%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : CAT009-3 : 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 : n029.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 18:14:07 EDT 2023

% Result   : Unsatisfiable 0.19s 0.58s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   17
% Syntax   : Number of formulae    :   51 (  23 unt;   8 typ;   0 def)
%            Number of atoms       :   65 (  31 equ)
%            Maximal formula atoms :    3 (   1 avg)
%            Number of connectives :   48 (  26   ~;  22   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    4 (   2 avg)
%            Maximal term depth    :    5 (   2 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    9 (   6   >;   3   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    6 (   6 usr;   2 con; 0-2 aty)
%            Number of variables   :   49 (   5 sgn;   0   !;   0   ?;   0   :)

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

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

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

tff(decl_25,type,
    codomain: $i > $i ).

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

tff(decl_27,type,
    f1: ( $i * $i ) > $i ).

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

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

cnf(domain_codomain_composition1,axiom,
    ( domain(X1) = codomain(X2)
    | ~ there_exists(compose(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',domain_codomain_composition1) ).

cnf(ab_exists,hypothesis,
    there_exists(compose(a,b)),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',ab_exists) ).

cnf(composition_implies_domain,axiom,
    ( there_exists(domain(X1))
    | ~ there_exists(compose(X1,X2)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',composition_implies_domain) ).

cnf(compose_codomain,axiom,
    compose(codomain(X1),X1) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',compose_codomain) ).

cnf(codomain_has_elements,axiom,
    ( there_exists(X1)
    | ~ there_exists(codomain(X1)) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',codomain_has_elements) ).

cnf(associativity_of_compose,axiom,
    compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',associativity_of_compose) ).

cnf(compose_domain,axiom,
    compose(X1,domain(X1)) = X1,
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',compose_domain) ).

cnf(domain_codomain_composition2,axiom,
    ( there_exists(compose(X1,X2))
    | ~ there_exists(domain(X1))
    | domain(X1) != codomain(X2) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/CAT003-0.ax',domain_codomain_composition2) ).

cnf(prove_domain_of_ab_equals_domain_of_b,negated_conjecture,
    domain(compose(a,b)) != domain(b),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',prove_domain_of_ab_equals_domain_of_b) ).

cnf(c_0_9,axiom,
    ( domain(X1) = codomain(X2)
    | ~ there_exists(compose(X1,X2)) ),
    domain_codomain_composition1 ).

cnf(c_0_10,hypothesis,
    there_exists(compose(a,b)),
    ab_exists ).

cnf(c_0_11,axiom,
    ( there_exists(domain(X1))
    | ~ there_exists(compose(X1,X2)) ),
    composition_implies_domain ).

cnf(c_0_12,axiom,
    compose(codomain(X1),X1) = X1,
    compose_codomain ).

cnf(c_0_13,hypothesis,
    codomain(b) = domain(a),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_14,axiom,
    ( there_exists(X1)
    | ~ there_exists(codomain(X1)) ),
    codomain_has_elements ).

cnf(c_0_15,hypothesis,
    there_exists(domain(a)),
    inference(spm,[status(thm)],[c_0_11,c_0_10]) ).

cnf(c_0_16,hypothesis,
    compose(domain(a),b) = b,
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_17,hypothesis,
    there_exists(b),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_13]),c_0_15])]) ).

cnf(c_0_18,axiom,
    compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
    associativity_of_compose ).

cnf(c_0_19,axiom,
    compose(X1,domain(X1)) = X1,
    compose_domain ).

cnf(c_0_20,axiom,
    ( there_exists(compose(X1,X2))
    | ~ there_exists(domain(X1))
    | domain(X1) != codomain(X2) ),
    domain_codomain_composition2 ).

cnf(c_0_21,hypothesis,
    domain(domain(a)) = domain(a),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_16]),c_0_13]),c_0_17])]) ).

cnf(c_0_22,plain,
    compose(X1,compose(domain(X1),X2)) = compose(X1,X2),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_23,plain,
    ( there_exists(domain(compose(X1,X2)))
    | ~ there_exists(compose(X1,compose(X2,X3))) ),
    inference(spm,[status(thm)],[c_0_11,c_0_18]) ).

