TSTP Solution File: CAT010-10 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : CAT010-10 : TPTP v8.1.2. Released v7.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n015.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 0.23s 0.58s
% Output   : CNFRefutation 0.23s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    5
%            Number of leaves      :   20
% Syntax   : Number of formulae    :   37 (  26 unt;  11 typ;   0 def)
%            Number of atoms       :   26 (  25 equ)
%            Maximal formula atoms :    1 (   1 avg)
%            Number of connectives :    2 (   2   ~;   0   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    2 (   1 avg)
%            Maximal term depth    :    4 (   2 avg)
%            Number of types       :    1 (   0 usr)
%            Number of type conns  :   19 (   8   >;  11   *;   0   +;   0  <<)
%            Number of predicates  :    2 (   0 usr;   1 prp; 0-2 aty)
%            Number of functors    :   11 (  11 usr;   3 con; 0-4 aty)
%            Number of variables   :   35 (   6 sgn;   0   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
tff(decl_22,type,
    ifeq3: ( $i * $i * $i * $i ) > $i ).

tff(decl_23,type,
    ifeq2: ( $i * $i * $i * $i ) > $i ).

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

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

tff(decl_26,type,
    true: $i ).

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

tff(decl_28,type,
    domain: $i > $i ).

tff(decl_29,type,
    codomain: $i > $i ).

tff(decl_30,type,
    compose: ( $i * $i ) > $i ).

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

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

cnf(domain_codomain_composition1,axiom,
    ifeq2(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_codomain_composition1) ).

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

cnf(ifeq_axiom_001,axiom,
    ifeq2(X1,X1,X2,X3) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_001) ).

cnf(associativity_of_compose,axiom,
    compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',associativity_of_compose) ).

cnf(compose_codomain,axiom,
    compose(codomain(X1),X1) = X1,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',compose_codomain) ).

cnf(composition_implies_domain,axiom,
    ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',composition_implies_domain) ).

cnf(ifeq_axiom_002,axiom,
    ifeq(X1,X1,X2,X3) = X2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',ifeq_axiom_002) ).

cnf(domain_has_elements,axiom,
    ifeq(there_exists(domain(X1)),true,there_exists(X1),true) = true,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',domain_has_elements) ).

cnf(prove_codomain_of_ab_equals_codomain_of_a,negated_conjecture,
    codomain(compose(a,b)) != codomain(a),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',prove_codomain_of_ab_equals_codomain_of_a) ).

cnf(c_0_9,axiom,
    ifeq2(there_exists(compose(X1,X2)),true,domain(X1),codomain(X2)) = codomain(X2),
    domain_codomain_composition1 ).

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

cnf(c_0_11,axiom,
    ifeq2(X1,X1,X2,X3) = X2,
    ifeq_axiom_001 ).

cnf(c_0_12,axiom,
    compose(X1,compose(X2,X3)) = compose(compose(X1,X2),X3),
    associativity_of_compose ).

cnf(c_0_13,axiom,
    compose(codomain(X1),X1) = X1,
    compose_codomain ).

cnf(c_0_14,axiom,
    ifeq(there_exists(compose(X1,X2)),true,there_exists(domain(X1)),true) = true,
    composition_implies_domain ).

cnf(c_0_15,hypothesis,
    domain(a) = codomain(b),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_9,c_0_10]),c_0_11]) ).

cnf(c_0_16,axiom,
    ifeq(X1,X1,X2,X3) = X2,
    ifeq_axiom_002 ).

cnf(c_0_17,plain,
    compose(codomain(X1),compose(X1,X2)) = compose(X1,X2),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

cnf(c_0_18,axiom,
    ifeq(there_exists(domain(X1)),true,there_exists(X1),true) = true,
    domain_has_elements ).

cnf(c_0_19,hypothesis,
    there_exists(codomain(b)) = true,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_14,c_0_10]),c_0_15]),c_0_16]) ).

cnf(c_0_20,plain,
    ifeq2(there_exists(compose(X1,X2)),true,domain(codomain(X1)),codomain(compose(X1,X2))) = codomain(compose(X1,X2)),
    inference(spm,[status(thm)],[c_0_9,c_0_17]) ).

cnf(c_0_21,plain,
    ifeq2(there_exists(X1),true,domain(codomain(X1)),codomain(X1)) = codomain(X1),
    inference(spm,[status(thm)],[c_0_9,c_0_13]) ).

cnf(c_0_22,hypothesis,
    there_exists(a) = true,
    inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_18,c_0_15]),c_0_19]),c_0_16]) ).

cnf(c_0_23,hypothesis,
    domain(codomain(a)) = codomain(compose(a,b)),
    inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_20,c_0_10]),c_0_11]) ).

cnf(c_0_24,negated_conjecture,
    codomain(compose(a,b)) != codomain(a),
    prove_codomain_of_ab_equals_codomain_of_a ).

cnf(c_0_25,hypothesis,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_21,c_0_22]),c_0_23]),c_0_11]),c_0_24]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : CAT010-10 : TPTP v8.1.2. Released v7.3.0.
% 0.00/0.14  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.15/0.36  % Computer : n015.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit   : 300
% 0.15/0.36  % WCLimit    : 300
% 0.15/0.36  % DateTime   : Sun Aug 27 01:03:08 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 0.23/0.56  start to proof: theBenchmark
% 0.23/0.58  % Version  : CSE_E---1.5
% 0.23/0.58  % Problem  : theBenchmark.p
% 0.23/0.58  % Proof found
% 0.23/0.58  % SZS status Theorem for theBenchmark.p
% 0.23/0.58  % SZS output start Proof
% See solution above
% 0.23/0.58  % Total time : 0.009000 s
% 0.23/0.58  % SZS output end Proof
% 0.23/0.58  % Total time : 0.012000 s
%------------------------------------------------------------------------------