%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO179^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 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 : Wed Feb 25 09:53:35 AM UTC 2026
% Result : Theorem 1.74s 1.49s
% Output : Refutation 1.74s
% Verified :
% SZS Type : Refutation
% Derivation depth : 14
% Number of leaves : 31
% Syntax : Number of formulae : 280 ( 1 unt; 0 typ; 30 def)
% Number of atoms : 2839 ( 468 equ; 0 cnn)
% Maximal formula atoms : 96 ( 10 avg)
% Number of connectives : 2472 ( 657 ~; 629 |; 120 &;1032 @)
% ( 30 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 4 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 41 ( 38 usr; 38 con; 0-2 aty)
% Number of variables : 96 ( 0 ^; 72 !; 24 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
thf(func_def_0,type,
cG: $i > $i > $o ).
thf(func_def_1,type,
cR: $i > $i > $o ).
thf(f653,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f34,f43,f52,f61,f70,f79,f88,f97,f106,f115,f124,f133,f142,f151,f160,f199,f206,f207,f225,f232,f243,f244,f245,f251,f262,f268,f270,f284,f293,f311,f317,f330,f345,f359,f361,f375,f429,f431,f433,f453,f479,f495,f521,f531,f537,f538,f554,f596,f614,f636,f652]) ).
thf(f652,plain,
( ~ spl0_21
| ~ spl0_24
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[status(thm)],[f651]) ).
thf(f651,plain,
( $false
| ~ spl0_21
| ~ spl0_24
| ~ spl0_28 ),
inference(subsumption_resolution,[status(thm)],[f649,f150]) ).
thf(f150,plain,
( ( ( cG @ cA @ cE )
= $true )
| ~ spl0_28 ),
inference(avatar_component_clause,[status(thm)],[f148]) ).
thf(f148,definition,
( spl0_28
<=> ( ( cG @ cA @ cE )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_28])],[avatar_definition]) ).
thf(f649,plain,
( ( ( cG @ cA @ cE )
!= $true )
| ~ spl0_21
| ~ spl0_24 ),
inference(trivial_inequality_removal,[status(thm)],[f647]) ).
thf(f647,plain,
( ( $true != $true )
| ( ( cG @ cA @ cE )
!= $true )
| ~ spl0_21
| ~ spl0_24 ),
inference(superposition,[status(thm)],[f560,f132]) ).
thf(f132,plain,
( ( ( cG @ cA @ cD )
= $true )
| ~ spl0_24 ),
inference(avatar_component_clause,[status(thm)],[f130]) ).
thf(f130,definition,
( spl0_24
<=> ( ( cG @ cA @ cD )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition]) ).
thf(f560,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cD ) )
| ( ( cG @ X0 @ cE )
!= $true ) )
| ~ spl0_21 ),
inference(trivial_inequality_removal,[status(thm)],[f559]) ).
thf(f559,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cD ) )
| ( $true != $true )
| ( ( cG @ X0 @ cE )
!= $true ) )
| ~ spl0_21 ),
inference(superposition,[status(thm)],[f15,f119]) ).
thf(f119,plain,
( ( ( cG @ cD @ cE )
= $true )
| ~ spl0_21 ),
inference(avatar_component_clause,[status(thm)],[f117]) ).
thf(f117,definition,
( spl0_21
<=> ( ( cG @ cD @ cE )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition]) ).
thf(f15,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( cG @ X1 @ X2 )
!= $true )
| ( ( cG @ X0 @ X1 )
!= $true )
| ( ( cG @ X0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
( ( ( ( cG @ cB @ cC )
= $true )
| ( ( cR @ cB @ cC )
= $true ) )
& ( ( ( cG @ cB @ cD )
= $true )
| ( ( cR @ cB @ cD )
= $true ) )
& ( ( ( cR @ cA @ cE )
= $true )
| ( ( cG @ cA @ cE )
= $true ) )
& ( ( ( cG @ cC @ cD )
= $true )
| ( ( cR @ cC @ cD )
= $true ) )
& ( ( ( cG @ cA @ cB )
= $true )
| ( ( cR @ cA @ cB )
= $true ) )
& ( ( ( cR @ cA @ cD )
= $true )
| ( ( cG @ cA @ cD )
= $true ) )
& ( ( ( cR @ cC @ cF )
= $true )
| ( ( cG @ cC @ cF )
= $true ) )
& ( ( ( cG @ cB @ cE )
= $true )
| ( ( cR @ cB @ cE )
= $true ) )
& ( ( ( cG @ cB @ cF )
= $true )
| ( ( cR @ cB @ cF )
= $true ) )
& ( ( ( cR @ cE @ cF )
= $true )
| ( ( cG @ cE @ cF )
= $true ) )
& ! [X0: $i,X1: $i,X2: $i] :
( ( ( cG @ X1 @ X2 )
!= $true )
| ( ( cG @ X0 @ X1 )
!= $true )
| ( ( cG @ X0 @ X2 )
!= $true ) )
& ( ( ( cR @ cA @ cF )
= $true )
| ( ( cG @ cA @ cF )
= $true ) )
& ! [X3: $i,X4: $i,X5: $i] :
( ( ( cR @ X4 @ X3 )
!= $true )
| ( ( cR @ X3 @ X5 )
!= $true )
| ( ( cR @ X4 @ X5 )
!= $true ) )
& ( ( ( cG @ cA @ cC )
= $true )
| ( ( cR @ cA @ cC )
= $true ) )
& ( ( ( cG @ cD @ cE )
= $true )
| ( ( cR @ cD @ cE )
= $true ) )
& ( ( ( cG @ cD @ cF )
= $true )
| ( ( cR @ cD @ cF )
= $true ) )
& ( ( ( cG @ cC @ cE )
= $true )
| ( ( cR @ cC @ cE )
= $true ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ( ( ( cG @ cB @ cC )
= $true )
| ( ( cR @ cB @ cC )
= $true ) )
& ( ( ( cG @ cB @ cD )
= $true )
| ( ( cR @ cB @ cD )
= $true ) )
& ( ( ( cR @ cA @ cE )
= $true )
| ( ( cG @ cA @ cE )
= $true ) )
& ( ( ( cG @ cC @ cD )
= $true )
| ( ( cR @ cC @ cD )
= $true ) )
& ( ( ( cG @ cA @ cB )
= $true )
| ( ( cR @ cA @ cB )
= $true ) )
& ( ( ( cR @ cA @ cD )
= $true )
| ( ( cG @ cA @ cD )
= $true ) )
& ( ( ( cR @ cC @ cF )
= $true )
| ( ( cG @ cC @ cF )
= $true ) )
& ( ( ( cG @ cB @ cE )
= $true )
| ( ( cR @ cB @ cE )
= $true ) )
& ( ( ( cG @ cB @ cF )
= $true )
| ( ( cR @ cB @ cF )
= $true ) )
& ( ( ( cR @ cE @ cF )
= $true )
| ( ( cG @ cE @ cF )
= $true ) )
& ! [X1: $i,X0: $i,X2: $i] :
( ( ( cG @ X0 @ X2 )
!= $true )
| ( ( cG @ X1 @ X0 )
!= $true )
| ( ( cG @ X1 @ X2 )
!= $true ) )
& ( ( ( cR @ cA @ cF )
= $true )
| ( ( cG @ cA @ cF )
= $true ) )
& ! [X3: $i,X4: $i,X5: $i] :
( ( ( cR @ X4 @ X3 )
!= $true )
| ( ( cR @ X3 @ X5 )
!= $true )
| ( ( cR @ X4 @ X5 )
!= $true ) )
& ( ( ( cG @ cA @ cC )
= $true )
| ( ( cR @ cA @ cC )
= $true ) )
& ( ( ( cG @ cD @ cE )
= $true )
| ( ( cR @ cD @ cE )
= $true ) )
& ( ( ( cG @ cD @ cF )
= $true )
| ( ( cR @ cD @ cF )
= $true ) )
& ( ( ( cG @ cC @ cE )
= $true )
| ( ( cR @ cC @ cE )
= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ! [X3: $i,X4: $i,X5: $i] :
( ( ( cR @ X4 @ X3 )
!= $true )
| ( ( cR @ X3 @ X5 )
!= $true )
| ( ( cR @ X4 @ X5 )
!= $true ) )
& ! [X1: $i,X0: $i,X2: $i] :
( ( ( cG @ X0 @ X2 )
!= $true )
| ( ( cG @ X1 @ X0 )
!= $true )
| ( ( cG @ X1 @ X2 )
!= $true ) )
& ( ( ( cG @ cB @ cF )
= $true )
| ( ( cR @ cB @ cF )
= $true ) )
& ( ( ( cG @ cD @ cE )
= $true )
| ( ( cR @ cD @ cE )
= $true ) )
& ( ( ( cG @ cA @ cC )
= $true )
| ( ( cR @ cA @ cC )
= $true ) )
& ( ( ( cR @ cA @ cE )
= $true )
| ( ( cG @ cA @ cE )
= $true ) )
& ( ( ( cG @ cB @ cC )
= $true )
| ( ( cR @ cB @ cC )
= $true ) )
& ( ( ( cG @ cC @ cD )
= $true )
| ( ( cR @ cC @ cD )
= $true ) )
& ( ( ( cG @ cB @ cE )
= $true )
| ( ( cR @ cB @ cE )
= $true ) )
& ( ( ( cG @ cC @ cE )
= $true )
| ( ( cR @ cC @ cE )
= $true ) )
& ( ( ( cR @ cE @ cF )
= $true )
| ( ( cG @ cE @ cF )
= $true ) )
& ( ( ( cR @ cC @ cF )
= $true )
| ( ( cG @ cC @ cF )
= $true ) )
& ( ( ( cR @ cA @ cF )
= $true )
| ( ( cG @ cA @ cF )
= $true ) )
& ( ( ( cR @ cA @ cD )
= $true )
| ( ( cG @ cA @ cD )
= $true ) )
& ( ( ( cG @ cD @ cF )
= $true )
| ( ( cR @ cD @ cF )
= $true ) )
& ( ( ( cG @ cB @ cD )
= $true )
| ( ( cR @ cB @ cD )
= $true ) )
& ( ( ( cG @ cA @ cB )
= $true )
| ( ( cR @ cA @ cB )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ( ( ( cG @ cB @ cF )
= $true )
| ( ( cR @ cB @ cF )
= $true ) )
& ( ( ( cG @ cD @ cE )
= $true )
| ( ( cR @ cD @ cE )
= $true ) )
& ( ( ( cG @ cA @ cC )
= $true )
| ( ( cR @ cA @ cC )
= $true ) )
& ( ( ( cR @ cA @ cE )
= $true )
| ( ( cG @ cA @ cE )
= $true ) )
& ( ( ( cG @ cB @ cC )
= $true )
| ( ( cR @ cB @ cC )
= $true ) )
& ( ( ( cG @ cC @ cD )
= $true )
| ( ( cR @ cC @ cD )
= $true ) )
& ( ( ( cG @ cB @ cE )
= $true )
| ( ( cR @ cB @ cE )
= $true ) )
& ( ( ( cG @ cC @ cE )
= $true )
| ( ( cR @ cC @ cE )
= $true ) )
& ( ( ( cR @ cE @ cF )
= $true )
| ( ( cG @ cE @ cF )
= $true ) )
& ( ( ( cR @ cC @ cF )
= $true )
| ( ( cG @ cC @ cF )
= $true ) )
& ( ( ( cR @ cA @ cF )
= $true )
| ( ( cG @ cA @ cF )
= $true ) )
& ( ( ( cR @ cA @ cD )
= $true )
| ( ( cG @ cA @ cD )
= $true ) )
& ( ( ( cG @ cD @ cF )
= $true )
| ( ( cR @ cD @ cF )
= $true ) )
& ( ( ( cG @ cB @ cD )
= $true )
| ( ( cR @ cB @ cD )
= $true ) )
& ( ( ( cG @ cA @ cB )
= $true )
| ( ( cR @ cA @ cB )
= $true ) ) )
=> ( ? [X5: $i,X4: $i,X3: $i] :
( ( ( cR @ X4 @ X5 )
= $true )
& ( ( cR @ X3 @ X5 )
= $true )
& ( ( cR @ X4 @ X3 )
= $true ) )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( cG @ X1 @ X2 )
= $true )
& ( ( cG @ X1 @ X0 )
= $true )
& ( ( cG @ X0 @ X2 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ( ( cG @ cD @ cE )
| ( cR @ cD @ cE ) )
& ( ( cG @ cE @ cF )
| ( cR @ cE @ cF ) )
& ( ( cG @ cC @ cD )
| ( cR @ cC @ cD ) )
& ( ( cR @ cD @ cF )
| ( cG @ cD @ cF ) )
& ( ( cR @ cA @ cF )
| ( cG @ cA @ cF ) )
& ( ( cG @ cA @ cB )
| ( cR @ cA @ cB ) )
& ( ( cR @ cB @ cF )
| ( cG @ cB @ cF ) )
& ( ( cR @ cB @ cD )
| ( cG @ cB @ cD ) )
& ( ( cR @ cB @ cE )
| ( cG @ cB @ cE ) )
& ( ( cG @ cB @ cC )
| ( cR @ cB @ cC ) )
& ( ( cG @ cC @ cE )
| ( cR @ cC @ cE ) )
& ( ( cG @ cC @ cF )
| ( cR @ cC @ cF ) )
& ( ( cR @ cA @ cE )
| ( cG @ cA @ cE ) )
& ( ( cG @ cA @ cC )
| ( cR @ cA @ cC ) )
& ( ( cG @ cA @ cD )
| ( cR @ cA @ cD ) ) )
=> ( ? [X0: $i,X1: $i,X2: $i] :
( ( cG @ X1 @ X0 )
& ( cG @ X0 @ X2 )
& ( cG @ X1 @ X2 ) )
| ? [X3: $i,X4: $i,X5: $i] :
( ( cR @ X4 @ X5 )
& ( cR @ X4 @ X3 )
& ( cR @ X3 @ X5 ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ( ( cG @ cD @ cE )
| ( cR @ cD @ cE ) )
& ( ( cG @ cE @ cF )
| ( cR @ cE @ cF ) )
& ( ( cG @ cC @ cD )
| ( cR @ cC @ cD ) )
& ( ( cR @ cD @ cF )
| ( cG @ cD @ cF ) )
& ( ( cR @ cA @ cF )
| ( cG @ cA @ cF ) )
& ( ( cG @ cA @ cB )
| ( cR @ cA @ cB ) )
& ( ( cR @ cB @ cF )
| ( cG @ cB @ cF ) )
& ( ( cR @ cB @ cD )
| ( cG @ cB @ cD ) )
& ( ( cR @ cB @ cE )
| ( cG @ cB @ cE ) )
& ( ( cG @ cB @ cC )
| ( cR @ cB @ cC ) )
& ( ( cG @ cC @ cE )
| ( cR @ cC @ cE ) )
& ( ( cG @ cC @ cF )
| ( cR @ cC @ cF ) )
& ( ( cR @ cA @ cE )
| ( cG @ cA @ cE ) )
& ( ( cG @ cA @ cC )
| ( cR @ cA @ cC ) )
& ( ( cG @ cA @ cD )
| ( cR @ cA @ cD ) ) )
=> ( ? [X1: $i,X0: $i,X2: $i] :
( ( cG @ X0 @ X1 )
& ( cG @ X1 @ X2 )
& ( cG @ X0 @ X2 ) )
| ? [X1: $i,X0: $i,X2: $i] :
( ( cR @ X0 @ X2 )
& ( cR @ X0 @ X1 )
& ( cR @ X1 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ( ( cG @ cD @ cE )
| ( cR @ cD @ cE ) )
& ( ( cG @ cE @ cF )
| ( cR @ cE @ cF ) )
& ( ( cG @ cC @ cD )
| ( cR @ cC @ cD ) )
& ( ( cR @ cD @ cF )
| ( cG @ cD @ cF ) )
& ( ( cR @ cA @ cF )
| ( cG @ cA @ cF ) )
& ( ( cG @ cA @ cB )
| ( cR @ cA @ cB ) )
& ( ( cR @ cB @ cF )
| ( cG @ cB @ cF ) )
& ( ( cR @ cB @ cD )
| ( cG @ cB @ cD ) )
& ( ( cR @ cB @ cE )
| ( cG @ cB @ cE ) )
& ( ( cG @ cB @ cC )
| ( cR @ cB @ cC ) )
& ( ( cG @ cC @ cE )
| ( cR @ cC @ cE ) )
& ( ( cG @ cC @ cF )
| ( cR @ cC @ cF ) )
& ( ( cR @ cA @ cE )
| ( cG @ cA @ cE ) )
& ( ( cG @ cA @ cC )
| ( cR @ cA @ cC ) )
& ( ( cG @ cA @ cD )
| ( cR @ cA @ cD ) ) )
=> ( ? [X1: $i,X0: $i,X2: $i] :
( ( cG @ X0 @ X1 )
& ( cG @ X1 @ X2 )
& ( cG @ X0 @ X2 ) )
| ? [X1: $i,X0: $i,X2: $i] :
( ( cR @ X0 @ X2 )
& ( cR @ X0 @ X1 )
& ( cR @ X1 @ X2 ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.tHlHL5CGp0/DTF2THF_5569.p',cSIX_THEOREM_B) ).
thf(f636,plain,
( ~ spl0_4
| ~ spl0_16
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[status(thm)],[f635]) ).
thf(f635,plain,
( $false
| ~ spl0_4
| ~ spl0_16
| ~ spl0_27 ),
inference(subsumption_resolution,[status(thm)],[f633,f96]) ).
thf(f96,plain,
( ( ( cR @ cE @ cF )
= $true )
| ~ spl0_16 ),
inference(avatar_component_clause,[status(thm)],[f94]) ).
thf(f94,definition,
( spl0_16
<=> ( ( cR @ cE @ cF )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition]) ).
thf(f633,plain,
( ( ( cR @ cE @ cF )
!= $true )
| ~ spl0_4
| ~ spl0_27 ),
inference(trivial_inequality_removal,[status(thm)],[f629]) ).
thf(f629,plain,
( ( $true != $true )
| ( ( cR @ cE @ cF )
!= $true )
| ~ spl0_4
| ~ spl0_27 ),
inference(superposition,[status(thm)],[f600,f146]) ).
