TSTP Solution File: GRP354-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP354-1 : 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 : n009.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 00:18:37 EDT 2023

% Result   : Unsatisfiable 0.54s 0.62s
% Output   : CNFRefutation 0.54s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   19
%            Number of leaves      :   23
% Syntax   : Number of formulae    :   67 (  20 unt;  12 typ;   0 def)
%            Number of atoms       :  166 ( 165 equ)
%            Maximal formula atoms :   14 (   3 avg)
%            Number of connectives :  207 (  96   ~; 111   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   15 (   3 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   :   58 (   2 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_c8: $i ).

tff(decl_26,type,
    sk_c7: $i ).

tff(decl_27,type,
    sk_c9: $i ).

tff(decl_28,type,
    sk_c3: $i ).

tff(decl_29,type,
    sk_c4: $i ).

tff(decl_30,type,
    sk_c5: $i ).

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

tff(decl_32,type,
    sk_c1: $i ).

tff(decl_33,type,
    sk_c2: $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_9,negated_conjecture,
    ( multiply(sk_c1,sk_c9) = sk_c8
    | multiply(sk_c3,sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_9) ).

cnf(prove_this_10,negated_conjecture,
    ( multiply(sk_c1,sk_c9) = sk_c8
    | inverse(sk_c3) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_10) ).

cnf(prove_this_17,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | multiply(sk_c3,sk_c9) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_17) ).

cnf(prove_this_18,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | inverse(sk_c3) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).

cnf(prove_this_49,negated_conjecture,
    ( multiply(sk_c8,sk_c7) != sk_c9
    | multiply(X1,sk_c9) != sk_c8
    | inverse(X1) != sk_c9
    | inverse(sk_c9) != sk_c7
    | multiply(X2,sk_c7) != sk_c8
    | inverse(X2) != sk_c7
    | multiply(X3,sk_c9) != sk_c8
    | inverse(X3) != sk_c9
    | multiply(sk_c9,sk_c7) != sk_c8
    | inverse(X4) != sk_c9
    | multiply(X4,sk_c8) != sk_c9
    | multiply(X5,X6) != sk_c8
    | inverse(X5) != X6
    | multiply(X6,sk_c7) != sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_49) ).

cnf(prove_this_5,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c9
    | multiply(sk_c4,sk_c8) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_5) ).

cnf(prove_this_27,negated_conjecture,
    ( inverse(sk_c9) = sk_c7
    | multiply(sk_c9,sk_c7) = sk_c8 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_27) ).

cnf(prove_this_4,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c9
    | inverse(sk_c4) = sk_c9 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_4) ).

cnf(c_0_11,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    associativity ).

cnf(c_0_12,axiom,
    multiply(inverse(X1),X1) = identity,
    left_inverse ).

cnf(c_0_13,axiom,
    multiply(identity,X1) = X1,
    left_identity ).

cnf(c_0_14,plain,
    multiply(inverse(X1),multiply(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]) ).

cnf(c_0_15,negated_conjecture,
    ( multiply(sk_c1,sk_c9) = sk_c8
    | multiply(sk_c3,sk_c9) = sk_c8 ),
    prove_this_9 ).

cnf(c_0_16,negated_conjecture,
    ( multiply(inverse(sk_c3),sk_c8) = sk_c9
    | multiply(sk_c1,sk_c9) = sk_c8 ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_17,negated_conjecture,
    ( multiply(sk_c1,sk_c9) = sk_c8
    | inverse(sk_c3) = sk_c9 ),
    prove_this_10 ).

cnf(c_0_18,negated_conjecture,
    ( multiply(sk_c1,sk_c9) = sk_c8
    | multiply(sk_c9,sk_c8) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_19,negated_conjecture,
    ( multiply(inverse(sk_c1),sk_c8) = sk_c9
    | multiply(sk_c9,sk_c8) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_14,c_0_18]) ).

cnf(c_0_20,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | multiply(sk_c3,sk_c9) = sk_c8 ),
    prove_this_17 ).

cnf(c_0_21,negated_conjecture,
    ( multiply(sk_c3,sk_c9) = sk_c8
    | multiply(sk_c9,sk_c8) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_22,negated_conjecture,
    ( multiply(inverse(sk_c3),sk_c8) = sk_c9
    | multiply(sk_c9,sk_c8) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_14,c_0_21]) ).

cnf(c_0_23,negated_conjecture,
    ( inverse(sk_c1) = sk_c9
    | inverse(sk_c3) = sk_c9 ),
    prove_this_18 ).

