TSTP Solution File: SWC354+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC354+1 : TPTP v8.1.2. Released v2.4.0.
% 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 : n004.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 11:02:16 EDT 2023

% Result   : Theorem 18.73s 6.91s
% Output   : CNFRefutation 18.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   20
%            Number of leaves      :   90
% Syntax   : Number of formulae    :  199 (  60 unt;  75 typ;   0 def)
%            Number of atoms       :  260 (  92 equ)
%            Maximal formula atoms :   16 (   2 avg)
%            Number of connectives :  242 ( 106   ~;  96   |;   8   &)
%                                         (   1 <=>;  31  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   22 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   85 (  68   >;  17   *;   0   +;   0  <<)
%            Number of predicates  :   21 (  19 usr;   1 prp; 0-2 aty)
%            Number of functors    :   56 (  56 usr;   7 con; 0-2 aty)
%            Number of variables   :   64 (;  60   !;   4   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ segmentP > rearsegP > neq > memberP > lt > leq > gt > geq > frontsegP > totalorderedP > totalorderP > strictorderedP > strictorderP > ssList > ssItem > singletonP > equalelemsP > duplicatefreeP > cyclefreeP > cons > app > #nlpp > tl > hd > nil > #skF_36 > #skF_25 > #skF_5 > #skF_44 > #skF_21 > #skF_16 > #skF_6 > #skF_49 > #skF_18 > #skF_24 > #skF_35 > #skF_19 > #skF_31 > #skF_22 > #skF_37 > #skF_40 > #skF_48 > #skF_3 > #skF_34 > #skF_29 > #skF_15 > #skF_32 > #skF_51 > #skF_28 > #skF_10 > #skF_41 > #skF_2 > #skF_38 > #skF_43 > #skF_1 > #skF_8 > #skF_39 > #skF_23 > #skF_33 > #skF_26 > #skF_50 > #skF_13 > #skF_17 > #skF_11 > #skF_14 > #skF_27 > #skF_12 > #skF_7 > #skF_46 > #skF_42 > #skF_45 > #skF_9 > #skF_30 > #skF_4 > #skF_20 > #skF_47

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_36',type,
    '#skF_36': $i > $i ).

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

tff('#skF_25',type,
    '#skF_25': $i > $i ).

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

tff('#skF_5',type,
    '#skF_5': $i > $i ).

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

tff('#skF_44',type,
    '#skF_44': $i > $i ).

tff('#skF_21',type,
    '#skF_21': $i > $i ).

tff('#skF_16',type,
    '#skF_16': $i > $i ).

tff('#skF_6',type,
    '#skF_6': ( $i * $i ) > $i ).

tff('#skF_49',type,
    '#skF_49': $i ).

tff('#skF_18',type,
    '#skF_18': $i > $i ).

tff('#skF_24',type,
    '#skF_24': $i > $i ).

tff('#skF_35',type,
    '#skF_35': $i > $i ).

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

tff('#skF_19',type,
    '#skF_19': $i > $i ).

tff('#skF_31',type,
    '#skF_31': $i > $i ).

tff('#skF_22',type,
    '#skF_22': $i > $i ).

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

tff('#skF_37',type,
    '#skF_37': $i > $i ).

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

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

tff('#skF_40',type,
    '#skF_40': $i > $i ).

tff('#skF_48',type,
    '#skF_48': $i ).

tff('#skF_3',type,
    '#skF_3': ( $i * $i ) > $i ).

tff('#skF_34',type,
    '#skF_34': $i > $i ).

tff('#skF_29',type,
    '#skF_29': $i > $i ).

tff('#skF_15',type,
    '#skF_15': $i > $i ).

tff('#skF_32',type,
    '#skF_32': $i > $i ).

tff('#skF_51',type,
    '#skF_51': $i ).

tff('#skF_28',type,
    '#skF_28': $i > $i ).

tff('#skF_10',type,
    '#skF_10': $i > $i ).

tff('#skF_41',type,
    '#skF_41': $i > $i ).

tff('#skF_2',type,
    '#skF_2': $i ).

tff('#skF_38',type,
    '#skF_38': $i > $i ).

tff('#skF_43',type,
    '#skF_43': $i > $i ).

