TSTP Solution File: SWW101+1 by Beagle---0.9.51

View Problem - Process Solution

%------------------------------------------------------------------------------
% File     : Beagle---0.9.51
% Problem  : SWW101+1 : TPTP v8.1.2. Released v5.2.0.
% 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 : n001.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 11:06:47 EDT 2023

% Result   : Theorem 7.80s 2.94s
% Output   : CNFRefutation 8.18s
% Verified : 
% SZS Type : Refutation
%            Derivation depth      :   12
%            Number of leaves      :   53
% Syntax   : Number of formulae    :  169 (  87 unt;  38 typ;   0 def)
%            Number of atoms       :  203 ( 147 equ)
%            Maximal formula atoms :    9 (   1 avg)
%            Number of connectives :  111 (  39   ~;  55   |;  12   &)
%                                         (   4 <=>;   1  =>;   0  <=;   0 <~>)
%            Maximal formula depth :   10 (   2 avg)
%            Maximal term depth    :    3 (   1 avg)
%            Number of types       :    2 (   0 usr)
%            Number of type conns  :   57 (  32   >;  25   *;   0   +;   0  <<)
%            Number of predicates  :    6 (   4 usr;   1 prp; 0-2 aty)
%            Number of functors    :   34 (  34 usr;   6 con; 0-3 aty)
%            Number of variables   :   48 (;  46   !;   2   ?;   0   :)

% Comments : 
%------------------------------------------------------------------------------
%$ forallprefers > existsprefers > d > bool > f4 > f3 > f2 > f1 > or2 > or1 > lazy_impl > lazy_and2 > lazy_and1 > impl > f6 > f5 > apply > and2 > and1 > #nlpp > prop > phi > not2 > not1 > f7 > exists2 > exists1 > true > false2 > false1 > false > err > #skF_4 > #skF_7 > #skF_3 > #skF_2 > #skF_1 > #skF_5 > #skF_6

%Foreground sorts:

%Background operators:

%Foreground operators:
tff(f5,type,
    f5: ( $i * $i ) > $i ).

tff(f1,type,
    f1: ( $i * $i * $i ) > $i ).

tff(or1,type,
    or1: ( $i * $i ) > $i ).

tff(exists2,type,
    exists2: $i > $i ).

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

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

tff(and1,type,
    and1: ( $i * $i ) > $i ).

tff(lazy_and1,type,
    lazy_and1: ( $i * $i ) > $i ).

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

tff(f7,type,
    f7: $i > $i ).

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

tff(false1,type,
    false1: $i ).

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

tff(and2,type,
    and2: ( $i * $i ) > $i ).

tff(not2,type,
    not2: $i > $i ).

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

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

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

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

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

tff(f2,type,
    f2: ( $i * $i * $i ) > $i ).

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

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

tff(f4,type,
    f4: ( $i * $i * $i ) > $i ).

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

tff(exists1,type,
    exists1: $i > $i ).

tff(not1,type,
    not1: $i > $i ).

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

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

tff(lazy_and2,type,
    lazy_and2: ( $i * $i ) > $i ).

tff(or2,type,
    or2: ( $i * $i ) > $i ).

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

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

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

tff(f6,type,
    f6: ( $i * $i ) > $i ).

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

tff(false2,type,
    false2: $i ).

tff(f3,type,
    f3: ( $i * $i * $i ) > $i ).

tff(f_82,axiom,
    ( d(true)
    & d(false)
    & d(err) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',false_true_err_in_d) ).

tff(f_150,axiom,
    ! [X] :
      ( ( d(X)
        & ( phi(X) = X ) )
      | ( ~ d(X)
        & ( phi(X) = err ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_phi) ).

tff(f_67,axiom,
    ! [X] :
      ( bool(X)
    <=> ( ( X = false )
        | ( X = true ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_bool) ).

tff(f_158,axiom,
    ! [X] :
      ( ( prop(X) = true )
    <=> bool(X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',prop_true) ).

tff(f_353,axiom,
    ! [P] : ( f7(P) = lazy_impl(prop(P),P) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_f7) ).

tff(f_202,axiom,
    ! [B] : ( lazy_impl(true,B) = phi(B) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom3) ).

tff(f_76,axiom,
    ( ( true != false )
    & ( true != err )
    & ( false != err ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',distinct_false_true_err) ).

