%------------------------------------------------------------------------------
% File : Vampire---5.0.1
% Problem : SEV034^5 : 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 : n011.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 08:37:31 AM UTC 2026
% Result : Theorem 0.24s 0.34s
% Output : Refutation 0.24s
% Verified :
% SZS Type : Refutation
% Derivation depth : 25
% Number of leaves : 5
% Syntax : Number of formulae : 69 ( 17 unt; 0 typ; 4 def)
% Number of atoms : 497 ( 181 equ; 0 cnn)
% Maximal formula atoms : 19 ( 7 avg)
% Number of connectives : 942 ( 115 ~; 101 |; 60 &; 614 @)
% ( 4 <=>; 48 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 5 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 3 ( 2 usr)
% Number of type conns : 49 ( 49 >; 0 *; 0 +; 0 <<)
% Number of symbols : 14 ( 11 usr; 8 con; 0-3 aty)
% Number of variables : 203 ( 0 sgn 185 !; 18 ?; 203 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(type_def_7,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_3,type,
sK0: a > a > $o ).
thf(func_def_4,type,
sK1: a > b > b > $o ).
thf(func_def_5,type,
sK2: a > b ).
thf(func_def_6,type,
sK3: a > b ).
thf(func_def_7,type,
sK4: a ).
thf(func_def_8,type,
sK5: a ).
thf(f1,conjecture,
! [X0: a > a > $o,X1: a > b > b > $o,X3: a > b,X2: a > b] :
( ! [X4: a] :
( ( X0 @ X4 @ X4 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X4 ) ) )
=> ( ! [X4: a,X5: a] :
( ( X0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X2 @ X5 ) ) )
=> ( ( ! [X5: a,X4: a] :
( ( X0 @ X4 @ X5 )
=> ( X0 @ X5 @ X4 ) )
& ( X0 = X0 )
& ! [X6: a,X5: a,X4: a] :
( ( ( X0 @ X5 @ X6 )
& ( X0 @ X4 @ X5 ) )
=> ( X0 @ X4 @ X6 ) ) )
=> ( ! [X5: a,X4: a] :
( ( X0 @ X4 @ X5 )
=> ( ! [X8: b,X7: b,X6: b] :
( ( ( X1 @ X4 @ X8 @ X6 )
& ( X1 @ X4 @ X7 @ X8 ) )
=> ( X1 @ X4 @ X7 @ X6 ) )
& ! [X8: b,X7: b] :
( ( X1 @ X4 @ X7 @ X8 )
=> ( X1 @ X4 @ X8 @ X7 ) )
& ( ( X1 @ X4 )
= ( X1 @ X5 ) ) ) )
=> ! [X5: a,X4: a] :
( ( X0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X5 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',cTHM518_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X1: a > b > b > $o,X3: a > b,X2: a > b] :
( ! [X4: a] :
( ( X0 @ X4 @ X4 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X4 ) ) )
=> ( ! [X4: a,X5: a] :
( ( X0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X2 @ X5 ) ) )
=> ( ( ! [X5: a,X4: a] :
( ( X0 @ X4 @ X5 )
