%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO179^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n026.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Sep 30 08:46:48 AM UTC 2026
% Result : Theorem 0.20s 0.30s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 51
% Number of leaves : 31
% Syntax : Number of formulae : 370 ( 24 unt; 0 typ; 30 def)
% Number of atoms : 3036 ( 469 equ; 0 cnn)
% Maximal formula atoms : 96 ( 8 avg)
% Number of connectives : 2742 ( 822 ~; 734 |; 120 &;1032 @)
% ( 30 <=>; 4 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 4 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 42 ( 39 usr; 38 con; 0-2 aty)
% Number of variables : 96 ( 0 sgn 72 !; 24 ?; 96 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cG: $i > $i > $o ).
thf(func_def_1,type,
cR: $i > $i > $o ).
thf(f1,conjecture,
( ( ( ( cR @ cB @ cF )
| ( cG @ cB @ cF ) )
& ( ( cR @ cD @ cF )
| ( cG @ cD @ cF ) )
& ( ( cG @ cD @ cE )
| ( cR @ cD @ cE ) )
& ( ( cG @ cA @ cC )
| ( cR @ cA @ cC ) )
& ( ( cG @ cC @ cE )
| ( cR @ cC @ cE ) )
& ( ( cR @ cA @ cE )
| ( cG @ cA @ cE ) )
& ( ( cR @ cB @ cD )
| ( cG @ cB @ cD ) )
& ( ( cR @ cB @ cC )
| ( cG @ cB @ cC ) )
& ( ( cG @ cC @ cD )
| ( cR @ cC @ cD ) )
& ( ( cG @ cA @ cF )
| ( cR @ cA @ cF ) )
& ( ( cR @ cE @ cF )
| ( cG @ cE @ cF ) )
& ( ( cR @ cA @ cD )
| ( cG @ cA @ cD ) )
& ( ( cR @ cC @ cF )
| ( cG @ cC @ cF ) )
& ( ( cG @ cA @ cB )
| ( cR @ cA @ cB ) )
& ( ( cG @ cB @ cE )
| ( cR @ cB @ cE ) ) )
=> ( ? [X0: $i,X1: $i,X2: $i] :
( ( cR @ X0 @ X1 )
& ( cR @ X1 @ X2 )
& ( cR @ X0 @ X2 ) )
| ? [X2: $i,X0: $i,X1: $i] :
( ( cG @ X0 @ X1 )
& ( cG @ X1 @ X2 )
& ( cG @ X0 @ X2 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cSIX_THEOREM_B) ).
thf(f2,negated_conjecture,
~ ( ( ( ( cR @ cB @ cF )
| ( cG @ cB @ cF ) )
& ( ( cR @ cD @ cF )
| ( cG @ cD @ cF ) )
& ( ( cG @ cD @ cE )
| ( cR @ cD @ cE ) )
& ( ( cG @ cA @ cC )
| ( cR @ cA @ cC ) )
& ( ( cG @ cC @ cE )
| ( cR @ cC @ cE ) )
& ( ( cR @ cA @ cE )
| ( cG @ cA @ cE ) )
& ( ( cR @ cB @ cD )
| ( cG @ cB @ cD ) )
& ( ( cR @ cB @ cC )
| ( cG @ cB @ cC ) )
& ( ( cG @ cC @ cD )
| ( cR @ cC @ cD ) )
& ( ( cG @ cA @ cF )
| ( cR @ cA @ cF ) )
& ( ( cR @ cE @ cF )
| ( cG @ cE @ cF ) )
& ( ( cR @ cA @ cD )
| ( cG @ cA @ cD ) )
& ( ( cR @ cC @ cF )
| ( cG @ cC @ cF ) )
& ( ( cG @ cA @ cB )
| ( cR @ cA @ cB ) )
& ( ( cG @ cB @ cE )
| ( cR @ cB @ cE ) ) )
=> ( ? [X0: $i,X1: $i,X2: $i] :
( ( cR @ X0 @ X1 )
& ( cR @ X1 @ X2 )
& ( cR @ X0 @ X2 ) )
| ? [X2: $i,X0: $i,X1: $i] :
( ( cG @ X0 @ X1 )
& ( cG @ X1 @ X2 )
& ( cG @ X0 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ( ( ( cR @ cB @ cF )
| ( cG @ cB @ cF ) )
& ( ( cR @ cD @ cF )
| ( cG @ cD @ cF ) )
& ( ( cG @ cD @ cE )
| ( cR @ cD @ cE ) )
& ( ( cG @ cA @ cC )
| ( cR @ cA @ cC ) )
& ( ( cG @ cC @ cE )
| ( cR @ cC @ cE ) )
& ( ( cR @ cA @ cE )
| ( cG @ cA @ cE ) )
& ( ( cR @ cB @ cD )
| ( cG @ cB @ cD ) )
& ( ( cR @ cB @ cC )
| ( cG @ cB @ cC ) )
& ( ( cG @ cC @ cD )
| ( cR @ cC @ cD ) )
& ( ( cG @ cA @ cF )
| ( cR @ cA @ cF ) )
& ( ( cR @ cE @ cF )
| ( cG @ cE @ cF ) )
& ( ( cR @ cA @ cD )
| ( cG @ cA @ cD ) )
& ( ( cR @ cC @ cF )
| ( cG @ cC @ cF ) )
& ( ( cG @ cA @ cB )
| ( cR @ cA @ cB ) )
& ( ( cG @ cB @ cE )
| ( cR @ cB @ cE ) ) )
=> ( ? [X0: $i,X1: $i,X2: $i] :
( ( cR @ X0 @ X1 )
& ( cR @ X1 @ X2 )
& ( cR @ X0 @ X2 ) )
| ? [X3: $i,X4: $i,X5: $i] :
( ( cG @ X4 @ X5 )
& ( cG @ X5 @ X3 )
& ( cG @ X4 @ X3 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ( ( ( ( ( cG @ cA @ cD )
= $true )
| ( ( cR @ cA @ cD )
= $true ) )
& ( ( ( cG @ cC @ cF )
= $true )
| ( ( cR @ cC @ cF )
= $true ) )
& ( ( ( cR @ cA @ cE )
= $true )
| ( ( cG @ cA @ cE )
= $true ) )
& ( ( ( cR @ cB @ cC )
= $true )
| ( ( cG @ cB @ cC )
= $true ) )
& ( ( ( cR @ cB @ cE )
= $true )
| ( ( cG @ cB @ cE )
= $true ) )
& ( ( ( cR @ cB @ cF )
= $true )
| ( ( cG @ cB @ cF )
= $true ) )
& ( ( ( cR @ cC @ cD )
= $true )
| ( ( cG @ cC @ cD )
= $true ) )
& ( ( ( cG @ cE @ cF )
= $true )
| ( ( cR @ cE @ cF )
= $true ) )
& ( ( ( cG @ cC @ cE )
= $true )
| ( ( cR @ cC @ cE )
= $true ) )
& ( ( ( cR @ cB @ cD )
= $true )
| ( ( cG @ cB @ cD )
= $true ) )
& ( ( ( cR @ cA @ cB )
= $true )
| ( ( cG @ cA @ cB )
= $true ) )
& ( ( ( cG @ cD @ cF )
= $true )
| ( ( cR @ cD @ cF )
= $true ) )
& ( ( ( cR @ cA @ cC )
= $true )
| ( ( cG @ cA @ cC )
= $true ) )
& ( ( ( cG @ cA @ cF )
= $true )
| ( ( cR @ cA @ cF )
= $true ) )
& ( ( ( cG @ cD @ cE )
= $true )
| ( ( cR @ cD @ cE )
= $true ) ) )
=> ( ? [X5: $i,X4: $i,X3: $i] :
( ( ( cG @ X4 @ X5 )
= $true )
& ( $true
= ( cG @ X5 @ X3 ) )
& ( ( cG @ X4 @ X3 )
= $true ) )
| ? [X2: $i,X0: $i,X1: $i] :
( ( ( cR @ X1 @ X2 )
= $true )
& ( ( cR @ X0 @ X2 )
= $true )
& ( ( cR @ X0 @ X1 )
= $true ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ! [X4: $i,X3: $i,X5: $i] :
( ( ( cG @ X4 @ X3 )
!= $true )
| ( ( cG @ X4 @ X5 )
!= $true )
| ( $true
!= ( cG @ X5 @ X3 ) ) )
& ! [X2: $i,X0: $i,X1: $i] :
( ( ( cR @ X1 @ X2 )
!= $true )
| ( ( cR @ X0 @ X1 )
!= $true )
| ( ( cR @ X0 @ X2 )
!= $true ) )
& ( ( ( cG @ cA @ cD )
= $true )
| ( ( cR @ cA @ cD )
= $true ) )
& ( ( ( cG @ cC @ cF )
= $true )
| ( ( cR @ cC @ cF )
= $true ) )
& ( ( ( cR @ cA @ cE )
= $true )
| ( ( cG @ cA @ cE )
= $true ) )
& ( ( ( cR @ cB @ cC )
= $true )
| ( ( cG @ cB @ cC )
= $true ) )
& ( ( ( cR @ cB @ cE )
= $true )
| ( ( cG @ cB @ cE )
= $true ) )
& ( ( ( cR @ cB @ cF )
= $true )
| ( ( cG @ cB @ cF )
= $true ) )
& ( ( ( cR @ cC @ cD )
= $true )
| ( ( cG @ cC @ cD )
= $true ) )
& ( ( ( cG @ cE @ cF )
= $true )
| ( ( cR @ cE @ cF )
= $true ) )
& ( ( ( cG @ cC @ cE )
= $true )
| ( ( cR @ cC @ cE )
= $true ) )
& ( ( ( cR @ cB @ cD )
= $true )
| ( ( cG @ cB @ cD )
= $true ) )
& ( ( ( cR @ cA @ cB )
= $true )
| ( ( cG @ cA @ cB )
= $true ) )
& ( ( ( cG @ cD @ cF )
= $true )
| ( ( cR @ cD @ cF )
= $true ) )
& ( ( ( cR @ cA @ cC )
= $true )
| ( ( cG @ cA @ cC )
= $true ) )
& ( ( ( cG @ cA @ cF )
= $true )
| ( ( cR @ cA @ cF )
= $true ) )
& ( ( ( cG @ cD @ cE )
= $true )
| ( ( cR @ cD @ cE )
= $true ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
( ! [X4: $i,X3: $i,X5: $i] :
( ( ( cG @ X4 @ X3 )
!= $true )
| ( ( cG @ X4 @ X5 )
!= $true )
| ( $true
!= ( cG @ X5 @ X3 ) ) )
& ( ( ( cR @ cB @ cE )
= $true )
| ( ( cG @ cB @ cE )
= $true ) )
& ( ( ( cR @ cB @ cD )
= $true )
| ( ( cG @ cB @ cD )
= $true ) )
& ( ( ( cR @ cC @ cD )
= $true )
| ( ( cG @ cC @ cD )
= $true ) )
& ( ( ( cR @ cA @ cC )
= $true )
| ( ( cG @ cA @ cC )
= $true ) )
& ( ( ( cR @ cB @ cF )
= $true )
| ( ( cG @ cB @ cF )
= $true ) )
& ( ( ( cR @ cA @ cB )
= $true )
| ( ( cG @ cA @ cB )
= $true ) )
& ! [X2: $i,X0: $i,X1: $i] :
( ( ( cR @ X1 @ X2 )
!= $true )
| ( ( cR @ X0 @ X1 )
!= $true )
| ( ( cR @ X0 @ X2 )
!= $true ) )
& ( ( ( cR @ cB @ cC )
= $true )
| ( ( cG @ cB @ cC )
= $true ) )
& ( ( ( cG @ cA @ cD )
