TSTP Solution File: SWC071+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWC071+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 : n023.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 11:01:02 EDT 2023

% Result   : Theorem 243.79s 219.29s
% Output   : CNFRefutation 243.79s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   89
% Syntax   : Number of formulae    :  184 (  48 unt;  78 typ;   0 def)
%            Number of atoms       :  237 (  98 equ)
%            Maximal formula atoms :   25 (   2 avg)
%            Number of connectives :  229 (  98   ~;  93   |;  11   &)
%                                         (   2 <=>;  25  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   27 (   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    :   59 (  59 usr;  10 con; 0-2 aty)
%            Number of variables   :   61 (;  57   !;   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_52 > #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_54 > #skF_40 > #skF_48 > #skF_3 > #skF_34 > #skF_29 > #skF_15 > #skF_32 > #skF_53 > #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_52',type,
    '#skF_52': $i ).

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_54',type,
    '#skF_54': $i ).

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_53',type,
    '#skF_53': $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_1042,negated_conjecture,
    ~ ! [U] :
        ( ssList(U)
       => ! [V] :
            ( ssList(V)
           => ! [W] :
                ( ssList(W)
               => ! [X] :
                    ( ssList(X)
                   => ( ( V != X )
                      | ( U != W )
                      | ? [Y] :
                          ( ssList(Y)
                          & neq(Y,nil)
                          & segmentP(V,Y)
                          & segmentP(U,Y) )
                      | ( ( nil = V )
                        & ( nil = U ) )
                      | ( ! [Z] :
                            ( ssItem(Z)
                           => ! [X1] :
                                ( ssList(X1)
                               => ! [X2] :
                                    ( ssList(X2)
                                   => ( ( cons(Z,nil) != W )
                                      | ( app(app(X1,W),X2) != X )
                                      | ? [X3] :
                                          ( ssItem(X3)
                                          & memberP(X1,X3)
                                          & lt(Z,X3) )
                                      | ? [X4] :
                                          ( ssItem(X4)
                                          & memberP(X2,X4)
                                          & lt(X4,Z) ) ) ) ) )
                        & ( ( nil != X )
                          | ( nil != W ) ) ) ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',co1) ).

tff(f_327,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssItem(V)
         => ( cons(V,U) != U ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax18) ).

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

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_667,axiom,
    ! [U] :
      ( ssList(U)
     => segmentP(U,U) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax55) ).

tff(f_399,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ssList(app(U,V)) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax26) ).

tff(f_859,axiom,
    ! [U] :
      ( ssList(U)
     => ( app(U,nil) = U ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax84) ).

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

tff(f_855,axiom,
    ! [U] :
      ( ssList(U)
     => ! [V] :
          ( ssList(V)
         => ( ( nil = app(U,V) )
          <=> ( ( nil = V )
              & ( nil = U ) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWC001+0.ax',ax83) ).

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_394,plain,
    ssList('#skF_50'),
    inference(cnfTransformation,[status(thm)],[f_1042]) ).

tff(c_412,plain,
    ( ssItem('#skF_52')
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1042]) ).

tff(c_441,plain,
    nil = '#skF_50',
    inference(splitLeft,[status(thm)],[c_412]) ).

tff(c_426,plain,
    ( ssItem('#skF_52')
    | ( nil = '#skF_51' ) ),
    inference(cnfTransformation,[status(thm)],[f_1042]) ).

tff(c_456,plain,
    ( ssItem('#skF_52')
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_441,c_426]) ).

tff(c_457,plain,
    '#skF_51' = '#skF_50',
    inference(splitLeft,[status(thm)],[c_456]) ).

tff(c_390,plain,
    '#skF_49' = '#skF_51',
    inference(cnfTransformation,[status(thm)],[f_1042]) ).

tff(c_388,plain,
    '#skF_48' = '#skF_50',
    inference(cnfTransformation,[status(thm)],[f_1042]) ).

tff(c_384,plain,
    ( ( nil != '#skF_48' )
    | ( nil != '#skF_49' ) ),
    inference(cnfTransformation,[status(thm)],[f_1042]) ).

tff(c_432,plain,
    ( ( nil != '#skF_50' )
    | ( nil != '#skF_51' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_388,c_384]) ).

tff(c_473,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_457,c_441,c_441,c_432]) ).

