%------------------------------------------------------------------------------
% File : Vampire-SAT---5.0.1
% Problem : SEV000^5 : TPTP v9.3.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% Computer : n007.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 08:38:50 AM UTC 2026
% Result : Theorem 0.18s 0.29s
% Output : Refutation 0.18s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 6
% Syntax : Number of formulae : 47 ( 7 unt; 0 typ; 5 def)
% Number of atoms : 192 ( 138 equ; 0 cnn)
% Maximal formula atoms : 14 ( 4 avg)
% Number of connectives : 1013 ( 54 ~; 52 |; 77 &; 814 @)
% ( 8 <=>; 6 =>; 0 <=; 2 <~>)
% Maximal formula depth : 18 ( 6 avg)
% Maximal term depth : 1 ( 1 avg)
% Number of types : 1 ( 1 usr)
% Number of type conns : 32 ( 32 >; 0 *; 0 +; 0 <<)
% Number of symbols : 16 ( 14 usr; 12 con; 0-2 aty)
% Number of variables : 263 ( 0 sgn 235 !; 28 ?; 263 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(type_def_6,type,
sTfun: ( $tType * $tType ) > $tType ).
thf(func_def_1,type,
sK0: a > a > a ).
thf(func_def_2,type,
sK1: a > a > a ).
thf(func_def_3,type,
sK2: a ).
thf(func_def_4,type,
sK3: a ).
thf(func_def_5,type,
sK4: a ).
thf(func_def_6,type,
sK5: a ).
thf(func_def_7,type,
sK6: a ).
thf(func_def_8,type,
sK7: a ).
thf(f1,conjecture,
! [X0: a > a > a,X1: a > a > a] :
( ( ! [X2: a,X3: a] :
( ( X1 @ ( X0 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X2: a,X3: a] :
( ( X0 @ ( X1 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
= ( X0 @ X3 @ X2 ) )
& ! [X2: a,X3: a,X4: a] :
( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) )
& ! [X2: a,X3: a,X4: a] :
( ( X0 @ ( X0 @ X2 @ X3 ) @ X4 )
= ( X0 @ X2 @ ( X0 @ X3 @ X4 ) ) )
& ! [X2: a] :
( ( X1 @ X2 @ X2 )
= X2 )
& ! [X2: a] :
( ( X0 @ X2 @ X2 )
= X2 ) )
=> ( ! [X2: a,X3: a,X4: a] :
( ( ( X0 @ X2 @ X4 )
= X4 )
=> ( ( X0 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X0 @ X2 @ X3 ) @ X4 ) ) )
<=> ! [X2: a,X3: a,X4: a] :
( ( X0 @ X2 @ ( X1 @ X3 @ ( X0 @ X2 @ X4 ) ) )
= ( X1 @ ( X0 @ X2 @ X3 ) @ ( X0 @ X2 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',cMODULAR_EQUIV_THM_pme) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > a,X1: a > a > a] :
( ( ! [X2: a,X3: a] :
( ( X1 @ ( X0 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X2: a,X3: a] :
( ( X0 @ ( X1 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X2: a,X3: a] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) )
& ! [X2: a,X3: a] :
( ( X0 @ X2 @ X3 )