= $true )
| ( ( cR @ cA @ cD )
= $true ) )
& ( ( ( cG @ cA @ cF )
= $true )
| ( ( cR @ cA @ cF )
= $true ) )
& ( ( ( cR @ cA @ cE )
= $true )
| ( ( cG @ cA @ cE )
= $true ) )
& ( ( ( cG @ cD @ cF )
= $true )
| ( ( cR @ cD @ cF )
= $true ) )
& ( ( ( cG @ cC @ cE )
= $true )
| ( ( cR @ cC @ cE )
= $true ) )
& ( ( ( cG @ cC @ cF )
= $true )
| ( ( cR @ cC @ cF )
= $true ) )
& ( ( ( cG @ cD @ cE )
= $true )
| ( ( cR @ cD @ cE )
= $true ) )
& ( ( ( cG @ cE @ cF )
= $true )
| ( ( cR @ cE @ cF )
= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
( ! [X0: $i,X1: $i,X2: $i] :
( ( ( cG @ X0 @ X1 )
!= $true )
| ( ( cG @ X0 @ X2 )
!= $true )
| ( ( cG @ X2 @ X1 )
!= $true ) )
& ( ( ( cR @ cB @ cE )
= $true )
| ( ( cG @ cB @ cE )
= $true ) )
& ( ( ( cR @ cB @ cD )
= $true )
| ( ( cG @ cB @ cD )
= $true ) )
& ( ( ( cR @ cC @ cD )
= $true )
| ( ( cG @ cC @ cD )
= $true ) )
& ( ( ( cR @ cA @ cC )
= $true )
| ( ( cG @ cA @ cC )
= $true ) )
& ( ( ( cR @ cB @ cF )
= $true )
| ( ( cG @ cB @ cF )
= $true ) )
& ( ( ( cR @ cA @ cB )
= $true )
| ( ( cG @ cA @ cB )
= $true ) )
& ! [X3: $i,X4: $i,X5: $i] :
( ( ( cR @ X5 @ X3 )
!= $true )
| ( ( cR @ X4 @ X5 )
!= $true )
| ( ( cR @ X4 @ X3 )
!= $true ) )
& ( ( ( cR @ cB @ cC )
= $true )
| ( ( cG @ cB @ cC )
= $true ) )
& ( ( ( cG @ cA @ cD )
= $true )
| ( ( cR @ cA @ cD )
= $true ) )
& ( ( ( cG @ cA @ cF )
= $true )
| ( ( cR @ cA @ cF )
= $true ) )
& ( ( ( cR @ cA @ cE )
= $true )
| ( ( cG @ cA @ cE )
= $true ) )
& ( ( ( cG @ cD @ cF )
= $true )
| ( ( cR @ cD @ cF )
= $true ) )
& ( ( ( cG @ cC @ cE )
= $true )
| ( ( cR @ cC @ cE )
= $true ) )
& ( ( ( cG @ cC @ cF )
= $true )
| ( ( cR @ cC @ cF )
= $true ) )
& ( ( ( cG @ cD @ cE )
= $true )
| ( ( cR @ cD @ cE )
= $true ) )
& ( ( ( cG @ cE @ cF )
= $true )
| ( ( cR @ cE @ cF )
= $true ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ( ( cG @ cE @ cF )
= $true )
| ( ( cR @ cE @ cF )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f9,plain,
( ( ( cR @ cD @ cE )
= $true )
| ( ( cG @ cD @ cE )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f10,plain,
( ( ( cG @ cC @ cF )
= $true )
| ( ( cR @ cC @ cF )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f11,plain,
( ( ( cR @ cC @ cE )
= $true )
| ( ( cG @ cC @ cE )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
( ( ( cR @ cD @ cF )
= $true )
| ( ( cG @ cD @ cF )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f13,plain,
( ( ( cG @ cA @ cE )
= $true )
| ( ( cR @ cA @ cE )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f14,plain,
( ( ( cG @ cA @ cF )
= $true )
| ( ( cR @ cA @ cF )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f15,plain,
( ( ( cR @ cA @ cD )
= $true )
| ( ( cG @ cA @ cD )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f16,plain,
( ( ( cR @ cB @ cC )
= $true )
| ( ( cG @ cB @ cC )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f17,plain,
! [X3: $i,X4: $i,X5: $i] :
( ( ( cR @ X5 @ X3 )
!= $true )
| ( ( cR @ X4 @ X3 )
!= $true )
| ( ( cR @ X4 @ X5 )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f18,plain,
( ( ( cG @ cA @ cB )
= $true )
| ( ( cR @ cA @ cB )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f19,plain,
( ( ( cR @ cB @ cF )
= $true )
| ( ( cG @ cB @ cF )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f20,plain,
( ( ( cR @ cA @ cC )
= $true )
| ( ( cG @ cA @ cC )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f21,plain,
( ( ( cR @ cC @ cD )
= $true )
| ( ( cG @ cC @ cD )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f22,plain,
( ( ( cG @ cB @ cD )
= $true )
| ( ( cR @ cB @ cD )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f23,plain,
( ( ( cG @ cB @ cE )
= $true )
| ( ( cR @ cB @ cE )
= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f24,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( ( cG @ X2 @ X1 )
!= $true )
| ( ( cG @ X0 @ X1 )
!= $true )
| ( ( cG @ X0 @ X2 )
!= $true ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f28,definition,
( spl0_1
<=> ( ( cR @ cC @ cE )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f30,plain,
( ( ( cR @ cC @ cE )
= $true )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f28]) ).
thf(f32,definition,
( spl0_2
<=> ( ( cG @ cC @ cE )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f34,plain,
( ( ( cG @ cC @ cE )
= $true )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f32]) ).
thf(f35,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f11,f32,f28]) ).
thf(f37,definition,
( spl0_3
<=> ( ( cR @ cA @ cE )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f39,plain,
( ( ( cR @ cA @ cE )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f37]) ).
thf(f41,definition,
( spl0_4
<=> ( ( cG @ cA @ cE )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f43,plain,
( ( ( cG @ cA @ cE )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f41]) ).
thf(f44,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f13,f41,f37]) ).
thf(f46,definition,
( spl0_5
<=> ( ( cG @ cC @ cF )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f48,plain,
( ( ( cG @ cC @ cF )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f46]) ).
thf(f50,definition,
( spl0_6
<=> ( ( cR @ cC @ cF )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
thf(f52,plain,
( ( ( cR @ cC @ cF )
= $true )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f50]) ).
thf(f53,plain,
( spl0_5
| spl0_6 ),
inference(avatar_split_clause,[],[f10,f50,f46]) ).
thf(f55,definition,
( spl0_7
<=> ( ( cR @ cD @ cE )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_7])],[avatar_definition]) ).
thf(f57,plain,
( ( ( cR @ cD @ cE )
= $true )
| ~ spl0_7 ),
inference(avatar_component_clause,[],[f55]) ).
thf(f59,definition,
( spl0_8
<=> ( ( cG @ cD @ cE )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_8])],[avatar_definition]) ).
thf(f61,plain,
( ( ( cG @ cD @ cE )
= $true )
| ~ spl0_8 ),
inference(avatar_component_clause,[],[f59]) ).
thf(f62,plain,
( spl0_7
| spl0_8 ),
inference(avatar_split_clause,[],[f9,f59,f55]) ).
thf(f64,definition,
( spl0_9
<=> ( ( cG @ cA @ cD )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_9])],[avatar_definition]) ).
thf(f66,plain,
( ( ( cG @ cA @ cD )
= $true )
| ~ spl0_9 ),
inference(avatar_component_clause,[],[f64]) ).
thf(f68,definition,
( spl0_10
<=> ( ( cR @ cA @ cD )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_10])],[avatar_definition]) ).
thf(f71,plain,
( spl0_9
| spl0_10 ),
inference(avatar_split_clause,[],[f15,f68,f64]) ).
thf(f73,definition,
( spl0_11
<=> ( ( cG @ cD @ cF )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_11])],[avatar_definition]) ).
thf(f75,plain,
( ( ( cG @ cD @ cF )
= $true )
| ~ spl0_11 ),
inference(avatar_component_clause,[],[f73]) ).
thf(f77,definition,
( spl0_12
<=> ( ( cR @ cD @ cF )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_12])],[avatar_definition]) ).