=> ( X0 @ X5 @ X4 ) )
& ( X0 = X0 )
& ! [X6: a,X5: a,X4: a] :
( ( ( X0 @ X5 @ X6 )
& ( X0 @ X4 @ X5 ) )
=> ( X0 @ X4 @ X6 ) ) )
=> ( ! [X5: a,X4: a] :
( ( X0 @ X4 @ X5 )
=> ( ! [X8: b,X7: b,X6: b] :
( ( ( X1 @ X4 @ X8 @ X6 )
& ( X1 @ X4 @ X7 @ X8 ) )
=> ( X1 @ X4 @ X7 @ X6 ) )
& ! [X8: b,X7: b] :
( ( X1 @ X4 @ X7 @ X8 )
=> ( X1 @ X4 @ X8 @ X7 ) )
& ( ( X1 @ X4 )
= ( X1 @ X5 ) ) ) )
=> ! [X5: a,X4: a] :
( ( X0 @ X4 @ X5 )
=> ( X1 @ X4 @ ( X2 @ X4 ) @ ( X3 @ X5 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > a > $o,X1: a > b > b > $o,X2: a > b,X3: a > b] :
( ! [X4: a] :
( ( X0 @ X4 @ X4 )
=> ( X1 @ X4 @ ( X3 @ X4 ) @ ( X2 @ X4 ) ) )
=> ( ! [X5: a,X6: a] :
( ( X0 @ X5 @ X6 )
=> ( X1 @ X5 @ ( X3 @ X5 ) @ ( X3 @ X6 ) ) )
=> ( ( ! [X7: a,X8: a] :
( ( X0 @ X8 @ X7 )
=> ( X0 @ X7 @ X8 ) )
& ( X0 = X0 )
& ! [X9: a,X10: a,X11: a] :
( ( ( X0 @ X10 @ X9 )
& ( X0 @ X11 @ X10 ) )
=> ( X0 @ X11 @ X9 ) ) )
=> ( ! [X12: a,X13: a] :
( ( X0 @ X13 @ X12 )
=> ( ! [X14: b,X15: b,X16: b] :
( ( ( X1 @ X13 @ X14 @ X16 )
& ( X1 @ X13 @ X15 @ X14 ) )
=> ( X1 @ X13 @ X15 @ X16 ) )
& ! [X17: b,X18: b] :
( ( X1 @ X13 @ X18 @ X17 )
=> ( X1 @ X13 @ X17 @ X18 ) )
& ( ( X1 @ X12 )
= ( X1 @ X13 ) ) ) )
=> ! [X19: a,X20: a] :
( ( X0 @ X20 @ X19 )
=> ( X1 @ X20 @ ( X3 @ X20 ) @ ( X2 @ X19 ) ) ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
~ ! [X2: a > b,X0: a > a > $o,X3: a > b,X1: a > b > b > $o] :
( ! [X4: a] :
( ( ( X0 @ X4 @ X4 )
= $true )
=> ( $true
= ( X1 @ X4 @ ( X3 @ X4 ) @ ( X2 @ X4 ) ) ) )
=> ( ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
= $true )
=> ( ( X1 @ X5 @ ( X3 @ X5 ) @ ( X3 @ X6 ) )
= $true ) )
=> ( ( ! [X9: a,X11: a,X10: a] :
( ( ( ( X0 @ X11 @ X10 )
= $true )
& ( ( X0 @ X10 @ X9 )
= $true ) )
=> ( ( X0 @ X11 @ X9 )
= $true ) )
& ! [X7: a,X8: a] :
( ( ( X0 @ X8 @ X7 )
= $true )
=> ( $true
= ( X0 @ X7 @ X8 ) ) )
& ( X0 = X0 ) )
=> ( ! [X13: a,X12: a] :
( ( ( X0 @ X13 @ X12 )
= $true )
=> ( ! [X18: b,X17: b] :
( ( ( X1 @ X13 @ X18 @ X17 )
= $true )
=> ( ( X1 @ X13 @ X17 @ X18 )
= $true ) )
& ! [X14: b,X15: b,X16: b] :
( ( ( $true
= ( X1 @ X13 @ X15 @ X14 ) )
& ( ( X1 @ X13 @ X14 @ X16 )
= $true ) )
=> ( $true
= ( X1 @ X13 @ X15 @ X16 ) ) )
& ( ( X1 @ X12 )
= ( X1 @ X13 ) ) ) )
=> ! [X19: a,X20: a] :
( ( ( X0 @ X20 @ X19 )
= $true )
=> ( $true
= ( X1 @ X20 @ ( X3 @ X20 ) @ ( X2 @ X19 ) ) ) ) ) ) ) ),
inference(fool_elimination,[],[f3]) ).
