%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV109^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n002.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:40:18 AM UTC 2026
% Result : Theorem 1.49s 1.40s
% Output : Refutation 1.49s
% Verified :
% SZS Type : Refutation
% Derivation depth : 26
% Number of leaves : 14
% Syntax : Number of formulae : 101 ( 3 unt; 0 typ; 7 def)
% Number of atoms : 1203 ( 422 equ; 0 cnn)
% Maximal formula atoms : 48 ( 11 avg)
% Number of connectives : 2065 ( 288 ~; 278 |; 126 &;1308 @)
% ( 7 <=>; 58 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 164 ( 164 >; 0 *; 0 +; 0 <<)
% Number of symbols : 23 ( 20 usr; 11 con; 0-4 aty)
% Number of variables : 473 ( 92 ^; 313 !; 68 ?; 473 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a ).
thf(func_def_5,type,
sK1: a ).
thf(func_def_6,type,
sK2: a > a > $o ).
thf(func_def_7,type,
sK3: a > a > $o ).
thf(func_def_8,type,
sK4: ( a > a > $o ) > a ).
thf(func_def_9,type,
sK5: ( a > a > $o ) > a ).
thf(func_def_10,type,
sK6: ( a > a > $o ) > a ).
thf(func_def_11,type,
sK7: ( a > a > $o ) > a ).
thf(func_def_12,type,
sK8: ( a > a > $o ) > a ).
thf(func_def_13,type,
sK9: a > a > $o ).
thf(func_def_14,type,
sK10: a > a > a > a > $o ).
thf(func_def_15,type,
sK11: a > a > a > a > $o ).
thf(func_def_18,type,
ph13:
!>[X0: $tType] : X0 ).
thf(f897,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f224,f236,f409,f534,f566,f571,f572,f715,f858,f868,f870,f873,f896]) ).
thf(f896,plain,
( ~ spl12_20
| spl12_4
| ~ spl12_27 ),
inference(avatar_split_clause,[status(thm)],[f895,f568,f82,f402]) ).
thf(f402,definition,
( spl12_20
<=> ( ( sK9 @ ( sK8 @ sK9 ) @ ( sK7 @ sK9 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl12_20])],[avatar_definition]) ).
thf(f82,definition,
( spl12_4
<=> ( ( sK9 @ ( sK6 @ sK9 ) @ ( sK7 @ sK9 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl12_4])],[avatar_definition]) ).
thf(f568,definition,
( spl12_27
<=> ( $true
= ( sK9 @ ( sK6 @ sK9 ) @ ( sK8 @ sK9 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl12_27])],[avatar_definition]) ).
thf(f895,plain,
( ( ( sK9 @ ( sK8 @ sK9 ) @ ( sK7 @ sK9 ) )
!= $true )
| spl12_4
| ~ spl12_27 ),
inference(trivial_inequality_removal,[status(thm)],[f894]) ).
thf(f894,plain,
( ( $true != $true )
| ( ( sK9 @ ( sK8 @ sK9 ) @ ( sK7 @ sK9 ) )
!= $true )
| spl12_4
| ~ spl12_27 ),
inference(superposition,[status(thm)],[f240,f570]) ).
thf(f570,plain,
( ( $true
= ( sK9 @ ( sK6 @ sK9 ) @ ( sK8 @ sK9 ) ) )
| ~ spl12_27 ),
inference(avatar_component_clause,[status(thm)],[f568]) ).
thf(f240,plain,
( ! [X0: a] :
( ( ( sK9 @ ( sK6 @ sK9 ) @ X0 )
!= $true )
| ( ( sK9 @ X0 @ ( sK7 @ sK9 ) )
!= $true ) )
| spl12_4 ),
inference(trivial_inequality_removal,[status(thm)],[f239]) ).
thf(f239,plain,
( ! [X0: a] :
( ( ( sK9 @ X0 @ ( sK7 @ sK9 ) )
!= $true )
| ( $true != $true )
| ( ( sK9 @ ( sK6 @ sK9 ) @ X0 )
!= $true ) )
| spl12_4 ),
inference(superposition,[status(thm)],[f84,f17]) ).
thf(f17,plain,
! [X26: a,X27: a,X25: a] :
( ( ( sK9 @ X25 @ X26 )
= $true )
| ( $true
!= ( sK9 @ X27 @ X26 ) )
| ( ( sK9 @ X25 @ X27 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
( ! [X4: a > a > $o] :
( ( ( ( ( sK2 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) )
= $true )
| ( ( sK3 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) )
= $true ) )
& ( $true
!= ( X4 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) ) ) )
| ( ( ( X4 @ ( sK6 @ X4 ) @ ( sK8 @ X4 ) )
= $true )
& ( ( X4 @ ( sK8 @ X4 ) @ ( sK7 @ X4 ) )
= $true )
& ( ( X4 @ ( sK6 @ X4 ) @ ( sK7 @ X4 ) )
!= $true ) )
| ( ( X4 @ sK1 @ sK0 )
= $true ) )
& ! [X11: a,X12: a] :
( ( ( sK9 @ X12 @ X11 )
= $true )
| ( ( ( sK10 @ X12 @ X11 @ X12 @ X11 )
!= $true )
& ! [X14: a,X15: a] :
( ( ( sK3 @ X14 @ X15 )
!= $true )
| ( ( sK10 @ X12 @ X11 @ X14 @ X15 )
= $true ) )
& ! [X16: a,X17: a,X18: a] :
( ( $true
= ( sK10 @ X12 @ X11 @ X16 @ X17 ) )
| ( ( sK10 @ X12 @ X11 @ X16 @ X18 )
!= $true )
| ( $true
!= ( sK10 @ X12 @ X11 @ X18 @ X17 ) ) )
& ! [X20: a,X21: a,X22: a] :
( ( $true
= ( sK11 @ X12 @ X11 @ X20 @ X22 ) )
| ( $true
!= ( sK11 @ X12 @ X11 @ X21 @ X22 ) )
| ( ( sK11 @ X12 @ X11 @ X20 @ X21 )
!= $true ) )
& ( $true
!= ( sK11 @ X12 @ X11 @ X12 @ X11 ) )
& ! [X23: a,X24: a] :
( ( ( sK2 @ X23 @ X24 )
!= $true )
| ( ( sK11 @ X12 @ X11 @ X23 @ X24 )
= $true ) ) ) )
& ! [X25: a,X26: a,X27: a] :
( ( ( sK9 @ X25 @ X26 )
= $true )
| ( $true
!= ( sK9 @ X27 @ X26 ) )
| ( ( sK9 @ X25 @ X27 )
!= $true ) )
& ( ( sK9 @ sK1 @ sK0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11])],[f8,f14,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: a,X1: a,X2: a > a > $o,X3: a > a > $o] :
( ! [X4: a > a > $o] :
( ? [X5: a,X6: a] :
( ( ( ( X2 @ X6 @ X5 )
= $true )
| ( ( X3 @ X6 @ X5 )
= $true ) )
& ( $true
!= ( X4 @ X6 @ X5 ) ) )
| ? [X7: a,X8: a,X9: a] :
( ( ( X4 @ X7 @ X9 )
= $true )
& ( ( X4 @ X9 @ X8 )
= $true )
& ( ( X4 @ X7 @ X8 )
!= $true ) )
| ( ( X4 @ X1 @ X0 )
= $true ) )
& ? [X10: a > a > $o] :
( ! [X11: a,X12: a] :
( ( $true
= ( X10 @ X12 @ X11 ) )
| ( ? [X13: a > a > $o] :
( ( ( X13 @ X12 @ X11 )
!= $true )
& ! [X14: a,X15: a] :
( ( $true
!= ( X3 @ X14 @ X15 ) )
| ( ( X13 @ X14 @ X15 )
= $true ) )
& ! [X16: a,X17: a,X18: a] :
( ( $true
= ( X13 @ X16 @ X17 ) )
| ( $true
!= ( X13 @ X16 @ X18 ) )
| ( ( X13 @ X18 @ X17 )
!= $true ) ) )
& ? [X19: a > a > $o] :
( ! [X20: a,X21: a,X22: a] :
( ( $true
= ( X19 @ X20 @ X22 ) )
| ( ( X19 @ X21 @ X22 )
!= $true )
| ( $true
!= ( X19 @ X20 @ X21 ) ) )
& ( ( X19 @ X12 @ X11 )
!= $true )
& ! [X23: a,X24: a] :
( ( $true
!= ( X2 @ X23 @ X24 ) )
| ( ( X19 @ X23 @ X24 )
= $true ) ) ) ) )
& ! [X25: a,X26: a,X27: a] :
( ( ( X10 @ X25 @ X26 )
= $true )
| ( ( X10 @ X27 @ X26 )
!= $true )
| ( $true
!= ( X10 @ X25 @ X27 ) ) )
& ( $true
!= ( X10 @ X1 @ X0 ) ) ) )
=> ( ! [X4: a > a > $o] :
( ? [X6: a,X5: a] :
( ( ( ( sK2 @ X6 @ X5 )
= $true )
| ( ( sK3 @ X6 @ X5 )
= $true ) )
& ( $true
!= ( X4 @ X6 @ X5 ) ) )
| ? [X7: a,X8: a,X9: a] :
( ( ( X4 @ X7 @ X9 )
= $true )
& ( ( X4 @ X9 @ X8 )
= $true )
& ( ( X4 @ X7 @ X8 )
!= $true ) )
| ( ( X4 @ sK1 @ sK0 )
= $true ) )
& ? [X10: a > a > $o] :
( ! [X12: a,X11: a] :
( ( $true
= ( X10 @ X12 @ X11 ) )
| ( ? [X13: a > a > $o] :
( ( ( X13 @ X12 @ X11 )
!= $true )
& ! [X15: a,X14: a] :
( ( ( sK3 @ X14 @ X15 )
!= $true )
| ( ( X13 @ X14 @ X15 )
= $true ) )
& ! [X16: a,X17: a,X18: a] :
( ( $true
= ( X13 @ X16 @ X17 ) )
| ( $true
!= ( X13 @ X16 @ X18 ) )
| ( ( X13 @ X18 @ X17 )
!= $true ) ) )
& ? [X19: a > a > $o] :
( ! [X20: a,X21: a,X22: a] :
( ( $true
= ( X19 @ X20 @ X22 ) )
| ( ( X19 @ X21 @ X22 )
!= $true )
| ( $true
!= ( X19 @ X20 @ X21 ) ) )
& ( ( X19 @ X12 @ X11 )
!= $true )
& ! [X24: a,X23: a] :
( ( ( sK2 @ X23 @ X24 )
!= $true )
| ( ( X19 @ X23 @ X24 )
= $true ) ) ) ) )
& ! [X25: a,X26: a,X27: a] :
( ( ( X10 @ X25 @ X26 )
= $true )
| ( ( X10 @ X27 @ X26 )
!= $true )
| ( $true
!= ( X10 @ X25 @ X27 ) ) )
& ( $true
!= ( X10 @ sK1 @ sK0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X4: a > a > $o] :
( ? [X6: a,X5: a] :
( ( ( ( sK2 @ X6 @ X5 )
= $true )
| ( ( sK3 @ X6 @ X5 )
= $true ) )
& ( $true
!= ( X4 @ X6 @ X5 ) ) )
=> ( ( ( ( sK2 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) )
= $true )
| ( ( sK3 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) )
= $true ) )
& ( $true
!= ( X4 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X4: a > a > $o] :
( ? [X7: a,X8: a,X9: a] :
( ( ( X4 @ X7 @ X9 )
= $true )
& ( ( X4 @ X9 @ X8 )
= $true )
& ( ( X4 @ X7 @ X8 )
!= $true ) )
=> ( ( ( X4 @ ( sK6 @ X4 ) @ ( sK8 @ X4 ) )
= $true )
& ( ( X4 @ ( sK8 @ X4 ) @ ( sK7 @ X4 ) )
= $true )
& ( ( X4 @ ( sK6 @ X4 ) @ ( sK7 @ X4 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X10: a > a > $o] :
( ! [X12: a,X11: a] :
( ( $true
= ( X10 @ X12 @ X11 ) )
| ( ? [X13: a > a > $o] :
( ( ( X13 @ X12 @ X11 )
!= $true )
& ! [X15: a,X14: a] :
( ( ( sK3 @ X14 @ X15 )
!= $true )
| ( ( X13 @ X14 @ X15 )
= $true ) )
& ! [X16: a,X17: a,X18: a] :
( ( $true
= ( X13 @ X16 @ X17 ) )
| ( $true
!= ( X13 @ X16 @ X18 ) )
| ( ( X13 @ X18 @ X17 )
!= $true ) ) )
& ? [X19: a > a > $o] :
( ! [X20: a,X21: a,X22: a] :
( ( $true
= ( X19 @ X20 @ X22 ) )
| ( ( X19 @ X21 @ X22 )
!= $true )
| ( $true
!= ( X19 @ X20 @ X21 ) ) )
& ( ( X19 @ X12 @ X11 )
!= $true )
& ! [X24: a,X23: a] :
( ( ( sK2 @ X23 @ X24 )
!= $true )
| ( ( X19 @ X23 @ X24 )
= $true ) ) ) ) )
& ! [X25: a,X26: a,X27: a] :
( ( ( X10 @ X25 @ X26 )
= $true )
| ( ( X10 @ X27 @ X26 )
!= $true )
| ( $true
!= ( X10 @ X25 @ X27 ) ) )
& ( $true
!= ( X10 @ sK1 @ sK0 ) ) )
=> ( ! [X12: a,X11: a] :
( ( ( sK9 @ X12 @ X11 )
= $true )
| ( ? [X13: a > a > $o] :
( ( ( X13 @ X12 @ X11 )
!= $true )
& ! [X15: a,X14: a] :
( ( ( sK3 @ X14 @ X15 )
!= $true )
| ( ( X13 @ X14 @ X15 )
= $true ) )
& ! [X16: a,X17: a,X18: a] :
( ( $true
= ( X13 @ X16 @ X17 ) )
| ( $true
!= ( X13 @ X16 @ X18 ) )
| ( ( X13 @ X18 @ X17 )
!= $true ) ) )
& ? [X19: a > a > $o] :
( ! [X20: a,X21: a,X22: a] :
( ( $true
= ( X19 @ X20 @ X22 ) )
| ( ( X19 @ X21 @ X22 )
!= $true )
| ( $true
!= ( X19 @ X20 @ X21 ) ) )
& ( ( X19 @ X12 @ X11 )
!= $true )
& ! [X24: a,X23: a] :
( ( ( sK2 @ X23 @ X24 )
!= $true )
| ( ( X19 @ X23 @ X24 )
= $true ) ) ) ) )
& ! [X27: a,X26: a,X25: a] :
( ( ( sK9 @ X25 @ X26 )
= $true )
| ( $true
!= ( sK9 @ X27 @ X26 ) )
| ( ( sK9 @ X25 @ X27 )
!= $true ) )
& ( ( sK9 @ sK1 @ sK0 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X11: a,X12: a] :
( ? [X13: a > a > $o] :
( ( ( X13 @ X12 @ X11 )
!= $true )
& ! [X15: a,X14: a] :
( ( ( sK3 @ X14 @ X15 )
!= $true )
| ( ( X13 @ X14 @ X15 )
= $true ) )
& ! [X16: a,X17: a,X18: a] :
( ( $true
= ( X13 @ X16 @ X17 ) )
| ( $true
!= ( X13 @ X16 @ X18 ) )
| ( ( X13 @ X18 @ X17 )
!= $true ) ) )
=> ( ( ( sK10 @ X12 @ X11 @ X12 @ X11 )
!= $true )
& ! [X15: a,X14: a] :
( ( ( sK3 @ X14 @ X15 )
!= $true )
| ( ( sK10 @ X12 @ X11 @ X14 @ X15 )
= $true ) )
& ! [X18: a,X17: a,X16: a] :
( ( $true
= ( sK10 @ X12 @ X11 @ X16 @ X17 ) )
| ( ( sK10 @ X12 @ X11 @ X16 @ X18 )
!= $true )
| ( $true
!= ( sK10 @ X12 @ X11 @ X18 @ X17 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
! [X11: a,X12: a] :
( ? [X19: a > a > $o] :
( ! [X20: a,X21: a,X22: a] :
( ( $true
= ( X19 @ X20 @ X22 ) )
| ( ( X19 @ X21 @ X22 )
!= $true )
| ( $true
!= ( X19 @ X20 @ X21 ) ) )
& ( ( X19 @ X12 @ X11 )
!= $true )
& ! [X24: a,X23: a] :
( ( ( sK2 @ X23 @ X24 )
!= $true )
| ( ( X19 @ X23 @ X24 )
= $true ) ) )
=> ( ! [X22: a,X21: a,X20: a] :
