TSTP Solution File: COL093-2 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : COL093-2 : TPTP v8.1.2. Released v2.7.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s

% Computer : n021.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 : Tue Aug 22 10:35:04 EDT 2023

% Result   : Unsatisfiable 57.60s 41.20s
% Output   : CNFRefutation 57.60s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   10
%            Number of leaves      :  106
% Syntax   : Number of formulae    :  168 (  33 unt;  92 typ;   0 def)
%            Number of atoms       :  134 (  32 equ)
%            Maximal formula atoms :    5 (   1 avg)
%            Number of connectives :  110 (  52   ~;  58   |;   0   &)
%                                         (   0 <=>;   0  =>;   0  <=;   0 <~>)
%            Maximal formula depth :    9 (   4 avg)
%            Maximal term depth    :    4 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  188 (  83   >; 105   *;   0   +;   0  <<)
%            Number of predicates  :   18 (  16 usr;   1 prp; 0-8 aty)
%            Number of functors    :   76 (  76 usr;   9 con; 0-4 aty)
%            Number of variables   :   87 (;  87   !;   0   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ rmultE_c2 > rmultE_c1 > ap_parcontractE_c4 > ap_parcontractE_c3 > ap_parcontractE_c2 > ap_parcontractE_c1 > ap_contractE_c4 > ap_contractE_c3 > ap_contractE_c2 > ap_contractE_c1 > subset > member > lt > le > ord > card > rmult > radd > vimageE_sk1 > sumE_sk2 > sumE_sk1 > subsetD_sk1 > qsumE_sk2 > qsumE_sk1 > imageE_sk1 > cons_subsetI_sk1 > cons_subsetE_sk1 > compE_sk3 > compE_sk2 > compE_sk1 > ap_parcontractE_sk2s > ap_parcontractE_sk2q > ap_parcontractE_sk1q > ap_parcontractE_sk1p > ap_contractE_sk3q > ap_contractE_sk2q > ap_contractE_sk1q > ap_contractE_sk1p > vimage > unionE_sk1 > un > subsetI_sk1 > rangeE_sk1 > qsum > qconverseE_sk2 > qconverseE_sk1 > qPair > powI_sk1 > pair > interI_sk1 > int > image > idE_sk1 > fieldE_sk2 > fieldE_sk1 > domainE_sk1 > disjsum > diff > converseE_sk2 > converseE_sk1 > cons > comp > comb_app > #nlpp > union > succ > rtrancl > range > qconverse > qInr > qInl > pow > order_Union_sk1 > order_Inter_sk1 > memrel > inter > inr > inl > id > fin > field > domain > converse > card_Union_sk1 > r > parcontract > p > nat > eptset > contract > combS > combK > comb

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(fin,type,
    fin: $i > $i ).

tff(ap_parcontractE_sk1p,type,
    ap_parcontractE_sk1p: ( $i * $i * $i ) > $i ).

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

tff(order_Union_sk1,type,
    order_Union_sk1: $i > $i ).

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

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

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

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

tff(disjsum,type,
    disjsum: ( $i * $i ) > $i ).

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

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

tff(un,type,
    un: ( $i * $i ) > $i ).

tff(compE_sk2,type,
    compE_sk2: ( $i * $i * $i ) > $i ).

tff(int,type,
    int: ( $i * $i ) > $i ).

tff(ap_parcontractE_sk2q,type,
    ap_parcontractE_sk2q: ( $i * $i * $i ) > $i ).

tff(domainE_sk1,type,
    domainE_sk1: ( $i * $i ) > $i ).

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

tff(r,type,
    r: $i ).

tff(powI_sk1,type,
    powI_sk1: ( $i * $i ) > $i ).

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

tff(vimage,type,
    vimage: ( $i * $i ) > $i ).

tff(imageE_sk1,type,
    imageE_sk1: ( $i * $i * $i ) > $i ).

tff(comp,type,
    comp: ( $i * $i ) > $i ).

tff(cons_subsetI_sk1,type,
    cons_subsetI_sk1: ( $i * $i * $i ) > $i ).

tff(card,type,
    card: $i > $o ).

tff(sumE_sk2,type,
    sumE_sk2: ( $i * $i * $i ) > $i ).

tff(comb_app,type,
    comb_app: ( $i * $i ) > $i ).

