%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : NUM808^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n006.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 08:19:34 AM UTC 2026
% Result : Theorem 0.93s 0.40s
% Output : Refutation 0.93s
% Verified :
% SZS Type : Refutation
% Derivation depth : 24
% Number of leaves : 13
% Syntax : Number of formulae : 106 ( 37 unt; 0 typ; 11 def)
% Number of atoms : 635 ( 176 equ; 0 cnn)
% Maximal formula atoms : 7 ( 5 avg)
% Number of connectives : 638 ( 56 ~; 102 |; 31 &; 384 @)
% ( 5 <=>; 33 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 29 ( 29 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 27 usr; 13 con; 0-4 aty)
% ( 27 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 136 ( 0 sgn 83 !; 7 ?; 136 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
cS: $i > $i ).
thf(func_def_2,type,
r: $i > $i > $o ).
thf(func_def_3,type,
cIND: $o ).
thf(func_def_5,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_6,type,
vIMP: $o > $o > $o ).
thf(func_def_7,type,
vAND: $o > $o > $o ).
thf(func_def_8,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_14,type,
sF1: $o ).
thf(func_def_15,type,
sF2: $i > $o ).
thf(func_def_16,type,
sF3: $i > $i ).
thf(func_def_17,type,
sF4: $i > $o ).
thf(func_def_18,type,
sF5: $i > $o ).
thf(func_def_19,type,
sF6: $o ).
thf(func_def_20,type,
vNOT: $o > $o ).
thf(func_def_21,type,
sK7: $i > $o ).
thf(func_def_23,type,
sK9: ( $i > $o ) > $i ).
thf(func_def_24,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
( cIND
= ( ! [X0: $i > $o] :
( ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( cS @ X1 ) ) )
& ( X0 @ c0 ) )
=> ! [X1: $i] : ( X0 @ X1 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cIND_def) ).
thf(f2,conjecture,
( ( ! [X0: $i] :
( ( r @ X0 @ X0 )
=> ( r @ ( cS @ X0 ) @ ( cS @ X0 ) ) )
& ( r @ c0 @ c0 )
& cIND )
=> ! [X0: $i] :
? [X1: $i] : ( r @ X0 @ X1 ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM130A) ).
thf(f3,negated_conjecture,
~ ( ( ! [X0: $i] :
( ( r @ X0 @ X0 )
=> ( r @ ( cS @ X0 ) @ ( cS @ X0 ) ) )
& ( r @ c0 @ c0 )
& cIND )
=> ! [X0: $i] :
? [X1: $i] : ( r @ X0 @ X1 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
( cIND
= ( ! [X0: $i > $o] :
( ( ! [X1: $i] :
( ( X0 @ X1 )
=> ( X0 @ ( cS @ X1 ) ) )
& ( X0 @ c0 ) )
=> ! [X2: $i] : ( X0 @ X2 ) ) ) ),
inference(rectify,[],[f1]) ).
thf(f5,plain,
( cIND
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
~ ( ( ! [X0: $i] :
( ( r @ X0 @ X0 )
=> ( r @ ( cS @ X0 ) @ ( cS @ X0 ) ) )
& ( r @ c0 @ c0 )
& cIND )
=> ! [X1: $i] :
? [X2: $i] : ( r @ X1 @ X2 ) ),
inference(rectify,[],[f3]) ).
thf(f7,plain,
~ ( ( ! [X0: $i] :
( ( ( r @ X0 @ X0 )
= $true )
=> ( ( r @ ( cS @ X0 ) @ ( cS @ X0 ) )
= $true ) )
& ( ( r @ c0 @ c0 )
= $true )
& ( cIND = $true ) )
=> ! [X1: $i] :
? [X2: $i] :
( ( r @ X1 @ X2 )
= $true ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( ? [X1: $i] :
! [X2: $i] :
( ( r @ X1 @ X2 )
!= $true )
& ! [X0: $i] :
( ( ( r @ ( cS @ X0 ) @ ( cS @ X0 ) )
= $true )
| ( ( r @ X0 @ X0 )
!= $true ) )
& ( ( r @ c0 @ c0 )
= $true )
& ( cIND = $true ) ),
inference(ennf_transformation,[],[f7]) ).