cnf(c_0_24,negated_conjecture,
    ( multiply(sk_c9,sk_c8) = sk_c9
    | inverse(sk_c1) = sk_c9 ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_25,plain,
    multiply(inverse(inverse(X1)),identity) = X1,
    inference(spm,[status(thm)],[c_0_14,c_0_12]) ).

cnf(c_0_26,plain,
    multiply(inverse(inverse(X1)),X2) = multiply(X1,X2),
    inference(spm,[status(thm)],[c_0_14,c_0_14]) ).

cnf(c_0_27,negated_conjecture,
    multiply(sk_c9,sk_c8) = sk_c9,
    inference(spm,[status(thm)],[c_0_19,c_0_24]) ).

cnf(c_0_28,plain,
    multiply(X1,identity) = X1,
    inference(rw,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_29,negated_conjecture,
    ( multiply(sk_c8,sk_c7) != sk_c9
    | multiply(X1,sk_c9) != sk_c8
    | inverse(X1) != sk_c9
    | inverse(sk_c9) != sk_c7
    | multiply(X2,sk_c7) != sk_c8
    | inverse(X2) != sk_c7
    | multiply(X3,sk_c9) != sk_c8
    | inverse(X3) != sk_c9
    | multiply(sk_c9,sk_c7) != sk_c8
    | inverse(X4) != sk_c9
    | multiply(X4,sk_c8) != sk_c9
    | multiply(X5,X6) != sk_c8
    | inverse(X5) != X6
    | multiply(X6,sk_c7) != sk_c8 ),
    prove_this_49 ).

cnf(c_0_30,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c9
    | multiply(sk_c4,sk_c8) = sk_c9 ),
    prove_this_5 ).

cnf(c_0_31,negated_conjecture,
    sk_c8 = identity,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_27]),c_0_12]) ).

cnf(c_0_32,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_28]),c_0_28]) ).

cnf(c_0_33,negated_conjecture,
    ( inverse(sk_c9) = sk_c7
    | multiply(sk_c9,sk_c7) = sk_c8 ),
    prove_this_27 ).

cnf(c_0_34,negated_conjecture,
    ( multiply(inverse(X1),sk_c7) != sk_c8
    | multiply(sk_c8,sk_c7) != sk_c9
    | multiply(sk_c9,sk_c7) != sk_c8
    | multiply(X1,inverse(X1)) != sk_c8
    | multiply(X2,sk_c8) != sk_c9
    | multiply(X3,sk_c9) != sk_c8
    | multiply(X4,sk_c7) != sk_c8
    | multiply(X5,sk_c9) != sk_c8
    | inverse(sk_c9) != sk_c7
    | inverse(X2) != sk_c9
    | inverse(X3) != sk_c9
    | inverse(X4) != sk_c7
    | inverse(X5) != sk_c9 ),
    inference(er,[status(thm)],[c_0_29]) ).

cnf(c_0_35,negated_conjecture,
    ( multiply(sk_c8,sk_c7) = sk_c9
    | inverse(sk_c4) = sk_c9 ),
    prove_this_4 ).

cnf(c_0_36,negated_conjecture,
    ( multiply(sk_c4,identity) = sk_c9
    | sk_c7 = sk_c9 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_30,c_0_31]),c_0_13]),c_0_31]) ).

cnf(c_0_37,plain,
    multiply(X1,inverse(X1)) = identity,
    inference(spm,[status(thm)],[c_0_12,c_0_32]) ).

cnf(c_0_38,negated_conjecture,
    ( multiply(sk_c9,sk_c7) = identity
    | inverse(sk_c9) = sk_c7 ),
    inference(rw,[status(thm)],[c_0_33,c_0_31]) ).

cnf(c_0_39,negated_conjecture,
    ( multiply(inverse(X1),sk_c7) != identity
    | multiply(sk_c9,sk_c7) != identity
    | multiply(X1,inverse(X1)) != identity
    | multiply(X2,identity) != sk_c9
    | multiply(X3,sk_c9) != identity
    | multiply(X4,sk_c7) != identity
    | multiply(X5,sk_c9) != identity
    | inverse(sk_c9) != sk_c7
    | inverse(X2) != sk_c9
    | inverse(X3) != sk_c9
    | inverse(X4) != sk_c7
    | inverse(X5) != sk_c9
    | sk_c7 != 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)],[c_0_34,c_0_31]),c_0_31]),c_0_13]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]),c_0_31]) ).

cnf(c_0_40,negated_conjecture,
    ( inverse(sk_c4) = sk_c9
    | sk_c7 = sk_c9 ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_35,c_0_31]),c_0_13]) ).