= ( X0 @ X3 @ X2 ) )
& ! [X2: a,X3: a,X4: a] :
( ( X1 @ ( X1 @ X2 @ X3 ) @ X4 )
= ( X1 @ X2 @ ( X1 @ X3 @ X4 ) ) )
& ! [X2: a,X3: a,X4: a] :
( ( X0 @ ( X0 @ X2 @ X3 ) @ X4 )
= ( X0 @ X2 @ ( X0 @ X3 @ X4 ) ) )
& ! [X2: a] :
( ( X1 @ X2 @ X2 )
= X2 )
& ! [X2: a] :
( ( X0 @ X2 @ X2 )
= X2 ) )
=> ( ! [X2: a,X3: a,X4: a] :
( ( ( X0 @ X2 @ X4 )
= X4 )
=> ( ( X0 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X0 @ X2 @ X3 ) @ X4 ) ) )
<=> ! [X2: a,X3: a,X4: a] :
( ( X0 @ X2 @ ( X1 @ X3 @ ( X0 @ X2 @ X4 ) ) )
= ( X1 @ ( X0 @ X2 @ X3 ) @ ( X0 @ X2 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f3,plain,
~ ! [X0: a > a > a,X1: a > a > a] :
( ( ! [X2: a,X3: a] :
( ( X1 @ ( X0 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X4: a,X5: a] :
( ( X0 @ ( X1 @ X4 @ X5 ) @ X5 )
= X5 )
& ! [X6: a,X7: a] :
( ( X1 @ X6 @ X7 )
= ( X1 @ X7 @ X6 ) )
& ! [X8: a,X9: a] :
( ( X0 @ X8 @ X9 )
= ( X0 @ X9 @ X8 ) )
& ! [X10: a,X11: a,X12: a] :
( ( X1 @ ( X1 @ X10 @ X11 ) @ X12 )
= ( X1 @ X10 @ ( X1 @ X11 @ X12 ) ) )
& ! [X13: a,X14: a,X15: a] :
( ( X0 @ ( X0 @ X13 @ X14 ) @ X15 )
= ( X0 @ X13 @ ( X0 @ X14 @ X15 ) ) )
& ! [X16: a] :
( ( X1 @ X16 @ X16 )
= X16 )
& ! [X17: a] :
( ( X0 @ X17 @ X17 )
= X17 ) )
=> ( ! [X18: a,X19: a,X20: a] :
( ( ( X0 @ X18 @ X20 )
= X20 )
=> ( ( X0 @ X18 @ ( X1 @ X19 @ X20 ) )
= ( X1 @ ( X0 @ X18 @ X19 ) @ X20 ) ) )
<=> ! [X21: a,X22: a,X23: a] :
( ( X0 @ X21 @ ( X1 @ X22 @ ( X0 @ X21 @ X23 ) ) )
= ( X1 @ ( X0 @ X21 @ X22 ) @ ( X0 @ X21 @ X23 ) ) ) ) ),
inference(rectify,[],[f2]) ).
thf(f4,plain,
? [X0: a > a > a,X1: a > a > a] :
( ( ! [X18: a,X19: a,X20: a] :
( ( ( X0 @ X18 @ ( X1 @ X19 @ X20 ) )
= ( X1 @ ( X0 @ X18 @ X19 ) @ X20 ) )
| ( ( X0 @ X18 @ X20 )
!= X20 ) )
<~> ! [X21: a,X22: a,X23: a] :
( ( X0 @ X21 @ ( X1 @ X22 @ ( X0 @ X21 @ X23 ) ) )
= ( X1 @ ( X0 @ X21 @ X22 ) @ ( X0 @ X21 @ X23 ) ) ) )
& ! [X2: a,X3: a] :
( ( X1 @ ( X0 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X4: a,X5: a] :
( ( X0 @ ( X1 @ X4 @ X5 ) @ X5 )
= X5 )
& ! [X6: a,X7: a] :
( ( X1 @ X6 @ X7 )
= ( X1 @ X7 @ X6 ) )
& ! [X8: a,X9: a] :
( ( X0 @ X8 @ X9 )
= ( X0 @ X9 @ X8 ) )
& ! [X10: a,X11: a,X12: a] :
( ( X1 @ ( X1 @ X10 @ X11 ) @ X12 )
= ( X1 @ X10 @ ( X1 @ X11 @ X12 ) ) )
& ! [X13: a,X14: a,X15: a] :
( ( X0 @ ( X0 @ X13 @ X14 ) @ X15 )
= ( X0 @ X13 @ ( X0 @ X14 @ X15 ) ) )
& ! [X16: a] :
( ( X1 @ X16 @ X16 )
= X16 )
& ! [X17: a] :
( ( X0 @ X17 @ X17 )
= X17 ) ),
inference(ennf_transformation,[],[f3]) ).