thf(f9,plain,
( ? [X1: $i] :
! [X2: $i] :
( ( r @ X1 @ X2 )
!= $true )
& ! [X0: $i] :
( ( ( r @ ( cS @ X0 ) @ ( cS @ X0 ) )
= $true )
| ( ( r @ X0 @ X0 )
!= $true ) )
& ( ( r @ c0 @ c0 )
= $true )
& ( cIND = $true ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
( ? [X0: $i] :
! [X1: $i] :
( ( r @ X0 @ X1 )
!= $true )
& ! [X2: $i] :
( ( $true
= ( r @ ( cS @ X2 ) @ ( cS @ X2 ) ) )
| ( $true
!= ( r @ X2 @ X2 ) ) )
& ( ( r @ c0 @ c0 )
= $true )
& ( cIND = $true ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ! [X1: $i] :
( $true
!= ( r @ sK0 @ X1 ) )
& ! [X2: $i] :
( ( $true
= ( r @ ( cS @ X2 ) @ ( cS @ X2 ) ) )
| ( $true
!= ( r @ X2 @ X2 ) ) )
& ( ( r @ c0 @ c0 )
= $true )
& ( cIND = $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0]),skolemize(X0,sK0)],[f10]) ).
thf(f12,plain,
( cIND
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f13,plain,
cIND = $true,
inference(cnf_transformation,[],[f11]) ).
thf(f14,plain,
( ( r @ c0 @ c0 )
= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
! [X2: $i] :
( ( $true
= ( r @ ( cS @ X2 ) @ ( cS @ X2 ) ) )
| ( $true
!= ( r @ X2 @ X2 ) ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f16,plain,
! [X1: $i] :
( $true
!= ( r @ sK0 @ X1 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f19,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
= $true ),
inference(definition_unfolding,[],[f12,f13]) ).
thf(f20,definition,
( sF1
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f21,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
= sF1 ),
inference(reorient_equations,[],[f20]) ).
thf(f22,plain,
$true = sF1,
inference(definition_folding,[],[f19,f21]) ).
thf(f23,definition,
! [X1: $i] :
( ( sF2 @ X1 )
= ( r @ sK0 @ X1 ) ),
introduced(definition,[new_symbols(definition,[sF2])],[function_definition]) ).
thf(f24,plain,
! [X1: $i] :
( ( r @ sK0 @ X1 )
= ( sF2 @ X1 ) ),
inference(reorient_equations,[],[f23]) ).
thf(f25,plain,
! [X1: $i] :
( $true
!= ( sF2 @ X1 ) ),
inference(definition_folding,[],[f16,f24]) ).
thf(f26,definition,
! [X2: $i] :
( ( sF3 @ X2 )
= ( cS @ X2 ) ),
introduced(definition,[new_symbols(definition,[sF3])],[function_definition]) ).
thf(f27,plain,
! [X2: $i] :
( ( cS @ X2 )
= ( sF3 @ X2 ) ),
inference(reorient_equations,[],[f26]) ).
thf(f28,definition,
! [X2: $i] :
( ( sF4 @ X2 )
= ( r @ ( sF3 @ X2 ) @ ( sF3 @ X2 ) ) ),
introduced(definition,[new_symbols(definition,[sF4])],[function_definition]) ).
thf(f29,plain,
! [X2: $i] :
( ( r @ ( sF3 @ X2 ) @ ( sF3 @ X2 ) )
= ( sF4 @ X2 ) ),
inference(reorient_equations,[],[f28]) ).
thf(f30,definition,
! [X2: $i] :
( ( sF5 @ X2 )
= ( r @ X2 @ X2 ) ),
introduced(definition,[new_symbols(definition,[sF5])],[function_definition]) ).
