TSTP Solution File: SWV373+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV373+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox2/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 21:38:18 EDT 2023

% Result   : Theorem 0.19s 0.60s
% Output   : CNFRefutation 0.19s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    6
%            Number of leaves      :   35
% Syntax   : Number of formulae    :   52 (   9 unt;  30 typ;   0 def)
%            Number of atoms       :   43 (  10 equ)
%            Maximal formula atoms :    6 (   1 avg)
%            Number of connectives :   43 (  22   ~;  10   |;   6   &)
%                                         (   1 <=>;   4  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   42 (  24   >;  18   *;   0   +;   0  <<)
%            Number of predicates  :   11 (   9 usr;   1 prp; 0-3 aty)
%            Number of functors    :   21 (  21 usr;   6 con; 0-3 aty)
%            Number of variables   :   41 (   6 sgn;  30   !;   0   ?;   0   :)

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

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

tff(decl_24,type,
    bottom: $i ).

tff(decl_25,type,
    create_slb: $i ).

tff(decl_26,type,
    isnonempty_slb: $i > $o ).

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

tff(decl_28,type,
    insert_slb: ( $i * $i ) > $i ).

tff(decl_29,type,
    contains_slb: ( $i * $i ) > $o ).

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

tff(decl_31,type,
    remove_slb: ( $i * $i ) > $i ).

tff(decl_32,type,
    lookup_slb: ( $i * $i ) > $i ).

tff(decl_33,type,
    update_slb: ( $i * $i ) > $i ).

tff(decl_34,type,
    succ_cpq: ( $i * $i ) > $o ).

tff(decl_35,type,
    insert_cpq: ( $i * $i ) > $i ).

tff(decl_36,type,
    remove_cpq: ( $i * $i ) > $i ).

tff(decl_37,type,
    findmin_cpq_eff: $i > $i ).

tff(decl_38,type,
    removemin_cpq_eff: $i > $i ).

tff(decl_39,type,
    triple: ( $i * $i * $i ) > $i ).

tff(decl_40,type,
    check_cpq: $i > $o ).

tff(decl_41,type,
    contains_cpq: ( $i * $i ) > $o ).

tff(decl_42,type,
    bad: $i ).

tff(decl_43,type,
    ok: $i > $o ).

tff(decl_44,type,
    insert_pqp: ( $i * $i ) > $i ).

tff(decl_45,type,
    remove_pqp: ( $i * $i ) > $i ).

tff(decl_46,type,
    findmin_pqp_res: $i > $i ).

tff(decl_47,type,
    findmin_cpq_res: $i > $i ).

tff(decl_48,type,
    removemin_cpq_res: $i > $i ).

tff(decl_49,type,
    esk1_0: $i ).

tff(decl_50,type,
    esk2_0: $i ).

tff(decl_51,type,
    esk3_0: $i ).

fof(l9_co,conjecture,
    ! [X1,X2,X3] :
      ( ~ contains_cpq(triple(X1,X2,X3),findmin_cpq_res(triple(X1,X2,X3)))
     => ~ ok(findmin_cpq_eff(triple(X1,X2,X3))) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l9_co) ).

fof(ax51,axiom,
    ! [X1,X2,X3,X4] :
      ( X2 != create_slb
     => findmin_cpq_res(triple(X1,X2,X3)) = findmin_pqp_res(X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax51) ).

fof(l9_l10,lemma,
    ! [X1,X2,X3] :
      ( ok(findmin_cpq_eff(triple(X1,X2,X3)))
     => ( X2 != create_slb
        & contains_slb(X2,findmin_pqp_res(X1))
        & less_than(lookup_slb(X2,findmin_pqp_res(X1)),findmin_pqp_res(X1)) ) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l9_l10) ).

fof(ax39,axiom,
    ! [X1,X2,X3,X4] :
      ( contains_cpq(triple(X1,X2,X3),X4)
    <=> contains_slb(X2,X4) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax39) ).

fof(ax20,axiom,
    ! [X1] : ~ contains_slb(create_slb,X1),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+2.ax',ax20) ).

fof(c_0_5,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( ~ contains_cpq(triple(X1,X2,X3),findmin_cpq_res(triple(X1,X2,X3)))
       => ~ ok(findmin_cpq_eff(triple(X1,X2,X3))) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l9_co])]) ).

