TSTP Solution File: SWC214+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC214+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 : n027.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 11:01:39 EDT 2023

% Result   : Theorem 19.73s 7.65s
% Output   : CNFRefutation 19.73s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   16
%            Number of leaves      :   91
% Syntax   : Number of formulae    :  168 (  36 unt;  75 typ;   0 def)
%            Number of atoms       :  228 (  62 equ)
%            Maximal formula atoms :   15 (   2 avg)
%            Number of connectives :  232 (  97   ~;  94   |;   9   &)
%                                         (   4 <=>;  28  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   21 (   4 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   :   62 (;  57   !;   5   ?;   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_1016,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( ( V != X )
                      | ( U != W )
                      | ~ neq(V,nil)
                      | ~ frontsegP(X,W)
                      | ~ strictorderedP(W)
                      | ? [Y] :
                          ( ssList(Y)
                          & neq(W,Y)
                          & frontsegP(X,Y)
                          & segmentP(Y,W)
                          & strictorderedP(Y) )
                      | neq(U,nil) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

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_519,axiom,
    ~ singletonP(nil),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax39) ).

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_371,axiom,
    ! [U] :
      ( ssList(U)
     => ( ( nil != U )
       => ssItem(hd(U)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax22) ).

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_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_413,axiom,
    ! [U] :
      ( ssList(U)
     => ( app(nil,U) = U ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax28) ).

tff(f_108,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( frontsegP(U,V)
          <=> ? [W] :
                ( ssList(W)
                & ( app(V,W) = U ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax5) ).

tff(f_732,axiom,
    ! [U] :
      ( ssItem(U)
     => strictorderedP(cons(U,nil)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax68) ).

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_577,axiom,
    ! [U] :
      ( ssItem(U)
     => ! [V] :
          ( ssItem(V)
         => ! [W] :
              ( ssList(W)
             => ! [X] :
                  ( ssList(X)
                 => ( frontsegP(cons(U,W),cons(V,X))
                  <=> ( ( U = V )
                      & frontsegP(W,X) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax44) ).

tff(f_686,axiom,
    ! [U] :
      ( ssList(U)
     => segmentP(U,nil) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax57) ).

tff(f_96,axiom,
    ! [U] :
      ( ssList(U)
     => ( singletonP(U)
      <=> ? [V] :
            ( ssItem(V)
            & ( cons(V,nil) = U ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax4) ).

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

tff(c_400,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1016]) ).

tff(c_891,plain,
    ! [U_1220] :
      ( ( hd(U_1220) = '#skF_46'(U_1220) )
      | ( nil = U_1220 )
      | ~ ssList(U_1220) ),
    inference(cnfTransformation,[status(thm)],[f_769]) ).

tff(c_1000,plain,
    ( ( hd('#skF_50') = '#skF_46'('#skF_50') )
    | ( nil = '#skF_50' ) ),
    inference(resolution,[status(thm)],[c_400,c_891]) ).

tff(c_1360,plain,
    nil = '#skF_50',
    inference(splitLeft,[status(thm)],[c_1000]) ).

tff(c_230,plain,
    ~ singletonP(nil),
    inference(cnfTransformation,[status(thm)],[f_519]) ).

tff(c_1401,plain,
    ~ singletonP('#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_1360,c_230]) ).

tff(c_398,plain,
    ssList('#skF_51'),
    inference(cnfTransformation,[status(thm)],[f_1016]) ).

tff(c_999,plain,
    ( ( hd('#skF_51') = '#skF_46'('#skF_51') )
    | ( nil = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_398,c_891]) ).

tff(c_1001,plain,
    nil = '#skF_51',
    inference(splitLeft,[status(thm)],[c_999]) ).

tff(c_396,plain,
    '#skF_49' = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1016]) ).

tff(c_392,plain,
    neq('#skF_49',nil),
    inference(cnfTransformation,[status(thm)],[f_1016]) ).

tff(c_409,plain,
    neq('#skF_51',nil),
    inference(demodulation,[status(thm),theory(equality)],[c_396,c_392]) ).

tff(c_1032,plain,
    neq('#skF_51','#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_1001,c_409]) ).

