%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO228^5 : 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 : n014.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 09:53:43 AM UTC 2026
% Result : Theorem 1.64s 1.38s
% Output : Refutation 1.64s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 22
% Syntax : Number of formulae : 122 ( 1 unt; 0 typ; 14 def)
% Number of atoms : 1286 ( 459 equ; 0 cnn)
% Maximal formula atoms : 58 ( 10 avg)
% Number of connectives : 2402 ( 269 ~; 275 |; 215 &;1572 @)
% ( 14 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 179 ( 179 >; 0 *; 0 +; 0 <<)
% Number of symbols : 35 ( 32 usr; 19 con; 0-5 aty)
% Number of variables : 365 ( 0 ^; 280 !; 85 ?; 365 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
g: $tType ).
thf(type_def_6,type,
b: $tType ).
thf(type_def_8,type,
a: $tType ).
thf(func_def_0,type,
g: $tType ).
thf(func_def_1,type,
b: $tType ).
thf(func_def_2,type,
a: $tType ).
thf(func_def_6,type,
sP0: ( g > g > g ) > ( a > a > a ) > ( b > a ) > ( g > b ) > ( g > $o ) > $o ).
thf(func_def_7,type,
sP1: ( g > $o ) > ( g > g > g ) > $o ).
thf(func_def_8,type,
sK2: ( g > $o ) > ( g > g > g ) > g ).
thf(func_def_9,type,
sK3: ( g > $o ) > ( g > g > g ) > g ).
thf(func_def_10,type,
sK4: ( g > g > g ) > ( a > a > a ) > ( b > a ) > ( g > b ) > ( g > $o ) > g ).
thf(func_def_11,type,
sK5: ( g > g > g ) > ( a > a > a ) > ( b > a ) > ( g > b ) > ( g > $o ) > g ).
thf(func_def_12,type,
sK6: a > a > a ).
thf(func_def_13,type,
sK7: a > $o ).
thf(func_def_14,type,
sK8: b > $o ).
thf(func_def_15,type,
sK9: b > a ).
thf(func_def_16,type,
sK10: b > b > b ).
thf(func_def_17,type,
sK11: g > b ).
thf(func_def_18,type,
sK12: g > g > g ).
thf(func_def_19,type,
sK13: g > $o ).
thf(func_def_20,type,
sK14: a ).
thf(func_def_21,type,
sK15: a ).
thf(func_def_22,type,
sK16: g ).
thf(func_def_24,type,
ph18:
!>[X0: $tType] : X0 ).
thf(f183,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f62,f67,f72,f77,f78,f79,f91,f96,f102,f127,f137,f148,f158,f163,f174,f178,f182]) ).
thf(f182,plain,
( ~ spl17_4
| spl17_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f181]) ).
thf(f181,plain,
( $false
| ~ spl17_4
| spl17_9 ),
inference(subsumption_resolution,[status(thm)],[f180,f61]) ).
thf(f61,plain,
( ( ( sP1 @ sK13 @ sK12 )
= $true )
| ~ spl17_4 ),
inference(avatar_component_clause,[status(thm)],[f59]) ).
thf(f59,definition,
( spl17_4
<=> ( ( sP1 @ sK13 @ sK12 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_4])],[avatar_definition]) ).
thf(f180,plain,
( ( ( sP1 @ sK13 @ sK12 )
!= $true )
| spl17_9 ),
inference(trivial_inequality_removal,[status(thm)],[f179]) ).
thf(f179,plain,
( ( ( sP1 @ sK13 @ sK12 )
!= $true )
| ( $true != $true )
| spl17_9 ),
inference(superposition,[status(thm)],[f90,f24]) ).
thf(f24,plain,
! [X0: g > g > g,X1: g > $o] :
( ( ( X1 @ ( sK3 @ X1 @ X0 ) )
= $true )
| ( ( sP1 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: g > g > g,X1: g > $o] :
( ( ( $true
!= ( X1 @ ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) ) ) )
& ( $true
= ( X1 @ ( sK2 @ X1 @ X0 ) ) )
& ( ( X1 @ ( sK3 @ X1 @ X0 ) )
= $true ) )
| ( ( sP1 @ X1 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f12,f13]) ).
thf(f13,plain,
! [X0: g > g > g,X1: g > $o] :
( ? [X2: g,X3: g] :
( ( ( X1 @ ( X0 @ X2 @ X3 ) )
!= $true )
& ( ( X1 @ X2 )
= $true )
& ( ( X1 @ X3 )
= $true ) )
=> ( ( $true
!= ( X1 @ ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) ) ) )
& ( $true
= ( X1 @ ( sK2 @ X1 @ X0 ) ) )
& ( ( X1 @ ( sK3 @ X1 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X0: g > g > g,X1: g > $o] :
( ? [X2: g,X3: g] :
( ( ( X1 @ ( X0 @ X2 @ X3 ) )
!= $true )
& ( ( X1 @ X2 )
= $true )
& ( ( X1 @ X3 )
= $true ) )
| ( ( sP1 @ X1 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
! [X4: g > g > g,X6: g > $o] :
( ? [X27: g,X28: g] :
( ( ( X6 @ ( X4 @ X27 @ X28 ) )
!= $true )
& ( ( X6 @ X27 )
= $true )
& ( ( X6 @ X28 )
= $true ) )
| ( $true
!= ( sP1 @ X6 @ X4 ) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
! [X4: g > g > g,X6: g > $o] :
( ? [X27: g,X28: g] :
( ( ( X6 @ ( X4 @ X27 @ X28 ) )
!= $true )
& ( ( X6 @ X27 )
= $true )
& ( ( X6 @ X28 )
= $true ) )
| ( $true
!= ( sP1 @ X6 @ X4 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f90,plain,
( ( ( sK13 @ ( sK3 @ sK13 @ sK12 ) )
!= $true )
| spl17_9 ),
inference(avatar_component_clause,[status(thm)],[f88]) ).
thf(f88,definition,
( spl17_9
<=> ( ( sK13 @ ( sK3 @ sK13 @ sK12 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_9])],[avatar_definition]) ).
thf(f178,plain,
( spl17_11
| ~ spl17_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f177]) ).
thf(f177,plain,
( $false
| spl17_11
| ~ spl17_13 ),
inference(subsumption_resolution,[status(thm)],[f176,f142]) ).
thf(f142,plain,
( ( ( sK13 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
= $true )
| ~ spl17_13 ),
inference(avatar_component_clause,[status(thm)],[f141]) ).
thf(f141,definition,
( spl17_13
<=> ( ( sK13 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_13])],[avatar_definition]) ).
thf(f176,plain,
( ( ( sK13 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
!= $true )
| spl17_11 ),
inference(trivial_inequality_removal,[status(thm)],[f175]) ).
thf(f175,plain,
( ( ( sK13 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
!= $true )
| ( $true != $true )
| spl17_11 ),
inference(superposition,[status(thm)],[f122,f41]) ).
thf(f41,plain,
! [X16: g] :
( ( ( sK8 @ ( sK11 @ X16 ) )
= $true )
| ( ( sK13 @ X16 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ! [X8: a,X9: a] :
( ( $true
= ( sK7 @ ( sK6 @ X9 @ X8 ) ) )
| ( $true
!= ( sK7 @ X8 ) )
| ( ( sK7 @ X9 )
!= $true ) )
& ! [X10: g,X11: g] :
( ( ( sK11 @ ( sK12 @ X11 @ X10 ) )
= ( sK10 @ ( sK11 @ X11 ) @ ( sK11 @ X10 ) ) )
| ( ( sK13 @ X10 )
!= $true )
| ( ( sK13 @ X11 )
!= $true ) )
& ! [X12: b,X13: b] :
( ( ( sK8 @ ( sK10 @ X12 @ X13 ) )
= $true )
| ( ( sK8 @ X13 )
!= $true )
| ( $true
!= ( sK8 @ X12 ) ) )
& ! [X14: b,X15: b] :
( ( ( sK8 @ ( sK10 @ X15 @ X14 ) )
= $true )
| ( ( sK8 @ X15 )
!= $true )
| ( $true
!= ( sK8 @ X14 ) ) )
& ! [X16: g] :
( ( ( sK8 @ ( sK11 @ X16 ) )
= $true )
| ( ( sK13 @ X16 )
!= $true ) )
& ! [X17: b] :
( ( ( sK7 @ ( sK9 @ X17 ) )
= $true )
| ( $true
!= ( sK8 @ X17 ) ) )
& ! [X18: g,X19: g] :
( ( $true
!= ( sK13 @ X18 ) )
| ( ( sK13 @ X19 )
!= $true )
| ( ( sK13 @ ( sK12 @ X18 @ X19 ) )
= $true ) )
& ! [X20: b,X21: b] :
( ( ( sK9 @ ( sK10 @ X21 @ X20 ) )
= ( sK6 @ ( sK9 @ X21 ) @ ( sK9 @ X20 ) ) )
| ( ( sK8 @ X21 )
!= $true )
| ( ( sK8 @ X20 )
!= $true ) )
& ( ( $true
= ( sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
| ( ( ( sK7 @ sK14 )
= $true )
& ( ( sK7 @ sK15 )
= $true )
& ( $true
!= ( sK7 @ ( sK6 @ sK14 @ sK15 ) ) ) )
| ( ( ( sK7 @ ( sK9 @ ( sK11 @ sK16 ) ) )
!= $true )
& ( $true
= ( sK13 @ sK16 ) ) )
| ( ( sP1 @ sK13 @ sK12 )
= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16])],[f19,f22,f21,f20]) ).
thf(f20,plain,
( ? [X0: a > a > a,X1: a > $o,X2: b > $o,X3: b > a,X4: b > b > b,X5: g > b,X6: g > g > g,X7: g > $o] :
( ! [X8: a,X9: a] :
( ( ( X1 @ ( X0 @ X9 @ X8 ) )
= $true )
| ( ( X1 @ X8 )
!= $true )
| ( ( X1 @ X9 )
!= $true ) )
& ! [X10: g,X11: g] :
( ( ( X5 @ ( X6 @ X11 @ X10 ) )
= ( X4 @ ( X5 @ X11 ) @ ( X5 @ X10 ) ) )
| ( ( X7 @ X10 )
!= $true )
| ( ( X7 @ X11 )
!= $true ) )
& ! [X12: b,X13: b] :
( ( $true
= ( X2 @ ( X4 @ X12 @ X13 ) ) )
| ( ( X2 @ X13 )
!= $true )
| ( $true
!= ( X2 @ X12 ) ) )
& ! [X14: b,X15: b] :
( ( $true
= ( X2 @ ( X4 @ X15 @ X14 ) ) )
| ( ( X2 @ X15 )
!= $true )
| ( $true
!= ( X2 @ X14 ) ) )
& ! [X16: g] :
( ( ( X2 @ ( X5 @ X16 ) )
= $true )
| ( ( X7 @ X16 )
!= $true ) )
& ! [X17: b] :
( ( ( X1 @ ( X3 @ X17 ) )
= $true )
| ( ( X2 @ X17 )
!= $true ) )
& ! [X18: g,X19: g] :
( ( ( X7 @ X18 )
!= $true )
| ( ( X7 @ X19 )
!= $true )
| ( ( X7 @ ( X6 @ X18 @ X19 ) )
= $true ) )
& ! [X20: b,X21: b] :
( ( ( X0 @ ( X3 @ X21 ) @ ( X3 @ X20 ) )
= ( X3 @ ( X4 @ X21 @ X20 ) ) )
| ( ( X2 @ X21 )
!= $true )
| ( ( X2 @ X20 )
!= $true ) )
& ( ( ( sP0 @ X6 @ X0 @ X3 @ X5 @ X7 )
= $true )
| ? [X22: a,X23: a] :
( ( ( X1 @ X22 )
= $true )
& ( ( X1 @ X23 )
= $true )
& ( ( X1 @ ( X0 @ X22 @ X23 ) )
!= $true ) )
| ? [X24: g] :
( ( ( X1 @ ( X3 @ ( X5 @ X24 ) ) )
!= $true )
& ( ( X7 @ X24 )
= $true ) )
| ( ( sP1 @ X7 @ X6 )
= $true ) ) )
=> ( ! [X9: a,X8: a] :
( ( $true
= ( sK7 @ ( sK6 @ X9 @ X8 ) ) )
| ( $true
!= ( sK7 @ X8 ) )
| ( ( sK7 @ X9 )
!= $true ) )
& ! [X11: g,X10: g] :
( ( ( sK11 @ ( sK12 @ X11 @ X10 ) )
= ( sK10 @ ( sK11 @ X11 ) @ ( sK11 @ X10 ) ) )
| ( ( sK13 @ X10 )
!= $true )
| ( ( sK13 @ X11 )
!= $true ) )
& ! [X13: b,X12: b] :
( ( ( sK8 @ ( sK10 @ X12 @ X13 ) )
= $true )
| ( ( sK8 @ X13 )
!= $true )
| ( $true
!= ( sK8 @ X12 ) ) )
& ! [X15: b,X14: b] :
( ( ( sK8 @ ( sK10 @ X15 @ X14 ) )
= $true )
| ( ( sK8 @ X15 )
!= $true )
| ( $true
!= ( sK8 @ X14 ) ) )
& ! [X16: g] :
( ( ( sK8 @ ( sK11 @ X16 ) )
= $true )
| ( ( sK13 @ X16 )
!= $true ) )
& ! [X17: b] :
( ( ( sK7 @ ( sK9 @ X17 ) )
= $true )
| ( $true
!= ( sK8 @ X17 ) ) )
& ! [X19: g,X18: g] :
( ( $true
!= ( sK13 @ X18 ) )
| ( ( sK13 @ X19 )
!= $true )
| ( ( sK13 @ ( sK12 @ X18 @ X19 ) )
= $true ) )
& ! [X21: b,X20: b] :
( ( ( sK9 @ ( sK10 @ X21 @ X20 ) )
= ( sK6 @ ( sK9 @ X21 ) @ ( sK9 @ X20 ) ) )
| ( ( sK8 @ X21 )
!= $true )
| ( ( sK8 @ X20 )
!= $true ) )
& ( ( $true
= ( sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
| ? [X23: a,X22: a] :
( ( ( sK7 @ X22 )
= $true )
& ( $true
= ( sK7 @ X23 ) )
& ( $true
!= ( sK7 @ ( sK6 @ X22 @ X23 ) ) ) )
| ? [X24: g] :
( ( ( sK7 @ ( sK9 @ ( sK11 @ X24 ) ) )
!= $true )
& ( ( sK13 @ X24 )
= $true ) )
| ( ( sP1 @ sK13 @ sK12 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X23: a,X22: a] :
( ( ( sK7 @ X22 )
= $true )
& ( $true
= ( sK7 @ X23 ) )
& ( $true
!= ( sK7 @ ( sK6 @ X22 @ X23 ) ) ) )
=> ( ( ( sK7 @ sK14 )
= $true )
& ( ( sK7 @ sK15 )
= $true )
& ( $true
!= ( sK7 @ ( sK6 @ sK14 @ sK15 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X24: g] :
( ( ( sK7 @ ( sK9 @ ( sK11 @ X24 ) ) )
!= $true )
& ( ( sK13 @ X24 )
= $true ) )
=> ( ( ( sK7 @ ( sK9 @ ( sK11 @ sK16 ) ) )
!= $true )
& ( $true
= ( sK13 @ sK16 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