thf(f79,plain,
( ( ( cR @ cD @ cF )
= $true )
| ~ spl0_12 ),
inference(avatar_component_clause,[],[f77]) ).
thf(f80,plain,
( spl0_11
| spl0_12 ),
inference(avatar_split_clause,[],[f12,f77,f73]) ).
thf(f82,definition,
( spl0_13
<=> ( ( cR @ cB @ cF )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_13])],[avatar_definition]) ).
thf(f84,plain,
( ( ( cR @ cB @ cF )
= $true )
| ~ spl0_13 ),
inference(avatar_component_clause,[],[f82]) ).
thf(f86,definition,
( spl0_14
<=> ( ( cG @ cB @ cF )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_14])],[avatar_definition]) ).
thf(f89,plain,
( spl0_13
| spl0_14 ),
inference(avatar_split_clause,[],[f19,f86,f82]) ).
thf(f91,definition,
( spl0_15
<=> ( ( cG @ cB @ cC )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_15])],[avatar_definition]) ).
thf(f93,plain,
( ( ( cG @ cB @ cC )
= $true )
| ~ spl0_15 ),
inference(avatar_component_clause,[],[f91]) ).
thf(f95,definition,
( spl0_16
<=> ( ( cR @ cB @ cC )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_16])],[avatar_definition]) ).
thf(f97,plain,
( ( ( cR @ cB @ cC )
= $true )
| ~ spl0_16 ),
inference(avatar_component_clause,[],[f95]) ).
thf(f98,plain,
( spl0_15
| spl0_16 ),
inference(avatar_split_clause,[],[f16,f95,f91]) ).
thf(f100,definition,
( spl0_17
<=> ( ( cG @ cE @ cF )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_17])],[avatar_definition]) ).
thf(f102,plain,
( ( ( cG @ cE @ cF )
= $true )
| ~ spl0_17 ),
inference(avatar_component_clause,[],[f100]) ).
thf(f104,definition,
( spl0_18
<=> ( ( cR @ cE @ cF )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_18])],[avatar_definition]) ).
thf(f106,plain,
( ( ( cR @ cE @ cF )
= $true )
| ~ spl0_18 ),
inference(avatar_component_clause,[],[f104]) ).
thf(f107,plain,
( spl0_17
| spl0_18 ),
inference(avatar_split_clause,[],[f8,f104,f100]) ).
thf(f109,definition,
( spl0_19
<=> ( ( cR @ cB @ cD )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_19])],[avatar_definition]) ).
thf(f111,plain,
( ( ( cR @ cB @ cD )
= $true )
| ~ spl0_19 ),
inference(avatar_component_clause,[],[f109]) ).
thf(f113,definition,
( spl0_20
<=> ( ( cG @ cB @ cD )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_20])],[avatar_definition]) ).
thf(f115,plain,
( ( ( cG @ cB @ cD )
= $true )
| ~ spl0_20 ),
inference(avatar_component_clause,[],[f113]) ).
thf(f116,plain,
( spl0_19
| spl0_20 ),
inference(avatar_split_clause,[],[f22,f113,f109]) ).
thf(f118,definition,
( spl0_21
<=> ( ( cG @ cB @ cE )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_21])],[avatar_definition]) ).
thf(f120,plain,
( ( ( cG @ cB @ cE )
= $true )
| ~ spl0_21 ),
inference(avatar_component_clause,[],[f118]) ).
thf(f122,definition,
( spl0_22
<=> ( ( cR @ cB @ cE )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_22])],[avatar_definition]) ).
thf(f124,plain,
( ( ( cR @ cB @ cE )
= $true )
| ~ spl0_22 ),
inference(avatar_component_clause,[],[f122]) ).
thf(f125,plain,
( spl0_21
| spl0_22 ),
inference(avatar_split_clause,[],[f23,f122,f118]) ).
thf(f127,definition,
( spl0_23
<=> ( ( cG @ cA @ cF )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_23])],[avatar_definition]) ).
thf(f129,plain,
( ( ( cG @ cA @ cF )
= $true )
| ~ spl0_23 ),
inference(avatar_component_clause,[],[f127]) ).
thf(f131,definition,
( spl0_24
<=> ( ( cR @ cA @ cF )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_24])],[avatar_definition]) ).
thf(f133,plain,
( ( ( cR @ cA @ cF )
= $true )
| ~ spl0_24 ),
inference(avatar_component_clause,[],[f131]) ).
thf(f134,plain,
( spl0_23
| spl0_24 ),
inference(avatar_split_clause,[],[f14,f131,f127]) ).
thf(f136,definition,
( spl0_25
<=> ( ( cG @ cA @ cB )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_25])],[avatar_definition]) ).
thf(f138,plain,
( ( ( cG @ cA @ cB )
= $true )
| ~ spl0_25 ),
inference(avatar_component_clause,[],[f136]) ).
thf(f140,definition,
( spl0_26
<=> ( ( cR @ cA @ cB )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_26])],[avatar_definition]) ).
thf(f142,plain,
( ( ( cR @ cA @ cB )
= $true )
| ~ spl0_26 ),
inference(avatar_component_clause,[],[f140]) ).
thf(f143,plain,
( spl0_25
| spl0_26 ),
inference(avatar_split_clause,[],[f18,f140,f136]) ).
thf(f145,definition,
( spl0_27
<=> ( ( cR @ cC @ cD )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_27])],[avatar_definition]) ).
thf(f147,plain,
( ( ( cR @ cC @ cD )
= $true )
| ~ spl0_27 ),
inference(avatar_component_clause,[],[f145]) ).
thf(f149,definition,
( spl0_28
<=> ( ( cG @ cC @ cD )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_28])],[avatar_definition]) ).
thf(f151,plain,
( ( ( cG @ cC @ cD )
= $true )
| ~ spl0_28 ),
inference(avatar_component_clause,[],[f149]) ).
thf(f152,plain,
( spl0_27
| spl0_28 ),
inference(avatar_split_clause,[],[f21,f149,f145]) ).
thf(f154,definition,
( spl0_29
<=> ( ( cR @ cA @ cC )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_29])],[avatar_definition]) ).
thf(f156,plain,
( ( ( cR @ cA @ cC )
= $true )
| ~ spl0_29 ),
inference(avatar_component_clause,[],[f154]) ).
thf(f158,definition,
( spl0_30
<=> ( ( cG @ cA @ cC )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_30])],[avatar_definition]) ).
thf(f160,plain,
( ( ( cG @ cA @ cC )
= $true )
| ~ spl0_30 ),
inference(avatar_component_clause,[],[f158]) ).
thf(f161,plain,
( spl0_29
| spl0_30 ),
inference(avatar_split_clause,[],[f20,f158,f154]) ).
thf(f162,plain,
( ! [X0: $i] :
( ( ( cR @ X0 @ cF )
!= $true )
| ( ( cR @ X0 @ cB )
!= $true )
| ( $true != $true ) )
| ~ spl0_13 ),
inference(constrained_superposition,[],[f17,f84]) ).
thf(f164,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ X0 @ cE ) )
| ( $true != $true )
| ( ( cR @ X0 @ cD )
!= $true ) )
| ~ spl0_7 ),
inference(constrained_superposition,[],[f17,f57]) ).
thf(f166,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cR @ X0 @ cD )
!= $true )
| ( $true
!= ( cR @ X0 @ cC ) ) )
| ~ spl0_27 ),
inference(constrained_superposition,[],[f17,f147]) ).
thf(f169,plain,
( ! [X0: $i] :
( ( ( cR @ X0 @ cB )
!= $true )
| ( ( cR @ X0 @ cF )
!= $true ) )
| ~ spl0_13 ),
inference(trivial_inequality_removal,[],[f162]) ).
thf(f170,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ X0 @ cC ) )
| ( ( cR @ X0 @ cD )
!= $true ) )
| ~ spl0_27 ),
inference(trivial_inequality_removal,[],[f166]) ).
thf(f171,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ X0 @ cE ) )
| ( ( cR @ X0 @ cD )
!= $true ) )
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f164]) ).
thf(f178,plain,
( ( ( cR @ cA @ cD )
!= $true )
| ( $true != $true )
| ~ spl0_27
| ~ spl0_29 ),
inference(constrained_superposition,[],[f170,f156]) ).
thf(f179,plain,
( ( ( cR @ cA @ cD )
!= $true )
| ~ spl0_27
| ~ spl0_29 ),
inference(trivial_inequality_removal,[],[f178]) ).
thf(f180,plain,
( ~ spl0_10
| ~ spl0_27
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f179,f154,f145,f68]) ).
thf(f181,plain,
( ( ( cR @ cA @ cD )
!= $true )
| ( $true != $true )
| ~ spl0_3
| ~ spl0_7 ),
inference(constrained_superposition,[],[f171,f39]) ).
thf(f183,plain,
( ( ( cR @ cA @ cD )
!= $true )
| ~ spl0_3
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f181]) ).
thf(f187,plain,
( ! [X0: $i] :
( ( ( cG @ X0 @ cF )
!= $true )
| ( $true != $true )
| ( ( cG @ X0 @ cE )
!= $true ) )
| ~ spl0_17 ),
inference(constrained_superposition,[],[f24,f102]) ).
thf(f188,plain,
( ! [X0: $i] :
( ( ( cG @ X0 @ cF )
!= $true )
| ( $true != $true )
| ( $true
!= ( cG @ X0 @ cD ) ) )
| ~ spl0_11 ),
inference(constrained_superposition,[],[f24,f75]) ).
thf(f189,plain,
( ! [X0: $i] :
( ( ( cG @ X0 @ cF )
!= $true )
| ( $true != $true )
| ( ( cG @ X0 @ cC )
!= $true ) )
| ~ spl0_5 ),
inference(constrained_superposition,[],[f24,f48]) ).
thf(f191,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cG @ X0 @ cE )
!= $true )
| ( ( cG @ X0 @ cC )
!= $true ) )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f24,f34]) ).
thf(f192,plain,
( ! [X0: $i] :
( ( ( cG @ X0 @ cB )
!= $true )
| ( ( cG @ X0 @ cE )
!= $true )
| ( $true != $true ) )
| ~ spl0_21 ),
inference(constrained_superposition,[],[f24,f120]) ).
