%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV146^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% Computer : n018.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 08:37:54 AM UTC 2026
% Result : Theorem 0.20s 0.32s
% Output : Refutation 0.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 39
% Number of leaves : 3
% Syntax : Number of formulae : 88 ( 11 unt; 0 typ; 2 def)
% Number of atoms : 816 ( 76 equ; 0 cnn)
% Maximal formula atoms : 2 ( 9 avg)
% Number of connectives : 2555 ( 86 ~; 72 |; 213 &;1521 @)
% ( 2 <=>; 311 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 3 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 160 ( 160 >; 0 *; 0 +; 0 <<)
% Number of symbols : 30 ( 26 usr; 13 con; 0-4 aty)
% ( 350 !!; 0 ??; 0 @@+; 0 @@-)
% Number of variables : 444 ( 0 sgn 78 !; 0 ?; 444 :)
% 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,
vPI:
!>[X0: $tType] : ( ( X0 > $o ) > $o ) ).
thf(func_def_3,type,
vAND: $o > $o > $o ).
thf(func_def_4,type,
vIMP: $o > $o > $o ).
thf(func_def_5,type,
db2:
!>[X0: $tType] : X0 ).
thf(func_def_6,type,
db0:
!>[X0: $tType] : X0 ).
thf(func_def_7,type,
db1:
!>[X0: $tType] : X0 ).
thf(func_def_8,type,
db5:
!>[X0: $tType] : X0 ).
thf(func_def_9,type,
vLAM:
!>[X0: $tType,X1: $tType] : ( X1 > X0 > X1 ) ).
thf(func_def_10,type,
db4:
!>[X0: $tType] : X0 ).
thf(func_def_11,type,
db6:
!>[X0: $tType] : X0 ).
thf(func_def_14,type,
vEQ:
!>[X0: $tType] : ( X0 > X0 > $o ) ).
thf(func_def_15,type,
sK0: a > a > $o ).
thf(func_def_17,type,
sK2: a ).
thf(func_def_18,type,
sK3: a ).
thf(func_def_19,type,
sK4: a ).
thf(func_def_20,type,
sK5: a > $o ).
thf(func_def_21,type,
sK6: a ).
thf(func_def_22,type,
sK7: a ).
thf(func_def_23,type,
sK8: a ).
thf(func_def_24,type,
sK9: a ).
thf(func_def_25,type,
sK10: a ).
thf(func_def_26,type,
sK11: a > $o ).
thf(f1,conjecture,
! [X0: a > a > $o] :
( ! [X2: a,X6: a,X1: a] :
( ( ! [X3: a > $o] :
( ( ! [X4: a,X5: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) )
& ! [X3: a > $o] :
( ( ! [X4: a] :
( ( X0 @ X2 @ X4 )
=> ( X3 @ X4 ) )
& ! [X5: a,X4: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X6 ) ) )
=> ! [X3: a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X6 ) ) )
& ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
=> ! [X3: a > $o] :
( ( ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
& ! [X5: a,X4: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM525_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o] :
( ! [X2: a,X6: a,X1: a] :
( ( ! [X3: a > $o] :
( ( ! [X4: a,X5: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) )
& ! [X3: a > $o] :
( ( ! [X4: a] :
( ( X0 @ X2 @ X4 )
=> ( X3 @ X4 ) )
& ! [X5: a,X4: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X6 ) ) )
=> ! [X3: a > $o] :
( ( ! [X5: a,X4: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X3 @ X4 ) )
& ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X6 ) ) )
& ! [X1: a,X2: a] :
( ( X0 @ X1 @ X2 )
=> ! [X3: a > $o] :
( ( ! [X4: a] :
( ( X0 @ X1 @ X4 )
=> ( X3 @ X4 ) )
& ! [X5: a,X4: a] :
( ( ( X3 @ X5 )
& ( X0 @ X5 @ X4 ) )
=> ( X3 @ X4 ) ) )
=> ( X3 @ X2 ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > a > $o] :
( ! [X1: a,X2: a,X3: a] :
( ( ! [X4: a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( X4 @ X6 )
& ( X0 @ X6 @ X5 ) )
=> ( X4 @ X5 ) )
& ! [X7: a] :
( ( X0 @ X3 @ X7 )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X1 ) )
& ! [X8: a > $o] :
( ( ! [X9: a] :