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

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

tff('#skF_1',type,
    '#skF_1': $i ).

tff('#skF_8',type,
    '#skF_8': ( $i * $i ) > $i ).

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

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

tff('#skF_39',type,
    '#skF_39': $i > $i ).

tff('#skF_23',type,
    '#skF_23': $i > $i ).

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

tff('#skF_33',type,
    '#skF_33': $i > $i ).

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

tff('#skF_26',type,
    '#skF_26': $i > $i ).

tff('#skF_50',type,
    '#skF_50': $i ).

tff('#skF_13',type,
    '#skF_13': $i > $i ).

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

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

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

tff('#skF_17',type,
    '#skF_17': $i > $i ).

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

tff('#skF_11',type,
    '#skF_11': $i > $i ).

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

tff('#skF_14',type,
    '#skF_14': $i > $i ).

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

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

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

tff('#skF_27',type,
    '#skF_27': $i > $i ).

tff('#skF_12',type,
    '#skF_12': $i > $i ).

tff('#skF_7',type,
    '#skF_7': ( $i * $i ) > $i ).

tff('#skF_46',type,
    '#skF_46': $i > $i ).

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

tff('#skF_42',type,
    '#skF_42': $i > $i ).

tff('#skF_45',type,
    '#skF_45': $i > $i ).

tff('#skF_9',type,
    '#skF_9': ( $i * $i ) > $i ).

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

tff('#skF_30',type,
    '#skF_30': $i > $i ).

tff('#skF_4',type,
    '#skF_4': ( $i * $i ) > $i ).

tff('#skF_20',type,
    '#skF_20': $i > $i ).

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

tff('#skF_47',type,
    '#skF_47': $i > $i ).

tff(f_1019,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( ( V != X )
                      | ( U != W )
                      | ( ( ~ neq(V,nil)
                          | ? [Y] :
                              ( ssList(Y)
                              & ( W != Y )
                              & ? [Z] :
                                  ( ssItem(Z)
                                  & ( cons(Z,nil) = Y )
                                  & ( hd(X) = Z )
                                  & neq(nil,X) ) )
                          | segmentP(V,U) )
                        & ( ~ neq(V,nil)
                          | neq(X,nil) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f_667,axiom,
    ! [U] :
      ( ssList(U)
     => segmentP(U,U) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).

tff(f_769,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ? [V] :
            ( ssItem(V)
            & ( hd(U) = V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax75) ).

tff(f_311,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( neq(U,V)
          <=> ( U != V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax15) ).

tff(f_779,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ? [V] :
            ( ssList(V)
            & ( tl(U) = V ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax76) ).

tff(f_385,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ssList(tl(U)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax24) ).

tff(f_371,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ssItem(hd(U)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).

tff(f_319,axiom,
    ssList(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax17) ).

tff(f_318,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => ssList(cons(V,U)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax16) ).

tff(f_364,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => ( nil != cons(V,U) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax21) ).

tff(f_378,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => ( hd(cons(V,U)) = V ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax23) ).

tff(f_834,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => ( cons(V,U) = app(cons(V,nil),U) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax81) ).

tff(f_803,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ( cons(hd(U),tl(U)) = U ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax78) ).

tff(f_413,axiom,
    ! [U] :
      ( ssList(U)
     => ( app(nil,U) = U ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).

tff(f_682,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( segmentP(U,V)
                   => segmentP(app(app(W,U),X),V) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax56) ).

tff(c_390,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1019]) ).

tff(c_270,plain,
    ! [U_1014] :
      ( segmentP(U_1014,U_1014)
      | ~ ssList(U_1014) ),
    inference(cnfTransformation,[status(thm)],[f_667]) ).

tff(c_388,plain,
    ssList('#skF_51'),
    inference(cnfTransformation,[status(thm)],[f_1019]) ).

tff(c_3354,plain,
    ! [U_1427] :
      ( ( hd(U_1427) = '#skF_46'(U_1427) )
      | ( nil = U_1427 )
      | ~ ssList(U_1427) ),
    inference(cnfTransformation,[status(thm)],[f_769]) ).

tff(c_3458,plain,
    ( ( hd('#skF_51') = '#skF_46'('#skF_51') )
    | ( nil = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_388,c_3354]) ).