thf(f146,plain,
( ( ( cR @ cA @ cE )
= $true )
| ~ spl0_27 ),
inference(avatar_component_clause,[status(thm)],[f144]) ).
thf(f144,definition,
( spl0_27
<=> ( ( cR @ cA @ cE )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_27])],[avatar_definition]) ).
thf(f600,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ cA @ X0 ) )
| ( ( cR @ X0 @ cF )
!= $true ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f598]) ).
thf(f598,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ cA @ X0 ) )
| ( $true != $true )
| ( ( cR @ X0 @ cF )
!= $true ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f13,f42]) ).
thf(f42,plain,
( ( ( cR @ cA @ cF )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl0_4
<=> ( ( cR @ cA @ cF )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition]) ).
thf(f13,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( cR @ X4 @ X5 )
!= $true )
| ( ( cR @ X4 @ X3 )
!= $true )
| ( ( cR @ X3 @ X5 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f614,plain,
( ~ spl0_1
| ~ spl0_12
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[status(thm)],[f613]) ).
thf(f613,plain,
( $false
| ~ spl0_1
| ~ spl0_12
| ~ spl0_21 ),
inference(subsumption_resolution,[status(thm)],[f612,f78]) ).
thf(f78,plain,
( ( ( cG @ cB @ cE )
= $true )
| ~ spl0_12 ),
inference(avatar_component_clause,[status(thm)],[f76]) ).
thf(f76,definition,
( spl0_12
<=> ( ( cG @ cB @ cE )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition]) ).
thf(f612,plain,
( ( ( cG @ cB @ cE )
!= $true )
| ~ spl0_1
| ~ spl0_21 ),
inference(trivial_inequality_removal,[status(thm)],[f611]) ).
thf(f611,plain,
( ( $true != $true )
| ( ( cG @ cB @ cE )
!= $true )
| ~ spl0_1
| ~ spl0_21 ),
inference(superposition,[status(thm)],[f560,f29]) ).
thf(f29,plain,
( ( ( cG @ cB @ cD )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[status(thm)],[f27]) ).
thf(f27,definition,
( spl0_1
<=> ( ( cG @ cB @ cD )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition]) ).
thf(f596,plain,
( ~ spl0_12
| ~ spl0_14
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[status(thm)],[f595]) ).
thf(f595,plain,
( $false
| ~ spl0_12
| ~ spl0_14
| ~ spl0_29 ),
inference(subsumption_resolution,[status(thm)],[f594,f78]) ).
thf(f594,plain,
( ( ( cG @ cB @ cE )
!= $true )
| ~ spl0_14
| ~ spl0_29 ),
inference(trivial_inequality_removal,[status(thm)],[f591]) ).
thf(f591,plain,
( ( $true != $true )
| ( ( cG @ cB @ cE )
!= $true )
| ~ spl0_14
| ~ spl0_29 ),
inference(superposition,[status(thm)],[f556,f155]) ).
thf(f155,plain,
( ( ( cG @ cB @ cC )
= $true )
| ~ spl0_29 ),
inference(avatar_component_clause,[status(thm)],[f153]) ).
thf(f153,definition,
( spl0_29
<=> ( ( cG @ cB @ cC )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_29])],[avatar_definition]) ).
thf(f556,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cC ) )
| ( ( cG @ X0 @ cE )
!= $true ) )
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f555]) ).
thf(f555,plain,
( ! [X0: $i] :
( ( ( cG @ X0 @ cE )
!= $true )
| ( $true
!= ( cG @ X0 @ cC ) )
| ( $true != $true ) )
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f15,f87]) ).
thf(f87,plain,
( ( ( cG @ cC @ cE )
= $true )
| ~ spl0_14 ),
inference(avatar_component_clause,[status(thm)],[f85]) ).
thf(f85,definition,
( spl0_14
<=> ( ( cG @ cC @ cE )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition]) ).
thf(f554,plain,
( ~ spl0_13
| ~ spl0_16
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[status(thm)],[f553]) ).
thf(f553,plain,
( $false
| ~ spl0_13
| ~ spl0_16
| ~ spl0_20 ),
inference(subsumption_resolution,[status(thm)],[f552,f96]) ).
thf(f552,plain,
( ( ( cR @ cE @ cF )
!= $true )
| ~ spl0_13
| ~ spl0_20 ),
inference(trivial_inequality_removal,[status(thm)],[f549]) ).
thf(f549,plain,
( ( ( cR @ cE @ cF )
!= $true )
| ( $true != $true )
| ~ spl0_13
| ~ spl0_20 ),
inference(superposition,[status(thm)],[f273,f83]) ).
thf(f83,plain,
( ( ( cR @ cC @ cE )
= $true )
| ~ spl0_13 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f81,definition,
( spl0_13
<=> ( ( cR @ cC @ cE )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition]) ).
thf(f273,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ cC @ X0 ) )
| ( ( cR @ X0 @ cF )
!= $true ) )
| ~ spl0_20 ),
inference(trivial_inequality_removal,[status(thm)],[f272]) ).
thf(f272,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cR @ X0 @ cF )
!= $true )
| ( $true
!= ( cR @ cC @ X0 ) ) )
| ~ spl0_20 ),
inference(superposition,[status(thm)],[f13,f114]) ).
thf(f114,plain,
( ( ( cR @ cC @ cF )
= $true )
| ~ spl0_20 ),
inference(avatar_component_clause,[status(thm)],[f112]) ).
thf(f112,definition,
( spl0_20
<=> ( ( cR @ cC @ cF )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition]) ).
thf(f538,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_24 ),
inference(avatar_split_clause,[status(thm)],[f506,f130,f54,f36]) ).
thf(f36,definition,
( spl0_3
<=> ( ( cG @ cA @ cF )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition]) ).
thf(f54,definition,
( spl0_7
<=> ( ( cG @ cD @ cF )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition]) ).
thf(f506,plain,
( ( ( cG @ cA @ cF )
!= $true )
| ~ spl0_7
| ~ spl0_24 ),
inference(trivial_inequality_removal,[status(thm)],[f504]) ).
thf(f504,plain,
( ( ( cG @ cA @ cF )
!= $true )
| ( $true != $true )
| ~ spl0_7
| ~ spl0_24 ),
inference(superposition,[status(thm)],[f443,f132]) ).
thf(f443,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cD ) )
| ( $true
!= ( cG @ X0 @ cF ) ) )
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f440]) ).
thf(f440,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cD ) )
| ( $true != $true )
| ( $true
!= ( cG @ X0 @ cF ) ) )
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f15,f56]) ).
thf(f56,plain,
( ( ( cG @ cD @ cF )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[status(thm)],[f54]) ).
thf(f537,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[status(thm)],[f536]) ).
thf(f536,plain,
( $false
| ~ spl0_1
| ~ spl0_7
| ~ spl0_26 ),
inference(subsumption_resolution,[status(thm)],[f535,f141]) ).
thf(f141,plain,
( ( ( cG @ cB @ cF )
= $true )
| ~ spl0_26 ),
inference(avatar_component_clause,[status(thm)],[f139]) ).
thf(f139,definition,
( spl0_26
<=> ( ( cG @ cB @ cF )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_26])],[avatar_definition]) ).
thf(f535,plain,
( ( ( cG @ cB @ cF )
!= $true )
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[status(thm)],[f532]) ).
thf(f532,plain,
( ( ( cG @ cB @ cF )
!= $true )
| ( $true != $true )
| ~ spl0_1
| ~ spl0_7 ),
inference(superposition,[status(thm)],[f443,f29]) ).
thf(f531,plain,
( ~ spl0_20
| ~ spl0_25
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[status(thm)],[f530]) ).
thf(f530,plain,
( $false
| ~ spl0_20
| ~ spl0_25
| ~ spl0_30 ),
inference(subsumption_resolution,[status(thm)],[f529,f114]) ).
thf(f529,plain,
( ( ( cR @ cC @ cF )
!= $true )
| ~ spl0_25
| ~ spl0_30 ),
inference(trivial_inequality_removal,[status(thm)],[f524]) ).
thf(f524,plain,
( ( ( cR @ cC @ cF )
!= $true )
| ( $true != $true )
| ~ spl0_25
| ~ spl0_30 ),
inference(superposition,[status(thm)],[f461,f159]) ).
thf(f159,plain,
( ( ( cR @ cB @ cC )
= $true )
| ~ spl0_30 ),
inference(avatar_component_clause,[status(thm)],[f157]) ).
thf(f157,definition,
( spl0_30
<=> ( ( cR @ cB @ cC )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_30])],[avatar_definition]) ).
thf(f461,plain,
( ! [X0: $i] :
( ( ( cR @ cB @ X0 )
!= $true )
| ( ( cR @ X0 @ cF )
!= $true ) )
| ~ spl0_25 ),
inference(trivial_inequality_removal,[status(thm)],[f460]) ).
thf(f460,plain,
( ! [X0: $i] :
( ( ( cR @ X0 @ cF )
!= $true )
| ( ( cR @ cB @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl0_25 ),
inference(superposition,[status(thm)],[f13,f137]) ).
thf(f137,plain,
( ( ( cR @ cB @ cF )
= $true )
| ~ spl0_25 ),
inference(avatar_component_clause,[status(thm)],[f135]) ).
thf(f135,definition,
( spl0_25
<=> ( ( cR @ cB @ cF )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition]) ).
thf(f521,plain,
( ~ spl0_13
| ~ spl0_18
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f520]) ).
thf(f520,plain,
( $false
| ~ spl0_13
| ~ spl0_18
| ~ spl0_22 ),
inference(subsumption_resolution,[status(thm)],[f519,f123]) ).
thf(f123,plain,
( ( ( cR @ cD @ cE )
= $true )
| ~ spl0_22 ),
inference(avatar_component_clause,[status(thm)],[f121]) ).
thf(f121,definition,
( spl0_22
<=> ( ( cR @ cD @ cE )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_22])],[avatar_definition]) ).
thf(f519,plain,
( ( ( cR @ cD @ cE )
!= $true )
| ~ spl0_13
| ~ spl0_18 ),
inference(trivial_inequality_removal,[status(thm)],[f516]) ).
thf(f516,plain,
( ( ( cR @ cD @ cE )
!= $true )
| ( $true != $true )
| ~ spl0_13
| ~ spl0_18 ),
inference(superposition,[status(thm)],[f459,f105]) ).
thf(f105,plain,
( ( ( cR @ cC @ cD )
= $true )
| ~ spl0_18 ),
inference(avatar_component_clause,[status(thm)],[f103]) ).
thf(f103,definition,
( spl0_18
<=> ( ( cR @ cC @ cD )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition]) ).
thf(f459,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ cC @ X0 ) )
| ( $true
!= ( cR @ X0 @ cE ) ) )
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f457]) ).
thf(f457,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cR @ cC @ X0 ) )
| ( $true
!= ( cR @ X0 @ cE ) ) )
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f13,f83]) ).
thf(f495,plain,
( ~ spl0_10
| ~ spl0_12
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[status(thm)],[f494]) ).
thf(f494,plain,
( $false
| ~ spl0_10
| ~ spl0_12
| ~ spl0_28 ),
inference(subsumption_resolution,[status(thm)],[f493,f150]) ).
thf(f493,plain,
( ( ( cG @ cA @ cE )
!= $true )
| ~ spl0_10
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f492]) ).
thf(f492,plain,
( ( $true != $true )
| ( ( cG @ cA @ cE )
!= $true )
| ~ spl0_10
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f455,f69]) ).
thf(f69,plain,
( ( ( cG @ cA @ cB )
= $true )
| ~ spl0_10 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f67,definition,
( spl0_10
<=> ( ( cG @ cA @ cB )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition]) ).
thf(f455,plain,
( ! [X0: $i] :
( ( ( cG @ X0 @ cB )
!= $true )
| ( ( cG @ X0 @ cE )
!= $true ) )
| ~ spl0_12 ),
inference(trivial_inequality_removal,[status(thm)],[f454]) ).
thf(f454,plain,
( ! [X0: $i] :
( ( ( cG @ X0 @ cE )
!= $true )
| ( $true != $true )
| ( ( cG @ X0 @ cB )
!= $true ) )
| ~ spl0_12 ),
inference(superposition,[status(thm)],[f15,f78]) ).
thf(f479,plain,
( ~ spl0_4
| ~ spl0_9
| ~ spl0_25 ),
inference(avatar_contradiction_clause,[status(thm)],[f478]) ).
thf(f478,plain,
( $false
| ~ spl0_4
| ~ spl0_9
| ~ spl0_25 ),
inference(subsumption_resolution,[status(thm)],[f475,f137]) ).
thf(f475,plain,
( ( ( cR @ cB @ cF )
!= $true )
| ~ spl0_4
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f473]) ).
thf(f473,plain,
( ( ( cR @ cB @ cF )
!= $true )
| ( $true != $true )
| ~ spl0_4
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f435,f65]) ).
thf(f65,plain,
( ( ( cR @ cA @ cB )
= $true )
| ~ spl0_9 ),
inference(avatar_component_clause,[status(thm)],[f63]) ).
thf(f63,definition,
( spl0_9
<=> ( ( cR @ cA @ cB )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition]) ).
thf(f435,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ cA @ X0 ) )
| ( ( cR @ X0 @ cF )
!= $true ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f434]) ).
thf(f434,plain,
( ! [X0: $i] :
( ( ( cR @ X0 @ cF )
!= $true )
| ( $true != $true )
| ( $true
!= ( cR @ cA @ X0 ) ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f13,f42]) ).
thf(f453,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_28 ),
inference(avatar_contradiction_clause,[status(thm)],[f452]) ).
thf(f452,plain,
( $false
| ~ spl0_5
| ~ spl0_14
| ~ spl0_28 ),
inference(subsumption_resolution,[status(thm)],[f451,f150]) ).
thf(f451,plain,
( ( ( cG @ cA @ cE )
!= $true )
| ~ spl0_5
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f450]) ).
thf(f450,plain,
( ( ( cG @ cA @ cE )
!= $true )
| ( $true != $true )
| ~ spl0_5
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f387,f47]) ).
thf(f47,plain,
( ( ( cG @ cA @ cC )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl0_5
<=> ( ( cG @ cA @ cC )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition]) ).
thf(f387,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cC ) )
| ( ( cG @ X0 @ cE )
!= $true ) )
| ~ spl0_14 ),
inference(trivial_inequality_removal,[status(thm)],[f386]) ).
thf(f386,plain,
( ! [X0: $i] :
( ( ( cG @ X0 @ cE )
!= $true )
| ( $true
!= ( cG @ X0 @ cC ) )
| ( $true != $true ) )
| ~ spl0_14 ),
inference(superposition,[status(thm)],[f15,f87]) ).
thf(f433,plain,
( ~ spl0_1
| ~ spl0_10
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[status(thm)],[f432]) ).
thf(f432,plain,
( $false
| ~ spl0_1
| ~ spl0_10
| ~ spl0_24 ),
inference(subsumption_resolution,[status(thm)],[f415,f69]) ).
thf(f415,plain,
( ( ( cG @ cA @ cB )
!= $true )
| ~ spl0_1
| ~ spl0_24 ),
inference(trivial_inequality_removal,[status(thm)],[f412]) ).
thf(f412,plain,
( ( $true != $true )
| ( ( cG @ cA @ cB )
!= $true )
| ~ spl0_1
| ~ spl0_24 ),
inference(superposition,[status(thm)],[f377,f132]) ).
thf(f377,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cD ) )
| ( ( cG @ X0 @ cB )
!= $true ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[status(thm)],[f376]) ).
thf(f376,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cD ) )
| ( $true != $true )
| ( ( cG @ X0 @ cB )
!= $true ) )
| ~ spl0_1 ),
inference(superposition,[status(thm)],[f15,f29]) ).
thf(f431,plain,
( ~ spl0_3
| ~ spl0_10
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[status(thm)],[f430]) ).
thf(f430,plain,
( $false
| ~ spl0_3
| ~ spl0_10
| ~ spl0_26 ),
inference(subsumption_resolution,[status(thm)],[f382,f69]) ).
thf(f382,plain,
( ( ( cG @ cA @ cB )
!= $true )
| ~ spl0_3
| ~ spl0_26 ),
inference(trivial_inequality_removal,[status(thm)],[f378]) ).
thf(f378,plain,
( ( ( cG @ cA @ cB )
!= $true )
| ( $true != $true )
| ~ spl0_3
| ~ spl0_26 ),
inference(superposition,[status(thm)],[f260,f38]) ).
thf(f38,plain,
( ( ( cG @ cA @ cF )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[status(thm)],[f36]) ).
thf(f260,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cF ) )
| ( ( cG @ X0 @ cB )
!= $true ) )
| ~ spl0_26 ),
inference(trivial_inequality_removal,[status(thm)],[f259]) ).
thf(f259,plain,
( ! [X0: $i] :
( ( ( cG @ X0 @ cB )
!= $true )
| ( $true
!= ( cG @ X0 @ cF ) )
| ( $true != $true ) )
| ~ spl0_26 ),
inference(superposition,[status(thm)],[f15,f141]) ).
thf(f429,plain,
( ~ spl0_6
| ~ spl0_9
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[status(thm)],[f428]) ).
thf(f428,plain,
( $false
| ~ spl0_6
| ~ spl0_9
| ~ spl0_30 ),
inference(subsumption_resolution,[status(thm)],[f427,f159]) ).
thf(f427,plain,
( ( ( cR @ cB @ cC )
!= $true )
| ~ spl0_6
| ~ spl0_9 ),
inference(trivial_inequality_removal,[status(thm)],[f422]) ).
thf(f422,plain,
( ( ( cR @ cB @ cC )
!= $true )
| ( $true != $true )
| ~ spl0_6
| ~ spl0_9 ),
inference(superposition,[status(thm)],[f385,f65]) ).
thf(f385,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ cA @ X0 ) )
| ( ( cR @ X0 @ cC )
!= $true ) )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f384]) ).
thf(f384,plain,
( ! [X0: $i] :
( ( ( cR @ X0 @ cC )
!= $true )
| ( $true
!= ( cR @ cA @ X0 ) )
| ( $true != $true ) )
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f13,f51]) ).
thf(f51,plain,
( ( ( cR @ cA @ cC )
= $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl0_6
<=> ( ( cR @ cA @ cC )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition]) ).
