TSTP Solution File: GRP247-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP247-1 : TPTP v8.1.2. Released v2.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s

% Computer : n015.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 00:17:55 EDT 2023

% Result   : Unsatisfiable 0.19s 0.63s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   28
% Syntax   : Number of formulae    :   85 (  19 unt;  12 typ;   0 def)
%            Number of atoms       :  167 ( 166 equ)
%            Maximal formula atoms :   12 (   2 avg)
%            Number of connectives :  147 (  53   ~;  94   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   13 (   2 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    3 (   2   >;   1   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;  10 con; 0-2 aty)
%            Number of variables   :   42 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    inverse: $i > $i ).

tff(decl_25,type,
    sk_c1: $i ).

tff(decl_26,type,
    sk_c9: $i ).

tff(decl_27,type,
    sk_c8: $i ).

tff(decl_28,type,
    sk_c4: $i ).

tff(decl_29,type,
    sk_c5: $i ).

tff(decl_30,type,
    sk_c7: $i ).

tff(decl_31,type,
    sk_c6: $i ).

tff(decl_32,type,
    sk_c2: $i ).

tff(decl_33,type,
    sk_c3: $i ).

cnf(associativity,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',associativity) ).

cnf(left_inverse,axiom,
    multiply(inverse(X1),X1) = identity,
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_inverse) ).

cnf(left_identity,axiom,
    multiply(identity,X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP004-0.ax',left_identity) ).

cnf(prove_this_1,negated_conjecture,
    ( multiply(sk_c1,sk_c9) = sk_c8
    | multiply(sk_c4,sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).

cnf(prove_this_15,negated_conjecture,
    ( multiply(sk_c2,sk_c8) = sk_c7
    | multiply(sk_c5,sk_c8) = sk_c7 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).

cnf(prove_this_2,negated_conjecture,
    ( multiply(sk_c1,sk_c9) = sk_c8
    | inverse(sk_c4) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_2) ).

cnf(prove_this_21,negated_conjecture,
    ( inverse(sk_c2) = sk_c8
    | multiply(sk_c5,sk_c8) = sk_c7 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).

cnf(prove_this_7,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | multiply(sk_c4,sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_7) ).

cnf(prove_this_16,negated_conjecture,
    ( multiply(sk_c2,sk_c8) = sk_c7
    | inverse(sk_c5) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_16) ).

cnf(prove_this_8,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | inverse(sk_c4) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_8) ).

cnf(prove_this_22,negated_conjecture,
    ( inverse(sk_c2) = sk_c8
    | inverse(sk_c5) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_22) ).

cnf(prove_this_30,negated_conjecture,
    ( inverse(sk_c3) = sk_c9
    | multiply(sk_c6,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_30) ).

cnf(prove_this_36,negated_conjecture,
    ( multiply(sk_c3,sk_c7) = sk_c9
    | multiply(sk_c6,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_36) ).

cnf(prove_this_35,negated_conjecture,
    ( multiply(sk_c3,sk_c7) = sk_c9
    | inverse(sk_c6) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_35) ).

cnf(prove_this_37,negated_conjecture,
    ( multiply(X1,sk_c9) != sk_c8
    | inverse(X1) != sk_c9
    | multiply(X2,sk_c8) != sk_c7
    | inverse(X2) != sk_c8
    | inverse(X3) != sk_c9
    | multiply(X3,sk_c7) != sk_c9
    | multiply(X4,sk_c9) != sk_c8
    | inverse(X4) != sk_c9
    | multiply(X5,sk_c8) != sk_c7
    | inverse(X5) != sk_c8
    | inverse(X6) != sk_c9
    | multiply(X6,sk_c8) != sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_37) ).

cnf(prove_this_29,negated_conjecture,
    ( inverse(sk_c3) = sk_c9
    | inverse(sk_c6) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_29) ).

cnf(c_0_16,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    associativity ).

