TSTP Solution File: GRP292-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP292-1 : 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 : n028.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 00:18:15 EDT 2023

% Result   : Unsatisfiable 0.19s 0.57s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   17
%            Number of leaves      :   19
% Syntax   : Number of formulae    :   58 (  18 unt;  10 typ;   0 def)
%            Number of atoms       :  113 ( 112 equ)
%            Maximal formula atoms :    9 (   2 avg)
%            Number of connectives :  116 (  51   ~;  65   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   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    :   10 (  10 usr;   8 con; 0-2 aty)
%            Number of variables   :   44 (   3 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_c7: $i ).

tff(decl_26,type,
    sk_c6: $i ).

tff(decl_27,type,
    sk_c5: $i ).

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

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

tff(decl_30,type,
    sk_c1: $i ).

tff(decl_31,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_19,negated_conjecture,
    ( inverse(sk_c2) = sk_c5
    | inverse(sk_c3) = sk_c4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_19) ).

cnf(prove_this_18,negated_conjecture,
    ( inverse(sk_c2) = sk_c5
    | multiply(sk_c3,sk_c4) = sk_c6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_18) ).

cnf(prove_this_15,negated_conjecture,
    ( multiply(sk_c2,sk_c5) = sk_c6
    | inverse(sk_c3) = sk_c4 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_15) ).

cnf(prove_this_21,negated_conjecture,
    ( multiply(sk_c7,sk_c6) != sk_c5
    | multiply(X1,sk_c7) != sk_c6
    | inverse(X1) != sk_c7
    | multiply(X2,sk_c5) != sk_c6
    | inverse(X2) != sk_c5
    | multiply(sk_c5,sk_c6) != sk_c7
    | multiply(X3,X4) != sk_c6
    | inverse(X3) != X4
    | multiply(X4,sk_c5) != sk_c6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_21) ).

cnf(prove_this_14,negated_conjecture,
    ( multiply(sk_c2,sk_c5) = sk_c6
    | multiply(sk_c3,sk_c4) = sk_c6 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_14) ).

cnf(prove_this_1,negated_conjecture,
    ( multiply(sk_c7,sk_c6) = sk_c5
    | multiply(sk_c5,sk_c6) = sk_c7 ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_this_1) ).

cnf(c_0_9,axiom,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    associativity ).

cnf(c_0_10,axiom,
    multiply(inverse(X1),X1) = identity,
    left_inverse ).

cnf(c_0_11,axiom,
    multiply(identity,X1) = X1,
    left_identity ).

cnf(c_0_12,plain,
    multiply(inverse(X1),multiply(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).

cnf(c_0_13,plain,
    multiply(inverse(inverse(X1)),identity) = X1,
    inference(spm,[status(thm)],[c_0_12,c_0_10]) ).

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

cnf(c_0_15,plain,
    multiply(X1,identity) = X1,
    inference(rw,[status(thm)],[c_0_13,c_0_14]) ).

cnf(c_0_16,plain,
    inverse(inverse(X1)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_15]),c_0_15]) ).

cnf(c_0_17,negated_conjecture,
    ( inverse(sk_c2) = sk_c5
    | inverse(sk_c3) = sk_c4 ),
    prove_this_19 ).

cnf(c_0_18,negated_conjecture,
    ( inverse(sk_c2) = sk_c5
    | multiply(sk_c3,sk_c4) = sk_c6 ),
    prove_this_18 ).

cnf(c_0_19,plain,
    multiply(X1,inverse(X1)) = identity,
    inference(spm,[status(thm)],[c_0_10,c_0_16]) ).

cnf(c_0_20,negated_conjecture,
    ( multiply(sk_c5,sk_c2) = identity
    | inverse(sk_c3) = sk_c4 ),
    inference(spm,[status(thm)],[c_0_10,c_0_17]) ).

cnf(c_0_21,negated_conjecture,
    ( multiply(sk_c3,sk_c4) = sk_c6
    | multiply(sk_c5,sk_c2) = identity ),
    inference(spm,[status(thm)],[c_0_10,c_0_18]) ).

cnf(c_0_22,negated_conjecture,
    ( multiply(sk_c5,sk_c2) = identity
    | multiply(sk_c3,sk_c4) = identity ),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_23,negated_conjecture,
    ( multiply(sk_c5,sk_c2) = identity
    | sk_c6 = identity ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_24,negated_conjecture,
    ( multiply(sk_c2,sk_c5) = sk_c6
    | inverse(sk_c3) = sk_c4 ),
    prove_this_15 ).

cnf(c_0_25,negated_conjecture,
    ( inverse(sk_c5) = sk_c2
    | sk_c6 = identity ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_23]),c_0_15]) ).

cnf(c_0_26,negated_conjecture,
    ( multiply(sk_c7,sk_c6) != sk_c5
    | multiply(X1,sk_c7) != sk_c6
    | inverse(X1) != sk_c7
    | multiply(X2,sk_c5) != sk_c6
    | inverse(X2) != sk_c5
    | multiply(sk_c5,sk_c6) != sk_c7
    | multiply(X3,X4) != sk_c6
    | inverse(X3) != X4
    | multiply(X4,sk_c5) != sk_c6 ),
    prove_this_21 ).

cnf(c_0_27,negated_conjecture,
    ( multiply(sk_c2,sk_c5) = sk_c6
    | multiply(sk_c3,sk_c4) = sk_c6 ),
    prove_this_14 ).

cnf(c_0_28,negated_conjecture,
    ( multiply(sk_c3,sk_c4) = sk_c6
    | multiply(sk_c2,sk_c5) = identity ),
    inference(spm,[status(thm)],[c_0_19,c_0_18]) ).