tff(c_3460,plain,
    nil = '#skF_51',
    inference(splitLeft,[status(thm)],[c_3458]) ).

tff(c_386,plain,
    '#skF_49' = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1019]) ).

tff(c_406,plain,
    neq('#skF_49',nil),
    inference(cnfTransformation,[status(thm)],[f_1019]) ).

tff(c_411,plain,
    neq('#skF_51',nil),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_406]) ).

tff(c_3598,plain,
    neq('#skF_51','#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_3460,c_411]) ).

tff(c_164,plain,
    ! [V_858] :
      ( ~ neq(V_858,V_858)
      | ~ ssList(V_858) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_3680,plain,
    ~ ssList('#skF_51'),
    inference(resolution,[status(thm)],[c_3598,c_164]) ).

tff(c_3685,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_3680]) ).

tff(c_3687,plain,
    nil != '#skF_51',
    inference(splitRight,[status(thm)],[c_3458]) ).

tff(c_3688,plain,
    ! [U_1433] :
      ( ( tl(U_1433) = '#skF_47'(U_1433) )
      | ( nil = U_1433 )
      | ~ ssList(U_1433) ),
    inference(cnfTransformation,[status(thm)],[f_779]) ).

tff(c_3763,plain,
    ( ( tl('#skF_51') = '#skF_47'('#skF_51') )
    | ( nil = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_388,c_3688]) ).

tff(c_3794,plain,
    tl('#skF_51') = '#skF_47'('#skF_51'),
    inference(negUnitSimplification,[status(thm)],[c_3687,c_3763]) ).

tff(c_188,plain,
    ! [U_892] :
      ( ssList(tl(U_892))
      | ( nil = U_892 )
      | ~ ssList(U_892) ),
    inference(cnfTransformation,[status(thm)],[f_385]) ).

tff(c_3900,plain,
    ( ssList('#skF_47'('#skF_51'))
    | ( nil = '#skF_51' )
    | ~ ssList('#skF_51') ),
    inference(superposition,[status(thm),theory(equality)],[c_3794,c_188]) ).

tff(c_3904,plain,
    ( ssList('#skF_47'('#skF_51'))
    | ( nil = '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_3900]) ).

tff(c_3905,plain,
    ssList('#skF_47'('#skF_51')),
    inference(negUnitSimplification,[status(thm)],[c_3687,c_3904]) ).

tff(c_3686,plain,
    hd('#skF_51') = '#skF_46'('#skF_51'),
    inference(splitRight,[status(thm)],[c_3458]) ).

tff(c_2945,plain,
    ! [U_1374] :
      ( ssItem(hd(U_1374))
      | ( nil = U_1374 )
      | ~ ssList(U_1374) ),
    inference(cnfTransformation,[status(thm)],[f_371]) ).

tff(c_2043,plain,
    ! [U_1341] :
      ( ( hd(U_1341) = '#skF_46'(U_1341) )
      | ( nil = U_1341 )
      | ~ ssList(U_1341) ),
    inference(cnfTransformation,[status(thm)],[f_769]) ).

tff(c_2159,plain,
    ( ( hd('#skF_51') = '#skF_46'('#skF_51') )
    | ( nil = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_388,c_2043]) ).

tff(c_2161,plain,
    nil = '#skF_51',
    inference(splitLeft,[status(thm)],[c_2159]) ).

tff(c_2196,plain,
    neq('#skF_51','#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_2161,c_411]) ).

tff(c_2357,plain,
    ~ ssList('#skF_51'),
    inference(resolution,[status(thm)],[c_2196,c_164]) ).

tff(c_2362,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_2357]) ).

tff(c_2364,plain,
    nil != '#skF_51',
    inference(splitRight,[status(thm)],[c_2159]) ).

tff(c_168,plain,
    ssList(nil),
    inference(cnfTransformation,[status(thm)],[f_319]) ).

tff(c_2775,plain,
    ! [U_1355,V_1356] :
      ( neq(U_1355,V_1356)
      | ( V_1356 = U_1355 )
      | ~ ssList(V_1356)
      | ~ ssList(U_1355) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_773,plain,
    ! [U_1248] :
      ( ( hd(U_1248) = '#skF_46'(U_1248) )
      | ( nil = U_1248 )
      | ~ ssList(U_1248) ),
    inference(cnfTransformation,[status(thm)],[f_769]) ).

