TSTP Solution File: GRP088-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP088-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n029.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 00:15:56 EDT 2023

% Result   : Unsatisfiable 0.19s 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   22
%            Number of leaves      :   16
% Syntax   : Number of formulae    :   68 (  49 unt;  12 typ;   0 def)
%            Number of atoms       :   73 (  72 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   42 (  25   ~;  17   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    5 (   3   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   12 (  12 usr;   9 con; 0-2 aty)
%            Number of variables   :  100 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    a1: $i ).

tff(decl_26,type,
    b1: $i ).

tff(decl_27,type,
    b2: $i ).

tff(decl_28,type,
    a2: $i ).

tff(decl_29,type,
    a3: $i ).

tff(decl_30,type,
    b3: $i ).

tff(decl_31,type,
    c3: $i ).

tff(decl_32,type,
    a4: $i ).

tff(decl_33,type,
    b4: $i ).

cnf(multiply,axiom,
    multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',multiply) ).

cnf(inverse,axiom,
    inverse(X1) = divide(divide(X2,X2),X1),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',inverse) ).

cnf(single_axiom,axiom,
    divide(X1,divide(X2,divide(X3,divide(X1,X2)))) = X3,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',single_axiom) ).

cnf(prove_these_axioms,negated_conjecture,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | multiply(multiply(inverse(b2),b2),a2) != a2
    | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | multiply(a4,b4) != multiply(b4,a4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms) ).

cnf(c_0_4,axiom,
    multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
    multiply ).

cnf(c_0_5,axiom,
    inverse(X1) = divide(divide(X2,X2),X1),
    inverse ).

cnf(c_0_6,plain,
    divide(X1,inverse(X2)) = multiply(X1,X2),
    inference(rw,[status(thm)],[c_0_4,c_0_5]) ).

cnf(c_0_7,axiom,
    divide(X1,divide(X2,divide(X3,divide(X1,X2)))) = X3,
    single_axiom ).

cnf(c_0_8,plain,
    divide(multiply(inverse(X1),X1),X2) = inverse(X2),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_9,plain,
    inverse(divide(X1,multiply(X2,X1))) = X2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_5,c_0_7]),c_0_5]),c_0_6]) ).

cnf(c_0_10,plain,
    multiply(divide(X1,X1),X2) = inverse(inverse(X2)),
    inference(spm,[status(thm)],[c_0_5,c_0_6]) ).

cnf(c_0_11,plain,
    divide(inverse(divide(X1,X1)),X2) = inverse(X2),
    inference(spm,[status(thm)],[c_0_5,c_0_5]) ).

cnf(c_0_12,plain,
    multiply(multiply(inverse(X1),X1),X2) = inverse(inverse(X2)),
    inference(spm,[status(thm)],[c_0_6,c_0_8]) ).

cnf(c_0_13,plain,
    multiply(divide(a1,a1),multiply(X1,divide(X2,X2))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_5]),c_0_10]) ).

cnf(c_0_14,plain,
    multiply(inverse(divide(X1,X1)),X2) = multiply(divide(a1,a1),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_6,c_0_11]),c_0_10]) ).

cnf(c_0_15,plain,
    inverse(multiply(X1,inverse(X1))) = multiply(inverse(X2),X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_12]),c_0_6]) ).

cnf(c_0_16,plain,
    inverse(divide(X1,X1)) = divide(a1,a1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_13]) ).

cnf(c_0_17,plain,
    multiply(inverse(X1),X1) = multiply(inverse(X2),X2),
    inference(spm,[status(thm)],[c_0_15,c_0_15]) ).

cnf(c_0_18,plain,
    inverse(multiply(inverse(X1),X1)) = divide(a1,a1),
    inference(spm,[status(thm)],[c_0_16,c_0_6]) ).

cnf(c_0_19,plain,
    multiply(inverse(X1),X1) = divide(a1,a1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_15]),c_0_12]),c_0_15]),c_0_18]) ).

cnf(c_0_20,plain,
    divide(a1,a1) = divide(X1,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_6]),c_0_15]),c_0_19]) ).

cnf(c_0_21,plain,
    divide(X1,divide(divide(X2,divide(X3,X1)),X2)) = X3,
    inference(spm,[status(thm)],[c_0_7,c_0_7]) ).

cnf(c_0_22,plain,
    divide(X1,X1) = divide(X2,X2),
    inference(spm,[status(thm)],[c_0_20,c_0_20]) ).

cnf(c_0_23,plain,
    inverse(divide(X1,divide(a1,a1))) = inverse(X1),
    inference(spm,[status(thm)],[c_0_9,c_0_19]) ).

cnf(c_0_24,plain,
    multiply(X1,divide(X2,X1)) = X2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_5]),c_0_6]) ).

cnf(c_0_25,plain,
    inverse(divide(X1,divide(X2,X2))) = inverse(X1),
    inference(spm,[status(thm)],[c_0_23,c_0_22]) ).

cnf(c_0_26,plain,
    multiply(divide(a1,a1),X1) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_24]),c_0_25]),c_0_10]) ).

cnf(c_0_27,plain,
    multiply(divide(X1,X1),X2) = X2,
    inference(spm,[status(thm)],[c_0_26,c_0_22]) ).

cnf(c_0_28,plain,
    divide(X1,divide(divide(X2,divide(X3,divide(X1,X2))),divide(X4,X3))) = X4,
    inference(spm,[status(thm)],[c_0_7,c_0_7]) ).

