TSTP Solution File: GRP659+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP659+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n032.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 00:22:50 EDT 2023

% Result   : Theorem 0.15s 0.49s
% Output   : CNFRefutation 0.15s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   56 (  47 unt;   5 typ;   0 def)
%            Number of atoms       :   55 (  54 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   10 (   6   ~;   2   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   0 con; 1-2 aty)
%            Number of variables   :  100 (   0 sgn;  25   !;   2   ?;   0   :)

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

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

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

tff(decl_25,type,
    esk1_1: $i > $i ).

tff(decl_26,type,
    esk2_1: $i > $i ).

fof(f04,axiom,
    ! [X1,X2] : rd(mult(X2,X1),X1) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).

fof(f05,axiom,
    ! [X3,X1,X2] : mult(mult(X2,mult(X1,X3)),X1) = mult(mult(X2,X1),mult(X3,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).

fof(f03,axiom,
    ! [X1,X2] : mult(rd(X2,X1),X1) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).

fof(f02,axiom,
    ! [X1,X2] : ld(X2,mult(X2,X1)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).

fof(f01,axiom,
    ! [X1,X2] : mult(X2,ld(X2,X1)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).

fof(goals,conjecture,
    ? [X4] :
    ! [X5] :
      ( mult(X5,X4) = X5
      & mult(X4,X5) = X5 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

fof(c_0_6,plain,
    ! [X12,X13] : rd(mult(X13,X12),X12) = X13,
    inference(variable_rename,[status(thm)],[f04]) ).

fof(c_0_7,plain,
    ! [X14,X15,X16] : mult(mult(X16,mult(X15,X14)),X15) = mult(mult(X16,X15),mult(X14,X15)),
    inference(variable_rename,[status(thm)],[f05]) ).

cnf(c_0_8,plain,
    rd(mult(X1,X2),X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_9,plain,
    mult(mult(X1,mult(X2,X3)),X2) = mult(mult(X1,X2),mult(X3,X2)),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_10,plain,
    ! [X10,X11] : mult(rd(X11,X10),X10) = X11,
    inference(variable_rename,[status(thm)],[f03]) ).

cnf(c_0_11,plain,
    rd(mult(mult(X1,X2),mult(X3,X2)),X2) = mult(X1,mult(X2,X3)),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,plain,
    mult(rd(X1,X2),X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

cnf(c_0_13,plain,
    rd(mult(mult(X1,X2),X3),X2) = mult(X1,mult(X2,rd(X3,X2))),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

fof(c_0_14,plain,
    ! [X8,X9] : ld(X9,mult(X9,X8)) = X8,
    inference(variable_rename,[status(thm)],[f02]) ).

cnf(c_0_15,plain,
    rd(mult(X1,X2),X3) = mult(rd(X1,X3),mult(X3,rd(X2,X3))),
    inference(spm,[status(thm)],[c_0_13,c_0_12]) ).

fof(c_0_16,plain,
    ! [X6,X7] : mult(X7,ld(X7,X6)) = X6,
    inference(variable_rename,[status(thm)],[f01]) ).

cnf(c_0_17,plain,
    ld(X1,mult(X1,X2)) = X2,
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_18,plain,
    mult(rd(rd(X1,X2),X3),mult(X3,rd(X2,X3))) = rd(X1,X3),
    inference(spm,[status(thm)],[c_0_15,c_0_12]) ).

cnf(c_0_19,plain,
    mult(X1,ld(X1,X2)) = X2,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_20,plain,
    mult(X1,mult(X2,rd(X2,X2))) = mult(X1,X2),
    inference(spm,[status(thm)],[c_0_8,c_0_13]) ).

cnf(c_0_21,plain,
    ld(rd(rd(X1,X2),X3),rd(X1,X3)) = mult(X3,rd(X2,X3)),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_22,plain,
    rd(X1,ld(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_8,c_0_19]) ).

cnf(c_0_23,plain,
    mult(X1,rd(X1,X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_20]),c_0_17]) ).

cnf(c_0_24,plain,
    mult(X1,rd(ld(X2,X3),X1)) = ld(rd(X2,X1),rd(X3,X1)),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_25,plain,
    rd(X1,X1) = ld(X1,X1),
    inference(spm,[status(thm)],[c_0_17,c_0_23]) ).

cnf(c_0_26,plain,
    rd(ld(X1,X2),X3) = ld(X3,ld(rd(X1,X3),rd(X2,X3))),
    inference(spm,[status(thm)],[c_0_17,c_0_24]) ).

cnf(c_0_27,plain,
    ld(ld(X1,ld(rd(X2,X1),rd(X2,X1))),rd(X2,X1)) = mult(X1,rd(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_25]),c_0_26]) ).

cnf(c_0_28,plain,
    ld(ld(ld(X1,X2),ld(X1,X1)),X1) = mult(ld(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_27,c_0_22]) ).

cnf(c_0_29,plain,
    ld(ld(X1,ld(X2,X2)),X2) = mult(X1,X2),
    inference(spm,[status(thm)],[c_0_28,c_0_17]) ).

