%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : LCL731^5 : 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 : n013.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 08:14:35 AM UTC 2026
% Result : Theorem 0.34s 0.49s
% Output : Refutation 1.07s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 7
% Syntax : Number of formulae : 100 ( 11 unt; 0 typ; 6 def)
% Number of atoms : 546 ( 88 equ; 0 cnn)
% Maximal formula atoms : 4 ( 5 avg)
% Number of connectives : 1119 ( 127 ~; 124 |; 0 &; 584 @)
% ( 9 <=>; 108 =>; 0 <=; 0 <~>)
% Maximal formula depth : 10 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 385 ( 385 >; 0 *; 0 +; 0 <<)
% Number of symbols : 31 ( 26 usr; 11 con; 0-4 aty)
% ( 68 !!; 99 ??; 0 @@+; 0 @@-)
% Number of variables : 177 ( 0 sgn 53 !; 12 ?; 177 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
vNOT: $o > $o ).
thf(func_def_2,type,
vIFF: $o > $o > $o ).
thf(func_def_3,type,
vSIGMA:
!>[X0: $tType] : ( ( X0 > $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,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_9,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_12,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_14,type,
sK1: ( ( a > $o ) > a ) > a > $o ).
thf(func_def_15,type,
sK2: ( ( a > $o ) > a ) > a ).
thf(func_def_16,type,
sK3: ( a > $o ) > a ).
thf(func_def_17,type,
sK4: ( a > $o ) > $o ).
thf(func_def_18,type,
sK5: ( ( a > $o ) > a ) > a > $o ).
thf(func_def_19,type,
sK6: ( ( a > $o ) > a ) > a ).
thf(func_def_20,type,
sK7: ( ( a > $o ) > $o ) > ( a > $o ) > a ).
thf(func_def_21,type,
sK8: ( ( a > $o ) > $o ) > a > $o ).
thf(func_def_22,type,
sK9: a ).
thf(f1,conjecture,
( ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ? [X2: a] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) )
<=> ! [X3: ( a > $o ) > $o] :
( ! [X1: a > $o] :
( ( X3 @ X1 )
=> ? [X2: a] : ( X1 @ X2 ) )
=> ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ( X3 @ X1 )
=> ( X1 @ ( X0 @ X1 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cTHM541) ).
thf(f2,negated_conjecture,
~ ( ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ? [X2: a] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) )
<=> ! [X3: ( a > $o ) > $o] :
( ! [X1: a > $o] :
( ( X3 @ X1 )
=> ? [X2: a] : ( X1 @ X2 ) )
=> ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ( X3 @ X1 )
=> ( X1 @ ( X0 @ X1 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ( ? [X0: ( a > $o ) > a] :
! [X1: a > $o] :
( ? [X2: a] : ( X1 @ X2 )
=> ( X1 @ ( X0 @ X1 ) ) )
<=> ! [X3: ( a > $o ) > $o] :
( ! [X4: a > $o] :
( ( X3 @ X4 )
=> ? [X5: a] : ( X4 @ X5 ) )
=> ? [X6: ( a > $o ) > a] :
! [X7: a > $o] :
( ( X3 @ X7 )
=> ( X7 @ ( X6 @ X7 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( ( ( ?? @ ( ( a > $o ) > a )
@ ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] : ( Y1 @ Y2 ) )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
!= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( ?? @ a
@ ^ [Y2: a] : ( Y1 @ Y2 ) ) ) )
=> ( ?? @ ( ( a > $o ) > a )
@ ^ [Y1: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( ( ( ?? @ ( ( a > $o ) > a )
@ ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a
@ ^ [Y2: a] : ( Y1 @ Y2 ) )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
!= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( ?? @ a
@ ^ [Y2: a] : ( Y1 @ Y2 ) ) ) )
=> ( ?? @ ( ( a > $o ) > a )
@ ^ [Y1: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(cnf_transformation,[],[f4]) ).
thf(f8,plain,
( ( ( ?? @ ( ( a > $o ) > a )
@ ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
!= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( ?? @ a @ Y1 ) ) )
=> ( ?? @ ( ( a > $o ) > a )
@ ^ [Y1: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
= $true ),
inference(beta-eta_normalization,[],[f5]) ).
thf(f9,plain,
( $false
= ( ( ?? @ ( ( a > $o ) > a )
@ ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( ?? @ a @ Y1 ) ) )
=> ( ?? @ ( ( a > $o ) > a )
@ ^ [Y1: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) ),
inference(not_proxy_clausification,[],[f8]) ).
thf(f10,plain,
( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( ?? @ a @ Y1 ) ) )
=> ( ?? @ ( ( a > $o ) > a )
@ ^ [Y1: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
!= ( ?? @ ( ( a > $o ) > a )
@ ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ),
inference(iff_proxy_clausification,[],[f9]) ).