thf(f5,plain,
? [X0: a > a > a,X1: a > a > a] :
( ( ! [X18: a,X19: a,X20: a] :
( ( ( X0 @ X18 @ ( X1 @ X19 @ X20 ) )
= ( X1 @ ( X0 @ X18 @ X19 ) @ X20 ) )
| ( ( X0 @ X18 @ X20 )
!= X20 ) )
<~> ! [X21: a,X22: a,X23: a] :
( ( X0 @ X21 @ ( X1 @ X22 @ ( X0 @ X21 @ X23 ) ) )
= ( X1 @ ( X0 @ X21 @ X22 ) @ ( X0 @ X21 @ X23 ) ) ) )
& ! [X2: a,X3: a] :
( ( X1 @ ( X0 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X4: a,X5: a] :
( ( X0 @ ( X1 @ X4 @ X5 ) @ X5 )
= X5 )
& ! [X6: a,X7: a] :
( ( X1 @ X6 @ X7 )
= ( X1 @ X7 @ X6 ) )
& ! [X8: a,X9: a] :
( ( X0 @ X8 @ X9 )
= ( X0 @ X9 @ X8 ) )
& ! [X10: a,X11: a,X12: a] :
( ( X1 @ ( X1 @ X10 @ X11 ) @ X12 )
= ( X1 @ X10 @ ( X1 @ X11 @ X12 ) ) )
& ! [X13: a,X14: a,X15: a] :
( ( X0 @ ( X0 @ X13 @ X14 ) @ X15 )
= ( X0 @ X13 @ ( X0 @ X14 @ X15 ) ) )
& ! [X16: a] :
( ( X1 @ X16 @ X16 )
= X16 )
& ! [X17: a] :
( ( X0 @ X17 @ X17 )
= X17 ) ),
inference(flattening,[],[f4]) ).
thf(f6,plain,
? [X0: a > a > a,X1: a > a > a] :
( ( ? [X21: a,X22: a,X23: a] :
( ( X0 @ X21 @ ( X1 @ X22 @ ( X0 @ X21 @ X23 ) ) )
!= ( X1 @ ( X0 @ X21 @ X22 ) @ ( X0 @ X21 @ X23 ) ) )
| ? [X18: a,X19: a,X20: a] :
( ( ( X0 @ X18 @ ( X1 @ X19 @ X20 ) )
!= ( X1 @ ( X0 @ X18 @ X19 ) @ X20 ) )
& ( ( X0 @ X18 @ X20 )
= X20 ) ) )
& ( ! [X21: a,X22: a,X23: a] :
( ( X0 @ X21 @ ( X1 @ X22 @ ( X0 @ X21 @ X23 ) ) )
= ( X1 @ ( X0 @ X21 @ X22 ) @ ( X0 @ X21 @ X23 ) ) )
| ! [X18: a,X19: a,X20: a] :
( ( ( X0 @ X18 @ ( X1 @ X19 @ X20 ) )
= ( X1 @ ( X0 @ X18 @ X19 ) @ X20 ) )
| ( ( X0 @ X18 @ X20 )
!= X20 ) ) )
& ! [X2: a,X3: a] :
( ( X1 @ ( X0 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X4: a,X5: a] :
( ( X0 @ ( X1 @ X4 @ X5 ) @ X5 )
= X5 )
& ! [X6: a,X7: a] :
( ( X1 @ X6 @ X7 )
= ( X1 @ X7 @ X6 ) )
& ! [X8: a,X9: a] :
( ( X0 @ X8 @ X9 )
= ( X0 @ X9 @ X8 ) )
& ! [X10: a,X11: a,X12: a] :
( ( X1 @ ( X1 @ X10 @ X11 ) @ X12 )
= ( X1 @ X10 @ ( X1 @ X11 @ X12 ) ) )
& ! [X13: a,X14: a,X15: a] :
( ( X0 @ ( X0 @ X13 @ X14 ) @ X15 )
= ( X0 @ X13 @ ( X0 @ X14 @ X15 ) ) )
& ! [X16: a] :
( ( X1 @ X16 @ X16 )
= X16 )
& ! [X17: a] :
( ( X0 @ X17 @ X17 )
= X17 ) ),
inference(nnf_transformation,[],[f5]) ).