thf(f375,plain,
( ~ spl0_8
| ~ spl0_18
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[status(thm)],[f374]) ).
thf(f374,plain,
( $false
| ~ spl0_8
| ~ spl0_18
| ~ spl0_20 ),
inference(subsumption_resolution,[status(thm)],[f373,f60]) ).
thf(f60,plain,
( ( ( cR @ cD @ cF )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl0_8
<=> ( ( cR @ cD @ cF )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition]) ).
thf(f373,plain,
( ( ( cR @ cD @ cF )
!= $true )
| ~ spl0_18
| ~ spl0_20 ),
inference(trivial_inequality_removal,[status(thm)],[f368]) ).
thf(f368,plain,
( ( $true != $true )
| ( ( cR @ cD @ cF )
!= $true )
| ~ spl0_18
| ~ spl0_20 ),
inference(superposition,[status(thm)],[f273,f105]) ).
thf(f361,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[status(thm)],[f360]) ).
thf(f360,plain,
( $false
| ~ spl0_4
| ~ spl0_8
| ~ spl0_23 ),
inference(subsumption_resolution,[status(thm)],[f356,f60]) ).
thf(f356,plain,
( ( ( cR @ cD @ cF )
!= $true )
| ~ spl0_4
| ~ spl0_23 ),
inference(trivial_inequality_removal,[status(thm)],[f353]) ).
thf(f353,plain,
( ( ( cR @ cD @ cF )
!= $true )
| ( $true != $true )
| ~ spl0_4
| ~ spl0_23 ),
inference(superposition,[status(thm)],[f319,f128]) ).
thf(f128,plain,
( ( ( cR @ cA @ cD )
= $true )
| ~ spl0_23 ),
inference(avatar_component_clause,[status(thm)],[f126]) ).
thf(f126,definition,
( spl0_23
<=> ( ( cR @ cA @ cD )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition]) ).
thf(f319,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ cA @ X0 ) )
| ( ( cR @ X0 @ cF )
!= $true ) )
| ~ spl0_4 ),
inference(trivial_inequality_removal,[status(thm)],[f318]) ).
thf(f318,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ cA @ X0 ) )
| ( ( cR @ X0 @ cF )
!= $true )
| ( $true != $true ) )
| ~ spl0_4 ),
inference(superposition,[status(thm)],[f13,f42]) ).
thf(f359,plain,
( ~ spl0_4
| ~ spl0_6
| ~ spl0_20 ),
inference(avatar_contradiction_clause,[status(thm)],[f358]) ).
thf(f358,plain,
( $false
| ~ spl0_4
| ~ spl0_6
| ~ spl0_20 ),
inference(subsumption_resolution,[status(thm)],[f357,f114]) ).
thf(f357,plain,
( ( ( cR @ cC @ cF )
!= $true )
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[status(thm)],[f352]) ).
thf(f352,plain,
( ( ( cR @ cC @ cF )
!= $true )
| ( $true != $true )
| ~ spl0_4
| ~ spl0_6 ),
inference(superposition,[status(thm)],[f319,f51]) ).
thf(f345,plain,
( ~ spl0_18
| ~ spl0_6
| ~ spl0_23 ),
inference(avatar_split_clause,[status(thm)],[f344,f126,f49,f103]) ).
thf(f344,plain,
( ( ( cR @ cC @ cD )
!= $true )
| ~ spl0_6
| ~ spl0_23 ),
inference(trivial_inequality_removal,[status(thm)],[f339]) ).
thf(f339,plain,
( ( ( cR @ cC @ cD )
!= $true )
| ( $true != $true )
| ~ spl0_6
| ~ spl0_23 ),
inference(superposition,[status(thm)],[f298,f51]) ).
thf(f298,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ cA @ X0 ) )
| ( $true
!= ( cR @ X0 @ cD ) ) )
| ~ spl0_23 ),
inference(trivial_inequality_removal,[status(thm)],[f296]) ).
thf(f296,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cR @ cA @ X0 ) )
| ( $true
!= ( cR @ X0 @ cD ) ) )
| ~ spl0_23 ),
inference(superposition,[status(thm)],[f13,f128]) ).
thf(f330,plain,
( ~ spl0_1
| ~ spl0_17
| ~ spl0_29 ),
inference(avatar_split_clause,[status(thm)],[f328,f153,f99,f27]) ).
thf(f99,definition,
( spl0_17
<=> ( ( cG @ cC @ cD )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition]) ).
thf(f328,plain,
( ( ( cG @ cB @ cD )
!= $true )
| ~ spl0_17
| ~ spl0_29 ),
inference(trivial_inequality_removal,[status(thm)],[f326]) ).
thf(f326,plain,
( ( $true != $true )
| ( ( cG @ cB @ cD )
!= $true )
| ~ spl0_17
| ~ spl0_29 ),
inference(superposition,[status(thm)],[f191,f155]) ).
thf(f191,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cC ) )
| ( $true
!= ( cG @ X0 @ cD ) ) )
| ~ spl0_17 ),
inference(trivial_inequality_removal,[status(thm)],[f180]) ).
thf(f180,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cG @ X0 @ cD ) )
| ( $true
!= ( cG @ X0 @ cC ) ) )
| ~ spl0_17 ),
inference(superposition,[status(thm)],[f15,f101]) ).
thf(f101,plain,
( ( ( cG @ cC @ cD )
= $true )
| ~ spl0_17 ),
inference(avatar_component_clause,[status(thm)],[f99]) ).
thf(f317,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[status(thm)],[f316]) ).
thf(f316,plain,
( $false
| ~ spl0_6
| ~ spl0_13
| ~ spl0_27 ),
inference(subsumption_resolution,[status(thm)],[f314,f83]) ).
thf(f314,plain,
( ( ( cR @ cC @ cE )
!= $true )
| ~ spl0_6
| ~ spl0_27 ),
inference(trivial_inequality_removal,[status(thm)],[f312]) ).
thf(f312,plain,
( ( ( cR @ cC @ cE )
!= $true )
| ( $true != $true )
| ~ spl0_6
| ~ spl0_27 ),
inference(superposition,[status(thm)],[f174,f51]) ).
thf(f174,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ cA @ X0 ) )
| ( $true
!= ( cR @ X0 @ cE ) ) )
| ~ spl0_27 ),
inference(trivial_inequality_removal,[status(thm)],[f166]) ).
thf(f166,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ cA @ X0 ) )
| ( $true != $true )
| ( $true
!= ( cR @ X0 @ cE ) ) )
| ~ spl0_27 ),
inference(superposition,[status(thm)],[f13,f146]) ).
thf(f311,plain,
( ~ spl0_14
| ~ spl0_17
| ~ spl0_21 ),
inference(avatar_contradiction_clause,[status(thm)],[f310]) ).
thf(f310,plain,
( $false
| ~ spl0_14
| ~ spl0_17
| ~ spl0_21 ),
inference(subsumption_resolution,[status(thm)],[f309,f87]) ).
thf(f309,plain,
( ( ( cG @ cC @ cE )
!= $true )
| ~ spl0_17
| ~ spl0_21 ),
inference(trivial_inequality_removal,[status(thm)],[f308]) ).
thf(f308,plain,
( ( ( cG @ cC @ cE )
!= $true )
| ( $true != $true )
| ~ spl0_17
| ~ spl0_21 ),
inference(superposition,[status(thm)],[f255,f101]) ).
thf(f255,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cD ) )
| ( ( cG @ X0 @ cE )
!= $true ) )
| ~ spl0_21 ),
inference(trivial_inequality_removal,[status(thm)],[f254]) ).
thf(f254,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cG @ X0 @ cE )
!= $true )
| ( $true
!= ( cG @ X0 @ cD ) ) )
| ~ spl0_21 ),
inference(superposition,[status(thm)],[f15,f119]) ).
thf(f293,plain,
( ~ spl0_24
| ~ spl0_5
| ~ spl0_17 ),
inference(avatar_split_clause,[status(thm)],[f290,f99,f45,f130]) ).
thf(f290,plain,
( ( ( cG @ cA @ cD )
!= $true )
| ~ spl0_5
| ~ spl0_17 ),
inference(trivial_inequality_removal,[status(thm)],[f289]) ).
thf(f289,plain,
( ( ( cG @ cA @ cD )
!= $true )
| ( $true != $true )
| ~ spl0_5
| ~ spl0_17 ),
inference(superposition,[status(thm)],[f191,f47]) ).
thf(f284,plain,
( ~ spl0_5
| ~ spl0_10
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[status(thm)],[f283]) ).
thf(f283,plain,
( $false
| ~ spl0_5
| ~ spl0_10
| ~ spl0_29 ),
inference(subsumption_resolution,[status(thm)],[f281,f69]) ).
thf(f281,plain,
( ( ( cG @ cA @ cB )
!= $true )
| ~ spl0_5
| ~ spl0_29 ),
inference(trivial_inequality_removal,[status(thm)],[f280]) ).
thf(f280,plain,
( ( $true != $true )
| ( ( cG @ cA @ cB )
!= $true )
| ~ spl0_5
| ~ spl0_29 ),
inference(superposition,[status(thm)],[f190,f47]) ).
thf(f190,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cC ) )
| ( ( cG @ X0 @ cB )
!= $true ) )
| ~ spl0_29 ),
inference(trivial_inequality_removal,[status(thm)],[f182]) ).
thf(f182,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cG @ X0 @ cC ) )
| ( ( cG @ X0 @ cB )
!= $true ) )
| ~ spl0_29 ),
inference(superposition,[status(thm)],[f15,f155]) ).
thf(f270,plain,
( ~ spl0_19
| ~ spl0_26
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[status(thm)],[f269]) ).
thf(f269,plain,
( $false
| ~ spl0_19
| ~ spl0_26
| ~ spl0_29 ),
inference(subsumption_resolution,[status(thm)],[f265,f141]) ).
thf(f265,plain,
( ( ( cG @ cB @ cF )
!= $true )
| ~ spl0_19
| ~ spl0_29 ),
inference(trivial_inequality_removal,[status(thm)],[f263]) ).
thf(f263,plain,
( ( $true != $true )
| ( ( cG @ cB @ cF )
!= $true )
| ~ spl0_19
| ~ spl0_29 ),
inference(superposition,[status(thm)],[f186,f155]) ).
thf(f186,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cC ) )
| ( $true
!= ( cG @ X0 @ cF ) ) )
| ~ spl0_19 ),
inference(trivial_inequality_removal,[status(thm)],[f181]) ).
thf(f181,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cC ) )
| ( $true != $true )
| ( $true
!= ( cG @ X0 @ cF ) ) )
| ~ spl0_19 ),
inference(superposition,[status(thm)],[f15,f110]) ).
thf(f110,plain,
( ( ( cG @ cC @ cF )
= $true )
| ~ spl0_19 ),
inference(avatar_component_clause,[status(thm)],[f108]) ).
thf(f108,definition,
( spl0_19
<=> ( ( cG @ cC @ cF )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition]) ).
thf(f268,plain,
( ~ spl0_3
| ~ spl0_5
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[status(thm)],[f267]) ).
thf(f267,plain,
( $false
| ~ spl0_3
| ~ spl0_5
| ~ spl0_19 ),
inference(subsumption_resolution,[status(thm)],[f266,f38]) ).
thf(f266,plain,
( ( ( cG @ cA @ cF )
!= $true )
| ~ spl0_5
| ~ spl0_19 ),
inference(trivial_inequality_removal,[status(thm)],[f264]) ).
thf(f264,plain,
( ( $true != $true )
| ( ( cG @ cA @ cF )
!= $true )
| ~ spl0_5
| ~ spl0_19 ),
inference(superposition,[status(thm)],[f186,f47]) ).
thf(f262,plain,
( ~ spl0_12
| ~ spl0_15
| ~ spl0_26 ),
inference(avatar_split_clause,[status(thm)],[f261,f139,f90,f76]) ).
thf(f90,definition,
( spl0_15
<=> ( ( cG @ cE @ cF )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition]) ).
thf(f261,plain,
( ( ( cG @ cB @ cE )
!= $true )
| ~ spl0_15
| ~ spl0_26 ),
inference(trivial_inequality_removal,[status(thm)],[f258]) ).
thf(f258,plain,
( ( $true != $true )
| ( ( cG @ cB @ cE )
!= $true )
| ~ spl0_15
| ~ spl0_26 ),
inference(superposition,[status(thm)],[f185,f141]) ).
thf(f185,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cF ) )
| ( ( cG @ X0 @ cE )
!= $true ) )
| ~ spl0_15 ),
inference(trivial_inequality_removal,[status(thm)],[f177]) ).
thf(f177,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cF ) )
| ( ( cG @ X0 @ cE )
!= $true )
| ( $true != $true ) )
| ~ spl0_15 ),
inference(superposition,[status(thm)],[f15,f92]) ).
thf(f92,plain,
( ( ( cG @ cE @ cF )
= $true )
| ~ spl0_15 ),
inference(avatar_component_clause,[status(thm)],[f90]) ).
thf(f251,plain,
( ~ spl0_2
| ~ spl0_11
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[status(thm)],[f250]) ).
thf(f250,plain,
( $false
| ~ spl0_2
| ~ spl0_11
| ~ spl0_22 ),
inference(subsumption_resolution,[status(thm)],[f249,f33]) ).
thf(f33,plain,
( ( ( cR @ cB @ cD )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[status(thm)],[f31]) ).
thf(f31,definition,
( spl0_2
<=> ( ( cR @ cB @ cD )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition]) ).
thf(f249,plain,
( ( ( cR @ cB @ cD )
!= $true )
| ~ spl0_11
| ~ spl0_22 ),
inference(trivial_inequality_removal,[status(thm)],[f246]) ).
thf(f246,plain,
( ( $true != $true )
| ( ( cR @ cB @ cD )
!= $true )
| ~ spl0_11
| ~ spl0_22 ),
inference(superposition,[status(thm)],[f169,f123]) ).
thf(f169,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ X0 @ cE ) )
| ( ( cR @ cB @ X0 )
!= $true ) )
| ~ spl0_11 ),
inference(trivial_inequality_removal,[status(thm)],[f162]) ).
thf(f162,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cR @ cB @ X0 )
!= $true )
| ( $true
!= ( cR @ X0 @ cE ) ) )
| ~ spl0_11 ),
inference(superposition,[status(thm)],[f13,f74]) ).
thf(f74,plain,
( ( ( cR @ cB @ cE )
= $true )
| ~ spl0_11 ),
inference(avatar_component_clause,[status(thm)],[f72]) ).
thf(f72,definition,
( spl0_11
<=> ( ( cR @ cB @ cE )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition]) ).
thf(f245,plain,
( ~ spl0_21
| ~ spl0_7
| ~ spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f240,f90,f54,f117]) ).
thf(f240,plain,
( ( ( cG @ cD @ cE )
!= $true )
| ~ spl0_7
| ~ spl0_15 ),
inference(trivial_inequality_removal,[status(thm)],[f234]) ).
thf(f234,plain,
( ( ( cG @ cD @ cE )
!= $true )
| ( $true != $true )
| ~ spl0_7
| ~ spl0_15 ),
inference(superposition,[status(thm)],[f185,f56]) ).
thf(f244,plain,
( ~ spl0_28
| ~ spl0_3
| ~ spl0_15 ),
inference(avatar_split_clause,[status(thm)],[f238,f90,f36,f148]) ).
thf(f238,plain,
( ( ( cG @ cA @ cE )
!= $true )
| ~ spl0_3
| ~ spl0_15 ),
inference(trivial_inequality_removal,[status(thm)],[f236]) ).
thf(f236,plain,
( ( ( cG @ cA @ cE )
!= $true )
| ( $true != $true )
| ~ spl0_3
| ~ spl0_15 ),
inference(superposition,[status(thm)],[f185,f38]) ).
thf(f243,plain,
( ~ spl0_14
| ~ spl0_15
| ~ spl0_19 ),
inference(avatar_split_clause,[status(thm)],[f239,f108,f90,f85]) ).
thf(f239,plain,
( ( ( cG @ cC @ cE )
!= $true )
| ~ spl0_15
| ~ spl0_19 ),
inference(trivial_inequality_removal,[status(thm)],[f235]) ).
thf(f235,plain,
( ( ( cG @ cC @ cE )
!= $true )
| ( $true != $true )
| ~ spl0_15
| ~ spl0_19 ),
inference(superposition,[status(thm)],[f185,f110]) ).
thf(f232,plain,
( ~ spl0_22
| ~ spl0_23
| ~ spl0_27 ),
inference(avatar_split_clause,[status(thm)],[f230,f144,f126,f121]) ).
thf(f230,plain,
( ( ( cR @ cD @ cE )
!= $true )
| ~ spl0_23
| ~ spl0_27 ),
inference(trivial_inequality_removal,[status(thm)],[f229]) ).
thf(f229,plain,
( ( ( cR @ cD @ cE )
!= $true )
| ( $true != $true )
| ~ spl0_23
| ~ spl0_27 ),
inference(superposition,[status(thm)],[f174,f128]) ).
thf(f225,plain,
( ~ spl0_2
| ~ spl0_9
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[status(thm)],[f224]) ).
thf(f224,plain,
( $false
| ~ spl0_2
| ~ spl0_9
| ~ spl0_23 ),
inference(subsumption_resolution,[status(thm)],[f222,f33]) ).
thf(f222,plain,
( ( ( cR @ cB @ cD )
!= $true )
| ~ spl0_9
| ~ spl0_23 ),
inference(trivial_inequality_removal,[status(thm)],[f218]) ).
thf(f218,plain,
( ( $true != $true )
| ( ( cR @ cB @ cD )
!= $true )
| ~ spl0_9
| ~ spl0_23 ),
inference(superposition,[status(thm)],[f173,f65]) ).
thf(f173,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ cA @ X0 ) )
| ( $true
!= ( cR @ X0 @ cD ) ) )
| ~ spl0_23 ),
inference(trivial_inequality_removal,[status(thm)],[f165]) ).
thf(f165,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ X0 @ cD ) )
| ( $true
!= ( cR @ cA @ X0 ) )
| ( $true != $true ) )
| ~ spl0_23 ),
inference(superposition,[status(thm)],[f13,f128]) ).