? [X0: a > a > a,X1: a > $o,X2: b > $o,X3: b > a,X4: b > b > b,X5: g > b,X6: g > g > g,X7: g > $o] :
( ! [X8: a,X9: a] :
( ( ( X1 @ ( X0 @ X9 @ X8 ) )
= $true )
| ( ( X1 @ X8 )
!= $true )
| ( ( X1 @ X9 )
!= $true ) )
& ! [X10: g,X11: g] :
( ( ( X5 @ ( X6 @ X11 @ X10 ) )
= ( X4 @ ( X5 @ X11 ) @ ( X5 @ X10 ) ) )
| ( ( X7 @ X10 )
!= $true )
| ( ( X7 @ X11 )
!= $true ) )
& ! [X12: b,X13: b] :
( ( $true
= ( X2 @ ( X4 @ X12 @ X13 ) ) )
| ( ( X2 @ X13 )
!= $true )
| ( $true
!= ( X2 @ X12 ) ) )
& ! [X14: b,X15: b] :
( ( $true
= ( X2 @ ( X4 @ X15 @ X14 ) ) )
| ( ( X2 @ X15 )
!= $true )
| ( $true
!= ( X2 @ X14 ) ) )
& ! [X16: g] :
( ( ( X2 @ ( X5 @ X16 ) )
= $true )
| ( ( X7 @ X16 )
!= $true ) )
& ! [X17: b] :
( ( ( X1 @ ( X3 @ X17 ) )
= $true )
| ( ( X2 @ X17 )
!= $true ) )
& ! [X18: g,X19: g] :
( ( ( X7 @ X18 )
!= $true )
| ( ( X7 @ X19 )
!= $true )
| ( ( X7 @ ( X6 @ X18 @ X19 ) )
= $true ) )
& ! [X20: b,X21: b] :
( ( ( X0 @ ( X3 @ X21 ) @ ( X3 @ X20 ) )
= ( X3 @ ( X4 @ X21 @ X20 ) ) )
| ( ( X2 @ X21 )
!= $true )
| ( ( X2 @ X20 )
!= $true ) )
& ( ( ( sP0 @ X6 @ X0 @ X3 @ X5 @ X7 )
= $true )
| ? [X22: a,X23: a] :
( ( ( X1 @ X22 )
= $true )
& ( ( X1 @ X23 )
= $true )
& ( ( X1 @ ( X0 @ X22 @ X23 ) )
!= $true ) )
| ? [X24: g] :
( ( ( X1 @ ( X3 @ ( X5 @ X24 ) ) )
!= $true )
& ( ( X7 @ X24 )
= $true ) )
| ( ( sP1 @ X7 @ X6 )
= $true ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
? [X5: a > a > a,X0: a > $o,X1: b > $o,X2: b > a,X3: b > b > b,X7: g > b,X4: g > g > g,X6: g > $o] :
( ! [X18: a,X19: a] :
( ( ( X0 @ ( X5 @ X19 @ X18 ) )
= $true )
| ( ( X0 @ X18 )
!= $true )
| ( ( X0 @ X19 )
!= $true ) )
& ! [X10: g,X9: g] :
( ( ( X3 @ ( X7 @ X9 ) @ ( X7 @ X10 ) )
= ( X7 @ ( X4 @ X9 @ X10 ) ) )
| ( $true
!= ( X6 @ X10 ) )
| ( ( X6 @ X9 )
!= $true ) )
& ! [X15: b,X16: b] :
( ( ( X1 @ ( X3 @ X15 @ X16 ) )
= $true )
| ( ( X1 @ X16 )
!= $true )
| ( $true
!= ( X1 @ X15 ) ) )
& ! [X21: b,X20: b] :
( ( ( X1 @ ( X3 @ X20 @ X21 ) )
= $true )
| ( $true
!= ( X1 @ X20 ) )
| ( ( X1 @ X21 )
!= $true ) )
& ! [X8: g] :
( ( ( X1 @ ( X7 @ X8 ) )
= $true )
| ( ( X6 @ X8 )
!= $true ) )
& ! [X17: b] :
( ( ( X0 @ ( X2 @ X17 ) )
= $true )
| ( ( X1 @ X17 )
!= $true ) )
& ! [X12: g,X11: g] :
( ( ( X6 @ X12 )
!= $true )
| ( ( X6 @ X11 )
!= $true )
| ( ( X6 @ ( X4 @ X12 @ X11 ) )
= $true ) )
& ! [X13: b,X14: b] :
( ( ( X2 @ ( X3 @ X14 @ X13 ) )
= ( X5 @ ( X2 @ X14 ) @ ( X2 @ X13 ) ) )
| ( $true
!= ( X1 @ X14 ) )
| ( $true
!= ( X1 @ X13 ) ) )
& ( ( ( sP0 @ X4 @ X5 @ X2 @ X7 @ X6 )
= $true )
| ? [X25: a,X26: a] :
( ( ( X0 @ X25 )
= $true )
& ( ( X0 @ X26 )
= $true )
& ( ( X0 @ ( X5 @ X25 @ X26 ) )
!= $true ) )
| ? [X24: g] :
( ( ( X0 @ ( X2 @ ( X7 @ X24 ) ) )
!= $true )
& ( ( X6 @ X24 )
= $true ) )
| ( $true
= ( sP1 @ X6 @ X4 ) ) ) ),
inference(definition_folding,[status(thm)],[f7,f9,f8]) ).
thf(f8,plain,
! [X6: g > $o,X7: g > b,X2: b > a,X5: a > a > a,X4: g > g > g] :
( ? [X22: g,X23: g] :
( ( ( X6 @ X23 )
= $true )
& ( ( X2 @ ( X7 @ ( X4 @ X23 @ X22 ) ) )
!= ( X5 @ ( X2 @ ( X7 @ X23 ) ) @ ( X2 @ ( X7 @ X22 ) ) ) )
& ( ( X6 @ X22 )
= $true )
& ( ( X6 @ X23 )
= $true )
& ( ( X6 @ X22 )
= $true ) )
| ( ( sP0 @ X4 @ X5 @ X2 @ X7 @ X6 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f7,plain,
? [X5: a > a > a,X0: a > $o,X1: b > $o,X2: b > a,X3: b > b > b,X7: g > b,X4: g > g > g,X6: g > $o] :
( ! [X18: a,X19: a] :
( ( ( X0 @ ( X5 @ X19 @ X18 ) )
= $true )
| ( ( X0 @ X18 )
!= $true )
| ( ( X0 @ X19 )
!= $true ) )
& ! [X10: g,X9: g] :
( ( ( X3 @ ( X7 @ X9 ) @ ( X7 @ X10 ) )
= ( X7 @ ( X4 @ X9 @ X10 ) ) )
| ( $true
!= ( X6 @ X10 ) )
| ( ( X6 @ X9 )
!= $true ) )
& ! [X15: b,X16: b] :
( ( ( X1 @ ( X3 @ X15 @ X16 ) )
= $true )
| ( ( X1 @ X16 )
!= $true )
| ( $true
!= ( X1 @ X15 ) ) )
& ! [X21: b,X20: b] :
( ( ( X1 @ ( X3 @ X20 @ X21 ) )
= $true )
| ( $true
!= ( X1 @ X20 ) )
| ( ( X1 @ X21 )
!= $true ) )
& ! [X8: g] :
( ( ( X1 @ ( X7 @ X8 ) )
= $true )
| ( ( X6 @ X8 )
!= $true ) )
& ! [X17: b] :
( ( ( X0 @ ( X2 @ X17 ) )
= $true )
| ( ( X1 @ X17 )
!= $true ) )
& ! [X12: g,X11: g] :
( ( ( X6 @ X12 )
!= $true )
| ( ( X6 @ X11 )
!= $true )
| ( ( X6 @ ( X4 @ X12 @ X11 ) )
= $true ) )
& ! [X13: b,X14: b] :
( ( ( X2 @ ( X3 @ X14 @ X13 ) )
= ( X5 @ ( X2 @ X14 ) @ ( X2 @ X13 ) ) )
| ( $true
!= ( X1 @ X14 ) )
| ( $true
!= ( X1 @ X13 ) ) )
& ( ? [X22: g,X23: g] :
( ( ( X6 @ X23 )
= $true )
& ( ( X2 @ ( X7 @ ( X4 @ X23 @ X22 ) ) )
!= ( X5 @ ( X2 @ ( X7 @ X23 ) ) @ ( X2 @ ( X7 @ X22 ) ) ) )
& ( ( X6 @ X22 )
= $true )
& ( ( X6 @ X23 )
= $true )
& ( ( X6 @ X22 )
= $true ) )
| ? [X25: a,X26: a] :
( ( ( X0 @ X25 )
= $true )
& ( ( X0 @ X26 )
= $true )
& ( ( X0 @ ( X5 @ X25 @ X26 ) )
!= $true ) )
| ? [X24: g] :
( ( ( X0 @ ( X2 @ ( X7 @ X24 ) ) )
!= $true )
& ( ( X6 @ X24 )
= $true ) )
| ? [X27: g,X28: g] :
( ( ( X6 @ ( X4 @ X27 @ X28 ) )
!= $true )
& ( ( X6 @ X27 )
= $true )
& ( ( X6 @ X28 )
= $true ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: a > $o,X1: b > $o,X7: g > b,X4: g > g > g,X6: g > $o,X5: a > a > a,X3: b > b > b,X2: b > a] :
( ( ? [X28: g,X27: g] :
( ( ( X6 @ ( X4 @ X27 @ X28 ) )
!= $true )
& ( ( X6 @ X27 )
= $true )
& ( ( X6 @ X28 )
= $true ) )
| ? [X24: g] :
( ( ( X0 @ ( X2 @ ( X7 @ X24 ) ) )
!= $true )
& ( ( X6 @ X24 )
= $true ) )
| ? [X25: a,X26: a] :
( ( ( X0 @ ( X5 @ X25 @ X26 ) )
!= $true )
& ( ( X0 @ X26 )
= $true )
& ( ( X0 @ X25 )
= $true ) )
| ? [X23: g,X22: g] :
( ( ( X2 @ ( X7 @ ( X4 @ X23 @ X22 ) ) )
!= ( X5 @ ( X2 @ ( X7 @ X23 ) ) @ ( X2 @ ( X7 @ X22 ) ) ) )
& ( ( X6 @ X22 )
= $true )
& ( ( X6 @ X22 )
= $true )
& ( ( X6 @ X23 )
= $true )
& ( ( X6 @ X23 )
= $true ) ) )
& ! [X8: g] :
( ( ( X1 @ ( X7 @ X8 ) )
= $true )
| ( ( X6 @ X8 )
!= $true ) )
& ! [X9: g,X10: g] :
( ( ( X3 @ ( X7 @ X9 ) @ ( X7 @ X10 ) )
= ( X7 @ ( X4 @ X9 @ X10 ) ) )
| ( ( X6 @ X9 )
!= $true )
| ( $true
!= ( X6 @ X10 ) ) )
& ! [X15: b,X16: b] :
( ( ( X1 @ ( X3 @ X15 @ X16 ) )
= $true )
| ( ( X1 @ X16 )
!= $true )
| ( $true
!= ( X1 @ X15 ) ) )
& ! [X20: b,X21: b] :
( ( ( X1 @ ( X3 @ X20 @ X21 ) )
= $true )
| ( ( X1 @ X21 )
!= $true )
| ( $true
!= ( X1 @ X20 ) ) )
& ! [X12: g,X11: g] :
( ( ( X6 @ ( X4 @ X12 @ X11 ) )
= $true )
| ( ( X6 @ X11 )
!= $true )
| ( ( X6 @ X12 )
!= $true ) )
& ! [X13: b,X14: b] :
( ( ( X2 @ ( X3 @ X14 @ X13 ) )
= ( X5 @ ( X2 @ X14 ) @ ( X2 @ X13 ) ) )
| ( $true
!= ( X1 @ X13 ) )
| ( $true
!= ( X1 @ X14 ) ) )
& ! [X19: a,X18: a] :
( ( ( X0 @ ( X5 @ X19 @ X18 ) )
= $true )
| ( ( X0 @ X18 )
!= $true )
| ( ( X0 @ X19 )
!= $true ) )
& ! [X17: b] :
( ( ( X0 @ ( X2 @ X17 ) )
= $true )
| ( ( X1 @ X17 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: a > $o,X1: b > $o,X7: g > b,X4: g > g > g,X6: g > $o,X5: a > a > a,X3: b > b > b,X2: b > a] :
( ( ! [X8: g] :
( ( ( X6 @ X8 )
= $true )
=> ( ( X1 @ ( X7 @ X8 ) )
= $true ) )
& ! [X9: g,X10: g] :
( ( ( ( X6 @ X9 )
= $true )
& ( $true
= ( X6 @ X10 ) ) )
=> ( ( X3 @ ( X7 @ X9 ) @ ( X7 @ X10 ) )
= ( X7 @ ( X4 @ X9 @ X10 ) ) ) )
& ! [X15: b,X16: b] :
( ( ( ( X1 @ X16 )
= $true )
& ( $true
= ( X1 @ X15 ) ) )
=> ( ( X1 @ ( X3 @ X15 @ X16 ) )
= $true ) )
& ! [X20: b,X21: b] :
( ( ( ( X1 @ X21 )
= $true )
& ( $true
= ( X1 @ X20 ) ) )
=> ( ( X1 @ ( X3 @ X20 @ X21 ) )
= $true ) )
& ! [X12: g,X11: g] :
( ( ( ( X6 @ X11 )
= $true )
& ( ( X6 @ X12 )
= $true ) )
=> ( ( X6 @ ( X4 @ X12 @ X11 ) )
= $true ) )
& ! [X13: b,X14: b] :
( ( ( $true
= ( X1 @ X13 ) )
& ( $true
= ( X1 @ X14 ) ) )
=> ( ( X2 @ ( X3 @ X14 @ X13 ) )
= ( X5 @ ( X2 @ X14 ) @ ( X2 @ X13 ) ) ) )
& ! [X19: a,X18: a] :
( ( ( ( X0 @ X18 )
= $true )
& ( ( X0 @ X19 )
= $true ) )
=> ( ( X0 @ ( X5 @ X19 @ X18 ) )
= $true ) )
& ! [X17: b] :
( ( ( X1 @ X17 )
= $true )
=> ( ( X0 @ ( X2 @ X17 ) )
= $true ) ) )
=> ( ! [X28: g,X27: g] :
( ( ( ( X6 @ X27 )
= $true )
& ( ( X6 @ X28 )
= $true ) )
=> ( ( X6 @ ( X4 @ X27 @ X28 ) )
= $true ) )
& ! [X24: g] :
( ( ( X6 @ X24 )
= $true )
=> ( ( X0 @ ( X2 @ ( X7 @ X24 ) ) )
= $true ) )
& ! [X25: a,X26: a] :
( ( ( ( X0 @ X26 )
= $true )
& ( ( X0 @ X25 )
= $true ) )
=> ( ( X0 @ ( X5 @ X25 @ X26 ) )
= $true ) )
& ! [X23: g,X22: g] :
( ( ( ( X6 @ X22 )
= $true )
& ( ( X6 @ X22 )
= $true )
& ( ( X6 @ X23 )
= $true )
& ( ( X6 @ X23 )
= $true ) )
=> ( ( X2 @ ( X7 @ ( X4 @ X23 @ X22 ) ) )
= ( X5 @ ( X2 @ ( X7 @ X23 ) ) @ ( X2 @ ( X7 @ X22 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: b > $o,X2: b > a,X3: b > b > b,X4: g > g > g,X5: a > a > a,X6: g > $o,X7: g > b] :
( ( ! [X8: g] :
( ( X6 @ X8 )
=> ( X1 @ ( X7 @ X8 ) ) )
& ! [X9: g,X10: g] :
( ( ( X6 @ X10 )
& ( X6 @ X9 ) )
=> ( ( X3 @ ( X7 @ X9 ) @ ( X7 @ X10 ) )
= ( X7 @ ( X4 @ X9 @ X10 ) ) ) )
& ! [X11: g,X12: g] :
( ( ( X6 @ X12 )
& ( X6 @ X11 ) )
=> ( X6 @ ( X4 @ X12 @ X11 ) ) )
& ! [X13: b,X14: b] :
( ( ( X1 @ X14 )
& ( X1 @ X13 ) )
=> ( ( X2 @ ( X3 @ X14 @ X13 ) )
= ( X5 @ ( X2 @ X14 ) @ ( X2 @ X13 ) ) ) )
& ! [X15: b,X16: b] :
( ( ( X1 @ X16 )
& ( X1 @ X15 ) )
=> ( X1 @ ( X3 @ X15 @ X16 ) ) )
& ! [X17: b] :
( ( X1 @ X17 )
=> ( X0 @ ( X2 @ X17 ) ) )
& ! [X18: a,X19: a] :
( ( ( X0 @ X19 )
& ( X0 @ X18 ) )
=> ( X0 @ ( X5 @ X19 @ X18 ) ) )
& ! [X20: b,X21: b] :
( ( ( X1 @ X20 )
& ( X1 @ X21 ) )
=> ( X1 @ ( X3 @ X20 @ X21 ) ) ) )
=> ( ! [X22: g,X23: g] :
( ( ( X6 @ X23 )
& ( X6 @ X22 )
& ( X6 @ X23 )
& ( X6 @ X22 ) )
=> ( ( X2 @ ( X7 @ ( X4 @ X23 @ X22 ) ) )
= ( X5 @ ( X2 @ ( X7 @ X23 ) ) @ ( X2 @ ( X7 @ X22 ) ) ) ) )
& ! [X24: g] :
( ( X6 @ X24 )
=> ( X0 @ ( X2 @ ( X7 @ X24 ) ) ) )
& ! [X25: a,X26: a] :
( ( ( X0 @ X25 )
& ( X0 @ X26 ) )
=> ( X0 @ ( X5 @ X25 @ X26 ) ) )
& ! [X27: g,X28: g] :
( ( ( X6 @ X27 )
& ( X6 @ X28 ) )
=> ( X6 @ ( X4 @ X27 @ X28 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X6: a > $o,X4: b > $o,X1: b > a,X5: b > b > b,X3: g > g > g,X7: a > a > a,X2: g > $o,X0: g > b] :
( ( ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( X0 @ X8 ) ) )
& ! [X8: g,X9: g] :
( ( ( X2 @ X9 )
& ( X2 @ X8 ) )
=> ( ( X0 @ ( X3 @ X8 @ X9 ) )
= ( X5 @ ( X0 @ X8 ) @ ( X0 @ X9 ) ) ) )
& ! [X9: g,X8: g] :
( ( ( X2 @ X8 )
& ( X2 @ X9 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) )
& ! [X9: b,X8: b] :
( ( ( X4 @ X8 )
& ( X4 @ X9 ) )
=> ( ( X1 @ ( X5 @ X8 @ X9 ) )
= ( X7 @ ( X1 @ X8 ) @ ( X1 @ X9 ) ) ) )
& ! [X8: b,X9: b] :
( ( ( X4 @ X9 )
& ( X4 @ X8 ) )
=> ( X4 @ ( X5 @ X8 @ X9 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) )
& ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( X6 @ X9 ) )
=> ( X6 @ ( X7 @ X8 @ X9 ) ) )
& ! [X8: b,X9: b] :
( ( ( X4 @ X8 )
& ( X4 @ X9 ) )
=> ( X4 @ ( X5 @ X8 @ X9 ) ) ) )
=> ( ! [X9: g,X8: g] :
( ( ( X2 @ X8 )
& ( X2 @ X9 )
& ( X2 @ X8 )
& ( X2 @ X9 ) )
=> ( ( X1 @ ( X0 @ ( X3 @ X8 @ X9 ) ) )
= ( X7 @ ( X1 @ ( X0 @ X8 ) ) @ ( X1 @ ( X0 @ X9 ) ) ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X6 @ ( X1 @ ( X0 @ X8 ) ) ) )
& ! [X8: a,X9: a] :
( ( ( X6 @ X8 )
& ( X6 @ X9 ) )
=> ( X6 @ ( X7 @ X8 @ X9 ) ) )
& ! [X8: g,X9: g] :
( ( ( X2 @ X8 )
& ( X2 @ X9 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X6: a > $o,X4: b > $o,X1: b > a,X5: b > b > b,X3: g > g > g,X7: a > a > a,X2: g > $o,X0: g > b] :
( ( ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( X0 @ X8 ) ) )
& ! [X8: g,X9: g] :
( ( ( X2 @ X9 )
& ( X2 @ X8 ) )
=> ( ( X0 @ ( X3 @ X8 @ X9 ) )
= ( X5 @ ( X0 @ X8 ) @ ( X0 @ X9 ) ) ) )
& ! [X9: g,X8: g] :
( ( ( X2 @ X8 )
& ( X2 @ X9 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) )
& ! [X9: b,X8: b] :
( ( ( X4 @ X8 )
& ( X4 @ X9 ) )
=> ( ( X1 @ ( X5 @ X8 @ X9 ) )
= ( X7 @ ( X1 @ X8 ) @ ( X1 @ X9 ) ) ) )
& ! [X8: b,X9: b] :
( ( ( X4 @ X9 )
& ( X4 @ X8 ) )
=> ( X4 @ ( X5 @ X8 @ X9 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) )
& ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( X6 @ X9 ) )
=> ( X6 @ ( X7 @ X8 @ X9 ) ) )
& ! [X8: b,X9: b] :
( ( ( X4 @ X8 )
& ( X4 @ X9 ) )
=> ( X4 @ ( X5 @ X8 @ X9 ) ) ) )
=> ( ! [X9: g,X8: g] :
( ( ( X2 @ X8 )
& ( X2 @ X9 )
& ( X2 @ X8 )
& ( X2 @ X9 ) )
=> ( ( X1 @ ( X0 @ ( X3 @ X8 @ X9 ) ) )
= ( X7 @ ( X1 @ ( X0 @ X8 ) ) @ ( X1 @ ( X0 @ X9 ) ) ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X6 @ ( X1 @ ( X0 @ X8 ) ) ) )
& ! [X8: a,X9: a] :
( ( ( X6 @ X8 )
& ( X6 @ X9 ) )
=> ( X6 @ ( X7 @ X8 @ X9 ) ) )
& ! [X8: g,X9: g] :
( ( ( X2 @ X8 )
& ( X2 @ X9 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.XTkA7cJxnS/DTF2THF_1319.p',cTHM126_EXPANDED_pme) ).
thf(f122,plain,
( ( ( sK8 @ ( sK11 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) )
!= $true )
| spl17_11 ),
inference(avatar_component_clause,[status(thm)],[f120]) ).
thf(f120,definition,
( spl17_11
<=> ( ( sK8 @ ( sK11 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_11])],[avatar_definition]) ).
thf(f174,plain,
( ~ spl17_1
| spl17_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f173]) ).
thf(f173,plain,
( $false
| ~ spl17_1
| spl17_14 ),
inference(subsumption_resolution,[status(thm)],[f169,f49]) ).
thf(f49,plain,
( ( $true
= ( sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
| ~ spl17_1 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f47,definition,
( spl17_1
<=> ( $true
= ( sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) ),
introduced(definition,[new_symbols(naming,[spl17_1])],[avatar_definition]) ).
thf(f169,plain,
( ( $true
!= ( sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
| spl17_14 ),
inference(trivial_inequality_removal,[status(thm)],[f168]) ).
thf(f168,plain,
( ( $true
!= ( sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
| ( $true != $true )
| spl17_14 ),
inference(superposition,[status(thm)],[f147,f27]) ).
thf(f27,plain,
! [X2: b > a,X3: a > a > a,X0: g > $o,X1: g > b,X4: g > g > g] :
( ( $true
= ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) )
| ( ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: g > $o,X1: g > b,X2: b > a,X3: a > a > a,X4: g > g > g] :
( ( ( ( X0 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
= $true )
& ( ( X3 @ ( X2 @ ( X1 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) @ ( X2 @ ( X1 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) )
!= ( X2 @ ( X1 @ ( X4 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) )
& ( $true
= ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) )
& ( ( X0 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
= $true )
& ( $true
= ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) )
| ( ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f16,f17]) ).
thf(f17,plain,
! [X0: g > $o,X1: g > b,X2: b > a,X3: a > a > a,X4: g > g > g] :
( ? [X5: g,X6: g] :
( ( ( X0 @ X6 )
= $true )
& ( ( X2 @ ( X1 @ ( X4 @ X6 @ X5 ) ) )
!= ( X3 @ ( X2 @ ( X1 @ X6 ) ) @ ( X2 @ ( X1 @ X5 ) ) ) )
& ( ( X0 @ X5 )
= $true )
& ( ( X0 @ X6 )
= $true )
& ( ( X0 @ X5 )
= $true ) )
=> ( ( ( X0 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
= $true )
& ( ( X3 @ ( X2 @ ( X1 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) @ ( X2 @ ( X1 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) )
!= ( X2 @ ( X1 @ ( X4 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) )
& ( $true
= ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) )
& ( ( X0 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
= $true )
& ( $true
= ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
! [X0: g > $o,X1: g > b,X2: b > a,X3: a > a > a,X4: g > g > g] :
( ? [X5: g,X6: g] :
( ( ( X0 @ X6 )
= $true )
& ( ( X2 @ ( X1 @ ( X4 @ X6 @ X5 ) ) )
!= ( X3 @ ( X2 @ ( X1 @ X6 ) ) @ ( X2 @ ( X1 @ X5 ) ) ) )
& ( ( X0 @ X5 )
= $true )
& ( ( X0 @ X6 )
= $true )
& ( ( X0 @ X5 )
= $true ) )
| ( ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,plain,
! [X6: g > $o,X7: g > b,X2: b > a,X5: a > a > a,X4: g > g > g] :
( ? [X22: g,X23: g] :
( ( ( X6 @ X23 )
= $true )
& ( ( X2 @ ( X7 @ ( X4 @ X23 @ X22 ) ) )
!= ( X5 @ ( X2 @ ( X7 @ X23 ) ) @ ( X2 @ ( X7 @ X22 ) ) ) )
& ( ( X6 @ X22 )
= $true )
& ( ( X6 @ X23 )
= $true )
& ( ( X6 @ X22 )
= $true ) )
| ( ( sP0 @ X4 @ X5 @ X2 @ X7 @ X6 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f147,plain,
( ( ( sK13 @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
!= $true )
| spl17_14 ),
inference(avatar_component_clause,[status(thm)],[f145]) ).
thf(f145,definition,
( spl17_14
<=> ( ( sK13 @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_14])],[avatar_definition]) ).
thf(f163,plain,
( ~ spl17_3
| ~ spl17_5
| spl17_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f162]) ).
thf(f162,plain,
( $false
| ~ spl17_3
| ~ spl17_5
| spl17_7 ),
inference(subsumption_resolution,[status(thm)],[f161,f57]) ).
thf(f57,plain,
( ( ( sK7 @ sK15 )
= $true )
| ~ spl17_3 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f55,definition,
( spl17_3
<=> ( ( sK7 @ sK15 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_3])],[avatar_definition]) ).
thf(f161,plain,
( ( ( sK7 @ sK15 )
!= $true )
| ~ spl17_5
| spl17_7 ),
inference(subsumption_resolution,[status(thm)],[f160,f66]) ).
thf(f66,plain,
( ( ( sK7 @ sK14 )
= $true )
| ~ spl17_5 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f64,definition,
( spl17_5
<=> ( ( sK7 @ sK14 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_5])],[avatar_definition]) ).
thf(f160,plain,
( ( ( sK7 @ sK14 )
!= $true )
| ( ( sK7 @ sK15 )
!= $true )
| spl17_7 ),
inference(trivial_inequality_removal,[status(thm)],[f159]) ).
thf(f159,plain,
( ( ( sK7 @ sK14 )
!= $true )
| ( ( sK7 @ sK15 )
!= $true )
| ( $true != $true )
| spl17_7 ),
inference(superposition,[status(thm)],[f76,f45]) ).
thf(f45,plain,
! [X8: a,X9: a] :
( ( $true
= ( sK7 @ ( sK6 @ X9 @ X8 ) ) )
| ( ( sK7 @ X9 )
!= $true )
| ( $true
!= ( sK7 @ X8 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f76,plain,
( ( $true
!= ( sK7 @ ( sK6 @ sK14 @ sK15 ) ) )
| spl17_7 ),
inference(avatar_component_clause,[status(thm)],[f74]) ).
thf(f74,definition,
( spl17_7
<=> ( $true
= ( sK7 @ ( sK6 @ sK14 @ sK15 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_7])],[avatar_definition]) ).
thf(f158,plain,
( ~ spl17_1
| spl17_13 ),
inference(avatar_split_clause,[status(thm)],[f151,f141,f47]) ).
thf(f151,plain,
( ( $true
!= ( sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
| spl17_13 ),
inference(trivial_inequality_removal,[status(thm)],[f150]) ).
thf(f150,plain,
( ( $true
!= ( sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
| ( $true != $true )
| spl17_13 ),
inference(superposition,[status(thm)],[f143,f31]) ).
thf(f31,plain,
! [X2: b > a,X3: a > a > a,X0: g > $o,X1: g > b,X4: g > g > g] :
( ( ( X0 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
= $true )
| ( ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f143,plain,
( ( ( sK13 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
!= $true )
| spl17_13 ),
inference(avatar_component_clause,[status(thm)],[f141]) ).
thf(f148,plain,
( ~ spl17_13
| ~ spl17_14
| spl17_12 ),
inference(avatar_split_clause,[status(thm)],[f139,f124,f145,f141]) ).
thf(f124,definition,
( spl17_12
<=> ( ( sK9 @ ( sK11 @ ( sK12 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) ) )
= ( sK9 @ ( sK10 @ ( sK11 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) @ ( sK11 @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_12])],[avatar_definition]) ).
thf(f139,plain,
( ( ( sK13 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
!= $true )
| ( ( sK13 @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
!= $true )
| spl17_12 ),
inference(trivial_inequality_removal,[status(thm)],[f138]) ).
thf(f138,plain,
( ( ( sK13 @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
!= $true )
| ( ( sK9 @ ( sK11 @ ( sK12 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) ) )
!= ( sK9 @ ( sK11 @ ( sK12 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) ) ) )
| ( ( sK13 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
!= $true )
| spl17_12 ),
inference(superposition,[status(thm)],[f126,f44]) ).
thf(f44,plain,
! [X10: g,X11: g] :
( ( ( sK11 @ ( sK12 @ X11 @ X10 ) )
= ( sK10 @ ( sK11 @ X11 ) @ ( sK11 @ X10 ) ) )
| ( ( sK13 @ X10 )
!= $true )
| ( ( sK13 @ X11 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f126,plain,
( ( ( sK9 @ ( sK11 @ ( sK12 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) ) )
!= ( sK9 @ ( sK10 @ ( sK11 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) @ ( sK11 @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) ) ) )
| spl17_12 ),
inference(avatar_component_clause,[status(thm)],[f124]) ).
thf(f137,plain,
( ~ spl17_1
| spl17_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f136]) ).
thf(f136,plain,
( $false
| ~ spl17_1
| spl17_10 ),
inference(subsumption_resolution,[status(thm)],[f132,f49]) ).