thf(f5,plain,
? [X2: a > b,X0: a > a > $o,X3: a > b,X1: a > b > b > $o] :
( ? [X20: a,X19: a] :
( ( $true
!= ( X1 @ X20 @ ( X3 @ X20 ) @ ( X2 @ X19 ) ) )
& ( ( X0 @ X20 @ X19 )
= $true ) )
& ! [X13: a,X12: a] :
( ( ! [X17: b,X18: b] :
( ( ( X1 @ X13 @ X18 @ X17 )
!= $true )
| ( ( X1 @ X13 @ X17 @ X18 )
= $true ) )
& ! [X14: b,X15: b,X16: b] :
( ( $true
= ( X1 @ X13 @ X15 @ X16 ) )
| ( $true
!= ( X1 @ X13 @ X15 @ X14 ) )
| ( ( X1 @ X13 @ X14 @ X16 )
!= $true ) )
& ( ( X1 @ X12 )
= ( X1 @ X13 ) ) )
| ( ( X0 @ X13 @ X12 )
!= $true ) )
& ! [X9: a,X11: a,X10: a] :
( ( ( X0 @ X11 @ X9 )
= $true )
| ( ( X0 @ X11 @ X10 )
!= $true )
| ( ( X0 @ X10 @ X9 )
!= $true ) )
& ! [X7: a,X8: a] :
( ( $true
= ( X0 @ X7 @ X8 ) )
| ( ( X0 @ X8 @ X7 )
!= $true ) )
& ( X0 = X0 )
& ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
!= $true )
| ( ( X1 @ X5 @ ( X3 @ X5 ) @ ( X3 @ X6 ) )
= $true ) )
& ! [X4: a] :
( ( ( X0 @ X4 @ X4 )
!= $true )
| ( $true
= ( X1 @ X4 @ ( X3 @ X4 ) @ ( X2 @ X4 ) ) ) ) ),
inference(ennf_transformation,[],[f4]) ).
thf(f6,plain,
? [X0: a > a > $o,X1: a > b > b > $o,X3: a > b,X2: a > b] :
( ! [X7: a,X8: a] :
( ( $true
= ( X0 @ X7 @ X8 ) )
| ( ( X0 @ X8 @ X7 )
!= $true ) )
& ! [X4: a] :
( ( ( X0 @ X4 @ X4 )
!= $true )
| ( $true
= ( X1 @ X4 @ ( X3 @ X4 ) @ ( X2 @ X4 ) ) ) )
& ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
!= $true )
| ( ( X1 @ X5 @ ( X3 @ X5 ) @ ( X3 @ X6 ) )
= $true ) )
& ! [X10: a,X11: a,X9: a] :
( ( ( X0 @ X11 @ X10 )
!= $true )
| ( ( X0 @ X11 @ X9 )
= $true )
| ( ( X0 @ X10 @ X9 )
!= $true ) )
& ( X0 = X0 )
& ? [X20: a,X19: a] :
( ( $true
!= ( X1 @ X20 @ ( X3 @ X20 ) @ ( X2 @ X19 ) ) )
& ( ( X0 @ X20 @ X19 )
= $true ) )
& ! [X13: a,X12: a] :
( ( ! [X15: b,X14: b,X16: b] :
( ( $true
= ( X1 @ X13 @ X15 @ X16 ) )
| ( $true
!= ( X1 @ X13 @ X15 @ X14 ) )
| ( ( X1 @ X13 @ X14 @ X16 )
!= $true ) )
& ! [X17: b,X18: b] :
( ( ( X1 @ X13 @ X18 @ X17 )
!= $true )
| ( ( X1 @ X13 @ X17 @ X18 )
= $true ) )
& ( ( X1 @ X12 )
= ( X1 @ X13 ) ) )
| ( ( X0 @ X13 @ X12 )
!= $true ) ) ),
inference(flattening,[],[f5]) ).