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

tff(c_1198,plain,
    ~ ssList('#skF_51'),
    inference(resolution,[status(thm)],[c_1032,c_164]) ).

tff(c_1205,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_398,c_1198]) ).

tff(c_1207,plain,
    nil != '#skF_51',
    inference(splitRight,[status(thm)],[c_999]) ).

tff(c_1206,plain,
    hd('#skF_51') = '#skF_46'('#skF_51'),
    inference(splitRight,[status(thm)],[c_999]) ).

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

tff(c_1211,plain,
    ( ssItem('#skF_46'('#skF_51'))
    | ( nil = '#skF_51' )
    | ~ ssList('#skF_51') ),
    inference(superposition,[status(thm),theory(equality)],[c_1206,c_184]) ).

tff(c_1215,plain,
    ( ssItem('#skF_46'('#skF_51'))
    | ( nil = '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_398,c_1211]) ).

tff(c_1216,plain,
    ssItem('#skF_46'('#skF_51')),
    inference(negUnitSimplification,[status(thm)],[c_1207,c_1215]) ).

tff(c_166,plain,
    ! [V_861,U_859] :
      ( ssList(cons(V_861,U_859))
      | ~ ssItem(V_861)
      | ~ ssList(U_859) ),
    inference(cnfTransformation,[status(thm)],[f_318]) ).

tff(c_1218,plain,
    ! [U_1226] :
      ( ( tl(U_1226) = '#skF_47'(U_1226) )
      | ( nil = U_1226 )
      | ~ ssList(U_1226) ),
    inference(cnfTransformation,[status(thm)],[f_779]) ).

tff(c_1296,plain,
    ( ( tl('#skF_51') = '#skF_47'('#skF_51') )
    | ( nil = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_398,c_1218]) ).

tff(c_1328,plain,
    tl('#skF_51') = '#skF_47'('#skF_51'),
    inference(negUnitSimplification,[status(thm)],[c_1207,c_1296]) ).

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

tff(c_1333,plain,
    ( ssList('#skF_47'('#skF_51'))
    | ( nil = '#skF_51' )
    | ~ ssList('#skF_51') ),
    inference(superposition,[status(thm),theory(equality)],[c_1328,c_188]) ).

tff(c_1337,plain,
    ( ssList('#skF_47'('#skF_51'))
    | ( nil = '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_398,c_1333]) ).

tff(c_1338,plain,
    ssList('#skF_47'('#skF_51')),
    inference(negUnitSimplification,[status(thm)],[c_1207,c_1337]) ).

tff(c_196,plain,
    ! [U_906] :
      ( ( app(nil,U_906) = U_906 )
      | ~ ssList(U_906) ),
    inference(cnfTransformation,[status(thm)],[f_413]) ).

tff(c_1358,plain,
    app(nil,'#skF_47'('#skF_51')) = '#skF_47'('#skF_51'),
    inference(resolution,[status(thm)],[c_1338,c_196]) ).

tff(c_1811,plain,
    app('#skF_50','#skF_47'('#skF_51')) = '#skF_47'('#skF_51'),
    inference(demodulation,[status(thm),theory(equality)],[c_1360,c_1358]) ).

tff(c_6176,plain,
    ! [V_1434,W_1435] :
      ( frontsegP(app(V_1434,W_1435),V_1434)
      | ~ ssList(W_1435)
      | ~ ssList(V_1434)
      | ~ ssList(app(V_1434,W_1435)) ),
    inference(cnfTransformation,[status(thm)],[f_108]) ).

tff(c_6337,plain,
    ( frontsegP('#skF_47'('#skF_51'),'#skF_50')
    | ~ ssList('#skF_47'('#skF_51'))
    | ~ ssList('#skF_50')
    | ~ ssList(app('#skF_50','#skF_47'('#skF_51'))) ),
    inference(superposition,[status(thm),theory(equality)],[c_1811,c_6176]) ).