thf(f11,plain,
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( ?? @ a @ Y1 ) ) )
=> ( ?? @ ( ( a > $o ) > a )
@ ^ [Y1: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ( ( ?? @ ( ( a > $o ) > a )
@ ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
= $true ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f12,plain,
( ( $false
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( ?? @ a @ Y1 ) ) )
=> ( ?? @ ( ( a > $o ) > a )
@ ^ [Y1: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
| ( $false
= ( ?? @ ( ( a > $o ) > a )
@ ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ) ),
inference(xor_proxy_clausification,[],[f10]) ).
thf(f14,definition,
( spl0_1
<=> ( $false
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( ?? @ a @ Y1 ) ) )
=> ( ?? @ ( ( a > $o ) > a )
@ ^ [Y1: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_1])],[avatar_definition]) ).
thf(f16,plain,
( ( $false
= ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( ?? @ a @ Y1 ) ) )
=> ( ?? @ ( ( a > $o ) > a )
@ ^ [Y1: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(avatar_component_clause,[],[f14]) ).
thf(f18,definition,
( spl0_2
<=> ( $false
= ( ?? @ ( ( a > $o ) > a )
@ ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_2])],[avatar_definition]) ).
thf(f20,plain,
( ( $false
= ( ?? @ ( ( a > $o ) > a )
@ ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_2 ),
inference(avatar_component_clause,[],[f18]) ).
thf(f21,plain,
( spl0_1
| spl0_2 ),
inference(avatar_split_clause,[],[f12,f18,f14]) ).
thf(f23,definition,
( spl0_3
<=> ( ( ?? @ ( ( a > $o ) > a )
@ ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_3])],[avatar_definition]) ).
thf(f25,plain,
( ( ( ?? @ ( ( a > $o ) > a )
@ ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
= $true )
| ~ spl0_3 ),
inference(avatar_component_clause,[],[f23]) ).
thf(f27,definition,
( spl0_4
<=> ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( ?? @ a @ Y1 ) ) )
=> ( ?? @ ( ( a > $o ) > a )
@ ^ [Y1: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_4])],[avatar_definition]) ).
thf(f29,plain,
( ( ( !! @ ( ( a > $o ) > $o )
@ ^ [Y0: ( a > $o ) > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( ?? @ a @ Y1 ) ) )
=> ( ?? @ ( ( a > $o ) > a )
@ ^ [Y1: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f30,plain,
( spl0_3
| spl0_4 ),
inference(avatar_split_clause,[],[f11,f27,f23]) ).
thf(f31,plain,
( ! [X1: ( a > $o ) > a] :
( ( ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) )
@ X1 )
= $false )
| ~ spl0_2 ),
inference(pi_proxy_clausification,[],[f20]) ).
thf(f32,plain,
( ! [X1: ( a > $o ) > a] :
( $false
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ?? @ a @ Y0 )
=> ( Y0 @ ( X1 @ Y0 ) ) ) ) )
| ~ spl0_2 ),
inference(beta-eta_normalization,[],[f31]) ).
thf(f33,plain,
( ! [X1: ( a > $o ) > a] :
( ( ^ [Y0: a > $o] :
( ( ?? @ a @ Y0 )
=> ( Y0 @ ( X1 @ Y0 ) ) )
@ ( sK1 @ X1 ) )
= $false )
| ~ spl0_2 ),
inference(sigma_proxy_clausification,[],[f32]) ).
thf(f34,plain,
( ! [X1: ( a > $o ) > a] :
( ( ( ?? @ a @ ( sK1 @ X1 ) )
=> ( sK1 @ X1 @ ( X1 @ ( sK1 @ X1 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(beta-eta_normalization,[],[f33]) ).
thf(f36,plain,
( ! [X1: ( a > $o ) > a] :
( ( ?? @ a @ ( sK1 @ X1 ) )
= $true )
| ~ spl0_2 ),
inference(imp_proxy_clausification,[],[f34]) ).
thf(f38,plain,
( ! [X0: ( a > $o ) > a] :
( ( $true
=> ( sK1 @ X0 @ ( X0 @ ( sK1 @ X0 ) ) ) )
= $false )
| ~ spl0_2 ),
inference(constrained_superposition,[],[f34,f36]) ).
thf(f44,plain,
( ( ( ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ?? @ a @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) )
@ sK3 )
= $true )
| ~ spl0_3 ),
inference(sigma_proxy_clausification,[],[f25]) ).
thf(f45,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ?? @ a @ Y0 )
=> ( Y0 @ ( sK3 @ Y0 ) ) ) )
= $true )
| ~ spl0_3 ),
inference(beta-eta_normalization,[],[f44]) ).
thf(f46,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_3 ),
inference(forward_demodulation,[],[f45,f32]) ).
thf(f47,plain,
( $false
| ~ spl0_2
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f46]) ).
thf(f48,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f47]) ).