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

tff(diff,type,
    diff: ( $i * $i ) > $i ).

tff(ord,type,
    ord: $i > $o ).

tff(qconverseE_sk2,type,
    qconverseE_sk2: ( $i * $i ) > $i ).

tff(ap_contractE_sk1q,type,
    ap_contractE_sk1q: ( $i * $i * $i ) > $i ).

tff(fieldE_sk1,type,
    fieldE_sk1: ( $i * $i ) > $i ).

tff(ap_contractE_sk2q,type,
    ap_contractE_sk2q: ( $i * $i * $i ) > $i ).

tff(qsum,type,
    qsum: ( $i * $i ) > $i ).

tff(nat,type,
    nat: $i ).

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

tff(rmultE_c1,type,
    rmultE_c1: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).

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

tff(qPair,type,
    qPair: ( $i * $i ) > $i ).

tff(ap_contractE_sk3q,type,
    ap_contractE_sk3q: ( $i * $i * $i ) > $i ).

tff(fieldE_sk2,type,
    fieldE_sk2: ( $i * $i ) > $i ).

tff(combS,type,
    combS: $i ).

tff(card_Union_sk1,type,
    card_Union_sk1: $i > $i ).

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

tff(converseE_sk1,type,
    converseE_sk1: ( $i * $i ) > $i ).

tff(parcontract,type,
    parcontract: $i ).

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

tff(compE_sk3,type,
    compE_sk3: ( $i * $i * $i ) > $i ).

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

tff(ap_contractE_c3,type,
    ap_contractE_c3: ( $i * $i * $i ) > $o ).

tff(ap_contractE_c4,type,
    ap_contractE_c4: ( $i * $i * $i ) > $o ).

tff(ap_parcontractE_c3,type,
    ap_parcontractE_c3: ( $i * $i * $i ) > $o ).

tff(ap_parcontractE_c2,type,
    ap_parcontractE_c2: ( $i * $i * $i ) > $o ).

tff(subsetD_sk1,type,
    subsetD_sk1: ( $i * $i * $i ) > $i ).

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

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

tff(ap_parcontractE_c1,type,
    ap_parcontractE_c1: ( $i * $i * $i ) > $o ).

tff(vimageE_sk1,type,
    vimageE_sk1: ( $i * $i * $i ) > $i ).

tff(contract,type,
    contract: $i ).

tff(ap_contractE_c2,type,
    ap_contractE_c2: ( $i * $i * $i ) > $o ).

tff(idE_sk1,type,
    idE_sk1: ( $i * $i ) > $i ).

tff(compE_sk1,type,
    compE_sk1: ( $i * $i * $i ) > $i ).

tff(image,type,
    image: ( $i * $i ) > $i ).

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

tff(cons_subsetE_sk1,type,
    cons_subsetE_sk1: ( $i * $i * $i ) > $i ).

tff(ap_parcontractE_c4,type,
    ap_parcontractE_c4: ( $i * $i * $i ) > $o ).

tff(cons,type,
    cons: ( $i * $i ) > $i ).

tff(rmult,type,
    rmult: ( $i * $i * $i * $i ) > $i ).

tff(qsumE_sk1,type,
    qsumE_sk1: ( $i * $i * $i ) > $i ).

tff(radd,type,
    radd: ( $i * $i * $i * $i ) > $i ).

tff(rangeE_sk1,type,
    rangeE_sk1: ( $i * $i ) > $i ).

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

tff(converseE_sk2,type,
    converseE_sk2: ( $i * $i ) > $i ).

tff(eptset,type,
    eptset: $i ).

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

tff(unionE_sk1,type,
    unionE_sk1: ( $i * $i ) > $i ).

tff(subsetI_sk1,type,
    subsetI_sk1: ( $i * $i ) > $i ).

tff(combK,type,
    combK: $i ).

tff(qconverseE_sk1,type,
    qconverseE_sk1: ( $i * $i ) > $i ).

tff(interI_sk1,type,
    interI_sk1: ( $i * $i ) > $i ).

tff(order_Inter_sk1,type,
    order_Inter_sk1: $i > $i ).

tff(ap_parcontractE_sk1q,type,
    ap_parcontractE_sk1q: ( $i * $i * $i ) > $i ).

tff(p,type,
    p: $i ).

tff(ap_parcontractE_sk2s,type,
    ap_parcontractE_sk2s: ( $i * $i * $i ) > $i ).

tff(qsumE_sk2,type,
    qsumE_sk2: ( $i * $i * $i ) > $i ).