thf(f31,plain,
! [X2: $i] :
( ( r @ X2 @ X2 )
= ( sF5 @ X2 ) ),
inference(reorient_equations,[],[f30]) ).
thf(f32,plain,
! [X2: $i] :
( ( $true
!= ( sF5 @ X2 ) )
| ( $true
= ( sF4 @ X2 ) ) ),
inference(definition_folding,[],[f15,f31,f29,f27,f27]) ).
thf(f33,definition,
( sF6
= ( r @ c0 @ c0 ) ),
introduced(definition,[new_symbols(definition,[sF6])],[function_definition]) ).
thf(f34,plain,
( ( r @ c0 @ c0 )
= sF6 ),
inference(reorient_equations,[],[f33]) ).
thf(f35,plain,
$true = sF6,
inference(definition_folding,[],[f14,f34]) ).
thf(f36,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) ) )
= $true )
| ( $false = sF1 ) ),
inference(iff_proxy_clausification,[],[f21]) ).
thf(f48,plain,
! [X1: $i > $o] :
( ( $true
= ( ^ [Y0: $i > $o] :
( ( ( Y0 @ c0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( cS @ Y1 ) ) ) ) )
=> ( !! @ $i
@ ^ [Y1: $i] : ( Y0 @ Y1 ) ) )
@ X1 ) )
| ( $false = sF1 ) ),
inference(pi_proxy_clausification,[],[f36]) ).
thf(f49,plain,
! [X1: $i > $o] :
( ( $true
= ( ( ( X1 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) ) )
=> ( !! @ $i @ X1 ) ) )
| ( $false = sF1 ) ),
inference(beta-eta_normalization,[],[f48]) ).
thf(f50,plain,
! [X1: $i > $o] :
( ( $false
= ( ( X1 @ c0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) ) ) )
| ( $false = sF1 )
| ( $true
= ( !! @ $i @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f49]) ).
thf(f51,plain,
! [X1: $i > $o] :
( ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) ) ) )
| ( $false = sF1 )
| ( $true
= ( !! @ $i @ X1 ) )
| ( $false
= ( X1 @ c0 ) ) ),
inference(and_proxy_clausification,[],[f50]) ).
thf(f52,plain,
! [X1: $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) )
@ ( sK9 @ X1 ) ) )
| ( $false = sF1 )
| ( $true
= ( !! @ $i @ X1 ) )
| ( $false
= ( X1 @ c0 ) ) ),
inference(sigma_proxy_clausification,[],[f51]) ).
thf(f53,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( cS @ Y0 ) ) )
@ ( sK9 @ X1 ) ) )
| ( $false = sF1 )
| ( $true
= ( X1 @ X2 ) )
| ( $false
= ( X1 @ c0 ) ) ),
inference(pi_proxy_clausification,[],[f52]) ).
thf(f54,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( ( X1 @ ( sK9 @ X1 ) )
=> ( X1 @ ( cS @ ( sK9 @ X1 ) ) ) ) )
| ( $false = sF1 )
| ( $true
= ( X1 @ X2 ) )
| ( $false
= ( X1 @ c0 ) ) ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( X1 @ ( cS @ ( sK9 @ X1 ) ) ) )
| ( $false = sF1 )
| ( $true
= ( X1 @ X2 ) )
| ( $false
= ( X1 @ c0 ) ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f56,plain,
! [X2: $i,X1: $i > $o] :
( ( $true
= ( X1 @ ( sK9 @ X1 ) ) )
| ( $false = sF1 )
| ( $true
= ( X1 @ X2 ) )
| ( $false
= ( X1 @ c0 ) ) ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f58,plain,
! [X1: $i] :
( ( ( r @ sK0 @ X1 )
= $false )
| ( $true
= ( sF2 @ X1 ) ) ),
inference(iff_proxy_clausification,[],[f24]) ).
thf(f59,plain,
! [X2: $i] :
( ( $true
= ( r @ ( sF3 @ X2 ) @ ( sF3 @ X2 ) ) )
| ( $false
= ( sF4 @ X2 ) ) ),
inference(iff_proxy_clausification,[],[f29]) ).