tff(c_6451,plain,
    frontsegP('#skF_47'('#skF_51'),'#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_1338,c_1811,c_400,c_1338,c_6337]) ).

tff(c_307,plain,
    ! [U_1039] :
      ( strictorderedP(cons(U_1039,nil))
      | ~ ssItem(U_1039) ),
    inference(cnfTransformation,[status(thm)],[f_732]) ).

tff(c_1378,plain,
    ! [U_1039] :
      ( strictorderedP(cons(U_1039,'#skF_50'))
      | ~ ssItem(U_1039) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1360,c_307]) ).

tff(c_1363,plain,
    '#skF_51' != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_1360,c_1207]) ).

tff(c_340,plain,
    ! [U_1052] :
      ( ( cons(hd(U_1052),tl(U_1052)) = U_1052 )
      | ( nil = U_1052 )
      | ~ ssList(U_1052) ),
    inference(cnfTransformation,[status(thm)],[f_803]) ).

tff(c_3048,plain,
    ! [U_1305] :
      ( ( cons(hd(U_1305),tl(U_1305)) = U_1305 )
      | ( U_1305 = '#skF_50' )
      | ~ ssList(U_1305) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1360,c_340]) ).

tff(c_3079,plain,
    ( ( cons(hd('#skF_51'),'#skF_47'('#skF_51')) = '#skF_51' )
    | ( '#skF_51' = '#skF_50' )
    | ~ ssList('#skF_51') ),
    inference(superposition,[status(thm),theory(equality)],[c_1328,c_3048]) ).

tff(c_3088,plain,
    ( ( cons('#skF_46'('#skF_51'),'#skF_47'('#skF_51')) = '#skF_51' )
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_398,c_1206,c_3079]) ).

tff(c_3089,plain,
    cons('#skF_46'('#skF_51'),'#skF_47'('#skF_51')) = '#skF_51',
    inference(negUnitSimplification,[status(thm)],[c_1363,c_3088]) ).

tff(c_12667,plain,
    ! [V_1660,W_1661,X_1662] :
      ( frontsegP(cons(V_1660,W_1661),cons(V_1660,X_1662))
      | ~ frontsegP(W_1661,X_1662)
      | ~ ssList(X_1662)
      | ~ ssList(W_1661)
      | ~ ssItem(V_1660) ),
    inference(cnfTransformation,[status(thm)],[f_577]) ).

tff(c_12692,plain,
    ! [X_1662] :
      ( frontsegP('#skF_51',cons('#skF_46'('#skF_51'),X_1662))
      | ~ frontsegP('#skF_47'('#skF_51'),X_1662)
      | ~ ssList(X_1662)
      | ~ ssList('#skF_47'('#skF_51'))
      | ~ ssItem('#skF_46'('#skF_51')) ),
    inference(superposition,[status(thm),theory(equality)],[c_3089,c_12667]) ).

tff(c_25852,plain,
    ! [X_1981] :
      ( frontsegP('#skF_51',cons('#skF_46'('#skF_51'),X_1981))
      | ~ frontsegP('#skF_47'('#skF_51'),X_1981)
      | ~ ssList(X_1981) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1216,c_1338,c_12692]) ).

tff(c_2198,plain,
    ! [U_1265,V_1266] :
      ( neq(U_1265,V_1266)
      | ( V_1266 = U_1265 )
      | ~ ssList(V_1266)
      | ~ ssList(U_1265) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_274,plain,
    ! [U_1030] :
      ( segmentP(U_1030,nil)
      | ~ ssList(U_1030) ),
    inference(cnfTransformation,[status(thm)],[f_686]) ).

tff(c_1526,plain,
    ! [U_1231] :
      ( segmentP(U_1231,'#skF_50')
      | ~ ssList(U_1231) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1360,c_274]) ).

