%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : PUZ108^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% Computer : n016.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 08:20:54 AM UTC 2026
% Result : Theorem 0.21s 0.31s
% Output : Refutation 0.21s
% Verified :
% SZS Type : Refutation
% Derivation depth : 32
% Number of leaves : 4
% Syntax : Number of formulae : 57 ( 31 unt; 0 typ; 2 def)
% Number of atoms : 381 ( 87 equ; 0 cnn)
% Maximal formula atoms : 4 ( 6 avg)
% Number of connectives : 775 ( 8 ~; 34 |; 32 &; 548 @)
% ( 0 <=>; 83 =>; 0 <=; 0 <~>)
% Maximal formula depth : 8 ( 2 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 60 ( 60 >; 0 *; 0 +; 0 <<)
% Number of symbols : 22 ( 18 usr; 7 con; 0-4 aty)
% ( 70 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 148 ( 127 ^; 21 !; 0 ?; 148 :)
% 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_3,type,
vNOT: $o > $o ).
thf(func_def_4,type,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_5,type,
vIMP: $o > $o > $o ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_11,type,
vAND: $o > $o > $o ).
thf(func_def_12,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_13,type,
sF0: $o ).
thf(func_def_14,type,
sF1: $o ).
thf(func_def_17,type,
sK4: $i > $o ).
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] :
( ( ( X2 @ X0 )
& ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ ( s @ X3 ) ) ) ) )
=> ( X2 @ X1 ) ) )
= cCKB_E2 ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB_E2_def) ).
thf(f2,conjecture,
! [X0: $i,X1: $i] :
( ( cCKB_E2 @ X0 @ X1 )
=> ( cCKB_E2 @ ( s @ X0 ) @ ( s @ X1 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cCKB_L35000) ).
thf(f3,negated_conjecture,
~ ! [X0: $i,X1: $i] :
( ( cCKB_E2 @ X0 @ X1 )
=> ( cCKB_E2 @ ( s @ X0 ) @ ( s @ X1 ) ) ),
inference(negated_conjecture,[status(cth)],[f2]) ).
thf(f4,plain,
~ ! [X0: $i,X1: $i] :
( ( cCKB_E2 @ X0 @ X1 )
=> ( cCKB_E2 @ ( s @ X0 ) @ ( s @ X1 ) ) ),
inference(rectify,[],[f3]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cCKB_E2 @ Y1 @ Y0 )
=> ( cCKB_E2 @ ( s @ Y1 ) @ ( s @ Y0 ) ) ) ) ) ) ),
inference(fool_elimination,[],[f4]) ).
thf(f6,plain,
( ( ^ [X0: $i,X1: $i] :
! [X2: $i > $o] :
( ( ( X2 @ X0 )
& ! [X3: $i] :
( ( X2 @ X3 )
=> ( X2 @ ( s @ ( s @ X3 ) ) ) ) )
=> ( X2 @ X1 ) ) )
= cCKB_E2 ),
inference(rectify,[],[f1]) ).
thf(f7,plain,
( cCKB_E2
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(fool_elimination,[],[f6]) ).
thf(f8,plain,
( $true
= ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( cCKB_E2 @ Y1 @ Y0 )
=> ( cCKB_E2 @ ( s @ Y1 ) @ ( s @ Y0 ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f5]) ).
thf(f9,plain,
( cCKB_E2
= ( ^ [Y0: $i,Y1: $i] :
( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y0 ) )
=> ( Y2 @ Y1 ) ) ) ) ),
inference(cnf_transformation,[],[f7]) ).
thf(f12,plain,
( ( ~ ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( s @ ( s @ Y5 ) ) ) ) )
& ( Y4 @ Y2 ) )
=> ( Y4 @ Y3 ) ) )
@ Y1
@ Y0 )
=> ( ^ [Y2: $i,Y3: $i] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( s @ ( s @ Y5 ) ) ) ) )
& ( Y4 @ Y2 ) )
=> ( Y4 @ Y3 ) ) )
@ ( s @ Y1 )
@ ( s @ Y0 ) ) ) ) ) )
= $true ),
inference(definition_unfolding,[],[f8,f9,f9]) ).