thf(f7,plain,
? [X0: a > a > a,X1: a > a > a] :
( ( ? [X21: a,X22: a,X23: a] :
( ( X0 @ X21 @ ( X1 @ X22 @ ( X0 @ X21 @ X23 ) ) )
!= ( X1 @ ( X0 @ X21 @ X22 ) @ ( X0 @ X21 @ X23 ) ) )
| ? [X18: a,X19: a,X20: a] :
( ( ( X0 @ X18 @ ( X1 @ X19 @ X20 ) )
!= ( X1 @ ( X0 @ X18 @ X19 ) @ X20 ) )
& ( ( X0 @ X18 @ X20 )
= X20 ) ) )
& ( ! [X21: a,X22: a,X23: a] :
( ( X0 @ X21 @ ( X1 @ X22 @ ( X0 @ X21 @ X23 ) ) )
= ( X1 @ ( X0 @ X21 @ X22 ) @ ( X0 @ X21 @ X23 ) ) )
| ! [X18: a,X19: a,X20: a] :
( ( ( X0 @ X18 @ ( X1 @ X19 @ X20 ) )
= ( X1 @ ( X0 @ X18 @ X19 ) @ X20 ) )
| ( ( X0 @ X18 @ X20 )
!= X20 ) ) )
& ! [X2: a,X3: a] :
( ( X1 @ ( X0 @ X2 @ X3 ) @ X3 )
= X3 )
& ! [X4: a,X5: a] :
( ( X0 @ ( X1 @ X4 @ X5 ) @ X5 )
= X5 )
& ! [X6: a,X7: a] :
( ( X1 @ X6 @ X7 )
= ( X1 @ X7 @ X6 ) )
& ! [X8: a,X9: a] :
( ( X0 @ X8 @ X9 )
= ( X0 @ X9 @ X8 ) )
& ! [X10: a,X11: a,X12: a] :
( ( X1 @ ( X1 @ X10 @ X11 ) @ X12 )
= ( X1 @ X10 @ ( X1 @ X11 @ X12 ) ) )
& ! [X13: a,X14: a,X15: a] :
( ( X0 @ ( X0 @ X13 @ X14 ) @ X15 )
= ( X0 @ X13 @ ( X0 @ X14 @ X15 ) ) )
& ! [X16: a] :
( ( X1 @ X16 @ X16 )
= X16 )
& ! [X17: a] :
( ( X0 @ X17 @ X17 )
= X17 ) ),
inference(flattening,[],[f6]) ).
thf(f8,plain,
? [X0: a > a > a,X1: a > a > a] :
( ( ? [X2: a,X3: a,X4: a] :
( ( X0 @ X2 @ ( X1 @ X3 @ ( X0 @ X2 @ X4 ) ) )
!= ( X1 @ ( X0 @ X2 @ X3 ) @ ( X0 @ X2 @ X4 ) ) )
| ? [X5: a,X6: a,X7: a] :
( ( ( X0 @ X5 @ ( X1 @ X6 @ X7 ) )
!= ( X1 @ ( X0 @ X5 @ X6 ) @ X7 ) )
& ( ( X0 @ X5 @ X7 )
= X7 ) ) )
& ( ! [X8: a,X9: a,X10: a] :
( ( X0 @ X8 @ ( X1 @ X9 @ ( X0 @ X8 @ X10 ) ) )
= ( X1 @ ( X0 @ X8 @ X9 ) @ ( X0 @ X8 @ X10 ) ) )
| ! [X11: a,X12: a,X13: a] :
( ( ( X0 @ X11 @ ( X1 @ X12 @ X13 ) )
= ( X1 @ ( X0 @ X11 @ X12 ) @ X13 ) )
| ( ( X0 @ X11 @ X13 )
!= X13 ) ) )
& ! [X14: a,X15: a] :
( ( X1 @ ( X0 @ X14 @ X15 ) @ X15 )
= X15 )
& ! [X16: a,X17: a] :
( ( X0 @ ( X1 @ X16 @ X17 ) @ X17 )
= X17 )
& ! [X18: a,X19: a] :
( ( X1 @ X18 @ X19 )
= ( X1 @ X19 @ X18 ) )
& ! [X20: a,X21: a] :
( ( X0 @ X20 @ X21 )
= ( X0 @ X21 @ X20 ) )
& ! [X22: a,X23: a,X24: a] :
( ( X1 @ ( X1 @ X22 @ X23 ) @ X24 )
= ( X1 @ X22 @ ( X1 @ X23 @ X24 ) ) )
& ! [X25: a,X26: a,X27: a] :
( ( X0 @ ( X0 @ X25 @ X26 ) @ X27 )
= ( X0 @ X25 @ ( X0 @ X26 @ X27 ) ) )
& ! [X28: a] :
( ( X1 @ X28 @ X28 )
= X28 )
& ! [X29: a] :
( ( X0 @ X29 @ X29 )
= X29 ) ),
inference(rectify,[],[f7]) ).
