%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP046-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/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 00:13:50 EDT 2023

% Result   : Unsatisfiable 0.20s 0.64s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    8
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   38 (  14 unt;   8 typ;   0 def)
%            Number of atoms       :   57 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   57 (  30   ~;  27   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   3 avg)
%            Maximal term depth    :    2 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    8 (   4   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    3 (   2 usr;   1 prp; 0-3 aty)
%            Number of functors    :    6 (   6 usr;   4 con; 0-2 aty)
%            Number of variables   :   63 (   0 sgn;   0   !;   0   ?;   0   :)

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

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

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

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

tff(decl_26,type,
    equalish: ( $i * $i ) > $o ).

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

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

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

cnf(product_substitution3,axiom,
    ( product(X3,X4,X2)
    | ~ equalish(X1,X2)
    | ~ product(X3,X4,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',product_substitution3) ).

cnf(left_identity,axiom,
    product(identity,X1,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',left_identity) ).

cnf(total_function2,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function2) ).

cnf(total_function1,axiom,
    product(X1,X2,multiply(X1,X2)),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',total_function1) ).

cnf(a_equals_b,hypothesis,
    equalish(a,b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',a_equals_b) ).

cnf(associativity2,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/GRP005-0.ax',associativity2) ).

cnf(prove_multiply_substitution1,negated_conjecture,
    ~ equalish(multiply(a,c),multiply(b,c)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_multiply_substitution1) ).

cnf(c_0_7,axiom,
    ( product(X3,X4,X2)
    | ~ equalish(X1,X2)
    | ~ product(X3,X4,X1) ),
    product_substitution3 ).

cnf(c_0_8,axiom,
    product(identity,X1,X1),
    left_identity ).

cnf(c_0_9,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    total_function2 ).

cnf(c_0_10,plain,
    ( product(identity,X1,X2)
    | ~ equalish(X1,X2) ),
    inference(spm,[status(thm)],[c_0_7,c_0_8]) ).

cnf(c_0_11,plain,
    ( equalish(X1,X2)
    | ~ equalish(X3,X2)
    | ~ product(identity,X3,X1) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_12,plain,
    ( equalish(X1,X2)
    | ~ product(identity,X2,X1) ),
    inference(spm,[status(thm)],[c_0_9,c_0_8]) ).

cnf(c_0_13,axiom,
    product(X1,X2,multiply(X1,X2)),
    total_function1 ).

cnf(c_0_14,plain,
    ( equalish(X1,X2)
    | ~ equalish(X3,X2)
    | ~ equalish(X3,X1) ),
    inference(spm,[status(thm)],[c_0_11,c_0_10]) ).

cnf(c_0_15,hypothesis,
    equalish(a,b),
    a_equals_b ).

cnf(c_0_16,plain,
    ( equalish(X1,X2)
    | ~ equalish(X2,X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_10]) ).

cnf(c_0_17,plain,
    equalish(multiply(identity,X1),X1),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_18,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    associativity2 ).

cnf(c_0_19,hypothesis,
    ( equalish(X1,b)
    | ~ equalish(a,X1) ),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_20,plain,
    equalish(X1,multiply(identity,X1)),
    inference(spm,[status(thm)],[c_0_16,c_0_17]) ).

cnf(c_0_21,negated_conjecture,
    ~ equalish(multiply(a,c),multiply(b,c)),
    prove_multiply_substitution1 ).

cnf(c_0_22,plain,
    ( equalish(X1,multiply(X2,X3))
    | ~ product(X2,X3,X1) ),
    inference(spm,[status(thm)],[c_0_9,c_0_13]) ).

cnf(c_0_23,plain,
    ( product(X1,X2,X3)
    | ~ product(X4,multiply(X5,X2),X3)
    | ~ product(X4,X5,X1) ),
    inference(spm,[status(thm)],[c_0_18,c_0_13]) ).

cnf(c_0_24,plain,
    ( product(X1,X2,X3)
    | ~ equalish(multiply(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_7,c_0_13]) ).

cnf(c_0_25,hypothesis,
    equalish(multiply(identity,a),b),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_26,negated_conjecture,
    ~ product(b,c,multiply(a,c)),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_27,plain,
    ( product(X1,X2,multiply(X3,X2))
    | ~ product(identity,X3,X1) ),
    inference(spm,[status(thm)],[c_0_23,c_0_8]) ).

cnf(c_0_28,hypothesis,
    product(identity,a,b),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_29,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_26,c_0_27]),c_0_28])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRP046-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.16/0.35  % Computer : n026.cluster.edu
% 0.16/0.35  % Model    : x86_64 x86_64
% 0.16/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.35  % Memory   : 8042.1875MB
% 0.16/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.16/0.35  % CPULimit   : 300
% 0.16/0.35  % WCLimit    : 300
% 0.16/0.35  % DateTime   : Tue Aug 29 02:31:05 EDT 2023
% 0.16/0.35  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 0.20/0.64  % Version  : CSE_E---1.5
% 0.20/0.64  % Problem  : theBenchmark.p
% 0.20/0.64  % Proof found
% 0.20/0.64  % SZS status Theorem for theBenchmark.p
% 0.20/0.64  % SZS output start Proof
% See solution above
% 0.20/0.64  % Total time : 0.047000 s
% 0.20/0.64  % SZS output end Proof
% 0.20/0.65  % Total time : 0.050000 s
%------------------------------------------------------------------------------