thf(f7,plain,
? [X0: a > a > $o,X1: a > b > b > $o,X2: a > b,X3: a > b] :
( ! [X4: a,X5: a] :
( ( ( X0 @ X4 @ X5 )
= $true )
| ( ( X0 @ X5 @ X4 )
!= $true ) )
& ! [X6: a] :
( ( $true
!= ( X0 @ X6 @ X6 ) )
| ( ( X1 @ X6 @ ( X2 @ X6 ) @ ( X3 @ X6 ) )
= $true ) )
& ! [X7: a,X8: a] :
( ( ( X0 @ X8 @ X7 )
!= $true )
| ( $true
= ( X1 @ X8 @ ( X2 @ X8 ) @ ( X2 @ X7 ) ) ) )
& ! [X9: a,X10: a,X11: a] :
( ( ( X0 @ X10 @ X9 )
!= $true )
| ( ( X0 @ X10 @ X11 )
= $true )
| ( ( X0 @ X9 @ X11 )
!= $true ) )
& ( X0 = X0 )
& ? [X12: a,X13: a] :
( ( ( X1 @ X12 @ ( X2 @ X12 ) @ ( X3 @ X13 ) )
!= $true )
& ( $true
= ( X0 @ X12 @ X13 ) ) )
& ! [X14: a,X15: a] :
( ( ! [X16: b,X17: b,X18: b] :
( ( ( X1 @ X14 @ X16 @ X18 )
= $true )
| ( ( X1 @ X14 @ X16 @ X17 )
!= $true )
| ( $true
!= ( X1 @ X14 @ X17 @ X18 ) ) )
& ! [X19: b,X20: b] :
( ( $true
!= ( X1 @ X14 @ X20 @ X19 ) )
| ( $true
= ( X1 @ X14 @ X19 @ X20 ) ) )
& ( ( X1 @ X15 )
= ( X1 @ X14 ) ) )
| ( $true
!= ( X0 @ X14 @ X15 ) ) ) ),
inference(rectify,[],[f6]) ).
thf(f8,plain,
( ! [X4: a,X5: a] :
( ( ( sK0 @ X4 @ X5 )
= $true )
| ( $true
!= ( sK0 @ X5 @ X4 ) ) )
& ! [X6: a] :
( ( ( sK0 @ X6 @ X6 )
!= $true )
| ( ( sK1 @ X6 @ ( sK2 @ X6 ) @ ( sK3 @ X6 ) )
= $true ) )
& ! [X7: a,X8: a] :
( ( $true
!= ( sK0 @ X8 @ X7 ) )
| ( $true
= ( sK1 @ X8 @ ( sK2 @ X8 ) @ ( sK2 @ X7 ) ) ) )
& ! [X9: a,X10: a,X11: a] :
( ( ( sK0 @ X10 @ X9 )
!= $true )
| ( $true
= ( sK0 @ X10 @ X11 ) )
| ( $true
!= ( sK0 @ X9 @ X11 ) ) )
& ( sK0 = sK0 )
& ( ( sK1 @ sK4 @ ( sK2 @ sK4 ) @ ( sK3 @ sK5 ) )
!= $true )
& ( $true
= ( sK0 @ sK4 @ sK5 ) )
& ! [X14: a,X15: a] :
( ( ! [X16: b,X17: b,X18: b] :
( ( ( sK1 @ X14 @ X16 @ X18 )
= $true )
| ( ( sK1 @ X14 @ X16 @ X17 )
!= $true )
| ( ( sK1 @ X14 @ X17 @ X18 )
!= $true ) )
& ! [X19: b,X20: b] :
( ( $true
!= ( sK1 @ X14 @ X20 @ X19 ) )
| ( ( sK1 @ X14 @ X19 @ X20 )
= $true ) )
& ( ( sK1 @ X15 )
= ( sK1 @ X14 ) ) )
| ( $true
!= ( sK0 @ X14 @ X15 ) ) ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X12,sK4),skolemize(X13,sK5)],[f7]) ).
thf(f9,plain,
! [X14: a,X15: a] :
( ( $true
!= ( sK0 @ X14 @ X15 ) )
| ( ( sK1 @ X15 )
= ( sK1 @ X14 ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f10,plain,
! [X19: b,X14: a,X15: a,X20: b] :
( ( $true
!= ( sK1 @ X14 @ X20 @ X19 ) )
| ( $true
!= ( sK0 @ X14 @ X15 ) )
| ( ( sK1 @ X14 @ X19 @ X20 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f11,plain,
! [X18: b,X16: b,X14: a,X17: b,X15: a] :
( ( ( sK1 @ X14 @ X17 @ X18 )
!= $true )
| ( ( sK1 @ X14 @ X16 @ X18 )
= $true )
| ( $true
!= ( sK0 @ X14 @ X15 ) )
| ( ( sK1 @ X14 @ X16 @ X17 )
!= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f12,plain,
( $true
= ( sK0 @ sK4 @ sK5 ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f13,plain,
( ( sK1 @ sK4 @ ( sK2 @ sK4 ) @ ( sK3 @ sK5 ) )
!= $true ),
inference(cnf_transformation,[],[f8]) ).
