%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SYO383^5 : 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 : n004.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 08:47:34 AM UTC 2026
% Result : Theorem 0.22s 0.26s
% Output : Refutation 0.22s
% Verified :
% SZS Type : Refutation
% Derivation depth : 20
% Number of leaves : 25
% Syntax : Number of formulae : 148 ( 47 unt; 0 typ; 24 def)
% Number of atoms : 825 ( 166 equ; 0 cnn)
% Maximal formula atoms : 23 ( 5 avg)
% Number of connectives : 816 ( 184 ~; 152 |; 42 &; 423 @)
% ( 15 <=>; 0 =>; 0 <=; 0 <~>)
% Maximal formula depth : 20 ( 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 : 37 ( 34 usr; 25 con; 0-3 aty)
% Number of variables : 159 ( 0 sgn 159 !; 0 ?; 159 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
cQ_2: $i > $i > $i > $o ).
thf(func_def_1,type,
f: $i > $i ).
thf(func_def_2,type,
cP_1: $i > $i > $o ).
thf(func_def_3,type,
cQ_1: $i > $i > $i > $o ).
thf(func_def_11,type,
sF0: $o ).
thf(func_def_12,type,
sF1: $i > $i > $i > $o ).
thf(func_def_13,type,
sF2: $i > $o ).
thf(func_def_14,type,
sF3: $i > $i > $o ).
thf(func_def_15,type,
sF4: $i > $i ).
thf(func_def_16,type,
sF5: $i > $i > $o ).
thf(func_def_17,type,
sF6: $o ).
thf(func_def_18,type,
sF7: $o ).
thf(func_def_19,type,
sF8: $o ).
thf(func_def_20,type,
sF9: $i > $i > $i > $o ).
thf(f1,conjecture,
~ ( ( cP_1 @ c @ c )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X0: $i,X2: $i,X1: $i] :
~ ( cQ_2 @ X0 @ X1 @ X2 )
& ! [X1: $i,X0: $i] :
( ~ ( cP_1 @ X0 @ X1 )
| ( cP_1 @ ( f @ X0 ) @ X1 ) )
& ( cP_1 @ b @ b )
& ! [X5: $i,X2: $i,X4: $i,X0: $i,X1: $i,X3: $i] :
( ~ ( cQ_1 @ X0 @ X1 @ X2 )
| ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ( cQ_2 @ X3 @ X4 @ X5 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 ) )
& ( cP_1 @ a @ a )
& ( cQ_1 @ a @ b @ c ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM409_1) ).
thf(f2,negated_conjecture,
~ ~ ( ( cP_1 @ c @ c )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X0: $i,X2: $i,X1: $i] :
~ ( cQ_2 @ X0 @ X1 @ X2 )
& ! [X1: $i,X0: $i] :
( ~ ( cP_1 @ X0 @ X1 )
| ( cP_1 @ ( f @ X0 ) @ X1 ) )
& ( cP_1 @ b @ b )
& ! [X5: $i,X2: $i,X4: $i,X0: $i,X1: $i,X3: $i] :
( ~ ( cQ_1 @ X0 @ X1 @ X2 )
| ~ ( cP_1 @ ( f @ X0 ) @ X3 )
| ~ ( cP_1 @ ( f @ X1 ) @ X4 )
| ( cQ_2 @ X3 @ X4 @ X5 )
| ~ ( cP_1 @ ( f @ X2 ) @ X5 ) )
& ( cP_1 @ a @ a )
& ( cQ_1 @ a @ b @ c ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ~ ( ( cP_1 @ c @ c )