( ( $true
= ( sK11 @ X12 @ X11 @ X20 @ X22 ) )
| ( $true
!= ( sK11 @ X12 @ X11 @ X21 @ X22 ) )
| ( ( sK11 @ X12 @ X11 @ X20 @ X21 )
!= $true ) )
& ( $true
!= ( sK11 @ X12 @ X11 @ X12 @ X11 ) )
& ! [X24: a,X23: a] :
( ( ( sK2 @ X23 @ X24 )
!= $true )
| ( ( sK11 @ X12 @ X11 @ X23 @ X24 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a,X1: a,X2: a > a > $o,X3: a > a > $o] :
( ! [X4: a > a > $o] :
( ? [X5: a,X6: a] :
( ( ( ( X2 @ X6 @ X5 )
= $true )
| ( ( X3 @ X6 @ X5 )
= $true ) )
& ( $true
!= ( X4 @ X6 @ X5 ) ) )
| ? [X7: a,X8: a,X9: a] :
( ( ( X4 @ X7 @ X9 )
= $true )
& ( ( X4 @ X9 @ X8 )
= $true )
& ( ( X4 @ X7 @ X8 )
!= $true ) )
| ( ( X4 @ X1 @ X0 )
= $true ) )
& ? [X10: a > a > $o] :
( ! [X11: a,X12: a] :
( ( $true
= ( X10 @ X12 @ X11 ) )
| ( ? [X13: a > a > $o] :
( ( ( X13 @ X12 @ X11 )
!= $true )
& ! [X14: a,X15: a] :
( ( $true
!= ( X3 @ X14 @ X15 ) )
| ( ( X13 @ X14 @ X15 )
= $true ) )
& ! [X16: a,X17: a,X18: a] :
( ( $true
= ( X13 @ X16 @ X17 ) )
| ( $true
!= ( X13 @ X16 @ X18 ) )
| ( ( X13 @ X18 @ X17 )
!= $true ) ) )
& ? [X19: a > a > $o] :
( ! [X20: a,X21: a,X22: a] :
( ( $true
= ( X19 @ X20 @ X22 ) )
| ( ( X19 @ X21 @ X22 )
!= $true )
| ( $true
!= ( X19 @ X20 @ X21 ) ) )
& ( ( X19 @ X12 @ X11 )
!= $true )
& ! [X23: a,X24: a] :
( ( $true
!= ( X2 @ X23 @ X24 ) )
| ( ( X19 @ X23 @ X24 )
= $true ) ) ) ) )
& ! [X25: a,X26: a,X27: a] :
( ( ( X10 @ X25 @ X26 )
= $true )
| ( ( X10 @ X27 @ X26 )
!= $true )
| ( $true
!= ( X10 @ X25 @ X27 ) ) )
& ( $true
!= ( X10 @ X1 @ X0 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X1: a,X2: a,X0: a > a > $o,X3: a > a > $o] :
( ! [X4: a > a > $o] :
( ? [X8: a,X9: a] :
( ( ( ( X0 @ X9 @ X8 )
= $true )
| ( ( X3 @ X9 @ X8 )
= $true ) )
& ( ( X4 @ X9 @ X8 )
!= $true ) )
| ? [X7: a,X6: a,X5: a] :
( ( ( X4 @ X7 @ X5 )
= $true )
& ( ( X4 @ X5 @ X6 )
= $true )
& ( $true
!= ( X4 @ X7 @ X6 ) ) )
| ( ( X4 @ X2 @ X1 )
= $true ) )
& ? [X10: a > a > $o] :
( ! [X15: a,X14: a] :
( ( ( X10 @ X14 @ X15 )
= $true )
| ( ? [X16: a > a > $o] :
( ( $true
!= ( X16 @ X14 @ X15 ) )
& ! [X18: a,X17: a] :
( ( $true
!= ( X3 @ X18 @ X17 ) )
| ( $true
= ( X16 @ X18 @ X17 ) ) )
& ! [X21: a,X19: a,X20: a] :
( ( ( X16 @ X21 @ X19 )
= $true )
| ( $true
!= ( X16 @ X21 @ X20 ) )
| ( ( X16 @ X20 @ X19 )
!= $true ) ) )
& ? [X22: a > a > $o] :
( ! [X25: a,X27: a,X26: a] :
( ( $true
= ( X22 @ X25 @ X26 ) )
| ( $true
!= ( X22 @ X27 @ X26 ) )
| ( ( X22 @ X25 @ X27 )
!= $true ) )
& ( ( X22 @ X14 @ X15 )
!= $true )
& ! [X23: a,X24: a] :
( ( $true
!= ( X0 @ X23 @ X24 ) )
| ( $true
= ( X22 @ X23 @ X24 ) ) ) ) ) )
& ! [X13: a,X11: a,X12: a] :
( ( ( X10 @ X13 @ X11 )
= $true )
| ( $true
!= ( X10 @ X12 @ X11 ) )
| ( ( X10 @ X13 @ X12 )
!= $true ) )
& ( ( X10 @ X2 @ X1 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X2: a,X0: a > a > $o,X3: a > a > $o,X1: a] :
( ? [X10: a > a > $o] :
( ( ( X10 @ X2 @ X1 )
!= $true )
& ! [X15: a,X14: a] :
( ( ( X10 @ X14 @ X15 )
= $true )
| ( ? [X16: a > a > $o] :
( ( $true
!= ( X16 @ X14 @ X15 ) )
& ! [X19: a,X21: a,X20: a] :
( ( ( X16 @ X21 @ X19 )
= $true )
| ( ( X16 @ X20 @ X19 )
!= $true )
| ( $true
!= ( X16 @ X21 @ X20 ) ) )
& ! [X18: a,X17: a] :
( ( $true
!= ( X3 @ X18 @ X17 ) )
| ( $true
= ( X16 @ X18 @ X17 ) ) ) )
& ? [X22: a > a > $o] :
( ( ( X22 @ X14 @ X15 )
!= $true )
& ! [X23: a,X24: a] :
( ( $true
!= ( X0 @ X23 @ X24 ) )
| ( $true
= ( X22 @ X23 @ X24 ) ) )
& ! [X26: a,X25: a,X27: a] :
( ( $true
= ( X22 @ X25 @ X26 ) )
| ( $true
!= ( X22 @ X27 @ X26 ) )
| ( ( X22 @ X25 @ X27 )
!= $true ) ) ) ) )
& ! [X13: a,X11: a,X12: a] :
( ( ( X10 @ X13 @ X11 )
= $true )
| ( $true
!= ( X10 @ X12 @ X11 ) )
| ( ( X10 @ X13 @ X12 )
!= $true ) ) )
& ! [X4: a > a > $o] :
( ( ( X4 @ X2 @ X1 )
= $true )
| ? [X7: a,X6: a,X5: a] :
( ( $true
!= ( X4 @ X7 @ X6 ) )
& ( ( X4 @ X5 @ X6 )
= $true )
& ( ( X4 @ X7 @ X5 )
= $true ) )
| ? [X8: a,X9: a] :
( ( ( ( X0 @ X9 @ X8 )
= $true )
| ( ( X3 @ X9 @ X8 )
= $true ) )
& ( ( X4 @ X9 @ X8 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X2: a,X0: a > a > $o,X3: a > a > $o,X1: a] :
( ! [X4: a > a > $o] :
( ( ! [X7: a,X6: a,X5: a] :
( ( ( ( X4 @ X5 @ X6 )
= $true )
& ( ( X4 @ X7 @ X5 )
= $true ) )
=> ( $true
= ( X4 @ X7 @ X6 ) ) )
& ! [X8: a,X9: a] :
( ( ( ( X0 @ X9 @ X8 )
= $true )
| ( ( X3 @ X9 @ X8 )
= $true ) )
=> ( ( X4 @ X9 @ X8 )
= $true ) ) )
=> ( ( X4 @ X2 @ X1 )
= $true ) )
=> ! [X10: a > a > $o] :
( ( ! [X15: a,X14: a] :
( ( ! [X16: a > a > $o] :
( ( ! [X19: a,X21: a,X20: a] :
( ( ( ( X16 @ X20 @ X19 )
= $true )
& ( $true
= ( X16 @ X21 @ X20 ) ) )
=> ( ( X16 @ X21 @ X19 )
= $true ) )
& ! [X17: a,X18: a] :
( ( $true
= ( X3 @ X18 @ X17 ) )
=> ( $true
= ( X16 @ X18 @ X17 ) ) ) )
=> ( $true
= ( X16 @ X14 @ X15 ) ) )
| ! [X22: a > a > $o] :
( ( ! [X24: a,X23: a] :
( ( $true
= ( X0 @ X23 @ X24 ) )
=> ( $true
= ( X22 @ X23 @ X24 ) ) )
& ! [X26: a,X25: a,X27: a] :
( ( ( $true
= ( X22 @ X27 @ X26 ) )
& ( ( X22 @ X25 @ X27 )
= $true ) )
=> ( $true
= ( X22 @ X25 @ X26 ) ) ) )
=> ( ( X22 @ X14 @ X15 )
= $true ) ) )
=> ( ( X10 @ X14 @ X15 )
= $true ) )
& ! [X13: a,X11: a,X12: a] :
( ( ( $true
= ( X10 @ X12 @ X11 ) )
& ( ( X10 @ X13 @ X12 )
= $true ) )
=> ( ( X10 @ X13 @ X11 )
= $true ) ) )
=> ( ( X10 @ X2 @ X1 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a,X2: a,X3: a > a > $o] :
( ! [X4: a > a > $o] :
( ( ! [X5: a,X6: a,X7: a] :
( ( ( X4 @ X5 @ X6 )
& ( X4 @ X7 @ X5 ) )
=> ( X4 @ X7 @ X6 ) )
& ! [X8: a,X9: a] :
( ( ( X3 @ X9 @ X8 )
| ( X0 @ X9 @ X8 ) )
=> ( X4 @ X9 @ X8 ) ) )
=> ( X4 @ X2 @ X1 ) )
=> ! [X10: a > a > $o] :
( ( ! [X11: a,X12: a,X13: a] :
( ( ( X10 @ X12 @ X11 )
& ( X10 @ X13 @ X12 ) )
=> ( X10 @ X13 @ X11 ) )
& ! [X14: a,X15: a] :
( ( ! [X16: a > a > $o] :
( ( ! [X17: a,X18: a] :
( ( X3 @ X18 @ X17 )
=> ( X16 @ X18 @ X17 ) )
& ! [X19: a,X20: a,X21: a] :
( ( ( X16 @ X20 @ X19 )
& ( X16 @ X21 @ X20 ) )
=> ( X16 @ X21 @ X19 ) ) )
=> ( X16 @ X14 @ X15 ) )
| ! [X22: a > a > $o] :
( ( ! [X23: a,X24: a] :
( ( X0 @ X23 @ X24 )
=> ( X22 @ X23 @ X24 ) )
& ! [X25: a,X26: a,X27: a] :
( ( ( X22 @ X25 @ X27 )
& ( X22 @ X27 @ X26 ) )
=> ( X22 @ X25 @ X26 ) ) )
=> ( X22 @ X14 @ X15 ) ) )
=> ( X10 @ X14 @ X15 ) ) )
=> ( X10 @ X2 @ X1 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X1: a > a > $o,X3: a,X2: a,X0: a > a > $o] :
( ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a,X7: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X7 @ X8 ) )
=> ( X4 @ X7 @ X9 ) )
& ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X10: a > a > $o] :
( ( ! [X9: a,X8: a,X7: a] :
( ( ( X10 @ X8 @ X9 )
& ( X10 @ X7 @ X8 ) )
=> ( X10 @ X7 @ X9 ) )
& ! [X11: a,X12: a] :
( ( ! [X13: a > a > $o] :
( ( ! [X15: a,X14: a] :
( ( X0 @ X14 @ X15 )
=> ( X13 @ X14 @ X15 ) )
& ! [X9: a,X8: a,X7: a] :
( ( ( X13 @ X8 @ X9 )
& ( X13 @ X7 @ X8 ) )
=> ( X13 @ X7 @ X9 ) ) )
=> ( X13 @ X11 @ X12 ) )
| ! [X16: a > a > $o] :
( ( ! [X17: a,X18: a] :
( ( X1 @ X17 @ X18 )
=> ( X16 @ X17 @ X18 ) )
& ! [X7: a,X9: a,X8: a] :
( ( ( X16 @ X7 @ X8 )
& ( X16 @ X8 @ X9 ) )
=> ( X16 @ X7 @ X9 ) ) )
=> ( X16 @ X11 @ X12 ) ) )
=> ( X10 @ X11 @ X12 ) ) )
=> ( X10 @ X2 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X1: a > a > $o,X3: a,X2: a,X0: a > a > $o] :
( ! [X4: a > a > $o] :
( ( ! [X8: a,X9: a,X7: a] :
( ( ( X4 @ X8 @ X9 )
& ( X4 @ X7 @ X8 ) )
=> ( X4 @ X7 @ X9 ) )
& ! [X6: a,X5: a] :
( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
=> ( X4 @ X5 @ X6 ) ) )
=> ( X4 @ X2 @ X3 ) )
=> ! [X10: a > a > $o] :
( ( ! [X9: a,X8: a,X7: a] :
( ( ( X10 @ X8 @ X9 )
& ( X10 @ X7 @ X8 ) )
=> ( X10 @ X7 @ X9 ) )
& ! [X11: a,X12: a] :
( ( ! [X13: a > a > $o] :
( ( ! [X15: a,X14: a] :
( ( X0 @ X14 @ X15 )
=> ( X13 @ X14 @ X15 ) )
& ! [X9: a,X8: a,X7: a] :
( ( ( X13 @ X8 @ X9 )
& ( X13 @ X7 @ X8 ) )
=> ( X13 @ X7 @ X9 ) ) )
=> ( X13 @ X11 @ X12 ) )
| ! [X16: a > a > $o] :
( ( ! [X17: a,X18: a] :
( ( X1 @ X17 @ X18 )
=> ( X16 @ X17 @ X18 ) )
& ! [X7: a,X9: a,X8: a] :
( ( ( X16 @ X7 @ X8 )
& ( X16 @ X8 @ X9 ) )
=> ( X16 @ X7 @ X9 ) ) )
=> ( X16 @ X11 @ X12 ) ) )
=> ( X10 @ X11 @ X12 ) ) )
=> ( X10 @ X2 @ X3 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.7LFs0HSWrT/DTF2THF_5730.p',cTHM251F_pme) ).
thf(f84,plain,
( ( ( sK9 @ ( sK6 @ sK9 ) @ ( sK7 @ sK9 ) )
!= $true )
| spl12_4 ),
inference(avatar_component_clause,[status(thm)],[f82]) ).
thf(f873,plain,
( spl12_5
| ~ spl12_18
| spl12_27 ),
inference(avatar_split_clause,[status(thm)],[f681,f568,f221,f86]) ).
thf(f86,definition,
( spl12_5
<=> ( ( sK9 @ sK1 @ sK0 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl12_5])],[avatar_definition]) ).
thf(f221,definition,
( spl12_18
<=> ( ( sK2 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl12_18])],[avatar_definition]) ).
thf(f681,plain,
( ( ( sK9 @ sK1 @ sK0 )
= $true )
| ( $true
= ( sK9 @ ( sK6 @ sK9 ) @ ( sK8 @ sK9 ) ) )
| ( ( sK2 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f658]) ).
thf(f658,plain,
( ( ( sK9 @ sK1 @ sK0 )
= $true )
| ( ( sK2 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
!= $true )
| ( $true
= ( sK9 @ ( sK6 @ sK9 ) @ ( sK8 @ sK9 ) ) )
| ( $true = $false ) ),
inference(superposition,[status(thm)],[f34,f346]) ).
thf(f346,plain,
! [X10: a > a > $o] :
( ( $false
= ( X10 @ ( sK5 @ X10 ) @ ( sK4 @ X10 ) ) )
| ( $true
= ( X10 @ sK1 @ sK0 ) )
| ( ( X10 @ ( sK6 @ X10 ) @ ( sK8 @ X10 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f345]) ).
thf(f345,plain,
! [X10: a > a > $o] :
( ( ( X10 @ ( sK6 @ X10 ) @ ( sK8 @ X10 ) )
= $true )
| ( $true
= ( X10 @ sK1 @ sK0 ) )
| ( ( ~ ( X10 @ ( sK5 @ X10 ) @ ( sK4 @ X10 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f344]) ).
thf(f344,plain,
! [X10: a > a > $o] :
( ( $false
= ( ~ ( X10 @ ( sK6 @ X10 ) @ ( sK8 @ X10 ) ) ) )
| ( ( ~ ( X10 @ ( sK5 @ X10 ) @ ( sK4 @ X10 ) ) )
= $true )
| ( $true
= ( X10 @ sK1 @ sK0 ) ) ),
inference(not_proxy_clausification,[status(thm)],[f343]) ).
thf(f343,plain,
! [X10: a > a > $o] :
( ( $false
= ( ~ ( X10 @ sK1 @ sK0 ) ) )
| ( $false
= ( ~ ( X10 @ ( sK6 @ X10 ) @ ( sK8 @ X10 ) ) ) )
| ( ( ~ ( X10 @ ( sK5 @ X10 ) @ ( sK4 @ X10 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f342]) ).
thf(f342,plain,
! [X10: a > a > $o] :
( ( $true
= ( ~ ( X10
@ ( sK5
@ ^ [Y0: a,Y1: a] : ( X10 @ Y0 @ Y1 ) )
@ ( sK4
@ ^ [Y0: a,Y1: a] : ( X10 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( ~ ( X10 @ sK1 @ sK0 ) ) )
| ( $false
= ( ~ ( X10 @ ( sK6 @ X10 ) @ ( sK8 @ X10 ) ) ) ) ),
inference(boolean_simplification,[status(thm)],[f341]) ).