tff(c_386,plain,
    ! [Y_1148] :
      ( ~ strictorderedP(Y_1148)
      | ~ segmentP(Y_1148,'#skF_50')
      | ~ frontsegP('#skF_51',Y_1148)
      | ~ neq('#skF_50',Y_1148)
      | ~ ssList(Y_1148) ),
    inference(cnfTransformation,[status(thm)],[f_1016]) ).

tff(c_1530,plain,
    ! [U_1231] :
      ( ~ strictorderedP(U_1231)
      | ~ frontsegP('#skF_51',U_1231)
      | ~ neq('#skF_50',U_1231)
      | ~ ssList(U_1231) ),
    inference(resolution,[status(thm)],[c_1526,c_386]) ).

tff(c_2202,plain,
    ! [V_1266] :
      ( ~ strictorderedP(V_1266)
      | ~ frontsegP('#skF_51',V_1266)
      | ( V_1266 = '#skF_50' )
      | ~ ssList(V_1266)
      | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_2198,c_1530]) ).

tff(c_2216,plain,
    ! [V_1266] :
      ( ~ strictorderedP(V_1266)
      | ~ frontsegP('#skF_51',V_1266)
      | ( V_1266 = '#skF_50' )
      | ~ ssList(V_1266) ),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_2202]) ).

tff(c_25896,plain,
    ! [X_1984] :
      ( ~ strictorderedP(cons('#skF_46'('#skF_51'),X_1984))
      | ( cons('#skF_46'('#skF_51'),X_1984) = '#skF_50' )
      | ~ ssList(cons('#skF_46'('#skF_51'),X_1984))
      | ~ frontsegP('#skF_47'('#skF_51'),X_1984)
      | ~ ssList(X_1984) ),
    inference(resolution,[status(thm)],[c_25852,c_2216]) ).

tff(c_25913,plain,
    ( ( cons('#skF_46'('#skF_51'),'#skF_50') = '#skF_50' )
    | ~ ssList(cons('#skF_46'('#skF_51'),'#skF_50'))
    | ~ frontsegP('#skF_47'('#skF_51'),'#skF_50')
    | ~ ssList('#skF_50')
    | ~ ssItem('#skF_46'('#skF_51')) ),
    inference(resolution,[status(thm)],[c_1378,c_25896]) ).

tff(c_25925,plain,
    ( ( cons('#skF_46'('#skF_51'),'#skF_50') = '#skF_50' )
    | ~ ssList(cons('#skF_46'('#skF_51'),'#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1216,c_400,c_6451,c_25913]) ).

tff(c_25926,plain,
    ~ ssList(cons('#skF_46'('#skF_51'),'#skF_50')),
    inference(splitLeft,[status(thm)],[c_25925]) ).

tff(c_25929,plain,
    ( ~ ssItem('#skF_46'('#skF_51'))
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_166,c_25926]) ).

tff(c_25933,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_1216,c_25929]) ).

tff(c_25934,plain,
    cons('#skF_46'('#skF_51'),'#skF_50') = '#skF_50',
    inference(splitRight,[status(thm)],[c_25925]) ).

tff(c_20,plain,
    ! [V_33] :
      ( singletonP(cons(V_33,nil))
      | ~ ssItem(V_33)
      | ~ ssList(cons(V_33,nil)) ),
    inference(cnfTransformation,[status(thm)],[f_96]) ).

tff(c_2676,plain,
    ! [V_1287] :
      ( singletonP(cons(V_1287,'#skF_50'))
      | ~ ssItem(V_1287)
      | ~ ssList(cons(V_1287,'#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1360,c_1360,c_20]) ).

tff(c_2683,plain,
    ! [V_861] :
      ( singletonP(cons(V_861,'#skF_50'))
      | ~ ssItem(V_861)
      | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_166,c_2676]) ).

tff(c_2686,plain,
    ! [V_861] :
      ( singletonP(cons(V_861,'#skF_50'))
      | ~ ssItem(V_861) ),
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_2683]) ).

tff(c_26154,plain,
    ( singletonP('#skF_50')
    | ~ ssItem('#skF_46'('#skF_51')) ),
    inference(superposition,[status(thm),theory(equality)],[c_25934,c_2686]) ).

tff(c_26282,plain,
    singletonP('#skF_50'),
    inference(demodulation,[status(thm),theory(equality)],[c_1216,c_26154]) ).

tff(c_26284,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1401,c_26282]) ).

tff(c_26286,plain,
    nil != '#skF_50',
    inference(splitRight,[status(thm)],[c_1000]) ).