& ! [X0: $i] : ( cP_1 @ d @ X0 )
& ! [X1: $i,X2: $i,X3: $i] :
~ ( cQ_2 @ X1 @ X3 @ X2 )
& ! [X4: $i,X5: $i] :
( ~ ( cP_1 @ X5 @ X4 )
| ( cP_1 @ ( f @ X5 ) @ X4 ) )
& ( cP_1 @ b @ b )
& ! [X6: $i,X7: $i,X8: $i,X9: $i,X10: $i,X11: $i] :
( ~ ( cQ_1 @ X9 @ X10 @ X7 )
| ~ ( cP_1 @ ( f @ X9 ) @ X11 )
| ~ ( cP_1 @ ( f @ X10 ) @ X8 )
| ( cQ_2 @ X11 @ X8 @ X6 )
| ~ ( cP_1 @ ( f @ X7 ) @ X6 ) )
& ( cP_1 @ a @ a )
& ( cQ_1 @ a @ b @ c ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ~ ( ( ( cP_1 @ c @ c )
= $true )
& ! [X0: $i] :
( ( cP_1 @ d @ X0 )
= $true )
& ! [X1: $i,X2: $i,X3: $i] :
( $true
!= ( cQ_2 @ X1 @ X3 @ X2 ) )
& ! [X4: $i,X5: $i] :
( ( ( cP_1 @ X5 @ X4 )
!= $true )
| ( $true
= ( cP_1 @ ( f @ X5 ) @ X4 ) ) )
& ( ( cP_1 @ b @ b )
= $true )
& ! [X6: $i,X7: $i,X8: $i,X9: $i,X10: $i,X11: $i] :
( ( $true
!= ( cQ_1 @ X9 @ X10 @ X7 ) )
| ( $true
!= ( cP_1 @ ( f @ X9 ) @ X11 ) )
| ( ( cP_1 @ ( f @ X10 ) @ X8 )
!= $true )
| ( $true
= ( cQ_2 @ X11 @ X8 @ X6 ) )
| ( ( cP_1 @ ( f @ X7 ) @ X6 )
!= $true ) )
& ( ( cP_1 @ a @ a )
= $true )
& ( ( cQ_1 @ a @ b @ c )
= $true ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( cQ_1 @ a @ b @ c )
= $true )
& ! [X1: $i,X3: $i,X2: $i] :
( $true
!= ( cQ_2 @ X1 @ X3 @ X2 ) )
& ! [X0: $i] :
( ( cP_1 @ d @ X0 )
= $true )
& ! [X5: $i,X4: $i] :
( ( ( cP_1 @ X5 @ X4 )
!= $true )
| ( $true
= ( cP_1 @ ( f @ X5 ) @ X4 ) ) )
& ( ( cP_1 @ a @ a )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ( ( cP_1 @ b @ b )
= $true )
& ! [X7: $i,X10: $i,X9: $i,X8: $i,X11: $i,X6: $i] :
( ( $true
!= ( cP_1 @ ( f @ X9 ) @ X11 ) )
| ( ( cP_1 @ ( f @ X10 ) @ X8 )
!= $true )
| ( $true
= ( cQ_2 @ X11 @ X8 @ X6 ) )
| ( $true
!= ( cQ_1 @ X9 @ X10 @ X7 ) )
| ( ( cP_1 @ ( f @ X7 ) @ X6 )
!= $true ) ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
( ( ( cQ_1 @ a @ b @ c )
= $true )
& ! [X0: $i,X1: $i,X2: $i] :
( ( cQ_2 @ X0 @ X1 @ X2 )
!= $true )
& ! [X3: $i] :
( $true
= ( cP_1 @ d @ X3 ) )
& ! [X4: $i,X5: $i] :
( ( ( cP_1 @ X4 @ X5 )
!= $true )
| ( ( cP_1 @ ( f @ X4 ) @ X5 )
= $true ) )
& ( ( cP_1 @ a @ a )
= $true )
& ( ( cP_1 @ c @ c )
= $true )
& ( ( cP_1 @ b @ b )
= $true )
& ! [X6: $i,X7: $i,X8: $i,X9: $i,X10: $i,X11: $i] :
( ( ( cP_1 @ ( f @ X8 ) @ X10 )
!= $true )
| ( ( cP_1 @ ( f @ X7 ) @ X9 )
!= $true )
| ( $true
= ( cQ_2 @ X10 @ X9 @ X11 ) )
| ( $true
!= ( cQ_1 @ X8 @ X7 @ X6 ) )
| ( ( cP_1 @ ( f @ X6 ) @ X11 )
!= $true ) ) ),
inference(rectify,[],[f5]) ).