cnf(c_0_17,axiom,
    multiply(inverse(X1),X1) = identity,
    left_inverse ).

cnf(c_0_18,axiom,
    multiply(identity,X1) = X1,
    left_identity ).

cnf(c_0_19,plain,
    multiply(inverse(X1),multiply(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_16,c_0_17]),c_0_18]) ).

cnf(c_0_20,negated_conjecture,
    ( multiply(sk_c1,sk_c9) = sk_c8
    | multiply(sk_c4,sk_c9) = sk_c8 ),
    prove_this_1 ).

cnf(c_0_21,negated_conjecture,
    ( multiply(sk_c2,sk_c8) = sk_c7
    | multiply(sk_c5,sk_c8) = sk_c7 ),
    prove_this_15 ).

cnf(c_0_22,negated_conjecture,
    ( multiply(inverse(sk_c4),sk_c8) = sk_c9
    | multiply(sk_c1,sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,negated_conjecture,
    ( multiply(sk_c1,sk_c9) = sk_c8
    | inverse(sk_c4) = sk_c9 ),
    prove_this_2 ).

cnf(c_0_24,negated_conjecture,
    ( multiply(inverse(sk_c2),sk_c7) = sk_c8
    | multiply(sk_c5,sk_c8) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_19,c_0_21]) ).

cnf(c_0_25,negated_conjecture,
    ( inverse(sk_c2) = sk_c8
    | multiply(sk_c5,sk_c8) = sk_c7 ),
    prove_this_21 ).

cnf(c_0_26,negated_conjecture,
    ( multiply(sk_c1,sk_c9) = sk_c8
    | multiply(sk_c9,sk_c8) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_27,negated_conjecture,
    ( multiply(sk_c5,sk_c8) = sk_c7
    | multiply(sk_c8,sk_c7) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_28,negated_conjecture,
    ( multiply(inverse(sk_c1),sk_c8) = sk_c9
    | multiply(sk_c9,sk_c8) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_19,c_0_26]) ).

cnf(c_0_29,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | multiply(sk_c4,sk_c9) = sk_c8 ),
    prove_this_7 ).

cnf(c_0_30,negated_conjecture,
    ( multiply(inverse(sk_c5),sk_c7) = sk_c8
    | multiply(sk_c8,sk_c7) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_19,c_0_27]) ).

cnf(c_0_31,negated_conjecture,
    ( multiply(sk_c2,sk_c8) = sk_c7
    | inverse(sk_c5) = sk_c8 ),
    prove_this_16 ).

cnf(c_0_32,negated_conjecture,
    ( multiply(sk_c4,sk_c9) = sk_c8
    | multiply(sk_c9,sk_c8) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,negated_conjecture,
    ( multiply(sk_c2,sk_c8) = sk_c7
    | multiply(sk_c8,sk_c7) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_34,negated_conjecture,
    ( multiply(inverse(sk_c4),sk_c8) = sk_c9
    | multiply(sk_c9,sk_c8) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_19,c_0_32]) ).

cnf(c_0_35,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | inverse(sk_c4) = sk_c9 ),
    prove_this_8 ).

cnf(c_0_36,negated_conjecture,
    ( multiply(inverse(sk_c2),sk_c7) = sk_c8
    | multiply(sk_c8,sk_c7) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_19,c_0_33]) ).

cnf(c_0_37,negated_conjecture,
    ( inverse(sk_c2) = sk_c8
    | inverse(sk_c5) = sk_c8 ),
    prove_this_22 ).

cnf(c_0_38,negated_conjecture,
    ( multiply(sk_c9,sk_c8) = sk_c9
    | inverse(sk_c1) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_39,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c8
    | inverse(sk_c5) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_36,c_0_37]) ).

cnf(c_0_40,negated_conjecture,
    multiply(sk_c9,sk_c8) = sk_c9,
    inference(spm,[status(thm)],[c_0_28,c_0_38]) ).

