TSTP Solution File: GRP655+2 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP655+2 : 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 : 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 : Thu Aug 31 00:22:47 EDT 2023

% Result   : Theorem 12.98s 13.04s
% Output   : CNFRefutation 13.03s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   23
%            Number of leaves      :   11
% Syntax   : Number of formulae    :   78 (  69 unt;   5 typ;   0 def)
%            Number of atoms       :   77 (  76 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :    9 (   5   ~;   2   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    6 (   3   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :  158 (   0 sgn;  26   !;   0   ?;   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_0: $i ).

tff(decl_26,type,
    esk2_0: $i ).

fof(f05,axiom,
    ! [X3,X1,X2] : mult(X2,mult(X1,mult(X3,X1))) = mult(mult(mult(X2,X1),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(f04,axiom,
    ! [X1,X2] : rd(mult(X2,X1),X1) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).

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

fof(c_0_6,plain,
    ! [X14,X15,X16] : mult(X16,mult(X15,mult(X14,X15))) = mult(mult(mult(X16,X15),X14),X15),
    inference(variable_rename,[status(thm)],[f05]) ).

fof(c_0_7,plain,
    ! [X10,X11] : mult(rd(X11,X10),X10) = X11,
    inference(variable_rename,[status(thm)],[f03]) ).

fof(c_0_8,plain,
    ! [X8,X9] : ld(X9,mult(X9,X8)) = X8,
    inference(variable_rename,[status(thm)],[f02]) ).

cnf(c_0_9,plain,
    mult(X1,mult(X2,mult(X3,X2))) = mult(mult(mult(X1,X2),X3),X2),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    mult(rd(X1,X2),X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

cnf(c_0_11,plain,
    ld(X1,mult(X1,X2)) = X2,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_12,plain,
    mult(rd(X1,X2),mult(X2,mult(X3,X2))) = mult(mult(X1,X3),X2),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

fof(c_0_13,plain,
    ! [X6,X7] : mult(X7,ld(X7,X6)) = X6,
    inference(variable_rename,[status(thm)],[f01]) ).

cnf(c_0_14,plain,
    ld(rd(X1,X2),mult(mult(X1,X3),X2)) = mult(X2,mult(X3,X2)),
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_15,plain,
    mult(X1,ld(X1,X2)) = X2,
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

fof(c_0_16,plain,
    ! [X12,X13] : rd(mult(X13,X12),X12) = X13,
    inference(variable_rename,[status(thm)],[f04]) ).

cnf(c_0_17,plain,
    ld(rd(X1,X2),mult(X3,X2)) = mult(X2,mult(ld(X1,X3),X2)),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_18,plain,
    rd(mult(X1,X2),X2) = X1,
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_19,plain,
    mult(X1,mult(ld(X2,rd(X2,X1)),X1)) = X1,
    inference(spm,[status(thm)],[c_0_11,c_0_17]) ).

cnf(c_0_20,plain,
    rd(mult(X1,mult(X2,mult(X3,X2))),X2) = mult(mult(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_18,c_0_9]) ).

cnf(c_0_21,plain,
    ld(rd(X1,X2),X1) = X2,
    inference(spm,[status(thm)],[c_0_11,c_0_10]) ).

cnf(c_0_22,plain,
    mult(ld(X1,rd(X1,X2)),X2) = ld(X2,X2),
    inference(spm,[status(thm)],[c_0_11,c_0_19]) ).

cnf(c_0_23,plain,
    rd(mult(X1,mult(X2,X3)),X2) = mult(mult(X1,X2),rd(X3,X2)),
    inference(spm,[status(thm)],[c_0_20,c_0_10]) ).

cnf(c_0_24,plain,
    mult(X1,mult(ld(mult(X2,X1),X2),X1)) = X1,
    inference(spm,[status(thm)],[c_0_21,c_0_17]) ).

cnf(c_0_25,plain,
    mult(mult(X1,ld(X2,rd(X2,X3))),X3) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_22]),c_0_15]),c_0_10]) ).

cnf(c_0_26,plain,
    mult(mult(X1,X2),rd(ld(X2,X3),X2)) = rd(mult(X1,X3),X2),
    inference(spm,[status(thm)],[c_0_23,c_0_15]) ).

cnf(c_0_27,plain,
    mult(ld(mult(X1,X2),X1),X2) = ld(X2,X2),
    inference(spm,[status(thm)],[c_0_11,c_0_24]) ).

cnf(c_0_28,plain,
    mult(X1,ld(X2,rd(X2,X3))) = rd(X1,X3),
    inference(spm,[status(thm)],[c_0_18,c_0_25]) ).

cnf(c_0_29,plain,
    rd(X1,ld(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_18,c_0_15]) ).

cnf(c_0_30,plain,
    mult(X1,rd(ld(X2,X3),X2)) = rd(mult(rd(X1,X2),X3),X2),
    inference(spm,[status(thm)],[c_0_26,c_0_10]) ).

