%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP514-1 : TPTP v8.1.2. Released v2.6.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n025.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 00:21:23 EDT 2023

% Result   : Unsatisfiable 0.21s 0.58s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :    6
% Syntax   : Number of formulae    :   21 (  17 unt;   4 typ;   0 def)
%            Number of atoms       :   17 (  16 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    :    8 (   2 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    :    4 (   4 usr;   2 con; 0-2 aty)
%            Number of variables   :   39 (   0 sgn;   0   !;   0   ?;   0   :)

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

tff(decl_23,type,
    inverse: $i > $i ).

tff(decl_24,type,
    b2: $i ).

tff(decl_25,type,
    a2: $i ).

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

cnf(prove_these_axioms_2,negated_conjecture,
    multiply(multiply(inverse(b2),b2),a2) != a2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_these_axioms_2) ).

cnf(c_0_2,axiom,
    multiply(X1,multiply(multiply(X2,X3),inverse(multiply(X1,X3)))) = X2,
    single_axiom ).

cnf(c_0_3,plain,
    multiply(X1,multiply(X2,inverse(multiply(X1,multiply(multiply(X2,X3),inverse(multiply(X4,X3))))))) = X4,
    inference(spm,[status(thm)],[c_0_2,c_0_2]) ).

cnf(c_0_4,plain,
    multiply(X1,multiply(X2,inverse(X2))) = X1,
    inference(spm,[status(thm)],[c_0_3,c_0_2]) ).

cnf(c_0_5,plain,
    multiply(X1,multiply(X2,inverse(X1))) = X2,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_4]),c_0_4]) ).

cnf(c_0_6,plain,
    multiply(X1,multiply(multiply(X2,multiply(multiply(X3,X4),inverse(multiply(X1,X4)))),inverse(X3))) = X2,
    inference(spm,[status(thm)],[c_0_2,c_0_2]) ).

cnf(c_0_7,plain,
    multiply(multiply(X1,X2),multiply(X3,inverse(multiply(X3,X2)))) = X1,
    inference(spm,[status(thm)],[c_0_3,c_0_5]) ).

cnf(c_0_8,plain,
    multiply(X1,multiply(multiply(X2,X3),inverse(X2))) = multiply(X1,X3),
    inference(spm,[status(thm)],[c_0_6,c_0_5]) ).

cnf(c_0_9,plain,
    multiply(multiply(X1,X2),multiply(X3,inverse(X1))) = multiply(X3,X2),
    inference(spm,[status(thm)],[c_0_6,c_0_7]) ).

cnf(c_0_10,plain,
    multiply(multiply(X1,X2),X3) = multiply(multiply(X1,X3),X2),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_11,plain,
    multiply(X1,multiply(multiply(X2,inverse(X1)),X3)) = multiply(X2,X3),
    inference(spm,[status(thm)],[c_0_5,c_0_10]) ).

cnf(c_0_12,plain,
    multiply(X1,inverse(multiply(X1,inverse(X2)))) = X2,
    inference(spm,[status(thm)],[c_0_4,c_0_11]) ).

cnf(c_0_13,plain,
    multiply(multiply(X1,X2),inverse(X2)) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_2,c_0_12]),c_0_10]) ).

cnf(c_0_14,negated_conjecture,
    multiply(multiply(inverse(b2),b2),a2) != a2,
    prove_these_axioms_2 ).

cnf(c_0_15,plain,
    multiply(X1,X2) = multiply(X2,X1),
    inference(spm,[status(thm)],[c_0_5,c_0_13]) ).

cnf(c_0_16,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[c_0_14,c_0_15]),c_0_15]),c_0_4])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRP514-1 : TPTP v8.1.2. Released v2.6.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n025.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   : Mon Aug 28 21:44:24 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.21/0.57  start to proof: theBenchmark
% 0.21/0.58  % Version  : CSE_E---1.5
% 0.21/0.58  % Problem  : theBenchmark.p
% 0.21/0.58  % Proof found
% 0.21/0.58  % SZS status Theorem for theBenchmark.p
% 0.21/0.58  % SZS output start Proof
% See solution above
% 0.21/0.59  % Total time : 0.007000 s
% 0.21/0.59  % SZS output end Proof
% 0.21/0.59  % Total time : 0.010000 s
%------------------------------------------------------------------------------