( ( X0 @ X1 @ X9 )
=> ( X8 @ X9 ) )
& ! [X10: a,X11: a] :
( ( ( X8 @ X10 )
& ( X0 @ X10 @ X11 ) )
=> ( X8 @ X11 ) ) )
=> ( X8 @ X2 ) ) )
=> ! [X12: a > $o] :
( ( ! [X13: a,X14: a] :
( ( ( X12 @ X13 )
& ( X0 @ X13 @ X14 ) )
=> ( X12 @ X14 ) )
& ! [X15: a] :
( ( X0 @ X3 @ X15 )
=> ( X12 @ X15 ) ) )
=> ( X12 @ X2 ) ) )
& ! [X16: a,X17: a] :
( ( X0 @ X16 @ X17 )
=> ! [X18: a > $o] :
( ( ! [X19: a] :
( ( X0 @ X16 @ X19 )
=> ( X18 @ X19 ) )
& ! [X20: a,X21: a] :
( ( ( X18 @ X20 )
& ( X0 @ X20 @ X21 ) )
=> ( X18 @ X21 ) ) )
=> ( X18 @ X17 ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y3 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
( $true
= ( ~ ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y3 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) ) ) ) ),
inference(cnf_transformation,[],[f4]) ).
thf(f8,plain,
( ( !! @ ( a > a > $o )
@ ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y3 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) ) )
= $false ),
inference(not_proxy_clausification,[],[f5]) ).
thf(f9,plain,
( ( ^ [Y0: a > a > $o] :
( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( Y0 @ Y2 @ Y1 )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( Y0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( Y0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y3 @ Y5 )
=> ( Y4 @ Y5 ) ) ) )
=> ( Y4 @ Y2 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y5 @ Y6 )
& ( Y4 @ Y5 ) )
=> ( Y4 @ Y6 ) ) ) ) )
=> ( Y4 @ Y3 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y4: a > $o] :
( ( ( !! @ a
@ ^ [Y5: a] :
( ( Y0 @ Y1 @ Y5 )
=> ( Y4 @ Y5 ) ) )
& ( !! @ a
@ ^ [Y5: a] :
( !! @ a
@ ^ [Y6: a] :
( ( ( Y0 @ Y6 @ Y5 )
& ( Y4 @ Y6 ) )
=> ( Y4 @ Y5 ) ) ) ) )
=> ( Y4 @ Y2 ) ) ) ) ) ) ) )
@ sK0 )
= $false ),
inference(sigma_proxy_clausification,[],[f8]) ).
thf(f12,plain,
( $false
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y1 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK0 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK0 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) ) ) ),
inference(beta-eta_normalization,[],[f9]) ).
thf(f13,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y1 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK0 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
= $false )
| ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK0 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) )
= $false ) ),
inference(and_proxy_clausification,[],[f12]) ).
thf(f15,definition,
( spl1_1
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y1 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK0 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_1])],[avatar_definition]) ).
thf(f17,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y1 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK0 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl1_1 ),
inference(avatar_component_clause,[],[f15]) ).
thf(f19,definition,
( spl1_2
<=> ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK0 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) )
= $false ) ),
introduced(definition,[new_symbols(definition,[spl1_2])],[avatar_definition]) ).
thf(f21,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK0 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) ) )
= $false )
| ~ spl1_2 ),
inference(avatar_component_clause,[],[f19]) ).
thf(f22,plain,
( spl1_1
| spl1_2 ),
inference(avatar_split_clause,[],[f13,f19,f15]) ).
