TSTP Solution File: GRP667-10 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP667-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n002.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 00:22:56 EDT 2023

% Result   : Unsatisfiable 5.56s 5.62s
% Output   : CNFRefutation 5.56s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   78 (  69 unt;   9 typ;   0 def)
%            Number of atoms       :   69 (  68 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   11 (   5   >;   6   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-4 aty)
%            Number of variables   :  139 (   2 sgn;   0   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    rd: ( $i * $i ) > $i ).

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

tff(decl_27,type,
    f: $i > $i ).

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

tff(decl_29,type,
    b: $i ).

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

cnf(f04,axiom,
    rd(mult(X1,X2),X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f04) ).

cnf(f08,axiom,
    mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f08) ).

cnf(f03,axiom,
    mult(rd(X1,X2),X2) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f03) ).

cnf(f06,axiom,
    mult(unit,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f06) ).

cnf(f07,axiom,
    mult(mult(X1,X2),mult(mult(X3,X2),X3)) = mult(mult(X1,mult(mult(X2,X3),X2)),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f07) ).

cnf(f05,axiom,
    mult(X1,unit) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f05) ).

cnf(f01,axiom,
    mult(X1,ld(X1,X2)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f01) ).

cnf(f02,axiom,
    ld(X1,mult(X1,X2)) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f02) ).

cnf(f12,axiom,
    ifeq(mult(mult(X1,X2),mult(X3,X1)),mult(X1,mult(mult(X2,X3),X1)),mult(X1,mult(X2,mult(X1,X3))),mult(mult(mult(X1,X2),X1),X3)) = mult(mult(mult(X1,X2),X1),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f12) ).

cnf(ifeq_axiom,axiom,
    ifeq(X1,X1,X2,X3) = X2,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ifeq_axiom) ).

cnf(f09,axiom,
    mult(f(X1),f(X1)) = X1,
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f09) ).

cnf(f10,axiom,
    ifeq(mult(X1,mult(X2,mult(X3,X2))),mult(mult(mult(X1,X2),X3),X2),mult(X2,mult(X1,mult(X2,X3))),mult(mult(mult(X2,X1),X2),X3)) = mult(mult(mult(X2,X1),X2),X3),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',f10) ).

cnf(goals,negated_conjecture,
    mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',goals) ).

cnf(c_0_13,axiom,
    rd(mult(X1,X2),X2) = X1,
    f04 ).

cnf(c_0_14,axiom,
    mult(mult(X1,X2),X1) = mult(X1,mult(X2,X1)),
    f08 ).

cnf(c_0_15,plain,
    rd(mult(X1,mult(X2,X1)),X1) = mult(X1,X2),
    inference(spm,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_16,axiom,
    mult(rd(X1,X2),X2) = X1,
    f03 ).

cnf(c_0_17,axiom,
    mult(unit,X1) = X1,
    f06 ).

cnf(c_0_18,axiom,
    mult(mult(X1,X2),mult(mult(X3,X2),X3)) = mult(mult(X1,mult(mult(X2,X3),X2)),X3),
    f07 ).

cnf(c_0_19,plain,
    rd(mult(X1,X2),X1) = mult(X1,rd(X2,X1)),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_20,axiom,
    mult(X1,unit) = X1,
    f05 ).

cnf(c_0_21,plain,
    rd(X1,X1) = unit,
    inference(spm,[status(thm)],[c_0_13,c_0_17]) ).

cnf(c_0_22,axiom,
    mult(X1,ld(X1,X2)) = X2,
    f01 ).

cnf(c_0_23,plain,
    mult(mult(X1,mult(X2,mult(X3,X2))),X3) = mult(mult(X1,X2),mult(X3,mult(X2,X3))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_18,c_0_14]),c_0_14]) ).

cnf(c_0_24,plain,
    mult(X1,rd(unit,X1)) = unit,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_21]) ).

cnf(c_0_25,plain,
    rd(X1,ld(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_13,c_0_22]) ).

cnf(c_0_26,plain,
    rd(mult(mult(X1,X2),mult(X3,mult(X2,X3))),X3) = mult(X1,mult(X2,mult(X3,X2))),
    inference(spm,[status(thm)],[c_0_13,c_0_23]) ).