thf(f15,plain,
! [X10: a,X11: a,X9: a] :
( ( $true
!= ( sK0 @ X9 @ X11 ) )
| ( $true
= ( sK0 @ X10 @ X11 ) )
| ( ( sK0 @ X10 @ X9 )
!= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f16,plain,
! [X8: a,X7: a] :
( ( $true
!= ( sK0 @ X8 @ X7 ) )
| ( $true
= ( sK1 @ X8 @ ( sK2 @ X8 ) @ ( sK2 @ X7 ) ) ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f17,plain,
! [X6: a] :
( ( ( sK0 @ X6 @ X6 )
!= $true )
| ( ( sK1 @ X6 @ ( sK2 @ X6 ) @ ( sK3 @ X6 ) )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f18,plain,
! [X4: a,X5: a] :
( ( $true
!= ( sK0 @ X5 @ X4 ) )
| ( ( sK0 @ X4 @ X5 )
= $true ) ),
inference(cnf_transformation,[],[f8]) ).
thf(f21,plain,
( ( $true != $true )
| ( ( sK0 @ sK5 @ sK4 )
= $true ) ),
inference(constrained_superposition,[],[f18,f12]) ).
thf(f22,plain,
( ( sK0 @ sK5 @ sK4 )
= $true ),
inference(trivial_inequality_removal,[],[f21]) ).
thf(f26,plain,
( ( $true != $true )
| ( ( sK1 @ sK5 )
= ( sK1 @ sK4 ) ) ),
inference(constrained_superposition,[],[f9,f22]) ).
thf(f27,plain,
( ( sK1 @ sK5 )
= ( sK1 @ sK4 ) ),
inference(trivial_inequality_removal,[],[f26]) ).
thf(f29,plain,
! [X1: b] :
( ( sK1 @ sK5 @ X1 )
= ( sK1 @ sK4 @ X1 ) ),
inference(argument_congruence,[],[f27]) ).
thf(f30,plain,
! [X2: b,X1: b] :
( ( sK1 @ sK4 @ X1 @ X2 )
= ( sK1 @ sK5 @ X1 @ X2 ) ),
inference(argument_congruence,[],[f29]) ).
thf(f31,plain,
! [X2: b,X1: b] :
( ( ( sK1 @ sK5 @ X1 @ X2 )
= $false )
| ( ( sK1 @ sK4 @ X1 @ X2 )
= $true ) ),
inference(iff_proxy_clausification,[],[f30]) ).
thf(f33,plain,
! [X0: a] :
( ( $true
= ( sK0 @ X0 @ sK5 ) )
| ( $true != $true )
| ( $true
!= ( sK0 @ X0 @ sK4 ) ) ),
inference(constrained_superposition,[],[f15,f12]) ).
thf(f36,plain,
! [X0: a] :
( ( $true
!= ( sK0 @ X0 @ sK4 ) )
| ( $true
= ( sK0 @ X0 @ sK5 ) ) ),
inference(trivial_inequality_removal,[],[f33]) ).
thf(f37,plain,
( ( $true != $true )
| ( ( sK0 @ sK5 @ sK5 )
= $true ) ),
inference(constrained_superposition,[],[f36,f22]) ).
thf(f38,plain,
( ( sK0 @ sK5 @ sK5 )
= $true ),
inference(trivial_inequality_removal,[],[f37]) ).
thf(f49,plain,
( ( $true
= ( sK1 @ sK5 @ ( sK2 @ sK5 ) @ ( sK2 @ sK4 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f16,f22]) ).
thf(f51,plain,
( $true
= ( sK1 @ sK5 @ ( sK2 @ sK5 ) @ ( sK2 @ sK4 ) ) ),
inference(trivial_inequality_removal,[],[f49]) ).
thf(f56,plain,
( ( $true
= ( sK1 @ sK5 @ ( sK2 @ sK5 ) @ ( sK3 @ sK5 ) ) )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f17,f38]) ).