thf(f207,plain,
( ~ spl0_8
| ~ spl0_2
| ~ spl0_25 ),
inference(avatar_split_clause,[status(thm)],[f203,f135,f31,f58]) ).
thf(f203,plain,
( ( ( cR @ cD @ cF )
!= $true )
| ~ spl0_2
| ~ spl0_25 ),
inference(trivial_inequality_removal,[status(thm)],[f200]) ).
thf(f200,plain,
( ( ( cR @ cD @ cF )
!= $true )
| ( $true != $true )
| ~ spl0_2
| ~ spl0_25 ),
inference(superposition,[status(thm)],[f170,f33]) ).
thf(f170,plain,
( ! [X0: $i] :
( ( ( cR @ cB @ X0 )
!= $true )
| ( ( cR @ X0 @ cF )
!= $true ) )
| ~ spl0_25 ),
inference(trivial_inequality_removal,[status(thm)],[f163]) ).
thf(f163,plain,
( ! [X0: $i] :
( ( ( cR @ X0 @ cF )
!= $true )
| ( $true != $true )
| ( ( cR @ cB @ X0 )
!= $true ) )
| ~ spl0_25 ),
inference(superposition,[status(thm)],[f13,f137]) ).
thf(f206,plain,
( ~ spl0_16
| ~ spl0_11
| ~ spl0_25 ),
inference(avatar_split_clause,[status(thm)],[f204,f135,f72,f94]) ).
thf(f204,plain,
( ( ( cR @ cE @ cF )
!= $true )
| ~ spl0_11
| ~ spl0_25 ),
inference(trivial_inequality_removal,[status(thm)],[f201]) ).
thf(f201,plain,
( ( $true != $true )
| ( ( cR @ cE @ cF )
!= $true )
| ~ spl0_11
| ~ spl0_25 ),
inference(superposition,[status(thm)],[f170,f74]) ).
thf(f199,plain,
( ~ spl0_30
| ~ spl0_11
| ~ spl0_13 ),
inference(avatar_split_clause,[status(thm)],[f198,f81,f72,f157]) ).
thf(f198,plain,
( ( ( cR @ cB @ cC )
!= $true )
| ~ spl0_11
| ~ spl0_13 ),
inference(trivial_inequality_removal,[status(thm)],[f195]) ).
thf(f195,plain,
( ( ( cR @ cB @ cC )
!= $true )
| ( $true != $true )
| ~ spl0_11
| ~ spl0_13 ),
inference(superposition,[status(thm)],[f169,f83]) ).
thf(f160,plain,
( spl0_29
| spl0_30 ),
inference(avatar_split_clause,[status(thm)],[f25,f157,f153]) ).
thf(f25,plain,
( ( ( cR @ cB @ cC )
= $true )
| ( ( cG @ cB @ cC )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f151,plain,
( spl0_27
| spl0_28 ),
inference(avatar_split_clause,[status(thm)],[f23,f148,f144]) ).
thf(f23,plain,
( ( ( cR @ cA @ cE )
= $true )
| ( ( cG @ cA @ cE )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f142,plain,
( spl0_25
| spl0_26 ),
inference(avatar_split_clause,[status(thm)],[f17,f139,f135]) ).
thf(f17,plain,
( ( ( cG @ cB @ cF )
= $true )
| ( ( cR @ cB @ cF )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f133,plain,
( spl0_23
| spl0_24 ),
inference(avatar_split_clause,[status(thm)],[f20,f130,f126]) ).
thf(f20,plain,
( ( ( cG @ cA @ cD )
= $true )
| ( ( cR @ cA @ cD )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f124,plain,
( spl0_21
| spl0_22 ),
inference(avatar_split_clause,[status(thm)],[f11,f121,f117]) ).
thf(f11,plain,
( ( ( cG @ cD @ cE )
= $true )
| ( ( cR @ cD @ cE )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f115,plain,
( spl0_19
| spl0_20 ),
inference(avatar_split_clause,[status(thm)],[f19,f112,f108]) ).
thf(f19,plain,
( ( ( cR @ cC @ cF )
= $true )
| ( ( cG @ cC @ cF )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f106,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[status(thm)],[f22,f103,f99]) ).
thf(f22,plain,
( ( ( cG @ cC @ cD )
= $true )
| ( ( cR @ cC @ cD )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f97,plain,
( spl0_15
| spl0_16 ),
inference(avatar_split_clause,[status(thm)],[f16,f94,f90]) ).
thf(f16,plain,
( ( ( cR @ cE @ cF )
= $true )
| ( ( cG @ cE @ cF )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f88,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[status(thm)],[f9,f85,f81]) ).
thf(f9,plain,
( ( ( cG @ cC @ cE )
= $true )
| ( ( cR @ cC @ cE )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f79,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[status(thm)],[f18,f76,f72]) ).
thf(f18,plain,
( ( ( cG @ cB @ cE )
= $true )
| ( ( cR @ cB @ cE )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f70,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[status(thm)],[f21,f67,f63]) ).
thf(f21,plain,
( ( ( cR @ cA @ cB )
= $true )
| ( ( cG @ cA @ cB )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f61,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[status(thm)],[f10,f58,f54]) ).
thf(f10,plain,
( ( ( cR @ cD @ cF )
= $true )
| ( ( cG @ cD @ cF )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f52,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[status(thm)],[f12,f49,f45]) ).
thf(f12,plain,
( ( ( cG @ cA @ cC )
= $true )
| ( ( cR @ cA @ cC )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f43,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[status(thm)],[f14,f40,f36]) ).
thf(f14,plain,
( ( ( cG @ cA @ cF )
= $true )
| ( ( cR @ cA @ cF )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
thf(f34,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[status(thm)],[f24,f31,f27]) ).
thf(f24,plain,
( ( ( cG @ cB @ cD )
= $true )
| ( ( cR @ cB @ cD )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f8]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SYO179^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.17/0.33 % Computer : n023.cluster.edu
% 0.17/0.33 % Model : x86_64 x86_64
% 0.17/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.33 % Memory : 8042.1875MB
% 0.17/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.33 % CPULimit : 300
% 0.17/0.33 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 14:26:49 EST 2026
% 0.17/0.34 % CPUTime :
% 0.17/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.46 ---- Original DTF file ---
% 0.20/0.46 thf(spec,logic,$$dhol).
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 % File : SYO179^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.46 % Domain : Syntactic
% 0.20/0.46 % Problem : TPS problem from BASIC-FO-THMS
% 0.20/0.46 % Version : Especial.
% 0.20/0.46 % English :
% 0.20/0.46
% 0.20/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.46 % Source : [Bro09]
% 0.20/0.46 % Names : tps_1173 [Bro09]
% 0.20/0.46
% 0.20/0.46 % Status : Theorem
% 0.20/0.46 % Rating : 0.25 v8.2.0, 0.27 v8.1.0, 0.25 v7.4.0, 0.33 v7.3.0, 0.30 v7.2.0, 0.38 v7.1.0, 0.43 v7.0.0, 0.38 v6.4.0, 0.43 v6.3.0, 0.50 v6.0.0, 0.33 v5.5.0, 0.20 v5.4.0, 0.25 v5.2.0, 0.50 v5.1.0, 0.75 v5.0.0, 0.25 v4.1.0, 0.67 v4.0.0
% 0.20/0.46 % Syntax : Number of formulae : 9 ( 0 unt; 8 typ; 0 def)
% 0.20/0.46 % Number of atoms : 36 ( 0 equ; 0 cnn)
% 0.20/0.46 % Maximal formula atoms : 36 ( 36 avg)
% 0.20/0.46 % Number of connectives : 107 ( 0 ~; 16 |; 18 &; 72 @)
% 0.20/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.20/0.46 % Maximal formula depth : 19 ( 19 avg)
% 0.20/0.46 % Number of types : 2 ( 0 usr)
% 0.20/0.46 % Number of type conns : 4 ( 4 >; 0 *; 0 +; 0 <<)
% 0.20/0.46 % Number of symbols : 8 ( 8 usr; 6 con; 0-2 aty)
% 0.20/0.46 % Number of variables : 6 ( 0 ^; 0 !; 6 ?; 6 :)
% 0.20/0.46 % SPC : TH0_THM_NEQ_NAR
% 0.20/0.46
% 0.20/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 thf(cG,type,
% 0.20/0.46 cG: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(cR,type,
% 0.20/0.46 cR: $i > $i > $o ).
% 0.20/0.46
% 0.20/0.46 thf(cF,type,
% 0.20/0.46 cF: $i ).
% 0.20/0.46
% 0.20/0.46 thf(cE,type,
% 0.20/0.46 cE: $i ).
% 0.20/0.46
% 0.20/0.46 thf(cD,type,
% 0.20/0.46 cD: $i ).
% 0.20/0.46
% 0.20/0.46 thf(cC,type,
% 0.20/0.46 cC: $i ).
% 0.20/0.46
% 0.20/0.46 thf(cB,type,
% 0.20/0.46 cB: $i ).
% 0.20/0.46
% 0.20/0.46 thf(cA,type,
% 0.20/0.46 cA: $i ).
% 0.20/0.46
% 0.20/0.46 thf(cSIX_THEOREM_B,conjecture,
% 0.20/0.46 ( ( ( ( cR @ cA @ cB )
% 0.20/0.46 | ( cG @ cA @ cB ) )
% 0.20/0.46 & ( ( cR @ cA @ cC )
% 0.20/0.46 | ( cG @ cA @ cC ) )
% 0.20/0.46 & ( ( cR @ cA @ cD )
% 0.20/0.46 | ( cG @ cA @ cD ) )
% 0.20/0.46 & ( ( cR @ cA @ cE )
% 0.20/0.46 | ( cG @ cA @ cE ) )
% 0.20/0.46 & ( ( cR @ cA @ cF )
% 0.20/0.46 | ( cG @ cA @ cF ) )
% 0.20/0.46 & ( ( cR @ cB @ cC )
% 0.20/0.46 | ( cG @ cB @ cC ) )
% 0.20/0.46 & ( ( cR @ cB @ cD )
% 0.20/0.46 | ( cG @ cB @ cD ) )
% 0.20/0.46 & ( ( cR @ cB @ cE )
% 0.20/0.46 | ( cG @ cB @ cE ) )
% 0.20/0.46 & ( ( cR @ cB @ cF )
% 0.20/0.46 | ( cG @ cB @ cF ) )
% 0.20/0.46 & ( ( cR @ cC @ cD )
% 0.20/0.46 | ( cG @ cC @ cD ) )
% 0.20/0.46 & ( ( cR @ cC @ cE )
% 0.20/0.46 | ( cG @ cC @ cE ) )
% 0.20/0.46 & ( ( cR @ cC @ cF )
% 0.20/0.46 | ( cG @ cC @ cF ) )
% 0.20/0.46 & ( ( cR @ cD @ cE )
% 0.20/0.46 | ( cG @ cD @ cE ) )
% 0.20/0.46 & ( ( cR @ cD @ cF )
% 0.20/0.46 | ( cG @ cD @ cF ) )
% 0.20/0.46 & ( ( cR @ cE @ cF )
% 0.20/0.46 | ( cG @ cE @ cF ) ) )
% 0.20/0.46 => ( ? [Xa: $i,Xb: $i,Xc: $i] :
% 0.20/0.46 ( ( cR @ Xa @ Xb )
% 0.20/0.46 & ( cR @ Xa @ Xc )
% 0.20/0.46 & ( cR @ Xb @ Xc ) )
% 0.20/0.46 | ? [Xa: $i,Xb: $i,Xc: $i] :
% 0.20/0.46 ( ( cG @ Xa @ Xb )
% 0.20/0.46 & ( cG @ Xa @ Xc )
% 0.20/0.46 & ( cG @ Xb @ Xc ) ) ) ) ).
% 0.20/0.46
% 0.20/0.46 %------------------------------------------------------------------------------
% 0.20/0.46 ------------------------
% 1.74/1.41 ---- Embedded in THF ---
% 1.74/1.41 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.74/1.41 %%% Generated on Tue Feb 24 14:26:50 EST 2026
% 1.74/1.41 %%% using '$$dhol' embedding, version 1.3.0.
% 1.74/1.41 %%% Logic specification used:
% 1.74/1.41 %%% thf(spec, logic, $$dhol).
% 1.74/1.41
% 1.74/1.41 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.tHlHL5CGp0/DTF2DTF5569.p
% See solution above
% 1.74/1.41 ------------------------
% 1.74/1.42 ---- Cleaned THF ---
% 1.74/1.42 thf(cG,type,
% 1.74/1.42 cG: $i > $i > $o ).
% 1.74/1.42
% 1.74/1.42 thf(cR,type,
% 1.74/1.42 cR: $i > $i > $o ).
% 1.74/1.42
% 1.74/1.42 thf(cF,type,
% 1.74/1.42 cF: $i ).
% 1.74/1.42
% 1.74/1.42 thf(cE,type,
% 1.74/1.42 cE: $i ).
% 1.74/1.42
% 1.74/1.42 thf(cD,type,
% 1.74/1.42 cD: $i ).
% 1.74/1.42
% 1.74/1.42 thf(cC,type,
% 1.74/1.42 cC: $i ).
% 1.74/1.42
% 1.74/1.42 thf(cB,type,
% 1.74/1.42 cB: $i ).
% 1.74/1.42
% 1.74/1.42 thf(cA,type,
% 1.74/1.42 cA: $i ).
% 1.74/1.42
% 1.74/1.42 thf(cSIX_THEOREM_B,conjecture,
% 1.74/1.42 ( ( ( ( cR @ cA @ cB )
% 1.74/1.42 | ( cG @ cA @ cB ) )
% 1.74/1.42 & ( ( cR @ cA @ cC )
% 1.74/1.42 | ( cG @ cA @ cC ) )
% 1.74/1.42 & ( ( cR @ cA @ cD )
% 1.74/1.42 | ( cG @ cA @ cD ) )
% 1.74/1.42 & ( ( cR @ cA @ cE )
% 1.74/1.42 | ( cG @ cA @ cE ) )
% 1.74/1.42 & ( ( cR @ cA @ cF )
% 1.74/1.42 | ( cG @ cA @ cF ) )
% 1.74/1.42 & ( ( cR @ cB @ cC )
% 1.74/1.42 | ( cG @ cB @ cC ) )
% 1.74/1.42 & ( ( cR @ cB @ cD )
% 1.74/1.42 | ( cG @ cB @ cD ) )
% 1.74/1.42 & ( ( cR @ cB @ cE )
% 1.74/1.42 | ( cG @ cB @ cE ) )
% 1.74/1.42 & ( ( cR @ cB @ cF )
% 1.74/1.42 | ( cG @ cB @ cF ) )
% 1.74/1.42 & ( ( cR @ cC @ cD )
% 1.74/1.42 | ( cG @ cC @ cD ) )
% 1.74/1.42 & ( ( cR @ cC @ cE )
% 1.74/1.42 | ( cG @ cC @ cE ) )
% 1.74/1.42 & ( ( cR @ cC @ cF )
% 1.74/1.42 | ( cG @ cC @ cF ) )
% 1.74/1.42 & ( ( cR @ cD @ cE )
% 1.74/1.42 | ( cG @ cD @ cE ) )
% 1.74/1.42 & ( ( cR @ cD @ cF )
% 1.74/1.42 | ( cG @ cD @ cF ) )
% 1.74/1.42 & ( ( cR @ cE @ cF )
% 1.74/1.42 | ( cG @ cE @ cF ) ) )
% 1.74/1.42 => ( ? [Xa: $i,Xb: $i,Xc: $i] :
% 1.74/1.42 ( ( cR @ Xa @ Xb )
% 1.74/1.42 & ( cR @ Xa @ Xc )
% 1.74/1.42 & ( cR @ Xb @ Xc ) )
% 1.74/1.42 | ? [Xa: $i,Xb: $i,Xc: $i] :
% 1.74/1.42 ( ( cG @ Xa @ Xb )
% 1.74/1.42 & ( cG @ Xa @ Xc )
% 1.74/1.42 & ( cG @ Xb @ Xc ) ) ) ) ).
% 1.74/1.42 ------------------------
% 1.74/1.44 % (5672)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5569 for (2999ds/2Mi)
% 1.74/1.44 % (5669)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5569 for (2999ds/183Mi)
% 1.74/1.44 % (5670)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_5569 for (2999ds/4Mi)
% 1.74/1.44 % (5671)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_5569 for (2999ds/27Mi)
% 1.74/1.44 % (5673)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_5569 for (2999ds/2Mi)
% 1.74/1.44 % (5674)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_5569 for (2999ds/275Mi)
% 1.74/1.44 % (5675)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5569 for (2999ds/18Mi)
% 1.74/1.45 % (5672)Instruction limit reached!
% 1.74/1.45 % (5672)------------------------------
% 1.74/1.45 % (5672)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.45 % (5672)Termination reason: Unknown
% 1.74/1.45 % (5672)Termination phase: Saturation
% 1.74/1.45
% 1.74/1.45 % (5673)Instruction limit reached!
% 1.74/1.45 % (5673)------------------------------
% 1.74/1.45 % (5673)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.45 % (5673)Termination reason: Unknown
% 1.74/1.45 % (5673)Termination phase: Property scanning
% 1.74/1.45
% 1.74/1.45 % (5673)Memory used [KB]: 1023
% 1.74/1.45 % (5673)Time elapsed: 0.003 s
% 1.74/1.45 % (5673)Instructions burned: 3 (million)
% 1.74/1.45 % (5673)------------------------------
% 1.74/1.45 % (5673)------------------------------
% 1.74/1.45 % (5672)Memory used [KB]: 1023
% 1.74/1.45 % (5672)Time elapsed: 0.003 s
% 1.74/1.45 % (5672)Instructions burned: 3 (million)
% 1.74/1.45 % (5672)------------------------------
% 1.74/1.45 % (5672)------------------------------
% 1.74/1.45 % (5670)Instruction limit reached!
% 1.74/1.45 % (5670)------------------------------
% 1.74/1.45 % (5670)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.45 % (5670)Termination reason: Unknown
% 1.74/1.45 % (5670)Termination phase: Saturation
% 1.74/1.45
% 1.74/1.45 % (5670)Memory used [KB]: 5500
% 1.74/1.45 % (5670)Time elapsed: 0.004 s
% 1.74/1.45 % (5670)Instructions burned: 4 (million)
% 1.74/1.45 % (5670)------------------------------
% 1.74/1.45 % (5670)------------------------------
% 1.74/1.45 % (5675)Instruction limit reached!