thf(f341,plain,
! [X10: a > a > $o] :
( ( $false
= ( ~ ( X10 @ sK1 @ sK0 ) ) )
| ( $true
= ( ~ ( X10
@ ( sK5
@ ^ [Y0: a,Y1: a] :
~ ~ ( X10 @ Y0 @ Y1 ) )
@ ( sK4
@ ^ [Y0: a,Y1: a] :
~ ~ ( X10 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( ~ ( X10 @ ( sK6 @ X10 ) @ ( sK8 @ X10 ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f340]) ).
thf(f340,plain,
! [X10: a > a > $o] :
( ( $true
= ( ~ ( X10
@ ( sK5
@ ^ [Y0: a,Y1: a] :
~ ~ ( X10 @ Y0 @ Y1 ) )
@ ( sK4
@ ^ [Y0: a,Y1: a] :
~ ~ ( X10 @ Y0 @ Y1 ) ) ) ) )
| ( ( ~ ( X10
@ ( sK6
@ ^ [Y0: a,Y1: a] : ( X10 @ Y0 @ Y1 ) )
@ ( sK8
@ ^ [Y0: a,Y1: a] : ( X10 @ Y0 @ Y1 ) ) ) )
= $false )
| ( $false
= ( ~ ( X10 @ sK1 @ sK0 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f339]) ).
thf(f339,plain,
! [X10: a > a > $o] :
( ( $false
= ( ~ ( X10
@ ( sK6
@ ^ [Y0: a,Y1: a] :
~ ~ ( X10 @ Y0 @ Y1 ) )
@ ( sK8
@ ^ [Y0: a,Y1: a] :
~ ~ ( X10 @ Y0 @ Y1 ) ) ) ) )
| ( $false
= ( ~ ( X10 @ sK1 @ sK0 ) ) )
| ( $true
= ( ~ ( X10
@ ( sK5
@ ^ [Y0: a,Y1: a] :
~ ~ ( X10 @ Y0 @ Y1 ) )
@ ( sK4
@ ^ [Y0: a,Y1: a] :
~ ~ ( X10 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f329]) ).
thf(f329,plain,
! [X10: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
~ ( X10 @ Y0 @ Y1 )
@ ( sK6
@ ^ [Y0: a,Y1: a] :
~ ( ^ [Y2: a,Y3: a] :
~ ( X10 @ Y2 @ Y3 )
@ Y0
@ Y1 ) )
@ ( sK8
@ ^ [Y0: a,Y1: a] :
~ ( ^ [Y2: a,Y3: a] :
~ ( X10 @ Y2 @ Y3 )
@ Y0
@ Y1 ) ) )
= $false )
| ( $true
= ( ^ [Y0: a,Y1: a] :
~ ( X10 @ Y0 @ Y1 )
@ ( sK5
@ ^ [Y0: a,Y1: a] :
~ ( ^ [Y2: a,Y3: a] :
~ ( X10 @ Y2 @ Y3 )
@ Y0
@ Y1 ) )
@ ( sK4
@ ^ [Y0: a,Y1: a] :
~ ( ^ [Y2: a,Y3: a] :
~ ( X10 @ Y2 @ Y3 )
@ Y0
@ Y1 ) ) ) )
| ( ( ^ [Y0: a,Y1: a] :
~ ( X10 @ Y0 @ Y1 )
@ sK1
@ sK0 )
= $false ) ),
inference(primitive_instantiation,[status(thm)],[f152]) ).
thf(f152,plain,
! [X7: a > a > $o] :
( ( $true
= ( X7
@ ( sK5
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) )
@ ( sK4
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) ) )
| ( ( X7 @ sK1 @ sK0 )
= $false )
| ( ( X7
@ ( sK6
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) )
@ ( sK8
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f151]) ).
thf(f151,plain,
! [X7: a > a > $o] :
( ( $true
= ( ~ ( X7
@ ( sK6
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) )
@ ( sK8
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) ) ) )
| ( ( X7 @ sK1 @ sK0 )
= $false )
| ( $true
= ( X7
@ ( sK5
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) )
@ ( sK4
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f150]) ).
thf(f150,plain,
! [X7: a > a > $o] :
( ( ( ~ ( X7 @ sK1 @ sK0 ) )
= $true )
| ( $true
= ( ~ ( X7
@ ( sK6
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) )
@ ( sK8
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) ) ) )
| ( $true
= ( X7
@ ( sK5
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) )
@ ( sK4
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) ) ) ),
inference(not_proxy_clausification,[status(thm)],[f149]) ).
thf(f149,plain,
! [X7: a > a > $o] :
( ( $true
!= ( ~ ( X7
@ ( sK5
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) )
@ ( sK4
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) ) ) )
| ( ( ~ ( X7 @ sK1 @ sK0 ) )
= $true )
| ( $true
= ( ~ ( X7
@ ( sK6
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) )
@ ( sK8
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) ) ) ) ),
inference(beta_eta_normalization,[status(thm)],[f140]) ).
thf(f140,plain,
! [X7: a > a > $o] :
( ( ( ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 )
@ sK1
@ sK0 )
= $true )
| ( ( ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 )
@ ( sK5
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) )
@ ( sK4
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) )
!= $true )
| ( ( ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 )
@ ( sK6
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) )
@ ( sK8
@ ^ [Y0: a,Y1: a] :
~ ( X7 @ Y0 @ Y1 ) ) )
= $true ) ),
inference(primitive_instantiation,[status(thm)],[f26]) ).
thf(f26,plain,
! [X4: a > a > $o] :
( ( ( X4 @ ( sK6 @ X4 ) @ ( sK8 @ X4 ) )
= $true )
| ( $true
!= ( X4 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) ) )
| ( ( X4 @ sK1 @ sK0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f34,plain,
! [X0: a,X1: a] :
( ( ( sK9 @ X0 @ X1 )
= $true )
| ( ( sK2 @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f33]) ).
thf(f33,plain,
! [X0: a,X1: a] :
( ( $true != $true )
| ( ( sK2 @ X0 @ X1 )
!= $true )
| ( ( sK9 @ X0 @ X1 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X0: a,X1: a] :
( ( $true != $true )
| ( ( sK9 @ X0 @ X1 )
= $true )
| ( ( sK2 @ X0 @ X1 )
!= $true )
| ( ( sK9 @ X0 @ X1 )
= $true ) ),
inference(superposition,[status(thm)],[f19,f18]) ).
thf(f18,plain,
! [X11: a,X24: a,X12: a,X23: a] :
( ( ( sK11 @ X12 @ X11 @ X23 @ X24 )
= $true )
| ( ( sK2 @ X23 @ X24 )
!= $true )
| ( ( sK9 @ X12 @ X11 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f19,plain,
! [X11: a,X12: a] :
( ( $true
!= ( sK11 @ X12 @ X11 @ X12 @ X11 ) )
| ( ( sK9 @ X12 @ X11 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f870,plain,
( ~ spl12_18
| spl12_21 ),
inference(avatar_split_clause,[status(thm)],[f865,f406,f221]) ).
thf(f406,definition,
( spl12_21
<=> ( $true
= ( sK9 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl12_21])],[avatar_definition]) ).
thf(f865,plain,
( ( ( sK2 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
!= $true )
| spl12_21 ),
inference(trivial_inequality_removal,[status(thm)],[f860]) ).
thf(f860,plain,
( ( $true != $true )
| ( ( sK2 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
!= $true )
| spl12_21 ),
inference(superposition,[status(thm)],[f408,f34]) ).
thf(f408,plain,
( ( $true
!= ( sK9 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) ) )
| spl12_21 ),
inference(avatar_component_clause,[status(thm)],[f406]) ).
thf(f868,plain,
( ~ spl12_19
| spl12_21 ),
inference(avatar_split_clause,[status(thm)],[f866,f406,f233]) ).
thf(f233,definition,
( spl12_19
<=> ( ( sK3 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl12_19])],[avatar_definition]) ).
thf(f866,plain,
( ( ( sK3 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
!= $true )
| spl12_21 ),
inference(trivial_inequality_removal,[status(thm)],[f859]) ).
thf(f859,plain,
( ( ( sK3 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
!= $true )
| ( $true != $true )
| spl12_21 ),
inference(superposition,[status(thm)],[f408,f37]) ).
thf(f37,plain,
! [X0: a,X1: a] :
( ( ( sK9 @ X0 @ X1 )
= $true )
| ( $true
!= ( sK3 @ X0 @ X1 ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f36]) ).
thf(f36,plain,
! [X0: a,X1: a] :
( ( $true != $true )
| ( $true
!= ( sK3 @ X0 @ X1 ) )
| ( ( sK9 @ X0 @ X1 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f35]) ).
thf(f35,plain,
! [X0: a,X1: a] :
( ( ( sK9 @ X0 @ X1 )
= $true )
| ( $true != $true )
| ( ( sK9 @ X0 @ X1 )
= $true )
| ( $true
!= ( sK3 @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f23,f22]) ).
thf(f22,plain,
! [X11: a,X14: a,X15: a,X12: a] :
( ( ( sK10 @ X12 @ X11 @ X14 @ X15 )
= $true )
| ( ( sK9 @ X12 @ X11 )
= $true )
| ( ( sK3 @ X14 @ X15 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f23,plain,
! [X11: a,X12: a] :
( ( ( sK10 @ X12 @ X11 @ X12 @ X11 )
!= $true )
| ( ( sK9 @ X12 @ X11 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f858,plain,
( spl12_5
| ~ spl12_21
| spl12_20 ),
inference(avatar_split_clause,[status(thm)],[f848,f402,f406,f86]) ).
thf(f848,plain,
( ( $true
!= ( sK9 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) ) )
| ( ( sK9 @ sK1 @ sK0 )
= $true )
| spl12_20 ),
inference(trivial_inequality_removal,[status(thm)],[f846]) ).
thf(f846,plain,
( ( ( sK9 @ sK1 @ sK0 )
= $true )
| ( $true
!= ( sK9 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) ) )
| ( $true != $true )
| spl12_20 ),
inference(superposition,[status(thm)],[f404,f25]) ).
thf(f25,plain,
! [X4: a > a > $o] :
( ( ( X4 @ ( sK8 @ X4 ) @ ( sK7 @ X4 ) )
= $true )
| ( ( X4 @ sK1 @ sK0 )
= $true )
| ( $true
!= ( X4 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f404,plain,
( ( ( sK9 @ ( sK8 @ sK9 ) @ ( sK7 @ sK9 ) )
!= $true )
| spl12_20 ),
inference(avatar_component_clause,[status(thm)],[f402]) ).
thf(f715,plain,
( spl12_27
| spl12_5
| ~ spl12_19 ),
inference(avatar_split_clause,[status(thm)],[f701,f233,f86,f568]) ).
thf(f701,plain,
( ( ( sK9 @ sK1 @ sK0 )
= $true )
| ( ( sK3 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
!= $true )
| ( $true
= ( sK9 @ ( sK6 @ sK9 ) @ ( sK8 @ sK9 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f657]) ).
thf(f657,plain,
( ( $true
= ( sK9 @ ( sK6 @ sK9 ) @ ( sK8 @ sK9 ) ) )
| ( ( sK9 @ sK1 @ sK0 )
= $true )
| ( $true = $false )
| ( ( sK3 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f37,f346]) ).
thf(f572,plain,
( ~ spl12_4
| spl12_5
| spl12_18
| spl12_19 ),
inference(avatar_split_clause,[status(thm)],[f563,f233,f221,f86,f82]) ).
thf(f563,plain,
( ( ( sK2 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
= $true )
| ( ( sK9 @ ( sK6 @ sK9 ) @ ( sK7 @ sK9 ) )
!= $true )
| ( ( sK9 @ sK1 @ sK0 )
= $true )
| spl12_19 ),
inference(trivial_inequality_removal,[status(thm)],[f562]) ).
thf(f562,plain,
( ( ( sK9 @ ( sK6 @ sK9 ) @ ( sK7 @ sK9 ) )
!= $true )
| ( ( sK9 @ sK1 @ sK0 )
= $true )
| ( ( sK2 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
= $true )
| ( $true != $true )
| spl12_19 ),
inference(superposition,[status(thm)],[f235,f27]) ).
thf(f27,plain,
! [X4: a > a > $o] :
( ( ( sK3 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) )
= $true )
| ( ( X4 @ ( sK6 @ X4 ) @ ( sK7 @ X4 ) )
!= $true )
| ( ( sK2 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) )
= $true )
| ( ( X4 @ sK1 @ sK0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f235,plain,
( ( ( sK3 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
!= $true )
| spl12_19 ),
inference(avatar_component_clause,[status(thm)],[f233]) ).
thf(f571,plain,
( spl12_5
| spl12_27
| spl12_18
| spl12_19 ),
inference(avatar_split_clause,[status(thm)],[f564,f233,f221,f568,f86]) ).
thf(f564,plain,
( ( $true
= ( sK9 @ ( sK6 @ sK9 ) @ ( sK8 @ sK9 ) ) )
| ( ( sK2 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
= $true )
| ( ( sK9 @ sK1 @ sK0 )
= $true )
| spl12_19 ),
inference(trivial_inequality_removal,[status(thm)],[f560]) ).
thf(f560,plain,
( ( $true != $true )
| ( ( sK9 @ sK1 @ sK0 )
= $true )
| ( $true
= ( sK9 @ ( sK6 @ sK9 ) @ ( sK8 @ sK9 ) ) )
| ( ( sK2 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
= $true )
| spl12_19 ),
inference(superposition,[status(thm)],[f235,f29]) ).
thf(f29,plain,
! [X4: a > a > $o] :
( ( ( sK3 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) )
= $true )
| ( ( X4 @ sK1 @ sK0 )
= $true )
| ( ( sK2 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) )
= $true )
| ( ( X4 @ ( sK6 @ X4 ) @ ( sK8 @ X4 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f566,plain,
( spl12_18
| spl12_20
| spl12_5
| spl12_19 ),
inference(avatar_split_clause,[status(thm)],[f565,f233,f86,f402,f221]) ).
thf(f565,plain,
( ( ( sK9 @ ( sK8 @ sK9 ) @ ( sK7 @ sK9 ) )
= $true )
| ( ( sK9 @ sK1 @ sK0 )
= $true )
| ( ( sK2 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
= $true )
| spl12_19 ),
inference(trivial_inequality_removal,[status(thm)],[f561]) ).
thf(f561,plain,
( ( $true != $true )
| ( ( sK2 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
= $true )
| ( ( sK9 @ ( sK8 @ sK9 ) @ ( sK7 @ sK9 ) )
= $true )
| ( ( sK9 @ sK1 @ sK0 )
= $true )
| spl12_19 ),
inference(superposition,[status(thm)],[f235,f28]) ).
thf(f28,plain,
! [X4: a > a > $o] :
( ( ( sK3 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) )
= $true )
| ( ( X4 @ ( sK8 @ X4 ) @ ( sK7 @ X4 ) )
= $true )
| ( ( X4 @ sK1 @ sK0 )
= $true )
| ( ( sK2 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f534,plain,
~ spl12_5,
inference(avatar_contradiction_clause,[status(thm)],[f533]) ).
thf(f533,plain,
( $false
| ~ spl12_5 ),
inference(trivial_inequality_removal,[status(thm)],[f524]) ).
thf(f524,plain,
( ( $true != $true )
| ~ spl12_5 ),
inference(superposition,[status(thm)],[f16,f88]) ).
thf(f88,plain,
( ( ( sK9 @ sK1 @ sK0 )
= $true )
| ~ spl12_5 ),
inference(avatar_component_clause,[status(thm)],[f86]) ).
thf(f16,plain,
( ( sK9 @ sK1 @ sK0 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f409,plain,
( ~ spl12_20
| ~ spl12_21
| spl12_5
| spl12_4 ),
inference(avatar_split_clause,[status(thm)],[f399,f82,f86,f406,f402]) ).
thf(f399,plain,
( ( ( sK9 @ sK1 @ sK0 )
= $true )
| ( ( sK9 @ ( sK8 @ sK9 ) @ ( sK7 @ sK9 ) )
!= $true )
| ( $true
!= ( sK9 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) ) )
| spl12_4 ),
inference(trivial_inequality_removal,[status(thm)],[f396]) ).
thf(f396,plain,
( ( ( sK9 @ sK1 @ sK0 )
= $true )
| ( $true
!= ( sK9 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) ) )
| ( $true != $true )
| ( ( sK9 @ ( sK8 @ sK9 ) @ ( sK7 @ sK9 ) )
!= $true )
| spl12_4 ),
inference(superposition,[status(thm)],[f240,f26]) ).
thf(f236,plain,
( ~ spl12_4
| ~ spl12_19
| spl12_5 ),
inference(avatar_split_clause,[status(thm)],[f228,f86,f233,f82]) ).
thf(f228,plain,
( ( ( sK3 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
!= $true )
| ( ( sK9 @ sK1 @ sK0 )
= $true )
| ( ( sK9 @ ( sK6 @ sK9 ) @ ( sK7 @ sK9 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f227]) ).
thf(f227,plain,
( ( ( sK3 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
!= $true )
| ( ( sK9 @ sK1 @ sK0 )
= $true )
| ( $true != $true )
| ( ( sK9 @ ( sK6 @ sK9 ) @ ( sK7 @ sK9 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f24,f37]) ).
thf(f24,plain,
! [X4: a > a > $o] :
( ( $true
!= ( X4 @ ( sK5 @ X4 ) @ ( sK4 @ X4 ) ) )
| ( ( X4 @ ( sK6 @ X4 ) @ ( sK7 @ X4 ) )
!= $true )
| ( ( X4 @ sK1 @ sK0 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f224,plain,
( spl12_5
| ~ spl12_18
| ~ spl12_4 ),
inference(avatar_split_clause,[status(thm)],[f217,f82,f221,f86]) ).
thf(f217,plain,
( ( ( sK9 @ sK1 @ sK0 )
= $true )
| ( ( sK2 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
!= $true )
| ( ( sK9 @ ( sK6 @ sK9 ) @ ( sK7 @ sK9 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f216]) ).
thf(f216,plain,
( ( ( sK9 @ sK1 @ sK0 )
= $true )
| ( ( sK9 @ ( sK6 @ sK9 ) @ ( sK7 @ sK9 ) )
!= $true )
| ( $true != $true )
| ( ( sK2 @ ( sK5 @ sK9 ) @ ( sK4 @ sK9 ) )
!= $true ) ),
inference(superposition,[status(thm)],[f24,f34]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.11 % Problem : SEV109^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.12 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.13/0.32 % Computer : n002.cluster.edu
% 0.13/0.32 % Model : x86_64 x86_64
% 0.13/0.32 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.13/0.32 % Memory : 8042.1875MB
% 0.13/0.32 % OS : Linux 3.10.0-693.el7.x86_64
% 0.13/0.32 % CPULimit : 300
% 0.13/0.32 % WCLimit : 300
% 0.13/0.32 % DateTime : Tue Feb 24 12:40:33 EST 2026
% 0.13/0.32 % CPUTime :
% 0.13/0.32 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.17/0.41 ---- Original DTF file ---
% 0.17/0.41 thf(spec,logic,$$dhol).