tff(f_200,axiom,
    ! [B] : ( lazy_impl(false,B) = true ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',lazy_impl_axiom2) ).

tff(f_163,axiom,
    ! [X] :
      ( ( prop(X) = false )
    <=> ~ bool(X) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',prop_false) ).

tff(f_114,axiom,
    ! [X,Y] :
      ( forallprefers(X,Y)
    <=> ( ( ~ d(X)
          & d(Y) )
        | ( d(X)
          & d(Y)
          & ~ bool(X)
          & bool(Y) )
        | ( ( X = false )
          & ( Y = true ) ) ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_forallprefers) ).

tff(f_359,axiom,
    ? [P] :
      ( ( false2 = phi(f7(P)) )
      & ~ ? [P1] : forallprefers(f7(P1),f7(P)) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_false2) ).

tff(f_348,axiom,
    false1 = false,
    file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_false1) ).

tff(f_380,negated_conjecture,
    false1 != false2,
    file('/export/starexec/sandbox/benchmark/theBenchmark.p',false1_false2) ).

tff(f_185,axiom,
    ! [B] :
      ( bool(B)
     => ( impl(false,B) = true ) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',impl_axiom3) ).

tff(f_376,axiom,
    ! [P] : ( not2(P) = impl(P,false2) ),
    file('/export/starexec/sandbox/benchmark/Axioms/SWV012+0.ax',def_not2) ).

tff(c_16,plain,
    d(false),
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_305,plain,
    ! [X_105] :
      ( ( phi(X_105) = X_105 )
      | ~ d(X_105) ),
    inference(cnfTransformation,[status(thm)],[f_150]) ).

tff(c_320,plain,
    phi(false) = false,
    inference(resolution,[status(thm)],[c_16,c_305]) ).

tff(c_6,plain,
    bool(false),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_248,plain,
    ! [X_98] :
      ( ( prop(X_98) = true )
      | ~ bool(X_98) ),
    inference(cnfTransformation,[status(thm)],[f_158]) ).

tff(c_255,plain,
    prop(false) = true,
    inference(resolution,[status(thm)],[c_6,c_248]) ).

tff(c_516,plain,
    ! [P_109] : ( lazy_impl(prop(P_109),P_109) = f7(P_109) ),
    inference(cnfTransformation,[status(thm)],[f_353]) ).

tff(c_528,plain,
    lazy_impl(true,false) = f7(false),
    inference(superposition,[status(thm),theory(equality)],[c_255,c_516]) ).

tff(c_124,plain,
    ! [B_18] : ( lazy_impl(true,B_18) = phi(B_18) ),
    inference(cnfTransformation,[status(thm)],[f_202]) ).

tff(c_4520,plain,
    phi(false) = f7(false),
    inference(superposition,[status(thm),theory(equality)],[c_528,c_124]) ).

tff(c_4526,plain,
    f7(false) = false,
    inference(demodulation,[status(thm),theory(equality)],[c_320,c_4520]) ).

tff(c_10,plain,
    true != err,
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_122,plain,
    ! [B_17] : ( lazy_impl(false,B_17) = true ),
    inference(cnfTransformation,[status(thm)],[f_200]) ).

tff(c_110,plain,
    ! [X_8] :
      ( ( prop(X_8) = false )
      | bool(X_8) ),
    inference(cnfTransformation,[status(thm)],[f_163]) ).

tff(c_684,plain,
    ! [X_114] :
      ( ( true = X_114 )
      | ( false = X_114 )
      | ~ bool(X_114) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_3168,plain,
    ! [X_207] :
      ( ( true = X_207 )
      | ( false = X_207 )
      | ( prop(X_207) = false ) ),
    inference(resolution,[status(thm)],[c_110,c_684]) ).

tff(c_184,plain,
    ! [P_89] : ( lazy_impl(prop(P_89),P_89) = f7(P_89) ),
    inference(cnfTransformation,[status(thm)],[f_353]) ).

tff(c_3189,plain,
    ! [X_207] :
      ( ( lazy_impl(false,X_207) = f7(X_207) )
      | ( true = X_207 )
      | ( false = X_207 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_3168,c_184]) ).

tff(c_3968,plain,
    ! [X_229] :
      ( ( f7(X_229) = true )
      | ( true = X_229 )
      | ( false = X_229 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_122,c_3189]) ).

