TSTP Solution File: GRP683+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP683+1 : TPTP v8.1.2. Released v4.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n021.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 00:23:03 EDT 2023

% Result   : Theorem 0.20s 0.61s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   28
%            Number of leaves      :   14
% Syntax   : Number of formulae    :   80 (  68 unt;   6 typ;   0 def)
%            Number of atoms       :   80 (  79 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   15 (   9   ~;   4   |;   2   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    6 (   2 avg)
%            Maximal term depth    :    5 (   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    :    6 (   6 usr;   3 con; 0-2 aty)
%            Number of variables   :  157 (   0 sgn;  38   !;   0   ?;   0   :)

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

tff(decl_23,type,
    ld: ( $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 ).

tff(decl_27,type,
    esk3_0: $i ).

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

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

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

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

fof(f07,axiom,
    ! [X2,X1] : ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f07) ).

fof(f06,axiom,
    ! [X3,X4,X2,X1] : rd(mult(mult(X1,X2),rd(X4,X3)),rd(X4,X3)) = mult(X1,rd(mult(X2,X3),X3)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f06) ).

fof(f05,axiom,
    ! [X3,X4,X2,X1] : ld(ld(X1,X2),mult(ld(X1,X2),mult(X4,X3))) = mult(ld(X1,mult(X1,X4)),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',f05) ).

fof(goals,conjecture,
    ! [X5,X6,X7] :
      ( mult(X5,ld(X6,mult(X6,X7))) = mult(X5,X7)
      & mult(rd(mult(X5,X6),X6),X7) = mult(X5,X7) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',goals) ).

fof(c_0_8,plain,
    ! [X8] : ld(X8,mult(X8,X8)) = X8,
    inference(variable_rename,[status(thm)],[f01]) ).

fof(c_0_9,plain,
    ! [X10,X11] : mult(X11,ld(X11,X10)) = ld(X11,mult(X11,X10)),
    inference(variable_rename,[status(thm)],[f03]) ).

fof(c_0_10,plain,
    ! [X9] : rd(mult(X9,X9),X9) = X9,
    inference(variable_rename,[status(thm)],[f02]) ).

fof(c_0_11,plain,
    ! [X12,X13] : mult(rd(X13,X12),X12) = rd(mult(X13,X12),X12),
    inference(variable_rename,[status(thm)],[f04]) ).

fof(c_0_12,plain,
    ! [X22,X23] : ld(X23,mult(X23,ld(X22,X22))) = rd(mult(rd(X23,X23),X22),X22),
    inference(variable_rename,[status(thm)],[f07]) ).

cnf(c_0_13,plain,
    ld(X1,mult(X1,X1)) = X1,
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_14,plain,
    mult(X1,ld(X1,X2)) = ld(X1,mult(X1,X2)),
    inference(split_conjunct,[status(thm)],[c_0_9]) ).

fof(c_0_15,plain,
    ! [X18,X19,X20,X21] : rd(mult(mult(X21,X20),rd(X19,X18)),rd(X19,X18)) = mult(X21,rd(mult(X20,X18),X18)),
    inference(variable_rename,[status(thm)],[f06]) ).

cnf(c_0_16,plain,
    rd(mult(X1,X1),X1) = X1,
    inference(split_conjunct,[status(thm)],[c_0_10]) ).

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

cnf(c_0_18,plain,
    ld(X1,mult(X1,ld(X2,X2))) = rd(mult(rd(X1,X1),X2),X2),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_19,plain,
    mult(X1,ld(X1,X1)) = X1,
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_20,plain,
    rd(mult(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,rd(mult(X2,X4),X4)),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_21,plain,
    mult(rd(X1,X1),X1) = X1,
    inference(rw,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_22,plain,
    mult(rd(rd(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_17]),c_0_14]) ).

cnf(c_0_23,plain,
    mult(X1,ld(X1,ld(X1,X1))) = ld(X1,X1),
    inference(spm,[status(thm)],[c_0_14,c_0_19]) ).

cnf(c_0_24,plain,
    mult(rd(mult(X1,X2),rd(X3,X4)),rd(X3,X4)) = mult(X1,mult(rd(X2,X4),X4)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_20,c_0_17]),c_0_17]) ).

cnf(c_0_25,plain,
    rd(X1,X1) = ld(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_21]),c_0_22]),c_0_23]) ).

cnf(c_0_26,plain,
    mult(rd(mult(X1,X2),ld(X3,X3)),ld(X3,X3)) = mult(X1,mult(rd(X2,X3),X3)),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_27,plain,
    mult(rd(ld(X1,X1),X2),X2) = mult(X1,ld(X1,ld(X2,X2))),
    inference(spm,[status(thm)],[c_0_22,c_0_25]) ).

cnf(c_0_28,plain,
    mult(mult(rd(X1,ld(X2,X2)),ld(X2,X2)),ld(X2,X2)) = mult(X1,ld(X2,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_17]),c_0_27]),c_0_23]) ).