tff(c_474,plain,
    ssItem('#skF_52'),
    inference(splitRight,[status(thm)],[c_456]) ).

tff(c_475,plain,
    '#skF_51' != '#skF_50',
    inference(splitRight,[status(thm)],[c_456]) ).

tff(c_420,plain,
    ( ( cons('#skF_52',nil) = '#skF_50' )
    | ( nil = '#skF_51' ) ),
    inference(cnfTransformation,[status(thm)],[f_1042]) ).

tff(c_500,plain,
    ( ( cons('#skF_52','#skF_50') = '#skF_50' )
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_441,c_441,c_420]) ).

tff(c_501,plain,
    cons('#skF_52','#skF_50') = '#skF_50',
    inference(negUnitSimplification,[status(thm)],[c_475,c_500]) ).

tff(c_1057,plain,
    ! [V_1583,U_1584] :
      ( ( cons(V_1583,U_1584) != U_1584 )
      | ~ ssItem(V_1583)
      | ~ ssList(U_1584) ),
    inference(cnfTransformation,[status(thm)],[f_327]) ).

tff(c_1059,plain,
    ( ~ ssItem('#skF_52')
    | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_501,c_1057]) ).

tff(c_1063,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_474,c_1059]) ).

tff(c_1065,plain,
    nil != '#skF_50',
    inference(splitRight,[status(thm)],[c_412]) ).

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

tff(c_162,plain,
    ! [U_856,V_858] :
      ( neq(U_856,V_858)
      | ( V_858 = U_856 )
      | ~ ssList(V_858)
      | ~ ssList(U_856) ),
    inference(cnfTransformation,[status(thm)],[f_311]) ).

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

tff(c_424,plain,
    ( ssList('#skF_53')
    | ( nil = '#skF_51' ) ),
    inference(cnfTransformation,[status(thm)],[f_1042]) ).

tff(c_1067,plain,
    nil = '#skF_51',
    inference(splitLeft,[status(thm)],[c_424]) ).

tff(c_1068,plain,
    '#skF_51' != '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_1067,c_1065]) ).

tff(c_410,plain,
    ( ssList('#skF_53')
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1042]) ).

tff(c_1087,plain,
    ( ssList('#skF_53')
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1067,c_410]) ).

tff(c_1088,plain,
    ssList('#skF_53'),
    inference(negUnitSimplification,[status(thm)],[c_1068,c_1087]) ).

tff(c_192,plain,
    ! [U_896,V_898] :
      ( ssList(app(U_896,V_898))
      | ~ ssList(V_898)
      | ~ ssList(U_896) ),
    inference(cnfTransformation,[status(thm)],[f_399]) ).

tff(c_356,plain,
    ! [U_1080] :
      ( ( app(U_1080,nil) = U_1080 )
      | ~ ssList(U_1080) ),
    inference(cnfTransformation,[status(thm)],[f_859]) ).

tff(c_1134,plain,
    ! [U_1600] :
      ( ( app(U_1600,'#skF_51') = U_1600 )
      | ~ ssList(U_1600) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1067,c_356]) ).

tff(c_1149,plain,
    app('#skF_50','#skF_51') = '#skF_50',
    inference(resolution,[status(thm)],[c_394,c_1134]) ).

tff(c_408,plain,
    ( ssList('#skF_54')
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1042]) ).

tff(c_1066,plain,
    ssList('#skF_54'),
    inference(negUnitSimplification,[status(thm)],[c_1065,c_408]) ).

tff(c_330,plain,
    ! [U_1045] :
      ( ( hd(U_1045) = '#skF_46'(U_1045) )
      | ( nil = U_1045 )
      | ~ ssList(U_1045) ),
    inference(cnfTransformation,[status(thm)],[f_769]) ).

tff(c_1544,plain,
    ! [U_1653] :
      ( ( hd(U_1653) = '#skF_46'(U_1653) )
      | ( U_1653 = '#skF_51' )
      | ~ ssList(U_1653) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1067,c_330]) ).

tff(c_1650,plain,
    ( ( hd('#skF_54') = '#skF_46'('#skF_54') )
    | ( '#skF_54' = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_1066,c_1544]) ).

tff(c_1667,plain,
    '#skF_54' = '#skF_51',
    inference(splitLeft,[status(thm)],[c_1650]) ).

