TSTP Solution File: NUM853+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : NUM853+1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n025.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 10:41:03 EDT 2023

% Result   : Theorem 0.20s 0.77s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :   27
% Syntax   : Number of formulae    :   62 (  32 unt;  16 typ;   0 def)
%            Number of atoms       :   69 (  46 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   48 (  25   ~;  19   |;   2   &)
%                                         (   2 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   3 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   22 (  12   >;  10   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   4 con; 0-2 aty)
%            Number of variables   :   88 (  10 sgn;  47   !;   3   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    vd486: $i ).

tff(decl_23,type,
    vd488: $i ).

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

tff(decl_25,type,
    vd487: $i ).

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

tff(decl_27,type,
    less: ( $i * $i ) > $o ).

tff(decl_28,type,
    vplus: ( $i * $i ) > $i ).

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

tff(decl_30,type,
    v1: $i ).

tff(decl_31,type,
    leq: ( $i * $i ) > $o ).

tff(decl_32,type,
    geq: ( $i * $i ) > $o ).

tff(decl_33,type,
    vskolem2: $i > $i ).

tff(decl_34,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_35,type,
    esk2_2: ( $i * $i ) > $i ).

tff(decl_36,type,
    esk3_2: ( $i * $i ) > $i ).

tff(decl_37,type,
    esk4_2: ( $i * $i ) > $i ).

fof('ass(cond(73, 0), 0)',axiom,
    ! [X82,X83] : X83 != vplus(X82,X83),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(73, 0), 0)') ).

fof('ass(cond(33, 0), 0)',axiom,
    ! [X89,X90,X91] : vplus(vplus(X89,X90),X91) = vplus(X89,vplus(X90,X91)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(33, 0), 0)') ).

fof('ass(cond(270, 0), 0)',axiom,
    ! [X14,X15] : vmul(X14,X15) = vmul(X15,X14),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(270, 0), 0)') ).

fof('ass(cond(61, 0), 0)',axiom,
    ! [X84,X85] : vplus(X85,X84) = vplus(X84,X85),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(61, 0), 0)') ).

fof('def(cond(conseq(axiom(3)), 11), 1)',axiom,
    ! [X72,X73] :
      ( greater(X73,X72)
    <=> ? [X74] : X73 = vplus(X72,X74) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 11), 1)') ).

fof('holds(antec(307), 489, 0)',axiom,
    greater(vmul(vd486,vd487),vmul(vd488,vd487)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(antec(307), 489, 0)') ).

fof('ass(cond(281, 0), 0)',axiom,
    ! [X11,X12,X13] : vmul(X11,vplus(X12,X13)) = vplus(vmul(X11,X12),vmul(X11,X13)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(281, 0), 0)') ).

fof('def(cond(conseq(axiom(3)), 12), 1)',axiom,
    ! [X69,X70] :
      ( less(X70,X69)
    <=> ? [X71] : X69 = vplus(X70,X71) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','def(cond(conseq(axiom(3)), 12), 1)') ).

fof('ass(cond(goal(130), 0), 0)',axiom,
    ! [X67,X68] :
      ( X67 = X68
      | greater(X67,X68)
      | less(X67,X68) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(130), 0), 0)') ).

fof('ass(cond(goal(88), 0), 1)',axiom,
    ! [X75,X76] :
      ( X75 != X76
      | ~ ? [X78] : X76 = vplus(X75,X78) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','ass(cond(goal(88), 0), 1)') ).

fof('holds(conseq(307), 490, 0)',conjecture,
    greater(vd486,vd488),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p','holds(conseq(307), 490, 0)') ).

fof(c_0_11,plain,
    ! [X218,X219] : X219 != vplus(X218,X219),
    inference(variable_rename,[status(thm)],['ass(cond(73, 0), 0)']) ).

fof(c_0_12,plain,
    ! [X225,X226,X227] : vplus(vplus(X225,X226),X227) = vplus(X225,vplus(X226,X227)),
    inference(variable_rename,[status(thm)],['ass(cond(33, 0), 0)']) ).

fof(c_0_13,plain,
    ! [X116,X117] : vmul(X116,X117) = vmul(X117,X116),
    inference(variable_rename,[status(thm)],['ass(cond(270, 0), 0)']) ).

cnf(c_0_14,plain,
    X1 != vplus(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_15,plain,
    vplus(vplus(X1,X2),X3) = vplus(X1,vplus(X2,X3)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_16,plain,
    ! [X220,X221] : vplus(X221,X220) = vplus(X220,X221),
    inference(variable_rename,[status(thm)],['ass(cond(61, 0), 0)']) ).

fof(c_0_17,plain,
    ! [X195,X196,X198,X199,X200] :
      ( ( ~ greater(X196,X195)
        | X196 = vplus(X195,esk2_2(X195,X196)) )
      & ( X199 != vplus(X198,X200)
        | greater(X199,X198) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 11), 1)'])])])])]) ).

cnf(c_0_18,plain,
    greater(vmul(vd486,vd487),vmul(vd488,vd487)),
    inference(split_conjunct,[status(thm)],['holds(antec(307), 489, 0)']) ).