% 1.74/1.45 % (5675)------------------------------
% 1.74/1.45 % (5675)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.45 % (5675)Termination reason: Unknown
% 1.74/1.45 % (5675)Termination phase: Saturation
% 1.74/1.45
% 1.74/1.46 % (5675)Memory used [KB]: 5628
% 1.74/1.46 % (5675)Time elapsed: 0.012 s
% 1.74/1.46 % (5675)Instructions burned: 19 (million)
% 1.74/1.46 % (5675)------------------------------
% 1.74/1.46 % (5675)------------------------------
% 1.74/1.46 % (5671)Instruction limit reached!
% 1.74/1.46 % (5671)------------------------------
% 1.74/1.46 % (5671)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.46 % (5671)Termination reason: Unknown
% 1.74/1.46 % (5671)Termination phase: Saturation
% 1.74/1.46
% 1.74/1.46 % (5671)Memory used [KB]: 5628
% 1.74/1.46 % (5671)Time elapsed: 0.017 s
% 1.74/1.46 % (5671)Instructions burned: 27 (million)
% 1.74/1.46 % (5671)------------------------------
% 1.74/1.46 % (5671)------------------------------
% 1.74/1.46 % (5676)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5569 for (2999ds/3Mi)
% 1.74/1.46 % (5677)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_5569 for (2999ds/37Mi)
% 1.74/1.46 % (5678)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_5569 for (2999ds/15Mi)
% 1.74/1.46 % (5676)Instruction limit reached!
% 1.74/1.46 % (5676)------------------------------
% 1.74/1.46 % (5676)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.46 % (5676)Termination reason: Unknown
% 1.74/1.46 % (5676)Termination phase: Saturation
% 1.74/1.46
% 1.74/1.46 % (5676)Memory used [KB]: 5500
% 1.74/1.46 % (5676)Time elapsed: 0.003 s
% 1.74/1.46 % (5676)Instructions burned: 3 (million)
% 1.74/1.46 % (5676)------------------------------
% 1.74/1.46 % (5676)------------------------------
% 1.74/1.47 % (5679)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5569 for (2999ds/3Mi)
% 1.74/1.47 % (5678)Instruction limit reached!
% 1.74/1.47 % (5678)------------------------------
% 1.74/1.47 % (5678)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.47 % (5678)Termination reason: Unknown
% 1.74/1.47 % (5678)Termination phase: Saturation
% 1.74/1.47
% 1.74/1.47 % (5678)Memory used [KB]: 5628
% 1.74/1.47 % (5678)Time elapsed: 0.010 s
% 1.74/1.47 % (5678)Instructions burned: 16 (million)
% 1.74/1.47 % (5678)------------------------------
% 1.74/1.47 % (5678)------------------------------
% 1.74/1.47 % (5679)Instruction limit reached!
% 1.74/1.47 % (5679)------------------------------
% 1.74/1.47 % (5679)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.47 % (5679)Termination reason: Unknown
% 1.74/1.47 % (5679)Termination phase: Saturation
% 1.74/1.47
% 1.74/1.47 % (5679)Memory used [KB]: 5500
% 1.74/1.47 % (5679)Time elapsed: 0.003 s
% 1.74/1.47 % (5679)Instructions burned: 3 (million)
% 1.74/1.47 % (5679)------------------------------
% 1.74/1.47 % (5679)------------------------------
% 1.74/1.48 % (5680)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_5569 for (2999ds/1041Mi)
% 1.74/1.48 % (5681)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5569 for (2999ds/7Mi)
% 1.74/1.48 % (5677)Instruction limit reached!
% 1.74/1.48 % (5677)------------------------------
% 1.74/1.48 % (5677)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.48 % (5677)Termination reason: Unknown
% 1.74/1.48 % (5677)Termination phase: Saturation
% 1.74/1.48
% 1.74/1.48 % (5677)Memory used [KB]: 5756
% 1.74/1.48 % (5677)Time elapsed: 0.019 s
% 1.74/1.48 % (5677)Instructions burned: 38 (million)
% 1.74/1.48 % (5677)------------------------------
% 1.74/1.48 % (5677)------------------------------
% 1.74/1.48 % (5681)Instruction limit reached!
% 1.74/1.48 % (5681)------------------------------
% 1.74/1.48 % (5681)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.48 % (5681)Termination reason: Unknown
% 1.74/1.48 % (5681)Termination phase: Saturation
% 1.74/1.48
% 1.74/1.48 % (5681)Memory used [KB]: 1023
% 1.74/1.48 % (5681)Time elapsed: 0.005 s
% 1.74/1.48 % (5681)Instructions burned: 7 (million)
% 1.74/1.48 % (5681)------------------------------
% 1.74/1.48 % (5681)------------------------------
% 1.74/1.49 % (5682)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5569 for (2999ds/16Mi)
% 1.74/1.49 % (5669)First to succeed.
% 1.74/1.49 % (5683)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_5569 for (2999ds/3Mi)
% 1.74/1.49 % (5683)Instruction limit reached!
% 1.74/1.49 % (5683)------------------------------
% 1.74/1.49 % (5683)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.49 % (5683)Termination reason: Unknown
% 1.74/1.49 % (5683)Termination phase: Twee Goal Transformation
% 1.74/1.49
% 1.74/1.49 % (5683)Memory used [KB]: 1023
% 1.74/1.49 % (5683)Time elapsed: 0.003 s
% 1.74/1.49 % (5683)Instructions burned: 4 (million)
% 1.74/1.49 % (5683)------------------------------
% 1.74/1.49 % (5683)------------------------------
% 1.74/1.49 % (5669)Refutation found. Thanks to Tanya!
% 1.74/1.49 % SZS status Theorem for DTF2THF_5569
% 1.74/1.49 % SZS output start Proof for DTF2THF_5569
% 1.74/1.49 thf(func_def_0, type, cG: $i > $i > $o).
% 1.74/1.49 thf(func_def_1, type, cR: $i > $i > $o).
% 1.74/1.49 thf(f653,plain,(
% 1.74/1.49 $false),
% 1.74/1.49 inference(avatar_sat_refutation,[status(thm)],[f34,f43,f52,f61,f70,f79,f88,f97,f106,f115,f124,f133,f142,f151,f160,f199,f206,f207,f225,f232,f243,f244,f245,f251,f262,f268,f270,f284,f293,f311,f317,f330,f345,f359,f361,f375,f429,f431,f433,f453,f479,f495,f521,f531,f537,f538,f554,f596,f614,f636,f652])).
% 1.74/1.49 thf(f652,plain,(
% 1.74/1.49 ~spl0_21 | ~spl0_24 | ~spl0_28),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f651])).
% 1.74/1.49 thf(f651,plain,(
% 1.74/1.49 $false | (~spl0_21 | ~spl0_24 | ~spl0_28)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f649,f150])).
% 1.74/1.49 thf(f150,plain,(
% 1.74/1.49 ((cG @ cA @ cE) = $true) | ~spl0_28),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f148])).
% 1.74/1.49 thf(f148,definition,(
% 1.74/1.49 spl0_28 <=> ((cG @ cA @ cE) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_28])],[avatar_definition])).
% 1.74/1.49 thf(f649,plain,(
% 1.74/1.49 ((cG @ cA @ cE) != $true) | (~spl0_21 | ~spl0_24)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f647])).
% 1.74/1.49 thf(f647,plain,(
% 1.74/1.49 ($true != $true) | ((cG @ cA @ cE) != $true) | (~spl0_21 | ~spl0_24)),
% 1.74/1.49 inference(superposition,[status(thm)],[f560,f132])).
% 1.74/1.49 thf(f132,plain,(
% 1.74/1.49 ((cG @ cA @ cD) = $true) | ~spl0_24),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f130])).
% 1.74/1.49 thf(f130,definition,(
% 1.74/1.49 spl0_24 <=> ((cG @ cA @ cD) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_24])],[avatar_definition])).
% 1.74/1.49 thf(f560,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cG @ X0 @ cD)) | ((cG @ X0 @ cE) != $true)) ) | ~spl0_21),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f559])).
% 1.74/1.49 thf(f559,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cG @ X0 @ cD)) | ($true != $true) | ((cG @ X0 @ cE) != $true)) ) | ~spl0_21),
% 1.74/1.49 inference(superposition,[status(thm)],[f15,f119])).
% 1.74/1.49 thf(f119,plain,(
% 1.74/1.49 ((cG @ cD @ cE) = $true) | ~spl0_21),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f117])).
% 1.74/1.49 thf(f117,definition,(
% 1.74/1.49 spl0_21 <=> ((cG @ cD @ cE) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_21])],[avatar_definition])).
% 1.74/1.49 thf(f15,plain,(
% 1.74/1.49 ( ! [X2 : $i,X0 : $i,X1 : $i] : (((cG @ X1 @ X2) != $true) | ((cG @ X0 @ X1) != $true) | ((cG @ X0 @ X2) != $true)) )),
% 1.74/1.49 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.49 thf(f8,plain,(
% 1.74/1.49 (((cG @ cB @ cC) = $true) | ((cR @ cB @ cC) = $true)) & (((cG @ cB @ cD) = $true) | ((cR @ cB @ cD) = $true)) & (((cR @ cA @ cE) = $true) | ((cG @ cA @ cE) = $true)) & (((cG @ cC @ cD) = $true) | ((cR @ cC @ cD) = $true)) & (((cG @ cA @ cB) = $true) | ((cR @ cA @ cB) = $true)) & (((cR @ cA @ cD) = $true) | ((cG @ cA @ cD) = $true)) & (((cR @ cC @ cF) = $true) | ((cG @ cC @ cF) = $true)) & (((cG @ cB @ cE) = $true) | ((cR @ cB @ cE) = $true)) & (((cG @ cB @ cF) = $true) | ((cR @ cB @ cF) = $true)) & (((cR @ cE @ cF) = $true) | ((cG @ cE @ cF) = $true)) & ! [X0 : $i,X1 : $i,X2 : $i] : (((cG @ X1 @ X2) != $true) | ((cG @ X0 @ X1) != $true) | ((cG @ X0 @ X2) != $true)) & (((cR @ cA @ cF) = $true) | ((cG @ cA @ cF) = $true)) & ! [X3 : $i,X4 : $i,X5 : $i] : (((cR @ X4 @ X3) != $true) | ((cR @ X3 @ X5) != $true) | ((cR @ X4 @ X5) != $true)) & (((cG @ cA @ cC) = $true) | ((cR @ cA @ cC) = $true)) & (((cG @ cD @ cE) = $true) | ((cR @ cD @ cE) = $true)) & (((cG @ cD @ cF) = $true) | ((cR @ cD @ cF) = $true)) & (((cG @ cC @ cE) = $true) | ((cR @ cC @ cE) = $true))),
% 1.74/1.49 inference(rectify,[status(thm)],[f7])).
% 1.74/1.49 thf(f7,plain,(
% 1.74/1.49 (((cG @ cB @ cC) = $true) | ((cR @ cB @ cC) = $true)) & (((cG @ cB @ cD) = $true) | ((cR @ cB @ cD) = $true)) & (((cR @ cA @ cE) = $true) | ((cG @ cA @ cE) = $true)) & (((cG @ cC @ cD) = $true) | ((cR @ cC @ cD) = $true)) & (((cG @ cA @ cB) = $true) | ((cR @ cA @ cB) = $true)) & (((cR @ cA @ cD) = $true) | ((cG @ cA @ cD) = $true)) & (((cR @ cC @ cF) = $true) | ((cG @ cC @ cF) = $true)) & (((cG @ cB @ cE) = $true) | ((cR @ cB @ cE) = $true)) & (((cG @ cB @ cF) = $true) | ((cR @ cB @ cF) = $true)) & (((cR @ cE @ cF) = $true) | ((cG @ cE @ cF) = $true)) & ! [X1 : $i,X0 : $i,X2 : $i] : (((cG @ X0 @ X2) != $true) | ((cG @ X1 @ X0) != $true) | ((cG @ X1 @ X2) != $true)) & (((cR @ cA @ cF) = $true) | ((cG @ cA @ cF) = $true)) & ! [X3 : $i,X4 : $i,X5 : $i] : (((cR @ X4 @ X3) != $true) | ((cR @ X3 @ X5) != $true) | ((cR @ X4 @ X5) != $true)) & (((cG @ cA @ cC) = $true) | ((cR @ cA @ cC) = $true)) & (((cG @ cD @ cE) = $true) | ((cR @ cD @ cE) = $true)) & (((cG @ cD @ cF) = $true) | ((cR @ cD @ cF) = $true)) & (((cG @ cC @ cE) = $true) | ((cR @ cC @ cE) = $true))),
% 1.74/1.49 inference(flattening,[status(thm)],[f6])).
% 1.74/1.49 thf(f6,plain,(
% 1.74/1.49 (! [X3 : $i,X4 : $i,X5 : $i] : (((cR @ X4 @ X3) != $true) | ((cR @ X3 @ X5) != $true) | ((cR @ X4 @ X5) != $true)) & ! [X1 : $i,X0 : $i,X2 : $i] : (((cG @ X0 @ X2) != $true) | ((cG @ X1 @ X0) != $true) | ((cG @ X1 @ X2) != $true))) & ((((cG @ cB @ cF) = $true) | ((cR @ cB @ cF) = $true)) & (((cG @ cD @ cE) = $true) | ((cR @ cD @ cE) = $true)) & (((cG @ cA @ cC) = $true) | ((cR @ cA @ cC) = $true)) & (((cR @ cA @ cE) = $true) | ((cG @ cA @ cE) = $true)) & (((cG @ cB @ cC) = $true) | ((cR @ cB @ cC) = $true)) & (((cG @ cC @ cD) = $true) | ((cR @ cC @ cD) = $true)) & (((cG @ cB @ cE) = $true) | ((cR @ cB @ cE) = $true)) & (((cG @ cC @ cE) = $true) | ((cR @ cC @ cE) = $true)) & (((cR @ cE @ cF) = $true) | ((cG @ cE @ cF) = $true)) & (((cR @ cC @ cF) = $true) | ((cG @ cC @ cF) = $true)) & (((cR @ cA @ cF) = $true) | ((cG @ cA @ cF) = $true)) & (((cR @ cA @ cD) = $true) | ((cG @ cA @ cD) = $true)) & (((cG @ cD @ cF) = $true) | ((cR @ cD @ cF) = $true)) & (((cG @ cB @ cD) = $true) | ((cR @ cB @ cD) = $true)) & (((cG @ cA @ cB) = $true) | ((cR @ cA @ cB) = $true)))),
% 1.74/1.49 inference(ennf_transformation,[status(thm)],[f5])).
% 1.74/1.49 thf(f5,plain,(
% 1.74/1.49 ~(((((cG @ cB @ cF) = $true) | ((cR @ cB @ cF) = $true)) & (((cG @ cD @ cE) = $true) | ((cR @ cD @ cE) = $true)) & (((cG @ cA @ cC) = $true) | ((cR @ cA @ cC) = $true)) & (((cR @ cA @ cE) = $true) | ((cG @ cA @ cE) = $true)) & (((cG @ cB @ cC) = $true) | ((cR @ cB @ cC) = $true)) & (((cG @ cC @ cD) = $true) | ((cR @ cC @ cD) = $true)) & (((cG @ cB @ cE) = $true) | ((cR @ cB @ cE) = $true)) & (((cG @ cC @ cE) = $true) | ((cR @ cC @ cE) = $true)) & (((cR @ cE @ cF) = $true) | ((cG @ cE @ cF) = $true)) & (((cR @ cC @ cF) = $true) | ((cG @ cC @ cF) = $true)) & (((cR @ cA @ cF) = $true) | ((cG @ cA @ cF) = $true)) & (((cR @ cA @ cD) = $true) | ((cG @ cA @ cD) = $true)) & (((cG @ cD @ cF) = $true) | ((cR @ cD @ cF) = $true)) & (((cG @ cB @ cD) = $true) | ((cR @ cB @ cD) = $true)) & (((cG @ cA @ cB) = $true) | ((cR @ cA @ cB) = $true))) => (? [X5 : $i,X4 : $i,X3 : $i] : (((cR @ X4 @ X5) = $true) & ((cR @ X3 @ X5) = $true) & ((cR @ X4 @ X3) = $true)) | ? [X2 : $i,X0 : $i,X1 : $i] : (((cG @ X1 @ X2) = $true) & ((cG @ X1 @ X0) = $true) & ((cG @ X0 @ X2) = $true))))),
% 1.74/1.49 inference(fool_elimination,[status(thm)],[f4])).
% 1.74/1.49 thf(f4,plain,(
% 1.74/1.49 ~((((cG @ cD @ cE) | (cR @ cD @ cE)) & ((cG @ cE @ cF) | (cR @ cE @ cF)) & ((cG @ cC @ cD) | (cR @ cC @ cD)) & ((cR @ cD @ cF) | (cG @ cD @ cF)) & ((cR @ cA @ cF) | (cG @ cA @ cF)) & ((cG @ cA @ cB) | (cR @ cA @ cB)) & ((cR @ cB @ cF) | (cG @ cB @ cF)) & ((cR @ cB @ cD) | (cG @ cB @ cD)) & ((cR @ cB @ cE) | (cG @ cB @ cE)) & ((cG @ cB @ cC) | (cR @ cB @ cC)) & ((cG @ cC @ cE) | (cR @ cC @ cE)) & ((cG @ cC @ cF) | (cR @ cC @ cF)) & ((cR @ cA @ cE) | (cG @ cA @ cE)) & ((cG @ cA @ cC) | (cR @ cA @ cC)) & ((cG @ cA @ cD) | (cR @ cA @ cD))) => (? [X0 : $i,X1 : $i,X2 : $i] : ((cG @ X1 @ X0) & (cG @ X0 @ X2) & (cG @ X1 @ X2)) | ? [X3 : $i,X4 : $i,X5 : $i] : ((cR @ X4 @ X5) & (cR @ X4 @ X3) & (cR @ X3 @ X5))))),
% 1.74/1.49 inference(rectify,[status(thm)],[f2])).