thf(f132,plain,
( ( $true
!= ( sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
| spl17_10 ),
inference(trivial_inequality_removal,[status(thm)],[f131]) ).
thf(f131,plain,
( ( $true != $true )
| ( $true
!= ( sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
| spl17_10 ),
inference(superposition,[status(thm)],[f129,f27]) ).
thf(f129,plain,
( ( ( sK13 @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
!= $true )
| spl17_10 ),
inference(trivial_inequality_removal,[status(thm)],[f128]) ).
thf(f128,plain,
( ( $true != $true )
| ( ( sK13 @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
!= $true )
| spl17_10 ),
inference(superposition,[status(thm)],[f118,f41]) ).
thf(f118,plain,
( ( ( sK8 @ ( sK11 @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) )
!= $true )
| spl17_10 ),
inference(avatar_component_clause,[status(thm)],[f116]) ).
thf(f116,definition,
( spl17_10
<=> ( ( sK8 @ ( sK11 @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_10])],[avatar_definition]) ).
thf(f127,plain,
( ~ spl17_10
| ~ spl17_11
| ~ spl17_12
| ~ spl17_1 ),
inference(avatar_split_clause,[status(thm)],[f114,f47,f124,f120,f116]) ).
thf(f114,plain,
( ( ( sK8 @ ( sK11 @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) )
!= $true )
| ( ( sK9 @ ( sK11 @ ( sK12 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) ) )
!= ( sK9 @ ( sK10 @ ( sK11 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) @ ( sK11 @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) ) ) )
| ( ( sK8 @ ( sK11 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) )
!= $true )
| ~ spl17_1 ),
inference(superposition,[status(thm)],[f113,f38]) ).
thf(f38,plain,
! [X21: b,X20: b] :
( ( ( sK9 @ ( sK10 @ X21 @ X20 ) )
= ( sK6 @ ( sK9 @ X21 ) @ ( sK9 @ X20 ) ) )
| ( ( sK8 @ X21 )
!= $true )
| ( ( sK8 @ X20 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f113,plain,
( ( ( sK9 @ ( sK11 @ ( sK12 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) ) )
!= ( sK6 @ ( sK9 @ ( sK11 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) ) @ ( sK9 @ ( sK11 @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) ) ) )
| ~ spl17_1 ),
inference(trivial_inequality_removal,[status(thm)],[f112]) ).
thf(f112,plain,
( ( $true != $true )
| ( ( sK9 @ ( sK11 @ ( sK12 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) ) )
!= ( sK6 @ ( sK9 @ ( sK11 @ ( sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) ) @ ( sK9 @ ( sK11 @ ( sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) ) ) )
| ~ spl17_1 ),
inference(superposition,[status(thm)],[f30,f49]) ).
thf(f30,plain,
! [X2: b > a,X3: a > a > a,X0: g > $o,X1: g > b,X4: g > g > g] :
( ( ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 )
!= $true )
| ( ( X3 @ ( X2 @ ( X1 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) @ ( X2 @ ( X1 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) )
!= ( X2 @ ( X1 @ ( X4 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f102,plain,
( spl17_2
| ~ spl17_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f101]) ).
thf(f101,plain,
( $false
| spl17_2
| ~ spl17_6 ),
inference(subsumption_resolution,[status(thm)],[f100,f71]) ).
thf(f71,plain,
( ( $true
= ( sK13 @ sK16 ) )
| ~ spl17_6 ),
inference(avatar_component_clause,[status(thm)],[f69]) ).
thf(f69,definition,
( spl17_6
<=> ( $true
= ( sK13 @ sK16 ) ) ),
introduced(definition,[new_symbols(naming,[spl17_6])],[avatar_definition]) ).
thf(f100,plain,
( ( $true
!= ( sK13 @ sK16 ) )
| spl17_2 ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
( ( $true
!= ( sK13 @ sK16 ) )
| ( $true != $true )
| spl17_2 ),
inference(superposition,[status(thm)],[f98,f41]) ).
thf(f98,plain,
( ( ( sK8 @ ( sK11 @ sK16 ) )
!= $true )
| spl17_2 ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( ( sK8 @ ( sK11 @ sK16 ) )
!= $true )
| ( $true != $true )
| spl17_2 ),
inference(superposition,[status(thm)],[f53,f40]) ).
thf(f40,plain,
! [X17: b] :
( ( ( sK7 @ ( sK9 @ X17 ) )
= $true )
| ( $true
!= ( sK8 @ X17 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f53,plain,
( ( ( sK7 @ ( sK9 @ ( sK11 @ sK16 ) ) )
!= $true )
| spl17_2 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl17_2
<=> ( ( sK7 @ ( sK9 @ ( sK11 @ sK16 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_2])],[avatar_definition]) ).
thf(f96,plain,
( ~ spl17_4
| spl17_8 ),
inference(avatar_split_clause,[status(thm)],[f93,f84,f59]) ).
thf(f84,definition,
( spl17_8
<=> ( ( sK13 @ ( sK2 @ sK13 @ sK12 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_8])],[avatar_definition]) ).
thf(f93,plain,
( ( ( sP1 @ sK13 @ sK12 )
!= $true )
| spl17_8 ),
inference(trivial_inequality_removal,[status(thm)],[f92]) ).
thf(f92,plain,
( ( $true != $true )
| ( ( sP1 @ sK13 @ sK12 )
!= $true )
| spl17_8 ),
inference(superposition,[status(thm)],[f86,f25]) ).
thf(f25,plain,
! [X0: g > g > g,X1: g > $o] :
( ( $true
= ( X1 @ ( sK2 @ X1 @ X0 ) ) )
| ( ( sP1 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f86,plain,
( ( ( sK13 @ ( sK2 @ sK13 @ sK12 ) )
!= $true )
| spl17_8 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f91,plain,
( ~ spl17_8
| ~ spl17_9
| ~ spl17_4 ),
inference(avatar_split_clause,[status(thm)],[f82,f59,f88,f84]) ).
thf(f82,plain,
( ( ( sK13 @ ( sK3 @ sK13 @ sK12 ) )
!= $true )
| ( ( sK13 @ ( sK2 @ sK13 @ sK12 ) )
!= $true )
| ~ spl17_4 ),
inference(subsumption_resolution,[status(thm)],[f81,f61]) ).
thf(f81,plain,
( ( ( sK13 @ ( sK3 @ sK13 @ sK12 ) )
!= $true )
| ( ( sP1 @ sK13 @ sK12 )
!= $true )
| ( ( sK13 @ ( sK2 @ sK13 @ sK12 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f80]) ).
thf(f80,plain,
( ( ( sP1 @ sK13 @ sK12 )
!= $true )
| ( ( sK13 @ ( sK3 @ sK13 @ sK12 ) )
!= $true )
| ( ( sK13 @ ( sK2 @ sK13 @ sK12 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f26,f39]) ).
thf(f39,plain,
! [X18: g,X19: g] :
( ( ( sK13 @ ( sK12 @ X18 @ X19 ) )
= $true )
| ( $true
!= ( sK13 @ X18 ) )
| ( ( sK13 @ X19 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f26,plain,
! [X0: g > g > g,X1: g > $o] :
( ( $true
!= ( X1 @ ( X0 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) ) ) )
| ( ( sP1 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f79,plain,
( spl17_5
| spl17_6
| spl17_4
| spl17_1 ),
inference(avatar_split_clause,[status(thm)],[f36,f47,f59,f69,f64]) ).
thf(f36,plain,
( ( $true
= ( sK13 @ sK16 ) )
| ( ( sK7 @ sK14 )
= $true )
| ( ( sP1 @ sK13 @ sK12 )
= $true )
| ( $true
= ( sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f78,plain,
( spl17_1
| ~ spl17_7
| spl17_4
| ~ spl17_2 ),
inference(avatar_split_clause,[status(thm)],[f33,f51,f59,f74,f47]) ).
thf(f33,plain,
( ( $true
= ( sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
| ( ( sK7 @ ( sK9 @ ( sK11 @ sK16 ) ) )
!= $true )
| ( ( sP1 @ sK13 @ sK12 )
= $true )
| ( $true
!= ( sK7 @ ( sK6 @ sK14 @ sK15 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f77,plain,
( spl17_6
| ~ spl17_7
| spl17_4
| spl17_1 ),
inference(avatar_split_clause,[status(thm)],[f32,f47,f59,f74,f69]) ).
thf(f32,plain,
( ( ( sP1 @ sK13 @ sK12 )
= $true )
| ( $true
!= ( sK7 @ ( sK6 @ sK14 @ sK15 ) ) )
| ( $true
= ( sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
| ( $true
= ( sK13 @ sK16 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f72,plain,
( spl17_4
| spl17_3
| spl17_1
| spl17_6 ),
inference(avatar_split_clause,[status(thm)],[f34,f69,f47,f55,f59]) ).
thf(f34,plain,
( ( ( sP1 @ sK13 @ sK12 )
= $true )
| ( $true
= ( sK13 @ sK16 ) )
| ( $true
= ( sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
| ( ( sK7 @ sK15 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f67,plain,
( spl17_1
| spl17_4
| spl17_5
| ~ spl17_2 ),
inference(avatar_split_clause,[status(thm)],[f37,f51,f64,f59,f47]) ).
thf(f37,plain,
( ( ( sK7 @ ( sK9 @ ( sK11 @ sK16 ) ) )
!= $true )
| ( $true
= ( sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
| ( ( sK7 @ sK14 )
= $true )
| ( ( sP1 @ sK13 @ sK12 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f62,plain,
( spl17_1
| ~ spl17_2
| spl17_3
| spl17_4 ),
inference(avatar_split_clause,[status(thm)],[f35,f59,f55,f51,f47]) ).
thf(f35,plain,
( ( ( sK7 @ sK15 )
= $true )
| ( ( sP1 @ sK13 @ sK12 )
= $true )
| ( $true
= ( sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13 ) )
| ( ( sK7 @ ( sK9 @ ( sK11 @ sK16 ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.09 % Problem : SYO228^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.10 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.11/0.29 % Computer : n014.cluster.edu
% 0.11/0.29 % Model : x86_64 x86_64
% 0.11/0.29 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.11/0.29 % Memory : 8042.1875MB
% 0.11/0.29 % OS : Linux 3.10.0-693.el7.x86_64
% 0.11/0.29 % CPULimit : 300
% 0.11/0.29 % WCLimit : 300
% 0.11/0.29 % DateTime : Tue Feb 24 14:26:27 EST 2026
% 0.11/0.29 % CPUTime :
% 0.11/0.29 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.39 ---- Original DTF file ---
% 0.16/0.39 thf(spec,logic,$$dhol).
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 % File : SYO228^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.39 % Domain : Syntactic
% 0.16/0.39 % Problem : TPS problem THM126-EXPANDED
% 0.16/0.39 % Version : Especial.
% 0.16/0.39 % English :
% 0.16/0.39
% 0.16/0.39 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.39 % Source : [Bro09]
% 0.16/0.39 % Names : tps_0540 [Bro09]
% 0.16/0.39 % : THM126-EXPANDED [TPS]
% 0.16/0.39
% 0.16/0.39 % Status : Theorem
% 0.16/0.39 % Rating : 0.22 v9.1.0, 0.25 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.29 v5.5.0, 0.33 v5.4.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.16/0.39 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.16/0.39 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.16/0.39 % Maximal formula atoms : 3 ( 3 avg)
% 0.16/0.39 % Number of connectives : 106 ( 0 ~; 0 |; 21 &; 72 @)
% 0.16/0.39 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.16/0.39 % Maximal formula depth : 22 ( 22 avg)
% 0.16/0.39 % Number of types : 4 ( 3 usr)
% 0.16/0.39 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.16/0.39 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.16/0.39 % Number of variables : 29 ( 0 ^; 29 !; 0 ?; 29 :)
% 0.16/0.39 % SPC : TH0_THM_EQU_NAR
% 0.16/0.39
% 0.16/0.39 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.39 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.39 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.39 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.39 % : Polymorphic definitions expanded.
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 thf(g_type,type,
% 0.16/0.39 g: $tType ).
% 0.16/0.39
% 0.16/0.39 thf(b_type,type,
% 0.16/0.39 b: $tType ).
% 0.16/0.39
% 0.16/0.39 thf(a_type,type,
% 0.16/0.39 a: $tType ).
% 0.16/0.39
% 0.16/0.39 thf(cTHM126_EXPANDED_pme,conjecture,
% 0.16/0.39 ! [Xh1: g > b,Xh2: b > a,Xs1: g > $o,Xf1: g > g > g,Xs2: b > $o,Xf2: b > b > b,Xs3: a > $o,Xf3: a > a > a] :
% 0.16/0.39 ( ( ! [Xx: g,Xy: g] :
% 0.16/0.39 ( ( ( Xs1 @ Xx )
% 0.16/0.39 & ( Xs1 @ Xy ) )
% 0.16/0.39 => ( Xs1 @ ( Xf1 @ Xx @ Xy ) ) )
% 0.16/0.39 & ! [Xx: b,Xy: b] :
% 0.16/0.39 ( ( ( Xs2 @ Xx )
% 0.16/0.39 & ( Xs2 @ Xy ) )
% 0.16/0.39 => ( Xs2 @ ( Xf2 @ Xx @ Xy ) ) )
% 0.16/0.39 & ! [Xx: g] :
% 0.16/0.39 ( ( Xs1 @ Xx )
% 0.16/0.39 => ( Xs2 @ ( Xh1 @ Xx ) ) )
% 0.16/0.39 & ! [Xx: g,Xy: g] :
% 0.16/0.39 ( ( ( Xs1 @ Xx )
% 0.16/0.39 & ( Xs1 @ Xy ) )
% 0.16/0.39 => ( ( Xh1 @ ( Xf1 @ Xx @ Xy ) )
% 0.16/0.39 = ( Xf2 @ ( Xh1 @ Xx ) @ ( Xh1 @ Xy ) ) ) )
% 0.16/0.39 & ! [Xx: b,Xy: b] :
% 0.16/0.39 ( ( ( Xs2 @ Xx )
% 0.16/0.39 & ( Xs2 @ Xy ) )
% 0.16/0.39 => ( Xs2 @ ( Xf2 @ Xx @ Xy ) ) )
% 0.16/0.39 & ! [Xx: a,Xy: a] :
% 0.16/0.39 ( ( ( Xs3 @ Xx )
% 0.16/0.39 & ( Xs3 @ Xy ) )
% 0.16/0.39 => ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
% 0.16/0.39 & ! [Xx: b] :
% 0.16/0.39 ( ( Xs2 @ Xx )
% 0.16/0.39 => ( Xs3 @ ( Xh2 @ Xx ) ) )
% 0.16/0.39 & ! [Xx: b,Xy: b] :
% 0.16/0.39 ( ( ( Xs2 @ Xx )
% 0.16/0.39 & ( Xs2 @ Xy ) )
% 0.16/0.39 => ( ( Xh2 @ ( Xf2 @ Xx @ Xy ) )
% 0.16/0.39 = ( Xf3 @ ( Xh2 @ Xx ) @ ( Xh2 @ Xy ) ) ) ) )
% 0.16/0.39 => ( ! [Xx: g,Xy: g] :
% 0.16/0.39 ( ( ( Xs1 @ Xx )
% 0.16/0.39 & ( Xs1 @ Xy ) )
% 0.16/0.39 => ( Xs1 @ ( Xf1 @ Xx @ Xy ) ) )
% 0.16/0.39 & ! [Xx: a,Xy: a] :
% 0.16/0.39 ( ( ( Xs3 @ Xx )
% 0.16/0.39 & ( Xs3 @ Xy ) )
% 0.16/0.39 => ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
% 0.16/0.39 & ! [Xx: g] :
% 0.16/0.39 ( ( Xs1 @ Xx )
% 0.16/0.39 => ( Xs3 @ ( Xh2 @ ( Xh1 @ Xx ) ) ) )
% 0.16/0.39 & ! [Xx: g,Xy: g] :
% 0.16/0.39 ( ( ( Xs1 @ Xx )
% 0.16/0.39 & ( Xs1 @ Xy )
% 0.16/0.39 & ( Xs1 @ Xx )
% 0.16/0.39 & ( Xs1 @ Xy ) )
% 0.16/0.39 => ( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx @ Xy ) ) )
% 0.16/0.39 = ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) @ ( Xh2 @ ( Xh1 @ Xy ) ) ) ) ) ) ) ).