tff(c_18,plain,
    d(true),
    inference(cnfTransformation,[status(thm)],[f_82]) ).

tff(c_1983,plain,
    ! [X_167] :
      ( ( true = X_167 )
      | ( false = X_167 )
      | ( prop(X_167) = false ) ),
    inference(resolution,[status(thm)],[c_110,c_684]) ).

tff(c_2004,plain,
    ! [X_167] :
      ( ( lazy_impl(false,X_167) = f7(X_167) )
      | ( true = X_167 )
      | ( false = X_167 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_1983,c_184]) ).

tff(c_2216,plain,
    ! [X_173] :
      ( ( f7(X_173) = true )
      | ( true = X_173 )
      | ( false = X_173 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_122,c_2004]) ).

tff(c_1211,plain,
    ! [Y_136,X_137] :
      ( ~ d(Y_136)
      | d(X_137)
      | forallprefers(X_137,Y_136) ),
    inference(cnfTransformation,[status(thm)],[f_114]) ).

tff(c_186,plain,
    ! [P1_91] : ~ forallprefers(f7(P1_91),f7('#skF_7')),
    inference(cnfTransformation,[status(thm)],[f_359]) ).

tff(c_1233,plain,
    ! [P1_91] :
      ( ~ d(f7('#skF_7'))
      | d(f7(P1_91)) ),
    inference(resolution,[status(thm)],[c_1211,c_186]) ).

tff(c_1234,plain,
    ~ d(f7('#skF_7')),
    inference(splitLeft,[status(thm)],[c_1233]) ).

tff(c_2225,plain,
    ( ~ d(true)
    | ( true = '#skF_7' )
    | ( false = '#skF_7' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_2216,c_1234]) ).

tff(c_2262,plain,
    ( ( true = '#skF_7' )
    | ( false = '#skF_7' ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_18,c_2225]) ).

tff(c_2278,plain,
    false = '#skF_7',
    inference(splitLeft,[status(thm)],[c_2262]) ).

tff(c_2329,plain,
    d('#skF_7'),
    inference(demodulation,[status(thm),theory(equality)],[c_2278,c_16]) ).

tff(c_710,plain,
    phi(false) = f7(false),
    inference(superposition,[status(thm),theory(equality)],[c_528,c_124]) ).

tff(c_716,plain,
    f7(false) = false,
    inference(demodulation,[status(thm),theory(equality)],[c_320,c_710]) ).

tff(c_2307,plain,
    f7('#skF_7') = '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_2278,c_2278,c_716]) ).

tff(c_2382,plain,
    ~ d('#skF_7'),
    inference(demodulation,[status(thm),theory(equality)],[c_2307,c_1234]) ).

tff(c_2388,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2329,c_2382]) ).

tff(c_2389,plain,
    true = '#skF_7',
    inference(splitRight,[status(thm)],[c_2262]) ).

tff(c_2445,plain,
    d('#skF_7'),
    inference(demodulation,[status(thm),theory(equality)],[c_2389,c_18]) ).

tff(c_321,plain,
    phi(true) = true,
    inference(resolution,[status(thm)],[c_18,c_305]) ).

tff(c_4,plain,
    bool(true),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_256,plain,
    prop(true) = true,
    inference(resolution,[status(thm)],[c_4,c_248]) ).

tff(c_525,plain,
    lazy_impl(true,true) = f7(true),
    inference(superposition,[status(thm),theory(equality)],[c_256,c_516]) ).

tff(c_605,plain,
    phi(true) = f7(true),
    inference(superposition,[status(thm),theory(equality)],[c_525,c_124]) ).

tff(c_611,plain,
    f7(true) = true,
    inference(demodulation,[status(thm),theory(equality)],[c_321,c_605]) ).

tff(c_2426,plain,
    f7('#skF_7') = '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_2389,c_2389,c_611]) ).

tff(c_2569,plain,
    ~ d('#skF_7'),
    inference(demodulation,[status(thm),theory(equality)],[c_2426,c_1234]) ).

tff(c_2575,plain,
    $false,
    inference(demodulation,[status(thm),theory(equality)],[c_2445,c_2569]) ).

tff(c_2578,plain,
    ! [P1_184] : d(f7(P1_184)),
    inference(splitRight,[status(thm)],[c_1233]) ).