tff(c_877,plain,
    ( ( hd('#skF_51') = '#skF_46'('#skF_51') )
    | ( nil = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_388,c_773]) ).

tff(c_879,plain,
    nil = '#skF_51',
    inference(splitLeft,[status(thm)],[c_877]) ).

tff(c_909,plain,
    neq('#skF_51','#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_879,c_411]) ).

tff(c_1056,plain,
    ~ ssList('#skF_51'),
    inference(resolution,[status(thm)],[c_909,c_164]) ).

tff(c_1061,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_1056]) ).

tff(c_1063,plain,
    nil != '#skF_51',
    inference(splitRight,[status(thm)],[c_877]) ).

tff(c_1062,plain,
    hd('#skF_51') = '#skF_46'('#skF_51'),
    inference(splitRight,[status(thm)],[c_877]) ).

tff(c_184,plain,
    ! [U_888] :
      ( ssItem(hd(U_888))
      | ( nil = U_888 )
      | ~ ssList(U_888) ),
    inference(cnfTransformation,[status(thm)],[f_371]) ).

tff(c_1068,plain,
    ( ssItem('#skF_46'('#skF_51'))
    | ( nil = '#skF_51' )
    | ~ ssList('#skF_51') ),
    inference(superposition,[status(thm),theory(equality)],[c_1062,c_184]) ).

tff(c_1072,plain,
    ( ssItem('#skF_46'('#skF_51'))
    | ( nil = '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_1068]) ).

tff(c_1073,plain,
    ssItem('#skF_46'('#skF_51')),
    inference(negUnitSimplification,[status(thm)],[c_1063,c_1072]) ).

tff(c_1366,plain,
    ! [V_1265,U_1266] :
      ( ssList(cons(V_1265,U_1266))
      | ~ ssItem(V_1265)
      | ~ ssList(U_1266) ),
    inference(cnfTransformation,[status(thm)],[f_318]) ).

tff(c_398,plain,
    ( ~ neq(nil,'#skF_51')
    | ~ ssItem(hd('#skF_51'))
    | ( cons(hd('#skF_51'),nil) = '#skF_50' )
    | ~ ssList(cons(hd('#skF_51'),nil))
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1019]) ).

tff(c_415,plain,
    ( ~ neq(nil,'#skF_51')
    | ~ ssItem(hd('#skF_51'))
    | ( cons(hd('#skF_51'),nil) = '#skF_50' )
    | ~ ssList(cons(hd('#skF_51'),nil)) ),
    inference(demodulation,[status(thm),theory(equality)],[c_411,c_398]) ).

tff(c_430,plain,
    ~ ssList(cons(hd('#skF_51'),nil)),
    inference(splitLeft,[status(thm)],[c_415]) ).

tff(c_1064,plain,
    ~ ssList(cons('#skF_46'('#skF_51'),nil)),
    inference(demodulation,[status(thm),theory(equality)],[c_1062,c_430]) ).

tff(c_1372,plain,
    ( ~ ssItem('#skF_46'('#skF_51'))
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_1366,c_1064]) ).

tff(c_1386,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_1073,c_1372]) ).

tff(c_1387,plain,
    ( ~ ssItem(hd('#skF_51'))
    | ~ neq(nil,'#skF_51')
    | ( cons(hd('#skF_51'),nil) = '#skF_50' ) ),
    inference(splitRight,[status(thm)],[c_415]) ).

tff(c_1401,plain,
    ~ neq(nil,'#skF_51'),
    inference(splitLeft,[status(thm)],[c_1387]) ).

tff(c_2778,plain,
    ( ( nil = '#skF_51' )
    | ~ ssList('#skF_51')
    | ~ ssList(nil) ),
    inference(resolution,[status(thm)],[c_2775,c_1401]) ).

tff(c_2789,plain,
    nil = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_388,c_2778]) ).

tff(c_2791,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2364,c_2789]) ).

tff(c_2792,plain,
    ( ~ ssItem(hd('#skF_51'))
    | ( cons(hd('#skF_51'),nil) = '#skF_50' ) ),
    inference(splitRight,[status(thm)],[c_1387]) ).