thf(f61,plain,
! [X2: $i] :
( ( $true
= ( r @ X2 @ X2 ) )
| ( $false
= ( sF5 @ X2 ) ) ),
inference(iff_proxy_clausification,[],[f31]) ).
thf(f62,plain,
! [X2: $i] :
( ( ( r @ X2 @ X2 )
= $false )
| ( $true
= ( sF5 @ X2 ) ) ),
inference(iff_proxy_clausification,[],[f31]) ).
thf(f63,plain,
( ( ( r @ c0 @ c0 )
= $true )
| ( $false = sF6 ) ),
inference(iff_proxy_clausification,[],[f34]) ).
thf(f65,plain,
! [X2: $i,X1: $i > $o] :
( ( $true = $false )
| ( $true
= ( X1 @ ( sK9 @ X1 ) ) )
| ( $true
= ( X1 @ X2 ) )
| ( $false
= ( X1 @ c0 ) ) ),
inference(forward_demodulation,[],[f56,f22]) ).
thf(f66,plain,
! [X2: $i,X1: $i > $o] :
( ( $true
= ( X1 @ ( sK9 @ X1 ) ) )
| ( $true
= ( X1 @ X2 ) )
| ( $false
= ( X1 @ c0 ) ) ),
inference(trivial_inequality_removal,[],[f65]) ).
thf(f67,plain,
! [X2: $i,X1: $i > $o] :
( ( $true = $false )
| ( $false
= ( X1 @ ( cS @ ( sK9 @ X1 ) ) ) )
| ( $true
= ( X1 @ X2 ) )
| ( $false
= ( X1 @ c0 ) ) ),
inference(forward_demodulation,[],[f55,f22]) ).
thf(f68,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( X1 @ ( cS @ ( sK9 @ X1 ) ) ) )
| ( $true
= ( X1 @ X2 ) )
| ( $false
= ( X1 @ c0 ) ) ),
inference(trivial_inequality_removal,[],[f67]) ).
thf(f69,plain,
! [X1: $i] :
( ( r @ sK0 @ X1 )
= $false ),
inference(forward_subsumption_resolution,[],[f58,f25]) ).
thf(f70,plain,
( ( $true = $false )
| ( ( r @ c0 @ c0 )
= $true ) ),
inference(forward_demodulation,[],[f63,f35]) ).
thf(f71,plain,
( ( r @ c0 @ c0 )
= $true ),
inference(trivial_inequality_removal,[],[f70]) ).
thf(f72,plain,
! [X2: $i,X1: $i > $o] :
( ( $false
= ( X1 @ ( sF3 @ ( sK9 @ X1 ) ) ) )
| ( $true
= ( X1 @ X2 ) )
| ( $false
= ( X1 @ c0 ) ) ),
inference(forward_demodulation,[],[f68,f27]) ).
thf(f214,plain,
( ( $true = $false )
| ( $false
= ( sF5 @ sK0 ) ) ),
inference(constrained_superposition,[],[f69,f61]) ).
thf(f215,plain,
( $false
= ( sF5 @ sK0 ) ),
inference(trivial_inequality_removal,[],[f214]) ).
thf(f219,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( ^ [Y0: $i] :
( sF5
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ ( sK9
@ ^ [Y0: $i] :
( sF5
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( sF5
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ c0 ) )
| ( sK0 != X0 ) ),
inference(constrained_superposition,[],[f215,f66]) ).
thf(f233,plain,
! [X0: $i] :
( ( $true
= ( ^ [Y0: $i] :
( sF5
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ ( sK9
@ ^ [Y0: $i] :
( sF5
@ ( ^ [Y1: $i] : Y1
@ Y0 ) ) ) ) )
| ( $false
= ( ^ [Y0: $i] :
( sF5
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ c0 ) )
| ( sK0 != X0 ) ),
inference(trivial_inequality_removal,[],[f219]) ).