thf(f58,plain,
( $true
= ( sK1 @ sK5 @ ( sK2 @ sK5 ) @ ( sK3 @ sK5 ) ) ),
inference(trivial_inequality_removal,[],[f56]) ).
thf(f76,plain,
! [X0: a] :
( ( $true
= ( sK1 @ sK5 @ ( sK3 @ sK5 ) @ ( sK2 @ sK5 ) ) )
| ( ( sK0 @ sK5 @ X0 )
!= $true )
| ( $true != $true ) ),
inference(constrained_superposition,[],[f10,f58]) ).
thf(f83,plain,
! [X0: a] :
( ( ( sK0 @ sK5 @ X0 )
!= $true )
| ( $true
= ( sK1 @ sK5 @ ( sK3 @ sK5 ) @ ( sK2 @ sK5 ) ) ) ),
inference(trivial_inequality_removal,[],[f76]) ).
thf(f93,definition,
( spl6_2
<=> ! [X0: a] :
( ( sK0 @ sK4 @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_2])],[avatar_definition]) ).
thf(f94,plain,
( ! [X0: a] :
( ( sK0 @ sK4 @ X0 )
!= $true )
| ~ spl6_2 ),
inference(avatar_component_clause,[],[f93]) ).
thf(f102,definition,
( spl6_4
<=> ( $true
= ( sK1 @ sK5 @ ( sK3 @ sK5 ) @ ( sK2 @ sK5 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_4])],[avatar_definition]) ).
thf(f104,plain,
( ( $true
= ( sK1 @ sK5 @ ( sK3 @ sK5 ) @ ( sK2 @ sK5 ) ) )
| ~ spl6_4 ),
inference(avatar_component_clause,[],[f102]) ).
thf(f106,definition,
( spl6_5
<=> ! [X0: a] :
( ( sK0 @ sK5 @ X0 )
!= $true ) ),
introduced(definition,[new_symbols(definition,[spl6_5])],[avatar_definition]) ).
thf(f107,plain,
( ! [X0: a] :
( ( sK0 @ sK5 @ X0 )
!= $true )
| ~ spl6_5 ),
inference(avatar_component_clause,[],[f106]) ).
thf(f108,plain,
( spl6_4
| spl6_5 ),
inference(avatar_split_clause,[],[f83,f106,f102]) ).
thf(f118,plain,
( ( $true != $true )
| ~ spl6_5 ),
inference(constrained_superposition,[],[f107,f22]) ).
thf(f122,plain,
( $false
| ~ spl6_5 ),
inference(trivial_inequality_removal,[],[f118]) ).
thf(f123,plain,
~ spl6_5,
inference(avatar_contradiction_clause,[],[f122]) ).
thf(f124,plain,
( ( $true != $true )
| ~ spl6_2 ),
inference(constrained_superposition,[],[f94,f12]) ).
thf(f128,plain,
( $false
| ~ spl6_2 ),
inference(trivial_inequality_removal,[],[f124]) ).
thf(f129,plain,
~ spl6_2,
inference(avatar_contradiction_clause,[],[f128]) ).
thf(f178,plain,
! [X0: b,X1: a] :
( ( ( sK1 @ sK5 @ X0 @ ( sK2 @ sK5 ) )
!= $true )
| ( $true != $true )
| ( $true
= ( sK1 @ sK5 @ X0 @ ( sK2 @ sK4 ) ) )
| ( ( sK0 @ sK5 @ X1 )
!= $true ) ),
inference(constrained_superposition,[],[f11,f51]) ).
thf(f206,plain,
! [X0: b,X1: a] :
( ( ( sK1 @ sK5 @ X0 @ ( sK2 @ sK5 ) )
!= $true )
| ( ( sK0 @ sK5 @ X1 )
!= $true )
| ( $true
= ( sK1 @ sK5 @ X0 @ ( sK2 @ sK4 ) ) ) ),
inference(trivial_inequality_removal,[],[f178]) ).