thf(f23,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y2 @ Y4 )
=> ( Y3 @ Y4 ) ) ) )
=> ( Y3 @ Y1 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK0 @ Y4 @ Y5 )
& ( Y3 @ Y4 ) )
=> ( Y3 @ Y5 ) ) ) ) )
=> ( Y3 @ Y2 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y3: a > $o] :
( ( ( !! @ a
@ ^ [Y4: a] :
( ( sK0 @ Y0 @ Y4 )
=> ( Y3 @ Y4 ) ) )
& ( !! @ a
@ ^ [Y4: a] :
( !! @ a
@ ^ [Y5: a] :
( ( ( sK0 @ Y5 @ Y4 )
& ( Y3 @ Y5 ) )
=> ( Y3 @ Y4 ) ) ) ) )
=> ( Y3 @ Y1 ) ) ) ) ) )
@ sK2 )
= $false )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f21]) ).
thf(f24,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK0 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ sK2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK0 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ sK2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK0 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f23]) ).
thf(f25,plain,
( ( ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK0 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ sK2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK0 @ Y3 @ Y4 )
& ( Y2 @ Y3 ) )
=> ( Y2 @ Y4 ) ) ) ) )
=> ( Y2 @ Y1 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ sK2 @ Y3 )
=> ( Y2 @ Y3 ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK0 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK3 )
= $false )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f24]) ).
thf(f26,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK0 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ sK2 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK0 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ sK2 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK0 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK3 ) ) ) ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f25]) ).
thf(f27,plain,
( ( ( ^ [Y0: a] :
( ( ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK0 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ sK2 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK0 @ Y2 @ Y3 )
& ( Y1 @ Y2 ) )
=> ( Y1 @ Y3 ) ) ) ) )
=> ( Y1 @ Y0 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ sK2 @ Y2 )
=> ( Y1 @ Y2 ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK0 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) ) )
=> ( Y1 @ sK3 ) ) ) )
@ sK4 )
= $false )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f26]) ).
thf(f28,plain,
( ( $false
= ( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 ) ) ) )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 ) ) ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f27]) ).
thf(f29,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 ) ) )
= $false )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f30,plain,
( ( $true
= ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK3 ) ) )
& ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 ) ) ) ) )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f28]) ).
thf(f31,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) ) )
=> ( Y0 @ sK3 ) )
@ sK5 ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f29]) ).
thf(f32,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK5 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK5 @ Y1 ) )
=> ( sK5 @ Y0 ) ) ) ) )
=> ( sK5 @ sK3 ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f31]) ).
thf(f33,plain,
( ( $false
= ( sK5 @ sK3 ) )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f32]) ).
thf(f34,plain,
( ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK5 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK5 @ Y1 ) )
=> ( sK5 @ Y0 ) ) ) ) )
= $true )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f32]) ).
thf(f39,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK5 @ Y1 ) )
=> ( sK5 @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f40,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK5 @ Y0 ) ) ) )
| ~ spl1_2 ),
inference(and_proxy_clausification,[],[f34]) ).
thf(f51,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK5 @ Y1 ) )
=> ( sK5 @ Y0 ) ) )
@ X1 ) )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f39]) ).
thf(f52,plain,
( ! [X1: a] :
( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK5 @ Y0 ) )
=> ( sK5 @ X1 ) ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f51]) ).
thf(f53,plain,
( ! [X2: a,X1: a] :
( $true
= ( ^ [Y0: a] :
( ( ( sK0 @ Y0 @ X1 )
& ( sK5 @ Y0 ) )
=> ( sK5 @ X1 ) )
@ X2 ) )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f52]) ).
thf(f54,plain,
( ! [X2: a,X1: a] :
( ( ( ( sK0 @ X2 @ X1 )
& ( sK5 @ X2 ) )
=> ( sK5 @ X1 ) )
= $true )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f53]) ).
thf(f80,plain,
( ( $true
= ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 ) ) ) )
| ~ spl1_2 ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f81,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK3 ) ) )
= $true )
| ~ spl1_2 ),
inference(and_proxy_clausification,[],[f30]) ).
thf(f82,plain,
( ! [X1: a > $o] :
( ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ sK2 @ Y1 )
=> ( Y0 @ Y1 ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y1 @ Y2 )
& ( Y0 @ Y1 ) )
=> ( Y0 @ Y2 ) ) ) ) )
=> ( Y0 @ sK4 ) )
@ X1 )
= $true )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f80]) ).