% 1.74/1.49 thf(f2,negated_conjecture,(
% 1.74/1.49 ~((((cG @ cD @ cE) | (cR @ cD @ cE)) & ((cG @ cE @ cF) | (cR @ cE @ cF)) & ((cG @ cC @ cD) | (cR @ cC @ cD)) & ((cR @ cD @ cF) | (cG @ cD @ cF)) & ((cR @ cA @ cF) | (cG @ cA @ cF)) & ((cG @ cA @ cB) | (cR @ cA @ cB)) & ((cR @ cB @ cF) | (cG @ cB @ cF)) & ((cR @ cB @ cD) | (cG @ cB @ cD)) & ((cR @ cB @ cE) | (cG @ cB @ cE)) & ((cG @ cB @ cC) | (cR @ cB @ cC)) & ((cG @ cC @ cE) | (cR @ cC @ cE)) & ((cG @ cC @ cF) | (cR @ cC @ cF)) & ((cR @ cA @ cE) | (cG @ cA @ cE)) & ((cG @ cA @ cC) | (cR @ cA @ cC)) & ((cG @ cA @ cD) | (cR @ cA @ cD))) => (? [X1 : $i,X0 : $i,X2 : $i] : ((cG @ X0 @ X1) & (cG @ X1 @ X2) & (cG @ X0 @ X2)) | ? [X1 : $i,X0 : $i,X2 : $i] : ((cR @ X0 @ X2) & (cR @ X0 @ X1) & (cR @ X1 @ X2))))),
% 1.74/1.49 inference(negated_conjecture,[status(cth)],[f1])).
% 1.74/1.49 thf(f1,conjecture,(
% 1.74/1.49 (((cG @ cD @ cE) | (cR @ cD @ cE)) & ((cG @ cE @ cF) | (cR @ cE @ cF)) & ((cG @ cC @ cD) | (cR @ cC @ cD)) & ((cR @ cD @ cF) | (cG @ cD @ cF)) & ((cR @ cA @ cF) | (cG @ cA @ cF)) & ((cG @ cA @ cB) | (cR @ cA @ cB)) & ((cR @ cB @ cF) | (cG @ cB @ cF)) & ((cR @ cB @ cD) | (cG @ cB @ cD)) & ((cR @ cB @ cE) | (cG @ cB @ cE)) & ((cG @ cB @ cC) | (cR @ cB @ cC)) & ((cG @ cC @ cE) | (cR @ cC @ cE)) & ((cG @ cC @ cF) | (cR @ cC @ cF)) & ((cR @ cA @ cE) | (cG @ cA @ cE)) & ((cG @ cA @ cC) | (cR @ cA @ cC)) & ((cG @ cA @ cD) | (cR @ cA @ cD))) => (? [X1 : $i,X0 : $i,X2 : $i] : ((cG @ X0 @ X1) & (cG @ X1 @ X2) & (cG @ X0 @ X2)) | ? [X1 : $i,X0 : $i,X2 : $i] : ((cR @ X0 @ X2) & (cR @ X0 @ X1) & (cR @ X1 @ X2)))),
% 1.74/1.49 file('/export/starexec/sandbox/tmp/tmp.tHlHL5CGp0/DTF2THF_5569.p',cSIX_THEOREM_B)).
% 1.74/1.49 thf(f636,plain,(
% 1.74/1.49 ~spl0_4 | ~spl0_16 | ~spl0_27),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f635])).
% 1.74/1.49 thf(f635,plain,(
% 1.74/1.49 $false | (~spl0_4 | ~spl0_16 | ~spl0_27)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f633,f96])).
% 1.74/1.49 thf(f96,plain,(
% 1.74/1.49 ((cR @ cE @ cF) = $true) | ~spl0_16),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f94])).
% 1.74/1.49 thf(f94,definition,(
% 1.74/1.49 spl0_16 <=> ((cR @ cE @ cF) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_16])],[avatar_definition])).
% 1.74/1.49 thf(f633,plain,(
% 1.74/1.49 ((cR @ cE @ cF) != $true) | (~spl0_4 | ~spl0_27)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f629])).
% 1.74/1.49 thf(f629,plain,(
% 1.74/1.49 ($true != $true) | ((cR @ cE @ cF) != $true) | (~spl0_4 | ~spl0_27)),
% 1.74/1.49 inference(superposition,[status(thm)],[f600,f146])).
% 1.74/1.49 thf(f146,plain,(
% 1.74/1.49 ((cR @ cA @ cE) = $true) | ~spl0_27),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f144])).
% 1.74/1.49 thf(f144,definition,(
% 1.74/1.49 spl0_27 <=> ((cR @ cA @ cE) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_27])],[avatar_definition])).
% 1.74/1.49 thf(f600,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cR @ cA @ X0)) | ((cR @ X0 @ cF) != $true)) ) | ~spl0_4),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f598])).
% 1.74/1.49 thf(f598,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cR @ cA @ X0)) | ($true != $true) | ((cR @ X0 @ cF) != $true)) ) | ~spl0_4),
% 1.74/1.49 inference(superposition,[status(thm)],[f13,f42])).
% 1.74/1.49 thf(f42,plain,(
% 1.74/1.49 ((cR @ cA @ cF) = $true) | ~spl0_4),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.74/1.49 thf(f40,definition,(
% 1.74/1.49 spl0_4 <=> ((cR @ cA @ cF) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_4])],[avatar_definition])).
% 1.74/1.49 thf(f13,plain,(
% 1.74/1.49 ( ! [X3 : $i,X4 : $i,X5 : $i] : (((cR @ X4 @ X5) != $true) | ((cR @ X4 @ X3) != $true) | ((cR @ X3 @ X5) != $true)) )),
% 1.74/1.49 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.49 thf(f614,plain,(
% 1.74/1.49 ~spl0_1 | ~spl0_12 | ~spl0_21),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f613])).
% 1.74/1.49 thf(f613,plain,(
% 1.74/1.49 $false | (~spl0_1 | ~spl0_12 | ~spl0_21)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f612,f78])).
% 1.74/1.49 thf(f78,plain,(
% 1.74/1.49 ((cG @ cB @ cE) = $true) | ~spl0_12),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f76])).
% 1.74/1.49 thf(f76,definition,(
% 1.74/1.49 spl0_12 <=> ((cG @ cB @ cE) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_12])],[avatar_definition])).
% 1.74/1.49 thf(f612,plain,(
% 1.74/1.49 ((cG @ cB @ cE) != $true) | (~spl0_1 | ~spl0_21)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f611])).
% 1.74/1.49 thf(f611,plain,(
% 1.74/1.49 ($true != $true) | ((cG @ cB @ cE) != $true) | (~spl0_1 | ~spl0_21)),
% 1.74/1.49 inference(superposition,[status(thm)],[f560,f29])).
% 1.74/1.49 thf(f29,plain,(
% 1.74/1.49 ((cG @ cB @ cD) = $true) | ~spl0_1),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f27])).
% 1.74/1.49 thf(f27,definition,(
% 1.74/1.49 spl0_1 <=> ((cG @ cB @ cD) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_1])],[avatar_definition])).
% 1.74/1.49 thf(f596,plain,(
% 1.74/1.49 ~spl0_12 | ~spl0_14 | ~spl0_29),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f595])).
% 1.74/1.49 thf(f595,plain,(
% 1.74/1.49 $false | (~spl0_12 | ~spl0_14 | ~spl0_29)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f594,f78])).
% 1.74/1.49 thf(f594,plain,(
% 1.74/1.49 ((cG @ cB @ cE) != $true) | (~spl0_14 | ~spl0_29)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f591])).
% 1.74/1.49 thf(f591,plain,(
% 1.74/1.49 ($true != $true) | ((cG @ cB @ cE) != $true) | (~spl0_14 | ~spl0_29)),
% 1.74/1.49 inference(superposition,[status(thm)],[f556,f155])).
% 1.74/1.49 thf(f155,plain,(
% 1.74/1.49 ((cG @ cB @ cC) = $true) | ~spl0_29),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f153])).
% 1.74/1.49 thf(f153,definition,(
% 1.74/1.49 spl0_29 <=> ((cG @ cB @ cC) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_29])],[avatar_definition])).
% 1.74/1.49 thf(f556,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cG @ X0 @ cC)) | ((cG @ X0 @ cE) != $true)) ) | ~spl0_14),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f555])).
% 1.74/1.49 thf(f555,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (((cG @ X0 @ cE) != $true) | ($true != (cG @ X0 @ cC)) | ($true != $true)) ) | ~spl0_14),
% 1.74/1.49 inference(superposition,[status(thm)],[f15,f87])).
% 1.74/1.49 thf(f87,plain,(
% 1.74/1.49 ((cG @ cC @ cE) = $true) | ~spl0_14),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f85])).
% 1.74/1.49 thf(f85,definition,(
% 1.74/1.49 spl0_14 <=> ((cG @ cC @ cE) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_14])],[avatar_definition])).
% 1.74/1.49 thf(f554,plain,(
% 1.74/1.49 ~spl0_13 | ~spl0_16 | ~spl0_20),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f553])).
% 1.74/1.49 thf(f553,plain,(
% 1.74/1.49 $false | (~spl0_13 | ~spl0_16 | ~spl0_20)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f552,f96])).
% 1.74/1.49 thf(f552,plain,(
% 1.74/1.49 ((cR @ cE @ cF) != $true) | (~spl0_13 | ~spl0_20)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f549])).
% 1.74/1.49 thf(f549,plain,(
% 1.74/1.49 ((cR @ cE @ cF) != $true) | ($true != $true) | (~spl0_13 | ~spl0_20)),
% 1.74/1.49 inference(superposition,[status(thm)],[f273,f83])).
% 1.74/1.49 thf(f83,plain,(
% 1.74/1.49 ((cR @ cC @ cE) = $true) | ~spl0_13),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f81])).
% 1.74/1.49 thf(f81,definition,(
% 1.74/1.49 spl0_13 <=> ((cR @ cC @ cE) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_13])],[avatar_definition])).
% 1.74/1.49 thf(f273,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cR @ cC @ X0)) | ((cR @ X0 @ cF) != $true)) ) | ~spl0_20),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f272])).
% 1.74/1.49 thf(f272,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != $true) | ((cR @ X0 @ cF) != $true) | ($true != (cR @ cC @ X0))) ) | ~spl0_20),
% 1.74/1.49 inference(superposition,[status(thm)],[f13,f114])).
% 1.74/1.49 thf(f114,plain,(
% 1.74/1.49 ((cR @ cC @ cF) = $true) | ~spl0_20),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f112])).
% 1.74/1.49 thf(f112,definition,(
% 1.74/1.49 spl0_20 <=> ((cR @ cC @ cF) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_20])],[avatar_definition])).
% 1.74/1.49 thf(f538,plain,(
% 1.74/1.49 ~spl0_3 | ~spl0_7 | ~spl0_24),
% 1.74/1.49 inference(avatar_split_clause,[status(thm)],[f506,f130,f54,f36])).
% 1.74/1.49 thf(f36,definition,(
% 1.74/1.49 spl0_3 <=> ((cG @ cA @ cF) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_3])],[avatar_definition])).
% 1.74/1.49 thf(f54,definition,(
% 1.74/1.49 spl0_7 <=> ((cG @ cD @ cF) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_7])],[avatar_definition])).
% 1.74/1.49 thf(f506,plain,(
% 1.74/1.49 ((cG @ cA @ cF) != $true) | (~spl0_7 | ~spl0_24)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f504])).
% 1.74/1.49 thf(f504,plain,(
% 1.74/1.49 ((cG @ cA @ cF) != $true) | ($true != $true) | (~spl0_7 | ~spl0_24)),
% 1.74/1.49 inference(superposition,[status(thm)],[f443,f132])).
% 1.74/1.49 thf(f443,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cG @ X0 @ cD)) | ($true != (cG @ X0 @ cF))) ) | ~spl0_7),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f440])).
% 1.74/1.49 thf(f440,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cG @ X0 @ cD)) | ($true != $true) | ($true != (cG @ X0 @ cF))) ) | ~spl0_7),
% 1.74/1.49 inference(superposition,[status(thm)],[f15,f56])).
% 1.74/1.49 thf(f56,plain,(
% 1.74/1.49 ((cG @ cD @ cF) = $true) | ~spl0_7),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f54])).
% 1.74/1.49 thf(f537,plain,(
% 1.74/1.49 ~spl0_1 | ~spl0_7 | ~spl0_26),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f536])).
% 1.74/1.49 thf(f536,plain,(
% 1.74/1.49 $false | (~spl0_1 | ~spl0_7 | ~spl0_26)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f535,f141])).
% 1.74/1.49 thf(f141,plain,(
% 1.74/1.49 ((cG @ cB @ cF) = $true) | ~spl0_26),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f139])).
% 1.74/1.49 thf(f139,definition,(
% 1.74/1.49 spl0_26 <=> ((cG @ cB @ cF) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_26])],[avatar_definition])).
% 1.74/1.49 thf(f535,plain,(
% 1.74/1.49 ((cG @ cB @ cF) != $true) | (~spl0_1 | ~spl0_7)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f532])).
% 1.74/1.49 thf(f532,plain,(
% 1.74/1.49 ((cG @ cB @ cF) != $true) | ($true != $true) | (~spl0_1 | ~spl0_7)),
% 1.74/1.49 inference(superposition,[status(thm)],[f443,f29])).
% 1.74/1.49 thf(f531,plain,(
% 1.74/1.49 ~spl0_20 | ~spl0_25 | ~spl0_30),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f530])).
% 1.74/1.49 thf(f530,plain,(
% 1.74/1.49 $false | (~spl0_20 | ~spl0_25 | ~spl0_30)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f529,f114])).
% 1.74/1.49 thf(f529,plain,(
% 1.74/1.49 ((cR @ cC @ cF) != $true) | (~spl0_25 | ~spl0_30)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f524])).
% 1.74/1.49 thf(f524,plain,(
% 1.74/1.49 ((cR @ cC @ cF) != $true) | ($true != $true) | (~spl0_25 | ~spl0_30)),
% 1.74/1.49 inference(superposition,[status(thm)],[f461,f159])).
% 1.74/1.49 thf(f159,plain,(
% 1.74/1.49 ((cR @ cB @ cC) = $true) | ~spl0_30),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f157])).
% 1.74/1.49 thf(f157,definition,(
% 1.74/1.49 spl0_30 <=> ((cR @ cB @ cC) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_30])],[avatar_definition])).
% 1.74/1.49 thf(f461,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (((cR @ cB @ X0) != $true) | ((cR @ X0 @ cF) != $true)) ) | ~spl0_25),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f460])).
% 1.74/1.49 thf(f460,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (((cR @ X0 @ cF) != $true) | ((cR @ cB @ X0) != $true) | ($true != $true)) ) | ~spl0_25),
% 1.74/1.49 inference(superposition,[status(thm)],[f13,f137])).
% 1.74/1.49 thf(f137,plain,(
% 1.74/1.49 ((cR @ cB @ cF) = $true) | ~spl0_25),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f135])).
% 1.74/1.49 thf(f135,definition,(
% 1.74/1.49 spl0_25 <=> ((cR @ cB @ cF) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_25])],[avatar_definition])).
% 1.74/1.49 thf(f521,plain,(
% 1.74/1.49 ~spl0_13 | ~spl0_18 | ~spl0_22),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f520])).
% 1.74/1.49 thf(f520,plain,(
% 1.74/1.49 $false | (~spl0_13 | ~spl0_18 | ~spl0_22)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f519,f123])).
% 1.74/1.49 thf(f123,plain,(
% 1.74/1.49 ((cR @ cD @ cE) = $true) | ~spl0_22),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f121])).
% 1.74/1.49 thf(f121,definition,(
% 1.74/1.49 spl0_22 <=> ((cR @ cD @ cE) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_22])],[avatar_definition])).
% 1.74/1.49 thf(f519,plain,(
% 1.74/1.49 ((cR @ cD @ cE) != $true) | (~spl0_13 | ~spl0_18)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f516])).
% 1.74/1.49 thf(f516,plain,(
% 1.74/1.49 ((cR @ cD @ cE) != $true) | ($true != $true) | (~spl0_13 | ~spl0_18)),
% 1.74/1.49 inference(superposition,[status(thm)],[f459,f105])).
% 1.74/1.49 thf(f105,plain,(
% 1.74/1.49 ((cR @ cC @ cD) = $true) | ~spl0_18),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f103])).
% 1.74/1.49 thf(f103,definition,(
% 1.74/1.49 spl0_18 <=> ((cR @ cC @ cD) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_18])],[avatar_definition])).
% 1.74/1.49 thf(f459,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cR @ cC @ X0)) | ($true != (cR @ X0 @ cE))) ) | ~spl0_13),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f457])).
% 1.74/1.49 thf(f457,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != $true) | ($true != (cR @ cC @ X0)) | ($true != (cR @ X0 @ cE))) ) | ~spl0_13),
% 1.74/1.49 inference(superposition,[status(thm)],[f13,f83])).
% 1.74/1.49 thf(f495,plain,(
% 1.74/1.49 ~spl0_10 | ~spl0_12 | ~spl0_28),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f494])).
% 1.74/1.49 thf(f494,plain,(
% 1.74/1.49 $false | (~spl0_10 | ~spl0_12 | ~spl0_28)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f493,f150])).
% 1.74/1.49 thf(f493,plain,(
% 1.74/1.49 ((cG @ cA @ cE) != $true) | (~spl0_10 | ~spl0_12)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f492])).
% 1.74/1.49 thf(f492,plain,(
% 1.74/1.49 ($true != $true) | ((cG @ cA @ cE) != $true) | (~spl0_10 | ~spl0_12)),
% 1.74/1.49 inference(superposition,[status(thm)],[f455,f69])).
% 1.74/1.49 thf(f69,plain,(
% 1.74/1.49 ((cG @ cA @ cB) = $true) | ~spl0_10),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.74/1.49 thf(f67,definition,(
% 1.74/1.49 spl0_10 <=> ((cG @ cA @ cB) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_10])],[avatar_definition])).
% 1.74/1.49 thf(f455,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (((cG @ X0 @ cB) != $true) | ((cG @ X0 @ cE) != $true)) ) | ~spl0_12),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f454])).
% 1.74/1.49 thf(f454,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (((cG @ X0 @ cE) != $true) | ($true != $true) | ((cG @ X0 @ cB) != $true)) ) | ~spl0_12),
% 1.74/1.49 inference(superposition,[status(thm)],[f15,f78])).
