TSTP Solution File: GEO127+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : GEO127+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 : n026.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 10:38:15 EDT 2023

% Result   : Theorem 7.77s 2.85s
% Output   : CNFRefutation 7.77s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   60
% Syntax   : Number of formulae    :  144 (  52 unt;  51 typ;   0 def)
%            Number of atoms       :  158 (  17 equ)
%            Maximal formula atoms :    8 (   1 avg)
%            Number of connectives :  115 (  50   ~;  47   |;   9   &)
%                                         (   6 <=>;   3  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   11 (   3 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :  102 (  45   >;  57   *;   0   +;   0  <<)
%            Number of predicates  :   15 (  13 usr;   1 prp; 0-4 aty)
%            Number of functors    :   38 (  38 usr;   6 con; 0-5 aty)
%            Number of variables   :   81 (;  76   !;   5   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ between_o > between_c > ordered_by > meet > start_point > part_of > inner_point > incident_o > incident_c > finish_point > end_point > open > closed > sum > #nlpp > underlying_curve > #skF_9 > #skF_33 > #skF_7 > #skF_24 > #skF_11 > #skF_26 > #skF_6 > #skF_30 > #skF_31 > #skF_19 > #skF_17 > #skF_36 > #skF_20 > #skF_8 > #skF_13 > #skF_14 > #skF_12 > #skF_18 > #skF_16 > #skF_10 > #skF_2 > #skF_32 > #skF_23 > #skF_28 > #skF_25 > #skF_3 > #skF_35 > #skF_29 > #skF_27 > #skF_1 > #skF_5 > #skF_22 > #skF_15 > #skF_4 > #skF_34 > #skF_21

%Foreground sorts:

%Background operators:

%Foreground operators:
tff('#skF_9',type,
    '#skF_9': $i > $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff('#skF_36',type,
    '#skF_36': $i ).

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

tff(f_152,axiom,
    ! [C] :
    ? [P] : inner_point(P,C),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',c3) ).

tff(f_91,axiom,
    ! [P,C] :
      ( inner_point(P,C)
    <=> ( incident_c(P,C)
        & ~ end_point(P,C) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',inner_point_defn) ).

tff(f_317,axiom,
    ! [O] :
    ? [C] :
      ( open(C)
      & ! [P] :
          ( incident_o(P,O)
        <=> incident_c(P,C) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',o2) ).

tff(f_330,axiom,
    ! [O] :
    ? [P] : start_point(P,O),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',o4) ).

tff(f_371,negated_conjecture,
    ~ ! [O,P] :
        ( incident_o(P,O)
      <=> ? [Q] :
            ( ordered_by(O,P,Q)
            | ordered_by(O,Q,P) ) ),
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',theorem_4_12) ).

tff(f_291,axiom,
    ! [P,O] :
      ( start_point(P,O)
    <=> ( incident_o(P,O)
        & ! [Q] :
            ( ( ( P != Q )
              & incident_o(Q,O) )
           => ordered_by(O,P,Q) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',start_point_defn) ).

tff(f_117,axiom,
    ! [C] :
      ( open(C)
    <=> ? [P] : end_point(P,C) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',open_defn) ).

tff(f_84,axiom,
    ! [P,C] :
      ( end_point(P,C)
    <=> ( incident_c(P,C)
        & ! [C1,C2] :
            ( ( part_of(C1,C)
              & part_of(C2,C)
              & incident_c(P,C1)
              & incident_c(P,C2) )
           => ( part_of(C1,C2)
              | part_of(C2,C1) ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO004+0.ax',end_point_defn) ).

tff(f_309,axiom,
    ! [O,P,Q] :
      ( ordered_by(O,P,Q)
     => ( incident_o(P,O)
        & incident_o(Q,O) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/GEO004+2.ax',o1) ).

tff(c_74,plain,
    ! [C_44] : inner_point('#skF_9'(C_44),C_44),
    inference(cnfTransformation,[status(thm)],[f_152]) ).

tff(c_1507,plain,
    ! [P_368,C_369] :
      ( incident_c(P_368,C_369)
      | ~ inner_point(P_368,C_369) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_1511,plain,
    ! [C_44] : incident_c('#skF_9'(C_44),C_44),
    inference(resolution,[status(thm)],[c_74,c_1507]) ).

tff(c_1549,plain,
    ! [P_395,O_396] :
      ( incident_o(P_395,O_396)
      | ~ incident_c(P_395,'#skF_19'(O_396)) ),
    inference(cnfTransformation,[status(thm)],[f_317]) ).