tff(c_100,plain,
    ! [X_6] :
      ( ( phi(X_6) = X_6 )
      | ~ d(X_6) ),
    inference(cnfTransformation,[status(thm)],[f_150]) ).

tff(c_2597,plain,
    ! [P1_187] : ( phi(f7(P1_187)) = f7(P1_187) ),
    inference(resolution,[status(thm)],[c_2578,c_100]) ).

tff(c_188,plain,
    phi(f7('#skF_7')) = false2,
    inference(cnfTransformation,[status(thm)],[f_359]) ).

tff(c_332,plain,
    ! [X_106] :
      ( ( phi(X_106) = X_106 )
      | ( phi(X_106) = err ) ),
    inference(cnfTransformation,[status(thm)],[f_150]) ).

tff(c_341,plain,
    ( ( f7('#skF_7') = false2 )
    | ( phi(f7('#skF_7')) = err ) ),
    inference(superposition,[status(thm),theory(equality)],[c_332,c_188]) ).

tff(c_366,plain,
    ( ( f7('#skF_7') = false2 )
    | ( false2 = err ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_188,c_341]) ).

tff(c_531,plain,
    false2 = err,
    inference(splitLeft,[status(thm)],[c_366]) ).

tff(c_533,plain,
    phi(f7('#skF_7')) = err,
    inference(demodulation,[status(thm),theory(equality)],[c_531,c_188]) ).

tff(c_2603,plain,
    f7('#skF_7') = err,
    inference(superposition,[status(thm),theory(equality)],[c_2597,c_533]) ).

tff(c_3979,plain,
    ( ( true = err )
    | ( true = '#skF_7' )
    | ( false = '#skF_7' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_3968,c_2603]) ).

tff(c_4009,plain,
    ( ( true = '#skF_7' )
    | ( false = '#skF_7' ) ),
    inference(negUnitSimplification,[status(thm)],[c_10,c_3979]) ).

tff(c_4024,plain,
    false = '#skF_7',
    inference(splitLeft,[status(thm)],[c_4009]) ).

tff(c_8,plain,
    false != err,
    inference(cnfTransformation,[status(thm)],[f_76]) ).

tff(c_4073,plain,
    err != '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_4024,c_8]) ).

tff(c_4054,plain,
    f7('#skF_7') = '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_4024,c_4024,c_716]) ).

tff(c_4151,plain,
    err = '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_4054,c_2603]) ).

tff(c_4153,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4073,c_4151]) ).

tff(c_4154,plain,
    true = '#skF_7',
    inference(splitRight,[status(thm)],[c_4009]) ).

tff(c_4210,plain,
    err != '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_4154,c_10]) ).

tff(c_4194,plain,
    f7('#skF_7') = '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_4154,c_4154,c_611]) ).

tff(c_4310,plain,
    err = '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_4194,c_2603]) ).

tff(c_4312,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4210,c_4310]) ).

tff(c_4313,plain,
    f7('#skF_7') = false2,
    inference(splitRight,[status(thm)],[c_366]) ).

tff(c_4315,plain,
    ! [P1_91] : ~ forallprefers(f7(P1_91),false2),
    inference(demodulation,[status(thm),theory(equality)],[c_4313,c_186]) ).

tff(c_4532,plain,
    ~ forallprefers(false,false2),
    inference(superposition,[status(thm),theory(equality)],[c_4526,c_4315]) ).

tff(c_182,plain,
    false1 = false,
    inference(cnfTransformation,[status(thm)],[f_348]) ).

tff(c_198,plain,
    false2 != false1,
    inference(cnfTransformation,[status(thm)],[f_380]) ).

tff(c_199,plain,
    false2 != false,
    inference(demodulation,[status(thm),theory(equality)],[c_182,c_198]) ).

tff(c_295,plain,
    ! [X_103] :
      ( ( prop(X_103) = false )
      | bool(X_103) ),
    inference(cnfTransformation,[status(thm)],[f_163]) ).

tff(c_106,plain,
    ! [X_7] :
      ( ( prop(X_7) = true )
      | ~ bool(X_7) ),
    inference(cnfTransformation,[status(thm)],[f_158]) ).