thf(f83,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK2 @ Y0 )
=> ( X1 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y0 @ Y1 )
& ( X1 @ Y0 ) )
=> ( X1 @ Y1 ) ) ) ) )
=> ( X1 @ sK4 ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f82]) ).
thf(f85,plain,
( ! [X1: a > $o] :
( $true
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ sK4 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK3 ) )
@ X1 ) )
| ~ spl1_2 ),
inference(pi_proxy_clausification,[],[f81]) ).
thf(f86,plain,
( ! [X1: a > $o] :
( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y1 @ Y0 )
& ( X1 @ Y1 ) )
=> ( X1 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK4 @ Y0 )
=> ( X1 @ Y0 ) ) ) )
=> ( X1 @ sK3 ) ) )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f85]) ).
thf(f88,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK5 @ Y1 ) )
=> ( sK5 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK5 @ Y0 ) ) ) )
=> $false ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f86,f33]) ).
thf(f90,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK5 @ Y1 ) )
=> ( sK5 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK5 @ Y0 ) ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f88]) ).
thf(f92,plain,
( ( $true
= ( ~ ( $true
& ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK5 @ Y0 ) ) ) ) ) )
| ~ spl1_2 ),
inference(forward_demodulation,[],[f90,f39]) ).
thf(f93,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK5 @ Y0 ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f92]) ).
thf(f94,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK5 @ Y0 ) ) )
= $false )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f93]) ).
thf(f95,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK0 @ sK4 @ Y0 )
=> ( sK5 @ Y0 ) )
@ sK6 ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f94]) ).
thf(f96,plain,
( ( ( ( sK0 @ sK4 @ sK6 )
=> ( sK5 @ sK6 ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f95]) ).
thf(f97,plain,
( ( $false
= ( sK5 @ sK6 ) )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f96]) ).
thf(f98,plain,
( ( $true
= ( sK0 @ sK4 @ sK6 ) )
| ~ spl1_2 ),
inference(imp_proxy_clausification,[],[f96]) ).
thf(f116,plain,
( ( $true
= ( ( $true
& ( sK5 @ sK4 ) )
=> ( sK5 @ sK6 ) ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f54,f98]) ).
thf(f117,plain,
( ( $true
= ( ( sK5 @ sK4 )
=> ( sK5 @ sK6 ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f116]) ).
thf(f119,plain,
( ( $true
= ( ( sK5 @ sK4 )
=> $false ) )
| ~ spl1_2 ),
inference(forward_demodulation,[],[f117,f97]) ).
thf(f120,plain,
( ( $true
= ( ~ ( sK5 @ sK4 ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f119]) ).
thf(f121,plain,
( ( $false
= ( sK5 @ sK4 ) )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f120]) ).
thf(f128,plain,
( ( $true
= ( ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK5 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK5 @ Y0 ) )
=> ( sK5 @ Y1 ) ) ) ) )
=> $false ) )
| ~ spl1_2 ),
inference(constrained_superposition,[],[f83,f121]) ).
thf(f134,plain,
( ( $true
= ( ~ ( ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK2 @ Y0 )
=> ( sK5 @ Y0 ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK5 @ Y0 ) )
=> ( sK5 @ Y1 ) ) ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f128]) ).
thf(f138,plain,
( ( $true
= ( ~ ( $true
& ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK5 @ Y0 ) )
=> ( sK5 @ Y1 ) ) ) ) ) ) )
| ~ spl1_2 ),
inference(forward_demodulation,[],[f134,f40]) ).
thf(f139,plain,
( ( $true
= ( ~ ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK5 @ Y0 ) )
=> ( sK5 @ Y1 ) ) ) ) ) )
| ~ spl1_2 ),
inference(boolean_simplification,[],[f138]) ).
thf(f248,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK5 @ Y0 ) )
=> ( sK5 @ Y1 ) ) ) )
= $false )
| ~ spl1_2 ),
inference(not_proxy_clausification,[],[f139]) ).
thf(f249,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y0 @ Y1 )
& ( sK5 @ Y0 ) )
=> ( sK5 @ Y1 ) ) )
@ sK7 ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f248]) ).