thf(f7,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( ( cP_1 @ ( f @ X8 ) @ X10 )
!= $true )
| ( ( cP_1 @ ( f @ X7 ) @ X9 )
!= $true )
| ( $true
= ( cQ_2 @ X10 @ X9 @ X11 ) )
| ( $true
!= ( cQ_1 @ X8 @ X7 @ X6 ) )
| ( ( cP_1 @ ( f @ X6 ) @ X11 )
!= $true ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f8,plain,
( ( cP_1 @ b @ b )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f9,plain,
( ( cP_1 @ c @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f10,plain,
( ( cP_1 @ a @ a )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f11,plain,
! [X4: $i,X5: $i] :
( ( ( cP_1 @ X4 @ X5 )
!= $true )
| ( ( cP_1 @ ( f @ X4 ) @ X5 )
= $true ) ),
inference(cnf_transformation,[],[f6]) ).
thf(f13,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( cQ_2 @ X0 @ X1 @ X2 )
!= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f14,plain,
( ( cQ_1 @ a @ b @ c )
= $true ),
inference(cnf_transformation,[],[f6]) ).
thf(f17,definition,
( sF0
= ( cQ_1 @ a @ b @ c ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f18,plain,
( ( cQ_1 @ a @ b @ c )
= sF0 ),
inference(reorient_equations,[],[f17]) ).
thf(f19,plain,
$true = sF0,
inference(definition_folding,[],[f14,f18]) ).
thf(f20,definition,
! [X2: $i,X0: $i,X1: $i] :
( ( sF1 @ X2 @ X1 @ X0 )
= ( cQ_2 @ X0 @ X1 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f21,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( cQ_2 @ X0 @ X1 @ X2 )
= ( sF1 @ X2 @ X1 @ X0 ) ),
inference(reorient_equations,[],[f20]) ).
thf(f22,plain,
! [X2: $i,X0: $i,X1: $i] :
( ( sF1 @ X2 @ X1 @ X0 )
!= $true ),
inference(definition_folding,[],[f13,f21]) ).
thf(f25,definition,
! [X4: $i,X5: $i] :
( ( sF3 @ X5 @ X4 )
= ( cP_1 @ X4 @ X5 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f26,plain,
! [X4: $i,X5: $i] :
( ( cP_1 @ X4 @ X5 )
= ( sF3 @ X5 @ X4 ) ),
inference(reorient_equations,[],[f25]) ).
thf(f27,definition,
! [X4: $i] :
( ( sF4 @ X4 )
= ( f @ X4 ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f28,definition,
! [X4: $i,X5: $i] :
( ( sF5 @ X5 @ X4 )
= ( cP_1 @ ( sF4 @ X4 ) @ X5 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f29,plain,
! [X4: $i,X5: $i] :
( ( cP_1 @ ( sF4 @ X4 ) @ X5 )
= ( sF5 @ X5 @ X4 ) ),
inference(reorient_equations,[],[f28]) ).
thf(f30,plain,
! [X4: $i,X5: $i] :
( ( $true
= ( sF5 @ X5 @ X4 ) )
| ( ( sF3 @ X5 @ X4 )
!= $true ) ),
inference(definition_folding,[],[f11,f29,f27,f26]) ).
thf(f31,definition,
( sF6
= ( cP_1 @ a @ a ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f32,plain,
( ( cP_1 @ a @ a )
= sF6 ),
inference(reorient_equations,[],[f31]) ).
thf(f33,plain,
$true = sF6,
inference(definition_folding,[],[f10,f32]) ).
thf(f34,definition,
( sF7
= ( cP_1 @ c @ c ) ),
introduced(definition,[new_symbols(definition,[sF7])],[function_definition]) ).
thf(f35,plain,
( ( cP_1 @ c @ c )
= sF7 ),
inference(reorient_equations,[],[f34]) ).
thf(f36,plain,
$true = sF7,
inference(definition_folding,[],[f9,f35]) ).
thf(f37,definition,
( sF8
= ( cP_1 @ b @ b ) ),
introduced(definition,[new_symbols(definition,[sF8])],[function_definition]) ).
thf(f38,plain,
( ( cP_1 @ b @ b )
= sF8 ),
inference(reorient_equations,[],[f37]) ).
thf(f39,plain,
$true = sF8,
inference(definition_folding,[],[f8,f38]) ).