% 0.16/0.39
% 0.16/0.39 %------------------------------------------------------------------------------
% 0.16/0.39 ------------------------
% 1.64/1.33 ---- Embedded in THF ---
% 1.64/1.33 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.33 %%% Generated on Tue Feb 24 14:26:28 EST 2026
% 1.64/1.33 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.33 %%% Logic specification used:
% 1.64/1.33 %%% thf(spec, logic, $$dhol).
% 1.64/1.33
% 1.64/1.33 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.XTkA7cJxnS/DTF2DTF1319.p
% See solution above
% 1.64/1.33 ------------------------
% 1.64/1.34 ---- Cleaned THF ---
% 1.64/1.34 thf(g_type,type,
% 1.64/1.34 g: $tType ).
% 1.64/1.34
% 1.64/1.34 thf(b_type,type,
% 1.64/1.34 b: $tType ).
% 1.64/1.34
% 1.64/1.34 thf(a_type,type,
% 1.64/1.34 a: $tType ).
% 1.64/1.34
% 1.64/1.34 thf(cTHM126_EXPANDED_pme,conjecture,
% 1.64/1.34 ! [Xh1: g > b,Xh2: b > a,Xs1: g > $o,Xf1: g > g > g,Xs2: b > $o,Xf2: b > b > b,Xs3: a > $o,Xf3: a > a > a] :
% 1.64/1.34 ( ( ! [Xx: g,Xy: g] :
% 1.64/1.34 ( ( ( Xs1 @ Xx )
% 1.64/1.34 & ( Xs1 @ Xy ) )
% 1.64/1.34 => ( Xs1 @ ( Xf1 @ Xx @ Xy ) ) )
% 1.64/1.34 & ! [Xx: b,Xy: b] :
% 1.64/1.34 ( ( ( Xs2 @ Xx )
% 1.64/1.34 & ( Xs2 @ Xy ) )
% 1.64/1.34 => ( Xs2 @ ( Xf2 @ Xx @ Xy ) ) )
% 1.64/1.34 & ! [Xx: g] :
% 1.64/1.34 ( ( Xs1 @ Xx )
% 1.64/1.34 => ( Xs2 @ ( Xh1 @ Xx ) ) )
% 1.64/1.34 & ! [Xx: g,Xy: g] :
% 1.64/1.34 ( ( ( Xs1 @ Xx )
% 1.64/1.34 & ( Xs1 @ Xy ) )
% 1.64/1.34 => ( ( Xh1 @ ( Xf1 @ Xx @ Xy ) )
% 1.64/1.34 = ( Xf2 @ ( Xh1 @ Xx ) @ ( Xh1 @ Xy ) ) ) )
% 1.64/1.34 & ! [Xx: b,Xy: b] :
% 1.64/1.34 ( ( ( Xs2 @ Xx )
% 1.64/1.34 & ( Xs2 @ Xy ) )
% 1.64/1.34 => ( Xs2 @ ( Xf2 @ Xx @ Xy ) ) )
% 1.64/1.34 & ! [Xx: a,Xy: a] :
% 1.64/1.34 ( ( ( Xs3 @ Xx )
% 1.64/1.34 & ( Xs3 @ Xy ) )
% 1.64/1.34 => ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
% 1.64/1.34 & ! [Xx: b] :
% 1.64/1.34 ( ( Xs2 @ Xx )
% 1.64/1.34 => ( Xs3 @ ( Xh2 @ Xx ) ) )
% 1.64/1.34 & ! [Xx: b,Xy: b] :
% 1.64/1.34 ( ( ( Xs2 @ Xx )
% 1.64/1.34 & ( Xs2 @ Xy ) )
% 1.64/1.34 => ( ( Xh2 @ ( Xf2 @ Xx @ Xy ) )
% 1.64/1.34 = ( Xf3 @ ( Xh2 @ Xx ) @ ( Xh2 @ Xy ) ) ) ) )
% 1.64/1.34 => ( ! [Xx: g,Xy: g] :
% 1.64/1.34 ( ( ( Xs1 @ Xx )
% 1.64/1.34 & ( Xs1 @ Xy ) )
% 1.64/1.34 => ( Xs1 @ ( Xf1 @ Xx @ Xy ) ) )
% 1.64/1.34 & ! [Xx: a,Xy: a] :
% 1.64/1.34 ( ( ( Xs3 @ Xx )
% 1.64/1.34 & ( Xs3 @ Xy ) )
% 1.64/1.34 => ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
% 1.64/1.34 & ! [Xx: g] :
% 1.64/1.34 ( ( Xs1 @ Xx )
% 1.64/1.34 => ( Xs3 @ ( Xh2 @ ( Xh1 @ Xx ) ) ) )
% 1.64/1.34 & ! [Xx: g,Xy: g] :
% 1.64/1.34 ( ( ( Xs1 @ Xx )
% 1.64/1.34 & ( Xs1 @ Xy )
% 1.64/1.34 & ( Xs1 @ Xx )
% 1.64/1.34 & ( Xs1 @ Xy ) )
% 1.64/1.34 => ( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx @ Xy ) ) )
% 1.64/1.34 = ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) @ ( Xh2 @ ( Xh1 @ Xy ) ) ) ) ) ) ) ).
% 1.64/1.34 ------------------------
% 1.64/1.36 % (1421)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_1319 for (2999ds/2Mi)
% 1.64/1.36 % (1419)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_1319 for (2999ds/27Mi)
% 1.64/1.36 % (1423)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_1319 for (2999ds/18Mi)
% 1.64/1.36 % (1422)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_1319 for (2999ds/275Mi)
% 1.64/1.36 % (1418)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_1319 for (2999ds/4Mi)
% 1.64/1.36 % (1417)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_1319 for (2999ds/183Mi)
% 1.64/1.36 % (1420)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_1319 for (2999ds/2Mi)
% 1.64/1.36 % (1420)Instruction limit reached!
% 1.64/1.36 % (1420)------------------------------
% 1.64/1.36 % (1420)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.36 % (1420)Termination reason: Unknown
% 1.64/1.36 % (1420)Termination phase: Property scanning
% 1.64/1.36
% 1.64/1.36 % (1421)Instruction limit reached!
% 1.64/1.36 % (1421)------------------------------
% 1.64/1.36 % (1421)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.36 % (1421)Termination reason: Unknown
% 1.64/1.36 % (1421)Termination phase: shuffling
% 1.64/1.36
% 1.64/1.36 % (1421)Memory used [KB]: 1023
% 1.64/1.36 % (1421)Time elapsed: 0.003 s
% 1.64/1.36 % (1421)Instructions burned: 2 (million)
% 1.64/1.36 % (1421)------------------------------
% 1.64/1.36 % (1421)------------------------------
% 1.64/1.36 % (1420)Memory used [KB]: 1023
% 1.64/1.36 % (1420)Time elapsed: 0.002 s
% 1.64/1.36 % (1420)Instructions burned: 2 (million)
% 1.64/1.36 % (1420)------------------------------
% 1.64/1.36 % (1420)------------------------------
% 1.64/1.36 % (1418)Instruction limit reached!
% 1.64/1.36 % (1418)------------------------------
% 1.64/1.36 % (1418)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.36 % (1418)Termination reason: Unknown
% 1.64/1.36 % (1418)Termination phase: Preprocessing 3
% 1.64/1.36
% 1.64/1.36 % (1418)Memory used [KB]: 1023
% 1.64/1.36 % (1418)Time elapsed: 0.004 s
% 1.64/1.36 % (1418)Instructions burned: 4 (million)
% 1.64/1.36 % (1418)------------------------------
% 1.64/1.36 % (1418)------------------------------
% 1.64/1.37 % (1423)Instruction limit reached!
% 1.64/1.37 % (1423)------------------------------
% 1.64/1.37 % (1423)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (1423)Termination reason: Unknown
% 1.64/1.37 % (1423)Termination phase: Saturation
% 1.64/1.37
% 1.64/1.37 % (1423)Memory used [KB]: 5756
% 1.64/1.37 % (1423)Time elapsed: 0.012 s
% 1.64/1.37 % (1423)Instructions burned: 18 (million)
% 1.64/1.37 % (1423)------------------------------
% 1.64/1.37 % (1423)------------------------------
% 1.64/1.37 % (1419)Instruction limit reached!
% 1.64/1.37 % (1419)------------------------------
% 1.64/1.37 % (1419)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.37 % (1419)Termination reason: Unknown
% 1.64/1.37 % (1419)Termination phase: Saturation
% 1.64/1.37
% 1.64/1.37 % (1419)Memory used [KB]: 5756
% 1.64/1.37 % (1419)Time elapsed: 0.017 s
% 1.64/1.37 % (1419)Instructions burned: 28 (million)
% 1.64/1.37 % (1419)------------------------------
% 1.64/1.37 % (1419)------------------------------
% 1.64/1.38 % (1425)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_1319 for (2999ds/37Mi)
% 1.64/1.38 % (1424)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_1319 for (2999ds/3Mi)
% 1.64/1.38 % (1426)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_1319 for (2999ds/15Mi)
% 1.64/1.38 % (1424)Instruction limit reached!
% 1.64/1.38 % (1424)------------------------------
% 1.64/1.38 % (1424)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (1424)Termination reason: Unknown
% 1.64/1.38 % (1424)Termination phase: Preprocessing 3
% 1.64/1.38
% 1.64/1.38 % (1424)Memory used [KB]: 1023
% 1.64/1.38 % (1424)Time elapsed: 0.003 s
% 1.64/1.38 % (1424)Instructions burned: 3 (million)
% 1.64/1.38 % (1424)------------------------------
% 1.64/1.38 % (1424)------------------------------
% 1.64/1.38 % (1422)First to succeed.
% 1.64/1.38 % (1426)Instruction limit reached!
% 1.64/1.38 % (1426)------------------------------
% 1.64/1.38 % (1426)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.38 % (1426)Termination reason: Unknown
% 1.64/1.38 % (1426)Termination phase: Saturation
% 1.64/1.38
% 1.64/1.38 % (1426)Memory used [KB]: 5884
% 1.64/1.38 % (1426)Time elapsed: 0.010 s
% 1.64/1.38 % (1426)Instructions burned: 16 (million)
% 1.64/1.38 % (1426)------------------------------
% 1.64/1.38 % (1426)------------------------------
% 1.64/1.38 % (1427)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_1319 for (2999ds/3Mi)
% 1.64/1.38 % (1422)Refutation found. Thanks to Tanya!
% 1.64/1.38 % SZS status Theorem for DTF2THF_1319
% 1.64/1.38 % SZS output start Proof for DTF2THF_1319
% 1.64/1.38 thf(type_def_5, type, g: $tType).
% 1.64/1.38 thf(type_def_6, type, b: $tType).
% 1.64/1.38 thf(type_def_8, type, a: $tType).
% 1.64/1.38 thf(func_def_0, type, g: $tType).
% 1.64/1.38 thf(func_def_1, type, b: $tType).
% 1.64/1.38 thf(func_def_2, type, a: $tType).
% 1.64/1.38 thf(func_def_6, type, sP0: (g > g > g) > (a > a > a) > (b > a) > (g > b) > (g > $o) > $o).
% 1.64/1.38 thf(func_def_7, type, sP1: (g > $o) > (g > g > g) > $o).
% 1.64/1.38 thf(func_def_8, type, sK2: (g > $o) > (g > g > g) > g).
% 1.64/1.38 thf(func_def_9, type, sK3: (g > $o) > (g > g > g) > g).
% 1.64/1.38 thf(func_def_10, type, sK4: (g > g > g) > (a > a > a) > (b > a) > (g > b) > (g > $o) > g).
% 1.64/1.38 thf(func_def_11, type, sK5: (g > g > g) > (a > a > a) > (b > a) > (g > b) > (g > $o) > g).
% 1.64/1.38 thf(func_def_12, type, sK6: a > a > a).
% 1.64/1.38 thf(func_def_13, type, sK7: a > $o).
% 1.64/1.38 thf(func_def_14, type, sK8: b > $o).
% 1.64/1.38 thf(func_def_15, type, sK9: b > a).
% 1.64/1.38 thf(func_def_16, type, sK10: b > b > b).
% 1.64/1.38 thf(func_def_17, type, sK11: g > b).
% 1.64/1.38 thf(func_def_18, type, sK12: g > g > g).
% 1.64/1.39 thf(func_def_19, type, sK13: g > $o).
% 1.64/1.39 thf(func_def_20, type, sK14: a).
% 1.64/1.39 thf(func_def_21, type, sK15: a).
% 1.64/1.39 thf(func_def_22, type, sK16: g).
% 1.64/1.39 thf(func_def_24, type, ph18: !>[X0: $tType]:(X0)).
% 1.64/1.39 thf(f183,plain,(
% 1.64/1.39 $false),
% 1.64/1.39 inference(avatar_sat_refutation,[status(thm)],[f62,f67,f72,f77,f78,f79,f91,f96,f102,f127,f137,f148,f158,f163,f174,f178,f182])).
% 1.64/1.39 thf(f182,plain,(
% 1.64/1.39 ~spl17_4 | spl17_9),
% 1.64/1.39 inference(avatar_contradiction_clause,[status(thm)],[f181])).
% 1.64/1.39 thf(f181,plain,(
% 1.64/1.39 $false | (~spl17_4 | spl17_9)),
% 1.64/1.39 inference(subsumption_resolution,[status(thm)],[f180,f61])).
% 1.64/1.39 thf(f61,plain,(
% 1.64/1.39 ((sP1 @ sK13 @ sK12) = $true) | ~spl17_4),
% 1.64/1.39 inference(avatar_component_clause,[status(thm)],[f59])).
% 1.64/1.39 thf(f59,definition,(
% 1.64/1.39 spl17_4 <=> ((sP1 @ sK13 @ sK12) = $true)),
% 1.64/1.39 introduced(definition,[new_symbols(naming,[spl17_4])],[avatar_definition])).
% 1.64/1.39 thf(f180,plain,(
% 1.64/1.39 ((sP1 @ sK13 @ sK12) != $true) | spl17_9),
% 1.64/1.39 inference(trivial_inequality_removal,[status(thm)],[f179])).
% 1.64/1.39 thf(f179,plain,(
% 1.64/1.39 ((sP1 @ sK13 @ sK12) != $true) | ($true != $true) | spl17_9),
% 1.64/1.39 inference(superposition,[status(thm)],[f90,f24])).
% 1.64/1.39 thf(f24,plain,(
% 1.64/1.39 ( ! [X0 : g > g > g,X1 : g > $o] : (((X1 @ (sK3 @ X1 @ X0)) = $true) | ((sP1 @ X1 @ X0) != $true)) )),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f14])).