tff(c_303,plain,
    ! [X_103] :
      ( ( prop(X_103) = true )
      | ( prop(X_103) = false ) ),
    inference(resolution,[status(thm)],[c_295,c_106]) ).

tff(c_104,plain,
    ! [X_7] :
      ( bool(X_7)
      | ( prop(X_7) != true ) ),
    inference(cnfTransformation,[status(thm)],[f_158]) ).

tff(c_4408,plain,
    ! [B_241] :
      ( ( impl(false,B_241) = true )
      | ~ bool(B_241) ),
    inference(cnfTransformation,[status(thm)],[f_185]) ).

tff(c_5348,plain,
    ! [X_281] :
      ( ( impl(false,X_281) = true )
      | ( prop(X_281) != true ) ),
    inference(resolution,[status(thm)],[c_104,c_4408]) ).

tff(c_196,plain,
    ! [P_93] : ( impl(P_93,false2) = not2(P_93) ),
    inference(cnfTransformation,[status(thm)],[f_376]) ).

tff(c_5364,plain,
    ( ( not2(false) = true )
    | ( prop(false2) != true ) ),
    inference(superposition,[status(thm),theory(equality)],[c_5348,c_196]) ).

tff(c_5405,plain,
    prop(false2) != true,
    inference(splitLeft,[status(thm)],[c_5364]) ).

tff(c_5409,plain,
    prop(false2) = false,
    inference(superposition,[status(thm),theory(equality)],[c_303,c_5405]) ).

tff(c_4454,plain,
    ! [X_242] :
      ( ( true = X_242 )
      | ( false = X_242 )
      | ~ bool(X_242) ),
    inference(cnfTransformation,[status(thm)],[f_67]) ).

tff(c_5811,plain,
    ! [X_296] :
      ( ( true = X_296 )
      | ( false = X_296 )
      | ( prop(X_296) = false ) ),
    inference(resolution,[status(thm)],[c_110,c_4454]) ).

tff(c_5832,plain,
    ! [X_296] :
      ( ( lazy_impl(false,X_296) = f7(X_296) )
      | ( true = X_296 )
      | ( false = X_296 ) ),
    inference(superposition,[status(thm),theory(equality)],[c_5811,c_184]) ).

tff(c_6303,plain,
    ! [X_309] :
      ( ( f7(X_309) = true )
      | ( true = X_309 )
      | ( false = X_309 ) ),
    inference(demodulation,[status(thm),theory(equality)],[c_122,c_5832]) ).

tff(c_6325,plain,
    ( ( true = false2 )
    | ( true = '#skF_7' )
    | ( false = '#skF_7' ) ),
    inference(superposition,[status(thm),theory(equality)],[c_6303,c_4313]) ).

tff(c_6357,plain,
    false = '#skF_7',
    inference(splitLeft,[status(thm)],[c_6325]) ).

tff(c_6422,plain,
    false2 != '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_6357,c_199]) ).

tff(c_6398,plain,
    f7('#skF_7') = '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_6357,c_6357,c_4526]) ).

tff(c_6458,plain,
    false2 = '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_6398,c_4313]) ).

tff(c_6460,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6422,c_6458]) ).

tff(c_6461,plain,
    ( ( true = '#skF_7' )
    | ( true = false2 ) ),
    inference(splitRight,[status(thm)],[c_6325]) ).

tff(c_6475,plain,
    true = false2,
    inference(splitLeft,[status(thm)],[c_6461]) ).

tff(c_6521,plain,
    prop(false2) = false2,
    inference(demodulation,[status(thm),theory(equality)],[c_6475,c_6475,c_256]) ).

tff(c_6535,plain,
    false2 = false,
    inference(demodulation,[status(thm),theory(equality)],[c_5409,c_6521]) ).

tff(c_6537,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_199,c_6535]) ).

tff(c_6538,plain,
    true = '#skF_7',
    inference(splitRight,[status(thm)],[c_6461]) ).

tff(c_6539,plain,
    true != false2,
    inference(splitRight,[status(thm)],[c_6461]) ).

tff(c_6629,plain,
    false2 != '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_6538,c_6539]) ).

tff(c_4438,plain,
    phi(true) = f7(true),
    inference(superposition,[status(thm),theory(equality)],[c_525,c_124]) ).

