TSTP Solution File: SWV378+1 by CSE_E---1.5

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%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV378+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 : n007.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 21:38:19 EDT 2023

% Result   : Theorem 0.21s 0.59s
% Output   : CNFRefutation 0.21s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   39
% Syntax   : Number of formulae    :   70 (  11 unt;  31 typ;   0 def)
%            Number of atoms       :   83 (  15 equ)
%            Maximal formula atoms :    7 (   2 avg)
%            Number of connectives :   82 (  38   ~;  26   |;   7   &)
%                                         (   3 <=>;   8  =>;   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  :   12 (   9 usr;   2 prp; 0-3 aty)
%            Number of functors    :   22 (  22 usr;   7 con; 0-3 aty)
%            Number of variables   :   91 (   9 sgn;  61   !;   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 ).

tff(decl_52,type,
    esk4_0: $i ).

fof(l14_co,conjecture,
    ! [X1,X2,X3,X4] :
      ( ~ ok(triple(X1,X2,X3))
     => ~ ok(remove_cpq(triple(X1,X2,X3),X4)) ),
    file('/export/starexec/sandbox2/benchmark/theBenchmark.p',l14_co) ).

fof(ax41,axiom,
    ! [X1,X2,X3] :
      ( ~ ok(triple(X1,X2,X3))
     => X3 = bad ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax41) ).

fof(ax40,axiom,
    ! [X1,X2] :
      ( ok(triple(X1,X2,bad))
    <=> ~ $true ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax40) ).

fof(ax43,axiom,
    ! [X1,X2,X3,X4] :
      ( ~ contains_slb(X2,X4)
     => remove_cpq(triple(X1,X2,X3),X4) = triple(X1,X2,bad) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax43) ).

fof(ax45,axiom,
    ! [X1,X2,X3,X4] :
      ( ( contains_slb(X2,X4)
        & strictly_less_than(X4,lookup_slb(X2,X4)) )
     => remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),bad) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax45) ).

fof(stricly_smaller_definition,axiom,
    ! [X1,X2] :
      ( strictly_less_than(X1,X2)
    <=> ( less_than(X1,X2)
        & ~ less_than(X2,X1) ) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',stricly_smaller_definition) ).

fof(ax44,axiom,
    ! [X1,X2,X3,X4] :
      ( ( contains_slb(X2,X4)
        & less_than(lookup_slb(X2,X4),X4) )
     => remove_cpq(triple(X1,X2,X3),X4) = triple(remove_pqp(X1,X4),remove_slb(X2,X4),X3) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+3.ax',ax44) ).

fof(totality,axiom,
    ! [X1,X2] :
      ( less_than(X1,X2)
      | less_than(X2,X1) ),
    file('/export/starexec/sandbox2/benchmark/Axioms/SWV007+0.ax',totality) ).

fof(c_0_8,negated_conjecture,
    ~ ! [X1,X2,X3,X4] :
        ( ~ ok(triple(X1,X2,X3))
       => ~ ok(remove_cpq(triple(X1,X2,X3),X4)) ),
    inference(fof_simplification,[status(thm)],[inference(assume_negation,[status(cth)],[l14_co])]) ).

fof(c_0_9,plain,
    ! [X1,X2,X3] :
      ( ~ ok(triple(X1,X2,X3))
     => X3 = bad ),
    inference(fof_simplification,[status(thm)],[ax41]) ).

fof(c_0_10,plain,
    ! [X1,X2] : ~ ok(triple(X1,X2,bad)),
    inference(fof_simplification,[status(thm)],[ax40]) ).

fof(c_0_11,plain,
    ! [X1,X2,X3,X4] :
      ( ~ contains_slb(X2,X4)
     => remove_cpq(triple(X1,X2,X3),X4) = triple(X1,X2,bad) ),
    inference(fof_simplification,[status(thm)],[ax43]) ).

fof(c_0_12,negated_conjecture,
    ( ~ ok(triple(esk1_0,esk2_0,esk3_0))
    & ok(remove_cpq(triple(esk1_0,esk2_0,esk3_0),esk4_0)) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_8])])]) ).

fof(c_0_13,plain,
    ! [X82,X83,X84] :
      ( ok(triple(X82,X83,X84))
      | X84 = bad ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).

fof(c_0_14,plain,
    ! [X80,X81] : ~ ok(triple(X80,X81,bad)),
    inference(variable_rename,[status(thm)],[c_0_10]) ).

fof(c_0_15,plain,
    ! [X97,X98,X99,X100] :
      ( ~ contains_slb(X98,X100)
      | ~ strictly_less_than(X100,lookup_slb(X98,X100))
      | remove_cpq(triple(X97,X98,X99),X100) = triple(remove_pqp(X97,X100),remove_slb(X98,X100),bad) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax45])]) ).

fof(c_0_16,plain,
    ! [X89,X90,X91,X92] :
      ( contains_slb(X90,X92)
      | remove_cpq(triple(X89,X90,X91),X92) = triple(X89,X90,bad) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_11])]) ).

fof(c_0_17,plain,
    ! [X1,X2] :
      ( strictly_less_than(X1,X2)
    <=> ( less_than(X1,X2)
        & ~ less_than(X2,X1) ) ),
    inference(fof_simplification,[status(thm)],[stricly_smaller_definition]) ).