tff(c_2823,plain,
    ~ ssItem(hd('#skF_51')),
    inference(splitLeft,[status(thm)],[c_2792]) ).

tff(c_2948,plain,
    ( ( nil = '#skF_51' )
    | ~ ssList('#skF_51') ),
    inference(resolution,[status(thm)],[c_2945,c_2823]) ).

tff(c_2951,plain,
    nil = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_2948]) ).

tff(c_2979,plain,
    neq('#skF_51','#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_2951,c_411]) ).

tff(c_3000,plain,
    ~ ssList('#skF_51'),
    inference(resolution,[status(thm)],[c_2979,c_164]) ).

tff(c_3005,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_3000]) ).

tff(c_3007,plain,
    ssItem(hd('#skF_51')),
    inference(splitRight,[status(thm)],[c_2792]) ).

tff(c_3797,plain,
    ssItem('#skF_46'('#skF_51')),
    inference(demodulation,[status(thm),theory(equality)],[c_3686,c_3007]) ).

tff(c_3459,plain,
    ( ( hd('#skF_50') = '#skF_46'('#skF_50') )
    | ( nil = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_390,c_3354]) ).

tff(c_3809,plain,
    nil = '#skF_50',
    inference(splitLeft,[status(thm)],[c_3459]) ).

tff(c_3006,plain,
    cons(hd('#skF_51'),nil) = '#skF_50',
    inference(splitRight,[status(thm)],[c_2792]) ).

tff(c_3796,plain,
    cons('#skF_46'('#skF_51'),nil) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_3686,c_3006]) ).

tff(c_3884,plain,
    cons('#skF_46'('#skF_51'),'#skF_50') = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_3809,c_3796]) ).

tff(c_182,plain,
    ! [V_887,U_885] :
      ( ( cons(V_887,U_885) != nil )
      | ~ ssItem(V_887)
      | ~ ssList(U_885) ),
    inference(cnfTransformation,[status(thm)],[f_364]) ).

tff(c_3863,plain,
    ! [V_887,U_885] :
      ( ( cons(V_887,U_885) != '#skF_50' )
      | ~ ssItem(V_887)
      | ~ ssList(U_885) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3809,c_182]) ).

tff(c_3887,plain,
    ( ~ ssItem('#skF_46'('#skF_51'))
    | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_3884,c_3863]) ).

tff(c_3893,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_3797,c_3887]) ).

tff(c_3895,plain,
    nil != '#skF_50',
    inference(splitRight,[status(thm)],[c_3459]) ).

tff(c_3894,plain,
    hd('#skF_50') = '#skF_46'('#skF_50'),
    inference(splitRight,[status(thm)],[c_3459]) ).

tff(c_3926,plain,
    ( ssItem('#skF_46'('#skF_50'))
    | ( nil = '#skF_50' )
    | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_3894,c_184]) ).

tff(c_3930,plain,
    ( ssItem('#skF_46'('#skF_50'))
    | ( nil = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_3926]) ).

tff(c_3931,plain,
    ssItem('#skF_46'('#skF_50')),
    inference(negUnitSimplification,[status(thm)],[c_3895,c_3930]) ).

tff(c_4398,plain,
    ! [V_1460,U_1461] :
      ( ( hd(cons(V_1460,U_1461)) = V_1460 )
      | ~ ssItem(V_1460)
      | ~ ssList(U_1461) ),
    inference(cnfTransformation,[status(thm)],[f_378]) ).

tff(c_4410,plain,
    ( ( hd('#skF_50') = '#skF_46'('#skF_51') )
    | ~ ssItem('#skF_46'('#skF_51'))
    | ~ ssList(nil) ),
    inference(superposition,[status(thm),theory(equality)],[c_3796,c_4398]) ).

tff(c_4414,plain,
    '#skF_46'('#skF_51') = '#skF_46'('#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_168,c_3797,c_3894,c_4410]) ).

tff(c_4416,plain,
    cons('#skF_46'('#skF_50'),nil) = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_4414,c_3796]) ).