fof(c_0_6,negated_conjecture,
    ( ~ contains_cpq(triple(esk1_0,esk2_0,esk3_0),findmin_cpq_res(triple(esk1_0,esk2_0,esk3_0)))
    & ok(findmin_cpq_eff(triple(esk1_0,esk2_0,esk3_0))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_5])])]) ).

fof(c_0_7,plain,
    ! [X114,X115,X116] :
      ( X115 = create_slb
      | findmin_cpq_res(triple(X114,X115,X116)) = findmin_pqp_res(X114) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax51])])]) ).

fof(c_0_8,lemma,
    ! [X119,X120,X121] :
      ( ( X120 != create_slb
        | ~ ok(findmin_cpq_eff(triple(X119,X120,X121))) )
      & ( contains_slb(X120,findmin_pqp_res(X119))
        | ~ ok(findmin_cpq_eff(triple(X119,X120,X121))) )
      & ( less_than(lookup_slb(X120,findmin_pqp_res(X119)),findmin_pqp_res(X119))
        | ~ ok(findmin_cpq_eff(triple(X119,X120,X121))) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l9_l10])])]) ).

cnf(c_0_9,negated_conjecture,
    ~ contains_cpq(triple(esk1_0,esk2_0,esk3_0),findmin_cpq_res(triple(esk1_0,esk2_0,esk3_0))),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

cnf(c_0_10,plain,
    ( X1 = create_slb
    | findmin_cpq_res(triple(X2,X1,X3)) = findmin_pqp_res(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_7]) ).

fof(c_0_11,plain,
    ! [X76,X77,X78,X79] :
      ( ( ~ contains_cpq(triple(X76,X77,X78),X79)
        | contains_slb(X77,X79) )
      & ( ~ contains_slb(X77,X79)
        | contains_cpq(triple(X76,X77,X78),X79) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax39])]) ).

cnf(c_0_12,lemma,
    ( contains_slb(X1,findmin_pqp_res(X2))
    | ~ ok(findmin_cpq_eff(triple(X2,X1,X3))) ),
    inference(split_conjunct,[status(thm)],[c_0_8]) ).

cnf(c_0_13,negated_conjecture,
    ok(findmin_cpq_eff(triple(esk1_0,esk2_0,esk3_0))),
    inference(split_conjunct,[status(thm)],[c_0_6]) ).

fof(c_0_14,plain,
    ! [X1] : ~ contains_slb(create_slb,X1),
    inference(fof_simplification,[status(thm)],[ax20]) ).

cnf(c_0_15,negated_conjecture,
    ( esk2_0 = create_slb
    | ~ contains_cpq(triple(esk1_0,esk2_0,esk3_0),findmin_pqp_res(esk1_0)) ),
    inference(spm,[status(thm)],[c_0_9,c_0_10]) ).

cnf(c_0_16,plain,
    ( contains_cpq(triple(X3,X1,X4),X2)
    | ~ contains_slb(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_17,negated_conjecture,
    contains_slb(esk2_0,findmin_pqp_res(esk1_0)),
    inference(spm,[status(thm)],[c_0_12,c_0_13]) ).

fof(c_0_18,plain,
    ! [X18] : ~ contains_slb(create_slb,X18),
    inference(variable_rename,[status(thm)],[c_0_14]) ).

cnf(c_0_19,negated_conjecture,
    esk2_0 = create_slb,
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_15,c_0_16]),c_0_17])]) ).

cnf(c_0_20,plain,
    ~ contains_slb(create_slb,X1),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_21,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[c_0_17,c_0_19]),c_0_20]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem    : SWV373+1 : TPTP v8.1.2. Released v3.3.0.
% 0.00/0.13  % Command    : java -jar /export/starexec/sandbox2/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 06:49:43 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.19/0.58  start to proof: theBenchmark
% 0.19/0.60  % Version  : CSE_E---1.5
% 0.19/0.60  % Problem  : theBenchmark.p
% 0.19/0.60  % Proof found
% 0.19/0.60  % SZS status Theorem for theBenchmark.p
% 0.19/0.60  % SZS output start Proof
% See solution above
% 0.19/0.60  % Total time : 0.013000 s
% 0.19/0.60  % SZS output end Proof
% 0.19/0.60  % Total time : 0.017000 s
%------------------------------------------------------------------------------