thf(f40,definition,
! [X8: $i,X6: $i,X7: $i] :
( ( sF9 @ X6 @ X7 @ X8 )
= ( cQ_1 @ X8 @ X7 @ X6 ) ),
introduced(definition,[new_symbols(definition,[sF9])],[function_definition]) ).
thf(f41,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( $true
!= ( sF5 @ X9 @ X7 ) )
| ( $true
= ( sF1 @ X11 @ X9 @ X10 ) )
| ( ( sF5 @ X11 @ X6 )
!= $true )
| ( ( sF5 @ X10 @ X8 )
!= $true )
| ( ( sF9 @ X6 @ X7 @ X8 )
!= $true ) ),
inference(definition_folding,[],[f7,f29,f27,f40,f21,f29,f27,f29,f27]) ).
thf(f44,plain,
( ( $false = sF6 )
| ( ( cP_1 @ a @ a )
= $true ) ),
inference(iff_proxy_clausification,[],[f32]) ).
thf(f46,plain,
( ( ( cQ_1 @ a @ b @ c )
= $true )
| ( $false = sF0 ) ),
inference(iff_proxy_clausification,[],[f18]) ).
thf(f50,plain,
( ( sF7 = $false )
| ( ( cP_1 @ c @ c )
= $true ) ),
inference(iff_proxy_clausification,[],[f35]) ).
thf(f54,plain,
( ( ( cP_1 @ b @ b )
= $true )
| ( $false = sF8 ) ),
inference(iff_proxy_clausification,[],[f38]) ).
thf(f57,plain,
! [X4: $i,X5: $i] :
( ( ( sF3 @ X5 @ X4 )
= $true )
| ( ( cP_1 @ X4 @ X5 )
= $false ) ),
inference(iff_proxy_clausification,[],[f26]) ).
thf(f58,plain,
! [X8: $i,X6: $i,X7: $i] :
( ( ( sF9 @ X6 @ X7 @ X8 )
= $true )
| ( ( cQ_1 @ X8 @ X7 @ X6 )
= $false ) ),
inference(iff_proxy_clausification,[],[f40]) ).
thf(f65,definition,
( spl10_2
<=> ( $true = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl10_2])],[avatar_definition]) ).
thf(f67,plain,
( ( $true = sF6 )
| ~ spl10_2 ),
inference(avatar_component_clause,[],[f65]) ).
thf(f70,definition,
( spl10_3
<=> ( ( cP_1 @ a @ a )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
thf(f72,plain,
( ( ( cP_1 @ a @ a )
= $true )
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f70]) ).
thf(f74,definition,
( spl10_4
<=> ( $false = sF6 ) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
thf(f76,plain,
( ( $false = sF6 )
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f74]) ).
thf(f77,plain,
( spl10_3
| spl10_4 ),
inference(avatar_split_clause,[],[f44,f74,f70]) ).
thf(f79,definition,
( spl10_5
<=> ( $true = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
thf(f81,plain,
( ( $true = sF0 )
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f79]) ).
thf(f88,definition,
( spl10_7
<=> ( $false = sF0 ) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
thf(f90,plain,
( ( $false = sF0 )
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f88]) ).
thf(f92,definition,
( spl10_8
<=> ( ( cQ_1 @ a @ b @ c )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
thf(f94,plain,
( ( ( cQ_1 @ a @ b @ c )
= $true )
| ~ spl10_8 ),
inference(avatar_component_clause,[],[f92]) ).
thf(f95,plain,
( spl10_7
| spl10_8 ),
inference(avatar_split_clause,[],[f46,f92,f88]) ).
thf(f101,definition,
( spl10_10
<=> ( $true = sF7 ) ),
introduced(definition,[new_symbols(definition,[spl10_10])],[avatar_definition]) ).
thf(f103,plain,
( ( $true = sF7 )
| ~ spl10_10 ),
inference(avatar_component_clause,[],[f101]) ).
thf(f106,definition,
( spl10_11
<=> ( ( cP_1 @ c @ c )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_11])],[avatar_definition]) ).
thf(f108,plain,
( ( ( cP_1 @ c @ c )
= $true )
| ~ spl10_11 ),
inference(avatar_component_clause,[],[f106]) ).