tff(c_8022,plain,
    ! [V_1595,U_1596] :
      ( ( app(cons(V_1595,nil),U_1596) = cons(V_1595,U_1596) )
      | ~ ssItem(V_1595)
      | ~ ssList(U_1596) ),
    inference(cnfTransformation,[status(thm)],[f_834]) ).

tff(c_8044,plain,
    ! [U_1596] :
      ( ( cons('#skF_46'('#skF_50'),U_1596) = app('#skF_50',U_1596) )
      | ~ ssItem('#skF_46'('#skF_50'))
      | ~ ssList(U_1596) ),
    inference(superposition,[status(thm),theory(equality)],[c_4416,c_8022]) ).

tff(c_8049,plain,
    ! [U_1597] :
      ( ( cons('#skF_46'('#skF_50'),U_1597) = app('#skF_50',U_1597) )
      | ~ ssList(U_1597) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3931,c_8044]) ).

tff(c_4418,plain,
    hd('#skF_51') = '#skF_46'('#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_4414,c_3686]) ).

tff(c_4935,plain,
    ! [U_1473] :
      ( ( cons(hd(U_1473),tl(U_1473)) = U_1473 )
      | ( nil = U_1473 )
      | ~ ssList(U_1473) ),
    inference(cnfTransformation,[status(thm)],[f_803]) ).

tff(c_4978,plain,
    ( ( cons(hd('#skF_51'),'#skF_47'('#skF_51')) = '#skF_51' )
    | ( nil = '#skF_51' )
    | ~ ssList('#skF_51') ),
    inference(superposition,[status(thm),theory(equality)],[c_3794,c_4935]) ).

tff(c_4996,plain,
    ( ( cons('#skF_46'('#skF_50'),'#skF_47'('#skF_51')) = '#skF_51' )
    | ( nil = '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_388,c_4418,c_4978]) ).

tff(c_4997,plain,
    cons('#skF_46'('#skF_50'),'#skF_47'('#skF_51')) = '#skF_51',
    inference(negUnitSimplification,[status(thm)],[c_3687,c_4996]) ).

tff(c_8066,plain,
    ( ( app('#skF_50','#skF_47'('#skF_51')) = '#skF_51' )
    | ~ ssList('#skF_47'('#skF_51')) ),
    inference(superposition,[status(thm),theory(equality)],[c_8049,c_4997]) ).

tff(c_8131,plain,
    app('#skF_50','#skF_47'('#skF_51')) = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_3905,c_8066]) ).

tff(c_3050,plain,
    ! [U_1381] :
      ( ( app(nil,U_1381) = U_1381 )
      | ~ ssList(U_1381) ),
    inference(cnfTransformation,[status(thm)],[f_413]) ).

tff(c_3063,plain,
    app(nil,'#skF_50') = '#skF_50',
    inference(resolution,[status(thm)],[c_390,c_3050]) ).

tff(c_22838,plain,
    ! [W_1843,U_1844,X_1845,V_1846] :
      ( segmentP(app(app(W_1843,U_1844),X_1845),V_1846)
      | ~ segmentP(U_1844,V_1846)
      | ~ ssList(X_1845)
      | ~ ssList(W_1843)
      | ~ ssList(V_1846)
      | ~ ssList(U_1844) ),
    inference(cnfTransformation,[status(thm)],[f_682]) ).

tff(c_23107,plain,
    ! [X_1845,V_1846] :
      ( segmentP(app('#skF_50',X_1845),V_1846)
      | ~ segmentP('#skF_50',V_1846)
      | ~ ssList(X_1845)
      | ~ ssList(nil)
      | ~ ssList(V_1846)
      | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_3063,c_22838]) ).

tff(c_24332,plain,
    ! [X_1879,V_1880] :
      ( segmentP(app('#skF_50',X_1879),V_1880)
      | ~ segmentP('#skF_50',V_1880)
      | ~ ssList(X_1879)
      | ~ ssList(V_1880) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_168,c_23107]) ).

tff(c_24346,plain,
    ! [V_1880] :
      ( segmentP('#skF_51',V_1880)
      | ~ segmentP('#skF_50',V_1880)
      | ~ ssList('#skF_47'('#skF_51'))
      | ~ ssList(V_1880) ),
    inference(superposition,[status(thm),theory(equality)],[c_8131,c_24332]) ).