thf(f13,definition,
( sF0
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( ^ [Y2: $i,Y3: $i] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( s @ ( s @ Y5 ) ) ) ) )
& ( Y4 @ Y2 ) )
=> ( Y4 @ Y3 ) ) )
@ Y1
@ Y0 )
=> ( ^ [Y2: $i,Y3: $i] :
( !! @ ( $i > $o )
@ ^ [Y4: $i > $o] :
( ( ( !! @ $i
@ ^ [Y5: $i] :
( ( Y4 @ Y5 )
=> ( Y4 @ ( s @ ( s @ Y5 ) ) ) ) )
& ( Y4 @ Y2 ) )
=> ( Y4 @ Y3 ) ) )
@ ( s @ Y1 )
@ ( s @ Y0 ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[sF0])],[function_definition]) ).
thf(f14,definition,
( sF1 = ( ~ sF0 ) ),
introduced(definition,[new_symbols(definition,[sF1])],[function_definition]) ).
thf(f15,plain,
( ( ~ sF0 ) = sF1 ),
inference(reorient_equations,[],[f14]) ).
thf(f16,plain,
sF1 = $true,
inference(definition_folding,[],[f12,f15,f13]) ).
thf(f17,plain,
( sF0
= ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y1 ) )
=> ( Y2 @ Y0 ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ ( s @ Y1 ) ) )
=> ( Y2 @ ( s @ Y0 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f13]) ).
thf(f18,plain,
( ( sF0 = $true )
| ( ( !! @ $i
@ ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y1 ) )
=> ( Y2 @ Y0 ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ ( s @ Y1 ) ) )
=> ( Y2 @ ( s @ Y0 ) ) ) ) ) ) )
= $false ) ),
inference(iff_proxy_clausification,[],[f17]) ).
thf(f20,plain,
( ( ~ sF0 ) = $true ),
inference(forward_demodulation,[],[f15,f16]) ).
thf(f23,plain,
( ( $false
= ( ^ [Y0: $i] :
( !! @ $i
@ ^ [Y1: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ Y1 ) )
=> ( Y2 @ Y0 ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y2: $i > $o] :
( ( ( !! @ $i
@ ^ [Y3: $i] :
( ( Y2 @ Y3 )
=> ( Y2 @ ( s @ ( s @ Y3 ) ) ) ) )
& ( Y2 @ ( s @ Y1 ) ) )
=> ( Y2 @ ( s @ Y0 ) ) ) ) ) )
@ sK2 ) )
| ( sF0 = $true ) ),
inference(sigma_proxy_clausification,[],[f18]) ).
thf(f24,plain,
( ( sF0 = $true )
| ( $false
= ( !! @ $i
@ ^ [Y0: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ ( s @ Y2 ) ) ) ) )
& ( Y1 @ Y0 ) )
=> ( Y1 @ sK2 ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ ( s @ Y2 ) ) ) ) )
& ( Y1 @ ( s @ Y0 ) ) )
=> ( Y1 @ ( s @ sK2 ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
sF0 = $false,
inference(not_proxy_clausification,[],[f20]) ).
thf(f28,plain,
( ( sF0 = $true )
| ( $false
= ( ^ [Y0: $i] :
( ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ ( s @ Y2 ) ) ) ) )
& ( Y1 @ Y0 ) )
=> ( Y1 @ sK2 ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y2: $i] :
( ( Y1 @ Y2 )
=> ( Y1 @ ( s @ ( s @ Y2 ) ) ) ) )
& ( Y1 @ ( s @ Y0 ) ) )
=> ( Y1 @ ( s @ sK2 ) ) ) ) )
@ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f24]) ).
thf(f29,plain,
( ( sF0 = $true )
| ( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ sK3 ) )
=> ( Y0 @ sK2 ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ ( s @ sK3 ) ) )
=> ( Y0 @ ( s @ sK2 ) ) ) ) )
= $false ) ),
inference(beta-eta_normalization,[],[f28]) ).
thf(f30,plain,
( ( $false = $true )
| ( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ sK3 ) )
=> ( Y0 @ sK2 ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ ( s @ sK3 ) ) )
=> ( Y0 @ ( s @ sK2 ) ) ) ) )
= $false ) ),
inference(forward_demodulation,[],[f29,f25]) ).
thf(f31,plain,
( ( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ sK3 ) )
=> ( Y0 @ sK2 ) ) )
=> ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ ( s @ sK3 ) ) )
=> ( Y0 @ ( s @ sK2 ) ) ) ) )
= $false ),
inference(trivial_inequality_removal,[],[f30]) ).
thf(f32,plain,
( $false
= ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ ( s @ sK3 ) ) )
=> ( Y0 @ ( s @ sK2 ) ) ) ) ),
inference(imp_proxy_clausification,[],[f31]) ).
