TSTP Solution File: SWV372+1 by CSE_E---1.5

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : CSE_E---1.5
% Problem  : SWV372+1 : TPTP v8.1.2. Released v3.3.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s

% Computer : n006.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 21:38:17 EDT 2023

% Result   : Theorem 0.18s 0.58s
% Output   : CNFRefutation 0.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :    7
%            Number of leaves      :   60
% Syntax   : Number of formulae    :   88 (  11 unt;  52 typ;   0 def)
%            Number of atoms       :   70 (  21 equ)
%            Maximal formula atoms :    4 (   1 avg)
%            Number of connectives :   63 (  29   ~;  19   |;   5   &)
%                                         (   3 <=>;   7  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    8 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   76 (  45   >;  31   *;   0   +;   0  <<)
%            Number of predicates  :   22 (  19 usr;   2 prp; 0-3 aty)
%            Number of functors    :   33 (  33 usr;   7 con; 0-3 aty)
%            Number of variables   :   89 (  15 sgn;  59   !;   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_pq: $i ).

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

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

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

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

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

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

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

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

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

tff(decl_35,type,
    create_slb: $i ).

tff(decl_36,type,
    isnonempty_slb: $i > $o ).

tff(decl_37,type,
    pair: ( $i * $i ) > $i ).

tff(decl_38,type,
    insert_slb: ( $i * $i ) > $i ).

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

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

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

tff(decl_42,type,
    lookup_slb: ( $i * $i ) > $i ).

tff(decl_43,type,
    update_slb: ( $i * $i ) > $i ).

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

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

tff(decl_46,type,
    remove_cpq: ( $i * $i ) > $i ).

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

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

tff(decl_49,type,
    triple: ( $i * $i * $i ) > $i ).

tff(decl_50,type,
    check_cpq: $i > $o ).

tff(decl_51,type,
    contains_cpq: ( $i * $i ) > $o ).

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

tff(decl_53,type,
    ok: $i > $o ).

tff(decl_54,type,
    insert_pqp: ( $i * $i ) > $i ).

tff(decl_55,type,
    remove_pqp: ( $i * $i ) > $i ).

tff(decl_56,type,
    findmin_pqp_res: $i > $i ).

tff(decl_57,type,
    findmin_cpq_res: $i > $i ).

tff(decl_58,type,
    removemin_cpq_res: $i > $i ).

tff(decl_59,type,
    i: $i > $i ).

tff(decl_60,type,
    pi_sharp_remove: ( $i * $i ) > $o ).

tff(decl_61,type,
    pi_remove: ( $i * $i ) > $o ).

tff(decl_62,type,
    pi_sharp_find_min: ( $i * $i ) > $o ).

tff(decl_63,type,
    pi_find_min: $i > $o ).

tff(decl_64,type,
    pi_sharp_removemin: ( $i * $i ) > $o ).

tff(decl_65,type,
    pi_removemin: $i > $o ).

tff(decl_66,type,
    phi: $i > $o ).

tff(decl_67,type,
    esk1_2: ( $i * $i ) > $i ).

tff(decl_68,type,
    esk2_1: $i > $i ).

tff(decl_69,type,
    esk3_1: $i > $i ).

tff(decl_70,type,
    esk4_1: $i > $i ).

tff(decl_71,type,
    esk5_0: $i ).

tff(decl_72,type,
    esk6_0: $i ).

tff(decl_73,type,
    esk7_0: $i ).

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

fof(l8_lX,lemma,
    ! [X1,X2,X3] :
      ( ~ ok(triple(X1,X2,X3))
     => ~ phi(triple(X1,X2,X3)) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l8_lX) ).

fof(l8_co,conjecture,
    ! [X1,X2,X3] :
      ( phi(findmin_cpq_eff(triple(X1,X2,X3)))
     => contains_pq(i(triple(X1,X2,X3)),findmin_cpq_res(triple(X1,X2,X3))) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l8_co) ).

fof(ax47,axiom,
    ! [X1,X2,X3,X4] :
      ( ( X2 != create_slb
        & ~ contains_slb(X2,findmin_pqp_res(X1)) )
     => findmin_cpq_eff(triple(X1,X2,X3)) = triple(X1,update_slb(X2,findmin_pqp_res(X1)),bad) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax47) ).

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

fof(l8_li56,lemma,
    ! [X1,X2,X3,X4] :
      ( contains_cpq(triple(X1,X2,X3),X4)
    <=> contains_pq(i(triple(X1,X2,X3)),X4) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',l8_li56) ).

