%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEU970^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n012.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 08:32:03 AM UTC 2026
% Result : Theorem 0.05s 0.19s
% Output : Refutation 0.05s
% Verified :
% SZS Type : Refutation
% Derivation depth : 29
% Number of leaves : 6
% Syntax : Number of formulae : 88 ( 29 unt; 0 typ; 4 def)
% Number of atoms : 528 ( 126 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 597 ( 42 ~; 77 |; 31 &; 367 @)
% ( 4 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 9 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 37 ( 37 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 22 usr; 10 con; 0-4 aty)
% ( 28 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 92 ( 0 sgn 35 !; 9 ?; 92 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_0,type,
s: $i > $i ).
thf(func_def_1,type,
cCKB_E2: $i > $i > $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,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_10,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_15,type,
vNOT: $o > $o ).
thf(func_def_16,type,
sK3: $i > $o ).
thf(func_def_17,type,
sK4: ( $i > $o ) > $i ).
thf(func_def_18,type,
sK5: ( $i > $o ) > $i ).
thf(func_def_19,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(f1,axiom,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ ( s @ X3 ) ) ) )
& ( X2 @ X0 ) )
=> ( X2 @ X1 ) ) )
= cCKB_E2 ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCKB_E2_def) ).
thf(f2,conjecture,
! [X2: $i,X1: $i,X0: $i] :
( ( ( cCKB_E2 @ X0 @ X1 )
& ( cCKB_E2 @ X1 @ X2 ) )
=> ( cCKB_E2 @ X0 @ X2 ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cCKB_L34000_pme) ).
thf(f3,negated_conjecture,
~ ! [X2: $i,X1: $i,X0: $i] :
( ( ( cCKB_E2 @ X0 @ X1 )
& ( cCKB_E2 @ X1 @ X2 ) )
=> ( cCKB_E2 @ X0 @ X2 ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i,X2: $i] :
( ( ( cCKB_E2 @ X2 @ X1 )
& ( cCKB_E2 @ X1 @ X0 ) )
=> ( cCKB_E2 @ X2 @ X0 ) ),
inference(rectify,[],[f3]) ).
thf(f5,plain,
~ ! [X1: $i,X0: $i,X2: $i] :
( ( ( $true
= ( cCKB_E2 @ X1 @ X0 ) )
& ( $true
= ( cCKB_E2 @ X2 @ X1 ) ) )
=> ( $true
= ( cCKB_E2 @ X2 @ X0 ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ ( s @ X3 ) ) ) )
& ( X2 @ X0 ) )
=> ( X2 @ X1 ) ) )
= cCKB_E2 ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( cCKB_E2
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
? [X1: $i,X0: $i,X2: $i] :
( ( $true
!= ( cCKB_E2 @ X2 @ X0 ) )
& ( $true
= ( cCKB_E2 @ X1 @ X0 ) )
& ( $true
= ( cCKB_E2 @ X2 @ X1 ) ) ),
inference(ennf_transformation,[],[f5]) ).
thf(f9,plain,
? [X1: $i,X0: $i,X2: $i] :
( ( $true
= ( cCKB_E2 @ X2 @ X1 ) )
& ( $true
= ( cCKB_E2 @ X1 @ X0 ) )
& ( $true
!= ( cCKB_E2 @ X2 @ X0 ) ) ),
inference(flattening,[],[f8]) ).
thf(f10,plain,
? [X0: $i,X1: $i,X2: $i] :
( ( $true
= ( cCKB_E2 @ X2 @ X0 ) )
& ( ( cCKB_E2 @ X0 @ X1 )
= $true )
& ( $true
!= ( cCKB_E2 @ X2 @ X1 ) ) ),
inference(rectify,[],[f9]) ).
thf(f11,plain,
( ( $true
= ( cCKB_E2 @ sK2 @ sK0 ) )
& ( $true
= ( cCKB_E2 @ sK0 @ sK1 ) )
& ( ( cCKB_E2 @ sK2 @ sK1 )
!= $true ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2)],[f10]) ).
thf(f12,plain,
( ( cCKB_E2 @ sK2 @ sK1 )
!= $true ),
inference(cnf_transformation,[],[f11]) ).