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

tff(ap_contractE_sk1p,type,
    ap_contractE_sk1p: ( $i * $i * $i ) > $i ).

tff(comb,type,
    comb: $i ).

tff(rmultE_c2,type,
    rmultE_c2: ( $i * $i * $i * $i * $i * $i * $i * $i ) > $o ).

tff(sumE_sk1,type,
    sumE_sk1: ( $i * $i * $i ) > $i ).

tff(ap_contractE_c1,type,
    ap_contractE_c1: ( $i * $i * $i ) > $o ).

tff(f_899,axiom,
    ! [P,Q] : ( combS != comb_app(P,Q) ),
    file(unknown,unknown) ).

tff(f_1063,axiom,
    ! [P] :
      ( ~ member(P,comb)
      | member(pair(P,P),parcontract) ),
    file(unknown,unknown) ).

tff(f_1196,axiom,
    ! [PP] :
      ( ( r != comb_app(combS,PP) )
      | ~ member(pair(p,PP),parcontract) ),
    file(unknown,unknown) ).

tff(f_1174,axiom,
    ! [P,Q,R] :
      ( ~ ap_parcontractE_c3(P,Q,R)
      | ( P = comb_app(comb_app(combS,ap_parcontractE_sk1p(P,Q,R)),ap_parcontractE_sk1q(P,Q,R)) ) ),
    file(unknown,unknown) ).

tff(f_1190,axiom,
    member(pair(comb_app(combS,p),r),parcontract),
    file(unknown,unknown) ).

tff(f_1124,axiom,
    ! [P,Q,R] :
      ( ~ member(pair(comb_app(P,Q),R),parcontract)
      | ap_parcontractE_c1(P,Q,R)
      | ap_parcontractE_c2(P,Q,R)
      | ap_parcontractE_c3(P,Q,R)
      | ap_parcontractE_c4(P,Q,R) ),
    file(unknown,unknown) ).

tff(f_1134,axiom,
    ! [P,Q,R] :
      ( ~ ap_parcontractE_c1(P,Q,R)
      | ( R = comb_app(P,Q) ) ),
    file(unknown,unknown) ).

tff(f_928,axiom,
    ! [P,Q] :
      ( ~ member(comb_app(P,Q),comb)
      | member(Q,comb) ),
    file(unknown,unknown) ).

tff(f_1129,axiom,
    ! [P,Q,R] :
      ( ~ ap_parcontractE_c1(P,Q,R)
      | member(comb_app(P,Q),comb) ),
    file(unknown,unknown) ).

tff(f_1179,axiom,
    ! [P,Q,R] :
      ( ~ ap_parcontractE_c4(P,Q,R)
      | member(pair(P,ap_parcontractE_sk2q(P,Q,R)),parcontract) ),
    file(unknown,unknown) ).

tff(f_1112,axiom,
    ! [R] :
      ( ~ member(pair(combS,R),parcontract)
      | ( R = combS ) ),
    file(unknown,unknown) ).

tff(f_1189,axiom,
    ! [P,Q,R] :
      ( ~ ap_parcontractE_c4(P,Q,R)
      | ( R = comb_app(ap_parcontractE_sk2q(P,Q,R),ap_parcontractE_sk2s(P,Q,R)) ) ),
    file(unknown,unknown) ).

tff(f_1184,axiom,
    ! [P,Q,R] :
      ( ~ ap_parcontractE_c4(P,Q,R)
      | member(pair(Q,ap_parcontractE_sk2s(P,Q,R)),parcontract) ),
    file(unknown,unknown) ).

tff(f_1149,axiom,
    ! [P,Q,R] :
      ( ~ ap_parcontractE_c2(P,Q,R)
      | ( P = comb_app(combK,R) ) ),
    file(unknown,unknown) ).

tff(c_293,plain,
    ! [P_450,Q_451] : ( comb_app(P_450,Q_451) != combS ),
    inference(cnfTransformation,[status(thm)],[f_899]) ).

tff(c_352,plain,
    ! [P_523] :
      ( member(pair(P_523,P_523),parcontract)
      | ~ member(P_523,comb) ),
    inference(cnfTransformation,[status(thm)],[f_1063]) ).