thf(f50,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ?? @ a @ Y0 )
=> ( Y0 @ ( sK3 @ Y0 ) ) )
@ X1 )
= $true )
| ~ spl0_3 ),
inference(pi_proxy_clausification,[],[f45]) ).
thf(f51,plain,
( ! [X1: a > $o] :
( ( ( ?? @ a @ X1 )
=> ( X1 @ ( sK3 @ X1 ) ) )
= $true )
| ~ spl0_3 ),
inference(beta-eta_normalization,[],[f50]) ).
thf(f53,plain,
( ( $false
= ( ^ [Y0: ( a > $o ) > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( ?? @ a @ Y1 ) ) )
=> ( ?? @ ( ( a > $o ) > a )
@ ^ [Y1: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) )
@ sK4 ) )
| ~ spl0_1 ),
inference(sigma_proxy_clausification,[],[f16]) ).
thf(f54,plain,
( ( $false
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK4 @ Y0 )
=> ( ?? @ a @ Y0 ) ) )
=> ( ?? @ ( ( a > $o ) > a )
@ ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( sK4 @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) ) )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f55,plain,
( ( $false
= ( ?? @ ( ( a > $o ) > a )
@ ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( sK4 @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) )
| ~ spl0_1 ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f56,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK4 @ Y0 )
=> ( ?? @ a @ Y0 ) ) )
= $true )
| ~ spl0_1 ),
inference(imp_proxy_clausification,[],[f54]) ).
thf(f57,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( sK4 @ Y0 )
=> ( ?? @ a @ Y0 ) )
@ X1 )
= $true )
| ~ spl0_1 ),
inference(pi_proxy_clausification,[],[f56]) ).
thf(f58,plain,
( ! [X1: a > $o] :
( ( ( sK4 @ X1 )
=> ( ?? @ a @ X1 ) )
= $true )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f57]) ).
thf(f60,plain,
( ! [X1: ( a > $o ) > a] :
( ( ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( sK4 @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) )
@ X1 )
= $false )
| ~ spl0_1 ),
inference(pi_proxy_clausification,[],[f55]) ).
thf(f61,plain,
( ! [X1: ( a > $o ) > a] :
( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( sK4 @ Y0 )
=> ( Y0 @ ( X1 @ Y0 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f60]) ).
thf(f62,plain,
( ! [X1: ( a > $o ) > a] :
( $false
= ( ^ [Y0: a > $o] :
( ( sK4 @ Y0 )
=> ( Y0 @ ( X1 @ Y0 ) ) )
@ ( sK5 @ X1 ) ) )
| ~ spl0_1 ),
inference(sigma_proxy_clausification,[],[f61]) ).
thf(f63,plain,
( ! [X1: ( a > $o ) > a] :
( ( ( sK4 @ ( sK5 @ X1 ) )
=> ( sK5 @ X1 @ ( X1 @ ( sK5 @ X1 ) ) ) )
= $false )
| ~ spl0_1 ),
inference(beta-eta_normalization,[],[f62]) ).
thf(f64,plain,
( ! [X1: ( a > $o ) > a] :
( ( sK5 @ X1 @ ( X1 @ ( sK5 @ X1 ) ) )
= $false )
| ~ spl0_1 ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f65,plain,
( ! [X1: ( a > $o ) > a] :
( ( sK4 @ ( sK5 @ X1 ) )
= $true )
| ~ spl0_1 ),
inference(imp_proxy_clausification,[],[f63]) ).
thf(f67,plain,
( ! [X0: ( a > $o ) > a] :
( $true
= ( $true
=> ( ?? @ a @ ( sK5 @ X0 ) ) ) )
| ~ spl0_1 ),
inference(constrained_superposition,[],[f58,f65]) ).
thf(f68,plain,
( ! [X0: ( a > $o ) > a] :
( ( ?? @ a @ ( sK5 @ X0 ) )
= $true )
| ~ spl0_1 ),
inference(boolean_simplification,[],[f67]) ).
thf(f76,plain,
( ( ( ( ?? @ a @ ( sK5 @ sK3 ) )
=> $false )
= $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(constrained_superposition,[],[f51,f64]) ).
thf(f77,plain,
( ( ( ~ ( ?? @ a @ ( sK5 @ sK3 ) ) )
= $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(boolean_simplification,[],[f76]) ).
thf(f79,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(forward_demodulation,[],[f77,f68]) ).
thf(f80,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_3 ),
inference(boolean_simplification,[],[f79]) ).
thf(f81,plain,
( $false
| ~ spl0_1
| ~ spl0_3 ),
inference(trivial_inequality_removal,[],[f80]) ).
thf(f82,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(avatar_contradiction_clause,[],[f81]) ).
thf(f88,plain,
( ! [X0: ( a > $o ) > a] :
( ( sK1 @ X0 @ ( X0 @ ( sK1 @ X0 ) ) )
= $false )
| ~ spl0_2 ),
inference(boolean_simplification,[],[f38]) ).