tff(c_4444,plain,
    f7(true) = true,
    inference(demodulation,[status(thm),theory(equality)],[c_321,c_4438]) ).

tff(c_6574,plain,
    f7('#skF_7') = '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_6538,c_6538,c_4444]) ).

tff(c_6742,plain,
    false2 = '#skF_7',
    inference(demodulation,[status(thm),theory(equality)],[c_6574,c_4313]) ).

tff(c_6744,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_6629,c_6742]) ).

tff(c_6746,plain,
    prop(false2) = true,
    inference(splitRight,[status(thm)],[c_5364]) ).

tff(c_4468,plain,
    ! [X_7] :
      ( ( true = X_7 )
      | ( false = X_7 )
      | ( prop(X_7) != true ) ),
    inference(resolution,[status(thm)],[c_104,c_4454]) ).

tff(c_6754,plain,
    ( ( true = false2 )
    | ( false2 = false ) ),
    inference(superposition,[status(thm),theory(equality)],[c_6746,c_4468]) ).

tff(c_6771,plain,
    true = false2,
    inference(negUnitSimplification,[status(thm)],[c_199,c_6754]) ).

tff(c_52,plain,
    forallprefers(false,true),
    inference(cnfTransformation,[status(thm)],[f_114]) ).

tff(c_6849,plain,
    forallprefers(false,false2),
    inference(demodulation,[status(thm),theory(equality)],[c_6771,c_52]) ).

tff(c_6859,plain,
    $false,
    inference(negUnitSimplification,[status(thm)],[c_4532,c_6849]) ).

%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.13  % Problem  : SWW101+1 : TPTP v8.1.2. Released v5.2.0.
% 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
% 0.15/0.36  % Computer : n001.cluster.edu
% 0.15/0.36  % Model    : x86_64 x86_64
% 0.15/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.36  % Memory   : 8042.1875MB
% 0.15/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.15/0.36  % CPULimit : 300
% 0.15/0.36  % WCLimit  : 300
% 0.15/0.36  % DateTime : Thu Aug  3 19:55:25 EDT 2023
% 0.15/0.36  % CPUTime  : 
% 7.80/2.94  % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p
% 8.18/2.96  
% 8.18/2.96  % SZS output start CNFRefutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 8.18/3.03  
% 8.18/3.03  Inference rules
% 8.18/3.03  ----------------------
% 8.18/3.03  #Ref     : 0
% 8.18/3.03  #Sup     : 1426
% 8.18/3.03  #Fact    : 4
% 8.18/3.03  #Define  : 0
% 8.18/3.03  #Split   : 10
% 8.18/3.03  #Chain   : 0
% 8.18/3.03  #Close   : 0
% 8.18/3.03  
% 8.18/3.03  Ordering : KBO
% 8.18/3.03  
% 8.18/3.03  Simplification rules
% 8.18/3.03  ----------------------
% 8.18/3.03  #Subsume      : 130
% 8.18/3.03  #Demod        : 1254
% 8.18/3.03  #Tautology    : 844
% 8.18/3.03  #SimpNegUnit  : 234
% 8.18/3.03  #BackRed      : 461
% 8.18/3.03  
% 8.18/3.03  #Partial instantiations: 0
% 8.18/3.03  #Strategies tried      : 1
% 8.18/3.03  
% 8.18/3.03  Timing (in seconds)
% 8.18/3.03  ----------------------
% 8.18/3.04  Preprocessing        : 0.68
% 8.18/3.04  Parsing              : 0.34
% 8.18/3.04  CNF conversion       : 0.05
% 8.18/3.04  Main loop            : 1.17
% 8.18/3.04  Inferencing          : 0.38
% 8.18/3.04  Reduction            : 0.40
% 8.18/3.04  Demodulation         : 0.27
% 8.18/3.04  BG Simplification    : 0.06
% 8.18/3.04  Subsumption          : 0.22
% 8.18/3.04  Abstraction          : 0.05
% 8.18/3.04  MUC search           : 0.00
% 8.18/3.04  Cooper               : 0.00
% 8.18/3.04  Total                : 1.95
% 8.18/3.04  Index Insertion      : 0.00
% 8.18/3.04  Index Deletion       : 0.00
% 8.18/3.04  Index Matching       : 0.00
% 8.18/3.04  BG Taut test         : 0.00
%------------------------------------------------------------------------------