tff(c_978,plain,
    ! [PP_760] :
      ( ~ member(pair(p,PP_760),parcontract)
      | ( comb_app(combS,PP_760) != r ) ),
    inference(cnfTransformation,[status(thm)],[f_1196]) ).

tff(c_983,plain,
    ( ( comb_app(combS,p) != r )
    | ~ member(p,comb) ),
    inference(resolution,[status(thm)],[c_352,c_978]) ).

tff(c_991,plain,
    ~ member(p,comb),
    inference(splitLeft,[status(thm)],[c_983]) ).

tff(c_10828,plain,
    ! [P_1324,Q_1325,R_1326] :
      ( ( comb_app(comb_app(combS,ap_parcontractE_sk1p(P_1324,Q_1325,R_1326)),ap_parcontractE_sk1q(P_1324,Q_1325,R_1326)) = P_1324 )
      | ~ ap_parcontractE_c3(P_1324,Q_1325,R_1326) ),
    inference(cnfTransformation,[status(thm)],[f_1174]) ).

tff(c_10864,plain,
    ! [Q_1325,R_1326] : ~ ap_parcontractE_c3(combS,Q_1325,R_1326),
    inference(superposition,[status(thm),theory(equality)],[c_10828,c_293]) ).

tff(c_396,plain,
    member(pair(comb_app(combS,p),r),parcontract),
    inference(cnfTransformation,[status(thm)],[f_1190]) ).

tff(c_14911,plain,
    ! [P_1464,Q_1465,R_1466] :
      ( ap_parcontractE_c4(P_1464,Q_1465,R_1466)
      | ap_parcontractE_c3(P_1464,Q_1465,R_1466)
      | ap_parcontractE_c2(P_1464,Q_1465,R_1466)
      | ap_parcontractE_c1(P_1464,Q_1465,R_1466)
      | ~ member(pair(comb_app(P_1464,Q_1465),R_1466),parcontract) ),
    inference(cnfTransformation,[status(thm)],[f_1124]) ).

tff(c_14964,plain,
    ( ap_parcontractE_c4(combS,p,r)
    | ap_parcontractE_c3(combS,p,r)
    | ap_parcontractE_c2(combS,p,r)
    | ap_parcontractE_c1(combS,p,r) ),
    inference(resolution,[status(thm)],[c_396,c_14911]) ).

tff(c_14975,plain,
    ( ap_parcontractE_c4(combS,p,r)
    | ap_parcontractE_c2(combS,p,r)
    | ap_parcontractE_c1(combS,p,r) ),
    inference(negUnitSimplification,[status(thm)],[c_10864,c_14964]) ).

tff(c_99286,plain,
    ap_parcontractE_c1(combS,p,r),
    inference(splitLeft,[status(thm)],[c_14975]) ).

tff(c_372,plain,
    ! [P_543,Q_544,R_545] :
      ( ( comb_app(P_543,Q_544) = R_545 )
      | ~ ap_parcontractE_c1(P_543,Q_544,R_545) ),
    inference(cnfTransformation,[status(thm)],[f_1134]) ).

tff(c_99293,plain,
    comb_app(combS,p) = r,
    inference(resolution,[status(thm)],[c_99286,c_372]) ).

tff(c_304,plain,
    ! [Q_467,P_466] :
      ( member(Q_467,comb)
      | ~ member(comb_app(P_466,Q_467),comb) ),
    inference(cnfTransformation,[status(thm)],[f_928]) ).

tff(c_99383,plain,
    ( member(p,comb)
    | ~ member(r,comb) ),
    inference(superposition,[status(thm),theory(equality)],[c_99293,c_304]) ).

tff(c_99409,plain,
    ~ member(r,comb),
    inference(negUnitSimplification,[status(thm)],[c_991,c_99383]) ).

tff(c_370,plain,
    ! [P_540,Q_541,R_542] :
      ( member(comb_app(P_540,Q_541),comb)
      | ~ ap_parcontractE_c1(P_540,Q_541,R_542) ),
    inference(cnfTransformation,[status(thm)],[f_1129]) ).

tff(c_99292,plain,
    member(comb_app(combS,p),comb),
    inference(resolution,[status(thm)],[c_99286,c_370]) ).