% 1.74/1.49 thf(f479,plain,(
% 1.74/1.49 ~spl0_4 | ~spl0_9 | ~spl0_25),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f478])).
% 1.74/1.49 thf(f478,plain,(
% 1.74/1.49 $false | (~spl0_4 | ~spl0_9 | ~spl0_25)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f475,f137])).
% 1.74/1.49 thf(f475,plain,(
% 1.74/1.49 ((cR @ cB @ cF) != $true) | (~spl0_4 | ~spl0_9)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f473])).
% 1.74/1.49 thf(f473,plain,(
% 1.74/1.49 ((cR @ cB @ cF) != $true) | ($true != $true) | (~spl0_4 | ~spl0_9)),
% 1.74/1.49 inference(superposition,[status(thm)],[f435,f65])).
% 1.74/1.49 thf(f65,plain,(
% 1.74/1.49 ((cR @ cA @ cB) = $true) | ~spl0_9),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f63])).
% 1.74/1.49 thf(f63,definition,(
% 1.74/1.49 spl0_9 <=> ((cR @ cA @ cB) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_9])],[avatar_definition])).
% 1.74/1.49 thf(f435,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cR @ cA @ X0)) | ((cR @ X0 @ cF) != $true)) ) | ~spl0_4),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f434])).
% 1.74/1.49 thf(f434,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (((cR @ X0 @ cF) != $true) | ($true != $true) | ($true != (cR @ cA @ X0))) ) | ~spl0_4),
% 1.74/1.49 inference(superposition,[status(thm)],[f13,f42])).
% 1.74/1.49 thf(f453,plain,(
% 1.74/1.49 ~spl0_5 | ~spl0_14 | ~spl0_28),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f452])).
% 1.74/1.49 thf(f452,plain,(
% 1.74/1.49 $false | (~spl0_5 | ~spl0_14 | ~spl0_28)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f451,f150])).
% 1.74/1.49 thf(f451,plain,(
% 1.74/1.49 ((cG @ cA @ cE) != $true) | (~spl0_5 | ~spl0_14)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f450])).
% 1.74/1.49 thf(f450,plain,(
% 1.74/1.49 ((cG @ cA @ cE) != $true) | ($true != $true) | (~spl0_5 | ~spl0_14)),
% 1.74/1.49 inference(superposition,[status(thm)],[f387,f47])).
% 1.74/1.49 thf(f47,plain,(
% 1.74/1.49 ((cG @ cA @ cC) = $true) | ~spl0_5),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.74/1.49 thf(f45,definition,(
% 1.74/1.49 spl0_5 <=> ((cG @ cA @ cC) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_5])],[avatar_definition])).
% 1.74/1.49 thf(f387,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cG @ X0 @ cC)) | ((cG @ X0 @ cE) != $true)) ) | ~spl0_14),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f386])).
% 1.74/1.49 thf(f386,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (((cG @ X0 @ cE) != $true) | ($true != (cG @ X0 @ cC)) | ($true != $true)) ) | ~spl0_14),
% 1.74/1.49 inference(superposition,[status(thm)],[f15,f87])).
% 1.74/1.49 thf(f433,plain,(
% 1.74/1.49 ~spl0_1 | ~spl0_10 | ~spl0_24),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f432])).
% 1.74/1.49 thf(f432,plain,(
% 1.74/1.49 $false | (~spl0_1 | ~spl0_10 | ~spl0_24)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f415,f69])).
% 1.74/1.49 thf(f415,plain,(
% 1.74/1.49 ((cG @ cA @ cB) != $true) | (~spl0_1 | ~spl0_24)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f412])).
% 1.74/1.49 thf(f412,plain,(
% 1.74/1.49 ($true != $true) | ((cG @ cA @ cB) != $true) | (~spl0_1 | ~spl0_24)),
% 1.74/1.49 inference(superposition,[status(thm)],[f377,f132])).
% 1.74/1.49 thf(f377,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cG @ X0 @ cD)) | ((cG @ X0 @ cB) != $true)) ) | ~spl0_1),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f376])).
% 1.74/1.49 thf(f376,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cG @ X0 @ cD)) | ($true != $true) | ((cG @ X0 @ cB) != $true)) ) | ~spl0_1),
% 1.74/1.49 inference(superposition,[status(thm)],[f15,f29])).
% 1.74/1.49 thf(f431,plain,(
% 1.74/1.49 ~spl0_3 | ~spl0_10 | ~spl0_26),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f430])).
% 1.74/1.49 thf(f430,plain,(
% 1.74/1.49 $false | (~spl0_3 | ~spl0_10 | ~spl0_26)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f382,f69])).
% 1.74/1.49 thf(f382,plain,(
% 1.74/1.49 ((cG @ cA @ cB) != $true) | (~spl0_3 | ~spl0_26)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f378])).
% 1.74/1.49 thf(f378,plain,(
% 1.74/1.49 ((cG @ cA @ cB) != $true) | ($true != $true) | (~spl0_3 | ~spl0_26)),
% 1.74/1.49 inference(superposition,[status(thm)],[f260,f38])).
% 1.74/1.49 thf(f38,plain,(
% 1.74/1.49 ((cG @ cA @ cF) = $true) | ~spl0_3),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f36])).
% 1.74/1.49 thf(f260,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cG @ X0 @ cF)) | ((cG @ X0 @ cB) != $true)) ) | ~spl0_26),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f259])).
% 1.74/1.49 thf(f259,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (((cG @ X0 @ cB) != $true) | ($true != (cG @ X0 @ cF)) | ($true != $true)) ) | ~spl0_26),
% 1.74/1.49 inference(superposition,[status(thm)],[f15,f141])).
% 1.74/1.49 thf(f429,plain,(
% 1.74/1.49 ~spl0_6 | ~spl0_9 | ~spl0_30),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f428])).
% 1.74/1.49 thf(f428,plain,(
% 1.74/1.49 $false | (~spl0_6 | ~spl0_9 | ~spl0_30)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f427,f159])).
% 1.74/1.49 thf(f427,plain,(
% 1.74/1.49 ((cR @ cB @ cC) != $true) | (~spl0_6 | ~spl0_9)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f422])).
% 1.74/1.49 thf(f422,plain,(
% 1.74/1.49 ((cR @ cB @ cC) != $true) | ($true != $true) | (~spl0_6 | ~spl0_9)),
% 1.74/1.49 inference(superposition,[status(thm)],[f385,f65])).
% 1.74/1.49 thf(f385,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cR @ cA @ X0)) | ((cR @ X0 @ cC) != $true)) ) | ~spl0_6),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f384])).
% 1.74/1.49 thf(f384,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (((cR @ X0 @ cC) != $true) | ($true != (cR @ cA @ X0)) | ($true != $true)) ) | ~spl0_6),
% 1.74/1.49 inference(superposition,[status(thm)],[f13,f51])).
% 1.74/1.49 thf(f51,plain,(
% 1.74/1.49 ((cR @ cA @ cC) = $true) | ~spl0_6),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.74/1.49 thf(f49,definition,(
% 1.74/1.49 spl0_6 <=> ((cR @ cA @ cC) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_6])],[avatar_definition])).
% 1.74/1.49 thf(f375,plain,(
% 1.74/1.49 ~spl0_8 | ~spl0_18 | ~spl0_20),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f374])).
% 1.74/1.49 thf(f374,plain,(
% 1.74/1.49 $false | (~spl0_8 | ~spl0_18 | ~spl0_20)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f373,f60])).
% 1.74/1.49 thf(f60,plain,(
% 1.74/1.49 ((cR @ cD @ cF) = $true) | ~spl0_8),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.74/1.49 thf(f58,definition,(
% 1.74/1.49 spl0_8 <=> ((cR @ cD @ cF) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_8])],[avatar_definition])).
% 1.74/1.49 thf(f373,plain,(
% 1.74/1.49 ((cR @ cD @ cF) != $true) | (~spl0_18 | ~spl0_20)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f368])).
% 1.74/1.49 thf(f368,plain,(
% 1.74/1.49 ($true != $true) | ((cR @ cD @ cF) != $true) | (~spl0_18 | ~spl0_20)),
% 1.74/1.49 inference(superposition,[status(thm)],[f273,f105])).
% 1.74/1.49 thf(f361,plain,(
% 1.74/1.49 ~spl0_4 | ~spl0_8 | ~spl0_23),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f360])).
% 1.74/1.49 thf(f360,plain,(
% 1.74/1.49 $false | (~spl0_4 | ~spl0_8 | ~spl0_23)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f356,f60])).
% 1.74/1.49 thf(f356,plain,(
% 1.74/1.49 ((cR @ cD @ cF) != $true) | (~spl0_4 | ~spl0_23)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f353])).
% 1.74/1.49 thf(f353,plain,(
% 1.74/1.49 ((cR @ cD @ cF) != $true) | ($true != $true) | (~spl0_4 | ~spl0_23)),
% 1.74/1.49 inference(superposition,[status(thm)],[f319,f128])).
% 1.74/1.49 thf(f128,plain,(
% 1.74/1.49 ((cR @ cA @ cD) = $true) | ~spl0_23),
% 1.74/1.49 inference(avatar_component_clause,[status(thm)],[f126])).
% 1.74/1.49 thf(f126,definition,(
% 1.74/1.49 spl0_23 <=> ((cR @ cA @ cD) = $true)),
% 1.74/1.49 introduced(definition,[new_symbols(naming,[spl0_23])],[avatar_definition])).
% 1.74/1.49 thf(f319,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cR @ cA @ X0)) | ((cR @ X0 @ cF) != $true)) ) | ~spl0_4),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f318])).
% 1.74/1.49 thf(f318,plain,(
% 1.74/1.49 ( ! [X0 : $i] : (($true != (cR @ cA @ X0)) | ((cR @ X0 @ cF) != $true) | ($true != $true)) ) | ~spl0_4),
% 1.74/1.49 inference(superposition,[status(thm)],[f13,f42])).
% 1.74/1.49 thf(f359,plain,(
% 1.74/1.49 ~spl0_4 | ~spl0_6 | ~spl0_20),
% 1.74/1.49 inference(avatar_contradiction_clause,[status(thm)],[f358])).
% 1.74/1.49 thf(f358,plain,(
% 1.74/1.49 $false | (~spl0_4 | ~spl0_6 | ~spl0_20)),
% 1.74/1.49 inference(subsumption_resolution,[status(thm)],[f357,f114])).
% 1.74/1.49 thf(f357,plain,(
% 1.74/1.49 ((cR @ cC @ cF) != $true) | (~spl0_4 | ~spl0_6)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f352])).
% 1.74/1.49 thf(f352,plain,(
% 1.74/1.49 ((cR @ cC @ cF) != $true) | ($true != $true) | (~spl0_4 | ~spl0_6)),
% 1.74/1.49 inference(superposition,[status(thm)],[f319,f51])).
% 1.74/1.49 thf(f345,plain,(
% 1.74/1.49 ~spl0_18 | ~spl0_6 | ~spl0_23),
% 1.74/1.49 inference(avatar_split_clause,[status(thm)],[f344,f126,f49,f103])).
% 1.74/1.49 thf(f344,plain,(
% 1.74/1.49 ((cR @ cC @ cD) != $true) | (~spl0_6 | ~spl0_23)),
% 1.74/1.49 inference(trivial_inequality_removal,[status(thm)],[f339])).
% 1.74/1.49 thf(f339,plain,(
% 1.74/1.49 ((cR @ cC @ cD) != $true) | ($true != $true) | (~spl0_6 | ~spl0_23)),
% 1.74/1.49 inference(superposition,[status(thm)],[f298,f51])).
% 1.74/1.50 thf(f298,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != (cR @ cA @ X0)) | ($true != (cR @ X0 @ cD))) ) | ~spl0_23),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f296])).
% 1.74/1.50 thf(f296,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != $true) | ($true != (cR @ cA @ X0)) | ($true != (cR @ X0 @ cD))) ) | ~spl0_23),
% 1.74/1.50 inference(superposition,[status(thm)],[f13,f128])).
% 1.74/1.50 thf(f330,plain,(
% 1.74/1.50 ~spl0_1 | ~spl0_17 | ~spl0_29),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f328,f153,f99,f27])).
% 1.74/1.50 thf(f99,definition,(
% 1.74/1.50 spl0_17 <=> ((cG @ cC @ cD) = $true)),
% 1.74/1.50 introduced(definition,[new_symbols(naming,[spl0_17])],[avatar_definition])).
% 1.74/1.50 thf(f328,plain,(
% 1.74/1.50 ((cG @ cB @ cD) != $true) | (~spl0_17 | ~spl0_29)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f326])).
% 1.74/1.50 thf(f326,plain,(
% 1.74/1.50 ($true != $true) | ((cG @ cB @ cD) != $true) | (~spl0_17 | ~spl0_29)),
% 1.74/1.50 inference(superposition,[status(thm)],[f191,f155])).
% 1.74/1.50 thf(f191,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != (cG @ X0 @ cC)) | ($true != (cG @ X0 @ cD))) ) | ~spl0_17),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f180])).
% 1.74/1.50 thf(f180,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != $true) | ($true != (cG @ X0 @ cD)) | ($true != (cG @ X0 @ cC))) ) | ~spl0_17),
% 1.74/1.50 inference(superposition,[status(thm)],[f15,f101])).
% 1.74/1.50 thf(f101,plain,(
% 1.74/1.50 ((cG @ cC @ cD) = $true) | ~spl0_17),
% 1.74/1.50 inference(avatar_component_clause,[status(thm)],[f99])).
% 1.74/1.50 thf(f317,plain,(
% 1.74/1.50 ~spl0_6 | ~spl0_13 | ~spl0_27),
% 1.74/1.50 inference(avatar_contradiction_clause,[status(thm)],[f316])).
% 1.74/1.50 thf(f316,plain,(
% 1.74/1.50 $false | (~spl0_6 | ~spl0_13 | ~spl0_27)),
% 1.74/1.50 inference(subsumption_resolution,[status(thm)],[f314,f83])).
% 1.74/1.50 thf(f314,plain,(
% 1.74/1.50 ((cR @ cC @ cE) != $true) | (~spl0_6 | ~spl0_27)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f312])).
% 1.74/1.50 thf(f312,plain,(
% 1.74/1.50 ((cR @ cC @ cE) != $true) | ($true != $true) | (~spl0_6 | ~spl0_27)),
% 1.74/1.50 inference(superposition,[status(thm)],[f174,f51])).
% 1.74/1.50 thf(f174,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != (cR @ cA @ X0)) | ($true != (cR @ X0 @ cE))) ) | ~spl0_27),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f166])).
% 1.74/1.50 thf(f166,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != (cR @ cA @ X0)) | ($true != $true) | ($true != (cR @ X0 @ cE))) ) | ~spl0_27),
% 1.74/1.50 inference(superposition,[status(thm)],[f13,f146])).
% 1.74/1.50 thf(f311,plain,(
% 1.74/1.50 ~spl0_14 | ~spl0_17 | ~spl0_21),
% 1.74/1.50 inference(avatar_contradiction_clause,[status(thm)],[f310])).
% 1.74/1.50 thf(f310,plain,(
% 1.74/1.50 $false | (~spl0_14 | ~spl0_17 | ~spl0_21)),
% 1.74/1.50 inference(subsumption_resolution,[status(thm)],[f309,f87])).
% 1.74/1.50 thf(f309,plain,(
% 1.74/1.50 ((cG @ cC @ cE) != $true) | (~spl0_17 | ~spl0_21)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f308])).
% 1.74/1.50 thf(f308,plain,(
% 1.74/1.50 ((cG @ cC @ cE) != $true) | ($true != $true) | (~spl0_17 | ~spl0_21)),
% 1.74/1.50 inference(superposition,[status(thm)],[f255,f101])).
% 1.74/1.50 thf(f255,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != (cG @ X0 @ cD)) | ((cG @ X0 @ cE) != $true)) ) | ~spl0_21),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f254])).
% 1.74/1.50 thf(f254,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != $true) | ((cG @ X0 @ cE) != $true) | ($true != (cG @ X0 @ cD))) ) | ~spl0_21),
% 1.74/1.50 inference(superposition,[status(thm)],[f15,f119])).
% 1.74/1.50 thf(f293,plain,(
% 1.74/1.50 ~spl0_24 | ~spl0_5 | ~spl0_17),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f290,f99,f45,f130])).
% 1.74/1.50 thf(f290,plain,(
% 1.74/1.50 ((cG @ cA @ cD) != $true) | (~spl0_5 | ~spl0_17)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f289])).
% 1.74/1.50 thf(f289,plain,(
% 1.74/1.50 ((cG @ cA @ cD) != $true) | ($true != $true) | (~spl0_5 | ~spl0_17)),
% 1.74/1.50 inference(superposition,[status(thm)],[f191,f47])).
% 1.74/1.50 thf(f284,plain,(
% 1.74/1.50 ~spl0_5 | ~spl0_10 | ~spl0_29),
% 1.74/1.50 inference(avatar_contradiction_clause,[status(thm)],[f283])).
% 1.74/1.50 thf(f283,plain,(
% 1.74/1.50 $false | (~spl0_5 | ~spl0_10 | ~spl0_29)),
% 1.74/1.50 inference(subsumption_resolution,[status(thm)],[f281,f69])).
% 1.74/1.50 thf(f281,plain,(
% 1.74/1.50 ((cG @ cA @ cB) != $true) | (~spl0_5 | ~spl0_29)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f280])).
% 1.74/1.50 thf(f280,plain,(
% 1.74/1.50 ($true != $true) | ((cG @ cA @ cB) != $true) | (~spl0_5 | ~spl0_29)),
% 1.74/1.50 inference(superposition,[status(thm)],[f190,f47])).
% 1.74/1.50 thf(f190,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != (cG @ X0 @ cC)) | ((cG @ X0 @ cB) != $true)) ) | ~spl0_29),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f182])).
% 1.74/1.50 thf(f182,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != $true) | ($true != (cG @ X0 @ cC)) | ((cG @ X0 @ cB) != $true)) ) | ~spl0_29),
% 1.74/1.50 inference(superposition,[status(thm)],[f15,f155])).