% 1.64/1.39 thf(f14,plain,(
% 1.64/1.39 ! [X0 : g > g > g,X1 : g > $o] : ((($true != (X1 @ (X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) & ($true = (X1 @ (sK2 @ X1 @ X0))) & ((X1 @ (sK3 @ X1 @ X0)) = $true)) | ((sP1 @ X1 @ X0) != $true))),
% 1.64/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f12,f13])).
% 1.64/1.39 thf(f13,plain,(
% 1.64/1.39 ! [X0 : g > g > g,X1 : g > $o] : (? [X2 : g,X3 : g] : (((X1 @ (X0 @ X2 @ X3)) != $true) & ((X1 @ X2) = $true) & ((X1 @ X3) = $true)) => (($true != (X1 @ (X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) & ($true = (X1 @ (sK2 @ X1 @ X0))) & ((X1 @ (sK3 @ X1 @ X0)) = $true)))),
% 1.64/1.39 introduced(definition,[],[choice_axiom])).
% 1.64/1.39 thf(f12,plain,(
% 1.64/1.39 ! [X0 : g > g > g,X1 : g > $o] : (? [X2 : g,X3 : g] : (((X1 @ (X0 @ X2 @ X3)) != $true) & ((X1 @ X2) = $true) & ((X1 @ X3) = $true)) | ((sP1 @ X1 @ X0) != $true))),
% 1.64/1.39 inference(rectify,[status(thm)],[f11])).
% 1.64/1.39 thf(f11,plain,(
% 1.64/1.39 ! [X4 : g > g > g,X6 : g > $o] : (? [X27 : g,X28 : g] : (((X6 @ (X4 @ X27 @ X28)) != $true) & ((X6 @ X27) = $true) & ((X6 @ X28) = $true)) | ($true != (sP1 @ X6 @ X4)))),
% 1.64/1.39 inference(nnf_transformation,[status(thm)],[f9])).
% 1.64/1.39 thf(f9,plain,(
% 1.64/1.39 ! [X4 : g > g > g,X6 : g > $o] : (? [X27 : g,X28 : g] : (((X6 @ (X4 @ X27 @ X28)) != $true) & ((X6 @ X27) = $true) & ((X6 @ X28) = $true)) | ~($true = (sP1 @ X6 @ X4)))),
% 1.64/1.39 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.64/1.39 thf(f90,plain,(
% 1.64/1.39 ((sK13 @ (sK3 @ sK13 @ sK12)) != $true) | spl17_9),
% 1.64/1.39 inference(avatar_component_clause,[status(thm)],[f88])).
% 1.64/1.39 thf(f88,definition,(
% 1.64/1.39 spl17_9 <=> ((sK13 @ (sK3 @ sK13 @ sK12)) = $true)),
% 1.64/1.39 introduced(definition,[new_symbols(naming,[spl17_9])],[avatar_definition])).
% 1.64/1.39 thf(f178,plain,(
% 1.64/1.39 spl17_11 | ~spl17_13),
% 1.64/1.39 inference(avatar_contradiction_clause,[status(thm)],[f177])).
% 1.64/1.39 thf(f177,plain,(
% 1.64/1.39 $false | (spl17_11 | ~spl17_13)),
% 1.64/1.39 inference(subsumption_resolution,[status(thm)],[f176,f142])).
% 1.64/1.39 thf(f142,plain,(
% 1.64/1.39 ((sK13 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) = $true) | ~spl17_13),
% 1.64/1.39 inference(avatar_component_clause,[status(thm)],[f141])).
% 1.64/1.39 thf(f141,definition,(
% 1.64/1.39 spl17_13 <=> ((sK13 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) = $true)),
% 1.64/1.39 introduced(definition,[new_symbols(naming,[spl17_13])],[avatar_definition])).
% 1.64/1.39 thf(f176,plain,(
% 1.64/1.39 ((sK13 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) != $true) | spl17_11),
% 1.64/1.39 inference(trivial_inequality_removal,[status(thm)],[f175])).
% 1.64/1.39 thf(f175,plain,(
% 1.64/1.39 ((sK13 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) != $true) | ($true != $true) | spl17_11),
% 1.64/1.39 inference(superposition,[status(thm)],[f122,f41])).
% 1.64/1.39 thf(f41,plain,(
% 1.64/1.39 ( ! [X16 : g] : (((sK8 @ (sK11 @ X16)) = $true) | ((sK13 @ X16) != $true)) )),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f23])).
% 1.64/1.39 thf(f23,plain,(
% 1.64/1.39 ! [X8 : a,X9 : a] : (($true = (sK7 @ (sK6 @ X9 @ X8))) | ($true != (sK7 @ X8)) | ((sK7 @ X9) != $true)) & ! [X10 : g,X11 : g] : (((sK11 @ (sK12 @ X11 @ X10)) = (sK10 @ (sK11 @ X11) @ (sK11 @ X10))) | ((sK13 @ X10) != $true) | ((sK13 @ X11) != $true)) & ! [X12 : b,X13 : b] : (((sK8 @ (sK10 @ X12 @ X13)) = $true) | ((sK8 @ X13) != $true) | ($true != (sK8 @ X12))) & ! [X14 : b,X15 : b] : (((sK8 @ (sK10 @ X15 @ X14)) = $true) | ((sK8 @ X15) != $true) | ($true != (sK8 @ X14))) & ! [X16 : g] : (((sK8 @ (sK11 @ X16)) = $true) | ((sK13 @ X16) != $true)) & ! [X17 : b] : (((sK7 @ (sK9 @ X17)) = $true) | ($true != (sK8 @ X17))) & ! [X18 : g,X19 : g] : (($true != (sK13 @ X18)) | ((sK13 @ X19) != $true) | ((sK13 @ (sK12 @ X18 @ X19)) = $true)) & ! [X20 : b,X21 : b] : (((sK9 @ (sK10 @ X21 @ X20)) = (sK6 @ (sK9 @ X21) @ (sK9 @ X20))) | ((sK8 @ X21) != $true) | ((sK8 @ X20) != $true)) & (($true = (sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) | (((sK7 @ sK14) = $true) & ((sK7 @ sK15) = $true) & ($true != (sK7 @ (sK6 @ sK14 @ sK15)))) | (((sK7 @ (sK9 @ (sK11 @ sK16))) != $true) & ($true = (sK13 @ sK16))) | ((sP1 @ sK13 @ sK12) = $true))),
% 1.64/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16])],[f19,f22,f21,f20])).
% 1.64/1.39 thf(f20,plain,(
% 1.64/1.39 ? [X0 : a > a > a,X1 : a > $o,X2 : b > $o,X3 : b > a,X4 : b > b > b,X5 : g > b,X6 : g > g > g,X7 : g > $o] : (! [X8 : a,X9 : a] : (((X1 @ (X0 @ X9 @ X8)) = $true) | ((X1 @ X8) != $true) | ((X1 @ X9) != $true)) & ! [X10 : g,X11 : g] : (((X5 @ (X6 @ X11 @ X10)) = (X4 @ (X5 @ X11) @ (X5 @ X10))) | ((X7 @ X10) != $true) | ((X7 @ X11) != $true)) & ! [X12 : b,X13 : b] : (($true = (X2 @ (X4 @ X12 @ X13))) | ((X2 @ X13) != $true) | ($true != (X2 @ X12))) & ! [X14 : b,X15 : b] : (($true = (X2 @ (X4 @ X15 @ X14))) | ((X2 @ X15) != $true) | ($true != (X2 @ X14))) & ! [X16 : g] : (((X2 @ (X5 @ X16)) = $true) | ((X7 @ X16) != $true)) & ! [X17 : b] : (((X1 @ (X3 @ X17)) = $true) | ((X2 @ X17) != $true)) & ! [X18 : g,X19 : g] : (((X7 @ X18) != $true) | ((X7 @ X19) != $true) | ((X7 @ (X6 @ X18 @ X19)) = $true)) & ! [X20 : b,X21 : b] : (((X0 @ (X3 @ X21) @ (X3 @ X20)) = (X3 @ (X4 @ X21 @ X20))) | ((X2 @ X21) != $true) | ((X2 @ X20) != $true)) & (((sP0 @ X6 @ X0 @ X3 @ X5 @ X7) = $true) | ? [X22 : a,X23 : a] : (((X1 @ X22) = $true) & ((X1 @ X23) = $true) & ((X1 @ (X0 @ X22 @ X23)) != $true)) | ? [X24 : g] : (((X1 @ (X3 @ (X5 @ X24))) != $true) & ((X7 @ X24) = $true)) | ((sP1 @ X7 @ X6) = $true))) => (! [X9 : a,X8 : a] : (($true = (sK7 @ (sK6 @ X9 @ X8))) | ($true != (sK7 @ X8)) | ((sK7 @ X9) != $true)) & ! [X11 : g,X10 : g] : (((sK11 @ (sK12 @ X11 @ X10)) = (sK10 @ (sK11 @ X11) @ (sK11 @ X10))) | ((sK13 @ X10) != $true) | ((sK13 @ X11) != $true)) & ! [X13 : b,X12 : b] : (((sK8 @ (sK10 @ X12 @ X13)) = $true) | ((sK8 @ X13) != $true) | ($true != (sK8 @ X12))) & ! [X15 : b,X14 : b] : (((sK8 @ (sK10 @ X15 @ X14)) = $true) | ((sK8 @ X15) != $true) | ($true != (sK8 @ X14))) & ! [X16 : g] : (((sK8 @ (sK11 @ X16)) = $true) | ((sK13 @ X16) != $true)) & ! [X17 : b] : (((sK7 @ (sK9 @ X17)) = $true) | ($true != (sK8 @ X17))) & ! [X19 : g,X18 : g] : (($true != (sK13 @ X18)) | ((sK13 @ X19) != $true) | ((sK13 @ (sK12 @ X18 @ X19)) = $true)) & ! [X21 : b,X20 : b] : (((sK9 @ (sK10 @ X21 @ X20)) = (sK6 @ (sK9 @ X21) @ (sK9 @ X20))) | ((sK8 @ X21) != $true) | ((sK8 @ X20) != $true)) & (($true = (sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) | ? [X23 : a,X22 : a] : (((sK7 @ X22) = $true) & ($true = (sK7 @ X23)) & ($true != (sK7 @ (sK6 @ X22 @ X23)))) | ? [X24 : g] : (((sK7 @ (sK9 @ (sK11 @ X24))) != $true) & ((sK13 @ X24) = $true)) | ((sP1 @ sK13 @ sK12) = $true)))),
% 1.64/1.39 introduced(definition,[],[choice_axiom])).
% 1.64/1.39 thf(f21,plain,(
% 1.64/1.39 ? [X23 : a,X22 : a] : (((sK7 @ X22) = $true) & ($true = (sK7 @ X23)) & ($true != (sK7 @ (sK6 @ X22 @ X23)))) => (((sK7 @ sK14) = $true) & ((sK7 @ sK15) = $true) & ($true != (sK7 @ (sK6 @ sK14 @ sK15))))),
% 1.64/1.39 introduced(definition,[],[choice_axiom])).
% 1.64/1.39 thf(f22,plain,(
% 1.64/1.39 ? [X24 : g] : (((sK7 @ (sK9 @ (sK11 @ X24))) != $true) & ((sK13 @ X24) = $true)) => (((sK7 @ (sK9 @ (sK11 @ sK16))) != $true) & ($true = (sK13 @ sK16)))),
% 1.64/1.39 introduced(definition,[],[choice_axiom])).
% 1.64/1.39 thf(f19,plain,(
% 1.64/1.39 ? [X0 : a > a > a,X1 : a > $o,X2 : b > $o,X3 : b > a,X4 : b > b > b,X5 : g > b,X6 : g > g > g,X7 : g > $o] : (! [X8 : a,X9 : a] : (((X1 @ (X0 @ X9 @ X8)) = $true) | ((X1 @ X8) != $true) | ((X1 @ X9) != $true)) & ! [X10 : g,X11 : g] : (((X5 @ (X6 @ X11 @ X10)) = (X4 @ (X5 @ X11) @ (X5 @ X10))) | ((X7 @ X10) != $true) | ((X7 @ X11) != $true)) & ! [X12 : b,X13 : b] : (($true = (X2 @ (X4 @ X12 @ X13))) | ((X2 @ X13) != $true) | ($true != (X2 @ X12))) & ! [X14 : b,X15 : b] : (($true = (X2 @ (X4 @ X15 @ X14))) | ((X2 @ X15) != $true) | ($true != (X2 @ X14))) & ! [X16 : g] : (((X2 @ (X5 @ X16)) = $true) | ((X7 @ X16) != $true)) & ! [X17 : b] : (((X1 @ (X3 @ X17)) = $true) | ((X2 @ X17) != $true)) & ! [X18 : g,X19 : g] : (((X7 @ X18) != $true) | ((X7 @ X19) != $true) | ((X7 @ (X6 @ X18 @ X19)) = $true)) & ! [X20 : b,X21 : b] : (((X0 @ (X3 @ X21) @ (X3 @ X20)) = (X3 @ (X4 @ X21 @ X20))) | ((X2 @ X21) != $true) | ((X2 @ X20) != $true)) & (((sP0 @ X6 @ X0 @ X3 @ X5 @ X7) = $true) | ? [X22 : a,X23 : a] : (((X1 @ X22) = $true) & ((X1 @ X23) = $true) & ((X1 @ (X0 @ X22 @ X23)) != $true)) | ? [X24 : g] : (((X1 @ (X3 @ (X5 @ X24))) != $true) & ((X7 @ X24) = $true)) | ((sP1 @ X7 @ X6) = $true)))),
% 1.64/1.39 inference(rectify,[status(thm)],[f10])).
% 1.64/1.39 thf(f10,plain,(
% 1.64/1.39 ? [X5 : a > a > a,X0 : a > $o,X1 : b > $o,X2 : b > a,X3 : b > b > b,X7 : g > b,X4 : g > g > g,X6 : g > $o] : (! [X18 : a,X19 : a] : (((X0 @ (X5 @ X19 @ X18)) = $true) | ((X0 @ X18) != $true) | ((X0 @ X19) != $true)) & ! [X10 : g,X9 : g] : (((X3 @ (X7 @ X9) @ (X7 @ X10)) = (X7 @ (X4 @ X9 @ X10))) | ($true != (X6 @ X10)) | ((X6 @ X9) != $true)) & ! [X15 : b,X16 : b] : (((X1 @ (X3 @ X15 @ X16)) = $true) | ((X1 @ X16) != $true) | ($true != (X1 @ X15))) & ! [X21 : b,X20 : b] : (((X1 @ (X3 @ X20 @ X21)) = $true) | ($true != (X1 @ X20)) | ((X1 @ X21) != $true)) & ! [X8 : g] : (((X1 @ (X7 @ X8)) = $true) | ((X6 @ X8) != $true)) & ! [X17 : b] : (((X0 @ (X2 @ X17)) = $true) | ((X1 @ X17) != $true)) & ! [X12 : g,X11 : g] : (((X6 @ X12) != $true) | ((X6 @ X11) != $true) | ((X6 @ (X4 @ X12 @ X11)) = $true)) & ! [X13 : b,X14 : b] : (((X2 @ (X3 @ X14 @ X13)) = (X5 @ (X2 @ X14) @ (X2 @ X13))) | ($true != (X1 @ X14)) | ($true != (X1 @ X13))) & (((sP0 @ X4 @ X5 @ X2 @ X7 @ X6) = $true) | ? [X25 : a,X26 : a] : (((X0 @ X25) = $true) & ((X0 @ X26) = $true) & ((X0 @ (X5 @ X25 @ X26)) != $true)) | ? [X24 : g] : (((X0 @ (X2 @ (X7 @ X24))) != $true) & ((X6 @ X24) = $true)) | ($true = (sP1 @ X6 @ X4))))),
% 1.64/1.39 inference(definition_folding,[status(thm)],[f7,f9,f8])).
