TSTP Solution File: GRP091-1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP091-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 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 00:15:57 EDT 2023

% Result   : Unsatisfiable 0.19s 0.72s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   21
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   65 (  48 unt;  13 typ;   0 def)
%            Number of atoms       :   63 (  62 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   27 (  16   ~;  11   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   1 avg)
%            Maximal term depth    :    5 (   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    :   13 (  13 usr;  10 con; 0-2 aty)
%            Number of variables   :  103 (   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,
    identity: $i ).

tff(decl_26,type,
    a1: $i ).

tff(decl_27,type,
    b1: $i ).

tff(decl_28,type,
    b2: $i ).

tff(decl_29,type,
    a2: $i ).

tff(decl_30,type,
    a3: $i ).

tff(decl_31,type,
    b3: $i ).

tff(decl_32,type,
    c3: $i ).

tff(decl_33,type,
    a4: $i ).

tff(decl_34,type,
    b4: $i ).

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

cnf(identity,axiom,
    identity = divide(X1,X1),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',identity) ).

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

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

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/sandbox2/benchmark/theBenchmark.p',prove_these_axioms) ).

cnf(c_0_5,axiom,
    multiply(X1,X2) = divide(X1,divide(divide(X3,X3),X2)),
    multiply ).

cnf(c_0_6,axiom,
    identity = divide(X1,X1),
    identity ).

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

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

cnf(c_0_9,plain,
    divide(multiply(X1,X2),X1) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_6]),c_0_8]) ).

cnf(c_0_10,plain,
    multiply(divide(identity,X1),X1) = identity,
    inference(spm,[status(thm)],[c_0_6,c_0_8]) ).

cnf(c_0_11,plain,
    multiply(identity,X1) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_8]) ).

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

cnf(c_0_13,plain,
    multiply(X1,identity) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_11]),c_0_12]) ).

cnf(c_0_14,plain,
    divide(X1,identity) = X1,
    inference(rw,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_15,plain,
    divide(X1,divide(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_7,c_0_14]),c_0_12]),c_0_13]) ).

cnf(c_0_16,plain,
    divide(multiply(X1,X2),X2) = X1,
    inference(spm,[status(thm)],[c_0_15,c_0_9]) ).

cnf(c_0_17,plain,
    multiply(multiply(X1,divide(identity,X2)),X2) = X1,
    inference(spm,[status(thm)],[c_0_8,c_0_16]) ).

cnf(c_0_18,plain,
    multiply(multiply(divide(identity,X1),X2),X1) = X2,
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_19,plain,
    multiply(X1,X2) = multiply(X2,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_18]),c_0_8]),c_0_11]) ).

cnf(c_0_20,plain,
    multiply(X1,multiply(X2,divide(identity,X1))) = X2,
    inference(rw,[status(thm)],[c_0_17,c_0_19]) ).

cnf(c_0_21,plain,
    divide(X1,X2) = multiply(X1,divide(identity,X2)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_8,c_0_8]),c_0_11]) ).

cnf(c_0_22,plain,
    multiply(X1,divide(X2,X1)) = X2,
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_23,plain,
    divide(X1,multiply(X1,X2)) = divide(identity,X2),
    inference(spm,[status(thm)],[c_0_15,c_0_8]) ).

cnf(c_0_24,plain,
    multiply(divide(identity,X1),multiply(X2,X1)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_8]),c_0_11]) ).

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

cnf(c_0_26,plain,
    multiply(divide(X1,multiply(X1,X2)),multiply(X3,X2)) = X3,
    inference(spm,[status(thm)],[c_0_24,c_0_23]) ).

cnf(c_0_27,plain,
    multiply(divide(X1,X2),divide(X2,X1)) = identity,
    inference(spm,[status(thm)],[c_0_25,c_0_22]) ).

cnf(c_0_28,plain,
    divide(X1,divide(X2,multiply(X2,X3))) = multiply(X1,X3),
    inference(spm,[status(thm)],[c_0_8,c_0_23]) ).

cnf(c_0_29,plain,
    multiply(divide(X1,X2),multiply(X3,divide(X2,X1))) = X3,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_14]) ).

cnf(c_0_30,plain,
    multiply(multiply(X1,X2),divide(identity,X2)) = X1,
    inference(rw,[status(thm)],[c_0_16,c_0_21]) ).