thf(f250,plain,
( ( ( !! @ a
@ ^ [Y0: a] :
( ( ( sK0 @ sK7 @ Y0 )
& ( sK5 @ sK7 ) )
=> ( sK5 @ Y0 ) ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f249]) ).
thf(f251,plain,
( ( $false
= ( ^ [Y0: a] :
( ( ( sK0 @ sK7 @ Y0 )
& ( sK5 @ sK7 ) )
=> ( sK5 @ Y0 ) )
@ sK8 ) )
| ~ spl1_2 ),
inference(sigma_proxy_clausification,[],[f250]) ).
thf(f252,plain,
( ( ( ( ( sK0 @ sK7 @ sK8 )
& ( sK5 @ sK7 ) )
=> ( sK5 @ sK8 ) )
= $false )
| ~ spl1_2 ),
inference(beta-eta_normalization,[],[f251]) ).
thf(f253,plain,
( ( $true = $false )
| ~ spl1_2 ),
inference(forward_demodulation,[],[f252,f54]) ).
thf(f254,plain,
( $false
| ~ spl1_2 ),
inference(trivial_inequality_removal,[],[f253]) ).
thf(f255,plain,
~ spl1_2,
inference(avatar_contradiction_clause,[],[f254]) ).
thf(f256,plain,
( ( $false
= ( ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ Y1 @ Y0 )
=> ( !! @ ( a > $o )
@ ^ [Y2: a > $o] :
( ( ( !! @ a
@ ^ [Y3: a] :
( !! @ a
@ ^ [Y4: a] :
( ( ( sK0 @ Y4 @ Y3 )
& ( Y2 @ Y4 ) )
=> ( Y2 @ Y3 ) ) ) )
& ( !! @ a
@ ^ [Y3: a] :
( ( sK0 @ Y1 @ Y3 )
=> ( Y2 @ Y3 ) ) ) )
=> ( Y2 @ Y0 ) ) ) ) )
@ sK9 ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f17]) ).
thf(f257,plain,
( ( $false
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ Y0 @ sK9 )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK0 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK9 ) ) ) ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f256]) ).
thf(f258,plain,
( ( $false
= ( ^ [Y0: a] :
( ( sK0 @ Y0 @ sK9 )
=> ( !! @ ( a > $o )
@ ^ [Y1: a > $o] :
( ( ( !! @ a
@ ^ [Y2: a] :
( !! @ a
@ ^ [Y3: a] :
( ( ( sK0 @ Y3 @ Y2 )
& ( Y1 @ Y3 ) )
=> ( Y1 @ Y2 ) ) ) )
& ( !! @ a
@ ^ [Y2: a] :
( ( sK0 @ Y0 @ Y2 )
=> ( Y1 @ Y2 ) ) ) )
=> ( Y1 @ sK9 ) ) ) )
@ sK10 ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f257]) ).
thf(f259,plain,
( ( $false
= ( ( sK0 @ sK10 @ sK9 )
=> ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f258]) ).
thf(f260,plain,
( ( ( !! @ ( a > $o )
@ ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) ) )
= $false )
| ~ spl1_1 ),
inference(imp_proxy_clausification,[],[f259]) ).
thf(f261,plain,
( ( $true
= ( sK0 @ sK10 @ sK9 ) )
| ~ spl1_1 ),
inference(imp_proxy_clausification,[],[f259]) ).
thf(f264,plain,
( ( $false
= ( ^ [Y0: a > $o] :
( ( ( !! @ a
@ ^ [Y1: a] :
( !! @ a
@ ^ [Y2: a] :
( ( ( sK0 @ Y2 @ Y1 )
& ( Y0 @ Y2 ) )
=> ( Y0 @ Y1 ) ) ) )
& ( !! @ a
@ ^ [Y1: a] :
( ( sK0 @ sK10 @ Y1 )
=> ( Y0 @ Y1 ) ) ) )
=> ( Y0 @ sK9 ) )
@ sK11 ) )
| ~ spl1_1 ),
inference(sigma_proxy_clausification,[],[f260]) ).
thf(f265,plain,
( ( $false
= ( ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK11 @ Y1 ) )
=> ( sK11 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK10 @ Y0 )
=> ( sK11 @ Y0 ) ) ) )
=> ( sK11 @ sK9 ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f264]) ).