thf(f194,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cG @ X0 @ cB )
!= $true )
| ( ( cG @ X0 @ cC )
!= $true ) )
| ~ spl0_15 ),
inference(constrained_superposition,[],[f24,f93]) ).
thf(f196,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cD ) )
| ( ( cG @ X0 @ cF )
!= $true ) )
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f188]) ).
thf(f199,plain,
( ! [X0: $i] :
( ( ( cG @ X0 @ cC )
!= $true )
| ( ( cG @ X0 @ cF )
!= $true ) )
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f189]) ).
thf(f200,plain,
( ! [X0: $i] :
( ( ( cG @ X0 @ cB )
!= $true )
| ( ( cG @ X0 @ cC )
!= $true ) )
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f194]) ).
thf(f201,plain,
( ! [X0: $i] :
( ( ( cG @ X0 @ cC )
!= $true )
| ( ( cG @ X0 @ cE )
!= $true ) )
| ~ spl0_2 ),
inference(trivial_inequality_removal,[],[f191]) ).
thf(f202,plain,
( ! [X0: $i] :
( ( ( cG @ X0 @ cB )
!= $true )
| ( ( cG @ X0 @ cE )
!= $true ) )
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f192]) ).
thf(f203,plain,
( ! [X0: $i] :
( ( ( cG @ X0 @ cE )
!= $true )
| ( ( cG @ X0 @ cF )
!= $true ) )
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f187]) ).
thf(f205,plain,
( ( $true != $true )
| ( ( cG @ cA @ cF )
!= $true )
| ~ spl0_9
| ~ spl0_11 ),
inference(constrained_superposition,[],[f196,f66]) ).
thf(f206,plain,
( ( ( cG @ cA @ cF )
!= $true )
| ~ spl0_9
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f205]) ).
thf(f209,plain,
( ! [X0: $i] :
( ( ( cR @ X0 @ cF )
!= $true )
| ( $true != $true )
| ( ( cR @ X0 @ cD )
!= $true ) )
| ~ spl0_12 ),
inference(constrained_superposition,[],[f17,f79]) ).
thf(f210,plain,
( ! [X0: $i] :
( ( ( cR @ X0 @ cD )
!= $true )
| ( ( cR @ X0 @ cF )
!= $true ) )
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f209]) ).
thf(f213,plain,
( ( $true != $true )
| ( ( cG @ cB @ cF )
!= $true )
| ~ spl0_5
| ~ spl0_15 ),
inference(constrained_superposition,[],[f199,f93]) ).
thf(f214,plain,
( ( ( cG @ cB @ cF )
!= $true )
| ~ spl0_5
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f213]) ).
thf(f215,plain,
( ~ spl0_14
| ~ spl0_5
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f214,f91,f46,f86]) ).
thf(f216,plain,
( ( ( cG @ cA @ cC )
!= $true )
| ( $true != $true )
| ~ spl0_15
| ~ spl0_25 ),
inference(constrained_superposition,[],[f200,f138]) ).
thf(f217,plain,
( ( ( cG @ cA @ cC )
!= $true )
| ~ spl0_15
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f216]) ).
thf(f218,plain,
( ~ spl0_30
| ~ spl0_15
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f217,f136,f91,f158]) ).
thf(f219,plain,
( ( $true != $true )
| ( ( cG @ cB @ cE )
!= $true )
| ~ spl0_2
| ~ spl0_15 ),
inference(constrained_superposition,[],[f201,f93]) ).
thf(f220,plain,
( ( ( cG @ cB @ cE )
!= $true )
| ~ spl0_2
| ~ spl0_15 ),
inference(trivial_inequality_removal,[],[f219]) ).
thf(f223,plain,
( ! [X0: $i] :
( ( ( cR @ X0 @ cB )
!= $true )
| ( $true != $true )
| ( $true
!= ( cR @ X0 @ cC ) ) )
| ~ spl0_16 ),
inference(constrained_superposition,[],[f17,f97]) ).
thf(f225,plain,
( ( ( cR @ cB @ cD )
!= $true )
| ( $true != $true )
| ~ spl0_16
| ~ spl0_27 ),
inference(constrained_superposition,[],[f170,f97]) ).
thf(f226,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ X0 @ cC ) )
| ( ( cR @ X0 @ cB )
!= $true ) )
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f223]) ).
thf(f227,plain,
( ( ( cR @ cB @ cD )
!= $true )
| ~ spl0_16
| ~ spl0_27 ),
inference(trivial_inequality_removal,[],[f225]) ).
thf(f229,plain,
( $false
| ~ spl0_16
| ~ spl0_19
| ~ spl0_27 ),
inference(forward_subsumption_resolution,[],[f227,f111]) ).
thf(f230,plain,
( ~ spl0_16
| ~ spl0_19
| ~ spl0_27 ),
inference(avatar_contradiction_clause,[],[f229]) ).
thf(f231,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cD ) )
| ( ( cG @ X0 @ cB )
!= $true )
| ( $true != $true ) )
| ~ spl0_20 ),
inference(constrained_superposition,[],[f24,f115]) ).
thf(f234,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cD ) )
| ( ( cG @ X0 @ cB )
!= $true ) )
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f231]) ).
thf(f235,plain,
( ( $true != $true )
| ( ( cG @ cA @ cE )
!= $true )
| ~ spl0_21
| ~ spl0_25 ),
inference(constrained_superposition,[],[f202,f138]) ).
thf(f236,plain,
( ( ( cG @ cA @ cE )
!= $true )
| ~ spl0_21
| ~ spl0_25 ),
inference(trivial_inequality_removal,[],[f235]) ).
thf(f237,plain,
( ~ spl0_4
| ~ spl0_21
| ~ spl0_25 ),
inference(avatar_split_clause,[],[f236,f136,f118,f41]) ).
thf(f238,plain,
( ( ( cG @ cC @ cF )
!= $true )
| ( $true != $true )
| ~ spl0_2
| ~ spl0_17 ),
inference(constrained_superposition,[],[f203,f34]) ).
thf(f239,plain,
( ( ( cG @ cB @ cF )
!= $true )
| ( $true != $true )
| ~ spl0_17
| ~ spl0_21 ),
inference(constrained_superposition,[],[f203,f120]) ).
thf(f240,plain,
( ( ( cG @ cC @ cF )
!= $true )
| ~ spl0_2
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f238]) ).
thf(f241,plain,
( ( ( cG @ cB @ cF )
!= $true )
| ~ spl0_17
| ~ spl0_21 ),
inference(trivial_inequality_removal,[],[f239]) ).
thf(f242,plain,
( $false
| ~ spl0_2
| ~ spl0_5
| ~ spl0_17 ),
inference(forward_subsumption_resolution,[],[f240,f48]) ).
thf(f243,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_17 ),
inference(avatar_contradiction_clause,[],[f242]) ).
thf(f244,plain,
( ! [X0: $i] :
( ( ( cR @ X0 @ cF )
!= $true )
| ( $true != $true )
| ( $true
!= ( cR @ X0 @ cE ) ) )
| ~ spl0_18 ),
inference(constrained_superposition,[],[f17,f106]) ).
thf(f245,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ X0 @ cE ) )
| ( ( cR @ X0 @ cF )
!= $true ) )
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f244]) ).
thf(f246,plain,
( ( $true != $true )
| ( ( cR @ cC @ cF )
!= $true )
| ~ spl0_12
| ~ spl0_27 ),
inference(constrained_superposition,[],[f210,f147]) ).
thf(f247,plain,
( ( ( cR @ cC @ cF )
!= $true )
| ~ spl0_12
| ~ spl0_27 ),
inference(trivial_inequality_removal,[],[f246]) ).
thf(f248,plain,
( ~ spl0_6
| ~ spl0_12
| ~ spl0_27 ),
inference(avatar_split_clause,[],[f247,f145,f77,f50]) ).
thf(f249,plain,
( ( $true != $true )
| ( ( cR @ cA @ cB )
!= $true )
| ~ spl0_16
| ~ spl0_29 ),
inference(constrained_superposition,[],[f226,f156]) ).
thf(f251,plain,
( ( ( cR @ cA @ cB )
!= $true )
| ~ spl0_16
| ~ spl0_29 ),
inference(trivial_inequality_removal,[],[f249]) ).
thf(f253,plain,
( ~ spl0_26
| ~ spl0_16
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f251,f154,f95,f140]) ).
thf(f254,plain,
( ( $true != $true )
| ( ( cG @ cA @ cB )
!= $true )
| ~ spl0_9
| ~ spl0_20 ),
inference(constrained_superposition,[],[f234,f66]) ).
thf(f256,plain,
( ( ( cG @ cA @ cB )
!= $true )
| ~ spl0_9
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f254]) ).
thf(f262,plain,
( ~ spl0_25
| ~ spl0_9
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f256,f113,f64,f136]) ).
thf(f263,plain,
( ~ spl0_10
| ~ spl0_3
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f183,f55,f37,f68]) ).
thf(f269,plain,
( ( $true != $true )
| ( ( cR @ cA @ cF )
!= $true )
| ~ spl0_13
| ~ spl0_26 ),
inference(constrained_superposition,[],[f169,f142]) ).
thf(f271,plain,
( ( ( cR @ cA @ cF )
!= $true )
| ~ spl0_13
| ~ spl0_26 ),
inference(trivial_inequality_removal,[],[f269]) ).
thf(f272,plain,
( ~ spl0_24
| ~ spl0_13
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f271,f140,f82,f131]) ).
thf(f273,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cG @ X0 @ cD ) )
| ( ( cG @ X0 @ cC )
!= $true ) )
| ~ spl0_28 ),
inference(constrained_superposition,[],[f24,f151]) ).
thf(f276,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cD ) )
| ( ( cG @ X0 @ cC )
!= $true ) )
| ~ spl0_28 ),
inference(trivial_inequality_removal,[],[f273]) ).