thf(f33,plain,
( ( !! @ ( $i > $o )
@ ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ sK3 ) )
=> ( Y0 @ sK2 ) ) )
= $true ),
inference(imp_proxy_clausification,[],[f31]) ).
thf(f34,plain,
( ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ ( s @ sK3 ) ) )
=> ( Y0 @ ( s @ sK2 ) ) )
@ sK4 )
= $false ),
inference(sigma_proxy_clausification,[],[f32]) ).
thf(f35,plain,
( $false
= ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ ( s @ Y0 ) ) ) ) )
& ( sK4 @ ( s @ sK3 ) ) )
=> ( sK4 @ ( s @ sK2 ) ) ) ),
inference(beta-eta_normalization,[],[f34]) ).
thf(f36,plain,
! [X1: $i > $o] :
( $true
= ( ^ [Y0: $i > $o] :
( ( ( !! @ $i
@ ^ [Y1: $i] :
( ( Y0 @ Y1 )
=> ( Y0 @ ( s @ ( s @ Y1 ) ) ) ) )
& ( Y0 @ sK3 ) )
=> ( Y0 @ sK2 ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f33]) ).
thf(f37,plain,
! [X1: $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) )
& ( X1 @ sK3 ) )
=> ( X1 @ sK2 ) )
= $true ),
inference(beta-eta_normalization,[],[f36]) ).
thf(f38,plain,
( ( sK4 @ ( s @ sK2 ) )
= $false ),
inference(imp_proxy_clausification,[],[f35]) ).
thf(f39,plain,
( $true
= ( ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ ( s @ Y0 ) ) ) ) )
& ( sK4 @ ( s @ sK3 ) ) ) ),
inference(imp_proxy_clausification,[],[f35]) ).
thf(f40,plain,
! [X1: $i > $o] :
( ( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) )
& ( X1 @ sK3 ) )
= $false )
| ( $true
= ( X1 @ sK2 ) ) ),
inference(imp_proxy_clausification,[],[f37]) ).
thf(f41,plain,
( ( sK4 @ ( s @ sK3 ) )
= $true ),
inference(and_proxy_clausification,[],[f39]) ).
thf(f42,plain,
( $true
= ( !! @ $i
@ ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ ( s @ Y0 ) ) ) ) ) ),
inference(and_proxy_clausification,[],[f39]) ).
thf(f43,plain,
! [X1: $i > $o] :
( ( ( !! @ $i
@ ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) ) )
= $false )
| ( $true
= ( X1 @ sK2 ) )
| ( $false
= ( X1 @ sK3 ) ) ),
inference(and_proxy_clausification,[],[f40]) ).
thf(f44,plain,
! [X1: $i] :
( $true
= ( ^ [Y0: $i] :
( ( sK4 @ Y0 )
=> ( sK4 @ ( s @ ( s @ Y0 ) ) ) )
@ X1 ) ),
inference(pi_proxy_clausification,[],[f42]) ).
thf(f45,plain,
! [X1: $i] :
( ( ( sK4 @ X1 )
=> ( sK4 @ ( s @ ( s @ X1 ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ sK2 ) )
| ( ( ^ [Y0: $i] :
( ( X1 @ Y0 )
=> ( X1 @ ( s @ ( s @ Y0 ) ) ) )
@ ( sK5 @ X1 ) )
= $false )
| ( $false
= ( X1 @ sK3 ) ) ),
inference(sigma_proxy_clausification,[],[f43]) ).
thf(f47,plain,
! [X1: $i > $o] :
( ( $false
= ( X1 @ sK3 ) )
| ( $true
= ( X1 @ sK2 ) )
| ( $false
= ( ( X1 @ ( sK5 @ X1 ) )
=> ( X1 @ ( s @ ( s @ ( sK5 @ X1 ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f46]) ).
thf(f48,plain,
! [X1: $i] :
( ( ( sK4 @ ( s @ ( s @ X1 ) ) )
= $true )
| ( ( sK4 @ X1 )
= $false ) ),
inference(imp_proxy_clausification,[],[f45]) ).
thf(f49,plain,
! [X1: $i > $o] :
( ( ( X1 @ ( s @ ( s @ ( sK5 @ X1 ) ) ) )
= $false )
| ( $true
= ( X1 @ sK2 ) )
| ( $false
= ( X1 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f47]) ).
thf(f50,plain,
! [X1: $i > $o] :
( ( $true
= ( X1 @ ( sK5 @ X1 ) ) )
| ( $true
= ( X1 @ sK2 ) )
| ( $false
= ( X1 @ sK3 ) ) ),
inference(imp_proxy_clausification,[],[f47]) ).
