TSTP Solution File: GRP048-10 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP048-10 : TPTP v8.1.2. Released v7.5.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n004.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 00:13:50 EDT 2023

% Result   : Unsatisfiable 12.39s 12.43s
% Output   : CNFRefutation 12.39s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   26
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   61 (  52 unt;   9 typ;   0 def)
%            Number of atoms       :   52 (  51 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    6 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   12 (   5   >;   7   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-4 aty)
%            Number of variables   :   77 (   2 sgn;   0   !;   0   ?;   0   :)

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

tff(decl_23,type,
    identity: $i ).

tff(decl_24,type,
    product: ( $i * $i * $i ) > $i ).

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

tff(decl_26,type,
    inverse: $i > $i ).

tff(decl_27,type,
    multiply: ( $i * $i ) > $i ).

tff(decl_28,type,
    equalish: ( $i * $i ) > $i ).

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

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

cnf(product_substitution3,axiom,
    ifeq(equalish(X1,X2),true,ifeq(product(X3,X4,X1),true,product(X3,X4,X2),true),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_substitution3) ).

cnf(left_identity,axiom,
    product(identity,X1,X1) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_identity) ).

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

cnf(total_function2,axiom,
    ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,equalish(X4,X3),true),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function2) ).

cnf(a_equals_b,hypothesis,
    equalish(a,b) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',a_equals_b) ).

cnf(associativity2,axiom,
    ifeq(product(X1,X2,X3),true,ifeq(product(X4,X3,X5),true,ifeq(product(X4,X1,X6),true,product(X6,X2,X5),true),true),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity2) ).

cnf(total_function1,axiom,
    product(X1,X2,multiply(X1,X2)) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',total_function1) ).

cnf(left_inverse,axiom,
    product(inverse(X1),X1,identity) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',left_inverse) ).

cnf(prove_inverse_substitution,negated_conjecture,
    equalish(inverse(a),inverse(b)) != true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_inverse_substitution) ).

cnf(c_0_9,axiom,
    ifeq(equalish(X1,X2),true,ifeq(product(X3,X4,X1),true,product(X3,X4,X2),true),true) = true,
    product_substitution3 ).

cnf(c_0_10,axiom,
    product(identity,X1,X1) = true,
    left_identity ).

cnf(c_0_11,axiom,
    ifeq(X1,X1,X2,X3) = X2,
    ifeq_axiom ).

cnf(c_0_12,axiom,
    ifeq(product(X1,X2,X3),true,ifeq(product(X1,X2,X4),true,equalish(X4,X3),true),true) = true,
    total_function2 ).

cnf(c_0_13,plain,
    ifeq(equalish(X1,X2),true,product(identity,X1,X2),true) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).

cnf(c_0_14,hypothesis,
    equalish(a,b) = true,
    a_equals_b ).

cnf(c_0_15,plain,
    ifeq(product(identity,X1,X2),true,equalish(X2,X1),true) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_10]),c_0_11]) ).

cnf(c_0_16,hypothesis,
    product(identity,a,b) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_14]),c_0_11]) ).

cnf(c_0_17,axiom,
    ifeq(product(X1,X2,X3),true,ifeq(product(X4,X3,X5),true,ifeq(product(X4,X1,X6),true,product(X6,X2,X5),true),true),true) = true,
    associativity2 ).

cnf(c_0_18,hypothesis,
    equalish(b,a) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_11]) ).

cnf(c_0_19,plain,
    ifeq(product(X1,X2,X3),true,ifeq(product(identity,X1,X4),true,product(X4,X2,X3),true),true) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_10]),c_0_11]) ).

cnf(c_0_20,hypothesis,
    product(identity,b,a) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_13,c_0_18]),c_0_11]) ).

cnf(c_0_21,axiom,
    product(X1,X2,multiply(X1,X2)) = true,
    total_function1 ).

cnf(c_0_22,hypothesis,
    ifeq(product(b,X1,X2),true,product(a,X1,X2),true) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_19,c_0_20]),c_0_11]) ).

cnf(c_0_23,axiom,
    product(inverse(X1),X1,identity) = true,
    left_inverse ).

cnf(c_0_24,plain,
    ifeq(product(X1,X2,X3),true,equalish(X3,multiply(X1,X2)),true) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_21]),c_0_11]) ).

cnf(c_0_25,hypothesis,
    product(a,X1,multiply(b,X1)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_21]),c_0_11]) ).