cnf(c_0_29,negated_conjecture,
    ( multiply(sk_c2,sk_c5) = sk_c6
    | multiply(sk_c3,sk_c4) = identity ),
    inference(spm,[status(thm)],[c_0_19,c_0_24]) ).

cnf(c_0_30,negated_conjecture,
    ( multiply(sk_c2,sk_c5) = identity
    | sk_c6 = identity ),
    inference(spm,[status(thm)],[c_0_10,c_0_25]) ).

cnf(c_0_31,negated_conjecture,
    ( multiply(sk_c7,sk_c6) = sk_c5
    | multiply(sk_c5,sk_c6) = sk_c7 ),
    prove_this_1 ).

cnf(c_0_32,plain,
    multiply(inverse(identity),X1) = X1,
    inference(spm,[status(thm)],[c_0_12,c_0_11]) ).

cnf(c_0_33,negated_conjecture,
    ( multiply(inverse(X1),sk_c5) != sk_c6
    | multiply(sk_c7,sk_c6) != sk_c5
    | multiply(sk_c5,sk_c6) != sk_c7
    | multiply(X1,inverse(X1)) != sk_c6
    | multiply(X2,sk_c5) != sk_c6
    | multiply(X3,sk_c7) != sk_c6
    | inverse(X2) != sk_c5
    | inverse(X3) != sk_c7 ),
    inference(er,[status(thm)],[c_0_26]) ).

cnf(c_0_34,negated_conjecture,
    ( multiply(sk_c3,sk_c4) = sk_c6
    | sk_c6 = identity ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

cnf(c_0_35,negated_conjecture,
    ( multiply(sk_c3,sk_c4) = identity
    | sk_c6 = identity ),
    inference(spm,[status(thm)],[c_0_29,c_0_30]) ).

cnf(c_0_36,negated_conjecture,
    ( multiply(sk_c7,multiply(sk_c6,X1)) = multiply(sk_c5,X1)
    | multiply(sk_c5,sk_c6) = sk_c7 ),
    inference(spm,[status(thm)],[c_0_9,c_0_31]) ).

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

cnf(c_0_38,negated_conjecture,
    ( multiply(inverse(X1),sk_c5) != sk_c6
    | multiply(sk_c7,sk_c6) != sk_c5
    | multiply(sk_c5,sk_c6) != sk_c7
    | multiply(X2,sk_c5) != sk_c6
    | multiply(X3,sk_c7) != sk_c6
    | inverse(X2) != sk_c5
    | inverse(X3) != sk_c7
    | sk_c6 != identity ),
    inference(rw,[status(thm)],[c_0_33,c_0_19]) ).

cnf(c_0_39,negated_conjecture,
    sk_c6 = identity,
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_40,negated_conjecture,
    ( multiply(sk_c5,inverse(sk_c6)) = sk_c7
    | multiply(sk_c5,sk_c6) = sk_c7 ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_19]),c_0_15]) ).

cnf(c_0_41,plain,
    inverse(identity) = identity,
    inference(spm,[status(thm)],[c_0_10,c_0_37]) ).

cnf(c_0_42,negated_conjecture,
    ( multiply(inverse(X1),sk_c5) != identity
    | multiply(X2,sk_c5) != identity
    | multiply(X3,sk_c7) != identity
    | inverse(X2) != sk_c5
    | inverse(X3) != sk_c7
    | sk_c7 != sk_c5 ),
    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)],[c_0_38,c_0_39]),c_0_39]),c_0_15]),c_0_39]),c_0_15]),c_0_39]),c_0_39]),c_0_39])]) ).

cnf(c_0_43,negated_conjecture,
    sk_c7 = sk_c5,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_40,c_0_39]),c_0_41]),c_0_15]),c_0_39]),c_0_15])]) ).

cnf(c_0_44,negated_conjecture,
    ( multiply(inverse(X1),sk_c5) != identity
    | multiply(X2,sk_c5) != identity
    | multiply(X3,sk_c5) != identity
    | inverse(X2) != sk_c5
    | inverse(X3) != sk_c5 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43]),c_0_43]),c_0_43])]) ).

cnf(c_0_45,negated_conjecture,
    ( multiply(X1,sk_c5) != identity
    | multiply(X2,sk_c5) != identity
    | inverse(X1) != sk_c5
    | inverse(X2) != sk_c5 ),
    inference(spm,[status(thm)],[c_0_44,c_0_10]) ).

cnf(c_0_46,negated_conjecture,
    ( multiply(X1,sk_c5) != identity
    | inverse(X1) != sk_c5 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_10]),c_0_16])]) ).

cnf(c_0_47,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[inference(spm,[status(thm)],[c_0_46,c_0_16])]),c_0_10])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.12  % Problem    : GRP292-1 : TPTP v8.1.2. Released v2.5.0.
% 0.12/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n028.cluster.edu
% 0.12/0.33  % Model    : x86_64 x86_64
% 0.12/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.33  % Memory   : 8042.1875MB
% 0.12/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.33  % CPULimit   : 300
% 0.12/0.33  % WCLimit    : 300
% 0.12/0.33  % DateTime   : Tue Aug 29 02:13:25 EDT 2023
% 0.12/0.33  % CPUTime  : 
% 0.19/0.55  start to proof: theBenchmark
% 0.19/0.57  % Version  : CSE_E---1.5
% 0.19/0.57  % Problem  : theBenchmark.p
% 0.19/0.57  % Proof found
% 0.19/0.57  % SZS status Theorem for theBenchmark.p
% 0.19/0.57  % SZS output start Proof
% See solution above
% 0.19/0.58  % Total time : 0.020000 s
% 0.19/0.58  % SZS output end Proof
% 0.19/0.58  % Total time : 0.023000 s
%------------------------------------------------------------------------------