thf(f104,plain,
( ! [X1: ( a > $o ) > $o] :
( ( ^ [Y0: ( a > $o ) > $o] :
( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( Y0 @ Y1 )
=> ( ?? @ a @ Y1 ) ) )
=> ( ?? @ ( ( a > $o ) > a )
@ ^ [Y1: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( Y0 @ Y2 )
=> ( Y2 @ ( Y1 @ Y2 ) ) ) ) ) )
@ X1 )
= $true )
| ~ spl0_4 ),
inference(pi_proxy_clausification,[],[f29]) ).
thf(f105,plain,
( ! [X1: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
=> ( ?? @ a @ Y0 ) ) )
=> ( ?? @ ( ( a > $o ) > a )
@ ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) ) ) )
= $true )
| ~ spl0_4 ),
inference(beta-eta_normalization,[],[f104]) ).
thf(f106,plain,
( ! [X1: ( a > $o ) > $o] :
( ( ( ?? @ ( ( a > $o ) > a )
@ ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) ) )
= $true )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
=> ( ?? @ a @ Y0 ) ) )
= $false ) )
| ~ spl0_4 ),
inference(imp_proxy_clausification,[],[f105]) ).
thf(f107,plain,
( ! [X1: ( a > $o ) > $o] :
( ( ( ^ [Y0: ( a > $o ) > a] :
( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( X1 @ Y1 )
=> ( Y1 @ ( Y0 @ Y1 ) ) ) )
@ ( sK7 @ X1 ) )
= $true )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
=> ( ?? @ a @ Y0 ) ) )
= $false ) )
| ~ spl0_4 ),
inference(sigma_proxy_clausification,[],[f106]) ).
thf(f108,plain,
( ! [X1: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
=> ( Y0 @ ( sK7 @ X1 @ Y0 ) ) ) )
= $true )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
=> ( ?? @ a @ Y0 ) ) )
= $false ) )
| ~ spl0_4 ),
inference(beta-eta_normalization,[],[f107]) ).
thf(f109,plain,
( ! [X2: a > $o,X1: ( a > $o ) > $o] :
( ( ( ^ [Y0: a > $o] :
( ( X1 @ Y0 )
=> ( Y0 @ ( sK7 @ X1 @ Y0 ) ) )
@ X2 )
= $true )
| ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
=> ( ?? @ a @ Y0 ) ) )
= $false ) )
| ~ spl0_4 ),
inference(pi_proxy_clausification,[],[f108]) ).
thf(f110,plain,
( ! [X2: a > $o,X1: ( a > $o ) > $o] :
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( X1 @ Y0 )
=> ( ?? @ a @ Y0 ) ) )
= $false )
| ( $true
= ( ( X1 @ X2 )
=> ( X2 @ ( sK7 @ X1 @ X2 ) ) ) ) )
| ~ spl0_4 ),
inference(beta-eta_normalization,[],[f109]) ).
thf(f111,plain,
( ! [X2: a > $o,X1: ( a > $o ) > $o] :
( ( $true
= ( ( X1 @ X2 )
=> ( X2 @ ( sK7 @ X1 @ X2 ) ) ) )
| ( ( ^ [Y0: a > $o] :
( ( X1 @ Y0 )
=> ( ?? @ a @ Y0 ) )
@ ( sK8 @ X1 ) )
= $false ) )
| ~ spl0_4 ),
inference(sigma_proxy_clausification,[],[f110]) ).
thf(f112,plain,
( ! [X2: a > $o,X1: ( a > $o ) > $o] :
( ( $false
= ( ( X1 @ ( sK8 @ X1 ) )
=> ( ?? @ a @ ( sK8 @ X1 ) ) ) )
| ( $true
= ( ( X1 @ X2 )
=> ( X2 @ ( sK7 @ X1 @ X2 ) ) ) ) )
| ~ spl0_4 ),
inference(beta-eta_normalization,[],[f111]) ).
thf(f114,plain,
( ! [X2: a > $o,X1: ( a > $o ) > $o] :
( ( $true
= ( ( X1 @ X2 )
=> ( X2 @ ( sK7 @ X1 @ X2 ) ) ) )
| ( $true
= ( X1 @ ( sK8 @ X1 ) ) ) )
| ~ spl0_4 ),
inference(imp_proxy_clausification,[],[f112]) ).
thf(f117,plain,
( ! [X0: ( a > $o ) > a] :
( ( $true
= ( ?? @ a @ ( sK8 @ ?? @ a ) ) )
| ( ( $true
=> ( sK1 @ X0 @ ( sK7 @ ?? @ a @ ( sK1 @ X0 ) ) ) )
= $true ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(constrained_superposition,[],[f114,f36]) ).