thf(f9,plain,
( ( ( ( sK0 @ sK2 @ ( sK1 @ sK3 @ ( sK0 @ sK2 @ sK4 ) ) )
!= ( sK1 @ ( sK0 @ sK2 @ sK3 ) @ ( sK0 @ sK2 @ sK4 ) ) )
| ( ( ( sK0 @ sK5 @ ( sK1 @ sK6 @ sK7 ) )
!= ( sK1 @ ( sK0 @ sK5 @ sK6 ) @ sK7 ) )
& ( sK7
= ( sK0 @ sK5 @ sK7 ) ) ) )
& ( ! [X8: a,X9: a,X10: a] :
( ( sK0 @ X8 @ ( sK1 @ X9 @ ( sK0 @ X8 @ X10 ) ) )
= ( sK1 @ ( sK0 @ X8 @ X9 ) @ ( sK0 @ X8 @ X10 ) ) )
| ! [X11: a,X12: a,X13: a] :
( ( ( sK0 @ X11 @ ( sK1 @ X12 @ X13 ) )
= ( sK1 @ ( sK0 @ X11 @ X12 ) @ X13 ) )
| ( ( sK0 @ X11 @ X13 )
!= X13 ) ) )
& ! [X14: a,X15: a] :
( ( sK1 @ ( sK0 @ X14 @ X15 ) @ X15 )
= X15 )
& ! [X16: a,X17: a] :
( ( sK0 @ ( sK1 @ X16 @ X17 ) @ X17 )
= X17 )
& ! [X18: a,X19: a] :
( ( sK1 @ X18 @ X19 )
= ( sK1 @ X19 @ X18 ) )
& ! [X20: a,X21: a] :
( ( sK0 @ X20 @ X21 )
= ( sK0 @ X21 @ X20 ) )
& ! [X22: a,X23: a,X24: a] :
( ( sK1 @ ( sK1 @ X22 @ X23 ) @ X24 )
= ( sK1 @ X22 @ ( sK1 @ X23 @ X24 ) ) )
& ! [X25: a,X26: a,X27: a] :
( ( sK0 @ ( sK0 @ X25 @ X26 ) @ X27 )
= ( sK0 @ X25 @ ( sK0 @ X26 @ X27 ) ) )
& ! [X28: a] :
( ( sK1 @ X28 @ X28 )
= X28 )
& ! [X29: a] :
( ( sK0 @ X29 @ X29 )
= X29 ) ),
inference(skolemize,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7]),skolemize(X0,sK0),skolemize(X1,sK1),skolemize(X2,sK2),skolemize(X3,sK3),skolemize(X4,sK4),skolemize(X5,sK5),skolemize(X6,sK6),skolemize(X7,sK7)],[f8]) ).
thf(f10,plain,
! [X29: a] :
( ( sK0 @ X29 @ X29 )
= X29 ),
inference(cnf_transformation,[],[f9]) ).
thf(f12,plain,
! [X26: a,X27: a,X25: a] :
( ( sK0 @ ( sK0 @ X25 @ X26 ) @ X27 )
= ( sK0 @ X25 @ ( sK0 @ X26 @ X27 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f18,plain,
! [X10: a,X11: a,X8: a,X9: a,X12: a,X13: a] :
( ( ( sK0 @ X8 @ ( sK1 @ X9 @ ( sK0 @ X8 @ X10 ) ) )
= ( sK1 @ ( sK0 @ X8 @ X9 ) @ ( sK0 @ X8 @ X10 ) ) )
| ( ( sK0 @ X11 @ ( sK1 @ X12 @ X13 ) )
= ( sK1 @ ( sK0 @ X11 @ X12 ) @ X13 ) )
| ( ( sK0 @ X11 @ X13 )
!= X13 ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f19,plain,
( ( ( sK0 @ sK2 @ ( sK1 @ sK3 @ ( sK0 @ sK2 @ sK4 ) ) )
!= ( sK1 @ ( sK0 @ sK2 @ sK3 ) @ ( sK0 @ sK2 @ sK4 ) ) )
| ( sK7
= ( sK0 @ sK5 @ sK7 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f20,plain,
( ( ( sK0 @ sK2 @ ( sK1 @ sK3 @ ( sK0 @ sK2 @ sK4 ) ) )
!= ( sK1 @ ( sK0 @ sK2 @ sK3 ) @ ( sK0 @ sK2 @ sK4 ) ) )
| ( ( sK0 @ sK5 @ ( sK1 @ sK6 @ sK7 ) )
!= ( sK1 @ ( sK0 @ sK5 @ sK6 ) @ sK7 ) ) ),
inference(cnf_transformation,[],[f9]) ).