cnf(c_0_30,plain,
    mult(ld(X1,X1),X1) = X1,
    inference(spm,[status(thm)],[c_0_12,c_0_25]) ).

cnf(c_0_31,plain,
    mult(ld(X1,ld(X2,X2)),mult(X1,X2)) = X2,
    inference(spm,[status(thm)],[c_0_19,c_0_29]) ).

cnf(c_0_32,plain,
    ld(rd(rd(X1,X2),X1),ld(X1,X1)) = mult(X1,rd(X2,X1)),
    inference(spm,[status(thm)],[c_0_21,c_0_25]) ).

cnf(c_0_33,plain,
    mult(mult(X1,ld(X2,X2)),X2) = mult(mult(X1,X2),ld(X2,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_30]),c_0_19]) ).

cnf(c_0_34,plain,
    mult(mult(X1,rd(X2,X1)),rd(X1,X2)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_31,c_0_32]),c_0_12]) ).

cnf(c_0_35,plain,
    rd(X1,mult(X2,X1)) = ld(X2,ld(X1,X1)),
    inference(spm,[status(thm)],[c_0_22,c_0_29]) ).

cnf(c_0_36,plain,
    mult(mult(X1,X1),ld(X1,X1)) = mult(X1,X1),
    inference(spm,[status(thm)],[c_0_33,c_0_19]) ).

cnf(c_0_37,plain,
    mult(mult(X1,X2),ld(X2,ld(X1,X1))) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_35]),c_0_15]),c_0_25]),c_0_19]),c_0_12]) ).

cnf(c_0_38,plain,
    ld(mult(X1,X1),mult(X1,X1)) = ld(X1,X1),
    inference(spm,[status(thm)],[c_0_17,c_0_36]) ).

cnf(c_0_39,plain,
    ld(mult(X1,X2),X1) = ld(X2,ld(X1,X1)),
    inference(spm,[status(thm)],[c_0_17,c_0_37]) ).

cnf(c_0_40,plain,
    mult(ld(X1,X1),mult(X1,X1)) = mult(X1,X1),
    inference(spm,[status(thm)],[c_0_30,c_0_38]) ).

fof(c_0_41,negated_conjecture,
    ~ ? [X4] :
      ! [X5] :
        ( mult(X5,X4) = X5
        & mult(X4,X5) = X5 ),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_42,plain,
    rd(X1,ld(X2,ld(X1,X1))) = mult(X1,X2),
    inference(spm,[status(thm)],[c_0_22,c_0_39]) ).

cnf(c_0_43,plain,
    ld(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_40]),c_0_25]),c_0_38]),c_0_38]) ).

fof(c_0_44,negated_conjecture,
    ! [X17] :
      ( mult(esk1_1(X17),X17) != esk1_1(X17)
      | mult(X17,esk2_1(X17)) != esk2_1(X17) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(shift_quantors,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_41])])])]) ).

cnf(c_0_45,plain,
    mult(ld(X1,X1),X2) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_43]),c_0_22]) ).

cnf(c_0_46,negated_conjecture,
    ( mult(esk1_1(X1),X1) != esk1_1(X1)
    | mult(X1,esk2_1(X1)) != esk2_1(X1) ),
    inference(split_conjunct,[status(thm)],[c_0_44]) ).

cnf(c_0_47,plain,
    ld(ld(X1,X1),X2) = X2,
    inference(spm,[status(thm)],[c_0_19,c_0_45]) ).

cnf(c_0_48,negated_conjecture,
    mult(esk1_1(ld(X1,X1)),ld(X1,X1)) != esk1_1(ld(X1,X1)),
    inference(spm,[status(thm)],[c_0_46,c_0_45]) ).

cnf(c_0_49,plain,
    mult(X1,ld(X2,X2)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_47]),c_0_22]) ).

cnf(c_0_50,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_48,c_0_49])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.09/0.10  % Problem    : GRP659+1 : TPTP v8.1.2. Released v4.0.0.
% 0.09/0.10  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.10/0.30  % Computer : n032.cluster.edu
% 0.10/0.30  % Model    : x86_64 x86_64
% 0.10/0.30  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.30  % Memory   : 8042.1875MB
% 0.10/0.30  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.10/0.30  % CPULimit   : 300
% 0.10/0.30  % WCLimit    : 300
% 0.10/0.30  % DateTime   : Mon Aug 28 20:55:31 EDT 2023
% 0.10/0.30  % CPUTime  : 
% 0.15/0.48  start to proof: theBenchmark
% 0.15/0.49  % Version  : CSE_E---1.5
% 0.15/0.49  % Problem  : theBenchmark.p
% 0.15/0.49  % Proof found
% 0.15/0.49  % SZS status Theorem for theBenchmark.p
% 0.15/0.49  % SZS output start Proof
% See solution above
% 0.15/0.50  % Total time : 0.011000 s
% 0.15/0.50  % SZS output end Proof
% 0.15/0.50  % Total time : 0.014000 s
%------------------------------------------------------------------------------