thf(f119,plain,
( ! [X0: ( a > $o ) > a] :
( ( $true
= ( ?? @ a @ ( sK8 @ ?? @ a ) ) )
| ( ( sK1 @ X0 @ ( sK7 @ ?? @ a @ ( sK1 @ X0 ) ) )
= $true ) )
| ~ spl0_2
| ~ spl0_4 ),
inference(boolean_simplification,[],[f117]) ).
thf(f121,definition,
( spl0_5
<=> ! [X0: ( a > $o ) > a] :
( ( sK1 @ X0 @ ( sK7 @ ?? @ a @ ( sK1 @ X0 ) ) )
= $true ) ),
introduced(definition,[new_symbols(definition,[spl0_5])],[avatar_definition]) ).
thf(f122,plain,
( ! [X0: ( a > $o ) > a] :
( ( sK1 @ X0 @ ( sK7 @ ?? @ a @ ( sK1 @ X0 ) ) )
= $true )
| ~ spl0_5 ),
inference(avatar_component_clause,[],[f121]) ).
thf(f124,definition,
( spl0_6
<=> ( $true
= ( ?? @ a @ ( sK8 @ ?? @ a ) ) ) ),
introduced(definition,[new_symbols(definition,[spl0_6])],[avatar_definition]) ).
thf(f126,plain,
( ( $true
= ( ?? @ a @ ( sK8 @ ?? @ a ) ) )
| ~ spl0_6 ),
inference(avatar_component_clause,[],[f124]) ).
thf(f127,plain,
( spl0_5
| spl0_6
| ~ spl0_2
| ~ spl0_4 ),
inference(avatar_split_clause,[],[f119,f27,f18,f124,f121]) ).
thf(f145,plain,
( ! [X0: a > $o] :
( ( $false
= ( $true
=> $true ) )
| ( $true
= ( ( ?? @ a @ X0 )
=> ( X0 @ ( sK7 @ ?? @ a @ X0 ) ) ) ) )
| ~ spl0_4
| ~ spl0_6 ),
inference(constrained_superposition,[],[f112,f126]) ).
thf(f146,plain,
( ! [X0: a > $o] :
( ( $true
= ( ( ?? @ a @ X0 )
=> ( X0 @ ( sK7 @ ?? @ a @ X0 ) ) ) )
| ( $false = $true ) )
| ~ spl0_4
| ~ spl0_6 ),
inference(boolean_simplification,[],[f145]) ).
thf(f147,plain,
( ! [X0: a > $o] :
( $true
= ( ( ?? @ a @ X0 )
=> ( X0 @ ( sK7 @ ?? @ a @ X0 ) ) ) )
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f146]) ).
thf(f152,plain,
( ( ( ( ?? @ a @ ( sK1 @ ( sK7 @ ?? @ a ) ) )
=> $false )
= $true )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(constrained_superposition,[],[f147,f88]) ).
thf(f158,plain,
( ( ( ~ ( ?? @ a @ ( sK1 @ ( sK7 @ ?? @ a ) ) ) )
= $true )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(boolean_simplification,[],[f152]) ).
thf(f160,plain,
( ( ( ~ $true ) = $true )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(forward_demodulation,[],[f158,f36]) ).
thf(f161,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(boolean_simplification,[],[f160]) ).
thf(f162,plain,
( $false
| ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(trivial_inequality_removal,[],[f161]) ).
thf(f163,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(avatar_contradiction_clause,[],[f162]) ).
thf(f171,plain,
( ( $false = $true )
| ~ spl0_2
| ~ spl0_5 ),
inference(constrained_superposition,[],[f122,f88]) ).
thf(f176,plain,
( $false
| ~ spl0_2
| ~ spl0_5 ),
inference(trivial_inequality_removal,[],[f171]) ).
thf(f177,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(avatar_contradiction_clause,[],[f176]) ).
thf(f195,plain,
( ( $false = $true )
| ~ spl0_1
| ~ spl0_4 ),
inference(forward_demodulation,[],[f54,f105]) ).
thf(f196,plain,
( $false
| ~ spl0_1
| ~ spl0_4 ),
inference(trivial_inequality_removal,[],[f195]) ).
thf(f197,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(avatar_contradiction_clause,[],[f196]) ).
cnf(s1,plain,
( spl0_1
| spl0_2 ),
inference(sat_conversion,[],[f21]) ).
cnf(s2,plain,
( spl0_3
| spl0_4 ),
inference(sat_conversion,[],[f30]) ).
cnf(s3,plain,
( ~ spl0_2
| ~ spl0_3 ),
inference(sat_conversion,[],[f48]) ).
cnf(s4,plain,
( ~ spl0_1
| ~ spl0_3 ),
inference(sat_conversion,[],[f82]) ).
cnf(s5,plain,
( ~ spl0_2
| ~ spl0_4
| spl0_5
| spl0_6 ),
inference(sat_conversion,[],[f127]) ).
cnf(s7,plain,
( ~ spl0_2
| ~ spl0_4
| ~ spl0_6 ),
inference(sat_conversion,[],[f163]) ).