thf(f129,plain,
( ( $false
= ( sK4
@ ( s
@ ( sK5
@ ^ [Y0: $i] :
( sK4
@ ( ^ [Y1: $i] :
( s
@ ( ^ [Y2: $i] : Y2
@ Y1 ) )
@ Y0 ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( sK4
@ ( ^ [Y1: $i] :
( s
@ ( ^ [Y2: $i] : Y2
@ Y1 ) )
@ Y0 ) )
@ sK3 )
= $false )
| ( ( ^ [Y0: $i] :
( sK4
@ ( ^ [Y1: $i] :
( s
@ ( ^ [Y2: $i] : Y2
@ Y1 ) )
@ Y0 ) )
@ sK2 )
= $true )
| ( $false = $true ) ),
inference(constrained_superposition,[],[f48,f49]) ).
thf(f141,plain,
( ( ( ^ [Y0: $i] :
( sK4
@ ( ^ [Y1: $i] :
( s
@ ( ^ [Y2: $i] : Y2
@ Y1 ) )
@ Y0 ) )
@ sK3 )
= $false )
| ( $false
= ( sK4
@ ( s
@ ( sK5
@ ^ [Y0: $i] :
( sK4
@ ( ^ [Y1: $i] :
( s
@ ( ^ [Y2: $i] : Y2
@ Y1 ) )
@ Y0 ) ) ) ) ) )
| ( ( ^ [Y0: $i] :
( sK4
@ ( ^ [Y1: $i] :
( s
@ ( ^ [Y2: $i] : Y2
@ Y1 ) )
@ Y0 ) )
@ sK2 )
= $true ) ),
inference(trivial_inequality_removal,[],[f129]) ).
thf(f142,plain,
( ( ( sK4 @ ( s @ sK3 ) )
= $false )
| ( ( sK4
@ ( s
@ ( sK5
@ ^ [Y0: $i] : ( sK4 @ ( s @ Y0 ) ) ) ) )
= $false )
| ( ( sK4 @ ( s @ sK2 ) )
= $true ) ),
inference(beta-eta_normalization,[],[f141]) ).
thf(f173,plain,
( ( $false = $true )
| ( ( sK4 @ ( s @ sK2 ) )
= $true )
| ( ( sK4
@ ( s
@ ( sK5
@ ^ [Y0: $i] : ( sK4 @ ( s @ Y0 ) ) ) ) )
= $false ) ),
inference(forward_demodulation,[],[f142,f41]) ).
thf(f174,plain,
( ( ( sK4 @ ( s @ sK2 ) )
= $true )
| ( ( sK4
@ ( s
@ ( sK5
@ ^ [Y0: $i] : ( sK4 @ ( s @ Y0 ) ) ) ) )
= $false ) ),
inference(trivial_inequality_removal,[],[f173]) ).
thf(f193,plain,
( ( $false = $true )
| ( ( sK4
@ ( s
@ ( sK5
@ ^ [Y0: $i] : ( sK4 @ ( s @ Y0 ) ) ) ) )
= $false ) ),
inference(forward_demodulation,[],[f174,f38]) ).
thf(f194,plain,
( ( sK4
@ ( s
@ ( sK5
@ ^ [Y0: $i] : ( sK4 @ ( s @ Y0 ) ) ) ) )
= $false ),
inference(trivial_inequality_removal,[],[f193]) ).
thf(f215,plain,
( ( ( ^ [Y0: $i] :
( sK4
@ ( ^ [Y1: $i] :
( s
@ ( ^ [Y2: $i] : Y2
@ Y1 ) )
@ Y0 ) )
@ sK2 )
= $true )
| ( $false = $true )
| ( ( ^ [Y0: $i] :
( sK4
@ ( ^ [Y1: $i] :
( s
@ ( ^ [Y2: $i] : Y2
@ Y1 ) )
@ Y0 ) )
@ sK3 )
= $false ) ),
inference(constrained_superposition,[],[f50,f194]) ).
thf(f217,plain,
( ( ( ^ [Y0: $i] :
( sK4
@ ( ^ [Y1: $i] :
( s
@ ( ^ [Y2: $i] : Y2
@ Y1 ) )
@ Y0 ) )
@ sK2 )
= $true )
| ( ( ^ [Y0: $i] :
( sK4
@ ( ^ [Y1: $i] :
( s
@ ( ^ [Y2: $i] : Y2
@ Y1 ) )
@ Y0 ) )
@ sK3 )
= $false ) ),
inference(trivial_inequality_removal,[],[f215]) ).