% 1.64/1.39 thf(f8,plain,(
% 1.64/1.39 ! [X6 : g > $o,X7 : g > b,X2 : b > a,X5 : a > a > a,X4 : g > g > g] : (? [X22 : g,X23 : g] : (((X6 @ X23) = $true) & ((X2 @ (X7 @ (X4 @ X23 @ X22))) != (X5 @ (X2 @ (X7 @ X23)) @ (X2 @ (X7 @ X22)))) & ((X6 @ X22) = $true) & ((X6 @ X23) = $true) & ((X6 @ X22) = $true)) | ~((sP0 @ X4 @ X5 @ X2 @ X7 @ X6) = $true))),
% 1.64/1.39 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.64/1.39 thf(f7,plain,(
% 1.64/1.39 ? [X5 : a > a > a,X0 : a > $o,X1 : b > $o,X2 : b > a,X3 : b > b > b,X7 : g > b,X4 : g > g > g,X6 : g > $o] : (! [X18 : a,X19 : a] : (((X0 @ (X5 @ X19 @ X18)) = $true) | ((X0 @ X18) != $true) | ((X0 @ X19) != $true)) & ! [X10 : g,X9 : g] : (((X3 @ (X7 @ X9) @ (X7 @ X10)) = (X7 @ (X4 @ X9 @ X10))) | ($true != (X6 @ X10)) | ((X6 @ X9) != $true)) & ! [X15 : b,X16 : b] : (((X1 @ (X3 @ X15 @ X16)) = $true) | ((X1 @ X16) != $true) | ($true != (X1 @ X15))) & ! [X21 : b,X20 : b] : (((X1 @ (X3 @ X20 @ X21)) = $true) | ($true != (X1 @ X20)) | ((X1 @ X21) != $true)) & ! [X8 : g] : (((X1 @ (X7 @ X8)) = $true) | ((X6 @ X8) != $true)) & ! [X17 : b] : (((X0 @ (X2 @ X17)) = $true) | ((X1 @ X17) != $true)) & ! [X12 : g,X11 : g] : (((X6 @ X12) != $true) | ((X6 @ X11) != $true) | ((X6 @ (X4 @ X12 @ X11)) = $true)) & ! [X13 : b,X14 : b] : (((X2 @ (X3 @ X14 @ X13)) = (X5 @ (X2 @ X14) @ (X2 @ X13))) | ($true != (X1 @ X14)) | ($true != (X1 @ X13))) & (? [X22 : g,X23 : g] : (((X6 @ X23) = $true) & ((X2 @ (X7 @ (X4 @ X23 @ X22))) != (X5 @ (X2 @ (X7 @ X23)) @ (X2 @ (X7 @ X22)))) & ((X6 @ X22) = $true) & ((X6 @ X23) = $true) & ((X6 @ X22) = $true)) | ? [X25 : a,X26 : a] : (((X0 @ X25) = $true) & ((X0 @ X26) = $true) & ((X0 @ (X5 @ X25 @ X26)) != $true)) | ? [X24 : g] : (((X0 @ (X2 @ (X7 @ X24))) != $true) & ((X6 @ X24) = $true)) | ? [X27 : g,X28 : g] : (((X6 @ (X4 @ X27 @ X28)) != $true) & ((X6 @ X27) = $true) & ((X6 @ X28) = $true))))),
% 1.64/1.39 inference(flattening,[status(thm)],[f6])).
% 1.64/1.39 thf(f6,plain,(
% 1.64/1.39 ? [X0 : a > $o,X1 : b > $o,X7 : g > b,X4 : g > g > g,X6 : g > $o,X5 : a > a > a,X3 : b > b > b,X2 : b > a] : ((? [X28 : g,X27 : g] : (((X6 @ (X4 @ X27 @ X28)) != $true) & (((X6 @ X27) = $true) & ((X6 @ X28) = $true))) | ? [X24 : g] : (((X0 @ (X2 @ (X7 @ X24))) != $true) & ((X6 @ X24) = $true)) | ? [X25 : a,X26 : a] : (((X0 @ (X5 @ X25 @ X26)) != $true) & (((X0 @ X26) = $true) & ((X0 @ X25) = $true))) | ? [X23 : g,X22 : g] : (((X2 @ (X7 @ (X4 @ X23 @ X22))) != (X5 @ (X2 @ (X7 @ X23)) @ (X2 @ (X7 @ X22)))) & (((X6 @ X22) = $true) & ((X6 @ X22) = $true) & ((X6 @ X23) = $true) & ((X6 @ X23) = $true)))) & (! [X8 : g] : (((X1 @ (X7 @ X8)) = $true) | ((X6 @ X8) != $true)) & ! [X9 : g,X10 : g] : (((X3 @ (X7 @ X9) @ (X7 @ X10)) = (X7 @ (X4 @ X9 @ X10))) | (((X6 @ X9) != $true) | ($true != (X6 @ X10)))) & ! [X15 : b,X16 : b] : (((X1 @ (X3 @ X15 @ X16)) = $true) | (((X1 @ X16) != $true) | ($true != (X1 @ X15)))) & ! [X20 : b,X21 : b] : (((X1 @ (X3 @ X20 @ X21)) = $true) | (((X1 @ X21) != $true) | ($true != (X1 @ X20)))) & ! [X12 : g,X11 : g] : (((X6 @ (X4 @ X12 @ X11)) = $true) | (((X6 @ X11) != $true) | ((X6 @ X12) != $true))) & ! [X13 : b,X14 : b] : (((X2 @ (X3 @ X14 @ X13)) = (X5 @ (X2 @ X14) @ (X2 @ X13))) | (($true != (X1 @ X13)) | ($true != (X1 @ X14)))) & ! [X19 : a,X18 : a] : (((X0 @ (X5 @ X19 @ X18)) = $true) | (((X0 @ X18) != $true) | ((X0 @ X19) != $true))) & ! [X17 : b] : (((X0 @ (X2 @ X17)) = $true) | ((X1 @ X17) != $true))))),
% 1.64/1.39 inference(ennf_transformation,[status(thm)],[f5])).
% 1.64/1.39 thf(f5,plain,(
% 1.64/1.39 ~! [X0 : a > $o,X1 : b > $o,X7 : g > b,X4 : g > g > g,X6 : g > $o,X5 : a > a > a,X3 : b > b > b,X2 : b > a] : ((! [X8 : g] : (((X6 @ X8) = $true) => ((X1 @ (X7 @ X8)) = $true)) & ! [X9 : g,X10 : g] : ((((X6 @ X9) = $true) & ($true = (X6 @ X10))) => ((X3 @ (X7 @ X9) @ (X7 @ X10)) = (X7 @ (X4 @ X9 @ X10)))) & ! [X15 : b,X16 : b] : ((((X1 @ X16) = $true) & ($true = (X1 @ X15))) => ((X1 @ (X3 @ X15 @ X16)) = $true)) & ! [X20 : b,X21 : b] : ((((X1 @ X21) = $true) & ($true = (X1 @ X20))) => ((X1 @ (X3 @ X20 @ X21)) = $true)) & ! [X12 : g,X11 : g] : ((((X6 @ X11) = $true) & ((X6 @ X12) = $true)) => ((X6 @ (X4 @ X12 @ X11)) = $true)) & ! [X13 : b,X14 : b] : ((($true = (X1 @ X13)) & ($true = (X1 @ X14))) => ((X2 @ (X3 @ X14 @ X13)) = (X5 @ (X2 @ X14) @ (X2 @ X13)))) & ! [X19 : a,X18 : a] : ((((X0 @ X18) = $true) & ((X0 @ X19) = $true)) => ((X0 @ (X5 @ X19 @ X18)) = $true)) & ! [X17 : b] : (((X1 @ X17) = $true) => ((X0 @ (X2 @ X17)) = $true))) => (! [X28 : g,X27 : g] : ((((X6 @ X27) = $true) & ((X6 @ X28) = $true)) => ((X6 @ (X4 @ X27 @ X28)) = $true)) & ! [X24 : g] : (((X6 @ X24) = $true) => ((X0 @ (X2 @ (X7 @ X24))) = $true)) & ! [X25 : a,X26 : a] : ((((X0 @ X26) = $true) & ((X0 @ X25) = $true)) => ((X0 @ (X5 @ X25 @ X26)) = $true)) & ! [X23 : g,X22 : g] : ((((X6 @ X22) = $true) & ((X6 @ X22) = $true) & ((X6 @ X23) = $true) & ((X6 @ X23) = $true)) => ((X2 @ (X7 @ (X4 @ X23 @ X22))) = (X5 @ (X2 @ (X7 @ X23)) @ (X2 @ (X7 @ X22)))))))),
% 1.64/1.39 inference(fool_elimination,[status(thm)],[f4])).
% 1.64/1.39 thf(f4,plain,(
% 1.64/1.39 ~! [X0 : a > $o,X1 : b > $o,X2 : b > a,X3 : b > b > b,X4 : g > g > g,X5 : a > a > a,X6 : g > $o,X7 : g > b] : ((! [X8 : g] : ((X6 @ X8) => (X1 @ (X7 @ X8))) & ! [X9 : g,X10 : g] : (((X6 @ X10) & (X6 @ X9)) => ((X3 @ (X7 @ X9) @ (X7 @ X10)) = (X7 @ (X4 @ X9 @ X10)))) & ! [X11 : g,X12 : g] : (((X6 @ X12) & (X6 @ X11)) => (X6 @ (X4 @ X12 @ X11))) & ! [X13 : b,X14 : b] : (((X1 @ X14) & (X1 @ X13)) => ((X2 @ (X3 @ X14 @ X13)) = (X5 @ (X2 @ X14) @ (X2 @ X13)))) & ! [X15 : b,X16 : b] : (((X1 @ X16) & (X1 @ X15)) => (X1 @ (X3 @ X15 @ X16))) & ! [X17 : b] : ((X1 @ X17) => (X0 @ (X2 @ X17))) & ! [X18 : a,X19 : a] : (((X0 @ X19) & (X0 @ X18)) => (X0 @ (X5 @ X19 @ X18))) & ! [X20 : b,X21 : b] : (((X1 @ X20) & (X1 @ X21)) => (X1 @ (X3 @ X20 @ X21)))) => (! [X22 : g,X23 : g] : (((X6 @ X23) & (X6 @ X22) & (X6 @ X23) & (X6 @ X22)) => ((X2 @ (X7 @ (X4 @ X23 @ X22))) = (X5 @ (X2 @ (X7 @ X23)) @ (X2 @ (X7 @ X22))))) & ! [X24 : g] : ((X6 @ X24) => (X0 @ (X2 @ (X7 @ X24)))) & ! [X25 : a,X26 : a] : (((X0 @ X25) & (X0 @ X26)) => (X0 @ (X5 @ X25 @ X26))) & ! [X27 : g,X28 : g] : (((X6 @ X27) & (X6 @ X28)) => (X6 @ (X4 @ X27 @ X28)))))),
% 1.64/1.39 inference(rectify,[status(thm)],[f2])).
% 1.64/1.39 thf(f2,negated_conjecture,(
% 1.64/1.39 ~! [X6 : a > $o,X4 : b > $o,X1 : b > a,X5 : b > b > b,X3 : g > g > g,X7 : a > a > a,X2 : g > $o,X0 : g > b] : ((! [X8 : g] : ((X2 @ X8) => (X4 @ (X0 @ X8))) & ! [X8 : g,X9 : g] : (((X2 @ X9) & (X2 @ X8)) => ((X0 @ (X3 @ X8 @ X9)) = (X5 @ (X0 @ X8) @ (X0 @ X9)))) & ! [X9 : g,X8 : g] : (((X2 @ X8) & (X2 @ X9)) => (X2 @ (X3 @ X8 @ X9))) & ! [X9 : b,X8 : b] : (((X4 @ X8) & (X4 @ X9)) => ((X1 @ (X5 @ X8 @ X9)) = (X7 @ (X1 @ X8) @ (X1 @ X9)))) & ! [X8 : b,X9 : b] : (((X4 @ X9) & (X4 @ X8)) => (X4 @ (X5 @ X8 @ X9))) & ! [X8 : b] : ((X4 @ X8) => (X6 @ (X1 @ X8))) & ! [X9 : a,X8 : a] : (((X6 @ X8) & (X6 @ X9)) => (X6 @ (X7 @ X8 @ X9))) & ! [X8 : b,X9 : b] : (((X4 @ X8) & (X4 @ X9)) => (X4 @ (X5 @ X8 @ X9)))) => (! [X9 : g,X8 : g] : (((X2 @ X8) & (X2 @ X9) & (X2 @ X8) & (X2 @ X9)) => ((X1 @ (X0 @ (X3 @ X8 @ X9))) = (X7 @ (X1 @ (X0 @ X8)) @ (X1 @ (X0 @ X9))))) & ! [X8 : g] : ((X2 @ X8) => (X6 @ (X1 @ (X0 @ X8)))) & ! [X8 : a,X9 : a] : (((X6 @ X8) & (X6 @ X9)) => (X6 @ (X7 @ X8 @ X9))) & ! [X8 : g,X9 : g] : (((X2 @ X8) & (X2 @ X9)) => (X2 @ (X3 @ X8 @ X9)))))),
% 1.64/1.39 inference(negated_conjecture,[status(cth)],[f1])).
% 1.64/1.39 thf(f1,conjecture,(
% 1.64/1.39 ! [X6 : a > $o,X4 : b > $o,X1 : b > a,X5 : b > b > b,X3 : g > g > g,X7 : a > a > a,X2 : g > $o,X0 : g > b] : ((! [X8 : g] : ((X2 @ X8) => (X4 @ (X0 @ X8))) & ! [X8 : g,X9 : g] : (((X2 @ X9) & (X2 @ X8)) => ((X0 @ (X3 @ X8 @ X9)) = (X5 @ (X0 @ X8) @ (X0 @ X9)))) & ! [X9 : g,X8 : g] : (((X2 @ X8) & (X2 @ X9)) => (X2 @ (X3 @ X8 @ X9))) & ! [X9 : b,X8 : b] : (((X4 @ X8) & (X4 @ X9)) => ((X1 @ (X5 @ X8 @ X9)) = (X7 @ (X1 @ X8) @ (X1 @ X9)))) & ! [X8 : b,X9 : b] : (((X4 @ X9) & (X4 @ X8)) => (X4 @ (X5 @ X8 @ X9))) & ! [X8 : b] : ((X4 @ X8) => (X6 @ (X1 @ X8))) & ! [X9 : a,X8 : a] : (((X6 @ X8) & (X6 @ X9)) => (X6 @ (X7 @ X8 @ X9))) & ! [X8 : b,X9 : b] : (((X4 @ X8) & (X4 @ X9)) => (X4 @ (X5 @ X8 @ X9)))) => (! [X9 : g,X8 : g] : (((X2 @ X8) & (X2 @ X9) & (X2 @ X8) & (X2 @ X9)) => ((X1 @ (X0 @ (X3 @ X8 @ X9))) = (X7 @ (X1 @ (X0 @ X8)) @ (X1 @ (X0 @ X9))))) & ! [X8 : g] : ((X2 @ X8) => (X6 @ (X1 @ (X0 @ X8)))) & ! [X8 : a,X9 : a] : (((X6 @ X8) & (X6 @ X9)) => (X6 @ (X7 @ X8 @ X9))) & ! [X8 : g,X9 : g] : (((X2 @ X8) & (X2 @ X9)) => (X2 @ (X3 @ X8 @ X9)))))),
% 1.64/1.39 file('/export/starexec/sandbox2/tmp/tmp.XTkA7cJxnS/DTF2THF_1319.p',cTHM126_EXPANDED_pme)).