tff(c_99499,plain,
    member(r,comb),
    inference(demodulation,[status(thm),theory(equality)],[c_99293,c_99292]) ).

tff(c_99500,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_99409,c_99499]) ).

tff(c_99501,plain,
    ( ap_parcontractE_c2(combS,p,r)
    | ap_parcontractE_c4(combS,p,r) ),
    inference(splitRight,[status(thm)],[c_14975]) ).

tff(c_99503,plain,
    ap_parcontractE_c4(combS,p,r),
    inference(splitLeft,[status(thm)],[c_99501]) ).

tff(c_6728,plain,
    ! [P_1083,Q_1084,R_1085] :
      ( member(pair(P_1083,ap_parcontractE_sk2q(P_1083,Q_1084,R_1085)),parcontract)
      | ~ ap_parcontractE_c4(P_1083,Q_1084,R_1085) ),
    inference(cnfTransformation,[status(thm)],[f_1179]) ).

tff(c_366,plain,
    ! [R_536] :
      ( ( combS = R_536 )
      | ~ member(pair(combS,R_536),parcontract) ),
    inference(cnfTransformation,[status(thm)],[f_1112]) ).

tff(c_6767,plain,
    ! [Q_1084,R_1085] :
      ( ( ap_parcontractE_sk2q(combS,Q_1084,R_1085) = combS )
      | ~ ap_parcontractE_c4(combS,Q_1084,R_1085) ),
    inference(resolution,[status(thm)],[c_6728,c_366]) ).

tff(c_99534,plain,
    ap_parcontractE_sk2q(combS,p,r) = combS,
    inference(resolution,[status(thm)],[c_99503,c_6767]) ).

tff(c_394,plain,
    ! [P_576,Q_577,R_578] :
      ( ( comb_app(ap_parcontractE_sk2q(P_576,Q_577,R_578),ap_parcontractE_sk2s(P_576,Q_577,R_578)) = R_578 )
      | ~ ap_parcontractE_c4(P_576,Q_577,R_578) ),
    inference(cnfTransformation,[status(thm)],[f_1189]) ).

tff(c_99628,plain,
    ( ( comb_app(combS,ap_parcontractE_sk2s(combS,p,r)) = r )
    | ~ ap_parcontractE_c4(combS,p,r) ),
    inference(superposition,[status(thm),theory(equality)],[c_99534,c_394]) ).

tff(c_99637,plain,
    comb_app(combS,ap_parcontractE_sk2s(combS,p,r)) = r,
    inference(demodulation,[status(thm),theory(equality)],[c_99503,c_99628]) ).

tff(c_6971,plain,
    ! [Q_1101,P_1102,R_1103] :
      ( member(pair(Q_1101,ap_parcontractE_sk2s(P_1102,Q_1101,R_1103)),parcontract)
      | ~ ap_parcontractE_c4(P_1102,Q_1101,R_1103) ),
    inference(cnfTransformation,[status(thm)],[f_1184]) ).

tff(c_398,plain,
    ! [PP_579] :
      ( ~ member(pair(p,PP_579),parcontract)
      | ( comb_app(combS,PP_579) != r ) ),
    inference(cnfTransformation,[status(thm)],[f_1196]) ).

tff(c_7007,plain,
    ! [P_1102,R_1103] :
      ( ( comb_app(combS,ap_parcontractE_sk2s(P_1102,p,R_1103)) != r )
      | ~ ap_parcontractE_c4(P_1102,p,R_1103) ),
    inference(resolution,[status(thm)],[c_6971,c_398]) ).

tff(c_100471,plain,
    ~ ap_parcontractE_c4(combS,p,r),
    inference(superposition,[status(thm),theory(equality)],[c_99637,c_7007]) ).

tff(c_100542,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_99503,c_100471]) ).

tff(c_100543,plain,
    ap_parcontractE_c2(combS,p,r),
    inference(splitRight,[status(thm)],[c_99501]) ).

tff(c_378,plain,
    ! [R_554,P_552,Q_553] :
      ( ( comb_app(combK,R_554) = P_552 )
      | ~ ap_parcontractE_c2(P_552,Q_553,R_554) ),
    inference(cnfTransformation,[status(thm)],[f_1149]) ).

tff(c_100547,plain,
    comb_app(combK,r) = combS,
    inference(resolution,[status(thm)],[c_100543,c_378]) ).