thf(f218,plain,
( ( ( sK4 @ ( s @ sK2 ) )
= $true )
| ( ( sK4 @ ( s @ sK3 ) )
= $false ) ),
inference(beta-eta_normalization,[],[f217]) ).
thf(f229,plain,
( ( $false = $true )
| ( ( sK4 @ ( s @ sK3 ) )
= $false ) ),
inference(forward_demodulation,[],[f218,f38]) ).
thf(f230,plain,
( ( sK4 @ ( s @ sK3 ) )
= $false ),
inference(trivial_inequality_removal,[],[f229]) ).
thf(f235,plain,
$false = $true,
inference(backward_demodulation,[],[f41,f230]) ).
thf(f236,plain,
$false,
inference(trivial_inequality_removal,[],[f235]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : PUZ108^5 : TPTP v9.3.1. Bugfixed v5.2.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.09/0.18 % Computer : n016.cluster.edu
% 0.09/0.18 % Model : x86_64 x86_64
% 0.09/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.09/0.18 % Memory : 8046.5625MB
% 0.09/0.18 % OS : Linux 6.8.0-71-generic
% 0.09/0.18 % CPULimit : 300
% 0.09/0.18 % WCLimit : 300
% 0.09/0.18 % DateTime : Tue Sep 29 13:28:34 UTC 2026
% 0.09/0.19 % CPUTime :
% 0.09/0.19 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
% 0.21/0.31 % (336127)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.21/0.31 % (336132)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=2542804202:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.21/0.31 % (336132)Refutation not found, incomplete strategy
% 0.21/0.31 % (336132)------------------------------
% 0.21/0.31 % (336132)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (336132)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (336132)CaDiCaL version: 2.1.3
% 0.21/0.31 % (336132)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (336132)Time elapsed: 0.003 s
% 0.21/0.31 % (336132)Peak memory usage: 12 MB
% 0.21/0.31 % (336132)Instructions burned: 7 (million)
% 0.21/0.31 % (336132)------------------------------
% 0.21/0.31 % (336132)------------------------------
% 0.21/0.31 % (336138)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.21/0.31 % (336138)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
% 0.21/0.31 % (336133)lrs+10_16_si=on:nwc=1.5:random_seed=1874895192:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.21/0.31 % (336134)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=2192774877:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.21/0.31 % (336135)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=831554464: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)
% 0.21/0.31 % (336136)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=831190856:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.21/0.31 % (336138)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=2656370026:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.21/0.31 % (336134)Refutation not found, incomplete strategy
% 0.21/0.31 % (336134)------------------------------
% 0.21/0.31 % (336134)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (336134)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (336134)CaDiCaL version: 2.1.3
% 0.21/0.31 % (336134)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (336134)Time elapsed: 0.001 s
% 0.21/0.31 % (336134)Peak memory usage: 12 MB
% 0.21/0.31 % (336134)Instructions burned: 1 (million)
% 0.21/0.31 % (336134)------------------------------
% 0.21/0.31 % (336134)------------------------------
% 0.21/0.31 % (336138)Refutation not found, incomplete strategy
% 0.21/0.31 % (336138)------------------------------
% 0.21/0.31 % (336138)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (336138)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (336138)CaDiCaL version: 2.1.3
% 0.21/0.31 % (336138)Termination reason: Refutation not found, incomplete strategy
% 0.21/0.31 % (336138)Time elapsed: 0.004 s
% 0.21/0.31 % (336138)Peak memory usage: 12 MB
% 0.21/0.31 % (336138)Instructions burned: 5 (million)
% 0.21/0.31 % (336138)------------------------------
% 0.21/0.31 % (336138)------------------------------
% 0.21/0.31 % (336140)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1858890543:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.21/0.31 % (336140)Instruction limit reached!
% 0.21/0.31 % (336140)------------------------------
% 0.21/0.31 % (336140)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (336140)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (336140)CaDiCaL version: 2.1.3
% 0.21/0.31 % (336140)Termination reason: Instruction limit
% 0.21/0.31 % (336140)Termination phase: Saturation
% 0.21/0.31 % (336140)Time elapsed: 0.001 s
% 0.21/0.31 % (336140)Peak memory usage: 12 MB
% 0.21/0.31 % (336140)Instructions burned: 2 (million)
% 0.21/0.31 % (336133)Instruction limit reached!
