%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : CAT002-1 : 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 : n032.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 : Wed Aug 30 18:14:01 EDT 2023

% Result   : Unsatisfiable 0.57s 0.81s
% Output   : CNFRefutation 0.57s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   11
%            Number of leaves      :   22
% Syntax   : Number of formulae    :   51 (  18 unt;  12 typ;   0 def)
%            Number of atoms       :   72 (  10 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   68 (  35   ~;  33   |;   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  :   10 (   6   >;   4   *;   0   +;   0  <<)
%            Number of predicates  :    5 (   3 usr;   1 prp; 0-3 aty)
%            Number of functors    :    9 (   9 usr;   6 con; 0-2 aty)
%            Number of variables   :   57 (   6 sgn;   0   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    identity_map: $i > $o ).

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

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

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

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

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

tff(decl_31,type,
    h: $i ).

tff(decl_32,type,
    d: $i ).

tff(decl_33,type,
    g: $i ).

cnf(associative_property1,axiom,
    ( defined(X1,X2)
    | ~ product(X1,X2,X3) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property1) ).

cnf(cg_equals_d,hypothesis,
    product(c,g,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cg_equals_d) ).

cnf(associative_property2,axiom,
    ( defined(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ defined(X3,X4) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',associative_property2) ).

cnf(ch_equals_d,hypothesis,
    product(c,h,d),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ch_equals_d) ).

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

cnf(category_theory_axiom2,axiom,
    ( product(X1,X6,X5)
    | ~ product(X1,X2,X3)
    | ~ product(X3,X4,X5)
    | ~ product(X2,X4,X6) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',category_theory_axiom2) ).

cnf(closure_of_composition,axiom,
    ( product(X1,X2,compose(X1,X2))
    | ~ defined(X1,X2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT001-0.ax',closure_of_composition) ).

cnf(cancellation_for_product1,hypothesis,
    ( X1 = X3
    | ~ product(a,X1,X2)
    | ~ product(a,X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product1) ).

cnf(cancellation_for_product2,hypothesis,
    ( X1 = X3
    | ~ product(b,X1,X2)
    | ~ product(b,X3,X2) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',cancellation_for_product2) ).

cnf(prove_h_equals_g,negated_conjecture,
    h != g,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_h_equals_g) ).

cnf(c_0_10,axiom,
    ( defined(X1,X2)
    | ~ product(X1,X2,X3) ),
    associative_property1 ).

cnf(c_0_11,hypothesis,
    product(c,g,d),
    cg_equals_d ).

cnf(c_0_12,axiom,
    ( defined(X2,X4)
    | ~ product(X1,X2,X3)
    | ~ defined(X3,X4) ),
    associative_property2 ).

cnf(c_0_13,hypothesis,
    defined(c,g),
    inference(spm,[status(thm)],[c_0_10,c_0_11]) ).

cnf(c_0_14,hypothesis,
    product(c,h,d),
    ch_equals_d ).

cnf(c_0_15,hypothesis,
    ( defined(X1,g)
    | ~ product(X2,X1,c) ),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_16,hypothesis,
    product(a,b,c),
    ab_equals_c ).

cnf(c_0_17,hypothesis,
    defined(c,h),
    inference(spm,[status(thm)],[c_0_10,c_0_14]) ).

cnf(c_0_18,axiom,
    ( product(X1,X6,X5)
    | ~ product(X1,X2,X3)
    | ~ product(X3,X4,X5)
    | ~ product(X2,X4,X6) ),
    category_theory_axiom2 ).

cnf(c_0_19,axiom,
    ( product(X1,X2,compose(X1,X2))
    | ~ defined(X1,X2) ),
    closure_of_composition ).

cnf(c_0_20,hypothesis,
    defined(b,g),
    inference(spm,[status(thm)],[c_0_15,c_0_16]) ).

cnf(c_0_21,hypothesis,
    ( defined(X1,h)
    | ~ product(X2,X1,c) ),
    inference(spm,[status(thm)],[c_0_12,c_0_17]) ).

