%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : CAT005-4 : 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 : n020.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 18:14:05 EDT 2023

% Result   : Unsatisfiable 0.20s 0.55s
% Output   : CNFRefutation 0.20s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   15
% Syntax   : Number of formulae    :   31 (  16 unt;   7 typ;   0 def)
%            Number of atoms       :   32 (  14 equ)
%            Maximal formula atoms :    2 (   1 avg)
%            Number of connectives :   20 (  12   ~;   8   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    3 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :    7 (   5   >;   2   *;   0   +;   0  <<)
%            Number of predicates  :    4 (   2 usr;   1 prp; 0-2 aty)
%            Number of functors    :    5 (   5 usr;   2 con; 0-2 aty)
%            Number of variables   :   16 (   2 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,
    a: $i ).

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

cnf(domain_codomain_composition1,axiom,
    ( domain(X1) = codomain(X2)
    | ~ there_exists(compose(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',domain_codomain_composition1) ).

cnf(ad_exists,hypothesis,
    there_exists(compose(a,d)),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ad_exists) ).

cnf(xd_equals_x,hypothesis,
    ( compose(X1,d) = X1
    | ~ there_exists(compose(X1,d)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',xd_equals_x) ).

cnf(compose_domain,axiom,
    compose(X1,domain(X1)) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',compose_domain) ).

cnf(prove_domain_of_a_is_d,negated_conjecture,
    domain(a) != d,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_domain_of_a_is_d) ).

cnf(composition_implies_domain,axiom,
    ( there_exists(domain(X1))
    | ~ there_exists(compose(X1,X2)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',composition_implies_domain) ).

cnf(compose_codomain,axiom,
    compose(codomain(X1),X1) = X1,
    file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',compose_codomain) ).

cnf(codomain_has_elements,axiom,
    ( there_exists(X1)
    | ~ there_exists(codomain(X1)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/CAT004-0.ax',codomain_has_elements) ).

cnf(c_0_8,axiom,
    ( domain(X1) = codomain(X2)
    | ~ there_exists(compose(X1,X2)) ),
    domain_codomain_composition1 ).

cnf(c_0_9,hypothesis,
    there_exists(compose(a,d)),
    ad_exists ).

cnf(c_0_10,hypothesis,
    ( compose(X1,d) = X1
    | ~ there_exists(compose(X1,d)) ),
    xd_equals_x ).

cnf(c_0_11,axiom,
    compose(X1,domain(X1)) = X1,
    compose_domain ).

cnf(c_0_12,hypothesis,
    domain(a) = codomain(d),
    inference(spm,[status(thm)],[c_0_8,c_0_9]) ).

cnf(c_0_13,hypothesis,
    compose(a,d) = a,
    inference(spm,[status(thm)],[c_0_10,c_0_9]) ).

cnf(c_0_14,negated_conjecture,
    domain(a) != d,
    prove_domain_of_a_is_d ).

cnf(c_0_15,axiom,
    ( there_exists(domain(X1))
    | ~ there_exists(compose(X1,X2)) ),
    composition_implies_domain ).

cnf(c_0_16,hypothesis,
    compose(a,codomain(d)) = a,
    inference(spm,[status(thm)],[c_0_11,c_0_12]) ).

cnf(c_0_17,hypothesis,
    there_exists(a),
    inference(rw,[status(thm)],[c_0_9,c_0_13]) ).

cnf(c_0_18,axiom,
    compose(codomain(X1),X1) = X1,
    compose_codomain ).

cnf(c_0_19,negated_conjecture,
    codomain(d) != d,
    inference(rw,[status(thm)],[c_0_14,c_0_12]) ).

cnf(c_0_20,axiom,
    ( there_exists(X1)
    | ~ there_exists(codomain(X1)) ),
    codomain_has_elements ).

cnf(c_0_21,hypothesis,
    there_exists(codomain(d)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_12]),c_0_17])]) ).

cnf(c_0_22,hypothesis,
    ~ there_exists(d),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_10,c_0_18]),c_0_19]) ).

cnf(c_0_23,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_21]),c_0_22]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : CAT005-4 : 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 : n020.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 00:19:14 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.20/0.53  start to proof: theBenchmark
% 0.20/0.55  % Version  : CSE_E---1.5
% 0.20/0.55  % Problem  : theBenchmark.p
% 0.20/0.55  % Proof found
% 0.20/0.55  % SZS status Theorem for theBenchmark.p
% 0.20/0.55  % SZS output start Proof
% See solution above
% 0.20/0.55  % Total time : 0.005000 s
% 0.20/0.55  % SZS output end Proof
% 0.20/0.55  % Total time : 0.007000 s
%------------------------------------------------------------------------------