TSTP Solution File: GRP201-1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP201-1 : TPTP v8.1.2. Released v2.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n026.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 00:17:42 EDT 2023

% Result   : Unsatisfiable 0.22s 0.78s
% Output   : CNFRefutation 0.22s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   13
%            Number of leaves      :   18
% Syntax   : Number of formulae    :   54 (  45 unt;   9 typ;   0 def)
%            Number of atoms       :   45 (  44 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    3 (   3   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :    8 (   5   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :    9 (   9 usr;   4 con; 0-2 aty)
%            Number of variables   :   86 (   0 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    identity: $i ).

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

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

tff(decl_25,type,
    right_division: ( $i * $i ) > $i ).

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

tff(decl_27,type,
    left_inverse: $i > $i ).

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

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

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

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

cnf(moufang2,axiom,
    multiply(multiply(multiply(X1,X2),X3),X2) = multiply(X1,multiply(X2,multiply(X3,X2))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',moufang2) ).

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

cnf(right_identity,axiom,
    multiply(X1,identity) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',right_identity) ).

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

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

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

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

cnf(prove_moufang3,negated_conjecture,
    multiply(multiply(multiply(a,b),a),c) != multiply(a,multiply(b,multiply(a,c))),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_moufang3) ).

cnf(c_0_9,axiom,
    right_division(multiply(X1,X2),X2) = X1,
    right_division_multiply ).

cnf(c_0_10,axiom,
    multiply(multiply(multiply(X1,X2),X3),X2) = multiply(X1,multiply(X2,multiply(X3,X2))),
    moufang2 ).

cnf(c_0_11,plain,
    right_division(multiply(X1,multiply(X2,multiply(X3,X2))),X2) = multiply(multiply(X1,X2),X3),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

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

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

cnf(c_0_14,axiom,
    multiply(identity,X1) = X1,
    left_identity ).

cnf(c_0_15,plain,
    multiply(multiply(X1,X2),left_inverse(X2)) = X1,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_11,c_0_12]),c_0_13]),c_0_9]) ).

cnf(c_0_16,axiom,
    multiply(right_division(X1,X2),X2) = X1,
    multiply_right_division ).

cnf(c_0_17,axiom,
    left_division(X1,multiply(X1,X2)) = X2,
    left_division_multiply ).

cnf(c_0_18,plain,
    multiply(multiply(X1,X2),X1) = multiply(X1,multiply(X2,X1)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_14]),c_0_14]) ).

cnf(c_0_19,plain,
    multiply(X1,left_inverse(X2)) = right_division(X1,X2),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_20,plain,
    left_division(right_division(X1,X2),X1) = X2,
    inference(spm,[status(thm)],[c_0_17,c_0_16]) ).

cnf(c_0_21,plain,
    right_division(X1,left_inverse(X2)) = multiply(X1,X2),
    inference(spm,[status(thm)],[c_0_9,c_0_15]) ).

cnf(c_0_22,plain,
    multiply(left_inverse(X1),right_division(X2,X1)) = right_division(multiply(left_inverse(X1),X2),X1),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_19]),c_0_19]) ).

cnf(c_0_23,plain,
    right_division(multiply(X1,multiply(X2,X1)),X1) = multiply(X1,X2),
    inference(spm,[status(thm)],[c_0_9,c_0_18]) ).

cnf(c_0_24,plain,
    left_division(multiply(X1,X2),X1) = left_inverse(X2),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_25,axiom,
    multiply(X1,left_division(X1,X2)) = X2,
    multiply_left_division ).

cnf(c_0_26,plain,
    multiply(left_inverse(X1),multiply(X1,X2)) = X2,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_23]),c_0_11]),c_0_12]),c_0_14]) ).

cnf(c_0_27,plain,
    multiply(X1,right_division(X2,X1)) = right_division(multiply(X1,X2),X1),
    inference(spm,[status(thm)],[c_0_23,c_0_16]) ).