thf(f266,plain,
( ( ( sK11 @ sK9 )
= $false )
| ~ spl1_1 ),
inference(imp_proxy_clausification,[],[f265]) ).
thf(f267,plain,
( ( $true
= ( ( !! @ a
@ ^ [Y0: a] :
( !! @ a
@ ^ [Y1: a] :
( ( ( sK0 @ Y1 @ Y0 )
& ( sK11 @ Y1 ) )
=> ( sK11 @ Y0 ) ) ) )
& ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK10 @ Y0 )
=> ( sK11 @ Y0 ) ) ) ) )
| ~ spl1_1 ),
inference(imp_proxy_clausification,[],[f265]) ).
thf(f272,plain,
( ( $true
= ( !! @ a
@ ^ [Y0: a] :
( ( sK0 @ sK10 @ Y0 )
=> ( sK11 @ Y0 ) ) ) )
| ~ spl1_1 ),
inference(and_proxy_clausification,[],[f267]) ).
thf(f274,plain,
( ! [X1: a] :
( $true
= ( ^ [Y0: a] :
( ( sK0 @ sK10 @ Y0 )
=> ( sK11 @ Y0 ) )
@ X1 ) )
| ~ spl1_1 ),
inference(pi_proxy_clausification,[],[f272]) ).
thf(f275,plain,
( ! [X1: a] :
( $true
= ( ( sK0 @ sK10 @ X1 )
=> ( sK11 @ X1 ) ) )
| ~ spl1_1 ),
inference(beta-eta_normalization,[],[f274]) ).
thf(f277,plain,
( ( $true
= ( ( sK0 @ sK10 @ sK9 )
=> $false ) )
| ~ spl1_1 ),
inference(constrained_superposition,[],[f275,f266]) ).
thf(f280,plain,
( ( $true
= ( ~ ( sK0 @ sK10 @ sK9 ) ) )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f277]) ).
thf(f284,plain,
( ( $true = ( ~ $true ) )
| ~ spl1_1 ),
inference(forward_demodulation,[],[f280,f261]) ).
thf(f285,plain,
( ( $true = $false )
| ~ spl1_1 ),
inference(boolean_simplification,[],[f284]) ).
thf(f286,plain,
( $false
| ~ spl1_1 ),
inference(trivial_inequality_removal,[],[f285]) ).
thf(f287,plain,
~ spl1_1,
inference(avatar_contradiction_clause,[],[f286]) ).
cnf(s1,plain,
( spl1_1
| spl1_2 ),
inference(sat_conversion,[],[f22]) ).
cnf(s2,plain,
~ spl1_2,
inference(sat_conversion,[],[f255]) ).
cnf(s4,plain,
~ spl1_1,
inference(sat_conversion,[],[f287]) ).
cnf(s5,plain,
$false,
inference(rat,[],[s1,s2,s4]) ).
thf(f288,plain,
$false,
inference(avatar_sat_refutation,[],[s5]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV146^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.05 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.18 % Computer : n018.cluster.edu
% 0.08/0.18 % Model : x86_64 x86_64
% 0.08/0.18 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.18 % Memory : 8046.5625MB
% 0.08/0.18 % OS : Linux 6.8.0-71-generic
% 0.08/0.18 % CPULimit : 300
% 0.08/0.18 % WCLimit : 300
% 0.08/0.18 % DateTime : Tue Sep 29 15:18:26 UTC 2026
% 0.08/0.18 % CPUTime :
% 0.08/0.18 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.08/0.21 Running higher-order theorem proving
% 0.08/0.23 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
% 0.20/0.32 % (208587)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.20/0.32 % (208596)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3753266804:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.20/0.32 % (208594)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=152201907:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.20/0.32 % (208592)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=3831015906:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.20/0.32 % (208593)lrs+10_16_si=on:nwc=1.5:random_seed=3380222821:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.20/0.32 % (208595)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=2534513517: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)
% 0.20/0.32 % (208596)Instruction limit reached!