thf(f234,plain,
! [X0: $i] :
( ( $true
= ( sF5 @ ( sK9 @ sF5 ) ) )
| ( $false
= ( sF5 @ c0 ) )
| ( sK0 != X0 ) ),
inference(beta-eta_normalization,[],[f233]) ).
thf(f239,definition,
( spl10_3
<=> ! [X0: $i] : ( sK0 != X0 ) ),
introduced(definition,[new_symbols(definition,[spl10_3])],[avatar_definition]) ).
thf(f240,plain,
( ! [X0: $i] : ( sK0 != X0 )
| ~ spl10_3 ),
inference(avatar_component_clause,[],[f239]) ).
thf(f242,definition,
( spl10_4
<=> ( $false
= ( sF5 @ c0 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_4])],[avatar_definition]) ).
thf(f244,plain,
( ( $false
= ( sF5 @ c0 ) )
| ~ spl10_4 ),
inference(avatar_component_clause,[],[f242]) ).
thf(f246,definition,
( spl10_5
<=> ( $true
= ( sF5 @ ( sK9 @ sF5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl10_5])],[avatar_definition]) ).
thf(f248,plain,
( ( $true
= ( sF5 @ ( sK9 @ sF5 ) ) )
| ~ spl10_5 ),
inference(avatar_component_clause,[],[f246]) ).
thf(f250,plain,
( spl10_3
| spl10_4
| spl10_5 ),
inference(avatar_split_clause,[],[f234,f246,f242,f239]) ).
thf(f260,plain,
( ( $true = $false )
| ( $true
= ( sF5 @ c0 ) ) ),
inference(constrained_superposition,[],[f71,f62]) ).
thf(f264,plain,
( $true
= ( sF5 @ c0 ) ),
inference(trivial_inequality_removal,[],[f260]) ).
thf(f277,plain,
( $false
| ~ spl10_3 ),
inference(equality_resolution,[],[f240]) ).
thf(f278,plain,
~ spl10_3,
inference(avatar_contradiction_clause,[],[f277]) ).
thf(f280,plain,
! [X0: $i] :
( ( $true = $false )
| ( $true
= ( sF5 @ ( sF3 @ X0 ) ) )
| ( $false
= ( sF4 @ X0 ) ) ),
inference(constrained_superposition,[],[f62,f59]) ).
thf(f281,plain,
! [X0: $i] :
( ( $true
= ( sF5 @ ( sF3 @ X0 ) ) )
| ( $false
= ( sF4 @ X0 ) ) ),
inference(trivial_inequality_removal,[],[f280]) ).
thf(f321,plain,
( ( $true = $false )
| ~ spl10_4 ),
inference(constrained_superposition,[],[f244,f264]) ).
thf(f335,plain,
( $false
| ~ spl10_4 ),
inference(trivial_inequality_removal,[],[f321]) ).
thf(f336,plain,
~ spl10_4,
inference(avatar_contradiction_clause,[],[f335]) ).
thf(f574,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sF4 @ X0 ) )
| ( $true
= ( ^ [Y0: $i] :
( sF5
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( sF5
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ c0 ) )
| ( ( sK9 @ sF5 )
!= X0 ) ),
inference(constrained_superposition,[],[f281,f72]) ).
thf(f590,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( sF4 @ X0 ) )
| ( $true
= ( ^ [Y0: $i] :
( sF5
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ X1 ) )
| ( $false
= ( ^ [Y0: $i] :
( sF5
@ ( ^ [Y1: $i] : Y1
@ Y0 ) )
@ c0 ) )
| ( ( sK9 @ sF5 )
!= X0 ) ),
inference(trivial_inequality_removal,[],[f574]) ).
thf(f591,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( sF4 @ X0 ) )
| ( $true
= ( sF5 @ X1 ) )
| ( $false
= ( sF5 @ c0 ) )
| ( ( sK9 @ sF5 )
!= X0 ) ),
inference(beta-eta_normalization,[],[f590]) ).