cnf(c_0_26,plain,
    ifeq(product(X1,X2,X3),true,ifeq(product(inverse(X1),X3,X4),true,product(identity,X2,X4),true),true) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_17,c_0_23]),c_0_11]) ).

cnf(c_0_27,plain,
    ifeq(equalish(multiply(X1,X2),X3),true,product(X1,X2,X3),true) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_21]),c_0_11]) ).

cnf(c_0_28,hypothesis,
    equalish(multiply(b,X1),multiply(a,X1)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_24,c_0_25]),c_0_11]) ).

cnf(c_0_29,plain,
    ifeq(product(X1,X2,X3),true,product(identity,X2,multiply(inverse(X1),X3)),true) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_21]),c_0_11]) ).

cnf(c_0_30,hypothesis,
    product(b,X1,multiply(a,X1)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_28]),c_0_11]) ).

cnf(c_0_31,hypothesis,
    product(identity,X1,multiply(inverse(b),multiply(a,X1))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_11]) ).

cnf(c_0_32,hypothesis,
    equalish(multiply(inverse(b),multiply(a,X1)),X1) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_31]),c_0_11]) ).

cnf(c_0_33,plain,
    ifeq(product(X1,X2,X1),true,product(identity,X2,identity),true) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_23]),c_0_11]) ).

cnf(c_0_34,hypothesis,
    product(inverse(b),multiply(a,X1),X1) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_32]),c_0_11]) ).

cnf(c_0_35,plain,
    ifeq(product(identity,X1,X2),true,equalish(X1,X2),true) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_12,c_0_10]),c_0_11]) ).

cnf(c_0_36,hypothesis,
    product(identity,multiply(a,inverse(b)),identity) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_11]) ).

cnf(c_0_37,hypothesis,
    equalish(multiply(a,inverse(b)),identity) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_11]) ).

cnf(c_0_38,hypothesis,
    product(a,inverse(b),identity) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_37]),c_0_11]) ).

cnf(c_0_39,hypothesis,
    product(identity,inverse(b),multiply(inverse(a),identity)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_38]),c_0_11]) ).

cnf(c_0_40,hypothesis,
    equalish(multiply(inverse(a),identity),inverse(b)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_39]),c_0_11]) ).

cnf(c_0_41,hypothesis,
    product(inverse(a),identity,inverse(b)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_40]),c_0_11]) ).

cnf(c_0_42,hypothesis,
    product(identity,identity,multiply(inverse(inverse(a)),inverse(b))) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_41]),c_0_11]) ).

cnf(c_0_43,hypothesis,
    equalish(multiply(inverse(inverse(a)),inverse(b)),identity) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_42]),c_0_11]) ).

cnf(c_0_44,hypothesis,
    product(inverse(inverse(a)),inverse(b),identity) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_43]),c_0_11]) ).

cnf(c_0_45,hypothesis,
    product(identity,inverse(b),multiply(inverse(inverse(inverse(a))),identity)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_44]),c_0_11]) ).

cnf(c_0_46,hypothesis,
    equalish(multiply(inverse(inverse(inverse(a))),identity),inverse(b)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_45]),c_0_11]) ).

cnf(c_0_47,plain,
    ifeq(product(inverse(inverse(X1)),identity,X2),true,product(identity,X1,X2),true) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_23]),c_0_11]) ).

cnf(c_0_48,hypothesis,
    product(inverse(inverse(inverse(a))),identity,inverse(b)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_27,c_0_46]),c_0_11]) ).

cnf(c_0_49,hypothesis,
    product(identity,inverse(a),inverse(b)) = true,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_47,c_0_48]),c_0_11]) ).

cnf(c_0_50,negated_conjecture,
    equalish(inverse(a),inverse(b)) != true,
    prove_inverse_substitution ).

cnf(c_0_51,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_49]),c_0_11]),c_0_50]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : GRP048-10 : TPTP v8.1.2. Released v7.5.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.33  % Computer : n004.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   : Mon Aug 28 20:09:52 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 12.39/12.43  % Version  : CSE_E---1.5
% 12.39/12.43  % Problem  : theBenchmark.p
% 12.39/12.43  % Proof found
% 12.39/12.43  % SZS status Theorem for theBenchmark.p
% 12.39/12.43  % SZS output start Proof
% See solution above
% 12.39/12.43  % Total time : 11.864000 s
% 12.39/12.43  % SZS output end Proof
% 12.39/12.43  % Total time : 11.867000 s
%------------------------------------------------------------------------------