cnf(c_0_29,plain,
    divide(X1,divide(X2,X2)) = X1,
    inference(spm,[status(thm)],[c_0_24,c_0_27]) ).

cnf(c_0_30,plain,
    divide(X1,divide(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_5]),c_0_6]),c_0_24]) ).

cnf(c_0_31,negated_conjecture,
    ( multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | multiply(multiply(inverse(b2),b2),a2) != a2
    | multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | multiply(a4,b4) != multiply(b4,a4) ),
    prove_these_axioms ).

cnf(c_0_32,plain,
    multiply(divide(X1,X2),X2) = X1,
    inference(spm,[status(thm)],[c_0_24,c_0_30]) ).

cnf(c_0_33,negated_conjecture,
    ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | multiply(a4,b4) != multiply(b4,a4)
    | inverse(inverse(a2)) != a2 ),
    inference(rw,[status(thm)],[c_0_31,c_0_12]) ).

cnf(c_0_34,plain,
    inverse(divide(X1,X2)) = divide(X2,X1),
    inference(spm,[status(thm)],[c_0_9,c_0_32]) ).

cnf(c_0_35,negated_conjecture,
    ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | multiply(inverse(a1),a1) != multiply(inverse(b1),b1)
    | multiply(a4,b4) != multiply(b4,a4)
    | multiply(divide(a1,a1),a2) != a2 ),
    inference(rw,[status(thm)],[c_0_33,c_0_10]) ).

cnf(c_0_36,plain,
    divide(multiply(X1,X2),X2) = X1,
    inference(rw,[status(thm)],[c_0_9,c_0_34]) ).

cnf(c_0_37,plain,
    multiply(inverse(X1),multiply(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_24,c_0_6]) ).

cnf(c_0_38,negated_conjecture,
    ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | multiply(a4,b4) != multiply(b4,a4)
    | multiply(divide(a1,a1),a2) != a2 ),
    inference(sr,[status(thm)],[c_0_35,c_0_17]) ).

cnf(c_0_39,plain,
    multiply(multiply(X1,inverse(X2)),X2) = X1,
    inference(spm,[status(thm)],[c_0_6,c_0_36]) ).

cnf(c_0_40,plain,
    multiply(inverse(multiply(X1,X2)),X1) = inverse(X2),
    inference(spm,[status(thm)],[c_0_37,c_0_37]) ).

cnf(c_0_41,plain,
    divide(X1,divide(inverse(X2),divide(X3,multiply(X1,X2)))) = X3,
    inference(spm,[status(thm)],[c_0_7,c_0_6]) ).

cnf(c_0_42,plain,
    divide(inverse(X1),X2) = inverse(multiply(X2,X1)),
    inference(spm,[status(thm)],[c_0_34,c_0_6]) ).

cnf(c_0_43,plain,
    multiply(X1,X2) = multiply(X2,X1),
    inference(spm,[status(thm)],[c_0_24,c_0_36]) ).

cnf(c_0_44,negated_conjecture,
    ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | multiply(a4,b4) != multiply(b4,a4)
    | multiply(divide(X1,X1),a2) != a2 ),
    inference(spm,[status(thm)],[c_0_38,c_0_20]) ).

cnf(c_0_45,plain,
    inverse(multiply(inverse(X1),X2)) = multiply(inverse(X2),X1),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_46,plain,
    multiply(inverse(X1),inverse(X2)) = inverse(multiply(X1,X2)),
    inference(spm,[status(thm)],[c_0_37,c_0_40]) ).

cnf(c_0_47,plain,
    multiply(X1,multiply(X2,divide(X3,multiply(X1,X2)))) = X3,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_41,c_0_42]),c_0_43]),c_0_6]) ).

cnf(c_0_48,plain,
    divide(multiply(X1,X2),X1) = X2,
    inference(spm,[status(thm)],[c_0_30,c_0_36]) ).

cnf(c_0_49,negated_conjecture,
    ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | multiply(a4,b4) != multiply(b4,a4) ),
    inference(spm,[status(thm)],[c_0_44,c_0_26]) ).

cnf(c_0_50,plain,
    multiply(inverse(X1),X2) = divide(X2,X1),
    inference(spm,[status(thm)],[c_0_37,c_0_32]) ).

cnf(c_0_51,plain,
    inverse(inverse(multiply(X1,X2))) = multiply(X2,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_46]),c_0_10]),c_0_26]) ).

cnf(c_0_52,plain,
    multiply(multiply(X1,X2),X3) = multiply(X1,multiply(X2,X3)),
    inference(spm,[status(thm)],[c_0_47,c_0_48]) ).

cnf(c_0_53,negated_conjecture,
    multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_43]),c_0_43])]) ).

cnf(c_0_54,plain,
    multiply(X1,multiply(X2,X3)) = multiply(X3,multiply(X2,X1)),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_50,c_0_51]),c_0_6]),c_0_52]) ).

cnf(c_0_55,negated_conjecture,
    $false,
    inference(ar,[status(thm)],[inference(rw,[status(thm)],[c_0_53,c_0_54]),c_0_43,c_0_52]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.08/0.12  % Problem    : GRP088-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.08/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n029.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 00:43:26 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.58  % Version  : CSE_E---1.5
% 0.19/0.58  % Problem  : theBenchmark.p
% 0.19/0.58  % Proof found
% 0.19/0.58  % SZS status Theorem for theBenchmark.p
% 0.19/0.58  % SZS output start Proof
% See solution above
% 0.19/0.59  % Total time : 0.015000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.017000 s
%------------------------------------------------------------------------------