cnf(c_0_28,plain,
    left_inverse(left_division(X1,X2)) = left_division(X2,X1),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_29,plain,
    left_division(left_inverse(X1),X2) = multiply(X1,X2),
    inference(spm,[status(thm)],[c_0_17,c_0_26]) ).

cnf(c_0_30,plain,
    multiply(left_inverse(X1),X2) = left_division(X1,X2),
    inference(spm,[status(thm)],[c_0_26,c_0_25]) ).

cnf(c_0_31,plain,
    left_division(X1,right_division(multiply(X1,X2),X1)) = right_division(X2,X1),
    inference(spm,[status(thm)],[c_0_17,c_0_27]) ).

cnf(c_0_32,plain,
    left_division(X1,left_inverse(X2)) = left_inverse(multiply(X2,X1)),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,plain,
    multiply(multiply(left_division(X1,X2),X3),X2) = left_division(X1,multiply(X2,multiply(X3,X2))),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_30]),c_0_30]) ).

cnf(c_0_34,plain,
    right_division(left_division(X1,X2),X1) = left_division(X1,right_division(X2,X1)),
    inference(spm,[status(thm)],[c_0_31,c_0_25]) ).

cnf(c_0_35,plain,
    left_inverse(right_division(X1,X2)) = right_division(X2,X1),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_32]),c_0_19]),c_0_19]) ).

cnf(c_0_36,plain,
    left_division(X1,left_division(X2,right_division(X3,X2))) = right_division(left_division(multiply(X2,X1),X3),X2),
    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(spm,[status(thm)],[c_0_19,c_0_33]),c_0_19]),c_0_22]),c_0_30]),c_0_34]),c_0_32]),c_0_30]) ).

cnf(c_0_37,plain,
    right_division(X1,left_division(X2,X3)) = multiply(X1,left_division(X3,X2)),
    inference(spm,[status(thm)],[c_0_21,c_0_28]) ).

cnf(c_0_38,plain,
    left_division(left_division(X1,X2),X3) = multiply(left_division(X2,X1),X3),
    inference(spm,[status(thm)],[c_0_29,c_0_28]) ).

cnf(c_0_39,plain,
    left_division(right_division(X1,X2),X3) = multiply(right_division(X2,X1),X3),
    inference(spm,[status(thm)],[c_0_29,c_0_35]) ).

cnf(c_0_40,negated_conjecture,
    multiply(multiply(multiply(a,b),a),c) != multiply(a,multiply(b,multiply(a,c))),
    prove_moufang3 ).

cnf(c_0_41,plain,
    multiply(X1,left_division(X2,multiply(X1,X3))) = multiply(multiply(right_division(X1,X2),X1),X3),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_28,c_0_36]),c_0_35]),c_0_37]),c_0_38]),c_0_39]) ).

cnf(c_0_42,negated_conjecture,
    multiply(multiply(a,multiply(b,a)),c) != multiply(a,multiply(b,multiply(a,c))),
    inference(rw,[status(thm)],[c_0_40,c_0_18]) ).

cnf(c_0_43,plain,
    multiply(multiply(X1,multiply(X2,X1)),X3) = multiply(X1,multiply(X2,multiply(X1,X3))),
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_41,c_0_29]),c_0_21]),c_0_18]) ).

cnf(c_0_44,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[c_0_42,c_0_43])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem    : GRP201-1 : TPTP v8.1.2. Released v2.2.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.14/0.35  % Computer : n026.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit   : 300
% 0.14/0.35  % WCLimit    : 300
% 0.14/0.35  % DateTime   : Mon Aug 28 20:20:35 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 0.22/0.58  start to proof: theBenchmark
% 0.22/0.78  % Version  : CSE_E---1.5
% 0.22/0.78  % Problem  : theBenchmark.p
% 0.22/0.78  % Proof found
% 0.22/0.78  % SZS status Theorem for theBenchmark.p
% 0.22/0.78  % SZS output start Proof
% See solution above
% 0.22/0.79  % Total time : 0.194000 s
% 0.22/0.79  % SZS output end Proof
% 0.22/0.79  % Total time : 0.196000 s
%------------------------------------------------------------------------------