tff(c_100557,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_293,c_100547]) ).

tff(c_100558,plain,
    comb_app(combS,p) != r,
    inference(splitRight,[status(thm)],[c_983]) ).

tff(c_109817,plain,
    ! [P_3421,Q_3422,R_3423] :
      ( ( comb_app(comb_app(combS,ap_parcontractE_sk1p(P_3421,Q_3422,R_3423)),ap_parcontractE_sk1q(P_3421,Q_3422,R_3423)) = P_3421 )
      | ~ ap_parcontractE_c3(P_3421,Q_3422,R_3423) ),
    inference(cnfTransformation,[status(thm)],[f_1174]) ).

tff(c_109853,plain,
    ! [Q_3422,R_3423] : ~ ap_parcontractE_c3(combS,Q_3422,R_3423),
    inference(superposition,[status(thm),theory(equality)],[c_109817,c_293]) ).

tff(c_114219,plain,
    ! [P_3518,Q_3519,R_3520] :
      ( ap_parcontractE_c4(P_3518,Q_3519,R_3520)
      | ap_parcontractE_c3(P_3518,Q_3519,R_3520)
      | ap_parcontractE_c2(P_3518,Q_3519,R_3520)
      | ap_parcontractE_c1(P_3518,Q_3519,R_3520)
      | ~ member(pair(comb_app(P_3518,Q_3519),R_3520),parcontract) ),
    inference(cnfTransformation,[status(thm)],[f_1124]) ).

tff(c_114272,plain,
    ( ap_parcontractE_c4(combS,p,r)
    | ap_parcontractE_c3(combS,p,r)
    | ap_parcontractE_c2(combS,p,r)
    | ap_parcontractE_c1(combS,p,r) ),
    inference(resolution,[status(thm)],[c_396,c_114219]) ).

tff(c_114283,plain,
    ( ap_parcontractE_c4(combS,p,r)
    | ap_parcontractE_c2(combS,p,r)
    | ap_parcontractE_c1(combS,p,r) ),
    inference(negUnitSimplification,[status(thm)],[c_109853,c_114272]) ).

tff(c_162220,plain,
    ap_parcontractE_c1(combS,p,r),
    inference(splitLeft,[status(thm)],[c_114283]) ).

tff(c_162225,plain,
    comb_app(combS,p) = r,
    inference(resolution,[status(thm)],[c_162220,c_372]) ).

tff(c_162230,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_100558,c_162225]) ).

tff(c_162231,plain,
    ( ap_parcontractE_c2(combS,p,r)
    | ap_parcontractE_c4(combS,p,r) ),
    inference(splitRight,[status(thm)],[c_114283]) ).

tff(c_162233,plain,
    ap_parcontractE_c4(combS,p,r),
    inference(splitLeft,[status(thm)],[c_162231]) ).

tff(c_105135,plain,
    ! [P_3226,Q_3227,R_3228] :
      ( member(pair(P_3226,ap_parcontractE_sk2q(P_3226,Q_3227,R_3228)),parcontract)
      | ~ ap_parcontractE_c4(P_3226,Q_3227,R_3228) ),
    inference(cnfTransformation,[status(thm)],[f_1179]) ).

tff(c_105170,plain,
    ! [Q_3227,R_3228] :
      ( ( ap_parcontractE_sk2q(combS,Q_3227,R_3228) = combS )
      | ~ ap_parcontractE_c4(combS,Q_3227,R_3228) ),
    inference(resolution,[status(thm)],[c_105135,c_366]) ).

tff(c_162257,plain,
    ap_parcontractE_sk2q(combS,p,r) = combS,
    inference(resolution,[status(thm)],[c_162233,c_105170]) ).

tff(c_162298,plain,
    ( ( comb_app(combS,ap_parcontractE_sk2s(combS,p,r)) = r )
    | ~ ap_parcontractE_c4(combS,p,r) ),
    inference(superposition,[status(thm),theory(equality)],[c_162257,c_394]) ).

tff(c_162307,plain,
    comb_app(combS,ap_parcontractE_sk2s(combS,p,r)) = r,
    inference(demodulation,[status(thm),theory(equality)],[c_162233,c_162298]) ).