cnf(s9,plain,
( ~ spl0_2
| ~ spl0_5 ),
inference(sat_conversion,[],[f177]) ).
cnf(s11,plain,
( ~ spl0_1
| ~ spl0_4 ),
inference(sat_conversion,[],[f197]) ).
cnf(s12,plain,
~ spl0_2,
inference(rat,[],[s5,s7,s2,s3,s9]) ).
cnf(s13,plain,
spl0_1,
inference(rat,[],[s1,s12]) ).
cnf(s14,plain,
~ spl0_4,
inference(rat,[],[s11,s13]) ).
cnf(s15,plain,
~ spl0_3,
inference(rat,[],[s4,s13]) ).
cnf(s16,plain,
$false,
inference(rat,[],[s2,s14,s15]) ).
thf(f198,plain,
$false,
inference(avatar_sat_refutation,[],[s16]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : LCL731^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 % Computer : n013.cluster.edu
% 0.11/0.27 % Model : x86_64 x86_64
% 0.11/0.27 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.27 % Memory : 8046.5625MB
% 0.11/0.27 % OS : Linux 6.8.0-71-generic
% 0.11/0.27 % CPULimit : 300
% 0.11/0.27 % WCLimit : 300
% 0.11/0.27 % DateTime : Tue Sep 29 10:03:21 UTC 2026
% 0.11/0.27 % CPUTime :
% 0.11/0.27 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM
% 0.27/0.32 Running higher-order theorem proving
% 0.27/0.33 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
% 0.34/0.48 % (1893557)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.34/0.48 % (1893569)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=490807645:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.34/0.48 % (1893564)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3121240345:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.34/0.48 % (1893570)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.34/0.48 % (1893570)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
% 0.34/0.48 % (1893567)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=563606146: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)
% 0.34/0.48 % (1893565)lrs+10_16_si=on:nwc=1.5:random_seed=3312576572:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.34/0.48 % (1893568)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3240122161:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.34/0.48 % (1893570)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=3354149014:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.34/0.48 % (1893566)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=889767917:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.34/0.48 % (1893566)Instruction limit reached!
% 0.34/0.48 % (1893566)------------------------------
% 0.34/0.48 % (1893566)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.48 % (1893566)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.48 % (1893566)CaDiCaL version: 2.1.3
% 0.34/0.48 % (1893566)Termination reason: Instruction limit
% 0.34/0.48 % (1893566)Termination phase: Saturation
% 0.34/0.48 % (1893566)Time elapsed: 0.004 s
% 0.34/0.48 % (1893566)Peak memory usage: 12 MB
% 0.34/0.48 % (1893566)Instructions burned: 3 (million)
% 0.34/0.48 % (1893570)Refutation not found, incomplete strategy
% 0.34/0.48 % (1893570)------------------------------
% 0.34/0.48 % (1893570)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.48 % (1893570)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.48 % (1893570)CaDiCaL version: 2.1.3
% 0.34/0.48 % (1893570)Termination reason: Refutation not found, incomplete strategy
% 0.34/0.48 % (1893570)Time elapsed: 0.009 s
% 0.34/0.48 % (1893570)Peak memory usage: 12 MB
% 0.34/0.48 % (1893570)Instructions burned: 8 (million)
% 0.34/0.48 % (1893570)------------------------------
% 0.34/0.48 % (1893570)------------------------------
% 0.34/0.48 % (1893565)Instruction limit reached!
% 0.34/0.48 % (1893565)------------------------------
% 0.34/0.48 % (1893565)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.48 % (1893565)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.48 % (1893565)CaDiCaL version: 2.1.3
% 0.34/0.48 % (1893565)Termination reason: Instruction limit
% 0.34/0.48 % (1893565)Termination phase: Saturation
% 0.34/0.48 % (1893565)Time elapsed: 0.019 s
% 0.34/0.48 % (1893565)Peak memory usage: 12 MB
% 0.34/0.48 % (1893565)Instructions burned: 19 (million)
% 0.34/0.48 % (1893569)Instruction limit reached!
% 0.34/0.48 % (1893569)------------------------------
% 0.34/0.48 % (1893569)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.48 % (1893568)Instruction limit reached!