cnf(c_0_27,plain,
    mult(ld(X1,unit),X1) = unit,
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_28,plain,
    mult(ld(X1,unit),mult(X1,mult(X2,X1))) = mult(X2,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_17]),c_0_19]),c_0_13]) ).

cnf(c_0_29,plain,
    mult(ld(X1,unit),mult(X1,X2)) = X2,
    inference(spm,[status(thm)],[c_0_28,c_0_16]) ).

cnf(c_0_30,plain,
    mult(mult(X1,X2),X2) = mult(X1,mult(X2,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_23]),c_0_20]),c_0_17]),c_0_17]) ).

cnf(c_0_31,axiom,
    ld(X1,mult(X1,X2)) = X2,
    f02 ).

cnf(c_0_32,plain,
    rd(X1,mult(X2,X1)) = ld(X2,unit),
    inference(spm,[status(thm)],[c_0_13,c_0_29]) ).

cnf(c_0_33,plain,
    mult(rd(X1,X2),mult(X2,X2)) = mult(X1,X2),
    inference(spm,[status(thm)],[c_0_30,c_0_16]) ).

cnf(c_0_34,plain,
    ld(ld(X1,unit),X2) = mult(X1,X2),
    inference(spm,[status(thm)],[c_0_31,c_0_29]) ).

cnf(c_0_35,plain,
    ld(rd(X1,X2),unit) = rd(X2,X1),
    inference(spm,[status(thm)],[c_0_32,c_0_16]) ).

cnf(c_0_36,plain,
    ld(rd(X1,X2),mult(X1,X2)) = mult(X2,X2),
    inference(spm,[status(thm)],[c_0_31,c_0_33]) ).

cnf(c_0_37,plain,
    ld(rd(X1,X2),X3) = mult(rd(X2,X1),X3),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_38,plain,
    mult(ld(X1,unit),X2) = ld(X1,X2),
    inference(spm,[status(thm)],[c_0_29,c_0_22]) ).

cnf(c_0_39,plain,
    mult(rd(X1,X2),mult(X2,X1)) = mult(X1,X1),
    inference(rw,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_40,plain,
    ld(X1,mult(X2,X2)) = mult(ld(X1,X2),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_38]),c_0_38]) ).

cnf(c_0_41,plain,
    rd(mult(X1,X1),mult(X2,X1)) = rd(X1,X2),
    inference(spm,[status(thm)],[c_0_13,c_0_39]) ).

cnf(c_0_42,plain,
    rd(mult(X1,mult(X2,mult(X1,X2))),X2) = mult(X1,mult(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_17]),c_0_17]) ).

cnf(c_0_43,plain,
    mult(X1,mult(ld(X1,X2),X2)) = mult(X2,X2),
    inference(spm,[status(thm)],[c_0_22,c_0_40]) ).

cnf(c_0_44,plain,
    rd(mult(X1,X1),X2) = rd(X1,rd(X2,X1)),
    inference(spm,[status(thm)],[c_0_41,c_0_16]) ).

cnf(c_0_45,plain,
    rd(ld(X1,X2),X2) = ld(X1,unit),
    inference(spm,[status(thm)],[c_0_32,c_0_22]) ).

cnf(c_0_46,plain,
    mult(X1,mult(ld(X1,X2),X1)) = mult(X2,X1),
    inference(spm,[status(thm)],[c_0_14,c_0_22]) ).

cnf(c_0_47,axiom,
    ifeq(mult(mult(X1,X2),mult(X3,X1)),mult(X1,mult(mult(X2,X3),X1)),mult(X1,mult(X2,mult(X1,X3))),mult(mult(mult(X1,X2),X1),X3)) = mult(mult(mult(X1,X2),X1),X3),
    f12 ).

cnf(c_0_48,plain,
    rd(X1,ld(X2,unit)) = mult(X1,X2),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_22]),c_0_43]),c_0_44]),c_0_45]),c_0_46]) ).

cnf(c_0_49,plain,
    ifeq(mult(mult(X1,X2),mult(X3,X1)),mult(X1,mult(mult(X2,X3),X1)),mult(X1,mult(X2,mult(X1,X3))),mult(mult(X1,mult(X2,X1)),X3)) = mult(mult(X1,mult(X2,X1)),X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_47,c_0_14]),c_0_14]) ).

cnf(c_0_50,axiom,
    ifeq(X1,X1,X2,X3) = X2,
    ifeq_axiom ).