% 0.21/0.31 % (336133)------------------------------
% 0.21/0.31 % (336133)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (336133)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (336133)CaDiCaL version: 2.1.3
% 0.21/0.31 % (336133)Termination reason: Instruction limit
% 0.21/0.31 % (336133)Termination phase: Saturation
% 0.21/0.31 % (336133)Time elapsed: 0.010 s
% 0.21/0.31 % (336133)Peak memory usage: 12 MB
% 0.21/0.31 % (336133)Instructions burned: 18 (million)
% 0.21/0.31 % (336137)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=3569587934:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.21/0.31 % (336136)Instruction limit reached!
% 0.21/0.31 % (336136)------------------------------
% 0.21/0.31 % (336136)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (336136)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (336136)CaDiCaL version: 2.1.3
% 0.21/0.31 % (336136)Termination reason: Instruction limit
% 0.21/0.31 % (336136)Termination phase: Saturation
% 0.21/0.31 % (336136)Time elapsed: 0.013 s
% 0.21/0.31 % (336136)Peak memory usage: 12 MB
% 0.21/0.31 % (336136)Instructions burned: 25 (million)
% 0.21/0.31 % (336147)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.31 % (336146)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=1997006400:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.21/0.31 % (336147)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=1130063344:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.21/0.31 % (336150)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
% 0.21/0.31 % (336150)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.21/0.31 % (336146)Instruction limit reached!
% 0.21/0.31 % (336146)------------------------------
% 0.21/0.31 % (336146)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (336146)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (336146)CaDiCaL version: 2.1.3
% 0.21/0.31 % (336146)Termination reason: Instruction limit
% 0.21/0.31 % (336146)Termination phase: Saturation
% 0.21/0.31 % (336146)Time elapsed: 0.004 s
% 0.21/0.31 % (336146)Peak memory usage: 12 MB
% 0.21/0.31 % (336146)Instructions burned: 6 (million)
% 0.21/0.31 % (336149)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=1194929420:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.21/0.31 % (336150)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2978956725:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.21/0.31 % (336147)Instruction limit reached!
% 0.21/0.31 % (336147)------------------------------
% 0.21/0.31 % (336147)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (336147)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (336147)CaDiCaL version: 2.1.3
% 0.21/0.31 % (336147)Termination reason: Instruction limit
% 0.21/0.31 % (336147)Termination phase: Saturation
% 0.21/0.31 % (336147)Time elapsed: 0.004 s
% 0.21/0.31 % (336147)Peak memory usage: 12 MB
% 0.21/0.31 % (336147)Instructions burned: 7 (million)
% 0.21/0.31 % (336152)lrs+1002_64_sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:sp=occurrence:lma=off:plsqr=32,1:uwa=interpreted_only:random_seed=501808077:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.21/0.31 % (336149)Instruction limit reached!
% 0.21/0.31 % (336149)------------------------------
% 0.21/0.31 % (336149)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (336149)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (336149)CaDiCaL version: 2.1.3
% 0.21/0.31 % (336149)Termination reason: Instruction limit
% 0.21/0.31 % (336149)Termination phase: Saturation
% 0.21/0.31 % (336149)Time elapsed: 0.007 s
% 0.21/0.31 % (336149)Peak memory usage: 12 MB
% 0.21/0.31 % (336149)Instructions burned: 12 (million)
% 0.21/0.31 % (336150) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-336127-336150"...
% 0.21/0.31 % (336158)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.21/0.31 % (336155)lrs+10_1_si=on:cs=on:random_seed=2038407917:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.21/0.31 % (336150)...printing done.
% 0.21/0.31 % (336150)Refutation found. Thanks to Tanya!
% 0.21/0.31 % SZS status Theorem for theBenchmark
% 0.21/0.31 % SZS output start Proof for theBenchmark
% See solution above
% 0.21/0.31 % (336150)------------------------------
% 0.21/0.31 % (336150)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.21/0.31 % (336150)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.21/0.31 % (336150)CaDiCaL version: 2.1.3
% 0.21/0.31 % (336150)Termination reason: Refutation
% 0.21/0.31 % (336150)Time elapsed: 0.014 s
% 0.21/0.31 % (336150)Peak memory usage: 12 MB
% 0.21/0.31 % (336150)Instructions burned: 27 (million)
% 0.21/0.31 % (336127)Success in time 0.076 s
% 0.21/0.31 % Vampire exiting
%------------------------------------------------------------------------------