thf(f278,plain,
( ( ( cG @ cA @ cE )
!= $true )
| ( $true != $true )
| ~ spl0_2
| ~ spl0_30 ),
inference(constrained_superposition,[],[f201,f160]) ).
thf(f279,plain,
( ( ( cG @ cA @ cF )
!= $true )
| ( $true != $true )
| ~ spl0_5
| ~ spl0_30 ),
inference(constrained_superposition,[],[f199,f160]) ).
thf(f281,plain,
( ( ( cG @ cA @ cF )
!= $true )
| ~ spl0_5
| ~ spl0_30 ),
inference(trivial_inequality_removal,[],[f279]) ).
thf(f282,plain,
( ( ( cG @ cA @ cE )
!= $true )
| ~ spl0_2
| ~ spl0_30 ),
inference(trivial_inequality_removal,[],[f278]) ).
thf(f283,plain,
( $false
| ~ spl0_5
| ~ spl0_23
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f281,f129]) ).
thf(f284,plain,
( ~ spl0_5
| ~ spl0_23
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[],[f283]) ).
thf(f287,plain,
( ( ( cR @ cA @ cF )
!= $true )
| ( $true != $true )
| ~ spl0_3
| ~ spl0_18 ),
inference(constrained_superposition,[],[f245,f39]) ).
thf(f288,plain,
( ( ( cR @ cD @ cF )
!= $true )
| ( $true != $true )
| ~ spl0_7
| ~ spl0_18 ),
inference(constrained_superposition,[],[f245,f57]) ).
thf(f289,plain,
( ( ( cR @ cA @ cF )
!= $true )
| ~ spl0_3
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f287]) ).
thf(f290,plain,
( ( ( cR @ cD @ cF )
!= $true )
| ~ spl0_7
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f288]) ).
thf(f291,plain,
( $false
| ~ spl0_7
| ~ spl0_12
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f290,f79]) ).
thf(f292,plain,
( ~ spl0_7
| ~ spl0_12
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f291]) ).
thf(f301,plain,
( ( $true != $true )
| ( ( cG @ cB @ cC )
!= $true )
| ~ spl0_20
| ~ spl0_28 ),
inference(constrained_superposition,[],[f276,f115]) ).
thf(f302,plain,
( ( $true != $true )
| ( ( cG @ cA @ cC )
!= $true )
| ~ spl0_9
| ~ spl0_28 ),
inference(constrained_superposition,[],[f276,f66]) ).
thf(f304,plain,
( ( ( cG @ cB @ cC )
!= $true )
| ~ spl0_20
| ~ spl0_28 ),
inference(trivial_inequality_removal,[],[f301]) ).
thf(f305,plain,
( ( ( cG @ cA @ cC )
!= $true )
| ~ spl0_9
| ~ spl0_28 ),
inference(trivial_inequality_removal,[],[f302]) ).
thf(f307,plain,
( $false
| ~ spl0_9
| ~ spl0_28
| ~ spl0_30 ),
inference(forward_subsumption_resolution,[],[f305,f160]) ).
thf(f308,plain,
( ~ spl0_9
| ~ spl0_28
| ~ spl0_30 ),
inference(avatar_contradiction_clause,[],[f307]) ).
thf(f309,plain,
( ~ spl0_23
| ~ spl0_9
| ~ spl0_11 ),
inference(avatar_split_clause,[],[f206,f73,f64,f127]) ).
thf(f310,plain,
( ~ spl0_14
| ~ spl0_17
| ~ spl0_21 ),
inference(avatar_split_clause,[],[f241,f118,f100,f86]) ).
thf(f311,plain,
( $false
| ~ spl0_3
| ~ spl0_18
| ~ spl0_24 ),
inference(forward_subsumption_resolution,[],[f289,f133]) ).
thf(f312,plain,
( ~ spl0_3
| ~ spl0_18
| ~ spl0_24 ),
inference(avatar_contradiction_clause,[],[f311]) ).
thf(f313,plain,
( ~ spl0_15
| ~ spl0_20
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f304,f149,f113,f91]) ).
thf(f314,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ X0 @ cC ) )
| ( $true != $true )
| ( $true
!= ( cR @ X0 @ cE ) ) )
| ~ spl0_1 ),
inference(constrained_superposition,[],[f17,f30]) ).
thf(f315,plain,
( ( $true != $true )
| ( ( cR @ cC @ cD )
!= $true )
| ~ spl0_1
| ~ spl0_7 ),
inference(constrained_superposition,[],[f171,f30]) ).
thf(f318,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ X0 @ cC ) )
| ( $true
!= ( cR @ X0 @ cE ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f314]) ).
thf(f319,plain,
( ( ( cR @ cC @ cD )
!= $true )
| ~ spl0_1
| ~ spl0_7 ),
inference(trivial_inequality_removal,[],[f315]) ).
thf(f322,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cR @ X0 @ cC ) )
| ( ( cR @ X0 @ cF )
!= $true ) )
| ~ spl0_6 ),
inference(constrained_superposition,[],[f17,f52]) ).
thf(f323,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ X0 @ cC ) )
| ( ( cR @ X0 @ cF )
!= $true ) )
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f322]) ).
thf(f324,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cR @ X0 @ cF )
!= $true )
| ( ( cR @ X0 @ cD )
!= $true ) )
| ~ spl0_12 ),
inference(constrained_superposition,[],[f17,f79]) ).
thf(f325,plain,
( ! [X0: $i] :
( ( ( cR @ X0 @ cD )
!= $true )
| ( ( cR @ X0 @ cF )
!= $true ) )
| ~ spl0_12 ),
inference(trivial_inequality_removal,[],[f324]) ).
thf(f330,plain,
( ! [X0: $i] :
( ( ( cG @ X0 @ cE )
!= $true )
| ( $true != $true )
| ( ( cG @ X0 @ cF )
!= $true ) )
| ~ spl0_17 ),
inference(constrained_superposition,[],[f24,f102]) ).
thf(f331,plain,
( ! [X0: $i] :
( ( ( cG @ X0 @ cE )
!= $true )
| ( ( cG @ X0 @ cF )
!= $true ) )
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f330]) ).
thf(f332,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cR @ X0 @ cB )
!= $true )
| ( ( cR @ X0 @ cD )
!= $true ) )
| ~ spl0_19 ),
inference(constrained_superposition,[],[f17,f111]) ).
thf(f333,plain,
( ! [X0: $i] :
( ( ( cR @ X0 @ cB )
!= $true )
| ( ( cR @ X0 @ cD )
!= $true ) )
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f332]) ).
thf(f342,plain,
( ( ( cR @ cA @ cE )
!= $true )
| ( $true != $true )
| ~ spl0_1
| ~ spl0_29 ),
inference(constrained_superposition,[],[f318,f156]) ).
thf(f343,plain,
( ( ( cR @ cA @ cE )
!= $true )
| ~ spl0_1
| ~ spl0_29 ),
inference(trivial_inequality_removal,[],[f342]) ).
thf(f349,plain,
( ( $true != $true )
| ( ( cR @ cB @ cD )
!= $true )
| ~ spl0_7
| ~ spl0_22 ),
inference(constrained_superposition,[],[f171,f124]) ).
thf(f351,plain,
( ( ( cR @ cB @ cD )
!= $true )
| ~ spl0_7
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f349]) ).
thf(f354,plain,
( $false
| ~ spl0_7
| ~ spl0_19
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f351,f111]) ).
thf(f355,plain,
( ~ spl0_7
| ~ spl0_19
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f354]) ).
thf(f364,plain,
( ( $true != $true )
| ( ( cR @ cA @ cF )
!= $true )
| ~ spl0_6
| ~ spl0_29 ),
inference(constrained_superposition,[],[f323,f156]) ).
thf(f365,plain,
( ( ( cR @ cA @ cF )
!= $true )
| ~ spl0_6
| ~ spl0_29 ),
inference(trivial_inequality_removal,[],[f364]) ).
thf(f366,plain,
( ( $true != $true )
| ( ( cR @ cB @ cF )
!= $true )
| ~ spl0_12
| ~ spl0_19 ),
inference(constrained_superposition,[],[f325,f111]) ).
thf(f367,plain,
( ( ( cR @ cB @ cF )
!= $true )
| ~ spl0_12
| ~ spl0_19 ),
inference(trivial_inequality_removal,[],[f366]) ).
thf(f368,plain,
( $false
| ~ spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(forward_subsumption_resolution,[],[f367,f84]) ).
thf(f369,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(avatar_contradiction_clause,[],[f368]) ).
thf(f372,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cD ) )
| ( $true != $true )
| ( ( cG @ X0 @ cF )
!= $true ) )
| ~ spl0_11 ),
inference(constrained_superposition,[],[f24,f75]) ).
thf(f373,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cD ) )
| ( ( cG @ X0 @ cF )
!= $true ) )
| ~ spl0_11 ),
inference(trivial_inequality_removal,[],[f372]) ).
thf(f376,plain,
( ( ( cG @ cA @ cF )
!= $true )
| ( $true != $true )
| ~ spl0_4
| ~ spl0_17 ),
inference(constrained_superposition,[],[f331,f43]) ).
thf(f378,plain,
( ( ( cG @ cA @ cF )
!= $true )
| ~ spl0_4
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f376]) ).
thf(f380,plain,
( $false
| ~ spl0_4
| ~ spl0_17
| ~ spl0_23 ),
inference(forward_subsumption_resolution,[],[f378,f129]) ).
thf(f381,plain,
( ~ spl0_4
| ~ spl0_17
| ~ spl0_23 ),
inference(avatar_contradiction_clause,[],[f380]) ).
thf(f389,plain,
( ( ( cG @ cD @ cF )
!= $true )
| ( $true != $true )
| ~ spl0_8
| ~ spl0_17 ),
inference(constrained_superposition,[],[f331,f61]) ).
thf(f390,plain,
( ( ( cG @ cD @ cF )
!= $true )
| ~ spl0_8
| ~ spl0_17 ),
inference(trivial_inequality_removal,[],[f389]) ).
