',axiom,
    ! [X8,X9] : vmul(vsucc(X8),X9) = vplus(vmul(X8,X9),X9),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(261, 0), 0)') ).

fof('qu(cond(conseq(axiom(3)), 3), and(holds(definiens(29), 45, 0), holds(definiens(29), 44, 0)))',axiom,
    ! [X14,X15] :
      ( vplus(X14,vsucc(X15)) = vsucc(vplus(X14,X15))
      & vplus(X14,v1) = vsucc(X14) ),
    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('qu(ind(296), imp(296))',conjecture,
    ! [X1] :
      ( vmul(vmul(vd448,vd449),X1) = vmul(vd448,vmul(vd449,X1))
     => vmul(vmul(vd448,vd449),vsucc(X1)) = vmul(vd448,vmul(vd449,vsucc(X1))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','qu(ind(296), imp(296))') ).

fof('qu(cond(conseq(axiom(3)), 32), and(holds(definiens(249), 399, 0), holds(definiens(249), 398, 0)))',axiom,
    ! [X10,X11] :
      ( vmul(X10,vsucc(X11)) = vplus(vmul(X10,X11),X10)
      & vmul(X10,v1) = X10 ),
    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,
    ! [X12,X13] : vplus(X13,X12) = vplus(X12,X13),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).

fof('ass(cond(270, 0), 0)',axiom,
    ! [X6,X7] : vmul(X6,X7) = vmul(X7,X6),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).

fof('ass(cond(conseq(292), 1), 1)',axiom,
    ! [X2] :
      ( vmul(vmul(vd448,vd449),X2) = vmul(vd448,vmul(vd449,X2))
     => vplus(vmul(vd448,vmul(vd449,X2)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,X2),vd449)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p','ass(cond(conseq(292), 1), 1)') ).

fof(c_0_7,plain,
    ! [X26,X27] : vmul(vsucc(X26),X27) = vplus(vmul(X26,X27),X27),
    inference(variable_rename,[status(thm)],['ass(cond(261, 0), 0)']) ).

fof(c_0_8,plain,
    ! [X32,X33] :
      ( vplus(X32,vsucc(X33)) = vsucc(vplus(X32,X33))
      & vplus(X32,v1) = vsucc(X32) ),
    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,negated_conjecture,
    ~ ! [X1] :
        ( vmul(vmul(vd448,vd449),X1) = vmul(vd448,vmul(vd449,X1))
       => vmul(vmul(vd448,vd449),vsucc(X1)) = vmul(vd448,vmul(vd449,vsucc(X1))) ),
    inference(assume_negation,[status(cth)],['qu(ind(296), imp(296))']) ).

fof(c_0_10,plain,
    ! [X28,X29] :
      ( vmul(X28,vsucc(X29)) = vplus(vmul(X28,X29),X28)
      & vmul(X28,v1) = X28 ),
    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,plain,
    vmul(vsucc(X1),X2) = vplus(vmul(X1,X2),X2),
    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]) ).

fof(c_0_13,plain,
    ! [X30,X31] : vplus(X31,X30) = vplus(X30,X31),
    inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).

fof(c_0_14,negated_conjecture,
    ( vmul(vmul(vd448,vd449),esk1_0) = vmul(vd448,vmul(vd449,esk1_0))
    & vmul(vmul(vd448,vd449),vsucc(esk1_0)) != vmul(vd448,vmul(vd449,vsucc(esk1_0))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])])]) ).

fof(c_0_15,plain,
    ! [X24,X25] : vmul(X24,X25) = vmul(X25,X24),
    inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).

cnf(c_0_16,plain,
    vmul(X1,vsucc(X2)) = vplus(vmul(X1,X2),X1),
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_17,plain,
    vmul(vplus(X1,v1),X2) = vplus(vmul(X1,X2),X2),
    inference(rw,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_18,plain,
    vplus(X1,X2) = vplus(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_19,negated_conjecture,
    vmul(vmul(vd448,vd449),esk1_0) = vmul(vd448,vmul(vd449,esk1_0)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_20,plain,
    vmul(X1,X2) = vmul(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

fof(c_0_21,plain,
    ! [X18] :
      ( vmul(vmul(vd448,vd449),X18) != vmul(vd448,vmul(vd449,X18))
      | vplus(vmul(vd448,vmul(vd449,X18)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,X18),vd449)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(conseq(292), 1), 1)'])]) ).

cnf(c_0_22,plain,
    vmul(X1,vplus(X2,v1)) = vplus(vmul(X1,X2),X1),
    inference(rw,[status(thm)],[c_0_16,c_0_12]) ).

cnf(c_0_23,negated_conjecture,
    vmul(vmul(vd448,vd449),vsucc(esk1_0)) != vmul(vd448,vmul(vd449,vsucc(esk1_0))),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_24,plain,
    vplus(X1,vmul(X2,X1)) = vmul(vplus(X2,v1),X1),
    inference(rw,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_25,negated_conjecture,
    vmul(esk1_0,vmul(vd449,vd448)) = vmul(vd448,vmul(vd449,esk1_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_19,c_0_20]),c_0_20]) ).

cnf(c_0_26,plain,
    ( vplus(vmul(vd448,vmul(vd449,X1)),vmul(vd448,vd449)) = vmul(vd448,vplus(vmul(vd449,X1),vd449))
    | vmul(vmul(vd448,vd449),X1) != vmul(vd448,vmul(vd449,X1)) ),
    inference(split_conjunct,[status(thm)],[c_0_21]) ).

cnf(c_0_27,plain,
    vplus(X1,vmul(X1,X2)) = vmul(X1,vplus(X2,v1)),
    inference(rw,[status(thm)],[c_0_22,c_0_18]) ).

cnf(c_0_28,negated_conjecture,
    vmul(vmul(vd448,vd449),vplus(esk1_0,v1)) != vmul(vd448,vmul(vd449,vplus(esk1_0,v1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_23,c_0_12]),c_0_12]) ).

cnf(c_0_29,negated_conjecture,
    vplus(vmul(vd449,vd448),vmul(vd448,vmul(vd449,esk1_0))) = vmul(vmul(vd449,vd448),vplus(v1,esk1_0)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_18]),c_0_20]) ).

cnf(c_0_30,plain,
    ( vplus(vmul(vd449,vd448),vmul(vd448,vmul(vd449,X1))) = vmul(vd448,vmul(vd449,vplus(X1,v1)))
    | vmul(vmul(vd449,vd448),X1) != vmul(vd448,vmul(vd449,X1)) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_26,c_0_20]),c_0_18]),c_0_18]),c_0_27]),c_0_20]) ).

cnf(c_0_31,negated_conjecture,
    vmul(vmul(vd449,vd448),vplus(v1,esk1_0)) != vmul(vd448,vmul(vd449,vplus(v1,esk1_0))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_28,c_0_20]),c_0_18]),c_0_18]) ).

cnf(c_0_32,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_18]),c_0_31]),c_0_20]),c_0_25])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM849+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
% 0.13/0.34  % Computer : n027.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 17:51:48 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 : 0.008000 s
% 0.20/0.59  % SZS output end Proof
% 0.20/0.59  % Total time : 0.010000 s
%------------------------------------------------------------------------------