thf(f256,definition,
( spl6_20
<=> ! [X0: b] :
( ( ( sK1 @ sK5 @ X0 @ ( sK2 @ sK5 ) )
!= $true )
| ( $true
= ( sK1 @ sK5 @ X0 @ ( sK2 @ sK4 ) ) ) ) ),
introduced(definition,[new_symbols(definition,[spl6_20])],[avatar_definition]) ).
thf(f257,plain,
( ! [X0: b] :
( ( ( sK1 @ sK5 @ X0 @ ( sK2 @ sK5 ) )
!= $true )
| ( $true
= ( sK1 @ sK5 @ X0 @ ( sK2 @ sK4 ) ) ) )
| ~ spl6_20 ),
inference(avatar_component_clause,[],[f256]) ).
thf(f258,plain,
( spl6_5
| spl6_20 ),
inference(avatar_split_clause,[],[f206,f256,f106]) ).
thf(f291,plain,
( ( ( sK1 @ sK5 @ ( sK3 @ sK5 ) @ ( sK2 @ sK4 ) )
= $true )
| ( $true != $true )
| ~ spl6_4
| ~ spl6_20 ),
inference(constrained_superposition,[],[f257,f104]) ).
thf(f297,plain,
( ( ( sK1 @ sK5 @ ( sK3 @ sK5 ) @ ( sK2 @ sK4 ) )
= $true )
| ~ spl6_4
| ~ spl6_20 ),
inference(trivial_inequality_removal,[],[f291]) ).
thf(f305,plain,
( ( ( sK1 @ sK4 @ ( sK3 @ sK5 ) @ ( sK2 @ sK4 ) )
= $true )
| ( $false = $true )
| ~ spl6_4
| ~ spl6_20 ),
inference(constrained_superposition,[],[f297,f31]) ).
thf(f309,plain,
( ( ( sK1 @ sK4 @ ( sK3 @ sK5 ) @ ( sK2 @ sK4 ) )
= $true )
| ~ spl6_4
| ~ spl6_20 ),
inference(trivial_inequality_removal,[],[f305]) ).
thf(f326,plain,
( ! [X0: a] :
( ( ( sK0 @ sK4 @ X0 )
!= $true )
| ( $true != $true )
| ( ( sK1 @ sK4 @ ( sK2 @ sK4 ) @ ( sK3 @ sK5 ) )
= $true ) )
| ~ spl6_4
| ~ spl6_20 ),
inference(constrained_superposition,[],[f10,f309]) ).
thf(f330,plain,
( ! [X0: a] :
( ( ( sK0 @ sK4 @ X0 )
!= $true )
| ( ( sK1 @ sK4 @ ( sK2 @ sK4 ) @ ( sK3 @ sK5 ) )
= $true ) )
| ~ spl6_4
| ~ spl6_20 ),
inference(trivial_inequality_removal,[],[f326]) ).
thf(f336,plain,
( ! [X0: a] :
( ( sK0 @ sK4 @ X0 )
!= $true )
| ~ spl6_4
| ~ spl6_20 ),
inference(forward_subsumption_resolution,[],[f330,f13]) ).
thf(f341,plain,
( spl6_2
| ~ spl6_4
| ~ spl6_20 ),
inference(avatar_split_clause,[],[f336,f256,f102,f93]) ).
cnf(s3,plain,
( spl6_4
| spl6_5 ),
inference(sat_conversion,[],[f108]) ).
cnf(s7,plain,
~ spl6_5,
inference(sat_conversion,[],[f123]) ).
cnf(s9,plain,
~ spl6_2,
inference(sat_conversion,[],[f129]) ).
cnf(s22,plain,
( spl6_5
| spl6_20 ),
inference(sat_conversion,[],[f258]) ).
cnf(s30,plain,
( spl6_2
| ~ spl6_4
| ~ spl6_20 ),
inference(sat_conversion,[],[f341]) ).
cnf(s35,plain,
spl6_20,
inference(rat,[],[s22,s7]) ).
cnf(s38,plain,
~ spl6_4,
inference(rat,[],[s30,s9,s35]) ).
cnf(s44,plain,
$false,
inference(rat,[],[s3,s7,s38]) ).