thf(f24,definition,
( spl8_1
<=> ! [X13: a,X12: a,X11: a] :
( ( ( sK0 @ X11 @ ( sK1 @ X12 @ X13 ) )
= ( sK1 @ ( sK0 @ X11 @ X12 ) @ X13 ) )
| ( ( sK0 @ X11 @ X13 )
!= X13 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_1])],[avatar_definition]) ).
thf(f25,plain,
( ! [X11: a,X12: a,X13: a] :
( ( ( sK0 @ X11 @ X13 )
!= X13 )
| ( ( sK0 @ X11 @ ( sK1 @ X12 @ X13 ) )
= ( sK1 @ ( sK0 @ X11 @ X12 ) @ X13 ) ) )
| ~ spl8_1 ),
inference(avatar_component_clause,[],[f24]) ).
thf(f27,definition,
( spl8_2
<=> ! [X9: a,X8: a,X10: a] :
( ( sK0 @ X8 @ ( sK1 @ X9 @ ( sK0 @ X8 @ X10 ) ) )
= ( sK1 @ ( sK0 @ X8 @ X9 ) @ ( sK0 @ X8 @ X10 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_2])],[avatar_definition]) ).
thf(f28,plain,
( ! [X10: a,X8: a,X9: a] :
( ( sK0 @ X8 @ ( sK1 @ X9 @ ( sK0 @ X8 @ X10 ) ) )
= ( sK1 @ ( sK0 @ X8 @ X9 ) @ ( sK0 @ X8 @ X10 ) ) )
| ~ spl8_2 ),
inference(avatar_component_clause,[],[f27]) ).
thf(f29,plain,
( spl8_1
| spl8_2 ),
inference(avatar_split_clause,[],[f18,f27,f24]) ).
thf(f31,definition,
( spl8_3
<=> ( sK7
= ( sK0 @ sK5 @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_3])],[avatar_definition]) ).
thf(f33,plain,
( ( sK7
= ( sK0 @ sK5 @ sK7 ) )
| ~ spl8_3 ),
inference(avatar_component_clause,[],[f31]) ).
thf(f35,definition,
( spl8_4
<=> ( ( sK0 @ sK2 @ ( sK1 @ sK3 @ ( sK0 @ sK2 @ sK4 ) ) )
= ( sK1 @ ( sK0 @ sK2 @ sK3 ) @ ( sK0 @ sK2 @ sK4 ) ) ) ),
introduced(definition,[new_symbols(definition,[spl8_4])],[avatar_definition]) ).
thf(f37,plain,
( ( ( sK0 @ sK2 @ ( sK1 @ sK3 @ ( sK0 @ sK2 @ sK4 ) ) )
!= ( sK1 @ ( sK0 @ sK2 @ sK3 ) @ ( sK0 @ sK2 @ sK4 ) ) )
| spl8_4 ),
inference(avatar_component_clause,[],[f35]) ).
thf(f38,plain,
( spl8_3
| ~ spl8_4 ),
inference(avatar_split_clause,[],[f19,f35,f31]) ).
thf(f40,definition,
( spl8_5
<=> ( ( sK0 @ sK5 @ ( sK1 @ sK6 @ sK7 ) )
= ( sK1 @ ( sK0 @ sK5 @ sK6 ) @ sK7 ) ) ),
introduced(definition,[new_symbols(definition,[spl8_5])],[avatar_definition]) ).
thf(f42,plain,
( ( ( sK0 @ sK5 @ ( sK1 @ sK6 @ sK7 ) )
!= ( sK1 @ ( sK0 @ sK5 @ sK6 ) @ sK7 ) )
| spl8_5 ),
inference(avatar_component_clause,[],[f40]) ).
thf(f43,plain,
( ~ spl8_5
| ~ spl8_4 ),
inference(avatar_split_clause,[],[f20,f35,f40]) ).
thf(f44,plain,
( $false
| ~ spl8_2
| spl8_4 ),
inference(forward_subsumption_resolution,[],[f37,f28]) ).