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

tff(c_1176,plain,
    ! [U_1602] :
      ( ( app('#skF_51',U_1602) = U_1602 )
      | ~ ssList(U_1602) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1067,c_196]) ).

tff(c_1191,plain,
    app('#skF_51','#skF_50') = '#skF_50',
    inference(resolution,[status(thm)],[c_394,c_1176]) ).

tff(c_1649,plain,
    ( ( hd('#skF_53') = '#skF_46'('#skF_53') )
    | ( '#skF_53' = '#skF_51' ) ),
    inference(resolution,[status(thm)],[c_1088,c_1544]) ).

tff(c_1666,plain,
    '#skF_53' = '#skF_51',
    inference(splitLeft,[status(thm)],[c_1649]) ).

tff(c_404,plain,
    ( ( app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_51' )
    | ( nil = '#skF_50' ) ),
    inference(cnfTransformation,[status(thm)],[f_1042]) ).

tff(c_1220,plain,
    ( ( app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_51' )
    | ( '#skF_51' = '#skF_50' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1067,c_404]) ).

tff(c_1221,plain,
    app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_51',
    inference(negUnitSimplification,[status(thm)],[c_1068,c_1220]) ).

tff(c_1669,plain,
    app(app('#skF_51','#skF_50'),'#skF_54') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_1666,c_1221]) ).

tff(c_1673,plain,
    app('#skF_50','#skF_54') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_1191,c_1669]) ).

tff(c_1692,plain,
    '#skF_51' = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_1149,c_1667,c_1673]) ).

tff(c_1693,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1068,c_1692]) ).

tff(c_1695,plain,
    '#skF_54' != '#skF_51',
    inference(splitRight,[status(thm)],[c_1650]) ).

tff(c_1697,plain,
    app(app('#skF_51','#skF_50'),'#skF_54') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_1666,c_1221]) ).

tff(c_1701,plain,
    app('#skF_50','#skF_54') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_1191,c_1697]) ).

tff(c_354,plain,
    ! [V_1079,U_1077] :
      ( ( nil = V_1079 )
      | ( app(U_1077,V_1079) != nil )
      | ~ ssList(V_1079)
      | ~ ssList(U_1077) ),
    inference(cnfTransformation,[status(thm)],[f_855]) ).

tff(c_2838,plain,
    ! [V_1696,U_1697] :
      ( ( V_1696 = '#skF_51' )
      | ( app(U_1697,V_1696) != '#skF_51' )
      | ~ ssList(V_1696)
      | ~ ssList(U_1697) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1067,c_1067,c_354]) ).

tff(c_2844,plain,
    ( ( '#skF_54' = '#skF_51' )
    | ~ ssList('#skF_54')
    | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_1701,c_2838]) ).

tff(c_2862,plain,
    '#skF_54' = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_1066,c_2844]) ).

tff(c_2864,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1695,c_2862]) ).

tff(c_2866,plain,
    '#skF_53' != '#skF_51',
    inference(splitRight,[status(thm)],[c_1649]) ).

tff(c_392,plain,
    ssList('#skF_51'),
    inference(cnfTransformation,[status(thm)],[f_1042]) ).

tff(c_2877,plain,
    '#skF_54' = '#skF_51',
    inference(splitLeft,[status(thm)],[c_1650]) ).

tff(c_2879,plain,
    app(app('#skF_53','#skF_50'),'#skF_51') = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_2877,c_1221]) ).

tff(c_352,plain,
    ! [U_1077,V_1079] :
      ( ( nil = U_1077 )
      | ( app(U_1077,V_1079) != nil )
      | ~ ssList(V_1079)
      | ~ ssList(U_1077) ),
    inference(cnfTransformation,[status(thm)],[f_855]) ).

tff(c_4594,plain,
    ! [U_1760,V_1761] :
      ( ( U_1760 = '#skF_51' )
      | ( app(U_1760,V_1761) != '#skF_51' )
      | ~ ssList(V_1761)
      | ~ ssList(U_1760) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1067,c_1067,c_352]) ).

tff(c_4604,plain,
    ( ( app('#skF_53','#skF_50') = '#skF_51' )
    | ~ ssList('#skF_51')
    | ~ ssList(app('#skF_53','#skF_50')) ),
    inference(superposition,[status(thm),theory(equality)],[c_2879,c_4594]) ).