cnf(c_0_29,plain,
    mult(rd(X1,ld(X1,X1)),ld(X1,X1)) = rd(X1,ld(X1,X1)),
    inference(spm,[status(thm)],[c_0_17,c_0_19]) ).

cnf(c_0_30,plain,
    rd(X1,ld(X1,X1)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_29]),c_0_19]) ).

fof(c_0_31,plain,
    ! [X14,X15,X16,X17] : ld(ld(X17,X16),mult(ld(X17,X16),mult(X15,X14))) = mult(ld(X17,mult(X17,X15)),X14),
    inference(variable_rename,[status(thm)],[f05]) ).

cnf(c_0_32,plain,
    mult(X1,mult(rd(X2,ld(X3,X3)),ld(X3,X3))) = mult(rd(mult(X1,X2),X3),X3),
    inference(spm,[status(thm)],[c_0_24,c_0_30]) ).

cnf(c_0_33,plain,
    ld(ld(X1,X2),mult(ld(X1,X2),mult(X3,X4))) = mult(ld(X1,mult(X1,X3)),X4),
    inference(split_conjunct,[status(thm)],[c_0_31]) ).

cnf(c_0_34,plain,
    mult(ld(X1,X1),X1) = X1,
    inference(rw,[status(thm)],[c_0_21,c_0_25]) ).

cnf(c_0_35,plain,
    mult(mult(rd(X1,X2),X2),X2) = mult(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_30]),c_0_19]),c_0_17]) ).

cnf(c_0_36,plain,
    mult(ld(X1,X2),ld(ld(X1,X2),mult(X3,X4))) = mult(mult(X1,ld(X1,X3)),X4),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_33,c_0_14]),c_0_14]) ).

cnf(c_0_37,plain,
    mult(rd(mult(X1,ld(X2,X2)),X2),X2) = mult(X1,ld(X2,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_25]),c_0_34]) ).

cnf(c_0_38,plain,
    mult(mult(X1,ld(X1,ld(X2,X2))),X2) = mult(ld(X1,X1),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_22]),c_0_25]) ).

cnf(c_0_39,plain,
    mult(ld(X1,X1),ld(ld(X1,X1),X1)) = ld(ld(X1,X1),X1),
    inference(spm,[status(thm)],[c_0_14,c_0_34]) ).

cnf(c_0_40,plain,
    mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(mult(X1,ld(X1,X3)),ld(X3,X3)),
    inference(spm,[status(thm)],[c_0_36,c_0_19]) ).

cnf(c_0_41,plain,
    mult(X1,ld(ld(X2,X2),ld(X2,X2))) = mult(X1,ld(X2,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_37]),c_0_27]),c_0_19]) ).

cnf(c_0_42,plain,
    mult(ld(ld(X1,X1),ld(X1,X1)),X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_38,c_0_19]),c_0_34]) ).

cnf(c_0_43,plain,
    mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(ld(X1,X1),X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_34]),c_0_38]) ).

cnf(c_0_44,plain,
    ld(ld(X1,X1),X1) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_40]),c_0_19]),c_0_19]) ).

cnf(c_0_45,plain,
    ld(ld(X1,X1),ld(X1,X1)) = ld(X1,X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_34,c_0_41]),c_0_42]) ).

cnf(c_0_46,plain,
    mult(ld(X1,X1),X2) = mult(X1,ld(X1,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_43,c_0_44]),c_0_45]) ).

cnf(c_0_47,plain,
    mult(rd(mult(X1,X2),X3),X3) = mult(X1,mult(rd(X2,X3),X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_45]),c_0_26]),c_0_32]) ).

cnf(c_0_48,plain,
    mult(mult(X1,ld(X1,X2)),X3) = mult(X1,ld(X1,mult(X2,X3))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_36,c_0_43]),c_0_46]) ).

cnf(c_0_49,plain,
    mult(X1,mult(X1,ld(X1,ld(X2,X2)))) = mult(rd(X1,X2),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_19]),c_0_27]) ).

cnf(c_0_50,plain,
    mult(X1,mult(X1,ld(X1,X2))) = mult(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_19]),c_0_14]) ).

cnf(c_0_51,plain,
    mult(rd(X1,X2),X2) = mult(X1,ld(X2,X2)),
    inference(rw,[status(thm)],[c_0_49,c_0_50]) ).

cnf(c_0_52,plain,
    mult(ld(X1,X2),ld(ld(X1,X2),X3)) = mult(X1,ld(X1,X3)),
    inference(rw,[status(thm)],[c_0_43,c_0_46]) ).

cnf(c_0_53,plain,
    mult(mult(X1,X2),ld(X3,X3)) = mult(X1,mult(X2,ld(X3,X3))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_51]),c_0_51]) ).

cnf(c_0_54,plain,
    mult(X1,ld(X1,ld(X1,X2))) = ld(X1,X2),
    inference(spm,[status(thm)],[c_0_19,c_0_52]) ).

cnf(c_0_55,plain,
    mult(X1,ld(X1,mult(X2,ld(X3,X3)))) = mult(X1,mult(ld(X1,X2),ld(X3,X3))),
    inference(spm,[status(thm)],[c_0_48,c_0_53]) ).