cnf(c_0_31,plain,
    multiply(divide(X1,multiply(divide(X1,X2),divide(identity,X3))),divide(identity,X2)) = X3,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_7,c_0_21]),c_0_21]) ).

cnf(c_0_32,plain,
    multiply(multiply(X1,X2),divide(identity,X1)) = X2,
    inference(rw,[status(thm)],[c_0_9,c_0_21]) ).

cnf(c_0_33,axiom,
    inverse(X1) = divide(divide(X2,X2),X1),
    inverse ).

cnf(c_0_34,plain,
    divide(X1,multiply(divide(X2,X3),divide(identity,X4))) = multiply(X1,multiply(X4,divide(X3,X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_29]),c_0_21]) ).

cnf(c_0_35,plain,
    divide(X1,multiply(divide(X1,X2),divide(identity,X3))) = multiply(X3,X2),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_31]),c_0_15]) ).

cnf(c_0_36,plain,
    multiply(multiply(X1,X2),divide(X3,multiply(X3,X1))) = X2,
    inference(spm,[status(thm)],[c_0_32,c_0_23]) ).

cnf(c_0_37,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_38,plain,
    inverse(X1) = divide(identity,X1),
    inference(rw,[status(thm)],[c_0_33,c_0_6]) ).

cnf(c_0_39,plain,
    multiply(X1,multiply(divide(identity,X1),X2)) = X2,
    inference(rw,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_40,plain,
    multiply(X1,multiply(X2,divide(X3,X1))) = multiply(X2,X3),
    inference(spm,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_41,plain,
    multiply(multiply(divide(X1,X2),X3),divide(X2,X1)) = X3,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_27]),c_0_14]) ).

cnf(c_0_42,negated_conjecture,
    ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | multiply(divide(identity,a1),a1) != multiply(divide(identity,b1),b1)
    | multiply(multiply(divide(identity,b2),b2),a2) != a2
    | multiply(a4,b4) != multiply(b4,a4) ),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_37,c_0_38]),c_0_38]),c_0_38]) ).

cnf(c_0_43,plain,
    multiply(divide(identity,X1),multiply(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_39,c_0_8]),c_0_11]) ).

cnf(c_0_44,plain,
    multiply(X1,multiply(divide(X2,multiply(X2,X1)),X3)) = X3,
    inference(spm,[status(thm)],[c_0_39,c_0_23]) ).

cnf(c_0_45,plain,
    multiply(X1,multiply(divide(X2,X1),X3)) = multiply(X2,X3),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_40,c_0_41]),c_0_19]) ).

cnf(c_0_46,negated_conjecture,
    ( multiply(multiply(a3,b3),c3) != multiply(a3,multiply(b3,c3))
    | multiply(a4,b4) != multiply(b4,a4)
    | multiply(identity,a2) != a2 ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_10]),c_0_10]),c_0_10])]) ).

cnf(c_0_47,plain,
    multiply(divide(X1,multiply(X1,X2)),multiply(X2,X3)) = X3,
    inference(spm,[status(thm)],[c_0_43,c_0_23]) ).

cnf(c_0_48,plain,
    multiply(multiply(X1,X2),X3) = multiply(X2,multiply(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_44,c_0_45]),c_0_28]) ).

cnf(c_0_49,negated_conjecture,
    multiply(c3,multiply(a3,b3)) != multiply(a3,multiply(b3,c3)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_46,c_0_11])]),c_0_19]),c_0_19])]) ).

cnf(c_0_50,plain,
    multiply(X1,multiply(X2,X3)) = multiply(X2,multiply(X1,X3)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_45,c_0_47]),c_0_48]) ).

cnf(c_0_51,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_49,c_0_50]),c_0_19])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRP091-1 : TPTP v8.1.2. Bugfixed v2.7.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n015.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 00:05:55 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.72  % Version  : CSE_E---1.5
% 0.19/0.72  % Problem  : theBenchmark.p
% 0.19/0.72  % Proof found
% 0.19/0.72  % SZS status Theorem for theBenchmark.p
% 0.19/0.72  % SZS output start Proof
% See solution above
% 0.19/0.72  % Total time : 0.146000 s
% 0.19/0.72  % SZS output end Proof
% 0.19/0.72  % Total time : 0.149000 s
%------------------------------------------------------------------------------