tff(c_1558,plain,
    ! [O_396] : incident_o('#skF_9'('#skF_19'(O_396)),O_396),
    inference(resolution,[status(thm)],[c_1511,c_1549]) ).

tff(c_166,plain,
    ! [O_115] : start_point('#skF_23'(O_115),O_115),
    inference(cnfTransformation,[status(thm)],[f_330]) ).

tff(c_202,plain,
    ( ~ incident_o('#skF_32','#skF_31')
    | incident_o('#skF_36','#skF_35') ),
    inference(cnfTransformation,[status(thm)],[f_371]) ).

tff(c_218,plain,
    ~ incident_o('#skF_32','#skF_31'),
    inference(splitLeft,[status(thm)],[c_202]) ).

tff(c_219,plain,
    ! [P_152,C_153] :
      ( incident_c(P_152,C_153)
      | ~ inner_point(P_152,C_153) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_223,plain,
    ! [C_44] : incident_c('#skF_9'(C_44),C_44),
    inference(resolution,[status(thm)],[c_74,c_219]) ).

tff(c_265,plain,
    ! [P_165,O_166] :
      ( incident_o(P_165,O_166)
      | ~ incident_c(P_165,'#skF_19'(O_166)) ),
    inference(cnfTransformation,[status(thm)],[f_317]) ).

tff(c_274,plain,
    ! [O_166] : incident_o('#skF_9'('#skF_19'(O_166)),O_166),
    inference(resolution,[status(thm)],[c_223,c_265]) ).

tff(c_204,plain,
    ( ordered_by('#skF_31','#skF_32','#skF_34')
    | ordered_by('#skF_31','#skF_33','#skF_32')
    | incident_o('#skF_36','#skF_35') ),
    inference(cnfTransformation,[status(thm)],[f_371]) ).

tff(c_340,plain,
    incident_o('#skF_36','#skF_35'),
    inference(splitLeft,[status(thm)],[c_204]) ).

tff(c_1006,plain,
    ! [O_330,P_331,Q_332] :
      ( ordered_by(O_330,P_331,Q_332)
      | ~ incident_o(Q_332,O_330)
      | ( Q_332 = P_331 )
      | ~ start_point(P_331,O_330) ),
    inference(cnfTransformation,[status(thm)],[f_291]) ).

tff(c_200,plain,
    ! [Q_136] :
      ( ordered_by('#skF_31','#skF_32','#skF_34')
      | ordered_by('#skF_31','#skF_33','#skF_32')
      | ~ ordered_by('#skF_35',Q_136,'#skF_36') ),
    inference(cnfTransformation,[status(thm)],[f_371]) ).

tff(c_416,plain,
    ! [Q_136] : ~ ordered_by('#skF_35',Q_136,'#skF_36'),
    inference(splitLeft,[status(thm)],[c_200]) ).

tff(c_1018,plain,
    ! [P_331] :
      ( ~ incident_o('#skF_36','#skF_35')
      | ( P_331 = '#skF_36' )
      | ~ start_point(P_331,'#skF_35') ),
    inference(resolution,[status(thm)],[c_1006,c_416]) ).

tff(c_1032,plain,
    ! [P_333] :
      ( ( P_333 = '#skF_36' )
      | ~ start_point(P_333,'#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_340,c_1018]) ).

tff(c_1042,plain,
    '#skF_23'('#skF_35') = '#skF_36',
    inference(resolution,[status(thm)],[c_166,c_1032]) ).

tff(c_1052,plain,
    start_point('#skF_36','#skF_35'),
    inference(superposition,[status(thm),theory(equality)],[c_1042,c_166]) ).

tff(c_196,plain,
    ! [Q_136] :
      ( ordered_by('#skF_31','#skF_32','#skF_34')
      | ordered_by('#skF_31','#skF_33','#skF_32')
      | ~ ordered_by('#skF_35','#skF_36',Q_136) ),
    inference(cnfTransformation,[status(thm)],[f_371]) ).

tff(c_474,plain,
    ! [Q_136] : ~ ordered_by('#skF_35','#skF_36',Q_136),
    inference(splitLeft,[status(thm)],[c_196]) ).

tff(c_1026,plain,
    ! [Q_332] :
      ( ~ incident_o(Q_332,'#skF_35')
      | ( Q_332 = '#skF_36' )
      | ~ start_point('#skF_36','#skF_35') ),
    inference(resolution,[status(thm)],[c_1006,c_474]) ).

tff(c_1070,plain,
    ! [Q_334] :
      ( ~ incident_o(Q_334,'#skF_35')
      | ( Q_334 = '#skF_36' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_1052,c_1026]) ).