thf(f13,plain,
( $true
= ( cCKB_E2 @ sK0 @ sK1 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f14,plain,
( $true
= ( cCKB_E2 @ sK2 @ sK0 ) ),
inference(cnf_transformation,[],[f11]) ).
thf(f15,plain,
( cCKB_E2
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f18,plain,
( ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ sK2
@ sK0 )
= $true ),
inference(definition_unfolding,[],[f14,f15]) ).
thf(f19,plain,
( $true
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ sK0
@ sK1 ) ),
inference(definition_unfolding,[],[f13,f15]) ).
thf(f20,plain,
( $true
!= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( Y2 @ Y0 )
& ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) ) )
=> ( Y2 @ Y1 ) ) )
@ sK2
@ sK1 ) ),
inference(definition_unfolding,[],[f12,f15]) ).
thf(f21,plain,
( $true
!= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ sK2 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f20]) ).
thf(f22,plain,
( ( ^ [Y0: $i > $o] :
( ( ( Y0 @ sK2 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK1 ) )
@ sK3 )
= $false ),
inference(sigma_proxy_clausification,[],[f21]) ).
thf(f23,plain,
( ( ( ( sK3 @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ ( s @ Y0 ) ) ) ) ) )
=> ( sK3 @ sK1 ) )
= $false ),
inference(beta-eta_normalization,[],[f22]) ).
thf(f24,plain,
( ( sK3 @ sK1 )
= $false ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f25,plain,
( $true
= ( ( sK3 @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ ( s @ Y0 ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f23]) ).
thf(f26,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ ( s @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f25]) ).
thf(f27,plain,
( $true
= ( sK3 @ sK2 ) ),
inference(and_proxy_clausification,[],[f25]) ).
thf(f28,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK3 @ Y0 )
=> ( sK3 @ ( s @ ( s @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f26]) ).
thf(f29,plain,
! [X1: $i] :
( $true
= ( ( sK3 @ X1 )
=> ( sK3 @ ( s @ ( s @ X1 ) ) ) ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
! [X1: $i] :
( ( $true
= ( sK3 @ ( s @ ( s @ X1 ) ) ) )
| ( $false
= ( sK3 @ X1 ) ) ),
inference(imp_proxy_clausification,[],[f29]) ).
thf(f31,plain,
( $true
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ sK0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK1 ) ) ) ),
inference(beta-eta_normalization,[],[f19]) ).
thf(f32,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ( Y0 @ sK0 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK1 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f31]) ).
thf(f33,plain,
! [X1: $i > $o] :
( ( ( ( X1 @ sK0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) ) )
=> ( X1 @ sK1 ) )
= $true ),
inference(beta-eta_normalization,[],[f32]) ).
thf(f34,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ sK1 ) )
| ( $false
= ( ( X1 @ sK0 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) ) ) ) ),
inference(imp_proxy_clausification,[],[f33]) ).
thf(f35,plain,
! [X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) )
= $false )
| ( ( X1 @ sK0 )
= $false )
| ( $true
= ( X1 @ sK1 ) ) ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f36,plain,
! [X1: $i > $o] :
( ( $false
= ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) )
@ ( sK4 @ X1 ) ) )
| ( $true
= ( X1 @ sK1 ) )
| ( ( X1 @ sK0 )
= $false ) ),
inference(sigma_proxy_clausification,[],[f35]) ).
thf(f37,plain,
! [X1: $i > $o] :
( ( $false
= ( ( X1 @ ( sK4 @ X1 ) )
=> ( X1 @ ( s @ ( s @ ( sK4 @ X1 ) ) ) ) ) )
| ( ( X1 @ sK0 )
= $false )
| ( $true
= ( X1 @ sK1 ) ) ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
! [X1: $i > $o] :
( ( ( X1 @ ( s @ ( s @ ( sK4 @ X1 ) ) ) )
= $false )
| ( $true
= ( X1 @ sK1 ) )
| ( ( X1 @ sK0 )
= $false ) ),
inference(imp_proxy_clausification,[],[f37]) ).