% 1.74/1.50 thf(f270,plain,(
% 1.74/1.50 ~spl0_19 | ~spl0_26 | ~spl0_29),
% 1.74/1.50 inference(avatar_contradiction_clause,[status(thm)],[f269])).
% 1.74/1.50 thf(f269,plain,(
% 1.74/1.50 $false | (~spl0_19 | ~spl0_26 | ~spl0_29)),
% 1.74/1.50 inference(subsumption_resolution,[status(thm)],[f265,f141])).
% 1.74/1.50 thf(f265,plain,(
% 1.74/1.50 ((cG @ cB @ cF) != $true) | (~spl0_19 | ~spl0_29)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f263])).
% 1.74/1.50 thf(f263,plain,(
% 1.74/1.50 ($true != $true) | ((cG @ cB @ cF) != $true) | (~spl0_19 | ~spl0_29)),
% 1.74/1.50 inference(superposition,[status(thm)],[f186,f155])).
% 1.74/1.50 thf(f186,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != (cG @ X0 @ cC)) | ($true != (cG @ X0 @ cF))) ) | ~spl0_19),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f181])).
% 1.74/1.50 thf(f181,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != (cG @ X0 @ cC)) | ($true != $true) | ($true != (cG @ X0 @ cF))) ) | ~spl0_19),
% 1.74/1.50 inference(superposition,[status(thm)],[f15,f110])).
% 1.74/1.50 thf(f110,plain,(
% 1.74/1.50 ((cG @ cC @ cF) = $true) | ~spl0_19),
% 1.74/1.50 inference(avatar_component_clause,[status(thm)],[f108])).
% 1.74/1.50 thf(f108,definition,(
% 1.74/1.50 spl0_19 <=> ((cG @ cC @ cF) = $true)),
% 1.74/1.50 introduced(definition,[new_symbols(naming,[spl0_19])],[avatar_definition])).
% 1.74/1.50 thf(f268,plain,(
% 1.74/1.50 ~spl0_3 | ~spl0_5 | ~spl0_19),
% 1.74/1.50 inference(avatar_contradiction_clause,[status(thm)],[f267])).
% 1.74/1.50 thf(f267,plain,(
% 1.74/1.50 $false | (~spl0_3 | ~spl0_5 | ~spl0_19)),
% 1.74/1.50 inference(subsumption_resolution,[status(thm)],[f266,f38])).
% 1.74/1.50 thf(f266,plain,(
% 1.74/1.50 ((cG @ cA @ cF) != $true) | (~spl0_5 | ~spl0_19)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f264])).
% 1.74/1.50 thf(f264,plain,(
% 1.74/1.50 ($true != $true) | ((cG @ cA @ cF) != $true) | (~spl0_5 | ~spl0_19)),
% 1.74/1.50 inference(superposition,[status(thm)],[f186,f47])).
% 1.74/1.50 thf(f262,plain,(
% 1.74/1.50 ~spl0_12 | ~spl0_15 | ~spl0_26),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f261,f139,f90,f76])).
% 1.74/1.50 thf(f90,definition,(
% 1.74/1.50 spl0_15 <=> ((cG @ cE @ cF) = $true)),
% 1.74/1.50 introduced(definition,[new_symbols(naming,[spl0_15])],[avatar_definition])).
% 1.74/1.50 thf(f261,plain,(
% 1.74/1.50 ((cG @ cB @ cE) != $true) | (~spl0_15 | ~spl0_26)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f258])).
% 1.74/1.50 thf(f258,plain,(
% 1.74/1.50 ($true != $true) | ((cG @ cB @ cE) != $true) | (~spl0_15 | ~spl0_26)),
% 1.74/1.50 inference(superposition,[status(thm)],[f185,f141])).
% 1.74/1.50 thf(f185,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != (cG @ X0 @ cF)) | ((cG @ X0 @ cE) != $true)) ) | ~spl0_15),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f177])).
% 1.74/1.50 thf(f177,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != (cG @ X0 @ cF)) | ((cG @ X0 @ cE) != $true) | ($true != $true)) ) | ~spl0_15),
% 1.74/1.50 inference(superposition,[status(thm)],[f15,f92])).
% 1.74/1.50 thf(f92,plain,(
% 1.74/1.50 ((cG @ cE @ cF) = $true) | ~spl0_15),
% 1.74/1.50 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.74/1.50 thf(f251,plain,(
% 1.74/1.50 ~spl0_2 | ~spl0_11 | ~spl0_22),
% 1.74/1.50 inference(avatar_contradiction_clause,[status(thm)],[f250])).
% 1.74/1.50 thf(f250,plain,(
% 1.74/1.50 $false | (~spl0_2 | ~spl0_11 | ~spl0_22)),
% 1.74/1.50 inference(subsumption_resolution,[status(thm)],[f249,f33])).
% 1.74/1.50 thf(f33,plain,(
% 1.74/1.50 ((cR @ cB @ cD) = $true) | ~spl0_2),
% 1.74/1.50 inference(avatar_component_clause,[status(thm)],[f31])).
% 1.74/1.50 thf(f31,definition,(
% 1.74/1.50 spl0_2 <=> ((cR @ cB @ cD) = $true)),
% 1.74/1.50 introduced(definition,[new_symbols(naming,[spl0_2])],[avatar_definition])).
% 1.74/1.50 thf(f249,plain,(
% 1.74/1.50 ((cR @ cB @ cD) != $true) | (~spl0_11 | ~spl0_22)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f246])).
% 1.74/1.50 thf(f246,plain,(
% 1.74/1.50 ($true != $true) | ((cR @ cB @ cD) != $true) | (~spl0_11 | ~spl0_22)),
% 1.74/1.50 inference(superposition,[status(thm)],[f169,f123])).
% 1.74/1.50 thf(f169,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != (cR @ X0 @ cE)) | ((cR @ cB @ X0) != $true)) ) | ~spl0_11),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f162])).
% 1.74/1.50 thf(f162,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != $true) | ((cR @ cB @ X0) != $true) | ($true != (cR @ X0 @ cE))) ) | ~spl0_11),
% 1.74/1.50 inference(superposition,[status(thm)],[f13,f74])).
% 1.74/1.50 thf(f74,plain,(
% 1.74/1.50 ((cR @ cB @ cE) = $true) | ~spl0_11),
% 1.74/1.50 inference(avatar_component_clause,[status(thm)],[f72])).
% 1.74/1.50 thf(f72,definition,(
% 1.74/1.50 spl0_11 <=> ((cR @ cB @ cE) = $true)),
% 1.74/1.50 introduced(definition,[new_symbols(naming,[spl0_11])],[avatar_definition])).
% 1.74/1.50 thf(f245,plain,(
% 1.74/1.50 ~spl0_21 | ~spl0_7 | ~spl0_15),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f240,f90,f54,f117])).
% 1.74/1.50 thf(f240,plain,(
% 1.74/1.50 ((cG @ cD @ cE) != $true) | (~spl0_7 | ~spl0_15)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f234])).
% 1.74/1.50 thf(f234,plain,(
% 1.74/1.50 ((cG @ cD @ cE) != $true) | ($true != $true) | (~spl0_7 | ~spl0_15)),
% 1.74/1.50 inference(superposition,[status(thm)],[f185,f56])).
% 1.74/1.50 thf(f244,plain,(
% 1.74/1.50 ~spl0_28 | ~spl0_3 | ~spl0_15),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f238,f90,f36,f148])).
% 1.74/1.50 thf(f238,plain,(
% 1.74/1.50 ((cG @ cA @ cE) != $true) | (~spl0_3 | ~spl0_15)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f236])).
% 1.74/1.50 thf(f236,plain,(
% 1.74/1.50 ((cG @ cA @ cE) != $true) | ($true != $true) | (~spl0_3 | ~spl0_15)),
% 1.74/1.50 inference(superposition,[status(thm)],[f185,f38])).
% 1.74/1.50 thf(f243,plain,(
% 1.74/1.50 ~spl0_14 | ~spl0_15 | ~spl0_19),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f239,f108,f90,f85])).
% 1.74/1.50 thf(f239,plain,(
% 1.74/1.50 ((cG @ cC @ cE) != $true) | (~spl0_15 | ~spl0_19)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f235])).
% 1.74/1.50 thf(f235,plain,(
% 1.74/1.50 ((cG @ cC @ cE) != $true) | ($true != $true) | (~spl0_15 | ~spl0_19)),
% 1.74/1.50 inference(superposition,[status(thm)],[f185,f110])).
% 1.74/1.50 thf(f232,plain,(
% 1.74/1.50 ~spl0_22 | ~spl0_23 | ~spl0_27),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f230,f144,f126,f121])).
% 1.74/1.50 thf(f230,plain,(
% 1.74/1.50 ((cR @ cD @ cE) != $true) | (~spl0_23 | ~spl0_27)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f229])).
% 1.74/1.50 thf(f229,plain,(
% 1.74/1.50 ((cR @ cD @ cE) != $true) | ($true != $true) | (~spl0_23 | ~spl0_27)),
% 1.74/1.50 inference(superposition,[status(thm)],[f174,f128])).
% 1.74/1.50 thf(f225,plain,(
% 1.74/1.50 ~spl0_2 | ~spl0_9 | ~spl0_23),
% 1.74/1.50 inference(avatar_contradiction_clause,[status(thm)],[f224])).
% 1.74/1.50 thf(f224,plain,(
% 1.74/1.50 $false | (~spl0_2 | ~spl0_9 | ~spl0_23)),
% 1.74/1.50 inference(subsumption_resolution,[status(thm)],[f222,f33])).
% 1.74/1.50 thf(f222,plain,(
% 1.74/1.50 ((cR @ cB @ cD) != $true) | (~spl0_9 | ~spl0_23)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f218])).
% 1.74/1.50 thf(f218,plain,(
% 1.74/1.50 ($true != $true) | ((cR @ cB @ cD) != $true) | (~spl0_9 | ~spl0_23)),
% 1.74/1.50 inference(superposition,[status(thm)],[f173,f65])).
% 1.74/1.50 thf(f173,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != (cR @ cA @ X0)) | ($true != (cR @ X0 @ cD))) ) | ~spl0_23),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f165])).
% 1.74/1.50 thf(f165,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (($true != (cR @ X0 @ cD)) | ($true != (cR @ cA @ X0)) | ($true != $true)) ) | ~spl0_23),
% 1.74/1.50 inference(superposition,[status(thm)],[f13,f128])).
% 1.74/1.50 thf(f207,plain,(
% 1.74/1.50 ~spl0_8 | ~spl0_2 | ~spl0_25),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f203,f135,f31,f58])).
% 1.74/1.50 thf(f203,plain,(
% 1.74/1.50 ((cR @ cD @ cF) != $true) | (~spl0_2 | ~spl0_25)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f200])).
% 1.74/1.50 thf(f200,plain,(
% 1.74/1.50 ((cR @ cD @ cF) != $true) | ($true != $true) | (~spl0_2 | ~spl0_25)),
% 1.74/1.50 inference(superposition,[status(thm)],[f170,f33])).
% 1.74/1.50 thf(f170,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (((cR @ cB @ X0) != $true) | ((cR @ X0 @ cF) != $true)) ) | ~spl0_25),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f163])).
% 1.74/1.50 thf(f163,plain,(
% 1.74/1.50 ( ! [X0 : $i] : (((cR @ X0 @ cF) != $true) | ($true != $true) | ((cR @ cB @ X0) != $true)) ) | ~spl0_25),
% 1.74/1.50 inference(superposition,[status(thm)],[f13,f137])).
% 1.74/1.50 thf(f206,plain,(
% 1.74/1.50 ~spl0_16 | ~spl0_11 | ~spl0_25),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f204,f135,f72,f94])).
% 1.74/1.50 thf(f204,plain,(
% 1.74/1.50 ((cR @ cE @ cF) != $true) | (~spl0_11 | ~spl0_25)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f201])).
% 1.74/1.50 thf(f201,plain,(
% 1.74/1.50 ($true != $true) | ((cR @ cE @ cF) != $true) | (~spl0_11 | ~spl0_25)),
% 1.74/1.50 inference(superposition,[status(thm)],[f170,f74])).
% 1.74/1.50 thf(f199,plain,(
% 1.74/1.50 ~spl0_30 | ~spl0_11 | ~spl0_13),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f198,f81,f72,f157])).
% 1.74/1.50 thf(f198,plain,(
% 1.74/1.50 ((cR @ cB @ cC) != $true) | (~spl0_11 | ~spl0_13)),
% 1.74/1.50 inference(trivial_inequality_removal,[status(thm)],[f195])).
% 1.74/1.50 thf(f195,plain,(
% 1.74/1.50 ((cR @ cB @ cC) != $true) | ($true != $true) | (~spl0_11 | ~spl0_13)),
% 1.74/1.50 inference(superposition,[status(thm)],[f169,f83])).
% 1.74/1.50 thf(f160,plain,(
% 1.74/1.50 spl0_29 | spl0_30),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f25,f157,f153])).
% 1.74/1.50 thf(f25,plain,(
% 1.74/1.50 ((cR @ cB @ cC) = $true) | ((cG @ cB @ cC) = $true)),
% 1.74/1.50 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.50 thf(f151,plain,(
% 1.74/1.50 spl0_27 | spl0_28),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f23,f148,f144])).
% 1.74/1.50 thf(f23,plain,(
% 1.74/1.50 ((cR @ cA @ cE) = $true) | ((cG @ cA @ cE) = $true)),
% 1.74/1.50 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.50 thf(f142,plain,(
% 1.74/1.50 spl0_25 | spl0_26),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f17,f139,f135])).
% 1.74/1.50 thf(f17,plain,(
% 1.74/1.50 ((cG @ cB @ cF) = $true) | ((cR @ cB @ cF) = $true)),
% 1.74/1.50 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.50 thf(f133,plain,(
% 1.74/1.50 spl0_23 | spl0_24),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f20,f130,f126])).
% 1.74/1.50 thf(f20,plain,(
% 1.74/1.50 ((cG @ cA @ cD) = $true) | ((cR @ cA @ cD) = $true)),
% 1.74/1.50 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.50 thf(f124,plain,(
% 1.74/1.50 spl0_21 | spl0_22),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f11,f121,f117])).
% 1.74/1.50 thf(f11,plain,(
% 1.74/1.50 ((cG @ cD @ cE) = $true) | ((cR @ cD @ cE) = $true)),
% 1.74/1.50 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.50 thf(f115,plain,(
% 1.74/1.50 spl0_19 | spl0_20),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f19,f112,f108])).
% 1.74/1.50 thf(f19,plain,(
% 1.74/1.50 ((cR @ cC @ cF) = $true) | ((cG @ cC @ cF) = $true)),
% 1.74/1.50 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.50 thf(f106,plain,(
% 1.74/1.50 spl0_17 | spl0_18),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f22,f103,f99])).
% 1.74/1.50 thf(f22,plain,(
% 1.74/1.50 ((cG @ cC @ cD) = $true) | ((cR @ cC @ cD) = $true)),
% 1.74/1.50 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.50 thf(f97,plain,(
% 1.74/1.50 spl0_15 | spl0_16),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f16,f94,f90])).
% 1.74/1.50 thf(f16,plain,(
% 1.74/1.50 ((cR @ cE @ cF) = $true) | ((cG @ cE @ cF) = $true)),
% 1.74/1.50 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.50 thf(f88,plain,(
% 1.74/1.50 spl0_13 | spl0_14),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f9,f85,f81])).
% 1.74/1.50 thf(f9,plain,(
% 1.74/1.50 ((cG @ cC @ cE) = $true) | ((cR @ cC @ cE) = $true)),
% 1.74/1.50 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.50 thf(f79,plain,(
% 1.74/1.50 spl0_11 | spl0_12),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f18,f76,f72])).
% 1.74/1.50 thf(f18,plain,(
% 1.74/1.50 ((cG @ cB @ cE) = $true) | ((cR @ cB @ cE) = $true)),
% 1.74/1.50 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.50 thf(f70,plain,(
% 1.74/1.50 spl0_9 | spl0_10),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f21,f67,f63])).
% 1.74/1.50 thf(f21,plain,(
% 1.74/1.50 ((cR @ cA @ cB) = $true) | ((cG @ cA @ cB) = $true)),
% 1.74/1.50 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.50 thf(f61,plain,(
% 1.74/1.50 spl0_7 | spl0_8),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f10,f58,f54])).
% 1.74/1.50 thf(f10,plain,(
% 1.74/1.50 ((cR @ cD @ cF) = $true) | ((cG @ cD @ cF) = $true)),
% 1.74/1.50 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.50 thf(f52,plain,(
% 1.74/1.50 spl0_5 | spl0_6),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f12,f49,f45])).
% 1.74/1.50 thf(f12,plain,(
% 1.74/1.50 ((cG @ cA @ cC) = $true) | ((cR @ cA @ cC) = $true)),
% 1.74/1.50 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.50 thf(f43,plain,(
% 1.74/1.50 spl0_3 | spl0_4),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f14,f40,f36])).
% 1.74/1.50 thf(f14,plain,(
% 1.74/1.50 ((cG @ cA @ cF) = $true) | ((cR @ cA @ cF) = $true)),
% 1.74/1.50 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.50 thf(f34,plain,(
% 1.74/1.50 spl0_1 | spl0_2),
% 1.74/1.50 inference(avatar_split_clause,[status(thm)],[f24,f31,f27])).
% 1.74/1.50 thf(f24,plain,(
% 1.74/1.50 ((cG @ cB @ cD) = $true) | ((cR @ cB @ cD) = $true)),
% 1.74/1.50 inference(cnf_transformation,[status(thm)],[f8])).
% 1.74/1.50 % SZS output end Proof for DTF2THF_5569
% 1.74/1.50 % (5669)------------------------------
% 1.74/1.50 % (5669)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.74/1.50 % (5669)Termination reason: Refutation
% 1.74/1.50
% 1.74/1.50 % (5669)Memory used [KB]: 5884
% 1.74/1.50 % (5669)Time elapsed: 0.050 s
% 1.74/1.50 % (5669)Instructions burned: 77 (million)
% 1.74/1.50 % (5669)------------------------------
% 1.74/1.50 % (5669)------------------------------
% 1.74/1.50 % (5668)Success in time 0.06 s
%------------------------------------------------------------------------------