thf(f404,plain,
( ( ( cR @ cA @ cD )
!= $true )
| ( $true != $true )
| ~ spl0_19
| ~ spl0_26 ),
inference(constrained_superposition,[],[f333,f142]) ).
thf(f405,plain,
( ( ( cR @ cA @ cD )
!= $true )
| ~ spl0_19
| ~ spl0_26 ),
inference(trivial_inequality_removal,[],[f404]) ).
thf(f408,plain,
( ~ spl0_21
| ~ spl0_2
| ~ spl0_15 ),
inference(avatar_split_clause,[],[f220,f91,f32,f118]) ).
thf(f411,plain,
( $false
| ~ spl0_6
| ~ spl0_24
| ~ spl0_29 ),
inference(forward_subsumption_resolution,[],[f365,f133]) ).
thf(f412,plain,
( ~ spl0_6
| ~ spl0_24
| ~ spl0_29 ),
inference(avatar_contradiction_clause,[],[f411]) ).
thf(f413,plain,
( ~ spl0_4
| ~ spl0_2
| ~ spl0_30 ),
inference(avatar_split_clause,[],[f282,f158,f32,f41]) ).
thf(f435,plain,
( ( $true != $true )
| ( ( cG @ cB @ cF )
!= $true )
| ~ spl0_11
| ~ spl0_20 ),
inference(constrained_superposition,[],[f373,f115]) ).
thf(f436,plain,
( ( ( cG @ cB @ cF )
!= $true )
| ~ spl0_11
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f435]) ).
thf(f440,plain,
( ~ spl0_27
| ~ spl0_1
| ~ spl0_7 ),
inference(avatar_split_clause,[],[f319,f55,f28,f145]) ).
thf(f441,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cR @ X0 @ cC ) )
| ( $true
!= ( cR @ X0 @ cE ) ) )
| ~ spl0_1 ),
inference(constrained_superposition,[],[f17,f30]) ).
thf(f442,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ X0 @ cC ) )
| ( $true
!= ( cR @ X0 @ cE ) ) )
| ~ spl0_1 ),
inference(trivial_inequality_removal,[],[f441]) ).
thf(f450,plain,
( ( $true != $true )
| ( ( cR @ cB @ cF )
!= $true )
| ~ spl0_6
| ~ spl0_16 ),
inference(constrained_superposition,[],[f323,f97]) ).
thf(f452,plain,
( ( ( cR @ cB @ cF )
!= $true )
| ~ spl0_6
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f450]) ).
thf(f473,plain,
( ( ( cR @ cB @ cE )
!= $true )
| ( $true != $true )
| ~ spl0_1
| ~ spl0_16 ),
inference(constrained_superposition,[],[f442,f97]) ).
thf(f474,plain,
( ( ( cR @ cB @ cE )
!= $true )
| ~ spl0_1
| ~ spl0_16 ),
inference(trivial_inequality_removal,[],[f473]) ).
thf(f477,plain,
( ~ spl0_14
| ~ spl0_11
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f436,f113,f73,f86]) ).
thf(f478,plain,
( $false
| ~ spl0_6
| ~ spl0_13
| ~ spl0_16 ),
inference(forward_subsumption_resolution,[],[f452,f84]) ).
thf(f479,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_16 ),
inference(avatar_contradiction_clause,[],[f478]) ).
thf(f480,plain,
( ~ spl0_11
| ~ spl0_8
| ~ spl0_17 ),
inference(avatar_split_clause,[],[f390,f100,f59,f73]) ).
thf(f481,plain,
( ~ spl0_10
| ~ spl0_19
| ~ spl0_26 ),
inference(avatar_split_clause,[],[f405,f140,f109,f68]) ).
thf(f486,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( cG @ X0 @ cE )
!= $true )
| ( $true
!= ( cG @ X0 @ cD ) ) )
| ~ spl0_8 ),
inference(constrained_superposition,[],[f24,f61]) ).
thf(f487,plain,
( ! [X0: $i] :
( ( $true
!= ( cG @ X0 @ cD ) )
| ( ( cG @ X0 @ cE )
!= $true ) )
| ~ spl0_8 ),
inference(trivial_inequality_removal,[],[f486]) ).
thf(f500,plain,
( ! [X0: $i] :
( ( ( cR @ X0 @ cB )
!= $true )
| ( $true != $true )
| ( $true
!= ( cR @ X0 @ cE ) ) )
| ~ spl0_22 ),
inference(constrained_superposition,[],[f17,f124]) ).
thf(f501,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ X0 @ cE ) )
| ( ( cR @ X0 @ cB )
!= $true ) )
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f500]) ).
thf(f518,plain,
( ( $true != $true )
| ( ( cG @ cC @ cE )
!= $true )
| ~ spl0_8
| ~ spl0_28 ),
inference(constrained_superposition,[],[f487,f151]) ).
thf(f519,plain,
( ( ( cG @ cA @ cE )
!= $true )
| ( $true != $true )
| ~ spl0_8
| ~ spl0_9 ),
inference(constrained_superposition,[],[f487,f66]) ).
thf(f520,plain,
( ( ( cG @ cC @ cE )
!= $true )
| ~ spl0_8
| ~ spl0_28 ),
inference(trivial_inequality_removal,[],[f518]) ).
thf(f521,plain,
( ( ( cG @ cA @ cE )
!= $true )
| ~ spl0_8
| ~ spl0_9 ),
inference(trivial_inequality_removal,[],[f519]) ).
thf(f524,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_9 ),
inference(avatar_split_clause,[],[f521,f64,f59,f41]) ).
thf(f525,plain,
( ~ spl0_3
| ~ spl0_1
| ~ spl0_29 ),
inference(avatar_split_clause,[],[f343,f154,f28,f37]) ).
thf(f526,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_28 ),
inference(avatar_split_clause,[],[f520,f149,f59,f32]) ).
thf(f535,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( cR @ X0 @ cE ) )
| ( ( cR @ X0 @ cF )
!= $true ) )
| ~ spl0_18 ),
inference(constrained_superposition,[],[f17,f106]) ).
thf(f536,plain,
( ! [X0: $i] :
( ( $true
!= ( cR @ X0 @ cE ) )
| ( ( cR @ X0 @ cF )
!= $true ) )
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f535]) ).
thf(f538,plain,
( ( $true != $true )
| ( ( cG @ cB @ cE )
!= $true )
| ~ spl0_8
| ~ spl0_20 ),
inference(constrained_superposition,[],[f487,f115]) ).
thf(f539,plain,
( ( ( cG @ cB @ cE )
!= $true )
| ~ spl0_8
| ~ spl0_20 ),
inference(trivial_inequality_removal,[],[f538]) ).
thf(f550,plain,
( ( ( cR @ cA @ cB )
!= $true )
| ( $true != $true )
| ~ spl0_3
| ~ spl0_22 ),
inference(constrained_superposition,[],[f501,f39]) ).
thf(f551,plain,
( ( ( cR @ cA @ cB )
!= $true )
| ~ spl0_3
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f550]) ).
thf(f553,plain,
( $false
| ~ spl0_3
| ~ spl0_22
| ~ spl0_26 ),
inference(forward_subsumption_resolution,[],[f551,f142]) ).
thf(f554,plain,
( ~ spl0_3
| ~ spl0_22
| ~ spl0_26 ),
inference(avatar_contradiction_clause,[],[f553]) ).
thf(f555,plain,
( ~ spl0_21
| ~ spl0_8
| ~ spl0_20 ),
inference(avatar_split_clause,[],[f539,f113,f59,f118]) ).
thf(f556,plain,
( ~ spl0_22
| ~ spl0_1
| ~ spl0_16 ),
inference(avatar_split_clause,[],[f474,f95,f28,f122]) ).
thf(f577,plain,
( ( $true != $true )
| ( ( cR @ cC @ cF )
!= $true )
| ~ spl0_1
| ~ spl0_18 ),
inference(constrained_superposition,[],[f536,f30]) ).
thf(f578,plain,
( ( $true != $true )
| ( ( cR @ cB @ cF )
!= $true )
| ~ spl0_18
| ~ spl0_22 ),
inference(constrained_superposition,[],[f536,f124]) ).
thf(f579,plain,
( ( ( cR @ cC @ cF )
!= $true )
| ~ spl0_1
| ~ spl0_18 ),
inference(trivial_inequality_removal,[],[f577]) ).
thf(f580,plain,
( ( ( cR @ cB @ cF )
!= $true )
| ~ spl0_18
| ~ spl0_22 ),
inference(trivial_inequality_removal,[],[f578]) ).
thf(f581,plain,
( $false
| ~ spl0_1
| ~ spl0_6
| ~ spl0_18 ),
inference(forward_subsumption_resolution,[],[f579,f52]) ).
thf(f582,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_18 ),
inference(avatar_contradiction_clause,[],[f581]) ).
thf(f583,plain,
( $false
| ~ spl0_13
| ~ spl0_18
| ~ spl0_22 ),
inference(forward_subsumption_resolution,[],[f580,f84]) ).
thf(f584,plain,
( ~ spl0_13
| ~ spl0_18
| ~ spl0_22 ),
inference(avatar_contradiction_clause,[],[f583]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f35]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f44]) ).
cnf(s3,plain,
( spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f53]) ).
cnf(s4,plain,
( spl0_7
| spl0_8 ),
inference(sat_conversion,[],[f62]) ).
cnf(s5,plain,
( spl0_9
| spl0_10 ),
inference(sat_conversion,[],[f71]) ).
cnf(s6,plain,
( spl0_11
| spl0_12 ),
inference(sat_conversion,[],[f80]) ).
cnf(s7,plain,
( spl0_13
| spl0_14 ),
inference(sat_conversion,[],[f89]) ).
cnf(s8,plain,
( spl0_15
| spl0_16 ),
inference(sat_conversion,[],[f98]) ).
cnf(s9,plain,
( spl0_17
| spl0_18 ),
inference(sat_conversion,[],[f107]) ).
cnf(s10,plain,
( spl0_19
| spl0_20 ),
inference(sat_conversion,[],[f116]) ).