thf(f39,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ ( sK4 @ X1 ) ) )
| ( ( X1 @ sK0 )
= $false )
| ( $true
= ( X1 @ sK1 ) ) ),
inference(imp_proxy_clausification,[],[f37]) ).
thf(f40,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( Y0 @ sK2 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK0 ) ) )
= $true ),
inference(beta-eta_normalization,[],[f18]) ).
thf(f41,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ( Y0 @ sK2 )
& ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) ) )
=> ( Y0 @ sK0 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f40]) ).
thf(f42,plain,
! [X1: $i > $o] :
( $true
= ( ( ( X1 @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) ) )
=> ( X1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f41]) ).
thf(f43,plain,
! [X1: $i > $o] :
( ( ( ( X1 @ sK2 )
& ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) ) )
= $false )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f42]) ).
thf(f44,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ sK0 ) )
| ( ( X1 @ sK2 )
= $false )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f43]) ).
thf(f45,plain,
! [X1: $i > $o] :
( ( ( X1 @ sK2 )
= $false )
| ( $false
= ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) )
@ ( sK5 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(sigma_proxy_clausification,[],[f44]) ).
thf(f46,plain,
! [X1: $i > $o] :
( ( ( X1 @ sK2 )
= $false )
| ( ( ( X1 @ ( sK5 @ X1 ) )
=> ( X1 @ ( s @ ( s @ ( sK5 @ X1 ) ) ) ) )
= $false )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(beta-eta_normalization,[],[f45]) ).
thf(f47,plain,
! [X1: $i > $o] :
( ( $false
= ( X1 @ ( s @ ( s @ ( sK5 @ X1 ) ) ) ) )
| ( ( X1 @ sK2 )
= $false )
| ( $true
= ( X1 @ sK0 ) ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f48,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( X1 @ sK0 ) )
| ( ( X1 @ sK2 )
= $false ) ),
inference(imp_proxy_clausification,[],[f46]) ).
thf(f102,plain,
( ( ( sK3 @ sK0 )
= $false )
| ( $true = $false )
| ( $false
= ( sK3 @ ( sK4 @ sK3 ) ) )
| ( $true
= ( sK3 @ sK1 ) ) ),
inference(constrained_superposition,[],[f38,f30]) ).
thf(f114,plain,
( ( $false
= ( sK3 @ ( sK4 @ sK3 ) ) )
| ( ( sK3 @ sK0 )
= $false )
| ( $true
= ( sK3 @ sK1 ) ) ),
inference(trivial_inequality_removal,[],[f102]) ).
thf(f123,plain,
( ( ( sK3 @ sK2 )
= $false )
| ( ( sK3 @ ( sK5 @ sK3 ) )
= $false )
| ( $true = $false )
| ( $true
= ( sK3 @ sK0 ) ) ),
inference(constrained_superposition,[],[f47,f30]) ).
thf(f133,plain,
( ( ( sK3 @ ( sK5 @ sK3 ) )
= $false )
| ( ( sK3 @ sK2 )
= $false )
| ( $true
= ( sK3 @ sK0 ) ) ),
inference(trivial_inequality_removal,[],[f123]) ).
thf(f149,plain,
( ( $true = $false )
| ( ( sK3 @ ( sK5 @ sK3 ) )
= $false )
| ( $true
= ( sK3 @ sK0 ) ) ),
inference(forward_demodulation,[],[f133,f27]) ).
thf(f150,plain,
( ( $true
= ( sK3 @ sK0 ) )
| ( ( sK3 @ ( sK5 @ sK3 ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f149]) ).
thf(f184,plain,
( ( $false
= ( sK3 @ ( sK4 @ sK3 ) ) )
| ( ( sK3 @ sK0 )
= $false )
| ( $true = $false ) ),
inference(forward_demodulation,[],[f114,f24]) ).
thf(f185,plain,
( ( $false
= ( sK3 @ ( sK4 @ sK3 ) ) )
| ( ( sK3 @ sK0 )
= $false ) ),
inference(trivial_inequality_removal,[],[f184]) ).
thf(f189,definition,
( spl6_8
<=> ( ( sK3 @ ( sK5 @ sK3 ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl6_8])],[avatar_definition]) ).