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 % File : SEV109^5 : TPTP v9.2.1. Released v4.0.0.
% 0.17/0.41 % Domain : Set Theory (Relations)
% 0.17/0.41 % Problem : TPS problem from RELN-THMS
% 0.17/0.41 % Version : Especial.
% 0.17/0.41 % English :
% 0.17/0.41
% 0.17/0.41 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.17/0.41 % Source : [Bro09]
% 0.17/0.41 % Names : tps_1164 [Bro09]
% 0.17/0.41 % : tps_1165 [Bro09]
% 0.17/0.41 % : tps_1166 [Bro09]
% 0.17/0.41 % : tps_1167 [Bro09]
% 0.17/0.41 % : tps_0501 [Bro09]
% 0.17/0.41 % : THM250B [TPS]
% 0.17/0.41
% 0.17/0.41 % Status : Theorem
% 0.17/0.41 % Rating : 0.00 v8.1.0, 0.08 v7.4.0, 0.00 v6.2.0, 0.17 v6.0.0, 0.00 v5.1.0, 0.25 v5.0.0, 0.00 v4.1.0, 0.33 v4.0.0
% 0.17/0.41 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.17/0.41 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.17/0.41 % Maximal formula atoms : 0 ( 0 avg)
% 0.17/0.41 % Number of connectives : 71 ( 0 ~; 2 |; 8 &; 48 @)
% 0.17/0.41 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.17/0.41 % Maximal formula depth : 23 ( 23 avg)
% 0.17/0.41 % Number of types : 2 ( 1 usr)
% 0.17/0.41 % Number of type conns : 12 ( 12 >; 0 *; 0 +; 0 <<)
% 0.17/0.41 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.17/0.41 % Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% 0.17/0.41 % SPC : TH0_THM_NEQ_NAR
% 0.17/0.41
% 0.17/0.41 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.17/0.41 % project in the Department of Mathematical Sciences at Carnegie
% 0.17/0.41 % Mellon University. Distributed under the Creative Commons copyleft
% 0.17/0.41 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 thf(a_type,type,
% 0.17/0.41 a: $tType ).
% 0.17/0.41
% 0.17/0.41 thf(cTHM251F_pme,conjecture,
% 0.17/0.41 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 0.17/0.41 ( ! [Xq1: a > a > $o] :
% 0.17/0.41 ( ( ! [Xs: a,Xt: a] :
% 0.17/0.41 ( ( ( R @ Xs @ Xt )
% 0.17/0.41 | ( S @ Xs @ Xt ) )
% 0.17/0.41 => ( Xq1 @ Xs @ Xt ) )
% 0.17/0.41 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.17/0.41 ( ( ( Xq1 @ Xx0 @ Xy0 )
% 0.17/0.41 & ( Xq1 @ Xy0 @ Xz ) )
% 0.17/0.41 => ( Xq1 @ Xx0 @ Xz ) ) )
% 0.17/0.41 => ( Xq1 @ Xx @ Xy ) )
% 0.17/0.41 => ! [Xp1: a > a > $o] :
% 0.17/0.41 ( ( ! [Xss: a,Xtt: a] :
% 0.17/0.41 ( ( ! [Xq2: a > a > $o] :
% 0.17/0.41 ( ( ! [Xsss: a,Xttt: a] :
% 0.17/0.41 ( ( R @ Xsss @ Xttt )
% 0.17/0.41 => ( Xq2 @ Xsss @ Xttt ) )
% 0.17/0.41 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.17/0.41 ( ( ( Xq2 @ Xx0 @ Xy0 )
% 0.17/0.41 & ( Xq2 @ Xy0 @ Xz ) )
% 0.17/0.41 => ( Xq2 @ Xx0 @ Xz ) ) )
% 0.17/0.41 => ( Xq2 @ Xss @ Xtt ) )
% 0.17/0.41 | ! [Xq3: a > a > $o] :
% 0.17/0.41 ( ( ! [Xssss: a,Xtttt: a] :
% 0.17/0.41 ( ( S @ Xssss @ Xtttt )
% 0.17/0.41 => ( Xq3 @ Xssss @ Xtttt ) )
% 0.17/0.41 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.17/0.41 ( ( ( Xq3 @ Xx0 @ Xy0 )
% 0.17/0.41 & ( Xq3 @ Xy0 @ Xz ) )
% 0.17/0.41 => ( Xq3 @ Xx0 @ Xz ) ) )
% 0.17/0.41 => ( Xq3 @ Xss @ Xtt ) ) )
% 0.17/0.41 => ( Xp1 @ Xss @ Xtt ) )
% 0.17/0.41 & ! [Xx0: a,Xy0: a,Xz: a] :
% 0.17/0.41 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 0.17/0.41 & ( Xp1 @ Xy0 @ Xz ) )
% 0.17/0.41 => ( Xp1 @ Xx0 @ Xz ) ) )
% 0.17/0.41 => ( Xp1 @ Xx @ Xy ) ) ) ).
% 0.17/0.41
% 0.17/0.41 %------------------------------------------------------------------------------
% 0.17/0.41 ------------------------
% 1.39/1.25 ---- Embedded in THF ---
% 1.39/1.25 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.39/1.25 %%% Generated on Tue Feb 24 12:40:34 EST 2026
% 1.39/1.25 %%% using '$$dhol' embedding, version 1.3.0.
% 1.39/1.25 %%% Logic specification used:
% 1.39/1.25 %%% thf(spec, logic, $$dhol).
% 1.39/1.25
% 1.39/1.25 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.7LFs0HSWrT/DTF2DTF5730.p
% See solution above
% 1.39/1.25 ------------------------
% 1.39/1.26 ---- Cleaned THF ---
% 1.39/1.26 thf(a_type,type,
% 1.39/1.26 a: $tType ).
% 1.39/1.26
% 1.39/1.26 thf(cTHM251F_pme,conjecture,
% 1.39/1.26 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 1.39/1.26 ( ! [Xq1: a > a > $o] :
% 1.39/1.26 ( ( ! [Xs: a,Xt: a] :
% 1.39/1.26 ( ( ( R @ Xs @ Xt )
% 1.39/1.26 | ( S @ Xs @ Xt ) )
% 1.39/1.26 => ( Xq1 @ Xs @ Xt ) )
% 1.39/1.26 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.39/1.26 ( ( ( Xq1 @ Xx0 @ Xy0 )
% 1.39/1.26 & ( Xq1 @ Xy0 @ Xz ) )
% 1.39/1.26 => ( Xq1 @ Xx0 @ Xz ) ) )
% 1.39/1.26 => ( Xq1 @ Xx @ Xy ) )
% 1.39/1.26 => ! [Xp1: a > a > $o] :
% 1.39/1.26 ( ( ! [Xss: a,Xtt: a] :
% 1.39/1.26 ( ( ! [Xq2: a > a > $o] :
% 1.39/1.26 ( ( ! [Xsss: a,Xttt: a] :
% 1.39/1.26 ( ( R @ Xsss @ Xttt )
% 1.39/1.26 => ( Xq2 @ Xsss @ Xttt ) )
% 1.39/1.26 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.39/1.26 ( ( ( Xq2 @ Xx0 @ Xy0 )
% 1.39/1.26 & ( Xq2 @ Xy0 @ Xz ) )
% 1.39/1.26 => ( Xq2 @ Xx0 @ Xz ) ) )
% 1.39/1.26 => ( Xq2 @ Xss @ Xtt ) )
% 1.39/1.26 | ! [Xq3: a > a > $o] :
% 1.39/1.26 ( ( ! [Xssss: a,Xtttt: a] :
% 1.39/1.26 ( ( S @ Xssss @ Xtttt )
% 1.39/1.26 => ( Xq3 @ Xssss @ Xtttt ) )
% 1.39/1.26 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.39/1.26 ( ( ( Xq3 @ Xx0 @ Xy0 )
% 1.39/1.26 & ( Xq3 @ Xy0 @ Xz ) )
% 1.39/1.26 => ( Xq3 @ Xx0 @ Xz ) ) )
% 1.39/1.26 => ( Xq3 @ Xss @ Xtt ) ) )
% 1.39/1.26 => ( Xp1 @ Xss @ Xtt ) )
% 1.39/1.26 & ! [Xx0: a,Xy0: a,Xz: a] :
% 1.39/1.26 ( ( ( Xp1 @ Xx0 @ Xy0 )
% 1.39/1.26 & ( Xp1 @ Xy0 @ Xz ) )
% 1.39/1.26 => ( Xp1 @ Xx0 @ Xz ) ) )
% 1.39/1.26 => ( Xp1 @ Xx @ Xy ) ) ) ).
% 1.39/1.26 ------------------------
% 1.39/1.27 % (5829)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5730 for (3000ds/183Mi)
% 1.39/1.28 % (5831)dis+1010_1:1_au=on:cbe=off:chr=on:fsr=off:hfsq=on:nm=64:sos=theory:sp=weighted_frequency:i=27:si=on:rtra=on_0 on DTF2THF_5730 for (3000ds/27Mi)
% 1.39/1.28 % (5832)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5730 for (3000ds/2Mi)
% 1.39/1.28 % (5834)lrs+1002_1:1_au=on:bd=off:e2e=on:sd=2:sos=on:ss=axioms:i=275:si=on:rtra=on_0 on DTF2THF_5730 for (3000ds/275Mi)
% 1.39/1.28 % (5833)lrs+1002_1:128_aac=none:au=on:cnfonf=lazy_not_gen_be_off:sos=all:i=2:si=on:rtra=on_0 on DTF2THF_5730 for (3000ds/2Mi)
% 1.39/1.28 % (5835)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5730 for (3000ds/18Mi)
% 1.39/1.28 % (5832)Instruction limit reached!
% 1.39/1.28 % (5832)------------------------------
% 1.39/1.28 % (5832)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.39/1.28 % (5832)Termination reason: Unknown
% 1.39/1.28 % (5832)Termination phase: Property scanning
% 1.39/1.28
% 1.39/1.28 % (5832)Memory used [KB]: 895
% 1.39/1.28 % (5832)Time elapsed: 0.002 s
% 1.39/1.28 % (5832)Instructions burned: 2 (million)
% 1.39/1.28 % (5832)------------------------------
% 1.39/1.28 % (5832)------------------------------
% 1.39/1.28 % (5830)lrs+10_1:1_c=on:cnfonf=conj_eager:fd=off:fe=off:kws=frequency:spb=intro:i=4:si=on:rtra=on_0 on DTF2THF_5730 for (3000ds/4Mi)
% 1.39/1.28 % (5833)Instruction limit reached!
% 1.39/1.28 % (5833)------------------------------
% 1.39/1.28 % (5833)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.39/1.28 % (5833)Termination reason: Unknown
% 1.39/1.28 % (5833)Termination phase: Property scanning
% 1.39/1.28
% 1.39/1.28 % (5833)Memory used [KB]: 1023
% 1.39/1.28 % (5833)Time elapsed: 0.003 s
% 1.39/1.28 % (5833)Instructions burned: 4 (million)
% 1.39/1.28 % (5833)------------------------------
% 1.39/1.28 % (5833)------------------------------
% 1.39/1.28 % (5830)Instruction limit reached!
% 1.39/1.28 % (5830)------------------------------
% 1.39/1.28 % (5830)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.39/1.28 % (5830)Termination reason: Unknown
% 1.39/1.28 % (5830)Termination phase: Property scanning
% 1.39/1.28
% 1.39/1.28 % (5830)Memory used [KB]: 1023
% 1.39/1.28 % (5830)Time elapsed: 0.003 s
% 1.39/1.28 % (5830)Instructions burned: 4 (million)
% 1.39/1.28 % (5830)------------------------------
% 1.39/1.28 % (5830)------------------------------
% 1.39/1.29 % (5835)Instruction limit reached!
% 1.39/1.29 % (5835)------------------------------
% 1.39/1.29 % (5835)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.39/1.29 % (5835)Termination reason: Unknown
% 1.39/1.29 % (5835)Termination phase: Saturation
% 1.39/1.29
% 1.39/1.29 % (5835)Memory used [KB]: 5628
% 1.39/1.29 % (5835)Time elapsed: 0.010 s
% 1.39/1.29 % (5835)Instructions burned: 18 (million)
% 1.39/1.29 % (5835)------------------------------
% 1.39/1.29 % (5835)------------------------------
% 1.39/1.29 % (5831)Instruction limit reached!
% 1.39/1.29 % (5831)------------------------------
% 1.39/1.29 % (5831)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.39/1.29 % (5831)Termination reason: Unknown
% 1.39/1.29 % (5831)Termination phase: Saturation
% 1.39/1.29
% 1.39/1.29 % (5831)Memory used [KB]: 5628
% 1.39/1.29 % (5831)Time elapsed: 0.015 s
% 1.39/1.29 % (5831)Instructions burned: 27 (million)
% 1.39/1.29 % (5831)------------------------------
% 1.39/1.29 % (5831)------------------------------
% 1.39/1.29 % (5836)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/3Mi)
% 1.39/1.30 % (5837)lrs+1002_1:1_cnfonf=lazy_not_be_gen:hud=14:prag=on:sp=weighted_frequency:tnu=1:i=37:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/37Mi)
% 1.49/1.30 % (5836)Instruction limit reached!
% 1.49/1.30 % (5836)------------------------------
% 1.49/1.30 % (5836)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.30 % (5836)Termination reason: Unknown
% 1.49/1.30 % (5836)Termination phase: Saturation
% 1.49/1.30
% 1.49/1.30 % (5836)Memory used [KB]: 1023
% 1.49/1.30 % (5836)Time elapsed: 0.003 s
% 1.49/1.30 % (5836)Instructions burned: 4 (million)
% 1.49/1.30 % (5836)------------------------------
% 1.49/1.30 % (5836)------------------------------
% 1.49/1.30 % (5838)lrs+2_16:1_acc=model:au=on:bd=off:c=on:e2e=on:nm=2:sos=all:i=15:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/15Mi)
% 1.49/1.30 % (5839)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/3Mi)
% 1.49/1.30 % (5839)Instruction limit reached!
% 1.49/1.30 % (5839)------------------------------
% 1.49/1.30 % (5839)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.30 % (5839)Termination reason: Unknown
% 1.49/1.30 % (5839)Termination phase: Saturation
% 1.49/1.30
% 1.49/1.30 % (5839)Memory used [KB]: 1023
% 1.49/1.30 % (5839)Time elapsed: 0.003 s
% 1.49/1.30 % (5839)Instructions burned: 4 (million)
% 1.49/1.30 % (5839)------------------------------
% 1.49/1.30 % (5839)------------------------------
% 1.49/1.30 % (5838)Instruction limit reached!
% 1.49/1.30 % (5838)------------------------------
% 1.49/1.30 % (5838)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.30 % (5838)Termination reason: Unknown
% 1.49/1.30 % (5838)Termination phase: Saturation
% 1.49/1.30
% 1.49/1.30 % (5838)Memory used [KB]: 5628
% 1.49/1.30 % (5838)Time elapsed: 0.009 s
% 1.49/1.30 % (5838)Instructions burned: 15 (million)
% 1.49/1.30 % (5838)------------------------------
% 1.49/1.30 % (5838)------------------------------
% 1.49/1.31 % (5840)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/1041Mi)
% 1.49/1.31 % (5841)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/7Mi)
% 1.49/1.31 % (5837)Instruction limit reached!
% 1.49/1.31 % (5837)------------------------------
% 1.49/1.31 % (5837)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.31 % (5837)Termination reason: Unknown
% 1.49/1.31 % (5837)Termination phase: Saturation
% 1.49/1.31
% 1.49/1.31 % (5837)Memory used [KB]: 5628
% 1.49/1.31 % (5837)Time elapsed: 0.018 s
% 1.49/1.31 % (5837)Instructions burned: 37 (million)
% 1.49/1.31 % (5837)------------------------------
% 1.49/1.31 % (5837)------------------------------
% 1.49/1.32 % (5841)Instruction limit reached!