thf(f110,definition,
( spl10_12
<=> ( sF7 = $false ) ),
introduced(definition,[new_symbols(definition,[spl10_12])],[avatar_definition]) ).
thf(f112,plain,
( ( sF7 = $false )
| ~ spl10_12 ),
inference(avatar_component_clause,[],[f110]) ).
thf(f113,plain,
( spl10_11
| spl10_12 ),
inference(avatar_split_clause,[],[f50,f110,f106]) ).
thf(f114,plain,
spl10_2,
inference(avatar_split_clause,[],[f33,f65]) ).
thf(f115,plain,
spl10_5,
inference(avatar_split_clause,[],[f19,f79]) ).
thf(f121,definition,
( spl10_14
<=> ( $true = sF8 ) ),
introduced(definition,[new_symbols(definition,[spl10_14])],[avatar_definition]) ).
thf(f123,plain,
( ( $true = sF8 )
| ~ spl10_14 ),
inference(avatar_component_clause,[],[f121]) ).
thf(f126,definition,
( spl10_15
<=> ( $false = sF8 ) ),
introduced(definition,[new_symbols(definition,[spl10_15])],[avatar_definition]) ).
thf(f128,plain,
( ( $false = sF8 )
| ~ spl10_15 ),
inference(avatar_component_clause,[],[f126]) ).
thf(f130,definition,
( spl10_16
<=> ( ( cP_1 @ b @ b )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_16])],[avatar_definition]) ).
thf(f132,plain,
( ( ( cP_1 @ b @ b )
= $true )
| ~ spl10_16 ),
inference(avatar_component_clause,[],[f130]) ).
thf(f133,plain,
( spl10_15
| spl10_16 ),
inference(avatar_split_clause,[],[f54,f130,f126]) ).
thf(f134,plain,
spl10_14,
inference(avatar_split_clause,[],[f39,f121]) ).
thf(f135,plain,
spl10_10,
inference(avatar_split_clause,[],[f36,f101]) ).
thf(f136,plain,
( ( $true = $false )
| ~ spl10_5
| ~ spl10_7 ),
inference(forward_demodulation,[],[f90,f81]) ).
thf(f137,plain,
( $false
| ~ spl10_5
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f136]) ).
thf(f138,plain,
( ~ spl10_5
| ~ spl10_7 ),
inference(avatar_contradiction_clause,[],[f137]) ).
thf(f152,plain,
( ( $true = $false )
| ~ spl10_14
| ~ spl10_15 ),
inference(forward_demodulation,[],[f128,f123]) ).
thf(f153,plain,
( $false
| ~ spl10_14
| ~ spl10_15 ),
inference(trivial_inequality_removal,[],[f152]) ).
thf(f154,plain,
( ~ spl10_14
| ~ spl10_15 ),
inference(avatar_contradiction_clause,[],[f153]) ).
thf(f156,plain,
! [X10: $i,X11: $i,X8: $i,X6: $i,X9: $i,X7: $i] :
( ( ( sF9 @ X6 @ X7 @ X8 )
!= $true )
| ( ( sF5 @ X10 @ X8 )
!= $true )
| ( $true
!= ( sF5 @ X9 @ X7 ) )
| ( ( sF5 @ X11 @ X6 )
!= $true ) ),
inference(forward_subsumption_resolution,[],[f41,f22]) ).
thf(f188,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $true
!= ( sF5 @ X3 @ X2 ) )
| ( $true != $true )
| ( $true
!= ( sF5 @ X5 @ X0 ) )
| ( $false
= ( cQ_1 @ X2 @ X1 @ X0 ) )
| ( $true
!= ( sF5 @ X4 @ X1 ) ) ),
inference(constrained_superposition,[],[f156,f58]) ).
thf(f189,plain,
! [X2: $i,X3: $i,X0: $i,X1: $i,X4: $i,X5: $i] :
( ( $false
= ( cQ_1 @ X2 @ X1 @ X0 ) )
| ( $true
!= ( sF5 @ X3 @ X2 ) )
| ( $true
!= ( sF5 @ X4 @ X1 ) )
| ( $true
!= ( sF5 @ X5 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f188]) ).
