%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : GRP045-2 : TPTP v8.1.2. Released v1.0.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n019.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 00:13:49 EDT 2023

% Result   : Unsatisfiable 1.05s 1.10s
% Output   : CNFRefutation 1.05s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   14
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   46 (  18 unt;   9 typ;   0 def)
%            Number of atoms       :   68 (   0 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   64 (  33   ~;  31   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    5 (   2 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    :    7 (   7 usr;   5 con; 0-2 aty)
%            Number of variables   :   65 (   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 ).

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

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

cnf(left_identity,axiom,
    product(identity,X1,X1),
    file('/export/starexec/sandbox/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/sandbox/benchmark/Axioms/GRP005-0.ax',total_function2) ).

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

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

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

cnf(product_with_a,hypothesis,
    product(c,a,result),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',product_with_a) ).

cnf(prove_product_with_b,negated_conjecture,
    ~ product(c,b,result),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_product_with_b) ).

cnf(c_0_8,axiom,
    ( product(X3,X4,X2)
    | ~ equalish(X1,X2)
    | ~ product(X3,X4,X1) ),
    product_substitution3 ).

cnf(c_0_9,axiom,
    product(identity,X1,X1),
    left_identity ).

cnf(c_0_10,axiom,
    ( equalish(X3,X4)
    | ~ product(X1,X2,X3)
    | ~ product(X1,X2,X4) ),
    total_function2 ).

cnf(c_0_11,plain,
    ( product(identity,X1,X2)
    | ~ equalish(X1,X2) ),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_12,plain,
    ( equalish(X1,X2)
    | ~ product(identity,X2,X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_9]) ).

cnf(c_0_13,plain,
    ( equalish(X1,X2)
    | ~ equalish(X3,X2)
    | ~ product(identity,X3,X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,plain,
    ( equalish(X1,X2)
    | ~ equalish(X2,X1) ),
    inference(spm,[status(thm)],[c_0_12,c_0_11]) ).

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

cnf(c_0_16,axiom,
    product(X1,X2,multiply(X1,X2)),
    total_function1 ).

cnf(c_0_17,plain,
    ( equalish(X1,X2)
    | ~ equalish(X3,X2)
    | ~ equalish(X3,X1) ),
    inference(spm,[status(thm)],[c_0_13,c_0_11]) ).

cnf(c_0_18,hypothesis,
    equalish(b,a),
    inference(spm,[status(thm)],[c_0_14,c_0_15]) ).

cnf(c_0_19,plain,
    equalish(multiply(identity,X1),X1),
    inference(spm,[status(thm)],[c_0_12,c_0_16]) ).

cnf(c_0_20,hypothesis,
    ( equalish(X1,a)
    | ~ equalish(b,X1) ),
    inference(spm,[status(thm)],[c_0_17,c_0_18]) ).

cnf(c_0_21,plain,
    equalish(X1,multiply(identity,X1)),
    inference(spm,[status(thm)],[c_0_14,c_0_19]) ).

cnf(c_0_22,plain,
    ( product(X1,X2,X3)
    | ~ equalish(multiply(X1,X2),X3) ),
    inference(spm,[status(thm)],[c_0_8,c_0_16]) ).

cnf(c_0_23,hypothesis,
    equalish(multiply(identity,b),a),
    inference(spm,[status(thm)],[c_0_20,c_0_21]) ).

cnf(c_0_24,axiom,
    ( product(X3,X4,X6)
    | ~ product(X1,X2,X3)
    | ~ product(X2,X4,X5)
    | ~ product(X1,X5,X6) ),
    associativity2 ).

cnf(c_0_25,hypothesis,
    product(identity,b,a),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_26,hypothesis,
    ( product(X1,b,X2)
    | ~ product(X3,a,X2)
    | ~ product(X3,identity,X1) ),
    inference(spm,[status(thm)],[c_0_24,c_0_25]) ).

cnf(c_0_27,hypothesis,
    product(c,a,result),
    product_with_a ).

cnf(c_0_28,hypothesis,
    ( product(X1,b,result)
    | ~ product(c,identity,X1) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_29,hypothesis,
    product(multiply(c,identity),b,result),
    inference(spm,[status(thm)],[c_0_28,c_0_16]) ).

cnf(c_0_30,plain,
    ( product(X1,X2,X3)
    | ~ product(X4,identity,X1)
    | ~ product(X4,X2,X3) ),
    inference(spm,[status(thm)],[c_0_24,c_0_9]) ).

cnf(c_0_31,hypothesis,
    ( equalish(X1,result)
    | ~ product(multiply(c,identity),b,X1) ),
    inference(spm,[status(thm)],[c_0_10,c_0_29]) ).

cnf(c_0_32,plain,
    ( product(multiply(X1,identity),X2,X3)
    | ~ product(X1,X2,X3) ),
    inference(spm,[status(thm)],[c_0_30,c_0_16]) ).

cnf(c_0_33,hypothesis,
    ( equalish(X1,result)
    | ~ product(c,b,X1) ),
    inference(spm,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_34,hypothesis,
    equalish(multiply(c,b),result),
    inference(spm,[status(thm)],[c_0_33,c_0_16]) ).

cnf(c_0_35,negated_conjecture,
    ~ product(c,b,result),
    prove_product_with_b ).

cnf(c_0_36,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_34]),c_0_35]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : GRP045-2 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n019.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 01:36:28 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.58  start to proof: theBenchmark
% 1.05/1.10  % Version  : CSE_E---1.5
% 1.05/1.10  % Problem  : theBenchmark.p
% 1.05/1.10  % Proof found
% 1.05/1.10  % SZS status Theorem for theBenchmark.p
% 1.05/1.10  % SZS output start Proof
% See solution above
% 1.05/1.11  % Total time : 0.520000 s
% 1.05/1.11  % SZS output end Proof
% 1.05/1.11  % Total time : 0.523000 s
%------------------------------------------------------------------------------