tff(c_1143,plain,
    '#skF_9'('#skF_19'('#skF_35')) = '#skF_36',
    inference(resolution,[status(thm)],[c_274,c_1070]) ).

tff(c_212,plain,
    ! [P_149,C_150] :
      ( ~ end_point(P_149,C_150)
      | ~ inner_point(P_149,C_150) ),
    inference(cnfTransformation,[status(thm)],[f_91]) ).

tff(c_216,plain,
    ! [C_44] : ~ end_point('#skF_9'(C_44),C_44),
    inference(resolution,[status(thm)],[c_74,c_212]) ).

tff(c_1209,plain,
    ~ end_point('#skF_36','#skF_19'('#skF_35')),
    inference(superposition,[status(thm),theory(equality)],[c_1143,c_216]) ).

tff(c_150,plain,
    ! [O_95] : open('#skF_19'(O_95)),
    inference(cnfTransformation,[status(thm)],[f_317]) ).

tff(c_66,plain,
    ! [C_32] :
      ( end_point('#skF_8'(C_32),C_32)
      | ~ open(C_32) ),
    inference(cnfTransformation,[status(thm)],[f_117]) ).

tff(c_28,plain,
    ! [P_12,C_13] :
      ( incident_c(P_12,C_13)
      | ~ end_point(P_12,C_13) ),
    inference(cnfTransformation,[status(thm)],[f_84]) ).

tff(c_324,plain,
    ! [P_193,O_194] :
      ( incident_o(P_193,O_194)
      | ~ end_point(P_193,'#skF_19'(O_194)) ),
    inference(resolution,[status(thm)],[c_28,c_265]) ).

tff(c_332,plain,
    ! [O_194] :
      ( incident_o('#skF_8'('#skF_19'(O_194)),O_194)
      | ~ open('#skF_19'(O_194)) ),
    inference(resolution,[status(thm)],[c_66,c_324]) ).

tff(c_338,plain,
    ! [O_194] : incident_o('#skF_8'('#skF_19'(O_194)),O_194),
    inference(demodulation,[status(thm),theory(equality)],[c_150,c_332]) ).

tff(c_1138,plain,
    '#skF_8'('#skF_19'('#skF_35')) = '#skF_36',
    inference(resolution,[status(thm)],[c_338,c_1070]) ).

tff(c_1156,plain,
    ( end_point('#skF_36','#skF_19'('#skF_35'))
    | ~ open('#skF_19'('#skF_35')) ),
    inference(superposition,[status(thm),theory(equality)],[c_1138,c_66]) ).

tff(c_1163,plain,
    end_point('#skF_36','#skF_19'('#skF_35')),
    inference(demodulation,[status(thm),theory(equality)],[c_150,c_1156]) ).

tff(c_1308,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_1209,c_1163]) ).

tff(c_1309,plain,
    ( ordered_by('#skF_31','#skF_33','#skF_32')
    | ordered_by('#skF_31','#skF_32','#skF_34') ),
    inference(splitRight,[status(thm)],[c_196]) ).

tff(c_1310,plain,
    ordered_by('#skF_31','#skF_32','#skF_34'),
    inference(splitLeft,[status(thm)],[c_1309]) ).

tff(c_144,plain,
    ! [P_93,O_92,Q_94] :
      ( incident_o(P_93,O_92)
      | ~ ordered_by(O_92,P_93,Q_94) ),
    inference(cnfTransformation,[status(thm)],[f_309]) ).

tff(c_1313,plain,
    incident_o('#skF_32','#skF_31'),
    inference(resolution,[status(thm)],[c_1310,c_144]) ).

tff(c_1320,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_218,c_1313]) ).

tff(c_1321,plain,
    ordered_by('#skF_31','#skF_33','#skF_32'),
    inference(splitRight,[status(thm)],[c_1309]) ).

tff(c_142,plain,
    ! [Q_94,O_92,P_93] :
      ( incident_o(Q_94,O_92)
      | ~ ordered_by(O_92,P_93,Q_94) ),
    inference(cnfTransformation,[status(thm)],[f_309]) ).

tff(c_1328,plain,
    incident_o('#skF_32','#skF_31'),
    inference(resolution,[status(thm)],[c_1321,c_142]) ).

tff(c_1333,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_218,c_1328]) ).

tff(c_1334,plain,
    ( ordered_by('#skF_31','#skF_33','#skF_32')
    | ordered_by('#skF_31','#skF_32','#skF_34') ),
    inference(splitRight,[status(thm)],[c_200]) ).