% 1.49/1.32 % (5841)------------------------------
% 1.49/1.32 % (5841)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.32 % (5841)Termination reason: Unknown
% 1.49/1.32 % (5841)Termination phase: Saturation
% 1.49/1.32
% 1.49/1.32 % (5841)Memory used [KB]: 1023
% 1.49/1.32 % (5841)Time elapsed: 0.005 s
% 1.49/1.32 % (5841)Instructions burned: 8 (million)
% 1.49/1.32 % (5841)------------------------------
% 1.49/1.32 % (5841)------------------------------
% 1.49/1.32 % (5842)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/16Mi)
% 1.49/1.32 % (5843)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/3Mi)
% 1.49/1.32 % (5843)Instruction limit reached!
% 1.49/1.32 % (5843)------------------------------
% 1.49/1.32 % (5843)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.32 % (5843)Termination reason: Unknown
% 1.49/1.32 % (5843)Termination phase: Twee Goal Transformation
% 1.49/1.32
% 1.49/1.32 % (5843)Memory used [KB]: 1023
% 1.49/1.32 % (5843)Time elapsed: 0.003 s
% 1.49/1.32 % (5843)Instructions burned: 4 (million)
% 1.49/1.32 % (5843)------------------------------
% 1.49/1.32 % (5843)------------------------------
% 1.49/1.33 % (5829)Instruction limit reached!
% 1.49/1.33 % (5829)------------------------------
% 1.49/1.33 % (5829)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.33 % (5829)Termination reason: Unknown
% 1.49/1.33 % (5829)Termination phase: Saturation
% 1.49/1.33
% 1.49/1.33 % (5829)Memory used [KB]: 6140
% 1.49/1.33 % (5829)Time elapsed: 0.055 s
% 1.49/1.33 % (5829)Instructions burned: 185 (million)
% 1.49/1.33 % (5829)------------------------------
% 1.49/1.33 % (5829)------------------------------
% 1.49/1.33 % (5842)Instruction limit reached!
% 1.49/1.33 % (5842)------------------------------
% 1.49/1.33 % (5842)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.33 % (5842)Termination reason: Unknown
% 1.49/1.33 % (5842)Termination phase: Saturation
% 1.49/1.33
% 1.49/1.33 % (5842)Memory used [KB]: 5628
% 1.49/1.33 % (5842)Time elapsed: 0.009 s
% 1.49/1.33 % (5842)Instructions burned: 17 (million)
% 1.49/1.33 % (5842)------------------------------
% 1.49/1.33 % (5842)------------------------------
% 1.49/1.33 % (5844)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/3Mi)
% 1.49/1.33 % (5844)Instruction limit reached!
% 1.49/1.33 % (5844)------------------------------
% 1.49/1.33 % (5844)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.33 % (5844)Termination reason: Unknown
% 1.49/1.33 % (5844)Termination phase: Property scanning
% 1.49/1.33
% 1.49/1.33 % (5844)Memory used [KB]: 1023
% 1.49/1.33 % (5844)Time elapsed: 0.003 s
% 1.49/1.33 % (5844)Instructions burned: 4 (million)
% 1.49/1.33 % (5844)------------------------------
% 1.49/1.33 % (5844)------------------------------
% 1.49/1.33 % (5845)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/7Mi)
% 1.49/1.33 % (5847)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/4Mi)
% 1.49/1.33 % (5845)Instruction limit reached!
% 1.49/1.33 % (5845)------------------------------
% 1.49/1.33 % (5845)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.33 % (5845)Termination reason: Unknown
% 1.49/1.33 % (5845)Termination phase: Saturation
% 1.49/1.33
% 1.49/1.33 % (5845)Memory used [KB]: 5500
% 1.49/1.33 % (5845)Time elapsed: 0.005 s
% 1.49/1.33 % (5845)Instructions burned: 8 (million)
% 1.49/1.33 % (5845)------------------------------
% 1.49/1.33 % (5845)------------------------------
% 1.49/1.34 % (5847)Instruction limit reached!
% 1.49/1.34 % (5847)------------------------------
% 1.49/1.34 % (5847)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.34 % (5847)Termination reason: Unknown
% 1.49/1.34 % (5847)Termination phase: Property scanning
% 1.49/1.34
% 1.49/1.34 % (5847)Memory used [KB]: 1023
% 1.49/1.34 % (5847)Time elapsed: 0.002 s
% 1.49/1.34 % (5847)Instructions burned: 4 (million)
% 1.49/1.34 % (5847)------------------------------
% 1.49/1.34 % (5847)------------------------------
% 1.49/1.34 % (5846)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/3Mi)
% 1.49/1.34 % (5846)Instruction limit reached!
% 1.49/1.34 % (5846)------------------------------
% 1.49/1.34 % (5846)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.34 % (5846)Termination reason: Unknown
% 1.49/1.34 % (5846)Termination phase: Saturation
% 1.49/1.34
% 1.49/1.34 % (5846)Memory used [KB]: 5500
% 1.49/1.34 % (5846)Time elapsed: 0.003 s
% 1.49/1.34 % (5846)Instructions burned: 4 (million)
% 1.49/1.34 % (5846)------------------------------
% 1.49/1.34 % (5846)------------------------------
% 1.49/1.34 % (5848)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/18Mi)
% 1.49/1.34 % (5851)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/902Mi)
% 1.49/1.35 % (5849)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/710Mi)
% 1.49/1.35 % (5850)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/6Mi)
% 1.49/1.35 % (5848)Instruction limit reached!
% 1.49/1.35 % (5848)------------------------------
% 1.49/1.35 % (5848)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.35 % (5848)Termination reason: Unknown
% 1.49/1.35 % (5848)Termination phase: Saturation
% 1.49/1.35
% 1.49/1.35 % (5848)Memory used [KB]: 5628
% 1.49/1.35 % (5848)Time elapsed: 0.010 s
% 1.49/1.35 % (5848)Instructions burned: 18 (million)
% 1.49/1.35 % (5848)------------------------------
% 1.49/1.35 % (5848)------------------------------
% 1.49/1.35 % (5850)Instruction limit reached!
% 1.49/1.35 % (5850)------------------------------
% 1.49/1.35 % (5850)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.35 % (5850)Termination reason: Unknown
% 1.49/1.35 % (5850)Termination phase: Saturation
% 1.49/1.35
% 1.49/1.35 % (5850)Memory used [KB]: 5500
% 1.49/1.35 % (5850)Time elapsed: 0.004 s
% 1.49/1.35 % (5850)Instructions burned: 6 (million)
% 1.49/1.35 % (5850)------------------------------
% 1.49/1.35 % (5850)------------------------------
% 1.49/1.35 % (5852)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/21Mi)
% 1.49/1.36 % (5852)Instruction limit reached!
% 1.49/1.36 % (5852)------------------------------
% 1.49/1.36 % (5852)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.36 % (5852)Termination reason: Unknown
% 1.49/1.36 % (5852)Termination phase: Saturation
% 1.49/1.36
% 1.49/1.36 % (5852)Memory used [KB]: 5628
% 1.49/1.36 % (5852)Time elapsed: 0.033 s
% 1.49/1.36 % (5852)Instructions burned: 23 (million)
% 1.49/1.36 % (5852)------------------------------
% 1.49/1.36 % (5852)------------------------------
% 1.49/1.37 % (5853)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_5730 for (2999ds/5Mi)
% 1.49/1.37 % (5854)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_5730 for (2998ds/6Mi)
% 1.49/1.37 % (5853)Instruction limit reached!
% 1.49/1.37 % (5853)------------------------------
% 1.49/1.37 % (5853)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.37 % (5853)Termination reason: Unknown
% 1.49/1.37 % (5853)Termination phase: Saturation
% 1.49/1.37
% 1.49/1.37 % (5853)Memory used [KB]: 5500
% 1.49/1.37 % (5853)Time elapsed: 0.004 s
% 1.49/1.37 % (5853)Instructions burned: 6 (million)
% 1.49/1.37 % (5853)------------------------------
% 1.49/1.37 % (5853)------------------------------
% 1.49/1.37 % (5855)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_5730 for (2998ds/377Mi)
% 1.49/1.37 % (5854)Instruction limit reached!
% 1.49/1.37 % (5854)------------------------------
% 1.49/1.37 % (5854)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.37 % (5854)Termination reason: Unknown
% 1.49/1.37 % (5854)Termination phase: Saturation
% 1.49/1.37
% 1.49/1.37 % (5854)Memory used [KB]: 5500
% 1.49/1.37 % (5854)Time elapsed: 0.004 s
% 1.49/1.37 % (5854)Instructions burned: 6 (million)
% 1.49/1.37 % (5854)------------------------------
% 1.49/1.37 % (5854)------------------------------
% 1.49/1.39 % (5856)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_5730 for (2998ds/779Mi)
% 1.49/1.39 % (5857)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_5730 for (2998ds/19Mi)
% 1.49/1.40 % (5851)First to succeed.
% 1.49/1.40 % (5857)Instruction limit reached!
% 1.49/1.40 % (5857)------------------------------
% 1.49/1.40 % (5857)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.40 % (5857)Termination reason: Unknown
% 1.49/1.40 % (5857)Termination phase: Saturation
% 1.49/1.40
% 1.49/1.40 % (5857)Memory used [KB]: 5500
% 1.49/1.40 % (5857)Time elapsed: 0.010 s
% 1.49/1.40 % (5857)Instructions burned: 20 (million)
% 1.49/1.40 % (5857)------------------------------
% 1.49/1.40 % (5857)------------------------------
% 1.49/1.40 % (5851)Refutation found. Thanks to Tanya!
% 1.49/1.40 % SZS status Theorem for DTF2THF_5730
% 1.49/1.40 % SZS output start Proof for DTF2THF_5730
% 1.49/1.40 thf(type_def_5, type, a: $tType).
% 1.49/1.40 thf(func_def_0, type, a: $tType).
% 1.49/1.40 thf(func_def_4, type, sK0: a).
% 1.49/1.40 thf(func_def_5, type, sK1: a).
% 1.49/1.40 thf(func_def_6, type, sK2: a > a > $o).
% 1.49/1.40 thf(func_def_7, type, sK3: a > a > $o).
% 1.49/1.40 thf(func_def_8, type, sK4: (a > a > $o) > a).
% 1.49/1.40 thf(func_def_9, type, sK5: (a > a > $o) > a).
% 1.49/1.40 thf(func_def_10, type, sK6: (a > a > $o) > a).
% 1.49/1.40 thf(func_def_11, type, sK7: (a > a > $o) > a).
% 1.49/1.40 thf(func_def_12, type, sK8: (a > a > $o) > a).
% 1.49/1.40 thf(func_def_13, type, sK9: a > a > $o).
% 1.49/1.40 thf(func_def_14, type, sK10: a > a > a > a > $o).
% 1.49/1.40 thf(func_def_15, type, sK11: a > a > a > a > $o).
% 1.49/1.40 thf(func_def_18, type, ph13: !>[X0: $tType]:(X0)).
% 1.49/1.40 thf(f897,plain,(
% 1.49/1.40 $false),
% 1.49/1.40 inference(avatar_sat_refutation,[status(thm)],[f224,f236,f409,f534,f566,f571,f572,f715,f858,f868,f870,f873,f896])).
% 1.49/1.40 thf(f896,plain,(
% 1.49/1.40 ~spl12_20 | spl12_4 | ~spl12_27),
% 1.49/1.40 inference(avatar_split_clause,[status(thm)],[f895,f568,f82,f402])).
% 1.49/1.40 thf(f402,definition,(
% 1.49/1.40 spl12_20 <=> ((sK9 @ (sK8 @ sK9) @ (sK7 @ sK9)) = $true)),
% 1.49/1.40 introduced(definition,[new_symbols(naming,[spl12_20])],[avatar_definition])).
% 1.49/1.40 thf(f82,definition,(
% 1.49/1.40 spl12_4 <=> ((sK9 @ (sK6 @ sK9) @ (sK7 @ sK9)) = $true)),
% 1.49/1.40 introduced(definition,[new_symbols(naming,[spl12_4])],[avatar_definition])).
% 1.49/1.40 thf(f568,definition,(
% 1.49/1.40 spl12_27 <=> ($true = (sK9 @ (sK6 @ sK9) @ (sK8 @ sK9)))),
% 1.49/1.40 introduced(definition,[new_symbols(naming,[spl12_27])],[avatar_definition])).
% 1.49/1.40 thf(f895,plain,(
% 1.49/1.40 ((sK9 @ (sK8 @ sK9) @ (sK7 @ sK9)) != $true) | (spl12_4 | ~spl12_27)),
% 1.49/1.40 inference(trivial_inequality_removal,[status(thm)],[f894])).
% 1.49/1.40 thf(f894,plain,(
% 1.49/1.40 ($true != $true) | ((sK9 @ (sK8 @ sK9) @ (sK7 @ sK9)) != $true) | (spl12_4 | ~spl12_27)),
% 1.49/1.40 inference(superposition,[status(thm)],[f240,f570])).
% 1.49/1.40 thf(f570,plain,(
% 1.49/1.40 ($true = (sK9 @ (sK6 @ sK9) @ (sK8 @ sK9))) | ~spl12_27),
% 1.49/1.40 inference(avatar_component_clause,[status(thm)],[f568])).
% 1.49/1.40 thf(f240,plain,(
% 1.49/1.40 ( ! [X0 : a] : (((sK9 @ (sK6 @ sK9) @ X0) != $true) | ((sK9 @ X0 @ (sK7 @ sK9)) != $true)) ) | spl12_4),
% 1.49/1.40 inference(trivial_inequality_removal,[status(thm)],[f239])).
% 1.49/1.40 thf(f239,plain,(
% 1.49/1.40 ( ! [X0 : a] : (((sK9 @ X0 @ (sK7 @ sK9)) != $true) | ($true != $true) | ((sK9 @ (sK6 @ sK9) @ X0) != $true)) ) | spl12_4),
% 1.49/1.40 inference(superposition,[status(thm)],[f84,f17])).
% 1.49/1.40 thf(f17,plain,(
% 1.49/1.40 ( ! [X26 : a,X27 : a,X25 : a] : (((sK9 @ X25 @ X26) = $true) | ($true != (sK9 @ X27 @ X26)) | ((sK9 @ X25 @ X27) != $true)) )),
% 1.49/1.40 inference(cnf_transformation,[status(thm)],[f15])).
% 1.49/1.40 thf(f15,plain,(
% 1.49/1.40 ! [X4 : a > a > $o] : (((((sK2 @ (sK5 @ X4) @ (sK4 @ X4)) = $true) | ((sK3 @ (sK5 @ X4) @ (sK4 @ X4)) = $true)) & ($true != (X4 @ (sK5 @ X4) @ (sK4 @ X4)))) | (((X4 @ (sK6 @ X4) @ (sK8 @ X4)) = $true) & ((X4 @ (sK8 @ X4) @ (sK7 @ X4)) = $true) & ((X4 @ (sK6 @ X4) @ (sK7 @ X4)) != $true)) | ((X4 @ sK1 @ sK0) = $true)) & (! [X11 : a,X12 : a] : (((sK9 @ X12 @ X11) = $true) | ((((sK10 @ X12 @ X11 @ X12 @ X11) != $true) & ! [X14 : a,X15 : a] : (((sK3 @ X14 @ X15) != $true) | ((sK10 @ X12 @ X11 @ X14 @ X15) = $true)) & ! [X16 : a,X17 : a,X18 : a] : (($true = (sK10 @ X12 @ X11 @ X16 @ X17)) | ((sK10 @ X12 @ X11 @ X16 @ X18) != $true) | ($true != (sK10 @ X12 @ X11 @ X18 @ X17)))) & (! [X20 : a,X21 : a,X22 : a] : (($true = (sK11 @ X12 @ X11 @ X20 @ X22)) | ($true != (sK11 @ X12 @ X11 @ X21 @ X22)) | ((sK11 @ X12 @ X11 @ X20 @ X21) != $true)) & ($true != (sK11 @ X12 @ X11 @ X12 @ X11)) & ! [X23 : a,X24 : a] : (((sK2 @ X23 @ X24) != $true) | ((sK11 @ X12 @ X11 @ X23 @ X24) = $true))))) & ! [X25 : a,X26 : a,X27 : a] : (((sK9 @ X25 @ X26) = $true) | ($true != (sK9 @ X27 @ X26)) | ((sK9 @ X25 @ X27) != $true)) & ((sK9 @ sK1 @ sK0) != $true))),
% 1.49/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11])],[f8,f14,f13,f12,f11,f10,f9])).