thf(f342,plain,
$false,
inference(avatar_sat_refutation,[],[s44]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.04 % Problem : SEV034^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.08 % Command : run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.22 % Computer : n011.cluster.edu
% 0.11/0.22 % Model : x86_64 x86_64
% 0.11/0.22 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.22 % Memory : 8046.5625MB
% 0.11/0.22 % OS : Linux 6.8.0-71-generic
% 0.11/0.22 % CPULimit : 300
% 0.11/0.22 % WCLimit : 300
% 0.11/0.22 % DateTime : Tue Sep 29 15:04:22 UTC 2026
% 0.11/0.22 % CPUTime :
% 0.11/0.22 Running run_vampire /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.11/0.27 Running higher-order theorem proving
% 0.24/0.29 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
% 0.24/0.34 % (192236)Detected a higher-order problem, will run a greedy HOL sequence.
% 0.24/0.34 % (192246)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=645925141: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)
% 0.24/0.34 % (192243)lrs+10_40_drc=off:e2e=on:si=on:uwa=one_side_interpreted:random_seed=208391211:s2a=on:i=87:rtra=on:ntd=on_2999 on theBenchmark for (2999ds/87Mi)
% 0.24/0.34 % (192249)WARNING Broken Constraint: if ho_split_queue_ratios(1,8) has been set then ho_split_queue(off) is equal to on
% 0.24/0.34 % (192249)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
% 0.24/0.34 % (192244)lrs+10_16_si=on:nwc=1.5:random_seed=1759607505:i=18:kws=arity_squared:rtra=on:fe=abstraction:ntd=on_2999 on theBenchmark for (2999ds/18Mi)
% 0.24/0.34 % (192245)lrs+10_1_cnfonf=off:si=on:uwa=one_side_interpreted:random_seed=519080085:i=3:rtra=on:inj=on:ntd=on_2999 on theBenchmark for (2999ds/3Mi)
% 0.24/0.34 % (192247)dis+21_4_fde=none:e2e=on:si=on:uwa=off:foolp=on:random_seed=3114049068:i=24:av=off:rtra=on_2999 on theBenchmark for (2999ds/24Mi)
% 0.24/0.34 % (192248)lrs+10_1_to=lpo:sil=128000:e2e=on:si=on:random_seed=2672608755:s2a=on:i=75:s2at=3:aac=none:bd=preordered:rtra=on:fe=abstraction_2999 on theBenchmark for (2999ds/75Mi)
% 0.24/0.34 % (192249)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=2847402827:hsqr=1,8:i=157:s2at=5:add=on:nm=2:rtra=on_2999 on theBenchmark for (2999ds/157Mi)
% 0.24/0.34 % (192243) found proof, printing to "/export/starexec/sandbox/tmp/vampire-proof-192236-192243"...
% 0.24/0.34 % (192245)Instruction limit reached!
% 0.24/0.34 % (192245)------------------------------
% 0.24/0.34 % (192245)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.34 % (192245)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.34 % (192245)CaDiCaL version: 2.1.3
% 0.24/0.34 % (192245)Termination reason: Instruction limit
% 0.24/0.34 % (192245)Termination phase: Saturation
% 0.24/0.34 % (192245)Time elapsed: 0.005 s
% 0.24/0.34 % (192245)Peak memory usage: 12 MB
% 0.24/0.34 % (192245)Instructions burned: 4 (million)
% 0.24/0.34 % (192243)...printing done.
% 0.24/0.34 % (192243)Refutation found. Thanks to Tanya!
% 0.24/0.34 % SZS status Theorem for theBenchmark
% 0.24/0.34 % SZS output start Proof for theBenchmark
% See solution above
% 0.24/0.35 % (192243)------------------------------
% 0.24/0.35 % (192243)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.24/0.35 % (192243)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.24/0.35 % (192243)CaDiCaL version: 2.1.3
% 0.24/0.35 % (192243)Termination reason: Refutation
% 0.24/0.35 % (192243)Time elapsed: 0.020 s
% 0.24/0.35 % (192243)Peak memory usage: 13 MB
% 0.24/0.35 % (192243)Instructions burned: 26 (million)
% 0.24/0.35 % (192236)Success in time 0.047 s
% 0.24/0.35 % Vampire exiting
%------------------------------------------------------------------------------