% 0.34/0.48 % (1893568)------------------------------
% 0.34/0.48 % (1893568)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.48 % (1893569)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.48 % (1893568)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.48 % (1893568)CaDiCaL version: 2.1.3
% 0.34/0.48 % (1893569)CaDiCaL version: 2.1.3
% 0.34/0.48 % (1893569)Termination reason: Instruction limit
% 0.34/0.48 % (1893569)Termination phase: Saturation
% 0.34/0.48 % (1893569)Time elapsed: 0.037 s
% 0.34/0.49 % (1893568)Termination reason: Instruction limit
% 0.34/0.49 % (1893568)Termination phase: Saturation
% 0.34/0.49 % (1893568)Time elapsed: 0.023 s
% 0.34/0.49 % (1893568)Peak memory usage: 12 MB
% 0.34/0.49 % (1893568)Instructions burned: 24 (million)
% 0.34/0.49 % (1893569)Peak memory usage: 13 MB
% 0.34/0.49 % (1893569)Instructions burned: 76 (million)
% 0.34/0.49 % (1893580)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.34/0.49 % (1893582)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
% 0.34/0.49 % (1893582)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.34/0.49 % (1893578)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=2567272145:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.34/0.49 % (1893579)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=346024647:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.34/0.49 % (1893582)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2546892606:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.34/0.49 % (1893580)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=2426261175:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.34/0.49 % (1893578)Instruction limit reached!
% 0.34/0.49 % (1893578)------------------------------
% 0.34/0.49 % (1893578)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.49 % (1893578)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.49 % (1893578)CaDiCaL version: 2.1.3
% 0.34/0.49 % (1893578)Termination reason: Instruction limit
% 0.34/0.49 % (1893578)Termination phase: Saturation
% 0.34/0.49 % (1893578)Time elapsed: 0.003 s
% 0.34/0.49 % (1893578)Peak memory usage: 12 MB
% 0.34/0.49 % (1893578)Instructions burned: 2 (million)
% 0.34/0.49 % (1893579)Instruction limit reached!
% 0.34/0.49 % (1893579)------------------------------
% 0.34/0.49 % (1893579)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.49 % (1893579)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.49 % (1893579)CaDiCaL version: 2.1.3
% 0.34/0.49 % (1893579)Termination reason: Instruction limit
% 0.34/0.49 % (1893579)Termination phase: Saturation
% 0.34/0.49 % (1893579)Time elapsed: 0.006 s
% 0.34/0.49 % (1893579)Peak memory usage: 12 MB
% 0.34/0.49 % (1893579)Instructions burned: 5 (million)
% 0.34/0.49 % (1893580)Instruction limit reached!
% 0.34/0.49 % (1893580)------------------------------
% 0.34/0.49 % (1893580)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.49 % (1893580)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.49 % (1893580)CaDiCaL version: 2.1.3
% 0.34/0.49 % (1893580)Termination reason: Instruction limit
% 0.34/0.49 % (1893580)Termination phase: Saturation
% 0.34/0.49 % (1893580)Time elapsed: 0.005 s
% 0.34/0.49 % (1893580)Peak memory usage: 12 MB
% 0.34/0.49 % (1893580)Instructions burned: 9 (million)
% 0.34/0.49 % (1893582)Instruction limit reached!
% 0.34/0.49 % (1893582)------------------------------
% 0.34/0.49 % (1893582)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.49 % (1893582)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.49 % (1893582)CaDiCaL version: 2.1.3
% 0.34/0.49 % (1893582)Termination reason: Instruction limit
% 0.34/0.49 % (1893582)Termination phase: Saturation
% 0.34/0.49 % (1893582)Time elapsed: 0.013 s
% 0.34/0.49 % (1893582)Peak memory usage: 12 MB
% 0.34/0.49 % (1893582)Instructions burned: 28 (million)
% 0.34/0.49 % (1893581)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=178012602:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.34/0.49 % (1893564)Instruction limit reached!
% 0.34/0.49 % (1893564)------------------------------
% 0.34/0.49 % (1893564)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.49 % (1893564)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.49 % (1893564)CaDiCaL version: 2.1.3
% 0.34/0.49 % (1893564)Termination reason: Instruction limit
% 0.34/0.49 % (1893564)Termination phase: Saturation
% 0.34/0.49 % (1893564)Time elapsed: 0.073 s
% 0.34/0.49 % (1893564)Peak memory usage: 12 MB
% 0.34/0.49 % (1893564)Instructions burned: 88 (million)
% 0.34/0.49 % (1893581)Instruction limit reached!
% 0.34/0.49 % (1893581)------------------------------
% 0.34/0.49 % (1893581)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.49 % (1893581)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.49 % (1893581)CaDiCaL version: 2.1.3
% 0.34/0.49 % (1893581)Termination reason: Instruction limit
% 0.34/0.49 % (1893581)Termination phase: Saturation
% 0.34/0.49 % (1893581)Time elapsed: 0.014 s
% 0.34/0.49 % (1893581)Peak memory usage: 12 MB
% 0.34/0.49 % (1893581)Instructions burned: 13 (million)
% 0.34/0.49 % (1893591)WARNING Broken Constraint: if positive_literal_split_queue_ratios(1,32) has been set then positive_literal_split_queue(off) is equal to on
% 0.34/0.49 % (1893590)lrs+10_1_si=on:cs=on:random_seed=3276448226:i=8:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/8Mi)
% 0.34/0.49 % (1893589)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=3971003899:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.34/0.49 % (1893591)ott+1002_20_sil=128000:cnfonf=lazy_not_gen_be_off:si=on:sp=unary_frequency:plsqr=1,32:bce=on:uwa=interpreted_only:foolp=on:random_seed=1959665569:i=2:add=on:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.34/0.49 % (1893591)Refutation not found, incomplete strategy
% 0.34/0.49 % (1893591)------------------------------
% 0.34/0.49 % (1893591)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.49 % (1893591)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.49 % (1893591)CaDiCaL version: 2.1.3
% 0.34/0.49 % (1893591)Termination reason: Refutation not found, incomplete strategy
% 0.34/0.49 % (1893591)Time elapsed: 0.002 s
% 0.34/0.49 % (1893591)Peak memory usage: 12 MB
% 0.34/0.49 % (1893591)Instructions burned: 1 (million)
% 0.34/0.49 % (1893591)------------------------------
% 0.34/0.49 % (1893591)------------------------------
% 0.34/0.49 % (1893590)Instruction limit reached!