% 1.49/1.40 thf(f9,plain,(
% 1.49/1.40 ? [X0 : a,X1 : a,X2 : a > a > $o,X3 : a > a > $o] : (! [X4 : a > a > $o] : (? [X5 : a,X6 : a] : ((((X2 @ X6 @ X5) = $true) | ((X3 @ X6 @ X5) = $true)) & ($true != (X4 @ X6 @ X5))) | ? [X7 : a,X8 : a,X9 : a] : (((X4 @ X7 @ X9) = $true) & ((X4 @ X9 @ X8) = $true) & ((X4 @ X7 @ X8) != $true)) | ((X4 @ X1 @ X0) = $true)) & ? [X10 : a > a > $o] : (! [X11 : a,X12 : a] : (($true = (X10 @ X12 @ X11)) | (? [X13 : a > a > $o] : (((X13 @ X12 @ X11) != $true) & ! [X14 : a,X15 : a] : (($true != (X3 @ X14 @ X15)) | ((X13 @ X14 @ X15) = $true)) & ! [X16 : a,X17 : a,X18 : a] : (($true = (X13 @ X16 @ X17)) | ($true != (X13 @ X16 @ X18)) | ((X13 @ X18 @ X17) != $true))) & ? [X19 : a > a > $o] : (! [X20 : a,X21 : a,X22 : a] : (($true = (X19 @ X20 @ X22)) | ((X19 @ X21 @ X22) != $true) | ($true != (X19 @ X20 @ X21))) & ((X19 @ X12 @ X11) != $true) & ! [X23 : a,X24 : a] : (($true != (X2 @ X23 @ X24)) | ((X19 @ X23 @ X24) = $true))))) & ! [X25 : a,X26 : a,X27 : a] : (((X10 @ X25 @ X26) = $true) | ((X10 @ X27 @ X26) != $true) | ($true != (X10 @ X25 @ X27))) & ($true != (X10 @ X1 @ X0)))) => (! [X4 : a > a > $o] : (? [X6 : a,X5 : a] : ((((sK2 @ X6 @ X5) = $true) | ((sK3 @ X6 @ X5) = $true)) & ($true != (X4 @ X6 @ X5))) | ? [X7 : a,X8 : a,X9 : a] : (((X4 @ X7 @ X9) = $true) & ((X4 @ X9 @ X8) = $true) & ((X4 @ X7 @ X8) != $true)) | ((X4 @ sK1 @ sK0) = $true)) & ? [X10 : a > a > $o] : (! [X12 : a,X11 : a] : (($true = (X10 @ X12 @ X11)) | (? [X13 : a > a > $o] : (((X13 @ X12 @ X11) != $true) & ! [X15 : a,X14 : a] : (((sK3 @ X14 @ X15) != $true) | ((X13 @ X14 @ X15) = $true)) & ! [X16 : a,X17 : a,X18 : a] : (($true = (X13 @ X16 @ X17)) | ($true != (X13 @ X16 @ X18)) | ((X13 @ X18 @ X17) != $true))) & ? [X19 : a > a > $o] : (! [X20 : a,X21 : a,X22 : a] : (($true = (X19 @ X20 @ X22)) | ((X19 @ X21 @ X22) != $true) | ($true != (X19 @ X20 @ X21))) & ((X19 @ X12 @ X11) != $true) & ! [X24 : a,X23 : a] : (((sK2 @ X23 @ X24) != $true) | ((X19 @ X23 @ X24) = $true))))) & ! [X25 : a,X26 : a,X27 : a] : (((X10 @ X25 @ X26) = $true) | ((X10 @ X27 @ X26) != $true) | ($true != (X10 @ X25 @ X27))) & ($true != (X10 @ sK1 @ sK0))))),
% 1.49/1.40 introduced(definition,[],[choice_axiom])).
% 1.49/1.40 thf(f10,plain,(
% 1.49/1.40 ! [X4 : a > a > $o] : (? [X6 : a,X5 : a] : ((((sK2 @ X6 @ X5) = $true) | ((sK3 @ X6 @ X5) = $true)) & ($true != (X4 @ X6 @ X5))) => ((((sK2 @ (sK5 @ X4) @ (sK4 @ X4)) = $true) | ((sK3 @ (sK5 @ X4) @ (sK4 @ X4)) = $true)) & ($true != (X4 @ (sK5 @ X4) @ (sK4 @ X4)))))),
% 1.49/1.40 introduced(definition,[],[choice_axiom])).
% 1.49/1.40 thf(f11,plain,(
% 1.49/1.40 ! [X4 : a > a > $o] : (? [X7 : a,X8 : a,X9 : a] : (((X4 @ X7 @ X9) = $true) & ((X4 @ X9 @ X8) = $true) & ((X4 @ X7 @ X8) != $true)) => (((X4 @ (sK6 @ X4) @ (sK8 @ X4)) = $true) & ((X4 @ (sK8 @ X4) @ (sK7 @ X4)) = $true) & ((X4 @ (sK6 @ X4) @ (sK7 @ X4)) != $true)))),
% 1.49/1.40 introduced(definition,[],[choice_axiom])).
% 1.49/1.40 thf(f12,plain,(
% 1.49/1.40 ? [X10 : a > a > $o] : (! [X12 : a,X11 : a] : (($true = (X10 @ X12 @ X11)) | (? [X13 : a > a > $o] : (((X13 @ X12 @ X11) != $true) & ! [X15 : a,X14 : a] : (((sK3 @ X14 @ X15) != $true) | ((X13 @ X14 @ X15) = $true)) & ! [X16 : a,X17 : a,X18 : a] : (($true = (X13 @ X16 @ X17)) | ($true != (X13 @ X16 @ X18)) | ((X13 @ X18 @ X17) != $true))) & ? [X19 : a > a > $o] : (! [X20 : a,X21 : a,X22 : a] : (($true = (X19 @ X20 @ X22)) | ((X19 @ X21 @ X22) != $true) | ($true != (X19 @ X20 @ X21))) & ((X19 @ X12 @ X11) != $true) & ! [X24 : a,X23 : a] : (((sK2 @ X23 @ X24) != $true) | ((X19 @ X23 @ X24) = $true))))) & ! [X25 : a,X26 : a,X27 : a] : (((X10 @ X25 @ X26) = $true) | ((X10 @ X27 @ X26) != $true) | ($true != (X10 @ X25 @ X27))) & ($true != (X10 @ sK1 @ sK0))) => (! [X12 : a,X11 : a] : (((sK9 @ X12 @ X11) = $true) | (? [X13 : a > a > $o] : (((X13 @ X12 @ X11) != $true) & ! [X15 : a,X14 : a] : (((sK3 @ X14 @ X15) != $true) | ((X13 @ X14 @ X15) = $true)) & ! [X16 : a,X17 : a,X18 : a] : (($true = (X13 @ X16 @ X17)) | ($true != (X13 @ X16 @ X18)) | ((X13 @ X18 @ X17) != $true))) & ? [X19 : a > a > $o] : (! [X20 : a,X21 : a,X22 : a] : (($true = (X19 @ X20 @ X22)) | ((X19 @ X21 @ X22) != $true) | ($true != (X19 @ X20 @ X21))) & ((X19 @ X12 @ X11) != $true) & ! [X24 : a,X23 : a] : (((sK2 @ X23 @ X24) != $true) | ((X19 @ X23 @ X24) = $true))))) & ! [X27 : a,X26 : a,X25 : a] : (((sK9 @ X25 @ X26) = $true) | ($true != (sK9 @ X27 @ X26)) | ((sK9 @ X25 @ X27) != $true)) & ((sK9 @ sK1 @ sK0) != $true))),
% 1.49/1.40 introduced(definition,[],[choice_axiom])).
% 1.49/1.40 thf(f13,plain,(
% 1.49/1.40 ! [X11 : a,X12 : a] : (? [X13 : a > a > $o] : (((X13 @ X12 @ X11) != $true) & ! [X15 : a,X14 : a] : (((sK3 @ X14 @ X15) != $true) | ((X13 @ X14 @ X15) = $true)) & ! [X16 : a,X17 : a,X18 : a] : (($true = (X13 @ X16 @ X17)) | ($true != (X13 @ X16 @ X18)) | ((X13 @ X18 @ X17) != $true))) => (((sK10 @ X12 @ X11 @ X12 @ X11) != $true) & ! [X15 : a,X14 : a] : (((sK3 @ X14 @ X15) != $true) | ((sK10 @ X12 @ X11 @ X14 @ X15) = $true)) & ! [X18 : a,X17 : a,X16 : a] : (($true = (sK10 @ X12 @ X11 @ X16 @ X17)) | ((sK10 @ X12 @ X11 @ X16 @ X18) != $true) | ($true != (sK10 @ X12 @ X11 @ X18 @ X17)))))),
% 1.49/1.40 introduced(definition,[],[choice_axiom])).
% 1.49/1.40 thf(f14,plain,(
% 1.49/1.40 ! [X11 : a,X12 : a] : (? [X19 : a > a > $o] : (! [X20 : a,X21 : a,X22 : a] : (($true = (X19 @ X20 @ X22)) | ((X19 @ X21 @ X22) != $true) | ($true != (X19 @ X20 @ X21))) & ((X19 @ X12 @ X11) != $true) & ! [X24 : a,X23 : a] : (((sK2 @ X23 @ X24) != $true) | ((X19 @ X23 @ X24) = $true))) => (! [X22 : a,X21 : a,X20 : a] : (($true = (sK11 @ X12 @ X11 @ X20 @ X22)) | ($true != (sK11 @ X12 @ X11 @ X21 @ X22)) | ((sK11 @ X12 @ X11 @ X20 @ X21) != $true)) & ($true != (sK11 @ X12 @ X11 @ X12 @ X11)) & ! [X24 : a,X23 : a] : (((sK2 @ X23 @ X24) != $true) | ((sK11 @ X12 @ X11 @ X23 @ X24) = $true))))),
% 1.49/1.40 introduced(definition,[],[choice_axiom])).
% 1.49/1.40 thf(f8,plain,(
% 1.49/1.40 ? [X0 : a,X1 : a,X2 : a > a > $o,X3 : a > a > $o] : (! [X4 : a > a > $o] : (? [X5 : a,X6 : a] : ((((X2 @ X6 @ X5) = $true) | ((X3 @ X6 @ X5) = $true)) & ($true != (X4 @ X6 @ X5))) | ? [X7 : a,X8 : a,X9 : a] : (((X4 @ X7 @ X9) = $true) & ((X4 @ X9 @ X8) = $true) & ((X4 @ X7 @ X8) != $true)) | ((X4 @ X1 @ X0) = $true)) & ? [X10 : a > a > $o] : (! [X11 : a,X12 : a] : (($true = (X10 @ X12 @ X11)) | (? [X13 : a > a > $o] : (((X13 @ X12 @ X11) != $true) & ! [X14 : a,X15 : a] : (($true != (X3 @ X14 @ X15)) | ((X13 @ X14 @ X15) = $true)) & ! [X16 : a,X17 : a,X18 : a] : (($true = (X13 @ X16 @ X17)) | ($true != (X13 @ X16 @ X18)) | ((X13 @ X18 @ X17) != $true))) & ? [X19 : a > a > $o] : (! [X20 : a,X21 : a,X22 : a] : (($true = (X19 @ X20 @ X22)) | ((X19 @ X21 @ X22) != $true) | ($true != (X19 @ X20 @ X21))) & ((X19 @ X12 @ X11) != $true) & ! [X23 : a,X24 : a] : (($true != (X2 @ X23 @ X24)) | ((X19 @ X23 @ X24) = $true))))) & ! [X25 : a,X26 : a,X27 : a] : (((X10 @ X25 @ X26) = $true) | ((X10 @ X27 @ X26) != $true) | ($true != (X10 @ X25 @ X27))) & ($true != (X10 @ X1 @ X0))))),
% 1.49/1.40 inference(rectify,[status(thm)],[f7])).
% 1.49/1.40 thf(f7,plain,(
% 1.49/1.40 ? [X1 : a,X2 : a,X0 : a > a > $o,X3 : a > a > $o] : (! [X4 : a > a > $o] : (? [X8 : a,X9 : a] : ((((X0 @ X9 @ X8) = $true) | ((X3 @ X9 @ X8) = $true)) & ((X4 @ X9 @ X8) != $true)) | ? [X7 : a,X6 : a,X5 : a] : (((X4 @ X7 @ X5) = $true) & ((X4 @ X5 @ X6) = $true) & ($true != (X4 @ X7 @ X6))) | ((X4 @ X2 @ X1) = $true)) & ? [X10 : a > a > $o] : (! [X15 : a,X14 : a] : (((X10 @ X14 @ X15) = $true) | (? [X16 : a > a > $o] : (($true != (X16 @ X14 @ X15)) & ! [X18 : a,X17 : a] : (($true != (X3 @ X18 @ X17)) | ($true = (X16 @ X18 @ X17))) & ! [X21 : a,X19 : a,X20 : a] : (((X16 @ X21 @ X19) = $true) | ($true != (X16 @ X21 @ X20)) | ((X16 @ X20 @ X19) != $true))) & ? [X22 : a > a > $o] : (! [X25 : a,X27 : a,X26 : a] : (($true = (X22 @ X25 @ X26)) | ($true != (X22 @ X27 @ X26)) | ((X22 @ X25 @ X27) != $true)) & ((X22 @ X14 @ X15) != $true) & ! [X23 : a,X24 : a] : (($true != (X0 @ X23 @ X24)) | ($true = (X22 @ X23 @ X24)))))) & ! [X13 : a,X11 : a,X12 : a] : (((X10 @ X13 @ X11) = $true) | ($true != (X10 @ X12 @ X11)) | ((X10 @ X13 @ X12) != $true)) & ((X10 @ X2 @ X1) != $true)))),
% 1.49/1.40 inference(flattening,[status(thm)],[f6])).
% 1.49/1.40 thf(f6,plain,(
% 1.49/1.40 ? [X2 : a,X0 : a > a > $o,X3 : a > a > $o,X1 : a] : (? [X10 : a > a > $o] : (((X10 @ X2 @ X1) != $true) & (! [X15 : a,X14 : a] : (((X10 @ X14 @ X15) = $true) | (? [X16 : a > a > $o] : (($true != (X16 @ X14 @ X15)) & (! [X19 : a,X21 : a,X20 : a] : (((X16 @ X21 @ X19) = $true) | (((X16 @ X20 @ X19) != $true) | ($true != (X16 @ X21 @ X20)))) & ! [X18 : a,X17 : a] : (($true != (X3 @ X18 @ X17)) | ($true = (X16 @ X18 @ X17))))) & ? [X22 : a > a > $o] : (((X22 @ X14 @ X15) != $true) & (! [X23 : a,X24 : a] : (($true != (X0 @ X23 @ X24)) | ($true = (X22 @ X23 @ X24))) & ! [X26 : a,X25 : a,X27 : a] : (($true = (X22 @ X25 @ X26)) | (($true != (X22 @ X27 @ X26)) | ((X22 @ X25 @ X27) != $true))))))) & ! [X13 : a,X11 : a,X12 : a] : (((X10 @ X13 @ X11) = $true) | (($true != (X10 @ X12 @ X11)) | ((X10 @ X13 @ X12) != $true))))) & ! [X4 : a > a > $o] : (((X4 @ X2 @ X1) = $true) | (? [X7 : a,X6 : a,X5 : a] : (($true != (X4 @ X7 @ X6)) & (((X4 @ X5 @ X6) = $true) & ((X4 @ X7 @ X5) = $true))) | ? [X8 : a,X9 : a] : ((((X0 @ X9 @ X8) = $true) | ((X3 @ X9 @ X8) = $true)) & ((X4 @ X9 @ X8) != $true)))))),
% 1.49/1.40 inference(ennf_transformation,[status(thm)],[f5])).
% 1.49/1.40 thf(f5,plain,(
% 1.49/1.40 ~! [X2 : a,X0 : a > a > $o,X3 : a > a > $o,X1 : a] : (! [X4 : a > a > $o] : ((! [X7 : a,X6 : a,X5 : a] : ((((X4 @ X5 @ X6) = $true) & ((X4 @ X7 @ X5) = $true)) => ($true = (X4 @ X7 @ X6))) & ! [X8 : a,X9 : a] : ((((X0 @ X9 @ X8) = $true) | ((X3 @ X9 @ X8) = $true)) => ((X4 @ X9 @ X8) = $true))) => ((X4 @ X2 @ X1) = $true)) => ! [X10 : a > a > $o] : ((! [X15 : a,X14 : a] : ((! [X16 : a > a > $o] : ((! [X19 : a,X21 : a,X20 : a] : ((((X16 @ X20 @ X19) = $true) & ($true = (X16 @ X21 @ X20))) => ((X16 @ X21 @ X19) = $true)) & ! [X17 : a,X18 : a] : (($true = (X3 @ X18 @ X17)) => ($true = (X16 @ X18 @ X17)))) => ($true = (X16 @ X14 @ X15))) | ! [X22 : a > a > $o] : ((! [X24 : a,X23 : a] : (($true = (X0 @ X23 @ X24)) => ($true = (X22 @ X23 @ X24))) & ! [X26 : a,X25 : a,X27 : a] : ((($true = (X22 @ X27 @ X26)) & ((X22 @ X25 @ X27) = $true)) => ($true = (X22 @ X25 @ X26)))) => ((X22 @ X14 @ X15) = $true))) => ((X10 @ X14 @ X15) = $true)) & ! [X13 : a,X11 : a,X12 : a] : ((($true = (X10 @ X12 @ X11)) & ((X10 @ X13 @ X12) = $true)) => ((X10 @ X13 @ X11) = $true))) => ((X10 @ X2 @ X1) = $true)))),
% 1.49/1.40 inference(fool_elimination,[status(thm)],[f4])).