cnf(c_0_22,hypothesis,
    ( product(X1,X2,d)
    | ~ product(X3,g,X2)
    | ~ product(X1,X3,c) ),
    inference(spm,[status(thm)],[c_0_18,c_0_11]) ).

cnf(c_0_23,hypothesis,
    product(b,g,compose(b,g)),
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_24,hypothesis,
    defined(b,h),
    inference(spm,[status(thm)],[c_0_21,c_0_16]) ).

cnf(c_0_25,hypothesis,
    ( product(X1,compose(b,g),d)
    | ~ product(X1,b,c) ),
    inference(spm,[status(thm)],[c_0_22,c_0_23]) ).

cnf(c_0_26,hypothesis,
    ( product(X1,X2,d)
    | ~ product(X3,h,X2)
    | ~ product(X1,X3,c) ),
    inference(spm,[status(thm)],[c_0_18,c_0_14]) ).

cnf(c_0_27,hypothesis,
    product(b,h,compose(b,h)),
    inference(spm,[status(thm)],[c_0_19,c_0_24]) ).

cnf(c_0_28,hypothesis,
    ( X1 = X3
    | ~ product(a,X1,X2)
    | ~ product(a,X3,X2) ),
    cancellation_for_product1 ).

cnf(c_0_29,hypothesis,
    product(a,compose(b,g),d),
    inference(spm,[status(thm)],[c_0_25,c_0_16]) ).

cnf(c_0_30,hypothesis,
    ( product(X1,compose(b,h),d)
    | ~ product(X1,b,c) ),
    inference(spm,[status(thm)],[c_0_26,c_0_27]) ).

cnf(c_0_31,hypothesis,
    ( X1 = X3
    | ~ product(b,X1,X2)
    | ~ product(b,X3,X2) ),
    cancellation_for_product2 ).

cnf(c_0_32,hypothesis,
    ( X1 = compose(b,g)
    | ~ product(a,X1,d) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,hypothesis,
    product(a,compose(b,h),d),
    inference(spm,[status(thm)],[c_0_30,c_0_16]) ).

cnf(c_0_34,hypothesis,
    ( X1 = g
    | ~ product(b,X1,compose(b,g)) ),
    inference(spm,[status(thm)],[c_0_31,c_0_23]) ).

cnf(c_0_35,hypothesis,
    compose(b,g) = compose(b,h),
    inference(spm,[status(thm)],[c_0_32,c_0_33]) ).

cnf(c_0_36,hypothesis,
    ( X1 = g
    | ~ product(b,X1,compose(b,h)) ),
    inference(rw,[status(thm)],[c_0_34,c_0_35]) ).

cnf(c_0_37,negated_conjecture,
    h != g,
    prove_h_equals_g ).

cnf(c_0_38,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_27]),c_0_37]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11  % Problem    : CAT002-1 : TPTP v8.1.2. Released v1.0.0.
% 0.00/0.12  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.11/0.33  % Computer : n032.cluster.edu
% 0.11/0.33  % Model    : x86_64 x86_64
% 0.11/0.33  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.33  % Memory   : 8042.1875MB
% 0.11/0.33  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.11/0.33  % CPULimit   : 300
% 0.11/0.33  % WCLimit    : 300
% 0.11/0.33  % DateTime   : Sun Aug 27 00:10:14 EDT 2023
% 0.11/0.33  % CPUTime  : 
% 0.18/0.57  start to proof: theBenchmark
% 0.57/0.81  % Version  : CSE_E---1.5
% 0.57/0.81  % Problem  : theBenchmark.p
% 0.57/0.81  % Proof found
% 0.57/0.81  % SZS status Theorem for theBenchmark.p
% 0.57/0.81  % SZS output start Proof
% See solution above
% 0.57/0.81  % Total time : 0.225000 s
% 0.57/0.81  % SZS output end Proof
% 0.57/0.81  % Total time : 0.227000 s
%------------------------------------------------------------------------------