cnf(s11,plain,
( spl0_21
| spl0_22 ),
inference(sat_conversion,[],[f125]) ).
cnf(s12,plain,
( spl0_23
| spl0_24 ),
inference(sat_conversion,[],[f134]) ).
cnf(s13,plain,
( spl0_25
| spl0_26 ),
inference(sat_conversion,[],[f143]) ).
cnf(s14,plain,
( spl0_27
| spl0_28 ),
inference(sat_conversion,[],[f152]) ).
cnf(s15,plain,
( spl0_29
| spl0_30 ),
inference(sat_conversion,[],[f161]) ).
cnf(s16,plain,
( ~ spl0_10
| ~ spl0_27
| ~ spl0_29 ),
inference(sat_conversion,[],[f180]) ).
cnf(s18,plain,
( ~ spl0_5
| ~ spl0_14
| ~ spl0_15 ),
inference(sat_conversion,[],[f215]) ).
cnf(s19,plain,
( ~ spl0_15
| ~ spl0_25
| ~ spl0_30 ),
inference(sat_conversion,[],[f218]) ).
cnf(s21,plain,
( ~ spl0_16
| ~ spl0_19
| ~ spl0_27 ),
inference(sat_conversion,[],[f230]) ).
cnf(s22,plain,
( ~ spl0_4
| ~ spl0_21
| ~ spl0_25 ),
inference(sat_conversion,[],[f237]) ).
cnf(s23,plain,
( ~ spl0_2
| ~ spl0_5
| ~ spl0_17 ),
inference(sat_conversion,[],[f243]) ).
cnf(s24,plain,
( ~ spl0_6
| ~ spl0_12
| ~ spl0_27 ),
inference(sat_conversion,[],[f248]) ).
cnf(s25,plain,
( ~ spl0_16
| ~ spl0_26
| ~ spl0_29 ),
inference(sat_conversion,[],[f253]) ).
cnf(s28,plain,
( ~ spl0_9
| ~ spl0_20
| ~ spl0_25 ),
inference(sat_conversion,[],[f262]) ).
cnf(s29,plain,
( ~ spl0_3
| ~ spl0_7
| ~ spl0_10 ),
inference(sat_conversion,[],[f263]) ).
cnf(s30,plain,
( ~ spl0_13
| ~ spl0_24
| ~ spl0_26 ),
inference(sat_conversion,[],[f272]) ).
cnf(s31,plain,
( ~ spl0_5
| ~ spl0_23
| ~ spl0_30 ),
inference(sat_conversion,[],[f284]) ).
cnf(s32,plain,
( ~ spl0_7
| ~ spl0_12
| ~ spl0_18 ),
inference(sat_conversion,[],[f292]) ).
cnf(s33,plain,
( ~ spl0_9
| ~ spl0_28
| ~ spl0_30 ),
inference(sat_conversion,[],[f308]) ).
cnf(s34,plain,
( ~ spl0_9
| ~ spl0_11
| ~ spl0_23 ),
inference(sat_conversion,[],[f309]) ).
cnf(s35,plain,
( ~ spl0_14
| ~ spl0_17
| ~ spl0_21 ),
inference(sat_conversion,[],[f310]) ).
cnf(s36,plain,
( ~ spl0_3
| ~ spl0_18
| ~ spl0_24 ),
inference(sat_conversion,[],[f312]) ).
cnf(s37,plain,
( ~ spl0_15
| ~ spl0_20
| ~ spl0_28 ),
inference(sat_conversion,[],[f313]) ).
cnf(s42,plain,
( ~ spl0_7
| ~ spl0_19
| ~ spl0_22 ),
inference(sat_conversion,[],[f355]) ).
cnf(s43,plain,
( ~ spl0_12
| ~ spl0_13
| ~ spl0_19 ),
inference(sat_conversion,[],[f369]) ).
cnf(s44,plain,
( ~ spl0_4
| ~ spl0_17
| ~ spl0_23 ),
inference(sat_conversion,[],[f381]) ).
cnf(s47,plain,
( ~ spl0_2
| ~ spl0_15
| ~ spl0_21 ),
inference(sat_conversion,[],[f408]) ).
cnf(s51,plain,
( ~ spl0_6
| ~ spl0_24
| ~ spl0_29 ),
inference(sat_conversion,[],[f412]) ).
cnf(s52,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_30 ),
inference(sat_conversion,[],[f413]) ).
cnf(s54,plain,
( ~ spl0_1
| ~ spl0_7
| ~ spl0_27 ),
inference(sat_conversion,[],[f440]) ).
cnf(s58,plain,
( ~ spl0_11
| ~ spl0_14
| ~ spl0_20 ),
inference(sat_conversion,[],[f477]) ).
cnf(s59,plain,
( ~ spl0_6
| ~ spl0_13
| ~ spl0_16 ),
inference(sat_conversion,[],[f479]) ).
cnf(s60,plain,
( ~ spl0_8
| ~ spl0_11
| ~ spl0_17 ),
inference(sat_conversion,[],[f480]) ).
cnf(s61,plain,
( ~ spl0_10
| ~ spl0_19
| ~ spl0_26 ),
inference(sat_conversion,[],[f481]) ).
cnf(s64,plain,
( ~ spl0_4
| ~ spl0_8
| ~ spl0_9 ),
inference(sat_conversion,[],[f524]) ).
cnf(s65,plain,
( ~ spl0_1
| ~ spl0_3
| ~ spl0_29 ),
inference(sat_conversion,[],[f525]) ).
cnf(s66,plain,
( ~ spl0_2
| ~ spl0_8
| ~ spl0_28 ),
inference(sat_conversion,[],[f526]) ).
cnf(s69,plain,
( ~ spl0_3
| ~ spl0_22
| ~ spl0_26 ),
inference(sat_conversion,[],[f554]) ).
cnf(s70,plain,
( ~ spl0_8
| ~ spl0_20
| ~ spl0_21 ),
inference(sat_conversion,[],[f555]) ).
cnf(s71,plain,
( ~ spl0_1
| ~ spl0_16
| ~ spl0_22 ),
inference(sat_conversion,[],[f556]) ).
cnf(s73,plain,
( ~ spl0_1
| ~ spl0_6
| ~ spl0_18 ),
inference(sat_conversion,[],[f582]) ).
cnf(s74,plain,
( ~ spl0_13
| ~ spl0_18
| ~ spl0_22 ),
inference(sat_conversion,[],[f584]) ).
cnf(s75,plain,
( ~ spl0_8
| ~ spl0_4
| ~ spl0_2 ),
inference(rat,[],[s16,s5,s14,s64,s66,s15,s52]) ).
cnf(s76,plain,
( ~ spl0_19
| ~ spl0_10
| ~ spl0_7
| ~ spl0_4 ),
inference(rat,[],[s22,s13,s11,s61,s42]) ).
cnf(s77,plain,
( ~ spl0_6
| ~ spl0_7
| ~ spl0_29
| ~ spl0_4 ),
inference(rat,[],[s59,s7,s8,s58,s37,s10,s76,s14,s16,s5,s34,s6,s32,s9,s44,s12,s51]) ).
cnf(s78,plain,
( ~ spl0_10
| ~ spl0_18
| ~ spl0_7
| ~ spl0_29
| ~ spl0_4 ),
inference(rat,[],[s22,s11,s13,s74,s25,s7,s8,s58,s37,s10,s14,s76,s16,s6,s32]) ).
cnf(s79,plain,
( ~ spl0_14
| ~ spl0_11
| ~ spl0_7
| ~ spl0_29
| ~ spl0_4 ),
inference(rat,[],[s22,s13,s11,s25,s42,s8,s10,s18,s58,s3,s77]) ).
cnf(s80,plain,
( ~ spl0_4
| ~ spl0_2 ),
inference(rat,[],[s22,s13,s11,s30,s74,s7,s79,s12,s34,s5,s78,s6,s32,s9,s23,s3,s77,s4,s75,s15,s52]) ).
cnf(s81,plain,
( ~ spl0_14
| ~ spl0_17
| ~ spl0_11
| ~ spl0_7 ),
inference(rat,[],[s42,s11,s10,s35,s58]) ).
cnf(s82,plain,
( ~ spl0_11
| ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s19,s13,s8,s30,s59,s7,s81,s15,s51,s3,s23,s9,s36,s12,s34,s5,s29,s2,s80]) ).
cnf(s83,plain,
( ~ spl0_22
| ~ spl0_7
| ~ spl0_3 ),
inference(rat,[],[s28,s10,s13,s42,s69,s5,s29]) ).
cnf(s84,plain,
( ~ spl0_7
| ~ spl0_2 ),
inference(rat,[],[s59,s7,s8,s35,s47,s11,s83,s3,s23,s9,s32,s6,s82,s2,s80]) ).
cnf(s85,plain,
( ~ spl0_11
| ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s19,s13,s15,s61,s16,s5,s34,s8,s12,s21,s36,s10,s9,s58,s60,s2,s80,s14,s66,s4,s84]) ).
cnf(s86,plain,
( ~ spl0_14
| ~ spl0_2 ),
inference(rat,[],[s28,s13,s5,s25,s16,s15,s31,s10,s12,s21,s36,s8,s9,s18,s23,s3,s24,s6,s85,s2,s80,s14,s66,s4,s84]) ).
cnf(s87,plain,
( ~ spl0_21
| ~ spl0_2 ),
inference(rat,[],[s21,s10,s8,s70,s47,s14,s66,s4,s84]) ).
cnf(s88,plain,
( ~ spl0_8
| ~ spl0_2 ),
inference(rat,[],[s24,s6,s3,s60,s23,s9,s74,s11,s87,s7,s86,s14,s66]) ).
cnf(s89,plain,
~ spl0_2,
inference(rat,[],[s88,s4,s84]) ).
cnf(s90,plain,
spl0_1,
inference(rat,[],[s1,s89]) ).
cnf(s91,plain,
( ~ spl0_26
| ~ spl0_19
| ~ spl0_16 ),
inference(rat,[],[s33,s5,s15,s61,s25,s14,s21]) ).