% 0.34/0.49 % (1893590)------------------------------
% 0.34/0.49 % (1893590)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.49 % (1893590)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.49 % (1893590)CaDiCaL version: 2.1.3
% 0.34/0.49 % (1893590)Termination reason: Instruction limit
% 0.34/0.49 % (1893590)Termination phase: Saturation
% 0.34/0.49 % (1893590)Time elapsed: 0.008 s
% 0.34/0.49 % (1893590)Peak memory usage: 12 MB
% 0.34/0.49 % (1893590)Instructions burned: 8 (million)
% 0.34/0.49 % (1893593)lrs+1002_3:1_sil=128000:e2e=on:si=on:urr=on:uwa=one_side_constant:nwc=1.5:random_seed=3573366238:i=38:bd=all:rtra=on:amm=off:ss=axioms:ntd=on_2999 on theBenchmark for (2999ds/38Mi)
% 0.34/0.49 % (1893596)dis+1002_1_sil=128000:fde=unused:e2e=on:si=on:cbe=off:uwa=off:random_seed=2996730877:hsq=on:st=2:i=25:kws=inv_frequency:rtra=on:ss=axioms:ntd=on_2998 on theBenchmark for (2998ds/25Mi)
% 0.34/0.49 % (1893596)Refutation not found, incomplete strategy
% 0.34/0.49 % (1893596)------------------------------
% 0.34/0.49 % (1893596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.49 % (1893596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.49 % (1893596)CaDiCaL version: 2.1.3
% 0.34/0.49 % (1893596)Termination reason: Refutation not found, incomplete strategy
% 0.34/0.49 % (1893596)Time elapsed: 0.002 s
% 0.34/0.49 % (1893596)Peak memory usage: 12 MB
% 0.34/0.49 % (1893596)Instructions burned: 4 (million)
% 0.34/0.49 % (1893596)------------------------------
% 0.34/0.49 % (1893596)------------------------------
% 0.34/0.49 % (1893595)lrs+1002_1_to=lpo:sil=128000:si=on:sos=on:spb=goal_then_units:uwa=off:random_seed=2584237771:st=2:i=249:sd=1:rtra=on:ss=axioms_2999 on theBenchmark for (2999ds/249Mi)
% 0.34/0.49 % (1893589) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-1893557-1893589"...
% 0.34/0.49 % (1893593)Refutation not found, incomplete strategy
% 0.34/0.49 % (1893593)------------------------------
% 0.34/0.49 % (1893593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.34/0.49 % (1893593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.34/0.49 % (1893593)CaDiCaL version: 2.1.3
% 0.34/0.49 % (1893593)Termination reason: Refutation not found, incomplete strategy
% 0.34/0.49 % (1893593)Time elapsed: 0.012 s
% 0.34/0.49 % (1893593)Peak memory usage: 12 MB
% 0.34/0.49 % (1893593)Instructions burned: 11 (million)
% 0.34/0.49 % (1893593)------------------------------
% 0.34/0.49 % (1893593)------------------------------
% 0.34/0.49 % (1893589)...printing done.
% 0.34/0.49 % (1893589)Refutation found. Thanks to Tanya!
% 0.34/0.49 % SZS status Theorem for theBenchmark
% 0.34/0.49 % SZS output start Proof for theBenchmark
% See solution above
% 1.07/0.49 % (1893589)------------------------------
% 1.07/0.49 % (1893589)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 1.07/0.49 % (1893589)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 1.07/0.49 % (1893589)CaDiCaL version: 2.1.3
% 1.07/0.49 % (1893589)Termination reason: Refutation
% 1.07/0.49 % (1893589)Time elapsed: 0.026 s
% 1.07/0.49 % (1893589)Peak memory usage: 13 MB
% 1.07/0.49 % (1893589)Instructions burned: 24 (million)
% 1.07/0.49 % (1893557)Success in time 0.141 s
% 1.07/0.49 % Vampire exiting
%------------------------------------------------------------------------------