thf(f191,plain,
( ( ( sK3 @ ( sK5 @ sK3 ) )
= $false )
| ~ spl6_8 ),
inference(avatar_component_clause,[],[f189]) ).
thf(f193,definition,
( spl6_9
<=> ( $true
= ( sK3 @ sK0 ) ) ),
introduced(definition,[new_symbols(definition,[spl6_9])],[avatar_definition]) ).
thf(f195,plain,
( ( $true
= ( sK3 @ sK0 ) )
| ~ spl6_9 ),
inference(avatar_component_clause,[],[f193]) ).
thf(f196,plain,
( spl6_8
| spl6_9 ),
inference(avatar_split_clause,[],[f150,f193,f189]) ).
thf(f199,definition,
( spl6_10
<=> ( $false
= ( sK3 @ ( sK4 @ sK3 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_10])],[avatar_definition]) ).
thf(f201,plain,
( ( $false
= ( sK3 @ ( sK4 @ sK3 ) ) )
| ~ spl6_10 ),
inference(avatar_component_clause,[],[f199]) ).
thf(f203,definition,
( spl6_11
<=> ( ( sK3 @ sK0 )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl6_11])],[avatar_definition]) ).
thf(f205,plain,
( ( ( sK3 @ sK0 )
= $false )
| ~ spl6_11 ),
inference(avatar_component_clause,[],[f203]) ).
thf(f206,plain,
( spl6_10
| spl6_11 ),
inference(avatar_split_clause,[],[f185,f203,f199]) ).
thf(f209,plain,
( ( $true
= ( sK3 @ sK0 ) )
| ( $true = $false )
| ( ( sK3 @ sK2 )
= $false )
| ~ spl6_8 ),
inference(constrained_superposition,[],[f48,f191]) ).
thf(f210,plain,
( ( ( sK3 @ sK2 )
= $false )
| ( $true
= ( sK3 @ sK0 ) )
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f209]) ).
thf(f212,plain,
( ( $true
= ( sK3 @ sK0 ) )
| ( $true = $false )
| ~ spl6_8 ),
inference(forward_demodulation,[],[f210,f27]) ).
thf(f213,plain,
( ( $true
= ( sK3 @ sK0 ) )
| ~ spl6_8 ),
inference(trivial_inequality_removal,[],[f212]) ).
thf(f216,plain,
( spl6_9
| ~ spl6_8 ),
inference(avatar_split_clause,[],[f213,f189,f193]) ).
thf(f218,plain,
( ( $true
= ( sK3 @ sK1 ) )
| ( $true = $false )
| ( ( sK3 @ sK0 )
= $false )
| ~ spl6_10 ),
inference(constrained_superposition,[],[f39,f201]) ).
thf(f220,plain,
( ( $true
= ( sK3 @ sK1 ) )
| ( ( sK3 @ sK0 )
= $false )
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f218]) ).
thf(f223,plain,
( ( $true = $false )
| ( ( sK3 @ sK0 )
= $false )
| ~ spl6_10 ),
inference(forward_demodulation,[],[f220,f24]) ).
thf(f224,plain,
( ( ( sK3 @ sK0 )
= $false )
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f223]) ).
thf(f228,plain,
( ( $true = $false )
| ~ spl6_9
| ~ spl6_10 ),
inference(forward_demodulation,[],[f224,f195]) ).
thf(f229,plain,
( $false
| ~ spl6_9
| ~ spl6_10 ),
inference(trivial_inequality_removal,[],[f228]) ).
thf(f230,plain,
( ~ spl6_9
| ~ spl6_10 ),
inference(avatar_contradiction_clause,[],[f229]) ).
thf(f231,plain,
( ( $true = $false )
| ~ spl6_9
| ~ spl6_11 ),
inference(forward_demodulation,[],[f205,f195]) ).
thf(f232,plain,
( $false
| ~ spl6_9
| ~ spl6_11 ),
inference(trivial_inequality_removal,[],[f231]) ).
thf(f233,plain,
( ~ spl6_9
| ~ spl6_11 ),
inference(avatar_contradiction_clause,[],[f232]) ).