cnf(c_0_31,plain,
    ld(ld(mult(X1,X2),X1),ld(X2,X2)) = X2,
    inference(spm,[status(thm)],[c_0_11,c_0_27]) ).

cnf(c_0_32,plain,
    rd(X1,ld(X2,X3)) = mult(X1,ld(X3,X2)),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,plain,
    mult(X1,mult(X2,mult(ld(X2,X2),X2))) = mult(X1,mult(X2,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_32]),c_0_11]),c_0_32]),c_0_11]),c_0_32]),c_0_11]),c_0_9]) ).

cnf(c_0_34,plain,
    mult(X1,mult(ld(X1,X1),X1)) = mult(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_33]),c_0_11]) ).

cnf(c_0_35,plain,
    mult(ld(X1,X1),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_34]),c_0_11]) ).

cnf(c_0_36,plain,
    ld(X1,X1) = rd(X1,X1),
    inference(spm,[status(thm)],[c_0_18,c_0_35]) ).

cnf(c_0_37,plain,
    mult(mult(X1,rd(X2,X3)),X3) = mult(rd(X1,X3),mult(X3,X2)),
    inference(spm,[status(thm)],[c_0_12,c_0_10]) ).

cnf(c_0_38,plain,
    mult(X1,rd(X1,X1)) = X1,
    inference(spm,[status(thm)],[c_0_15,c_0_36]) ).

cnf(c_0_39,plain,
    rd(X1,rd(X2,X2)) = mult(X1,rd(X2,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_36]),c_0_36]) ).

cnf(c_0_40,plain,
    mult(mult(rd(X1,mult(X2,X3)),X2),rd(X3,X2)) = rd(X1,X2),
    inference(spm,[status(thm)],[c_0_23,c_0_10]) ).

cnf(c_0_41,plain,
    mult(rd(X1,X1),mult(X1,X1)) = mult(X1,X1),
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_42,plain,
    mult(rd(X1,X2),mult(X2,X2)) = mult(mult(X1,X2),rd(X2,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_38]),c_0_10]),c_0_39]),c_0_37]) ).

cnf(c_0_43,plain,
    mult(X1,mult(ld(X2,rd(X3,X1)),X1)) = ld(rd(X2,X1),X3),
    inference(spm,[status(thm)],[c_0_17,c_0_10]) ).

cnf(c_0_44,plain,
    rd(rd(X1,X2),rd(X3,X2)) = mult(rd(X1,mult(X2,X3)),X2),
    inference(spm,[status(thm)],[c_0_18,c_0_40]) ).

cnf(c_0_45,plain,
    mult(mult(X1,ld(X2,X3)),ld(X3,X2)) = X1,
    inference(spm,[status(thm)],[c_0_18,c_0_32]) ).

cnf(c_0_46,plain,
    ld(X1,rd(mult(rd(X1,X2),X3),X2)) = rd(ld(X2,X3),X2),
    inference(spm,[status(thm)],[c_0_11,c_0_30]) ).

cnf(c_0_47,plain,
    mult(mult(X1,X1),rd(X1,X1)) = mult(X1,X1),
    inference(rw,[status(thm)],[c_0_41,c_0_42]) ).

cnf(c_0_48,plain,
    mult(X1,mult(mult(rd(X2,mult(X1,X2)),X1),X1)) = ld(rd(rd(X2,X1),X1),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_36]),c_0_44]) ).

cnf(c_0_49,plain,
    mult(mult(X1,rd(X2,X2)),rd(X2,X2)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_36]),c_0_36]) ).

cnf(c_0_50,plain,
    ld(mult(X1,X2),rd(mult(X1,X3),X2)) = rd(ld(X2,X3),X2),
    inference(spm,[status(thm)],[c_0_46,c_0_18]) ).

cnf(c_0_51,plain,
    mult(ld(rd(X1,X1),X2),rd(X1,X1)) = mult(rd(X1,X1),mult(X2,rd(X1,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_39]),c_0_39]),c_0_9]),c_0_11]),c_0_39]) ).

cnf(c_0_52,plain,
    mult(rd(X1,mult(X2,mult(X3,X2))),X2) = rd(rd(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_44,c_0_18]) ).

cnf(c_0_53,plain,
    mult(mult(X1,mult(X2,rd(X3,X3))),rd(X3,X3)) = mult(mult(X1,rd(X3,X3)),mult(rd(X3,X3),X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_37,c_0_39]),c_0_39]) ).

cnf(c_0_54,plain,
    mult(mult(rd(X1,X2),rd(X1,X2)),mult(rd(X1,mult(X2,X1)),X2)) = mult(rd(X1,X2),rd(X1,X2)),
    inference(spm,[status(thm)],[c_0_47,c_0_44]) ).

cnf(c_0_55,plain,
    mult(rd(X1,X1),rd(X2,mult(rd(X1,X1),X2))) = rd(X2,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_39]),c_0_39]),c_0_49]),c_0_36]) ).