cnf(s92,plain,
( ~ spl0_3
| ~ spl0_18 ),
inference(rat,[],[s31,s12,s15,s36,s65,s3,s73,s90]) ).
cnf(s93,plain,
( ~ spl0_18
| ~ spl0_14 ),
inference(rat,[],[s32,s6,s4,s58,s70,s10,s91,s13,s22,s2,s92,s11,s71,s8,s18,s3,s73,s90]) ).
cnf(s94,plain,
( ~ spl0_11
| ~ spl0_14 ),
inference(rat,[],[s4,s81,s60,s9,s93]) ).
cnf(s95,plain,
( ~ spl0_4
| ~ spl0_14 ),
inference(rat,[],[s19,s13,s15,s61,s51,s5,s12,s64,s44,s4,s42,s10,s37,s14,s24,s6,s94,s3,s18,s8,s71,s11,s35,s9,s93,s90]) ).
cnf(s96,plain,
( ~ spl0_17
| ~ spl0_14 ),
inference(rat,[],[s19,s13,s15,s69,s65,s2,s95,s8,s71,s11,s35,s90]) ).
cnf(s97,plain,
~ spl0_14,
inference(rat,[],[s96,s9,s93]) ).
cnf(s98,plain,
spl0_13,
inference(rat,[],[s7,s97]) ).
cnf(s99,plain,
( ~ spl0_7
| ~ spl0_22 ),
inference(rat,[],[s37,s10,s14,s42,s54,s8,s71,s90]) ).
cnf(s100,plain,
( ~ spl0_25
| ~ spl0_4 ),
inference(rat,[],[s37,s14,s10,s16,s43,s5,s6,s64,s60,s4,s99,s15,s19,s9,s8,s74,s71,s11,s22,s90,s98]) ).
cnf(s101,plain,
( ~ spl0_10
| ~ spl0_4 ),
inference(rat,[],[s37,s10,s14,s61,s16,s8,s25,s15,s31,s3,s73,s9,s44,s12,s30,s13,s100,s98,s90]) ).
cnf(s102,plain,
( ~ spl0_23
| ~ spl0_4 ),
inference(rat,[],[s32,s6,s4,s34,s64,s5,s101,s9,s44]) ).
cnf(s103,plain,
~ spl0_4,
inference(rat,[],[s102,s12,s30,s13,s100,s98]) ).
cnf(s104,plain,
spl0_3,
inference(rat,[],[s2,s103]) ).
cnf(s105,plain,
~ spl0_29,
inference(rat,[],[s65,s90,s104]) ).
cnf(s106,plain,
~ spl0_18,
inference(rat,[],[s92,s104]) ).
cnf(s107,plain,
spl0_30,
inference(rat,[],[s15,s105]) ).
cnf(s108,plain,
spl0_17,
inference(rat,[],[s9,s106]) ).
cnf(s109,plain,
~ spl0_7,
inference(rat,[],[s33,s5,s14,s29,s54,s107,s104,s90]) ).
cnf(s110,plain,
spl0_8,
inference(rat,[],[s4,s109]) ).
cnf(s111,plain,
~ spl0_11,
inference(rat,[],[s60,s108,s110]) ).
cnf(s112,plain,
spl0_12,
inference(rat,[],[s6,s111]) ).
cnf(s113,plain,
~ spl0_19,
inference(rat,[],[s43,s98,s112]) ).
cnf(s114,plain,
spl0_20,
inference(rat,[],[s10,s113]) ).
cnf(s115,plain,
~ spl0_21,
inference(rat,[],[s70,s110,s114]) ).
cnf(s116,plain,
spl0_22,
inference(rat,[],[s11,s115]) ).
cnf(s117,plain,
~ spl0_16,
inference(rat,[],[s71,s90,s116]) ).
cnf(s118,plain,
~ spl0_26,
inference(rat,[],[s69,s104,s116]) ).
cnf(s119,plain,
spl0_15,
inference(rat,[],[s8,s117]) ).
cnf(s120,plain,
spl0_25,
inference(rat,[],[s13,s118]) ).
cnf(s121,plain,
$false,
inference(rat,[],[s19,s107,s120,s119]) ).
thf(f585,plain,
$false,
inference(avatar_sat_refutation,[],[s121]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.02 % Problem : SYO179^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.17 % Computer : n026.cluster.edu
% 0.09/0.17 % Model : x86_64 x86_64
% 0.09/0.17 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.17 % Memory : 8046.5625MB
% 0.09/0.17 % OS : Linux 6.8.0-71-generic
% 0.09/0.17 % CPULimit : 300
% 0.09/0.17 % WCLimit : 300
% 0.09/0.17 % DateTime : Tue Sep 29 16:39:57 UTC 2026
% 0.09/0.18 % CPUTime :
% 0.09/0.18 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.21 Running higher-order theorem proving
% 0.09/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.20/0.30 % (838274)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.30 % (838292)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2358580767:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.30 % (838292)Instruction limit reached!
% 0.20/0.30 % (838292)------------------------------
% 0.20/0.30 % (838292)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (838292)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (838292)CaDiCaL version: 2.1.3
% 0.20/0.30 % (838292)Termination reason: Instruction limit
% 0.20/0.30 % (838292)Termination phase: Saturation
% 0.20/0.30 % (838292)Time elapsed: 0.002 s
% 0.20/0.30 % (838292)Peak memory usage: 12 MB
% 0.20/0.30 % (838292)Instructions burned: 5 (million)
% 0.20/0.30 % (838297)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.30 % (838297)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.30 % (838293)dis+1002_4:1_sfv=off:to=lpo:plsq=on:fde=none:e2e=on:si=on:spb=non_intro:acc=on:uwa=off:fd=preordered:foolp=on:s2agt=32:slsqc=1:slsq=on:random_seed=2810178732:hsq=on:hsqr=16,1:s2a=on:i=634:add=on:nm=16:nicw=on:rtra=on:gtg=position:ss=included:ixr=off:c=on:inj=on:ntd=on:rawr=on_2999 on theBenchmark for (2999ds/634Mi)
% 0.20/0.30 % (838290)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2224302723:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.30 % (838291)lrs+10_16_si=on:nwc=1.5:random_seed=1603211568:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.30 % (838294)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=1209187714:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.30 % (838295)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2782938807:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.30 % (838297)dis+1002_8_to=kbo:sil=128000:tgt=full:drc=off:si=on:sp=const_max:lma=off:spb=non_intro:cbe=off:uwa=interpreted_only:random_seed=1579177559:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.30 % (838307)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=3943131400:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.30 % (838307)Instruction limit reached!
% 0.20/0.30 % (838307)------------------------------
% 0.20/0.30 % (838307)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (838307)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (838307)CaDiCaL version: 2.1.3
% 0.20/0.30 % (838307)Termination reason: Instruction limit
% 0.20/0.30 % (838307)Termination phase: Saturation
% 0.20/0.30 % (838307)Time elapsed: 0.001 s
% 0.20/0.30 % (838307)Peak memory usage: 12 MB
% 0.20/0.30 % (838307)Instructions burned: 3 (million)
% 0.20/0.30 % (838291)Instruction limit reached!
% 0.20/0.30 % (838291)------------------------------
% 0.20/0.30 % (838291)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (838291)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (838291)CaDiCaL version: 2.1.3
% 0.20/0.30 % (838291)Termination reason: Instruction limit
% 0.20/0.30 % (838291)Termination phase: Saturation
% 0.20/0.30 % (838291)Time elapsed: 0.010 s
% 0.20/0.30 % (838291)Peak memory usage: 12 MB
% 0.20/0.30 % (838291)Instructions burned: 18 (million)
% 0.20/0.30 % (838294)Instruction limit reached!
% 0.20/0.30 % (838294)------------------------------
% 0.20/0.30 % (838294)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (838294)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (838294)CaDiCaL version: 2.1.3
% 0.20/0.30 % (838294)Termination reason: Instruction limit
% 0.20/0.30 % (838294)Termination phase: Saturation
% 0.20/0.30 % (838294)Time elapsed: 0.013 s
% 0.20/0.30 % (838294)Peak memory usage: 11 MB
% 0.20/0.30 % (838294)Instructions burned: 26 (million)
% 0.20/0.30 % (838323)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=262932823:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.30 % (838323)Instruction limit reached!
% 0.20/0.30 % (838323)------------------------------
% 0.20/0.30 % (838323)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (838323)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (838323)CaDiCaL version: 2.1.3
% 0.20/0.30 % (838323)Termination reason: Instruction limit
% 0.20/0.30 % (838323)Termination phase: Saturation
% 0.20/0.30 % (838323)Time elapsed: 0.002 s
% 0.20/0.30 % (838323)Peak memory usage: 11 MB
% 0.20/0.30 % (838323)Instructions burned: 6 (million)
% 0.20/0.30 % (838327)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.30 % (838290) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-838274-838290"...
% 0.20/0.30 % (838334)WARNING Broken Constraint: if sine_to_age_tolerance(5) has been set then sine_to_age(off) is equal to on or sine_to_pred_levels(off) is not equal to off or sine_level_split_queue(off) is equal to on
% 0.20/0.30 % (838334)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.30 % (838327)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1129853554:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.30 % (838334)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=3398451939:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.30 % (838329)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=296762198:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.30 % (838290)...printing done.
% 0.20/0.30 % (838290)Refutation found. Thanks to Tanya!
% 0.20/0.30 % SZS status Theorem for theBenchmark
% 0.20/0.30 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.30 % (838290)------------------------------
% 0.20/0.30 % (838290)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.30 % (838290)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.30 % (838290)CaDiCaL version: 2.1.3
% 0.20/0.30 % (838290)Termination reason: Refutation
% 0.20/0.30 % (838290)Time elapsed: 0.032 s
% 0.20/0.30 % (838290)Peak memory usage: 13 MB
% 0.20/0.30 % (838290)Instructions burned: 57 (million)
% 0.20/0.30 % (838274)Success in time 0.07 s
% 0.20/0.30 % Vampire exiting
%------------------------------------------------------------------------------