thf(f45,plain,
( ~ spl8_2
| spl8_4 ),
inference(avatar_contradiction_clause,[],[f44]) ).
thf(f62,plain,
! [X0: a,X1: a] :
( ( sK0 @ X0 @ X1 )
= ( sK0 @ X0 @ ( sK0 @ X0 @ X1 ) ) ),
inference(constrained_superposition,[],[f12,f10]) ).
thf(f183,plain,
( ! [X2: a,X0: a,X1: a] :
( ( ( sK0 @ X0 @ X1 )
!= ( sK0 @ X0 @ X1 ) )
| ( ( sK0 @ X0 @ ( sK1 @ X2 @ ( sK0 @ X0 @ X1 ) ) )
= ( sK1 @ ( sK0 @ X0 @ X2 ) @ ( sK0 @ X0 @ X1 ) ) ) )
| ~ spl8_1 ),
inference(constrained_superposition,[],[f25,f62]) ).
thf(f187,plain,
( ! [X2: a,X0: a,X1: a] :
( ( sK0 @ X0 @ ( sK1 @ X2 @ ( sK0 @ X0 @ X1 ) ) )
= ( sK1 @ ( sK0 @ X0 @ X2 ) @ ( sK0 @ X0 @ X1 ) ) )
| ~ spl8_1 ),
inference(trivial_inequality_removal,[],[f183]) ).
thf(f189,plain,
( spl8_2
| ~ spl8_1 ),
inference(avatar_split_clause,[],[f187,f24,f27]) ).
thf(f220,plain,
( ! [X0: a] :
( ( sK0 @ sK5 @ ( sK1 @ X0 @ sK7 ) )
= ( sK1 @ ( sK0 @ sK5 @ X0 ) @ sK7 ) )
| ~ spl8_2
| ~ spl8_3 ),
inference(constrained_superposition,[],[f28,f33]) ).
thf(f1408,plain,
( ( ( sK0 @ sK5 @ ( sK1 @ sK6 @ sK7 ) )
!= ( sK0 @ sK5 @ ( sK1 @ sK6 @ sK7 ) ) )
| ~ spl8_2
| ~ spl8_3
| spl8_5 ),
inference(constrained_superposition,[],[f42,f220]) ).
thf(f1409,plain,
( $false
| ~ spl8_2
| ~ spl8_3
| spl8_5 ),
inference(trivial_inequality_removal,[],[f1408]) ).
thf(f1410,plain,
( ~ spl8_2
| ~ spl8_3
| spl8_5 ),
inference(avatar_contradiction_clause,[],[f1409]) ).
cnf(s1,plain,
( spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f29]) ).
cnf(s2,plain,
( spl8_3
| ~ spl8_4 ),
inference(sat_conversion,[],[f38]) ).
cnf(s3,plain,
( ~ spl8_4
| ~ spl8_5 ),
inference(sat_conversion,[],[f43]) ).
cnf(s4,plain,
( ~ spl8_2
| spl8_4 ),
inference(sat_conversion,[],[f45]) ).
cnf(s5,plain,
( ~ spl8_1
| spl8_2 ),
inference(sat_conversion,[],[f189]) ).
cnf(s7,plain,
( ~ spl8_2
| ~ spl8_3
| spl8_5 ),
inference(sat_conversion,[],[f1410]) ).
cnf(s8,plain,
~ spl8_2,
inference(rat,[],[s7,s2,s3,s4]) ).
cnf(s9,plain,
~ spl8_1,
inference(rat,[],[s5,s8]) ).
cnf(s10,plain,
$false,
inference(rat,[],[s1,s8,s9]) ).
thf(f1439,plain,
$false,
inference(avatar_sat_refutation,[],[s10]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV000^5 : TPTP v9.3.1. Released v4.0.0.
% 0.00/0.06 % Command : run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.19 % Computer : n007.cluster.edu
% 0.08/0.19 % Model : x86_64 x86_64
% 0.08/0.19 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.08/0.19 % Memory : 8046.5625MB
% 0.08/0.19 % OS : Linux 6.8.0-71-generic
% 0.08/0.19 % CPULimit : 300
% 0.08/0.19 % WCLimit : 300
% 0.08/0.19 % DateTime : Tue Sep 29 14:55:41 UTC 2026
% 0.08/0.19 % CPUTime :
% 0.08/0.19 Running run_vampire /export/starexec/sandbox2/benchmark/theBenchmark.p 300 SAT
% 0.08/0.23 Running first-order model finding
% 0.08/0.23 Running: /export/starexec/sandbox2/solver/bin/vampire-ho --input_syntax tptp --output_axiom_names on --mode casc --intent sat -m 16384 --cores 7 -t 300 /export/starexec/sandbox2/benchmark/theBenchmark.p
% 0.18/0.29 % (3467591)Will run a generic schedule for satisfiability detection.