tff(c_1335,plain,
    ordered_by('#skF_31','#skF_32','#skF_34'),
    inference(splitLeft,[status(thm)],[c_1334]) ).

tff(c_1338,plain,
    incident_o('#skF_32','#skF_31'),
    inference(resolution,[status(thm)],[c_1335,c_144]) ).

tff(c_1345,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_218,c_1338]) ).

tff(c_1346,plain,
    ordered_by('#skF_31','#skF_33','#skF_32'),
    inference(splitRight,[status(thm)],[c_1334]) ).

tff(c_1353,plain,
    incident_o('#skF_32','#skF_31'),
    inference(resolution,[status(thm)],[c_1346,c_142]) ).

tff(c_1358,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_218,c_1353]) ).

tff(c_1359,plain,
    ( ordered_by('#skF_31','#skF_33','#skF_32')
    | ordered_by('#skF_31','#skF_32','#skF_34') ),
    inference(splitRight,[status(thm)],[c_204]) ).

tff(c_1441,plain,
    ordered_by('#skF_31','#skF_32','#skF_34'),
    inference(splitLeft,[status(thm)],[c_1359]) ).

tff(c_1444,plain,
    incident_o('#skF_32','#skF_31'),
    inference(resolution,[status(thm)],[c_1441,c_144]) ).

tff(c_1451,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_218,c_1444]) ).

tff(c_1452,plain,
    ordered_by('#skF_31','#skF_33','#skF_32'),
    inference(splitRight,[status(thm)],[c_1359]) ).

tff(c_1461,plain,
    incident_o('#skF_32','#skF_31'),
    inference(resolution,[status(thm)],[c_1452,c_142]) ).

tff(c_1466,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_218,c_1461]) ).

tff(c_1467,plain,
    incident_o('#skF_36','#skF_35'),
    inference(splitRight,[status(thm)],[c_202]) ).

tff(c_2604,plain,
    ! [O_603,P_604,Q_605] :
      ( ordered_by(O_603,P_604,Q_605)
      | ~ incident_o(Q_605,O_603)
      | ( Q_605 = P_604 )
      | ~ start_point(P_604,O_603) ),
    inference(cnfTransformation,[status(thm)],[f_291]) ).

tff(c_1468,plain,
    incident_o('#skF_32','#skF_31'),
    inference(splitRight,[status(thm)],[c_202]) ).

tff(c_198,plain,
    ! [Q_136] :
      ( ~ incident_o('#skF_32','#skF_31')
      | ~ ordered_by('#skF_35',Q_136,'#skF_36') ),
    inference(cnfTransformation,[status(thm)],[f_371]) ).

tff(c_1525,plain,
    ! [Q_136] : ~ ordered_by('#skF_35',Q_136,'#skF_36'),
    inference(demodulation,[status(thm),theory(equality)],[c_1468,c_198]) ).

tff(c_2619,plain,
    ! [P_604] :
      ( ~ incident_o('#skF_36','#skF_35')
      | ( P_604 = '#skF_36' )
      | ~ start_point(P_604,'#skF_35') ),
    inference(resolution,[status(thm)],[c_2604,c_1525]) ).

tff(c_2635,plain,
    ! [P_606] :
      ( ( P_606 = '#skF_36' )
      | ~ start_point(P_606,'#skF_35') ),
    inference(demodulation,[status(thm),theory(equality)],[c_1467,c_2619]) ).

tff(c_2645,plain,
    '#skF_23'('#skF_35') = '#skF_36',
    inference(resolution,[status(thm)],[c_166,c_2635]) ).

tff(c_2656,plain,
    start_point('#skF_36','#skF_35'),
    inference(superposition,[status(thm),theory(equality)],[c_2645,c_166]) ).

tff(c_194,plain,
    ! [Q_136] :
      ( ~ incident_o('#skF_32','#skF_31')
      | ~ ordered_by('#skF_35','#skF_36',Q_136) ),
    inference(cnfTransformation,[status(thm)],[f_371]) ).

tff(c_1486,plain,
    ! [Q_136] : ~ ordered_by('#skF_35','#skF_36',Q_136),
    inference(demodulation,[status(thm),theory(equality)],[c_1468,c_194]) ).

tff(c_2634,plain,
    ! [Q_605] :
      ( ~ incident_o(Q_605,'#skF_35')
      | ( Q_605 = '#skF_36' )
      | ~ start_point('#skF_36','#skF_35') ),
    inference(resolution,[status(thm)],[c_2604,c_1486]) ).

tff(c_2675,plain,
    ! [Q_607] :
      ( ~ incident_o(Q_607,'#skF_35')
      | ( Q_607 = '#skF_36' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_2656,c_2634]) ).