cnf(c_0_41,negated_conjecture,
    multiply(sk_c8,sk_c7) = sk_c8,
    inference(spm,[status(thm)],[c_0_30,c_0_39]) ).

cnf(c_0_42,plain,
    multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
    inference(spm,[status(thm)],[c_0_19,c_0_19]) ).

cnf(c_0_43,negated_conjecture,
    ( inverse(sk_c3) = sk_c9
    | multiply(sk_c6,sk_c8) = sk_c9 ),
    prove_this_30 ).

cnf(c_0_44,negated_conjecture,
    sk_c8 = identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_40]),c_0_17]) ).

cnf(c_0_45,negated_conjecture,
    ( multiply(sk_c3,sk_c7) = sk_c9
    | multiply(sk_c6,sk_c8) = sk_c9 ),
    prove_this_36 ).

cnf(c_0_46,negated_conjecture,
    sk_c7 = identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_41]),c_0_17]) ).

cnf(c_0_47,negated_conjecture,
    ( multiply(sk_c3,sk_c7) = sk_c9
    | inverse(sk_c6) = sk_c9 ),
    prove_this_35 ).

cnf(c_0_48,negated_conjecture,
    ( multiply(X1,sk_c9) != sk_c8
    | inverse(X1) != sk_c9
    | multiply(X2,sk_c8) != sk_c7
    | inverse(X2) != sk_c8
    | inverse(X3) != sk_c9
    | multiply(X3,sk_c7) != sk_c9
    | multiply(X4,sk_c9) != sk_c8
    | inverse(X4) != sk_c9
    | multiply(X5,sk_c8) != sk_c7
    | inverse(X5) != sk_c8
    | inverse(X6) != sk_c9
    | multiply(X6,sk_c8) != sk_c9 ),
    prove_this_37 ).

cnf(c_0_49,plain,
    multiply(X1,identity) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_17]),c_0_42]) ).

cnf(c_0_50,negated_conjecture,
    ( multiply(sk_c6,identity) = sk_c9
    | inverse(sk_c3) = sk_c9 ),
    inference(rw,[status(thm)],[c_0_43,c_0_44]) ).

cnf(c_0_51,negated_conjecture,
    ( multiply(sk_c3,identity) = sk_c9
    | multiply(sk_c6,identity) = sk_c9 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_45,c_0_46]),c_0_44]) ).

cnf(c_0_52,negated_conjecture,
    ( multiply(sk_c3,sk_c7) = sk_c9
    | multiply(sk_c9,sk_c6) = identity ),
    inference(spm,[status(thm)],[c_0_17,c_0_47]) ).

cnf(c_0_53,negated_conjecture,
    ( multiply(X1,identity) != sk_c9
    | multiply(X2,identity) != identity
    | multiply(X3,sk_c9) != identity
    | multiply(X4,identity) != sk_c9
    | multiply(X5,identity) != identity
    | multiply(X6,sk_c9) != identity
    | inverse(X1) != sk_c9
    | inverse(X2) != identity
    | inverse(X3) != sk_c9
    | inverse(X4) != sk_c9
    | inverse(X5) != identity
    | inverse(X6) != sk_c9 ),
    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)],[c_0_48,c_0_46]),c_0_46]),c_0_46]),c_0_44]),c_0_44]),c_0_44]),c_0_44]),c_0_44]),c_0_44]),c_0_44]) ).

cnf(c_0_54,plain,
    inverse(identity) = identity,
    inference(spm,[status(thm)],[c_0_17,c_0_49]) ).

cnf(c_0_55,negated_conjecture,
    ( inverse(sk_c3) = sk_c9
    | sk_c6 = sk_c9 ),
    inference(rw,[status(thm)],[c_0_50,c_0_49]) ).

cnf(c_0_56,negated_conjecture,
    ( sk_c6 = sk_c9
    | sk_c3 = sk_c9 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_51,c_0_49]),c_0_49]) ).