% 0.20/0.32 % (208596)------------------------------
% 0.20/0.32 % (208596)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (208596)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (208596)CaDiCaL version: 2.1.3
% 0.20/0.32 % (208596)Termination reason: Instruction limit
% 0.20/0.32 % (208596)Termination phase: Saturation
% 0.20/0.32 % (208596)Time elapsed: 0.008 s
% 0.20/0.32 % (208596)Peak memory usage: 12 MB
% 0.20/0.32 % (208596)Instructions burned: 28 (million)
% 0.20/0.32 % (208594)Instruction limit reached!
% 0.20/0.32 % (208594)------------------------------
% 0.20/0.32 % (208594)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (208594)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (208594)CaDiCaL version: 2.1.3
% 0.20/0.32 % (208594)Termination reason: Instruction limit
% 0.20/0.32 % (208594)Termination phase: Saturation
% 0.20/0.32 % (208594)Time elapsed: 0.002 s
% 0.20/0.32 % (208594)Peak memory usage: 11 MB
% 0.20/0.32 % (208594)Instructions burned: 3 (million)
% 0.20/0.32 % (208597)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=4199995677:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.20/0.32 % (208593)Instruction limit reached!
% 0.20/0.32 % (208593)------------------------------
% 0.20/0.32 % (208593)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (208593)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (208593)CaDiCaL version: 2.1.3
% 0.20/0.32 % (208593)Termination reason: Instruction limit
% 0.20/0.32 % (208593)Termination phase: Saturation
% 0.20/0.32 % (208593)Time elapsed: 0.011 s
% 0.20/0.32 % (208593)Peak memory usage: 12 MB
% 0.20/0.32 % (208593)Instructions burned: 18 (million)
% 0.20/0.32 % (208598)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.20/0.32 % (208598)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
% 0.20/0.32 % (208604)dis+10_1024_sil=128000:si=on:sp=unary_first:urr=on:uwa=all:fd=off:random_seed=1605182978:i=2:hud=10:rtra=on_2999 on theBenchmark for (2999ds/2Mi)
% 0.20/0.32 % (208604)Instruction limit reached!
% 0.20/0.32 % (208604)------------------------------
% 0.20/0.32 % (208604)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (208604)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (208604)CaDiCaL version: 2.1.3
% 0.20/0.32 % (208604)Termination reason: Instruction limit
% 0.20/0.32 % (208604)Termination phase: Saturation
% 0.20/0.32 % (208604)Time elapsed: 0.001 s
% 0.20/0.32 % (208604)Peak memory usage: 11 MB
% 0.20/0.32 % (208604)Instructions burned: 3 (million)
% 0.20/0.32 % (208598)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=3481121187:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.20/0.32 % (208605)lrs+1010_2:3_cha=on:si=on:uwa=off:nwc=1:random_seed=3420044307:i=5:fgj=on:av=off:rtra=on:fe=axiom:ntd=on_2999 on theBenchmark for (2999ds/5Mi)
% 0.20/0.32 % (208609)lrs+10_1_sil=128000:si=on:urr=on:slsqc=1:slsq=on:random_seed=697851626:i=12:s2at=2:kws=inv_frequency:bd=all:rtra=on_2999 on theBenchmark for (2999ds/12Mi)
% 0.20/0.32 % (208605)Instruction limit reached!
% 0.20/0.32 % (208605)------------------------------
% 0.20/0.32 % (208605)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (208605)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (208605)CaDiCaL version: 2.1.3
% 0.20/0.32 % (208605)Termination reason: Instruction limit
% 0.20/0.32 % (208605)Termination phase: Saturation
% 0.20/0.32 % (208605)Time elapsed: 0.003 s
% 0.20/0.32 % (208605)Peak memory usage: 11 MB
% 0.20/0.32 % (208605)Instructions burned: 5 (million)
% 0.20/0.32 % (208607)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(5) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.32 % (208609)Instruction limit reached!