tff(c_4627,plain,
    ( ( app('#skF_53','#skF_50') = '#skF_51' )
    | ~ ssList(app('#skF_53','#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_392,c_4604]) ).

tff(c_4642,plain,
    ~ ssList(app('#skF_53','#skF_50')),
    inference(splitLeft,[status(thm)],[c_4627]) ).

tff(c_4645,plain,
    ( ~ ssList('#skF_50')
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_4642]) ).

tff(c_4649,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1088,c_394,c_4645]) ).

tff(c_4650,plain,
    app('#skF_53','#skF_50') = '#skF_51',
    inference(splitRight,[status(thm)],[c_4627]) ).

tff(c_4593,plain,
    ! [U_1077,V_1079] :
      ( ( U_1077 = '#skF_51' )
      | ( app(U_1077,V_1079) != '#skF_51' )
      | ~ ssList(V_1079)
      | ~ ssList(U_1077) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1067,c_1067,c_352]) ).

tff(c_4699,plain,
    ( ( '#skF_53' = '#skF_51' )
    | ~ ssList('#skF_50')
    | ~ ssList('#skF_53') ),
    inference(superposition,[status(thm),theory(equality)],[c_4650,c_4593]) ).

tff(c_4709,plain,
    '#skF_53' = '#skF_51',
    inference(demodulation,[status(thm),theory(equality)],[c_1088,c_394,c_4699]) ).

tff(c_4711,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2866,c_4709]) ).

tff(c_4713,plain,
    '#skF_54' != '#skF_51',
    inference(splitRight,[status(thm)],[c_1650]) ).

tff(c_5687,plain,
    ! [V_1797,U_1798] :
      ( ( V_1797 = '#skF_51' )
      | ( app(U_1798,V_1797) != '#skF_51' )
      | ~ ssList(V_1797)
      | ~ ssList(U_1798) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1067,c_1067,c_354]) ).

tff(c_5697,plain,
    ( ( '#skF_54' = '#skF_51' )
    | ~ ssList('#skF_54')
    | ~ ssList(app('#skF_53','#skF_50')) ),
    inference(superposition,[status(thm),theory(equality)],[c_1221,c_5687]) ).

tff(c_5724,plain,
    ( ( '#skF_54' = '#skF_51' )
    | ~ ssList(app('#skF_53','#skF_50')) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1066,c_5697]) ).

tff(c_5725,plain,
    ~ ssList(app('#skF_53','#skF_50')),
    inference(negUnitSimplification,[status(thm)],[c_4713,c_5724]) ).

tff(c_5747,plain,
    ( ~ ssList('#skF_50')
    | ~ ssList('#skF_53') ),
    inference(resolution,[status(thm)],[c_192,c_5725]) ).

tff(c_5751,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_1088,c_394,c_5747]) ).

tff(c_5752,plain,
    ssList('#skF_53'),
    inference(splitRight,[status(thm)],[c_424]) ).

tff(c_5838,plain,
    app(app('#skF_53','#skF_50'),'#skF_54') = '#skF_51',
    inference(negUnitSimplification,[status(thm)],[c_1065,c_404]) ).

tff(c_369126,plain,
    ! [W_6825,U_6826,X_6827,V_6828] :
      ( segmentP(app(app(W_6825,U_6826),X_6827),V_6828)
      | ~ segmentP(U_6826,V_6828)
      | ~ ssList(X_6827)
      | ~ ssList(W_6825)
      | ~ ssList(V_6828)
      | ~ ssList(U_6826) ),
    inference(cnfTransformation,[status(thm)],[f_682]) ).

tff(c_369365,plain,
    ! [V_6828] :
      ( segmentP('#skF_51',V_6828)
      | ~ segmentP('#skF_50',V_6828)
      | ~ ssList('#skF_54')
      | ~ ssList('#skF_53')
      | ~ ssList(V_6828)
      | ~ ssList('#skF_50') ),
    inference(superposition,[status(thm),theory(equality)],[c_5838,c_369126]) ).

tff(c_369527,plain,
    ! [V_6829] :
      ( segmentP('#skF_51',V_6829)
      | ~ segmentP('#skF_50',V_6829)
      | ~ ssList(V_6829) ),
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_5752,c_1066,c_369365]) ).