cnf(c_0_57,negated_conjecture,
    ( multiply(sk_c9,sk_c6) = identity
    | multiply(sk_c3,identity) = sk_c9 ),
    inference(rw,[status(thm)],[c_0_52,c_0_46]) ).

cnf(c_0_58,negated_conjecture,
    ( multiply(X1,sk_c9) != identity
    | multiply(X2,sk_c9) != identity
    | inverse(sk_c9) != sk_c9
    | inverse(X1) != sk_c9
    | inverse(X2) != sk_c9 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(er,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_49]),c_0_49]),c_0_49]),c_0_49])])])])]),c_0_54])]) ).

cnf(c_0_59,negated_conjecture,
    ( inverse(sk_c9) = sk_c9
    | sk_c6 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_55,c_0_56]) ).

cnf(c_0_60,negated_conjecture,
    ( multiply(inverse(sk_c3),sk_c9) = identity
    | multiply(sk_c9,sk_c6) = identity ),
    inference(spm,[status(thm)],[c_0_19,c_0_57]) ).

cnf(c_0_61,negated_conjecture,
    ( inverse(sk_c3) = sk_c9
    | inverse(sk_c6) = sk_c9 ),
    prove_this_29 ).

cnf(c_0_62,negated_conjecture,
    ( sk_c6 = sk_c9
    | multiply(X1,sk_c9) != identity
    | multiply(X2,sk_c9) != identity
    | inverse(X1) != sk_c9
    | inverse(X2) != sk_c9 ),
    inference(spm,[status(thm)],[c_0_58,c_0_59]) ).

cnf(c_0_63,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_42,c_0_49]),c_0_49]) ).

cnf(c_0_64,negated_conjecture,
    ( multiply(sk_c9,sk_c6) = identity
    | multiply(sk_c9,sk_c9) = identity
    | inverse(sk_c6) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_60,c_0_61]) ).

cnf(c_0_65,negated_conjecture,
    ( sk_c6 = sk_c9
    | multiply(X1,sk_c9) != identity
    | inverse(X1) != sk_c9 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_62,c_0_17]),c_0_63])]) ).

cnf(c_0_66,negated_conjecture,
    ( multiply(sk_c9,sk_c9) = identity
    | multiply(sk_c9,sk_c6) = identity ),
    inference(spm,[status(thm)],[c_0_17,c_0_64]) ).

cnf(c_0_67,negated_conjecture,
    sk_c6 = sk_c9,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_65,c_0_63])]),c_0_17])]) ).

cnf(c_0_68,negated_conjecture,
    multiply(sk_c9,sk_c9) = identity,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_66,c_0_67])]) ).

cnf(c_0_69,negated_conjecture,
    inverse(sk_c9) = sk_c9,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_68]),c_0_49]) ).

cnf(c_0_70,negated_conjecture,
    ( multiply(X1,sk_c9) != identity
    | multiply(X2,sk_c9) != identity
    | inverse(X1) != sk_c9
    | inverse(X2) != sk_c9 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_58,c_0_69])]) ).

cnf(c_0_71,negated_conjecture,
    ( multiply(X1,sk_c9) != identity
    | inverse(X1) != sk_c9 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_70,c_0_68]),c_0_69])]) ).

cnf(c_0_72,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_71,c_0_69]),c_0_68])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRP247-1 : TPTP v8.1.2. Released v2.5.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n015.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 29 01:39:40 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.63  % Version  : CSE_E---1.5
% 0.19/0.63  % Problem  : theBenchmark.p
% 0.19/0.63  % Proof found
% 0.19/0.63  % SZS status Theorem for theBenchmark.p
% 0.19/0.63  % SZS output start Proof
% See solution above
% 0.19/0.63  % Total time : 0.062000 s
% 0.19/0.63  % SZS output end Proof
% 0.19/0.63  % Total time : 0.065000 s
%------------------------------------------------------------------------------