thf(f194,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( sF5 @ X1 @ b ) )
| ( ( sF5 @ X0 @ a )
!= $true )
| ( $true
!= ( sF5 @ X2 @ c ) )
| ( $true = $false ) )
| ~ spl10_8 ),
inference(constrained_superposition,[],[f94,f189]) ).
thf(f196,plain,
( ! [X2: $i,X0: $i,X1: $i] :
( ( $true
!= ( sF5 @ X2 @ c ) )
| ( ( sF5 @ X0 @ a )
!= $true )
| ( $true
!= ( sF5 @ X1 @ b ) ) )
| ~ spl10_8 ),
inference(trivial_inequality_removal,[],[f194]) ).
thf(f199,definition,
( spl10_17
<=> ! [X1: $i] :
( $true
!= ( sF5 @ X1 @ b ) ) ),
introduced(definition,[new_symbols(definition,[spl10_17])],[avatar_definition]) ).
thf(f200,plain,
( ! [X1: $i] :
( $true
!= ( sF5 @ X1 @ b ) )
| ~ spl10_17 ),
inference(avatar_component_clause,[],[f199]) ).
thf(f202,definition,
( spl10_18
<=> ! [X2: $i] :
( $true
!= ( sF5 @ X2 @ c ) ) ),
introduced(definition,[new_symbols(definition,[spl10_18])],[avatar_definition]) ).
thf(f203,plain,
( ! [X2: $i] :
( $true
!= ( sF5 @ X2 @ c ) )
| ~ spl10_18 ),
inference(avatar_component_clause,[],[f202]) ).
thf(f205,definition,
( spl10_19
<=> ! [X0: $i] :
( ( sF5 @ X0 @ a )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl10_19])],[avatar_definition]) ).
thf(f206,plain,
( ! [X0: $i] :
( ( sF5 @ X0 @ a )
!= $true )
| ~ spl10_19 ),
inference(avatar_component_clause,[],[f205]) ).
thf(f208,plain,
( spl10_19
| spl10_17
| spl10_18
| ~ spl10_8 ),
inference(avatar_split_clause,[],[f196,f92,f202,f199,f205]) ).
thf(f209,plain,
( ! [X0: $i] :
( ( ( sF3 @ X0 @ b )
!= $true )
| ( $true != $true ) )
| ~ spl10_17 ),
inference(constrained_superposition,[],[f200,f30]) ).
thf(f211,plain,
( ! [X0: $i] :
( ( sF3 @ X0 @ b )
!= $true )
| ~ spl10_17 ),
inference(trivial_inequality_removal,[],[f209]) ).
thf(f217,plain,
( ! [X0: $i] :
( ( ( cP_1 @ b @ X0 )
= $false )
| ( $true != $true ) )
| ~ spl10_17 ),
inference(constrained_superposition,[],[f211,f57]) ).
thf(f221,plain,
( ! [X0: $i] :
( ( cP_1 @ b @ X0 )
= $false )
| ~ spl10_17 ),
inference(trivial_inequality_removal,[],[f217]) ).
thf(f236,plain,
( ( $true = $false )
| ~ spl10_16
| ~ spl10_17 ),
inference(constrained_superposition,[],[f221,f132]) ).
thf(f241,plain,
( $false
| ~ spl10_16
| ~ spl10_17 ),
inference(trivial_inequality_removal,[],[f236]) ).
thf(f242,plain,
( ~ spl10_16
| ~ spl10_17 ),
inference(avatar_contradiction_clause,[],[f241]) ).
thf(f244,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( $true
!= ( sF3 @ X0 @ c ) ) )
| ~ spl10_18 ),
inference(constrained_superposition,[],[f203,f30]) ).
thf(f247,plain,
( ! [X0: $i] :
( $true
!= ( sF3 @ X0 @ c ) )
| ~ spl10_18 ),
inference(trivial_inequality_removal,[],[f244]) ).
thf(f255,plain,
( ! [X0: $i] :
( ( ( cP_1 @ c @ X0 )
= $false )
| ( $true != $true ) )
| ~ spl10_18 ),
inference(constrained_superposition,[],[f247,f57]) ).
thf(f258,plain,
( ! [X0: $i] :
( ( cP_1 @ c @ X0 )
= $false )
| ~ spl10_18 ),
inference(trivial_inequality_removal,[],[f255]) ).