thf(f594,plain,
! [X0: $i,X1: $i] :
( ( $true = $false )
| ( $false
= ( sF4 @ X0 ) )
| ( $true
= ( sF5 @ X1 ) )
| ( ( sK9 @ sF5 )
!= X0 ) ),
inference(forward_demodulation,[],[f591,f264]) ).
thf(f595,plain,
! [X0: $i,X1: $i] :
( ( $false
= ( sF4 @ X0 ) )
| ( $true
= ( sF5 @ X1 ) )
| ( ( sK9 @ sF5 )
!= X0 ) ),
inference(trivial_inequality_removal,[],[f594]) ).
thf(f597,definition,
( spl10_7
<=> ! [X0: $i] :
( ( $false
= ( sF4 @ X0 ) )
| ( ( sK9 @ sF5 )
!= X0 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_7])],[avatar_definition]) ).
thf(f598,plain,
( ! [X0: $i] :
( ( ( sK9 @ sF5 )
!= X0 )
| ( $false
= ( sF4 @ X0 ) ) )
| ~ spl10_7 ),
inference(avatar_component_clause,[],[f597]) ).
thf(f600,definition,
( spl10_8
<=> ! [X1: $i] :
( $true
= ( sF5 @ X1 ) ) ),
introduced(definition,[new_symbols(definition,[spl10_8])],[avatar_definition]) ).
thf(f601,plain,
( ! [X1: $i] :
( $true
= ( sF5 @ X1 ) )
| ~ spl10_8 ),
inference(avatar_component_clause,[],[f600]) ).
thf(f603,plain,
( spl10_8
| spl10_7 ),
inference(avatar_split_clause,[],[f595,f597,f600]) ).
thf(f607,plain,
( ( $true != $true )
| ( $true
= ( sF4 @ ( sK9 @ sF5 ) ) )
| ~ spl10_5 ),
inference(constrained_superposition,[],[f32,f248]) ).
thf(f611,plain,
( ( $true
= ( sF4 @ ( sK9 @ sF5 ) ) )
| ~ spl10_5 ),
inference(trivial_inequality_removal,[],[f607]) ).
thf(f673,plain,
( ( $false
= ( sF4 @ ( sK9 @ sF5 ) ) )
| ~ spl10_7 ),
inference(equality_resolution,[],[f598]) ).
thf(f680,plain,
( ( $true = $false )
| ~ spl10_5
| ~ spl10_7 ),
inference(constrained_superposition,[],[f673,f611]) ).
thf(f699,plain,
( $false
| ~ spl10_5
| ~ spl10_7 ),
inference(trivial_inequality_removal,[],[f680]) ).
thf(f700,plain,
( ~ spl10_5
| ~ spl10_7 ),
inference(avatar_contradiction_clause,[],[f699]) ).
thf(f738,plain,
( ( $true = $false )
| ~ spl10_8 ),
inference(constrained_superposition,[],[f601,f215]) ).
thf(f751,plain,
( $false
| ~ spl10_8 ),
inference(trivial_inequality_removal,[],[f738]) ).
thf(f752,plain,
~ spl10_8,
inference(avatar_contradiction_clause,[],[f751]) ).
cnf(s3,plain,
( spl10_3
| spl10_4
| spl10_5 ),
inference(sat_conversion,[],[f250]) ).
cnf(s4,plain,
~ spl10_3,
inference(sat_conversion,[],[f278]) ).
cnf(s6,plain,
~ spl10_4,
inference(sat_conversion,[],[f336]) ).
cnf(s10,plain,
( spl10_7
| spl10_8 ),
inference(sat_conversion,[],[f603]) ).
cnf(s13,plain,
( ~ spl10_5
| ~ spl10_7 ),
inference(sat_conversion,[],[f700]) ).
cnf(s19,plain,
~ spl10_8,
inference(sat_conversion,[],[f752]) ).
cnf(s20,plain,
spl10_7,
inference(rat,[],[s10,s19]) ).
cnf(s21,plain,
~ spl10_5,
inference(rat,[],[s13,s20]) ).
cnf(s23,plain,
$false,
inference(rat,[],[s3,s21,s6,s4]) ).