cnf(c_0_19,plain,
    vmul(X1,X2) = vmul(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_20,plain,
    vplus(X1,vplus(X2,X3)) != X3,
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_21,plain,
    vplus(X1,X2) = vplus(X2,X1),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_22,plain,
    ( X1 = vplus(X2,esk2_2(X2,X1))
    | ~ greater(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_23,plain,
    greater(vmul(vd486,vd487),vmul(vd487,vd488)),
    inference(rw,[status(thm)],[c_0_18,c_0_19]) ).

fof(c_0_24,plain,
    ! [X113,X114,X115] : vmul(X113,vplus(X114,X115)) = vplus(vmul(X113,X114),vmul(X113,X115)),
    inference(variable_rename,[status(thm)],['ass(cond(281, 0), 0)']) ).

cnf(c_0_25,plain,
    vplus(X1,vplus(X2,X3)) != X2,
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_26,plain,
    vplus(vmul(vd487,vd488),esk2_2(vmul(vd487,vd488),vmul(vd486,vd487))) = vmul(vd486,vd487),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_27,plain,
    vmul(X1,vplus(X2,X3)) = vplus(vmul(X1,X2),vmul(X1,X3)),
    inference(split_conjunct,[status(thm)],[c_0_24]) ).

cnf(c_0_28,plain,
    vplus(X1,vmul(vd486,vd487)) != vmul(vd487,vd488),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_29,plain,
    vplus(vmul(X1,X2),vmul(X3,X1)) = vmul(X1,vplus(X2,X3)),
    inference(spm,[status(thm)],[c_0_27,c_0_19]) ).

fof(c_0_30,plain,
    ! [X189,X190,X192,X193,X194] :
      ( ( ~ less(X190,X189)
        | X189 = vplus(X190,esk1_2(X189,X190)) )
      & ( X192 != vplus(X193,X194)
        | less(X193,X192) ) ),
    inference(shift_quantors,[status(thm)],[inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],['def(cond(conseq(axiom(3)), 12), 1)'])])])])]) ).

fof(c_0_31,plain,
    ! [X181,X182] :
      ( X181 = X182
      | greater(X181,X182)
      | less(X181,X182) ),
    inference(variable_rename,[status(thm)],['ass(cond(goal(130), 0), 0)']) ).

fof(c_0_32,plain,
    ! [X205,X206,X207] :
      ( X205 != X206
      | X206 != vplus(X205,X207) ),
    inference(shift_quantors,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],['ass(cond(goal(88), 0), 1)'])])]) ).

cnf(c_0_33,plain,
    vmul(vd487,vplus(X1,vd486)) != vmul(vd487,vd488),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_34,plain,
    ( X2 = vplus(X1,esk1_2(X2,X1))
    | ~ less(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_30]) ).

cnf(c_0_35,plain,
    ( X1 = X2
    | greater(X1,X2)
    | less(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_36,plain,
    ( X1 != X2
    | X2 != vplus(X1,X3) ),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_37,plain,
    vmul(vd487,vplus(vd486,X1)) != vmul(vd487,vd488),
    inference(spm,[status(thm)],[c_0_33,c_0_21]) ).

cnf(c_0_38,plain,
    ( vplus(X1,esk1_2(X2,X1)) = X2
    | X1 = X2
    | greater(X1,X2) ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

fof(c_0_39,negated_conjecture,
    ~ greater(vd486,vd488),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],['holds(conseq(307), 490, 0)'])]) ).

cnf(c_0_40,plain,
    vplus(X1,X2) != X1,
    inference(er,[status(thm)],[c_0_36]) ).

cnf(c_0_41,plain,
    ( vd486 = X1
    | greater(vd486,X1)
    | vmul(vd487,X1) != vmul(vd487,vd488) ),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_42,negated_conjecture,
    ~ greater(vd486,vd488),
    inference(split_conjunct,[status(thm)],[c_0_39]) ).

cnf(c_0_43,plain,
    vmul(vd487,vd488) != vmul(vd486,vd487),
    inference(spm,[status(thm)],[c_0_40,c_0_26]) ).

cnf(c_0_44,plain,
    vd488 = vd486,
    inference(sr,[status(thm)],[inference(er,[status(thm)],[c_0_41]),c_0_42]) ).

cnf(c_0_45,plain,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_44]),c_0_19])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : NUM853+1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.34  % Computer : n025.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit   : 300
% 0.14/0.34  % WCLimit    : 300
% 0.14/0.34  % DateTime   : Fri Aug 25 16:36:52 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 0.20/0.56  start to proof: theBenchmark
% 0.20/0.77  % Version  : CSE_E---1.5
% 0.20/0.77  % Problem  : theBenchmark.p
% 0.20/0.77  % Proof found
% 0.20/0.77  % SZS status Theorem for theBenchmark.p
% 0.20/0.77  % SZS output start Proof
% See solution above
% 0.20/0.78  % Total time : 0.206000 s
% 0.20/0.78  % SZS output end Proof
% 0.20/0.78  % Total time : 0.210000 s
%------------------------------------------------------------------------------