cnf(c_0_41,negated_conjecture,
    ( sk_c7 = sk_c9
    | sk_c4 = sk_c9 ),
    inference(rw,[status(thm)],[c_0_36,c_0_28]) ).

cnf(c_0_42,negated_conjecture,
    multiply(sk_c9,sk_c7) = identity,
    inference(spm,[status(thm)],[c_0_37,c_0_38]) ).

cnf(c_0_43,negated_conjecture,
    ( multiply(inverse(X1),sk_c7) != identity
    | multiply(sk_c9,sk_c7) != identity
    | multiply(X1,inverse(X1)) != identity
    | multiply(X2,sk_c9) != identity
    | multiply(X3,sk_c7) != identity
    | multiply(X4,sk_c9) != identity
    | inverse(sk_c9) != sk_c7
    | inverse(sk_c9) != sk_c9
    | inverse(X2) != sk_c9
    | inverse(X3) != sk_c7
    | inverse(X4) != sk_c9
    | sk_c7 != sk_c9 ),
    inference(er,[status(thm)],[inference(rw,[status(thm)],[c_0_39,c_0_28])]) ).

cnf(c_0_44,negated_conjecture,
    ( inverse(sk_c9) = sk_c9
    | sk_c7 = sk_c9 ),
    inference(spm,[status(thm)],[c_0_40,c_0_41]) ).

cnf(c_0_45,negated_conjecture,
    inverse(sk_c9) = sk_c7,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_42]),c_0_28]) ).

cnf(c_0_46,negated_conjecture,
    ( multiply(inverse(X1),sk_c7) != identity
    | multiply(sk_c9,sk_c7) != identity
    | multiply(X2,sk_c9) != identity
    | multiply(X3,sk_c7) != identity
    | multiply(X4,sk_c9) != identity
    | inverse(sk_c9) != sk_c7
    | inverse(sk_c9) != sk_c9
    | inverse(X2) != sk_c9
    | inverse(X3) != sk_c7
    | inverse(X4) != sk_c9
    | sk_c7 != sk_c9 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_43,c_0_37])]) ).

cnf(c_0_47,negated_conjecture,
    sk_c7 = sk_c9,
    inference(spm,[status(thm)],[c_0_44,c_0_45]) ).

cnf(c_0_48,negated_conjecture,
    ( multiply(inverse(X1),sk_c9) != identity
    | multiply(X2,sk_c9) != identity
    | multiply(X3,sk_c9) != identity
    | multiply(X4,sk_c9) != identity
    | inverse(X2) != sk_c9
    | inverse(X3) != sk_c9
    | inverse(X4) != sk_c9 ),
    inference(cn,[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(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_42])]),c_0_47]),c_0_47]),c_0_45]),c_0_47]),c_0_47]),c_0_45]),c_0_47]),c_0_47]),c_0_47])]) ).

cnf(c_0_49,negated_conjecture,
    inverse(sk_c9) = sk_c9,
    inference(rw,[status(thm)],[c_0_45,c_0_47]) ).

cnf(c_0_50,negated_conjecture,
    multiply(sk_c9,sk_c9) = identity,
    inference(rw,[status(thm)],[c_0_42,c_0_47]) ).

cnf(c_0_51,negated_conjecture,
    ( multiply(X1,sk_c9) != identity
    | multiply(X2,sk_c9) != identity
    | multiply(X3,sk_c9) != identity
    | inverse(X1) != sk_c9
    | inverse(X2) != sk_c9
    | inverse(X3) != sk_c9 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_48,c_0_49]),c_0_50])]) ).

cnf(c_0_52,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)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_51,c_0_50]),c_0_45]),c_0_47])]) ).

cnf(c_0_53,negated_conjecture,
    ( multiply(X1,sk_c9) != identity
    | inverse(X1) != sk_c9 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_52,c_0_50]),c_0_45]),c_0_47])]) ).

cnf(c_0_54,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_53,c_0_49]),c_0_50])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : GRP354-1 : TPTP v8.1.2. Released v2.5.0.
% 0.06/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n009.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   : Tue Aug 29 01:18:35 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.57  start to proof: theBenchmark
% 0.54/0.62  % Version  : CSE_E---1.5
% 0.54/0.62  % Problem  : theBenchmark.p
% 0.54/0.62  % Proof found
% 0.54/0.62  % SZS status Theorem for theBenchmark.p
% 0.54/0.62  % SZS output start Proof
% See solution above
% 0.54/0.63  % Total time : 0.045000 s
% 0.54/0.63  % SZS output end Proof
% 0.54/0.63  % Total time : 0.048000 s
%------------------------------------------------------------------------------