% 0.20/0.32 % (208609)------------------------------
% 0.20/0.32 % (208609)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (208609)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (208609)CaDiCaL version: 2.1.3
% 0.20/0.32 % (208609)Termination reason: Instruction limit
% 0.20/0.32 % (208609)Termination phase: Saturation
% 0.20/0.32 % (208609)Time elapsed: 0.004 s
% 0.20/0.32 % (208609)Peak memory usage: 12 MB
% 0.20/0.32 % (208609)Instructions burned: 15 (million)
% 0.20/0.32 % (208607)dis+21_1_to=kbo:sil=128000:plsq=on:plsqc=1:cnfonf=lazy_gen:si=on:plsqr=64,1:uwa=hol:random_seed=308646794:uwa_fpi=on:i=7:fgj=on:hud=10:fsr=off:rtra=on:rawr=on:fsdmm=5_2999 on theBenchmark for (2999ds/7Mi)
% 0.20/0.32 % (208607)Instruction limit reached!
% 0.20/0.32 % (208607)------------------------------
% 0.20/0.32 % (208607)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (208607)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (208607)CaDiCaL version: 2.1.3
% 0.20/0.32 % (208607)Termination reason: Instruction limit
% 0.20/0.32 % (208607)Termination phase: Saturation
% 0.20/0.32 % (208607)Time elapsed: 0.004 s
% 0.20/0.32 % (208607)Peak memory usage: 12 MB
% 0.20/0.32 % (208607)Instructions burned: 8 (million)
% 0.20/0.32 % (208613)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
% 0.20/0.32 % (208613)WARNING Broken Constraint: if forward_subsumption_demodulation_max_matches(1) has been set then forward_subsumption_demodulation(off) is equal to on
% 0.20/0.32 % (208614)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=1133994751:i=86:piset=equals:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/86Mi)
% 0.20/0.32 % (208613)ott+1010_64_tgt=ground:cnfonf=lazy_simp:si=on:lma=off:spb=goal:lcm=predicate:random_seed=2803097979:i=28:s2at=5:piset=not:hud=10:bd=all:av=off:rtra=on:ixr=off:fsdmm=1_2999 on theBenchmark for (2999ds/28Mi)
% 0.20/0.32 % (208592)Instruction limit reached!
% 0.20/0.32 % (208592)------------------------------
% 0.20/0.32 % (208592)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (208592)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (208592)CaDiCaL version: 2.1.3
% 0.20/0.32 % (208592)Termination reason: Instruction limit
% 0.20/0.32 % (208592)Termination phase: Saturation
% 0.20/0.32 % (208592)Time elapsed: 0.047 s
% 0.20/0.32 % (208592)Peak memory usage: 13 MB
% 0.20/0.32 % (208592)Instructions burned: 88 (million)
% 0.20/0.32 % (208597)Instruction limit reached!
% 0.20/0.32 % (208597)------------------------------
% 0.20/0.32 % (208597)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (208597)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (208597)CaDiCaL version: 2.1.3
% 0.20/0.32 % (208597)Termination reason: Instruction limit
% 0.20/0.32 % (208597)Termination phase: Saturation
% 0.20/0.32 % (208597)Time elapsed: 0.042 s
% 0.20/0.32 % (208597)Peak memory usage: 13 MB
% 0.20/0.32 % (208597)Instructions burned: 77 (million)
% 0.20/0.32 % (208614) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-208587-208614"...
% 0.20/0.32 % (208614)...printing done.
% 0.20/0.32 % (208614)Refutation found. Thanks to Tanya!
% 0.20/0.32 % SZS status Theorem for theBenchmark
% 0.20/0.32 % SZS output start Proof for theBenchmark
% See solution above
% 0.20/0.32 % (208614)------------------------------
% 0.20/0.32 % (208614)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.20/0.32 % (208614)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.20/0.32 % (208614)CaDiCaL version: 2.1.3
% 0.20/0.32 % (208614)Termination reason: Refutation
% 0.20/0.32 % (208614)Time elapsed: 0.012 s
% 0.20/0.32 % (208614)Peak memory usage: 13 MB
% 0.20/0.32 % (208614)Instructions burned: 45 (million)
% 0.20/0.32 % (208587)Success in time 0.083 s
% 0.20/0.32 % Vampire exiting
%------------------------------------------------------------------------------