cnf(c_0_56,plain,
    mult(X1,ld(X1,mult(ld(X1,X2),X3))) = mult(ld(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_48,c_0_54]) ).

cnf(c_0_57,plain,
    ld(X1,mult(X2,ld(X3,X3))) = mult(ld(X1,X2),ld(X3,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_55]),c_0_14]),c_0_56]),c_0_54]) ).

cnf(c_0_58,plain,
    mult(ld(X1,X2),ld(X2,X2)) = ld(X1,X2),
    inference(spm,[status(thm)],[c_0_57,c_0_19]) ).

cnf(c_0_59,plain,
    ld(ld(X1,X2),ld(X1,X2)) = mult(X1,ld(X1,ld(X2,X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_58]),c_0_52]) ).

fof(c_0_60,negated_conjecture,
    ~ ! [X5,X6,X7] :
        ( mult(X5,ld(X6,mult(X6,X7))) = mult(X5,X7)
        & mult(rd(mult(X5,X6),X6),X7) = mult(X5,X7) ),
    inference(assume_negation,[status(cth)],[goals]) ).

cnf(c_0_61,plain,
    mult(X1,ld(X1,mult(X2,ld(X2,X3)))) = mult(X1,ld(X1,X3)),
    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_59]),c_0_48]),c_0_46]),c_0_43]),c_0_46]) ).

fof(c_0_62,negated_conjecture,
    ( mult(esk1_0,ld(esk2_0,mult(esk2_0,esk3_0))) != mult(esk1_0,esk3_0)
    | mult(rd(mult(esk1_0,esk2_0),esk2_0),esk3_0) != mult(esk1_0,esk3_0) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_60])])]) ).

cnf(c_0_63,plain,
    ld(X1,mult(X2,ld(X2,X3))) = ld(X1,X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_61]),c_0_14]),c_0_54]),c_0_54]) ).

cnf(c_0_64,negated_conjecture,
    ( mult(esk1_0,ld(esk2_0,mult(esk2_0,esk3_0))) != mult(esk1_0,esk3_0)
    | mult(rd(mult(esk1_0,esk2_0),esk2_0),esk3_0) != mult(esk1_0,esk3_0) ),
    inference(split_conjunct,[status(thm)],[c_0_62]) ).

cnf(c_0_65,plain,
    mult(mult(X1,mult(rd(X2,X3),X3)),X3) = mult(mult(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_35,c_0_47]) ).

cnf(c_0_66,plain,
    mult(X1,mult(X2,ld(X2,X3))) = mult(X1,X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_63]),c_0_50]) ).

cnf(c_0_67,negated_conjecture,
    ( mult(esk1_0,mult(esk2_0,ld(esk2_0,esk3_0))) != mult(esk1_0,esk3_0)
    | mult(mult(rd(esk1_0,esk2_0),esk2_0),esk3_0) != mult(esk1_0,esk3_0) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_14]),c_0_17]) ).

cnf(c_0_68,plain,
    mult(mult(X1,mult(X2,ld(X3,X3))),X3) = mult(mult(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_65,c_0_51]) ).

cnf(c_0_69,plain,
    mult(rd(X1,X2),mult(X2,ld(X3,X3))) = mult(X1,ld(X3,X3)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_51]),c_0_53]),c_0_46]),c_0_66]) ).

cnf(c_0_70,plain,
    mult(mult(X1,ld(X2,X2)),X2) = mult(X1,X2),
    inference(rw,[status(thm)],[c_0_35,c_0_51]) ).

cnf(c_0_71,negated_conjecture,
    ( mult(esk1_0,mult(esk2_0,ld(esk2_0,esk3_0))) != mult(esk1_0,esk3_0)
    | mult(mult(esk1_0,ld(esk2_0,esk2_0)),esk3_0) != mult(esk1_0,esk3_0) ),
    inference(rw,[status(thm)],[c_0_67,c_0_51]) ).

cnf(c_0_72,plain,
    mult(mult(X1,ld(X2,X2)),X3) = mult(X1,X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_68,c_0_69]),c_0_70]),c_0_51]) ).

cnf(c_0_73,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_71,c_0_66])]),c_0_72])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem    : GRP683+1 : TPTP v8.1.2. Released v4.0.0.
% 0.07/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.35  % Computer : n021.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit   : 300
% 0.13/0.35  % WCLimit    : 300
% 0.13/0.35  % DateTime   : Mon Aug 28 20:20:58 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.61  % Version  : CSE_E---1.5
% 0.20/0.61  % Problem  : theBenchmark.p
% 0.20/0.61  % Proof found
% 0.20/0.61  % SZS status Theorem for theBenchmark.p
% 0.20/0.61  % SZS output start Proof
% See solution above
% 0.20/0.61  % Total time : 0.021000 s
% 0.20/0.61  % SZS output end Proof
% 0.20/0.61  % Total time : 0.023000 s
%------------------------------------------------------------------------------