tff(c_386,plain,
    ! [Y_1493] :
      ( ~ segmentP('#skF_48',Y_1493)
      | ~ segmentP('#skF_49',Y_1493)
      | ~ neq(Y_1493,nil)
      | ~ ssList(Y_1493) ),
    inference(cnfTransformation,[status(thm)],[f_1042]) ).

tff(c_431,plain,
    ! [Y_1493] :
      ( ~ segmentP('#skF_50',Y_1493)
      | ~ segmentP('#skF_51',Y_1493)
      | ~ neq(Y_1493,nil)
      | ~ ssList(Y_1493) ),
    inference(demodulation,[status(thm),theory(equality)],[c_390,c_388,c_386]) ).

tff(c_370010,plain,
    ! [V_6837] :
      ( ~ neq(V_6837,nil)
      | ~ segmentP('#skF_50',V_6837)
      | ~ ssList(V_6837) ),
    inference(resolution,[status(thm)],[c_369527,c_431]) ).

tff(c_370014,plain,
    ( ~ neq('#skF_50',nil)
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_270,c_370010]) ).

tff(c_370021,plain,
    ~ neq('#skF_50',nil),
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_370014]) ).

tff(c_370056,plain,
    ( ( nil = '#skF_50' )
    | ~ ssList(nil)
    | ~ ssList('#skF_50') ),
    inference(resolution,[status(thm)],[c_162,c_370021]) ).

tff(c_370062,plain,
    nil = '#skF_50',
    inference(demodulation,[status(thm),theory(equality)],[c_394,c_168,c_370056]) ).

tff(c_370064,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1065,c_370062]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.07/0.13  % Problem  : SWC071+1 : TPTP v8.1.2. Released v2.4.0.
% 0.07/0.14  % 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
% 0.14/0.36  % Computer : n023.cluster.edu
% 0.14/0.36  % Model    : x86_64 x86_64
% 0.14/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.36  % Memory   : 8042.1875MB
% 0.14/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.36  % CPULimit : 300
% 0.14/0.36  % WCLimit  : 300
% 0.14/0.36  % DateTime : Thu Aug  3 21:49:22 EDT 2023
% 0.14/0.36  % CPUTime  : 
% 243.79/219.29  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 243.79/219.30  
% 243.79/219.30  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 243.79/219.34  
% 243.79/219.34  Inference rules
% 243.79/219.34  ----------------------
% 243.79/219.34  #Ref     : 28
% 243.79/219.34  #Sup     : 79533
% 243.79/219.34  #Fact    : 0
% 243.79/219.34  #Define  : 0
% 243.79/219.34  #Split   : 446
% 243.79/219.34  #Chain   : 0
% 243.79/219.34  #Close   : 0
% 243.79/219.34  
% 243.79/219.34  Ordering : KBO
% 243.79/219.34  
% 243.79/219.34  Simplification rules
% 243.79/219.34  ----------------------
% 243.79/219.34  #Subsume      : 14011
% 243.79/219.34  #Demod        : 98852
% 243.79/219.34  #Tautology    : 13302
% 243.79/219.34  #SimpNegUnit  : 8466
% 243.79/219.34  #BackRed      : 1151
% 243.79/219.34  
% 243.79/219.34  #Partial instantiations: 0
% 243.79/219.34  #Strategies tried      : 1
% 243.79/219.34  
% 243.79/219.34  Timing (in seconds)
% 243.79/219.34  ----------------------
% 243.79/219.34  Preprocessing        : 0.88
% 243.79/219.34  Parsing              : 0.40
% 243.79/219.34  CNF conversion       : 0.11
% 243.79/219.34  Main loop            : 217.34
% 243.79/219.34  Inferencing          : 22.39
% 243.79/219.34  Reduction            : 108.57
% 243.79/219.34  Demodulation         : 78.05
% 243.79/219.34  BG Simplification    : 0.60
% 243.79/219.34  Subsumption          : 65.38
% 243.79/219.34  Abstraction          : 1.16
% 243.79/219.34  MUC search           : 0.00
% 243.79/219.34  Cooper               : 0.00
% 243.79/219.34  Total                : 218.31
% 243.79/219.35  Index Insertion      : 0.00
% 243.79/219.35  Index Deletion       : 0.00
% 243.79/219.35  Index Matching       : 0.00
% 243.79/219.35  BG Taut test         : 0.00
%------------------------------------------------------------------------------