% 0.18/0.29 % (3467601)ott+1_1_to=lpo:sil=16000:sp=reverse_arity:erd=off:random_seed=2872420833:i=131_2999 on theBenchmark for (2999ds/131Mi)
% 0.18/0.29 % (3467597)% WARNING: option uhcvi not known.
% 0.18/0.29 % (3467599)dis+10_1_sil=32000:sp=arity:random_seed=3341119457:i=103:fgj=on_2999 on theBenchmark for (2999ds/103Mi)
% 0.18/0.29 % (3467596)fmb+10_1_sas=cadical:bce=on:rp=on:random_seed=959869563_2999 on theBenchmark for (2999ds/0Mi)
% 0.18/0.29 % (3467597)dis+11_61:31_drc=ordering:lsd=5:bsr=unit_only:rp=on:newcnf=on:random_seed=2384345294:i=135531:add=off:rawr=on_2999 on theBenchmark for (2999ds/135531Mi)
% 0.18/0.29 % (3467598)dis+10_161_sil=256000:plsq=on:plsqr=61199697,1048576:gs=on:alpa=true:sac=on:slsq=on:cn=on:random_seed=1322683351:i=88024:add=on:rawr=on_2999 on theBenchmark for (2999ds/88024Mi)
% 0.18/0.29 % (3467600)ott+31_1_sil=16000:lcm=predicate:bce=on:newcnf=on:random_seed=2789075822:i=116_2999 on theBenchmark for (2999ds/116Mi)
% 0.18/0.29 % (3467597)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.29 % (3467602)ott-3_16_to=lpo:sil=16000:sp=arity:fd=off:rp=on:random_seed=1116996898:i=159:bs=unit_only:nicw=on:fsr=off:amm=off_2999 on theBenchmark for (2999ds/159Mi)
% 0.18/0.29 % (3467600)WARNING: Not using 'newcnf' as currently not compatible with higher-order inputs.
% 0.18/0.29 % Exception at run slice level
% 0.18/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.29 % (3467597)WARNING: Look ahead literal selection is not currently compatible with higher-order. Ignoring request to use
% 0.18/0.29 % (3467610)fmb+10_1_fmbas=predicate:sil=64000:sas=cadical:random_seed=3792456115:i=714:nm=2_2999 on theBenchmark for (2999ds/714Mi)
% 0.18/0.29 % Exception at run slice level
% 0.18/0.29 User error: Finite model building is currently not compatible with polymorphism or higher-order constructs
% 0.18/0.29 % (3467601) found proof, printing to "/export/starexec/sandbox2/tmp/vampire-proof-3467591-3467601"...
% 0.18/0.29 % (3467601)...printing done.
% 0.18/0.29 % (3467601)Refutation found. Thanks to Tanya!
% 0.18/0.29 % SZS status Theorem for theBenchmark
% 0.18/0.29 % SZS output start Proof for theBenchmark
% See solution above
% 0.18/0.29 % (3467601)------------------------------
% 0.18/0.29 % (3467601)Version: Vampire 5.0.1 (Release build, commit 5ef7c2677 on 2026-07-16 16:54:09 +0200)
% 0.18/0.29 % (3467601)Linked with Z3 4.14.0.0 3c47fd96cf5645d0c42b2c819d9e9a84380aa721 z3-4.8.4-9178-g3c47fd96c
% 0.18/0.29 % (3467601)CaDiCaL version: 2.1.3
% 0.18/0.29 % (3467601)Termination reason: Refutation
% 0.18/0.29 % (3467601)Time elapsed: 0.036 s
% 0.18/0.29 % (3467601)Peak memory usage: 14 MB
% 0.18/0.29 % (3467601)Instructions burned: 132 (million)
% 0.18/0.29 % (3467591)Success in time 0.062 s
% 0.18/0.29 % Vampire exiting
%------------------------------------------------------------------------------