thf(f262,plain,
( ( $true = $false )
| ~ spl10_11
| ~ spl10_18 ),
inference(constrained_superposition,[],[f108,f258]) ).
thf(f268,plain,
( $false
| ~ spl10_11
| ~ spl10_18 ),
inference(trivial_inequality_removal,[],[f262]) ).
thf(f269,plain,
( ~ spl10_11
| ~ spl10_18 ),
inference(avatar_contradiction_clause,[],[f268]) ).
thf(f272,plain,
( ( $true = $false )
| ~ spl10_10
| ~ spl10_12 ),
inference(forward_demodulation,[],[f112,f103]) ).
thf(f273,plain,
( $false
| ~ spl10_10
| ~ spl10_12 ),
inference(trivial_inequality_removal,[],[f272]) ).
thf(f274,plain,
( ~ spl10_10
| ~ spl10_12 ),
inference(avatar_contradiction_clause,[],[f273]) ).
thf(f276,plain,
( ! [X0: $i] :
( ( $true != $true )
| ( ( sF3 @ X0 @ a )
!= $true ) )
| ~ spl10_19 ),
inference(constrained_superposition,[],[f206,f30]) ).
thf(f279,plain,
( ! [X0: $i] :
( ( sF3 @ X0 @ a )
!= $true )
| ~ spl10_19 ),
inference(trivial_inequality_removal,[],[f276]) ).
thf(f287,plain,
( ! [X0: $i] :
( ( $false
= ( cP_1 @ a @ X0 ) )
| ( $true != $true ) )
| ~ spl10_19 ),
inference(constrained_superposition,[],[f279,f57]) ).
thf(f291,plain,
( ! [X0: $i] :
( $false
= ( cP_1 @ a @ X0 ) )
| ~ spl10_19 ),
inference(trivial_inequality_removal,[],[f287]) ).
thf(f300,plain,
( ( $true = $false )
| ~ spl10_3
| ~ spl10_19 ),
inference(constrained_superposition,[],[f291,f72]) ).
thf(f306,plain,
( $false
| ~ spl10_3
| ~ spl10_19 ),
inference(trivial_inequality_removal,[],[f300]) ).
thf(f307,plain,
( ~ spl10_3
| ~ spl10_19 ),
inference(avatar_contradiction_clause,[],[f306]) ).
thf(f309,plain,
( ( $true = $false )
| ~ spl10_2
| ~ spl10_4 ),
inference(forward_demodulation,[],[f76,f67]) ).
thf(f310,plain,
( $false
| ~ spl10_2
| ~ spl10_4 ),
inference(trivial_inequality_removal,[],[f309]) ).
thf(f311,plain,
( ~ spl10_2
| ~ spl10_4 ),
inference(avatar_contradiction_clause,[],[f310]) ).
cnf(s2,plain,
( spl10_3
| spl10_4 ),
inference(sat_conversion,[],[f77]) ).
cnf(s4,plain,
( spl10_7
| spl10_8 ),
inference(sat_conversion,[],[f95]) ).
cnf(s6,plain,
( spl10_11
| spl10_12 ),
inference(sat_conversion,[],[f113]) ).
cnf(s7,plain,
spl10_2,
inference(sat_conversion,[],[f114]) ).
cnf(s8,plain,
spl10_5,
inference(sat_conversion,[],[f115]) ).
cnf(s10,plain,
( spl10_15
| spl10_16 ),
inference(sat_conversion,[],[f133]) ).
cnf(s11,plain,
spl10_14,
inference(sat_conversion,[],[f134]) ).
cnf(s12,plain,
spl10_10,
inference(sat_conversion,[],[f135]) ).
cnf(s13,plain,
( ~ spl10_5
| ~ spl10_7 ),
inference(sat_conversion,[],[f138]) ).
cnf(s14,plain,
( ~ spl10_14
| ~ spl10_15 ),
inference(sat_conversion,[],[f154]) ).
cnf(s17,plain,
( ~ spl10_8
| spl10_17
| spl10_18
| spl10_19 ),
inference(sat_conversion,[],[f208]) ).
cnf(s19,plain,
( ~ spl10_16
| ~ spl10_17 ),
inference(sat_conversion,[],[f242]) ).