% 1.49/1.40 thf(f4,plain,(
% 1.49/1.40 ~! [X0 : a > a > $o,X1 : a,X2 : a,X3 : a > a > $o] : (! [X4 : a > a > $o] : ((! [X5 : a,X6 : a,X7 : a] : (((X4 @ X5 @ X6) & (X4 @ X7 @ X5)) => (X4 @ X7 @ X6)) & ! [X8 : a,X9 : a] : (((X3 @ X9 @ X8) | (X0 @ X9 @ X8)) => (X4 @ X9 @ X8))) => (X4 @ X2 @ X1)) => ! [X10 : a > a > $o] : ((! [X11 : a,X12 : a,X13 : a] : (((X10 @ X12 @ X11) & (X10 @ X13 @ X12)) => (X10 @ X13 @ X11)) & ! [X14 : a,X15 : a] : ((! [X16 : a > a > $o] : ((! [X17 : a,X18 : a] : ((X3 @ X18 @ X17) => (X16 @ X18 @ X17)) & ! [X19 : a,X20 : a,X21 : a] : (((X16 @ X20 @ X19) & (X16 @ X21 @ X20)) => (X16 @ X21 @ X19))) => (X16 @ X14 @ X15)) | ! [X22 : a > a > $o] : ((! [X23 : a,X24 : a] : ((X0 @ X23 @ X24) => (X22 @ X23 @ X24)) & ! [X25 : a,X26 : a,X27 : a] : (((X22 @ X25 @ X27) & (X22 @ X27 @ X26)) => (X22 @ X25 @ X26))) => (X22 @ X14 @ X15))) => (X10 @ X14 @ X15))) => (X10 @ X2 @ X1)))),
% 1.49/1.40 inference(rectify,[status(thm)],[f2])).
% 1.49/1.40 thf(f2,negated_conjecture,(
% 1.49/1.40 ~! [X1 : a > a > $o,X3 : a,X2 : a,X0 : a > a > $o] : (! [X4 : a > a > $o] : ((! [X8 : a,X9 : a,X7 : a] : (((X4 @ X8 @ X9) & (X4 @ X7 @ X8)) => (X4 @ X7 @ X9)) & ! [X6 : a,X5 : a] : (((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)) => ! [X10 : a > a > $o] : ((! [X9 : a,X8 : a,X7 : a] : (((X10 @ X8 @ X9) & (X10 @ X7 @ X8)) => (X10 @ X7 @ X9)) & ! [X11 : a,X12 : a] : ((! [X13 : a > a > $o] : ((! [X15 : a,X14 : a] : ((X0 @ X14 @ X15) => (X13 @ X14 @ X15)) & ! [X9 : a,X8 : a,X7 : a] : (((X13 @ X8 @ X9) & (X13 @ X7 @ X8)) => (X13 @ X7 @ X9))) => (X13 @ X11 @ X12)) | ! [X16 : a > a > $o] : ((! [X17 : a,X18 : a] : ((X1 @ X17 @ X18) => (X16 @ X17 @ X18)) & ! [X7 : a,X9 : a,X8 : a] : (((X16 @ X7 @ X8) & (X16 @ X8 @ X9)) => (X16 @ X7 @ X9))) => (X16 @ X11 @ X12))) => (X10 @ X11 @ X12))) => (X10 @ X2 @ X3)))),
% 1.49/1.40 inference(negated_conjecture,[status(cth)],[f1])).
% 1.49/1.40 thf(f1,conjecture,(
% 1.49/1.40 ! [X1 : a > a > $o,X3 : a,X2 : a,X0 : a > a > $o] : (! [X4 : a > a > $o] : ((! [X8 : a,X9 : a,X7 : a] : (((X4 @ X8 @ X9) & (X4 @ X7 @ X8)) => (X4 @ X7 @ X9)) & ! [X6 : a,X5 : a] : (((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) => (X4 @ X5 @ X6))) => (X4 @ X2 @ X3)) => ! [X10 : a > a > $o] : ((! [X9 : a,X8 : a,X7 : a] : (((X10 @ X8 @ X9) & (X10 @ X7 @ X8)) => (X10 @ X7 @ X9)) & ! [X11 : a,X12 : a] : ((! [X13 : a > a > $o] : ((! [X15 : a,X14 : a] : ((X0 @ X14 @ X15) => (X13 @ X14 @ X15)) & ! [X9 : a,X8 : a,X7 : a] : (((X13 @ X8 @ X9) & (X13 @ X7 @ X8)) => (X13 @ X7 @ X9))) => (X13 @ X11 @ X12)) | ! [X16 : a > a > $o] : ((! [X17 : a,X18 : a] : ((X1 @ X17 @ X18) => (X16 @ X17 @ X18)) & ! [X7 : a,X9 : a,X8 : a] : (((X16 @ X7 @ X8) & (X16 @ X8 @ X9)) => (X16 @ X7 @ X9))) => (X16 @ X11 @ X12))) => (X10 @ X11 @ X12))) => (X10 @ X2 @ X3)))),
% 1.49/1.40 file('/export/starexec/sandbox2/tmp/tmp.7LFs0HSWrT/DTF2THF_5730.p',cTHM251F_pme)).
% 1.49/1.40 thf(f84,plain,(
% 1.49/1.40 ((sK9 @ (sK6 @ sK9) @ (sK7 @ sK9)) != $true) | spl12_4),
% 1.49/1.40 inference(avatar_component_clause,[status(thm)],[f82])).
% 1.49/1.40 thf(f873,plain,(
% 1.49/1.40 spl12_5 | ~spl12_18 | spl12_27),
% 1.49/1.40 inference(avatar_split_clause,[status(thm)],[f681,f568,f221,f86])).
% 1.49/1.40 thf(f86,definition,(
% 1.49/1.40 spl12_5 <=> ((sK9 @ sK1 @ sK0) = $true)),
% 1.49/1.40 introduced(definition,[new_symbols(naming,[spl12_5])],[avatar_definition])).
% 1.49/1.40 thf(f221,definition,(
% 1.49/1.40 spl12_18 <=> ((sK2 @ (sK5 @ sK9) @ (sK4 @ sK9)) = $true)),
% 1.49/1.40 introduced(definition,[new_symbols(naming,[spl12_18])],[avatar_definition])).
% 1.49/1.40 thf(f681,plain,(
% 1.49/1.40 ((sK9 @ sK1 @ sK0) = $true) | ($true = (sK9 @ (sK6 @ sK9) @ (sK8 @ sK9))) | ((sK2 @ (sK5 @ sK9) @ (sK4 @ sK9)) != $true)),
% 1.49/1.40 inference(trivial_inequality_removal,[status(thm)],[f658])).
% 1.49/1.40 thf(f658,plain,(
% 1.49/1.40 ((sK9 @ sK1 @ sK0) = $true) | ((sK2 @ (sK5 @ sK9) @ (sK4 @ sK9)) != $true) | ($true = (sK9 @ (sK6 @ sK9) @ (sK8 @ sK9))) | ($true = $false)),
% 1.49/1.40 inference(superposition,[status(thm)],[f34,f346])).
% 1.49/1.40 thf(f346,plain,(
% 1.49/1.40 ( ! [X10 : a > a > $o] : (($false = (X10 @ (sK5 @ X10) @ (sK4 @ X10))) | ($true = (X10 @ sK1 @ sK0)) | ((X10 @ (sK6 @ X10) @ (sK8 @ X10)) = $true)) )),
% 1.49/1.40 inference(not_proxy_clausification,[status(thm)],[f345])).
% 1.49/1.40 thf(f345,plain,(
% 1.49/1.40 ( ! [X10 : a > a > $o] : (((X10 @ (sK6 @ X10) @ (sK8 @ X10)) = $true) | ($true = (X10 @ sK1 @ sK0)) | ((~ (X10 @ (sK5 @ X10) @ (sK4 @ X10))) = $true)) )),
% 1.49/1.40 inference(not_proxy_clausification,[status(thm)],[f344])).
% 1.49/1.40 thf(f344,plain,(
% 1.49/1.40 ( ! [X10 : a > a > $o] : (($false = (~ (X10 @ (sK6 @ X10) @ (sK8 @ X10)))) | ((~ (X10 @ (sK5 @ X10) @ (sK4 @ X10))) = $true) | ($true = (X10 @ sK1 @ sK0))) )),
% 1.49/1.40 inference(not_proxy_clausification,[status(thm)],[f343])).
% 1.49/1.40 thf(f343,plain,(
% 1.49/1.40 ( ! [X10 : a > a > $o] : (($false = (~ (X10 @ sK1 @ sK0))) | ($false = (~ (X10 @ (sK6 @ X10) @ (sK8 @ X10)))) | ((~ (X10 @ (sK5 @ X10) @ (sK4 @ X10))) = $true)) )),
% 1.49/1.40 inference(beta_eta_normalization,[status(thm)],[f342])).
% 1.49/1.40 thf(f342,plain,(
% 1.49/1.40 ( ! [X10 : a > a > $o] : (($true = (~ (X10 @ (sK5 @ (^[Y0 : a]: ((^[Y1 : a]: (X10 @ Y0 @ Y1))))) @ (sK4 @ (^[Y0 : a]: ((^[Y1 : a]: (X10 @ Y0 @ Y1)))))))) | ($false = (~ (X10 @ sK1 @ sK0))) | ($false = (~ (X10 @ (sK6 @ X10) @ (sK8 @ X10))))) )),
% 1.49/1.40 inference(boolean_simplification,[status(thm)],[f341])).
% 1.49/1.40 thf(f341,plain,(
% 1.49/1.40 ( ! [X10 : a > a > $o] : (($false = (~ (X10 @ sK1 @ sK0))) | ($true = (~ (X10 @ (sK5 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (~ (X10 @ Y0 @ Y1))))))) @ (sK4 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (~ (X10 @ Y0 @ Y1)))))))))) | ($false = (~ (X10 @ (sK6 @ X10) @ (sK8 @ X10))))) )),
% 1.49/1.40 inference(beta_eta_normalization,[status(thm)],[f340])).
% 1.49/1.40 thf(f340,plain,(
% 1.49/1.40 ( ! [X10 : a > a > $o] : (($true = (~ (X10 @ (sK5 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (~ (X10 @ Y0 @ Y1))))))) @ (sK4 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (~ (X10 @ Y0 @ Y1)))))))))) | ((~ (X10 @ (sK6 @ (^[Y0 : a]: ((^[Y1 : a]: (X10 @ Y0 @ Y1))))) @ (sK8 @ (^[Y0 : a]: ((^[Y1 : a]: (X10 @ Y0 @ Y1))))))) = $false) | ($false = (~ (X10 @ sK1 @ sK0)))) )),
% 1.49/1.40 inference(boolean_simplification,[status(thm)],[f339])).
% 1.49/1.40 thf(f339,plain,(
% 1.49/1.40 ( ! [X10 : a > a > $o] : (($false = (~ (X10 @ (sK6 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (~ (X10 @ Y0 @ Y1))))))) @ (sK8 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (~ (X10 @ Y0 @ Y1)))))))))) | ($false = (~ (X10 @ sK1 @ sK0))) | ($true = (~ (X10 @ (sK5 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (~ (X10 @ Y0 @ Y1))))))) @ (sK4 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (~ (X10 @ Y0 @ Y1))))))))))) )),
% 1.49/1.40 inference(beta_eta_normalization,[status(thm)],[f329])).
% 1.49/1.40 thf(f329,plain,(
% 1.49/1.40 ( ! [X10 : a > a > $o] : ((((^[Y0 : a]: ((^[Y1 : a]: (~ (X10 @ Y0 @ Y1))))) @ (sK6 @ (^[Y0 : a]: ((^[Y1 : a]: (~ ((^[Y2 : a]: ((^[Y3 : a]: (~ (X10 @ Y2 @ Y3))))) @ Y0 @ Y1)))))) @ (sK8 @ (^[Y0 : a]: ((^[Y1 : a]: (~ ((^[Y2 : a]: ((^[Y3 : a]: (~ (X10 @ Y2 @ Y3))))) @ Y0 @ Y1))))))) = $false) | ($true = ((^[Y0 : a]: ((^[Y1 : a]: (~ (X10 @ Y0 @ Y1))))) @ (sK5 @ (^[Y0 : a]: ((^[Y1 : a]: (~ ((^[Y2 : a]: ((^[Y3 : a]: (~ (X10 @ Y2 @ Y3))))) @ Y0 @ Y1)))))) @ (sK4 @ (^[Y0 : a]: ((^[Y1 : a]: (~ ((^[Y2 : a]: ((^[Y3 : a]: (~ (X10 @ Y2 @ Y3))))) @ Y0 @ Y1)))))))) | (((^[Y0 : a]: ((^[Y1 : a]: (~ (X10 @ Y0 @ Y1))))) @ sK1 @ sK0) = $false)) )),
% 1.49/1.40 inference(primitive_instantiation,[status(thm)],[f152])).
% 1.49/1.40 thf(f152,plain,(
% 1.49/1.40 ( ! [X7 : a > a > $o] : (($true = (X7 @ (sK5 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1)))))) @ (sK4 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1)))))))) | ((X7 @ sK1 @ sK0) = $false) | ((X7 @ (sK6 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1)))))) @ (sK8 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1))))))) = $false)) )),
% 1.49/1.40 inference(not_proxy_clausification,[status(thm)],[f151])).
% 1.49/1.40 thf(f151,plain,(
% 1.49/1.40 ( ! [X7 : a > a > $o] : (($true = (~ (X7 @ (sK6 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1)))))) @ (sK8 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1))))))))) | ((X7 @ sK1 @ sK0) = $false) | ($true = (X7 @ (sK5 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1)))))) @ (sK4 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1))))))))) )),
% 1.49/1.40 inference(not_proxy_clausification,[status(thm)],[f150])).
% 1.49/1.40 thf(f150,plain,(
% 1.49/1.40 ( ! [X7 : a > a > $o] : (((~ (X7 @ sK1 @ sK0)) = $true) | ($true = (~ (X7 @ (sK6 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1)))))) @ (sK8 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1))))))))) | ($true = (X7 @ (sK5 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1)))))) @ (sK4 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1))))))))) )),
% 1.49/1.40 inference(not_proxy_clausification,[status(thm)],[f149])).
% 1.49/1.40 thf(f149,plain,(
% 1.49/1.40 ( ! [X7 : a > a > $o] : (($true != (~ (X7 @ (sK5 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1)))))) @ (sK4 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1))))))))) | ((~ (X7 @ sK1 @ sK0)) = $true) | ($true = (~ (X7 @ (sK6 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1)))))) @ (sK8 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1)))))))))) )),
% 1.49/1.40 inference(beta_eta_normalization,[status(thm)],[f140])).
% 1.49/1.40 thf(f140,plain,(
% 1.49/1.40 ( ! [X7 : a > a > $o] : ((((^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1))))) @ sK1 @ sK0) = $true) | (((^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1))))) @ (sK5 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1)))))) @ (sK4 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1))))))) != $true) | (((^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1))))) @ (sK6 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1)))))) @ (sK8 @ (^[Y0 : a]: ((^[Y1 : a]: (~ (X7 @ Y0 @ Y1))))))) = $true)) )),
% 1.49/1.40 inference(primitive_instantiation,[status(thm)],[f26])).
% 1.49/1.40 thf(f26,plain,(
% 1.49/1.40 ( ! [X4 : a > a > $o] : (((X4 @ (sK6 @ X4) @ (sK8 @ X4)) = $true) | ($true != (X4 @ (sK5 @ X4) @ (sK4 @ X4))) | ((X4 @ sK1 @ sK0) = $true)) )),
% 1.49/1.40 inference(cnf_transformation,[status(thm)],[f15])).
% 1.49/1.40 thf(f34,plain,(
% 1.49/1.40 ( ! [X0 : a,X1 : a] : (((sK9 @ X0 @ X1) = $true) | ((sK2 @ X0 @ X1) != $true)) )),
% 1.49/1.40 inference(trivial_inequality_removal,[status(thm)],[f33])).
% 1.49/1.40 thf(f33,plain,(
% 1.49/1.40 ( ! [X0 : a,X1 : a] : (($true != $true) | ((sK2 @ X0 @ X1) != $true) | ((sK9 @ X0 @ X1) = $true)) )),
% 1.49/1.40 inference(duplicate_literal_removal,[status(thm)],[f32])).
% 1.49/1.40 thf(f32,plain,(
% 1.49/1.40 ( ! [X0 : a,X1 : a] : (($true != $true) | ((sK9 @ X0 @ X1) = $true) | ((sK2 @ X0 @ X1) != $true) | ((sK9 @ X0 @ X1) = $true)) )),
% 1.49/1.40 inference(superposition,[status(thm)],[f19,f18])).
% 1.49/1.40 thf(f18,plain,(
% 1.49/1.40 ( ! [X11 : a,X24 : a,X12 : a,X23 : a] : (((sK11 @ X12 @ X11 @ X23 @ X24) = $true) | ((sK2 @ X23 @ X24) != $true) | ((sK9 @ X12 @ X11) = $true)) )),
% 1.49/1.40 inference(cnf_transformation,[status(thm)],[f15])).
% 1.49/1.40 thf(f19,plain,(
% 1.49/1.40 ( ! [X11 : a,X12 : a] : (($true != (sK11 @ X12 @ X11 @ X12 @ X11)) | ((sK9 @ X12 @ X11) = $true)) )),
% 1.49/1.40 inference(cnf_transformation,[status(thm)],[f15])).
% 1.49/1.40 thf(f870,plain,(
% 1.49/1.40 ~spl12_18 | spl12_21),
% 1.49/1.40 inference(avatar_split_clause,[status(thm)],[f865,f406,f221])).