tff(c_2765,plain,
    '#skF_9'('#skF_19'('#skF_35')) = '#skF_36',
    inference(resolution,[status(thm)],[c_1558,c_2675]) ).

tff(c_2869,plain,
    ~ end_point('#skF_36','#skF_19'('#skF_35')),
    inference(superposition,[status(thm),theory(equality)],[c_2765,c_216]) ).

tff(c_1566,plain,
    ! [P_400,O_401] :
      ( incident_o(P_400,O_401)
      | ~ end_point(P_400,'#skF_19'(O_401)) ),
    inference(resolution,[status(thm)],[c_28,c_1549]) ).

tff(c_1570,plain,
    ! [O_401] :
      ( incident_o('#skF_8'('#skF_19'(O_401)),O_401)
      | ~ open('#skF_19'(O_401)) ),
    inference(resolution,[status(thm)],[c_66,c_1566]) ).

tff(c_1577,plain,
    ! [O_401] : incident_o('#skF_8'('#skF_19'(O_401)),O_401),
    inference(demodulation,[status(thm),theory(equality)],[c_150,c_1570]) ).

tff(c_2764,plain,
    '#skF_8'('#skF_19'('#skF_35')) = '#skF_36',
    inference(resolution,[status(thm)],[c_1577,c_2675]) ).

tff(c_2886,plain,
    ( end_point('#skF_36','#skF_19'('#skF_35'))
    | ~ open('#skF_19'('#skF_35')) ),
    inference(superposition,[status(thm),theory(equality)],[c_2764,c_66]) ).

tff(c_2893,plain,
    end_point('#skF_36','#skF_19'('#skF_35')),
    inference(demodulation,[status(thm),theory(equality)],[c_150,c_2886]) ).

tff(c_2928,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_2869,c_2893]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : GEO127+1 : TPTP v8.1.2. Released v2.4.0.
% 0.00/0.14  % 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
% 0.14/0.35  % Computer : n026.cluster.edu
% 0.14/0.35  % Model    : x86_64 x86_64
% 0.14/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35  % Memory   : 8042.1875MB
% 0.14/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35  % CPULimit : 300
% 0.14/0.35  % WCLimit  : 300
% 0.14/0.35  % DateTime : Fri Aug  4 01:03:32 EDT 2023
% 0.14/0.35  % CPUTime  : 
% 7.77/2.85  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 7.77/2.86  
% 7.77/2.86  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 7.77/2.90  
% 7.77/2.90  Inference rules
% 7.77/2.90  ----------------------
% 7.77/2.90  #Ref     : 0
% 7.77/2.90  #Sup     : 576
% 7.77/2.90  #Fact    : 0
% 7.77/2.90  #Define  : 0
% 7.77/2.90  #Split   : 14
% 7.77/2.90  #Chain   : 0
% 7.77/2.90  #Close   : 0
% 7.77/2.90  
% 7.77/2.90  Ordering : KBO
% 7.77/2.90  
% 7.77/2.90  Simplification rules
% 7.77/2.90  ----------------------
% 7.77/2.90  #Subsume      : 59
% 7.77/2.90  #Demod        : 60
% 7.77/2.90  #Tautology    : 99
% 7.77/2.90  #SimpNegUnit  : 15
% 7.77/2.90  #BackRed      : 1
% 7.77/2.90  
% 7.77/2.90  #Partial instantiations: 0
% 7.77/2.90  #Strategies tried      : 1
% 7.77/2.90  
% 7.77/2.90  Timing (in seconds)
% 7.77/2.90  ----------------------
% 7.77/2.91  Preprocessing        : 0.70
% 7.77/2.91  Parsing              : 0.34
% 7.77/2.91  CNF conversion       : 0.07
% 7.77/2.91  Main loop            : 1.07
% 7.77/2.91  Inferencing          : 0.41
% 7.77/2.91  Reduction            : 0.28
% 7.77/2.91  Demodulation         : 0.18
% 7.77/2.91  BG Simplification    : 0.06
% 7.77/2.91  Subsumption          : 0.22
% 7.77/2.91  Abstraction          : 0.04
% 7.77/2.91  MUC search           : 0.00
% 7.77/2.91  Cooper               : 0.00
% 7.77/2.91  Total                : 1.84
% 7.77/2.91  Index Insertion      : 0.00
% 7.77/2.91  Index Deletion       : 0.00
% 7.77/2.91  Index Matching       : 0.00
% 7.77/2.91  BG Taut test         : 0.00
%------------------------------------------------------------------------------