cnf(s22,plain,
( ~ spl10_11
| ~ spl10_18 ),
inference(sat_conversion,[],[f269]) ).
cnf(s23,plain,
( ~ spl10_10
| ~ spl10_12 ),
inference(sat_conversion,[],[f274]) ).
cnf(s25,plain,
( ~ spl10_3
| ~ spl10_19 ),
inference(sat_conversion,[],[f307]) ).
cnf(s26,plain,
( ~ spl10_2
| ~ spl10_4 ),
inference(sat_conversion,[],[f311]) ).
cnf(s27,plain,
~ spl10_12,
inference(rat,[],[s23,s12]) ).
cnf(s28,plain,
~ spl10_15,
inference(rat,[],[s14,s11]) ).
cnf(s29,plain,
spl10_16,
inference(rat,[],[s10,s28]) ).
cnf(s30,plain,
~ spl10_17,
inference(rat,[],[s19,s29]) ).
cnf(s31,plain,
~ spl10_7,
inference(rat,[],[s13,s8]) ).
cnf(s32,plain,
~ spl10_4,
inference(rat,[],[s26,s7]) ).
cnf(s33,plain,
spl10_11,
inference(rat,[],[s6,s27]) ).
cnf(s34,plain,
~ spl10_18,
inference(rat,[],[s22,s33]) ).
cnf(s36,plain,
spl10_8,
inference(rat,[],[s4,s31]) ).
cnf(s37,plain,
spl10_19,
inference(rat,[],[s17,s34,s30,s36]) ).
cnf(s38,plain,
~ spl10_3,
inference(rat,[],[s25,s37]) ).
cnf(s39,plain,
$false,
inference(rat,[],[s2,s32,s38]) ).
thf(f312,plain,
$false,
inference(avatar_sat_refutation,[],[s39]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SYO383^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.20 % Computer : n004.cluster.edu
% 0.10/0.20 % Model : x86_64 x86_64
% 0.10/0.20 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.20 % Memory : 8046.5625MB
% 0.10/0.20 % OS : Linux 6.8.0-71-generic
% 0.10/0.20 % CPULimit : 300
% 0.10/0.20 % WCLimit : 300
% 0.10/0.20 % DateTime : Tue Sep 29 16:49:53 UTC 2026
% 0.10/0.20 % CPUTime :
% 0.10/0.20 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.10/0.23 Running higher-order theorem proving
% 0.10/0.24 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
% 0.22/0.26 % (1551426)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.22/0.26 % (1551437)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.22/0.26 % (1551437)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
% 0.22/0.26 % (1551437)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=1284412650:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_3000 on theBenchmark for (3000ds/157Mi)
% 0.22/0.26 % (1551437) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1551426-1551437"...
% 0.22/0.26 % (1551437)...printing done.
% 0.22/0.26 % (1551433)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2280537827:i=3:rtra=on:inj=on:ntd=on_3000 on theBenchmark for (3000ds/3Mi)
% 0.22/0.26 % (1551431)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1201043265:s2a=on:i=87:rtra=on:ntd=on_3000 on theBenchmark for (3000ds/87Mi)
% 0.22/0.26 % (1551432)lrs+10_16_si=on:nwc=1.5:random_seed=3542650646:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_3000 on theBenchmark for (3000ds/18Mi)
% 0.22/0.26 % (1551437)Refutation found. Thanks to Tanya!
% 0.22/0.26 % SZS status Theorem for theBenchmark
% 0.22/0.26 % SZS output start Proof for theBenchmark
% See solution above
% 0.22/0.27 % (1551437)------------------------------
% 0.22/0.27 % (1551437)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.22/0.27 % (1551437)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.22/0.27 % (1551437)CaDiCaL version: 2.1.3
% 0.22/0.27 % (1551437)Termination reason: Refutation
% 0.22/0.27 % (1551437)Time elapsed: 0.006 s
% 0.22/0.27 % (1551437)Peak memory usage: 13 MB
% 0.22/0.27 % (1551437)Instructions burned: 18 (million)
% 0.22/0.27 % (1551426)Success in time 0.021 s
% 0.22/0.27 % Vampire exiting
%------------------------------------------------------------------------------