tff(c_24589,plain,
    ! [V_1890] :
      ( segmentP('#skF_51',V_1890)
      | ~ segmentP('#skF_50',V_1890)
      | ~ ssList(V_1890) ),
    inference(demodulation,[status(thm),theory(equality)],[c_3905,c_24346]) ).

tff(c_384,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1019]) ).

tff(c_396,plain,
    ( ~ segmentP('#skF_49','#skF_48')
    | ~ neq('#skF_51',nil) ),
    inference(cnfTransformation,[status(thm)],[f_1019]) ).

tff(c_412,plain,
    ( ~ segmentP('#skF_51','#skF_48')
    | ~ neq('#skF_51',nil) ),
    inference(demodulation,[status(thm),theory(equality)],[c_386,c_396]) ).

tff(c_417,plain,
    ~ segmentP('#skF_51','#skF_48'),
    inference(demodulation,[status(thm),theory(equality)],[c_411,c_412]) ).

tff(c_419,plain,
    ~ segmentP('#skF_51','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_384,c_417]) ).

tff(c_24596,plain,
    ( ~ segmentP('#skF_50','#skF_50')
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_24589,c_419]) ).

tff(c_24605,plain,
    ~ segmentP('#skF_50','#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_24596]) ).

tff(c_24608,plain,
    ~ ssList('#skF_50'),
    inference(resolution,[status(thm)],[c_270,c_24605]) ).

tff(c_24612,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_24608]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.13/0.12  % Problem  : SWC354+1 : TPTP v8.1.2. Released v2.4.0.
% 0.13/0.13  % 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
% 0.14/0.34  % Computer : n004.cluster.edu
% 0.14/0.34  % Model    : x86_64 x86_64
% 0.14/0.34  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34  % Memory   : 8042.1875MB
% 0.14/0.34  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34  % CPULimit : 300
% 0.14/0.34  % WCLimit  : 300
% 0.14/0.34  % DateTime : Thu Aug  3 21:42:26 EDT 2023
% 0.14/0.34  % CPUTime  : 
% 18.73/6.91  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 18.73/6.92  
% 18.73/6.92  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 18.73/6.96  
% 18.73/6.96  Inference rules
% 18.73/6.96  ----------------------
% 18.73/6.96  #Ref     : 5
% 18.73/6.96  #Sup     : 5312
% 18.73/6.96  #Fact    : 0
% 18.73/6.96  #Define  : 0
% 18.73/6.96  #Split   : 52
% 18.73/6.96  #Chain   : 0
% 18.73/6.96  #Close   : 0
% 18.73/6.96  
% 18.73/6.96  Ordering : KBO
% 18.73/6.96  
% 18.73/6.96  Simplification rules
% 18.73/6.96  ----------------------
% 18.73/6.96  #Subsume      : 613
% 18.73/6.96  #Demod        : 4264
% 18.73/6.96  #Tautology    : 1510
% 18.73/6.96  #SimpNegUnit  : 353
% 18.73/6.96  #BackRed      : 393
% 18.73/6.96  
% 18.73/6.96  #Partial instantiations: 0
% 18.73/6.96  #Strategies tried      : 1
% 18.73/6.96  
% 18.73/6.96  Timing (in seconds)
% 18.73/6.96  ----------------------
% 18.73/6.96  Preprocessing        : 0.90
% 18.73/6.96  Parsing              : 0.42
% 18.73/6.96  CNF conversion       : 0.11
% 18.73/6.96  Main loop            : 4.99
% 18.73/6.96  Inferencing          : 1.25
% 18.73/6.96  Reduction            : 2.03
% 18.73/6.96  Demodulation         : 1.47
% 18.73/6.96  BG Simplification    : 0.12
% 18.73/6.96  Subsumption          : 1.26
% 18.73/6.97  Abstraction          : 0.11
% 18.73/6.97  MUC search           : 0.00
% 18.73/6.97  Cooper               : 0.00
% 18.73/6.97  Total                : 5.96
% 18.73/6.97  Index Insertion      : 0.00
% 18.73/6.97  Index Deletion       : 0.00
% 18.73/6.97  Index Matching       : 0.00
% 18.73/6.97  BG Taut test         : 0.00
%------------------------------------------------------------------------------