tff(c_104251,plain,
    ! [Q_3136,P_3137,R_3138] :
      ( member(pair(Q_3136,ap_parcontractE_sk2s(P_3137,Q_3136,R_3138)),parcontract)
      | ~ ap_parcontractE_c4(P_3137,Q_3136,R_3138) ),
    inference(cnfTransformation,[status(thm)],[f_1184]) ).

tff(c_104280,plain,
    ! [P_3137,R_3138] :
      ( ( comb_app(combS,ap_parcontractE_sk2s(P_3137,p,R_3138)) != r )
      | ~ ap_parcontractE_c4(P_3137,p,R_3138) ),
    inference(resolution,[status(thm)],[c_104251,c_398]) ).

tff(c_162653,plain,
    ~ ap_parcontractE_c4(combS,p,r),
    inference(superposition,[status(thm),theory(equality)],[c_162307,c_104280]) ).

tff(c_162724,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_162233,c_162653]) ).

tff(c_162725,plain,
    ap_parcontractE_c2(combS,p,r),
    inference(splitRight,[status(thm)],[c_162231]) ).

tff(c_162729,plain,
    comb_app(combK,r) = combS,
    inference(resolution,[status(thm)],[c_162725,c_378]) ).

tff(c_162739,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_293,c_162729]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : COL093-2 : TPTP v8.1.2. Released v2.7.0.
% 0.00/0.13  % Command  : java -Dfile.encoding=UTF-8 -Xms512M -Xmx4G -Xss10M -jar /export/starexec/sandbox/solver/bin/beagle.jar -auto -q -proof -print tff -smtsolver /export/starexec/sandbox/solver/bin/cvc4-1.4-x86_64-linux-opt -liasolver cooper -t %d %s
% 0.15/0.35  % Computer : n021.cluster.edu
% 0.15/0.35  % Model    : x86_64 x86_64
% 0.15/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.35  % Memory   : 8042.1875MB
% 0.15/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.35  % CPULimit : 300
% 0.15/0.35  % WCLimit  : 300
% 0.15/0.35  % DateTime : Thu Aug  3 18:13:51 EDT 2023
% 0.15/0.35  % CPUTime  : 
% 57.60/41.20  % SZS status Unsatisfiable for /export/starexec/sandbox/benchmark/theBenchmark.p
% 57.60/41.21  
% 57.60/41.21  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 57.60/41.25  
% 57.60/41.25  Inference rules
% 57.60/41.25  ----------------------
% 57.60/41.25  #Ref     : 23
% 57.60/41.25  #Sup     : 38982
% 57.60/41.25  #Fact    : 0
% 57.60/41.25  #Define  : 0
% 57.60/41.25  #Split   : 32
% 57.60/41.25  #Chain   : 0
% 57.60/41.25  #Close   : 0
% 57.60/41.25  
% 57.60/41.25  Ordering : KBO
% 57.60/41.25  
% 57.60/41.25  Simplification rules
% 57.60/41.25  ----------------------
% 57.60/41.25  #Subsume      : 3084
% 57.60/41.25  #Demod        : 10143
% 57.60/41.25  #Tautology    : 7453
% 57.60/41.25  #SimpNegUnit  : 448
% 57.60/41.25  #BackRed      : 260
% 57.60/41.25  
% 57.60/41.25  #Partial instantiations: 0
% 57.60/41.25  #Strategies tried      : 1
% 57.60/41.25  
% 57.60/41.25  Timing (in seconds)
% 57.60/41.25  ----------------------
% 57.60/41.25  Preprocessing        : 0.85
% 57.60/41.25  Parsing              : 0.45
% 57.60/41.25  CNF conversion       : 0.07
% 57.60/41.25  Main loop            : 39.33
% 57.60/41.25  Inferencing          : 5.57
% 57.60/41.25  Reduction            : 19.45
% 57.60/41.25  Demodulation         : 16.05
% 57.60/41.25  BG Simplification    : 0.27
% 57.60/41.25  Subsumption          : 11.14
% 57.60/41.25  Abstraction          : 0.35
% 57.60/41.25  MUC search           : 0.00
% 57.60/41.25  Cooper               : 0.00
% 57.60/41.25  Total                : 40.25
% 57.60/41.25  Index Insertion      : 0.00
% 57.60/41.25  Index Deletion       : 0.00
% 57.60/41.25  Index Matching       : 0.00
% 57.60/41.25  BG Taut test         : 0.00
%------------------------------------------------------------------------------