cnf(c_0_56,plain,
    ld(X1,mult(mult(X1,X2),rd(X1,X1))) = mult(rd(X1,X1),mult(X2,rd(X1,X1))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_38]),c_0_39]),c_0_39]),c_0_51]) ).

cnf(c_0_57,plain,
    rd(X1,mult(rd(X2,X2),mult(X3,rd(X2,X2)))) = mult(rd(mult(X1,rd(X2,X2)),X3),rd(X2,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_52]),c_0_39]) ).

cnf(c_0_58,plain,
    rd(mult(X1,X1),mult(X1,X1)) = rd(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_47]),c_0_36]) ).

cnf(c_0_59,plain,
    mult(X1,ld(mult(X2,X3),X2)) = rd(X1,X3),
    inference(spm,[status(thm)],[c_0_28,c_0_18]) ).

cnf(c_0_60,plain,
    mult(rd(X1,X2),rd(X2,X2)) = mult(rd(X1,mult(X2,X2)),X2),
    inference(spm,[status(thm)],[c_0_44,c_0_39]) ).

cnf(c_0_61,plain,
    mult(rd(mult(X1,X2),mult(X2,X3)),X2) = rd(X1,rd(X3,X2)),
    inference(spm,[status(thm)],[c_0_44,c_0_18]) ).

cnf(c_0_62,plain,
    mult(mult(X1,mult(rd(X2,X2),X1)),rd(X1,X1)) = mult(X1,mult(rd(X2,X2),X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_54]),c_0_39]),c_0_39]),c_0_53]),c_0_49]),c_0_39]),c_0_39]),c_0_53]),c_0_49]),c_0_55]) ).

cnf(c_0_63,plain,
    mult(rd(mult(X1,rd(X2,X2)),X3),rd(X2,X2)) = mult(X1,ld(mult(mult(X2,X3),rd(X2,X2)),X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_56]),c_0_57]) ).

cnf(c_0_64,plain,
    mult(rd(X1,mult(X1,X1)),X1) = rd(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_58,c_0_59]),c_0_44]),c_0_59]),c_0_39]),c_0_37]),c_0_42]),c_0_27]),c_0_36]),c_0_60]),c_0_32]),c_0_11]),c_0_27]),c_0_36]) ).

fof(c_0_65,negated_conjecture,
    ~ ! [X4,X5] :
        ( mult(X4,rd(X5,X5)) = X4
        & mult(rd(X5,X5),X4) = X4 ),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_66,plain,
    mult(rd(X1,mult(rd(X1,X1),X2)),rd(X1,X1)) = rd(X1,mult(X2,rd(X1,X1))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_61,c_0_38]),c_0_39]) ).

cnf(c_0_67,plain,
    mult(rd(X1,X1),rd(X2,X2)) = rd(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_63]),c_0_53]),c_0_38]),c_0_59]),c_0_55]),c_0_39]),c_0_60]),c_0_64]),c_0_53]),c_0_38]),c_0_59]),c_0_55]) ).

fof(c_0_68,negated_conjecture,
    ( mult(esk1_0,rd(esk2_0,esk2_0)) != esk1_0
    | mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0 ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_65])])]) ).

cnf(c_0_69,plain,
    mult(X1,rd(X2,X2)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_66,c_0_67]),c_0_39]),c_0_38]),c_0_38]),c_0_67]),c_0_39]) ).

cnf(c_0_70,negated_conjecture,
    ( mult(esk1_0,rd(esk2_0,esk2_0)) != esk1_0
    | mult(rd(esk2_0,esk2_0),esk1_0) != esk1_0 ),
    inference(split_conjunct,[status(thm)],[c_0_68]) ).

cnf(c_0_71,plain,
    mult(rd(X1,X1),X2) = X2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_56,c_0_69]),c_0_11]),c_0_69]) ).

cnf(c_0_72,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_70,c_0_69])]),c_0_71])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GRP655+2 : TPTP v8.1.2. Released v4.0.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.14/0.37  % Computer : n026.cluster.edu
% 0.14/0.37  % Model    : x86_64 x86_64
% 0.14/0.37  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.37  % Memory   : 8042.1875MB
% 0.14/0.37  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.37  % CPULimit   : 300
% 0.14/0.37  % WCLimit    : 300
% 0.14/0.37  % DateTime   : Tue Aug 29 01:17:20 EDT 2023
% 0.14/0.37  % CPUTime  : 
% 0.22/0.59  start to proof: theBenchmark
% 12.98/13.04  % Version  : CSE_E---1.5
% 12.98/13.04  % Problem  : theBenchmark.p
% 12.98/13.04  % Proof found
% 12.98/13.04  % SZS status Theorem for theBenchmark.p
% 12.98/13.04  % SZS output start Proof
% See solution above
% 13.03/13.05  % Total time : 12.439000 s
% 13.03/13.05  % SZS output end Proof
% 13.03/13.05  % Total time : 12.442000 s
%------------------------------------------------------------------------------