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

fof(ax46,axiom,
    ! [X1,X2] : findmin_cpq_eff(triple(X1,create_slb,X2)) = triple(X1,create_slb,bad),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV007+3.ax',ax46) ).

fof(c_0_8,plain,
    ! [X1,X2] : ~ ok(triple(X1,X2,bad)),
    inference(fof_simplification,[status(thm)],[ax40]) ).

fof(c_0_9,lemma,
    ! [X1,X2,X3] :
      ( ~ ok(triple(X1,X2,X3))
     => ~ phi(triple(X1,X2,X3)) ),
    inference(fof_simplification,[status(thm)],[l8_lX]) ).

fof(c_0_10,negated_conjecture,
    ~ ! [X1,X2,X3] :
        ( phi(findmin_cpq_eff(triple(X1,X2,X3)))
       => contains_pq(i(triple(X1,X2,X3)),findmin_cpq_res(triple(X1,X2,X3))) ),
    inference(assume_negation,[status(cth)],[l8_co]) ).

fof(c_0_11,plain,
    ! [X108,X109] : ~ ok(triple(X108,X109,bad)),
    inference(variable_rename,[status(thm)],[c_0_8]) ).

fof(c_0_12,lemma,
    ! [X181,X182,X183] :
      ( ok(triple(X181,X182,X183))
      | ~ phi(triple(X181,X182,X183)) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_9])]) ).

fof(c_0_13,plain,
    ! [X1,X2,X3,X4] :
      ( ( X2 != create_slb
        & ~ contains_slb(X2,findmin_pqp_res(X1)) )
     => findmin_cpq_eff(triple(X1,X2,X3)) = triple(X1,update_slb(X2,findmin_pqp_res(X1)),bad) ),
    inference(fof_simplification,[status(thm)],[ax47]) ).

fof(c_0_14,negated_conjecture,
    ( phi(findmin_cpq_eff(triple(esk5_0,esk6_0,esk7_0)))
    & ~ contains_pq(i(triple(esk5_0,esk6_0,esk7_0)),findmin_cpq_res(triple(esk5_0,esk6_0,esk7_0))) ),
    inference(skolemize,[status(esa)],[inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[c_0_10])])]) ).

fof(c_0_15,plain,
    ! [X142,X143,X144] :
      ( X143 = create_slb
      | findmin_cpq_res(triple(X142,X143,X144)) = findmin_pqp_res(X142) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[ax51])])]) ).

fof(c_0_16,lemma,
    ! [X174,X175,X176,X177] :
      ( ( ~ contains_cpq(triple(X174,X175,X176),X177)
        | contains_pq(i(triple(X174,X175,X176)),X177) )
      & ( ~ contains_pq(i(triple(X174,X175,X176)),X177)
        | contains_cpq(triple(X174,X175,X176),X177) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[l8_li56])]) ).

fof(c_0_17,plain,
    ! [X104,X105,X106,X107] :
      ( ( ~ contains_cpq(triple(X104,X105,X106),X107)
        | contains_slb(X105,X107) )
      & ( ~ contains_slb(X105,X107)
        | contains_cpq(triple(X104,X105,X106),X107) ) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[ax39])]) ).

cnf(c_0_18,plain,
    ~ ok(triple(X1,X2,bad)),
    inference(split_conjunct,[status(thm)],[c_0_11]) ).

cnf(c_0_19,lemma,
    ( ok(triple(X1,X2,X3))
    | ~ phi(triple(X1,X2,X3)) ),
    inference(split_conjunct,[status(thm)],[c_0_12]) ).

fof(c_0_20,plain,
    ! [X131,X132,X133] :
      ( X132 = create_slb
      | contains_slb(X132,findmin_pqp_res(X131))
      | findmin_cpq_eff(triple(X131,X132,X133)) = triple(X131,update_slb(X132,findmin_pqp_res(X131)),bad) ),
    inference(variable_rename,[status(thm)],[inference(fof_nnf,[status(thm)],[inference(fof_simplification,[status(thm)],[c_0_13])])]) ).

cnf(c_0_21,negated_conjecture,
    ~ contains_pq(i(triple(esk5_0,esk6_0,esk7_0)),findmin_cpq_res(triple(esk5_0,esk6_0,esk7_0))),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_22,plain,
    ( X1 = create_slb
    | findmin_cpq_res(triple(X2,X1,X3)) = findmin_pqp_res(X2) ),
    inference(split_conjunct,[status(thm)],[c_0_15]) ).