cnf(c_0_51,plain,
    mult(X1,ld(X2,unit)) = rd(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_34]),c_0_20]) ).

cnf(c_0_52,axiom,
    mult(f(X1),f(X1)) = X1,
    f09 ).

cnf(c_0_53,plain,
    mult(mult(X1,X1),X2) = mult(X1,mult(X1,X2)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_49,c_0_17]),c_0_20]),c_0_17]),c_0_17]),c_0_50]) ).

cnf(c_0_54,plain,
    ld(X1,rd(X1,X2)) = ld(X2,unit),
    inference(spm,[status(thm)],[c_0_31,c_0_51]) ).

cnf(c_0_55,plain,
    mult(rd(X1,f(X2)),X2) = mult(X1,f(X2)),
    inference(spm,[status(thm)],[c_0_33,c_0_52]) ).

cnf(c_0_56,plain,
    mult(mult(X1,mult(X2,X3)),ld(X3,X2)) = mult(mult(X1,X3),mult(ld(X3,X2),X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_46]),c_0_22]) ).

cnf(c_0_57,plain,
    mult(f(X1),mult(f(X1),X2)) = mult(X1,X2),
    inference(spm,[status(thm)],[c_0_53,c_0_52]) ).

cnf(c_0_58,plain,
    ld(mult(X1,X2),X1) = ld(X2,unit),
    inference(spm,[status(thm)],[c_0_54,c_0_13]) ).

cnf(c_0_59,plain,
    mult(ld(X1,f(X2)),f(X2)) = ld(X1,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_55,c_0_45]),c_0_38]) ).

cnf(c_0_60,plain,
    rd(mult(X1,mult(X2,X3)),X3) = mult(mult(X1,X3),ld(X3,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(spm,[status(thm)],[c_0_56,c_0_57]),c_0_58]),c_0_51]),c_0_58]),c_0_38]),c_0_56]),c_0_59]) ).

cnf(c_0_61,axiom,
    ifeq(mult(X1,mult(X2,mult(X3,X2))),mult(mult(mult(X1,X2),X3),X2),mult(X2,mult(X1,mult(X2,X3))),mult(mult(mult(X2,X1),X2),X3)) = mult(mult(mult(X2,X1),X2),X3),
    f10 ).

cnf(c_0_62,plain,
    mult(mult(mult(X1,X2),ld(X2,X3)),X2) = mult(X1,mult(X3,X2)),
    inference(spm,[status(thm)],[c_0_16,c_0_60]) ).

cnf(c_0_63,negated_conjecture,
    mult(a,mult(b,mult(a,c))) != mult(mult(mult(a,b),a),c),
    goals ).

cnf(c_0_64,plain,
    ifeq(mult(X1,mult(X2,mult(X3,X2))),mult(mult(mult(X1,X2),X3),X2),mult(X2,mult(X1,mult(X2,X3))),mult(mult(X2,mult(X1,X2)),X3)) = mult(mult(X2,mult(X1,X2)),X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_61,c_0_14]),c_0_14]) ).

cnf(c_0_65,plain,
    mult(mult(mult(X1,X2),X3),X2) = mult(X1,mult(X2,mult(X3,X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_31]),c_0_14]) ).

cnf(c_0_66,negated_conjecture,
    mult(mult(a,mult(b,a)),c) != mult(a,mult(b,mult(a,c))),
    inference(rw,[status(thm)],[c_0_63,c_0_14]) ).

cnf(c_0_67,plain,
    mult(mult(X1,mult(X2,X1)),X3) = mult(X1,mult(X2,mult(X1,X3))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_64,c_0_65]),c_0_50]) ).

cnf(c_0_68,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRP667-10 : TPTP v8.1.2. Released v7.5.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n002.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   : Mon Aug 28 23:42:19 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 5.56/5.62  % Version  : CSE_E---1.5
% 5.56/5.62  % Problem  : theBenchmark.p
% 5.56/5.62  % Proof found
% 5.56/5.62  % SZS status Theorem for theBenchmark.p
% 5.56/5.62  % SZS output start Proof
% See solution above
% 5.56/5.62  % Total time : 5.049000 s
% 5.56/5.62  % SZS output end Proof
% 5.56/5.62  % Total time : 5.053000 s
%------------------------------------------------------------------------------