thf(f757,plain,
$false,
inference(avatar_sat_refutation,[],[s23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : NUM808^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.18 % Computer : n006.cluster.edu
% 0.10/0.18 % Model : x86_64 x86_64
% 0.10/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.10/0.18 % Memory : 8046.5625MB
% 0.10/0.18 % OS : Linux 6.8.0-71-generic
% 0.10/0.18 % CPULimit : 300
% 0.10/0.18 % WCLimit : 300
% 0.10/0.18 % DateTime : Tue Sep 29 13:00:54 UTC 2026
% 0.10/0.19 % CPUTime :
% 0.10/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.10/0.22 Running first-order model finding
% 0.10/0.22 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.93/0.40 % (674189)Will run a generic schedule for satisfiability detection.
% 0.93/0.40 % (674200)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=2081886622_2999 on theBenchmark for (2999ds/0Mi)
% 0.93/0.40 % Exception at run slice level
% 0.93/0.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.93/0.40 % (674201)% WARNING: option uhcvi not known.
% 0.93/0.40 % (674201)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=3700897018:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.93/0.40 % (674202)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=4055666445:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.93/0.40 % (674203)dis+10_1_sil=32000:sp=arity:random_seed=3193462948:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.93/0.40 % (674204)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=3454607491:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.93/0.40 % (674206)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=129489365:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.93/0.40 % (674201)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.93/0.40 % (674205)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=1894731980:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.93/0.40 % (674204)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.93/0.40 % (674201)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.93/0.40 % (674212)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=299188416:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.93/0.40 % Exception at run slice level
% 0.93/0.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.93/0.40 % (674225)ott+32_1_sil=16000:bsd=on:sp=const_max:bce=on:random_seed=2258216655:i=131:bd=preordered:fsd=on_2999 on theBenchmark for (2999ds/131Mi)
% 0.93/0.40 % (674225)Instruction limit reached!
% 0.93/0.40 % (674225)------------------------------
% 0.93/0.40 % (674225)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.40 % (674225)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.40 % (674225)CaDiCaL version: 2.1.3
% 0.93/0.40 % (674225)Termination reason: Instruction limit
% 0.93/0.40 % (674225)Termination phase: Saturation
% 0.93/0.40 % (674225)Time elapsed: 0.037 s
% 0.93/0.40 % (674225)Peak memory usage: 12 MB
% 0.93/0.40 % (674225)Instructions burned: 133 (million)
% 0.93/0.40 % (674203)Instruction limit reached!
% 0.93/0.40 % (674203)------------------------------
% 0.93/0.40 % (674203)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.40 % (674203)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.40 % (674203)CaDiCaL version: 2.1.3
% 0.93/0.40 % (674203)Termination reason: Instruction limit
% 0.93/0.40 % (674203)Termination phase: Saturation
% 0.93/0.40 % (674203)Time elapsed: 0.051 s
% 0.93/0.40 % (674203)Peak memory usage: 12 MB
% 0.93/0.40 % (674203)Instructions burned: 103 (million)
% 0.93/0.40 % (674204)Instruction limit reached!
% 0.93/0.40 % (674204)------------------------------
% 0.93/0.40 % (674204)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.40 % (674204)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.40 % (674204)CaDiCaL version: 2.1.3
% 0.93/0.40 % (674204)Termination reason: Instruction limit
% 0.93/0.40 % (674204)Termination phase: Saturation
% 0.93/0.40 % (674204)Time elapsed: 0.056 s
% 0.93/0.40 % (674204)Peak memory usage: 12 MB
% 0.93/0.40 % (674204)Instructions burned: 117 (million)
% 0.93/0.40 % (674250)dis+11_32_anc=none:slsqr=2,1:sil=64000:sas=cadical:lma=off:lsd=50:s2agt=8:slsqc=1:kmz=on:newcnf=on:slsq=on:random_seed=176301160:i=684:slsql=off:bs=unit_only:nicw=on:rawr=on_2999 on theBenchmark for (2999ds/684Mi)
% 0.93/0.40 % (674250)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.93/0.40 % (674250)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.93/0.40 % (674205)Instruction limit reached!