% 1.49/1.40 thf(f406,definition,(
% 1.49/1.40 spl12_21 <=> ($true = (sK9 @ (sK5 @ sK9) @ (sK4 @ sK9)))),
% 1.49/1.40 introduced(definition,[new_symbols(naming,[spl12_21])],[avatar_definition])).
% 1.49/1.40 thf(f865,plain,(
% 1.49/1.40 ((sK2 @ (sK5 @ sK9) @ (sK4 @ sK9)) != $true) | spl12_21),
% 1.49/1.40 inference(trivial_inequality_removal,[status(thm)],[f860])).
% 1.49/1.40 thf(f860,plain,(
% 1.49/1.40 ($true != $true) | ((sK2 @ (sK5 @ sK9) @ (sK4 @ sK9)) != $true) | spl12_21),
% 1.49/1.40 inference(superposition,[status(thm)],[f408,f34])).
% 1.49/1.40 thf(f408,plain,(
% 1.49/1.40 ($true != (sK9 @ (sK5 @ sK9) @ (sK4 @ sK9))) | spl12_21),
% 1.49/1.40 inference(avatar_component_clause,[status(thm)],[f406])).
% 1.49/1.40 thf(f868,plain,(
% 1.49/1.40 ~spl12_19 | spl12_21),
% 1.49/1.40 inference(avatar_split_clause,[status(thm)],[f866,f406,f233])).
% 1.49/1.40 thf(f233,definition,(
% 1.49/1.40 spl12_19 <=> ((sK3 @ (sK5 @ sK9) @ (sK4 @ sK9)) = $true)),
% 1.49/1.40 introduced(definition,[new_symbols(naming,[spl12_19])],[avatar_definition])).
% 1.49/1.40 thf(f866,plain,(
% 1.49/1.40 ((sK3 @ (sK5 @ sK9) @ (sK4 @ sK9)) != $true) | spl12_21),
% 1.49/1.40 inference(trivial_inequality_removal,[status(thm)],[f859])).
% 1.49/1.40 thf(f859,plain,(
% 1.49/1.40 ((sK3 @ (sK5 @ sK9) @ (sK4 @ sK9)) != $true) | ($true != $true) | spl12_21),
% 1.49/1.40 inference(superposition,[status(thm)],[f408,f37])).
% 1.49/1.40 thf(f37,plain,(
% 1.49/1.40 ( ! [X0 : a,X1 : a] : (((sK9 @ X0 @ X1) = $true) | ($true != (sK3 @ X0 @ X1))) )),
% 1.49/1.40 inference(trivial_inequality_removal,[status(thm)],[f36])).
% 1.49/1.40 thf(f36,plain,(
% 1.49/1.40 ( ! [X0 : a,X1 : a] : (($true != $true) | ($true != (sK3 @ X0 @ X1)) | ((sK9 @ X0 @ X1) = $true)) )),
% 1.49/1.40 inference(duplicate_literal_removal,[status(thm)],[f35])).
% 1.49/1.40 thf(f35,plain,(
% 1.49/1.40 ( ! [X0 : a,X1 : a] : (((sK9 @ X0 @ X1) = $true) | ($true != $true) | ((sK9 @ X0 @ X1) = $true) | ($true != (sK3 @ X0 @ X1))) )),
% 1.49/1.40 inference(superposition,[status(thm)],[f23,f22])).
% 1.49/1.40 thf(f22,plain,(
% 1.49/1.40 ( ! [X11 : a,X14 : a,X15 : a,X12 : a] : (((sK10 @ X12 @ X11 @ X14 @ X15) = $true) | ((sK9 @ X12 @ X11) = $true) | ((sK3 @ X14 @ X15) != $true)) )),
% 1.49/1.40 inference(cnf_transformation,[status(thm)],[f15])).
% 1.49/1.40 thf(f23,plain,(
% 1.49/1.40 ( ! [X11 : a,X12 : a] : (((sK10 @ X12 @ X11 @ X12 @ X11) != $true) | ((sK9 @ X12 @ X11) = $true)) )),
% 1.49/1.40 inference(cnf_transformation,[status(thm)],[f15])).
% 1.49/1.40 thf(f858,plain,(
% 1.49/1.40 spl12_5 | ~spl12_21 | spl12_20),
% 1.49/1.40 inference(avatar_split_clause,[status(thm)],[f848,f402,f406,f86])).
% 1.49/1.40 thf(f848,plain,(
% 1.49/1.40 ($true != (sK9 @ (sK5 @ sK9) @ (sK4 @ sK9))) | ((sK9 @ sK1 @ sK0) = $true) | spl12_20),
% 1.49/1.40 inference(trivial_inequality_removal,[status(thm)],[f846])).
% 1.49/1.40 thf(f846,plain,(
% 1.49/1.40 ((sK9 @ sK1 @ sK0) = $true) | ($true != (sK9 @ (sK5 @ sK9) @ (sK4 @ sK9))) | ($true != $true) | spl12_20),
% 1.49/1.40 inference(superposition,[status(thm)],[f404,f25])).
% 1.49/1.40 thf(f25,plain,(
% 1.49/1.40 ( ! [X4 : a > a > $o] : (((X4 @ (sK8 @ X4) @ (sK7 @ X4)) = $true) | ((X4 @ sK1 @ sK0) = $true) | ($true != (X4 @ (sK5 @ X4) @ (sK4 @ X4)))) )),
% 1.49/1.40 inference(cnf_transformation,[status(thm)],[f15])).
% 1.49/1.40 thf(f404,plain,(
% 1.49/1.40 ((sK9 @ (sK8 @ sK9) @ (sK7 @ sK9)) != $true) | spl12_20),
% 1.49/1.40 inference(avatar_component_clause,[status(thm)],[f402])).
% 1.49/1.40 thf(f715,plain,(
% 1.49/1.40 spl12_27 | spl12_5 | ~spl12_19),
% 1.49/1.40 inference(avatar_split_clause,[status(thm)],[f701,f233,f86,f568])).
% 1.49/1.40 thf(f701,plain,(
% 1.49/1.40 ((sK9 @ sK1 @ sK0) = $true) | ((sK3 @ (sK5 @ sK9) @ (sK4 @ sK9)) != $true) | ($true = (sK9 @ (sK6 @ sK9) @ (sK8 @ sK9)))),
% 1.49/1.40 inference(trivial_inequality_removal,[status(thm)],[f657])).
% 1.49/1.40 thf(f657,plain,(
% 1.49/1.40 ($true = (sK9 @ (sK6 @ sK9) @ (sK8 @ sK9))) | ((sK9 @ sK1 @ sK0) = $true) | ($true = $false) | ((sK3 @ (sK5 @ sK9) @ (sK4 @ sK9)) != $true)),
% 1.49/1.40 inference(superposition,[status(thm)],[f37,f346])).
% 1.49/1.40 thf(f572,plain,(
% 1.49/1.40 ~spl12_4 | spl12_5 | spl12_18 | spl12_19),
% 1.49/1.40 inference(avatar_split_clause,[status(thm)],[f563,f233,f221,f86,f82])).
% 1.49/1.40 thf(f563,plain,(
% 1.49/1.40 ((sK2 @ (sK5 @ sK9) @ (sK4 @ sK9)) = $true) | ((sK9 @ (sK6 @ sK9) @ (sK7 @ sK9)) != $true) | ((sK9 @ sK1 @ sK0) = $true) | spl12_19),
% 1.49/1.40 inference(trivial_inequality_removal,[status(thm)],[f562])).
% 1.49/1.40 thf(f562,plain,(
% 1.49/1.40 ((sK9 @ (sK6 @ sK9) @ (sK7 @ sK9)) != $true) | ((sK9 @ sK1 @ sK0) = $true) | ((sK2 @ (sK5 @ sK9) @ (sK4 @ sK9)) = $true) | ($true != $true) | spl12_19),
% 1.49/1.40 inference(superposition,[status(thm)],[f235,f27])).
% 1.49/1.40 thf(f27,plain,(
% 1.49/1.40 ( ! [X4 : a > a > $o] : (((sK3 @ (sK5 @ X4) @ (sK4 @ X4)) = $true) | ((X4 @ (sK6 @ X4) @ (sK7 @ X4)) != $true) | ((sK2 @ (sK5 @ X4) @ (sK4 @ X4)) = $true) | ((X4 @ sK1 @ sK0) = $true)) )),
% 1.49/1.40 inference(cnf_transformation,[status(thm)],[f15])).
% 1.49/1.40 thf(f235,plain,(
% 1.49/1.40 ((sK3 @ (sK5 @ sK9) @ (sK4 @ sK9)) != $true) | spl12_19),
% 1.49/1.40 inference(avatar_component_clause,[status(thm)],[f233])).
% 1.49/1.40 thf(f571,plain,(
% 1.49/1.40 spl12_5 | spl12_27 | spl12_18 | spl12_19),
% 1.49/1.40 inference(avatar_split_clause,[status(thm)],[f564,f233,f221,f568,f86])).
% 1.49/1.40 thf(f564,plain,(
% 1.49/1.40 ($true = (sK9 @ (sK6 @ sK9) @ (sK8 @ sK9))) | ((sK2 @ (sK5 @ sK9) @ (sK4 @ sK9)) = $true) | ((sK9 @ sK1 @ sK0) = $true) | spl12_19),
% 1.49/1.40 inference(trivial_inequality_removal,[status(thm)],[f560])).
% 1.49/1.40 thf(f560,plain,(
% 1.49/1.40 ($true != $true) | ((sK9 @ sK1 @ sK0) = $true) | ($true = (sK9 @ (sK6 @ sK9) @ (sK8 @ sK9))) | ((sK2 @ (sK5 @ sK9) @ (sK4 @ sK9)) = $true) | spl12_19),
% 1.49/1.40 inference(superposition,[status(thm)],[f235,f29])).
% 1.49/1.40 thf(f29,plain,(
% 1.49/1.40 ( ! [X4 : a > a > $o] : (((sK3 @ (sK5 @ X4) @ (sK4 @ X4)) = $true) | ((X4 @ sK1 @ sK0) = $true) | ((sK2 @ (sK5 @ X4) @ (sK4 @ X4)) = $true) | ((X4 @ (sK6 @ X4) @ (sK8 @ X4)) = $true)) )),
% 1.49/1.40 inference(cnf_transformation,[status(thm)],[f15])).
% 1.49/1.40 thf(f566,plain,(
% 1.49/1.40 spl12_18 | spl12_20 | spl12_5 | spl12_19),
% 1.49/1.40 inference(avatar_split_clause,[status(thm)],[f565,f233,f86,f402,f221])).
% 1.49/1.40 thf(f565,plain,(
% 1.49/1.40 ((sK9 @ (sK8 @ sK9) @ (sK7 @ sK9)) = $true) | ((sK9 @ sK1 @ sK0) = $true) | ((sK2 @ (sK5 @ sK9) @ (sK4 @ sK9)) = $true) | spl12_19),
% 1.49/1.40 inference(trivial_inequality_removal,[status(thm)],[f561])).
% 1.49/1.40 thf(f561,plain,(
% 1.49/1.40 ($true != $true) | ((sK2 @ (sK5 @ sK9) @ (sK4 @ sK9)) = $true) | ((sK9 @ (sK8 @ sK9) @ (sK7 @ sK9)) = $true) | ((sK9 @ sK1 @ sK0) = $true) | spl12_19),
% 1.49/1.40 inference(superposition,[status(thm)],[f235,f28])).
% 1.49/1.40 thf(f28,plain,(
% 1.49/1.40 ( ! [X4 : a > a > $o] : (((sK3 @ (sK5 @ X4) @ (sK4 @ X4)) = $true) | ((X4 @ (sK8 @ X4) @ (sK7 @ X4)) = $true) | ((X4 @ sK1 @ sK0) = $true) | ((sK2 @ (sK5 @ X4) @ (sK4 @ X4)) = $true)) )),
% 1.49/1.40 inference(cnf_transformation,[status(thm)],[f15])).
% 1.49/1.40 thf(f534,plain,(
% 1.49/1.40 ~spl12_5),
% 1.49/1.40 inference(avatar_contradiction_clause,[status(thm)],[f533])).
% 1.49/1.40 thf(f533,plain,(
% 1.49/1.40 $false | ~spl12_5),
% 1.49/1.40 inference(trivial_inequality_removal,[status(thm)],[f524])).
% 1.49/1.40 thf(f524,plain,(
% 1.49/1.40 ($true != $true) | ~spl12_5),
% 1.49/1.40 inference(superposition,[status(thm)],[f16,f88])).
% 1.49/1.40 thf(f88,plain,(
% 1.49/1.40 ((sK9 @ sK1 @ sK0) = $true) | ~spl12_5),
% 1.49/1.40 inference(avatar_component_clause,[status(thm)],[f86])).
% 1.49/1.40 thf(f16,plain,(
% 1.49/1.40 ((sK9 @ sK1 @ sK0) != $true)),
% 1.49/1.40 inference(cnf_transformation,[status(thm)],[f15])).
% 1.49/1.40 thf(f409,plain,(
% 1.49/1.40 ~spl12_20 | ~spl12_21 | spl12_5 | spl12_4),
% 1.49/1.40 inference(avatar_split_clause,[status(thm)],[f399,f82,f86,f406,f402])).
% 1.49/1.40 thf(f399,plain,(
% 1.49/1.40 ((sK9 @ sK1 @ sK0) = $true) | ((sK9 @ (sK8 @ sK9) @ (sK7 @ sK9)) != $true) | ($true != (sK9 @ (sK5 @ sK9) @ (sK4 @ sK9))) | spl12_4),
% 1.49/1.40 inference(trivial_inequality_removal,[status(thm)],[f396])).
% 1.49/1.40 thf(f396,plain,(
% 1.49/1.40 ((sK9 @ sK1 @ sK0) = $true) | ($true != (sK9 @ (sK5 @ sK9) @ (sK4 @ sK9))) | ($true != $true) | ((sK9 @ (sK8 @ sK9) @ (sK7 @ sK9)) != $true) | spl12_4),
% 1.49/1.40 inference(superposition,[status(thm)],[f240,f26])).
% 1.49/1.40 thf(f236,plain,(
% 1.49/1.40 ~spl12_4 | ~spl12_19 | spl12_5),
% 1.49/1.40 inference(avatar_split_clause,[status(thm)],[f228,f86,f233,f82])).
% 1.49/1.40 thf(f228,plain,(
% 1.49/1.40 ((sK3 @ (sK5 @ sK9) @ (sK4 @ sK9)) != $true) | ((sK9 @ sK1 @ sK0) = $true) | ((sK9 @ (sK6 @ sK9) @ (sK7 @ sK9)) != $true)),
% 1.49/1.40 inference(trivial_inequality_removal,[status(thm)],[f227])).
% 1.49/1.40 thf(f227,plain,(
% 1.49/1.40 ((sK3 @ (sK5 @ sK9) @ (sK4 @ sK9)) != $true) | ((sK9 @ sK1 @ sK0) = $true) | ($true != $true) | ((sK9 @ (sK6 @ sK9) @ (sK7 @ sK9)) != $true)),
% 1.49/1.40 inference(superposition,[status(thm)],[f24,f37])).
% 1.49/1.40 thf(f24,plain,(
% 1.49/1.40 ( ! [X4 : a > a > $o] : (($true != (X4 @ (sK5 @ X4) @ (sK4 @ X4))) | ((X4 @ (sK6 @ X4) @ (sK7 @ X4)) != $true) | ((X4 @ sK1 @ sK0) = $true)) )),
% 1.49/1.40 inference(cnf_transformation,[status(thm)],[f15])).
% 1.49/1.40 thf(f224,plain,(
% 1.49/1.40 spl12_5 | ~spl12_18 | ~spl12_4),
% 1.49/1.40 inference(avatar_split_clause,[status(thm)],[f217,f82,f221,f86])).
% 1.49/1.40 thf(f217,plain,(
% 1.49/1.40 ((sK9 @ sK1 @ sK0) = $true) | ((sK2 @ (sK5 @ sK9) @ (sK4 @ sK9)) != $true) | ((sK9 @ (sK6 @ sK9) @ (sK7 @ sK9)) != $true)),
% 1.49/1.40 inference(trivial_inequality_removal,[status(thm)],[f216])).
% 1.49/1.40 thf(f216,plain,(
% 1.49/1.40 ((sK9 @ sK1 @ sK0) = $true) | ((sK9 @ (sK6 @ sK9) @ (sK7 @ sK9)) != $true) | ($true != $true) | ((sK2 @ (sK5 @ sK9) @ (sK4 @ sK9)) != $true)),
% 1.49/1.40 inference(superposition,[status(thm)],[f24,f34])).
% 1.49/1.40 % SZS output end Proof for DTF2THF_5730
% 1.49/1.40 % (5851)------------------------------
% 1.49/1.40 % (5851)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.49/1.40 % (5851)Termination reason: Refutation
% 1.49/1.40
% 1.49/1.40 % (5851)Memory used [KB]: 6012
% 1.49/1.40 % (5851)Time elapsed: 0.080 s
% 1.49/1.40 % (5851)Instructions burned: 106 (million)
% 1.49/1.40 % (5851)------------------------------
% 1.49/1.40 % (5851)------------------------------
% 1.49/1.40 % (5828)Success in time 0.147 s
%------------------------------------------------------------------------------