cnf(c_0_23,lemma,
    ( contains_pq(i(triple(X1,X2,X3)),X4)
    | ~ contains_cpq(triple(X1,X2,X3),X4) ),
    inference(split_conjunct,[status(thm)],[c_0_16]) ).

cnf(c_0_24,plain,
    ( contains_cpq(triple(X3,X1,X4),X2)
    | ~ contains_slb(X1,X2) ),
    inference(split_conjunct,[status(thm)],[c_0_17]) ).

cnf(c_0_25,lemma,
    ~ phi(triple(X1,X2,bad)),
    inference(spm,[status(thm)],[c_0_18,c_0_19]) ).

cnf(c_0_26,plain,
    ( X1 = create_slb
    | contains_slb(X1,findmin_pqp_res(X2))
    | findmin_cpq_eff(triple(X2,X1,X3)) = triple(X2,update_slb(X1,findmin_pqp_res(X2)),bad) ),
    inference(split_conjunct,[status(thm)],[c_0_20]) ).

cnf(c_0_27,negated_conjecture,
    ( esk6_0 = create_slb
    | ~ contains_pq(i(triple(esk5_0,esk6_0,esk7_0)),findmin_pqp_res(esk5_0)) ),
    inference(spm,[status(thm)],[c_0_21,c_0_22]) ).

cnf(c_0_28,lemma,
    ( contains_pq(i(triple(X1,X2,X3)),X4)
    | ~ contains_slb(X2,X4) ),
    inference(spm,[status(thm)],[c_0_23,c_0_24]) ).

cnf(c_0_29,lemma,
    ( X1 = create_slb
    | contains_slb(X1,findmin_pqp_res(X2))
    | ~ phi(findmin_cpq_eff(triple(X2,X1,X3))) ),
    inference(spm,[status(thm)],[c_0_25,c_0_26]) ).

cnf(c_0_30,negated_conjecture,
    phi(findmin_cpq_eff(triple(esk5_0,esk6_0,esk7_0))),
    inference(split_conjunct,[status(thm)],[c_0_14]) ).

cnf(c_0_31,negated_conjecture,
    ( esk6_0 = create_slb
    | ~ contains_slb(esk6_0,findmin_pqp_res(esk5_0)) ),
    inference(spm,[status(thm)],[c_0_27,c_0_28]) ).

fof(c_0_32,plain,
    ! [X129,X130] : findmin_cpq_eff(triple(X129,create_slb,X130)) = triple(X129,create_slb,bad),
    inference(variable_rename,[status(thm)],[ax46]) ).

cnf(c_0_33,negated_conjecture,
    esk6_0 = create_slb,
    inference(csr,[status(thm)],[inference(spm,[status(thm)],[c_0_29,c_0_30]),c_0_31]) ).

cnf(c_0_34,plain,
    findmin_cpq_eff(triple(X1,create_slb,X2)) = triple(X1,create_slb,bad),
    inference(split_conjunct,[status(thm)],[c_0_32]) ).

cnf(c_0_35,negated_conjecture,
    $false,
    inference(sr,[status(thm)],[inference(rw,[status(thm)],[inference(spm,[status(thm)],[c_0_30,c_0_33]),c_0_34]),c_0_25]),
    [proof] ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12  % Problem    : SWV372+1 : TPTP v8.1.2. Released v3.3.0.
% 0.11/0.13  % Command    : java -jar /export/starexec/sandbox/solver/bin/mcs_scs.jar %d %s
% 0.12/0.34  % Computer : n006.cluster.edu
% 0.12/0.34  % Model    : x86_64 x86_64
% 0.12/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.12/0.34  % Memory   : 8042.1875MB
% 0.12/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.12/0.34  % CPULimit   : 300
% 0.12/0.34  % WCLimit    : 300
% 0.12/0.34  % DateTime   : Tue Aug 29 02:50:36 EDT 2023
% 0.12/0.34  % CPUTime  : 
% 0.18/0.55  start to proof: theBenchmark
% 0.18/0.58  % Version  : CSE_E---1.5
% 0.18/0.58  % Problem  : theBenchmark.p
% 0.18/0.58  % Proof found
% 0.18/0.58  % SZS status Theorem for theBenchmark.p
% 0.18/0.58  % SZS output start Proof
% See solution above
% 0.18/0.58  % Total time : 0.020000 s
% 0.18/0.58  % SZS output end Proof
% 0.18/0.58  % Total time : 0.023000 s
%------------------------------------------------------------------------------