% 0.93/0.40 % (674205)------------------------------
% 0.93/0.40 % (674205)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.40 % (674205)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.40 % (674205)CaDiCaL version: 2.1.3
% 0.93/0.40 % (674205)Termination reason: Instruction limit
% 0.93/0.40 % (674205)Termination phase: Saturation
% 0.93/0.40 % (674205)Time elapsed: 0.065 s
% 0.93/0.40 % (674205)Peak memory usage: 12 MB
% 0.93/0.40 % (674205)Instructions burned: 132 (million)
% 0.93/0.40 % (674251)ott-21_1_sil=16000:fs=off:random_seed=1425241611:i=180:av=off:fsr=off_2999 on theBenchmark for (2999ds/180Mi)
% 0.93/0.40 % (674206)Instruction limit reached!
% 0.93/0.40 % (674206)------------------------------
% 0.93/0.40 % (674206)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.40 % (674206)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.40 % (674206)CaDiCaL version: 2.1.3
% 0.93/0.40 % (674206)Termination reason: Instruction limit
% 0.93/0.40 % (674206)Termination phase: Saturation
% 0.93/0.40 % (674206)Time elapsed: 0.074 s
% 0.93/0.40 % (674206)Peak memory usage: 12 MB
% 0.93/0.40 % (674206)Instructions burned: 159 (million)
% 0.93/0.40 % (674256)dis+10_4_sil=64000:sp=reverse_arity:bsr=on:sac=on:cn=on:random_seed=3793647642:i=477:bd=all_2999 on theBenchmark for (2999ds/477Mi)
% 0.93/0.40 % (674261)fmb+10_1_sil=64000:erd=off:updr=off:random_seed=3517294627:fmbsr=1.3:i=865:ins=25_2998 on theBenchmark for (2998ds/865Mi)
% 0.93/0.40 % Exception at run slice level
% 0.93/0.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.93/0.40 % (674264)ott+10_1_to=lpo:sil=64000:tgt=full:sp=arity:spb=goal_then_units:random_seed=2280197330:i=1179_2998 on theBenchmark for (2998ds/1179Mi)
% 0.93/0.40 % (674272)fmb+10_1_sil=64000:erd=off:fmbss=14:random_seed=4251996828:i=889:ins=1_2998 on theBenchmark for (2998ds/889Mi)
% 0.93/0.40 % Exception at run slice level
% 0.93/0.40 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.93/0.40 % (674276)ott+1_16_sil=32000:plsq=on:plsqc=2:sas=cadical:avsql=on:sp=reverse_frequency:plsqr=128,1:bsr=unit_only:rp=on:newcnf=on:random_seed=3970808096:avsq=on:s2a=on:i=692:avsqr=8,1:kws=arity_squared:bs=unit_only:nm=2:rawr=on_2998 on theBenchmark for (2998ds/692Mi)
% 0.93/0.40 % (674276)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.93/0.40 % (674264) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-674189-674264"...
% 0.93/0.40 % (674264)...printing done.
% 0.93/0.40 % (674264)Refutation found. Thanks to Tanya!
% 0.93/0.40 % SZS status Theorem for theBenchmark
% 0.93/0.40 % SZS output start Proof for theBenchmark
% See solution above
% 0.93/0.40 % (674264)------------------------------
% 0.93/0.40 % (674264)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.93/0.40 % (674264)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.93/0.40 % (674264)CaDiCaL version: 2.1.3
% 0.93/0.40 % (674264)Termination reason: Refutation
% 0.93/0.40 % (674264)Time elapsed: 0.035 s
% 0.93/0.40 % (674264)Peak memory usage: 13 MB
% 0.93/0.40 % (674264)Instructions burned: 55 (million)
% 0.93/0.40 % (674189)Success in time 0.177 s
% 0.93/0.40 % Vampire exiting
%------------------------------------------------------------------------------