fof(c_0_18,plain,
    ! [X93,X94,X95,X96] :
      ( ~ contains_slb(X94,X96)
      | ~ less_than(lookup_slb(X94,X96),X96)
      | remove_cpq(triple(X93,X94,X95),X96) = triple(remove_pqp(X93,X96),remove_slb(X94,X96),X95) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax44])]) ).

cnf(c_0_19,negated_conjecture,
    ~ ok(triple(esk1_0,esk2_0,esk3_0)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_20,plain,
    ( ok(triple(X1,X2,X3))
    | X3 = bad ),
    inference(split_conjunct,[status(thm)],[c_0_13]) ).

cnf(c_0_21,plain,
    ~ ok(triple(X1,X2,bad)),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,plain,
    ( remove_cpq(triple(X3,X1,X4),X2) = triple(remove_pqp(X3,X2),remove_slb(X1,X2),bad)
    | ~ contains_slb(X1,X2)
    | ~ strictly_less_than(X2,lookup_slb(X1,X2)) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_23,negated_conjecture,
    ok(remove_cpq(triple(esk1_0,esk2_0,esk3_0),esk4_0)),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

cnf(c_0_24,plain,
    ( contains_slb(X1,X2)
    | remove_cpq(triple(X3,X1,X4),X2) = triple(X3,X1,bad) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

fof(c_0_25,plain,
    ! [X12,X13] :
      ( ( less_than(X12,X13)
        | ~ strictly_less_than(X12,X13) )
      & ( ~ less_than(X13,X12)
        | ~ strictly_less_than(X12,X13) )
      & ( ~ less_than(X12,X13)
        | less_than(X13,X12)
        | strictly_less_than(X12,X13) ) ),
    inference(distribute,[status(thm)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_17])])]) ).

fof(c_0_26,plain,
    ! [X9,X10] :
      ( less_than(X9,X10)
      | less_than(X10,X9) ),
    inference(variable_rename,[status(thm)],[totality]) ).

cnf(c_0_27,plain,
    ( remove_cpq(triple(X3,X1,X4),X2) = triple(remove_pqp(X3,X2),remove_slb(X1,X2),X4)
    | ~ contains_slb(X1,X2)
    | ~ less_than(lookup_slb(X1,X2),X2) ),
    inference(split_conjunct,[status(thm)],[c_0_18]) ).

cnf(c_0_28,negated_conjecture,
    esk3_0 = bad,
    inference(spm,[status(thm)],[c_0_19,c_0_20]) ).

cnf(c_0_29,plain,
    ( ~ ok(remove_cpq(triple(X1,X2,X3),X4))
    | ~ contains_slb(X2,X4)
    | ~ strictly_less_than(X4,lookup_slb(X2,X4)) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_30,negated_conjecture,
    contains_slb(esk2_0,esk4_0),
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_23,c_0_24]),c_0_21]) ).

cnf(c_0_31,plain,
    ( less_than(X2,X1)
    | strictly_less_than(X1,X2)
    | ~ less_than(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_25]) ).

cnf(c_0_32,plain,
    ( less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(split_conjunct,[status(thm)],[c_0_26]) ).

cnf(c_0_33,plain,
    ( ~ ok(remove_cpq(triple(X1,X2,bad),X3))
    | ~ contains_slb(X2,X3)
    | ~ less_than(lookup_slb(X2,X3),X3) ),
    inference(spm,[status(thm)],[c_0_21,c_0_27]) ).

cnf(c_0_34,negated_conjecture,
    ok(remove_cpq(triple(esk1_0,esk2_0,bad),esk4_0)),
    inference(spm,[status(thm)],[c_0_23,c_0_28]) ).

cnf(c_0_35,negated_conjecture,
    ~ strictly_less_than(esk4_0,lookup_slb(esk2_0,esk4_0)),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_23]),c_0_30])]) ).

cnf(c_0_36,plain,
    ( strictly_less_than(X1,X2)
    | less_than(X2,X1) ),
    inference(csr,[status(thm)],[c_0_31,c_0_32]) ).

cnf(c_0_37,negated_conjecture,
    ~ less_than(lookup_slb(esk2_0,esk4_0),esk4_0),
    inference(cn,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_33,c_0_34]),c_0_30])]) ).

cnf(c_0_38,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(spm,[status(thm)],[c_0_35,c_0_36]),c_0_37]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.06/0.12  % Problem    : SWV378+1 : TPTP v8.1.2. Released v3.3.0.
% 0.06/0.13  % Command    : java -jar /export/starexec/sandbox2/solver/bin/mcs_scs.jar %d %s
% 0.13/0.34  % Computer : n007.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 08:11:58 EDT 2023
% 0.13/0.34  % CPUTime  : 
% 0.21/0.56  start to proof: theBenchmark
% 0.21/0.59  % Version  : CSE_E---1.5
% 0.21/0.59  % Problem  : theBenchmark.p
% 0.21/0.59  % Proof found
% 0.21/0.59  % SZS status Theorem for theBenchmark.p
% 0.21/0.59  % SZS output start Proof
% See solution above
% 0.21/0.60  % Total time : 0.018000 s
% 0.21/0.60  % SZS output end Proof
% 0.21/0.60  % Total time : 0.022000 s
%------------------------------------------------------------------------------