cnf(c_0_24,hypothesis,
    ( there_exists(compose(domain(a),X1))
    | codomain(X1) != domain(a) ),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_15])]) ).

cnf(c_0_25,plain,
    compose(X1,compose(X2,domain(compose(X1,X2)))) = compose(X1,X2),
    inference(spm,[status(thm)],[c_0_19,c_0_18]) ).

cnf(c_0_26,plain,
    compose(X1,domain(domain(X1))) = X1,
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_22,c_0_19]),c_0_19]) ).

cnf(c_0_27,hypothesis,
    compose(domain(a),compose(b,X1)) = compose(b,X1),
    inference(spm,[status(thm)],[c_0_18,c_0_16]) ).

cnf(c_0_28,hypothesis,
    ( there_exists(domain(compose(domain(a),X1)))
    | codomain(compose(X1,X2)) != domain(a) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_29,plain,
    compose(X1,compose(domain(domain(X1)),domain(X1))) = X1,
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_30,hypothesis,
    ( there_exists(compose(a,X1))
    | codomain(X1) != domain(a) ),
    inference(spm,[status(thm)],[c_0_20,c_0_15]) ).

cnf(c_0_31,hypothesis,
    ( codomain(compose(b,X1)) = domain(a)
    | ~ there_exists(compose(b,X1)) ),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_27]),c_0_21]) ).

cnf(c_0_32,hypothesis,
    ( there_exists(domain(compose(domain(a),X1)))
    | codomain(X1) != domain(a) ),
    inference(spm,[status(thm)],[c_0_28,c_0_29]) ).

cnf(c_0_33,plain,
    ( codomain(X1) = domain(compose(X2,X3))
    | ~ there_exists(compose(X2,compose(X3,X1))) ),
    inference(spm,[status(thm)],[c_0_9,c_0_18]) ).

cnf(c_0_34,hypothesis,
    ( there_exists(compose(a,compose(b,X1)))
    | ~ there_exists(compose(b,X1)) ),
    inference(spm,[status(thm)],[c_0_30,c_0_31]) ).

cnf(c_0_35,hypothesis,
    there_exists(domain(b)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_32,c_0_16]),c_0_13])]) ).

cnf(c_0_36,negated_conjecture,
    domain(compose(a,b)) != domain(b),
    prove_domain_of_ab_equals_domain_of_b ).

cnf(c_0_37,hypothesis,
    ( codomain(X1) = domain(compose(a,b))
    | ~ there_exists(compose(b,X1)) ),
    inference(spm,[status(thm)],[c_0_33,c_0_34]) ).

cnf(c_0_38,hypothesis,
    ( there_exists(compose(b,X1))
    | codomain(X1) != domain(b) ),
    inference(spm,[status(thm)],[c_0_20,c_0_35]) ).

cnf(c_0_39,negated_conjecture,
    codomain(X1) != domain(b),
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_36,c_0_37]),c_0_38]) ).

cnf(c_0_40,plain,
    ( codomain(domain(domain(X1))) = domain(X1)
    | ~ there_exists(X1) ),
    inference(spm,[status(thm)],[c_0_9,c_0_26]) ).

cnf(c_0_41,negated_conjecture,
    ( domain(X1) != domain(b)
    | ~ there_exists(X1) ),
    inference(spm,[status(thm)],[c_0_39,c_0_40]) ).

cnf(c_0_42,negated_conjecture,
    $false,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(er,[status(thm)],[c_0_41]),c_0_17])]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : CAT009-3 : 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
% 0.13/0.34  % Computer : n029.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   : Sun Aug 27 00:51:10 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.56  start to proof: theBenchmark
% 0.19/0.58  % Version  : CSE_E---1.5
% 0.19/0.58  % Problem  : theBenchmark.p
% 0.19/0.58  % Proof found
% 0.19/0.58  % SZS status Theorem for theBenchmark.p
% 0.19/0.58  % SZS output start Proof
% See solution above
% 0.19/0.59  % Total time : 0.021000 s
% 0.19/0.59  % SZS output end Proof
% 0.19/0.59  % Total time : 0.024000 s
%------------------------------------------------------------------------------