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

tff(c_26538,plain,
    ! [U_1993,V_1994] :
      ( neq(U_1993,V_1994)
      | ( V_1994 = U_1993 )
      | ~ ssList(V_1994)
      | ~ ssList(U_1993) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

tff(c_394,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1016]) ).

tff(c_384,plain,
    ~ neq('#skF_48',nil),
    inference(cnfTransformation,[status(thm)],[f_1016]) ).

tff(c_410,plain,
    ~ neq('#skF_50',nil),
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_384]) ).

tff(c_26552,plain,
    ( ( nil = '#skF_50' )
    | ~ ssList(nil)
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_26538,c_410]) ).

tff(c_26563,plain,
    nil = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_400,c_168,c_26552]) ).

tff(c_26565,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_26286,c_26563]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12  % Problem  : SWC214+1 : TPTP v8.1.2. Released v2.4.0.
% 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
% 0.13/0.35  % Computer : n027.cluster.edu
% 0.13/0.35  % Model    : x86_64 x86_64
% 0.13/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.35  % Memory   : 8042.1875MB
% 0.13/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.13/0.35  % CPULimit : 300
% 0.13/0.35  % WCLimit  : 300
% 0.13/0.35  % DateTime : Thu Aug  3 22:00:09 EDT 2023
% 0.13/0.35  % CPUTime  : 
% 19.73/7.65  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 19.73/7.66  
% 19.73/7.66  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 19.73/7.69  
% 19.73/7.69  Inference rules
% 19.73/7.69  ----------------------
% 19.73/7.69  #Ref     : 5
% 19.73/7.69  #Sup     : 5765
% 19.73/7.69  #Fact    : 0
% 19.73/7.69  #Define  : 0
% 19.73/7.69  #Split   : 43
% 19.73/7.69  #Chain   : 0
% 19.73/7.69  #Close   : 0
% 19.73/7.69  
% 19.73/7.69  Ordering : KBO
% 19.73/7.69  
% 19.73/7.69  Simplification rules
% 19.73/7.69  ----------------------
% 19.73/7.69  #Subsume      : 950
% 19.73/7.69  #Demod        : 4653
% 19.73/7.69  #Tautology    : 1464
% 19.73/7.69  #SimpNegUnit  : 403
% 19.73/7.69  #BackRed      : 142
% 19.73/7.69  
% 19.73/7.69  #Partial instantiations: 0
% 19.73/7.69  #Strategies tried      : 1
% 19.73/7.69  
% 19.73/7.69  Timing (in seconds)
% 19.73/7.69  ----------------------
% 19.73/7.70  Preprocessing        : 0.86
% 19.73/7.70  Parsing              : 0.39
% 19.73/7.70  CNF conversion       : 0.11
% 19.73/7.70  Main loop            : 5.76
% 19.73/7.70  Inferencing          : 1.44
% 19.73/7.70  Reduction            : 2.18
% 19.73/7.70  Demodulation         : 1.55
% 19.73/7.70  BG Simplification    : 0.12
% 19.73/7.70  Subsumption          : 1.54
% 19.73/7.70  Abstraction          : 0.10
% 19.73/7.70  MUC search           : 0.00
% 19.73/7.70  Cooper               : 0.00
% 19.73/7.70  Total                : 6.69
% 19.73/7.70  Index Insertion      : 0.00
% 19.73/7.70  Index Deletion       : 0.00
% 19.73/7.70  Index Matching       : 0.00
% 19.73/7.70  BG Taut test         : 0.00
%------------------------------------------------------------------------------