cnf(s9,plain,
( spl6_8
| spl6_9 ),
inference(sat_conversion,[],[f196]) ).
cnf(s11,plain,
( spl6_10
| spl6_11 ),
inference(sat_conversion,[],[f206]) ).
cnf(s13,plain,
( ~ spl6_8
| spl6_9 ),
inference(sat_conversion,[],[f216]) ).
cnf(s16,plain,
( ~ spl6_9
| ~ spl6_10 ),
inference(sat_conversion,[],[f230]) ).
cnf(s17,plain,
( ~ spl6_9
| ~ spl6_11 ),
inference(sat_conversion,[],[f233]) ).
cnf(s20,plain,
~ spl6_9,
inference(rat,[],[s11,s16,s17]) ).
cnf(s21,plain,
~ spl6_8,
inference(rat,[],[s13,s20]) ).
cnf(s22,plain,
$false,
inference(rat,[],[s9,s20,s21]) ).
thf(f234,plain,
$false,
inference(avatar_sat_refutation,[],[s22]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.01 % Problem : SEU970^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.03 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.13 % Computer : n012.cluster.edu
% 0.05/0.13 % Model : x86_64 x86_64
% 0.05/0.13 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.05/0.13 % Memory : 8046.5625MB
% 0.05/0.13 % OS : Linux 6.8.0-71-generic
% 0.05/0.13 % CPULimit : 300
% 0.05/0.13 % WCLimit : 300
% 0.05/0.13 % DateTime : Tue Sep 29 14:53:04 UTC 2026
% 0.05/0.13 % CPUTime :
% 0.05/0.13 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.05/0.15 Running higher-order theorem proving
% 0.05/0.15 Running: /export/starexec/sandbox/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc -m 16384 --cores 7 -t 300 /export/starexec/sandbox/benchmark/theBenchmark.p
% 0.05/0.19 % (211668)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.05/0.19 % (211679)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.05/0.19 % (211679)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
% 0.05/0.19 % (211676)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=1119641635: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)
% 0.05/0.19 % (211675)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=797424482:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.05/0.19 % (211674)lrs+10_16_si=on:nwc=1.5:random_seed=3024982979:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.05/0.19 % (211673)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=1624599759:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.05/0.19 % (211677)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3011199714:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.05/0.19 % (211678)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4230777048:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.05/0.19 % (211679)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=142130945:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.05/0.19 % (211675)Refutation not found, incomplete strategy
% 0.05/0.19 % (211675)------------------------------
% 0.05/0.19 % (211675)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.05/0.19 % (211675)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.05/0.19 % (211675)CaDiCaL version: 2.1.3
% 0.05/0.19 % (211675)Termination reason: Refutation not found, incomplete strategy
% 0.05/0.19 % (211675)Time elapsed: 0.001 s
% 0.05/0.19 % (211675)Peak memory usage: 12 MB
% 0.05/0.19 % (211675)Instructions burned: 2 (million)
% 0.05/0.19 % (211675)------------------------------
% 0.05/0.19 % (211675)------------------------------
% 0.05/0.19 % (211679) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-211668-211679"...
% 0.05/0.19 % (211673) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-211668-211673"...
% 0.05/0.19 % (211673)...printing done.
% 0.05/0.19 % (211673)Refutation found. Thanks to Tanya!
% 0.05/0.19 % SZS status Theorem for theBenchmark
% 0.05/0.19 % SZS output start Proof for theBenchmark
% See solution above
% 0.05/0.20 % (211673)------------------------------
% 0.05/0.20 % (211673)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.05/0.20 % (211673)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.05/0.20 % (211673)CaDiCaL version: 2.1.3
% 0.05/0.20 % (211673)Termination reason: Refutation
% 0.05/0.20 % (211673)Time elapsed: 0.004 s
% 0.05/0.20 % (211673)Peak memory usage: 13 MB
% 0.05/0.20 % (211673)Instructions burned: 12 (million)
% 0.05/0.20 % (211668)Success in time 0.035 s
% 0.05/0.20 % Vampire exiting
%------------------------------------------------------------------------------