% 1.64/1.39 thf(f122,plain,(
% 1.64/1.39 ((sK8 @ (sK11 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13))) != $true) | spl17_11),
% 1.64/1.39 inference(avatar_component_clause,[status(thm)],[f120])).
% 1.64/1.39 thf(f120,definition,(
% 1.64/1.39 spl17_11 <=> ((sK8 @ (sK11 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13))) = $true)),
% 1.64/1.39 introduced(definition,[new_symbols(naming,[spl17_11])],[avatar_definition])).
% 1.64/1.39 thf(f174,plain,(
% 1.64/1.39 ~spl17_1 | spl17_14),
% 1.64/1.39 inference(avatar_contradiction_clause,[status(thm)],[f173])).
% 1.64/1.39 thf(f173,plain,(
% 1.64/1.39 $false | (~spl17_1 | spl17_14)),
% 1.64/1.39 inference(subsumption_resolution,[status(thm)],[f169,f49])).
% 1.64/1.39 thf(f49,plain,(
% 1.64/1.39 ($true = (sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) | ~spl17_1),
% 1.64/1.39 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.64/1.39 thf(f47,definition,(
% 1.64/1.39 spl17_1 <=> ($true = (sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13))),
% 1.64/1.39 introduced(definition,[new_symbols(naming,[spl17_1])],[avatar_definition])).
% 1.64/1.39 thf(f169,plain,(
% 1.64/1.39 ($true != (sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) | spl17_14),
% 1.64/1.39 inference(trivial_inequality_removal,[status(thm)],[f168])).
% 1.64/1.39 thf(f168,plain,(
% 1.64/1.39 ($true != (sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) | ($true != $true) | spl17_14),
% 1.64/1.39 inference(superposition,[status(thm)],[f147,f27])).
% 1.64/1.39 thf(f27,plain,(
% 1.64/1.39 ( ! [X2 : b > a,X3 : a > a > a,X0 : g > $o,X1 : g > b,X4 : g > g > g] : (($true = (X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) | ((sP0 @ X4 @ X3 @ X2 @ X1 @ X0) != $true)) )),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f18])).
% 1.64/1.39 thf(f18,plain,(
% 1.64/1.39 ! [X0 : g > $o,X1 : g > b,X2 : b > a,X3 : a > a > a,X4 : g > g > g] : ((((X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true) & ((X3 @ (X2 @ (X1 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0))) @ (X2 @ (X1 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0)))) != (X2 @ (X1 @ (X4 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0) @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))))) & ($true = (X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) & ((X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true) & ($true = (X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0)))) | ((sP0 @ X4 @ X3 @ X2 @ X1 @ X0) != $true))),
% 1.64/1.39 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f16,f17])).
% 1.64/1.39 thf(f17,plain,(
% 1.64/1.39 ! [X0 : g > $o,X1 : g > b,X2 : b > a,X3 : a > a > a,X4 : g > g > g] : (? [X5 : g,X6 : g] : (((X0 @ X6) = $true) & ((X2 @ (X1 @ (X4 @ X6 @ X5))) != (X3 @ (X2 @ (X1 @ X6)) @ (X2 @ (X1 @ X5)))) & ((X0 @ X5) = $true) & ((X0 @ X6) = $true) & ((X0 @ X5) = $true)) => (((X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true) & ((X3 @ (X2 @ (X1 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0))) @ (X2 @ (X1 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0)))) != (X2 @ (X1 @ (X4 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0) @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))))) & ($true = (X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) & ((X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true) & ($true = (X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0)))))),
% 1.64/1.39 introduced(definition,[],[choice_axiom])).
% 1.64/1.39 thf(f16,plain,(
% 1.64/1.39 ! [X0 : g > $o,X1 : g > b,X2 : b > a,X3 : a > a > a,X4 : g > g > g] : (? [X5 : g,X6 : g] : (((X0 @ X6) = $true) & ((X2 @ (X1 @ (X4 @ X6 @ X5))) != (X3 @ (X2 @ (X1 @ X6)) @ (X2 @ (X1 @ X5)))) & ((X0 @ X5) = $true) & ((X0 @ X6) = $true) & ((X0 @ X5) = $true)) | ((sP0 @ X4 @ X3 @ X2 @ X1 @ X0) != $true))),
% 1.64/1.39 inference(rectify,[status(thm)],[f15])).
% 1.64/1.39 thf(f15,plain,(
% 1.64/1.39 ! [X6 : g > $o,X7 : g > b,X2 : b > a,X5 : a > a > a,X4 : g > g > g] : (? [X22 : g,X23 : g] : (((X6 @ X23) = $true) & ((X2 @ (X7 @ (X4 @ X23 @ X22))) != (X5 @ (X2 @ (X7 @ X23)) @ (X2 @ (X7 @ X22)))) & ((X6 @ X22) = $true) & ((X6 @ X23) = $true) & ((X6 @ X22) = $true)) | ((sP0 @ X4 @ X5 @ X2 @ X7 @ X6) != $true))),
% 1.64/1.39 inference(nnf_transformation,[status(thm)],[f8])).
% 1.64/1.39 thf(f147,plain,(
% 1.64/1.39 ((sK13 @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) != $true) | spl17_14),
% 1.64/1.39 inference(avatar_component_clause,[status(thm)],[f145])).
% 1.64/1.39 thf(f145,definition,(
% 1.64/1.39 spl17_14 <=> ((sK13 @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) = $true)),
% 1.64/1.39 introduced(definition,[new_symbols(naming,[spl17_14])],[avatar_definition])).
% 1.64/1.39 thf(f163,plain,(
% 1.64/1.39 ~spl17_3 | ~spl17_5 | spl17_7),
% 1.64/1.39 inference(avatar_contradiction_clause,[status(thm)],[f162])).
% 1.64/1.39 thf(f162,plain,(
% 1.64/1.39 $false | (~spl17_3 | ~spl17_5 | spl17_7)),
% 1.64/1.39 inference(subsumption_resolution,[status(thm)],[f161,f57])).
% 1.64/1.39 thf(f57,plain,(
% 1.64/1.39 ((sK7 @ sK15) = $true) | ~spl17_3),
% 1.64/1.39 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.64/1.39 thf(f55,definition,(
% 1.64/1.39 spl17_3 <=> ((sK7 @ sK15) = $true)),
% 1.64/1.39 introduced(definition,[new_symbols(naming,[spl17_3])],[avatar_definition])).
% 1.64/1.39 thf(f161,plain,(
% 1.64/1.39 ((sK7 @ sK15) != $true) | (~spl17_5 | spl17_7)),
% 1.64/1.39 inference(subsumption_resolution,[status(thm)],[f160,f66])).
% 1.64/1.39 thf(f66,plain,(
% 1.64/1.39 ((sK7 @ sK14) = $true) | ~spl17_5),
% 1.64/1.39 inference(avatar_component_clause,[status(thm)],[f64])).
% 1.64/1.39 thf(f64,definition,(
% 1.64/1.39 spl17_5 <=> ((sK7 @ sK14) = $true)),
% 1.64/1.39 introduced(definition,[new_symbols(naming,[spl17_5])],[avatar_definition])).
% 1.64/1.39 thf(f160,plain,(
% 1.64/1.39 ((sK7 @ sK14) != $true) | ((sK7 @ sK15) != $true) | spl17_7),
% 1.64/1.39 inference(trivial_inequality_removal,[status(thm)],[f159])).
% 1.64/1.39 thf(f159,plain,(
% 1.64/1.39 ((sK7 @ sK14) != $true) | ((sK7 @ sK15) != $true) | ($true != $true) | spl17_7),
% 1.64/1.39 inference(superposition,[status(thm)],[f76,f45])).
% 1.64/1.39 thf(f45,plain,(
% 1.64/1.39 ( ! [X8 : a,X9 : a] : (($true = (sK7 @ (sK6 @ X9 @ X8))) | ((sK7 @ X9) != $true) | ($true != (sK7 @ X8))) )),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f23])).
% 1.64/1.39 thf(f76,plain,(
% 1.64/1.39 ($true != (sK7 @ (sK6 @ sK14 @ sK15))) | spl17_7),
% 1.64/1.39 inference(avatar_component_clause,[status(thm)],[f74])).
% 1.64/1.39 thf(f74,definition,(
% 1.64/1.39 spl17_7 <=> ($true = (sK7 @ (sK6 @ sK14 @ sK15)))),
% 1.64/1.39 introduced(definition,[new_symbols(naming,[spl17_7])],[avatar_definition])).
% 1.64/1.39 thf(f158,plain,(
% 1.64/1.39 ~spl17_1 | spl17_13),
% 1.64/1.39 inference(avatar_split_clause,[status(thm)],[f151,f141,f47])).
% 1.64/1.39 thf(f151,plain,(
% 1.64/1.39 ($true != (sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) | spl17_13),
% 1.64/1.39 inference(trivial_inequality_removal,[status(thm)],[f150])).
% 1.64/1.39 thf(f150,plain,(
% 1.64/1.39 ($true != (sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) | ($true != $true) | spl17_13),
% 1.64/1.39 inference(superposition,[status(thm)],[f143,f31])).
% 1.64/1.39 thf(f31,plain,(
% 1.64/1.39 ( ! [X2 : b > a,X3 : a > a > a,X0 : g > $o,X1 : g > b,X4 : g > g > g] : (((X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true) | ((sP0 @ X4 @ X3 @ X2 @ X1 @ X0) != $true)) )),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f18])).
% 1.64/1.39 thf(f143,plain,(
% 1.64/1.39 ((sK13 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) != $true) | spl17_13),
% 1.64/1.39 inference(avatar_component_clause,[status(thm)],[f141])).
% 1.64/1.39 thf(f148,plain,(
% 1.64/1.39 ~spl17_13 | ~spl17_14 | spl17_12),
% 1.64/1.39 inference(avatar_split_clause,[status(thm)],[f139,f124,f145,f141])).
% 1.64/1.39 thf(f124,definition,(
% 1.64/1.39 spl17_12 <=> ((sK9 @ (sK11 @ (sK12 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13) @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)))) = (sK9 @ (sK10 @ (sK11 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) @ (sK11 @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)))))),
% 1.64/1.39 introduced(definition,[new_symbols(naming,[spl17_12])],[avatar_definition])).
% 1.64/1.39 thf(f139,plain,(
% 1.64/1.39 ((sK13 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) != $true) | ((sK13 @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) != $true) | spl17_12),
% 1.64/1.39 inference(trivial_inequality_removal,[status(thm)],[f138])).
% 1.64/1.39 thf(f138,plain,(
% 1.64/1.39 ((sK13 @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) != $true) | ((sK9 @ (sK11 @ (sK12 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13) @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)))) != (sK9 @ (sK11 @ (sK12 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13) @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13))))) | ((sK13 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) != $true) | spl17_12),
% 1.64/1.39 inference(superposition,[status(thm)],[f126,f44])).
% 1.64/1.39 thf(f44,plain,(
% 1.64/1.39 ( ! [X10 : g,X11 : g] : (((sK11 @ (sK12 @ X11 @ X10)) = (sK10 @ (sK11 @ X11) @ (sK11 @ X10))) | ((sK13 @ X10) != $true) | ((sK13 @ X11) != $true)) )),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f23])).
% 1.64/1.39 thf(f126,plain,(
% 1.64/1.39 ((sK9 @ (sK11 @ (sK12 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13) @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)))) != (sK9 @ (sK10 @ (sK11 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) @ (sK11 @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13))))) | spl17_12),
% 1.64/1.39 inference(avatar_component_clause,[status(thm)],[f124])).
% 1.64/1.39 thf(f137,plain,(
% 1.64/1.39 ~spl17_1 | spl17_10),
% 1.64/1.39 inference(avatar_contradiction_clause,[status(thm)],[f136])).
% 1.64/1.39 thf(f136,plain,(
% 1.64/1.39 $false | (~spl17_1 | spl17_10)),
% 1.64/1.39 inference(subsumption_resolution,[status(thm)],[f132,f49])).
% 1.64/1.39 thf(f132,plain,(
% 1.64/1.39 ($true != (sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) | spl17_10),
% 1.64/1.39 inference(trivial_inequality_removal,[status(thm)],[f131])).
% 1.64/1.39 thf(f131,plain,(
% 1.64/1.39 ($true != $true) | ($true != (sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) | spl17_10),
% 1.64/1.39 inference(superposition,[status(thm)],[f129,f27])).
% 1.64/1.39 thf(f129,plain,(
% 1.64/1.39 ((sK13 @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) != $true) | spl17_10),
% 1.64/1.39 inference(trivial_inequality_removal,[status(thm)],[f128])).
% 1.64/1.39 thf(f128,plain,(
% 1.64/1.39 ($true != $true) | ((sK13 @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) != $true) | spl17_10),
% 1.64/1.39 inference(superposition,[status(thm)],[f118,f41])).
% 1.64/1.39 thf(f118,plain,(
% 1.64/1.39 ((sK8 @ (sK11 @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13))) != $true) | spl17_10),
% 1.64/1.39 inference(avatar_component_clause,[status(thm)],[f116])).
% 1.64/1.39 thf(f116,definition,(
% 1.64/1.39 spl17_10 <=> ((sK8 @ (sK11 @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13))) = $true)),
% 1.64/1.39 introduced(definition,[new_symbols(naming,[spl17_10])],[avatar_definition])).
% 1.64/1.39 thf(f127,plain,(
% 1.64/1.39 ~spl17_10 | ~spl17_11 | ~spl17_12 | ~spl17_1),
% 1.64/1.39 inference(avatar_split_clause,[status(thm)],[f114,f47,f124,f120,f116])).
% 1.64/1.39 thf(f114,plain,(
% 1.64/1.39 ((sK8 @ (sK11 @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13))) != $true) | ((sK9 @ (sK11 @ (sK12 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13) @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)))) != (sK9 @ (sK10 @ (sK11 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) @ (sK11 @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13))))) | ((sK8 @ (sK11 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13))) != $true) | ~spl17_1),
% 1.64/1.39 inference(superposition,[status(thm)],[f113,f38])).
% 1.64/1.39 thf(f38,plain,(
% 1.64/1.39 ( ! [X21 : b,X20 : b] : (((sK9 @ (sK10 @ X21 @ X20)) = (sK6 @ (sK9 @ X21) @ (sK9 @ X20))) | ((sK8 @ X21) != $true) | ((sK8 @ X20) != $true)) )),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f23])).
% 1.64/1.39 thf(f113,plain,(
% 1.64/1.39 ((sK9 @ (sK11 @ (sK12 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13) @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)))) != (sK6 @ (sK9 @ (sK11 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13))) @ (sK9 @ (sK11 @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13))))) | ~spl17_1),
% 1.64/1.39 inference(trivial_inequality_removal,[status(thm)],[f112])).
% 1.64/1.39 thf(f112,plain,(
% 1.64/1.39 ($true != $true) | ((sK9 @ (sK11 @ (sK12 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13) @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)))) != (sK6 @ (sK9 @ (sK11 @ (sK5 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13))) @ (sK9 @ (sK11 @ (sK4 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13))))) | ~spl17_1),
% 1.64/1.39 inference(superposition,[status(thm)],[f30,f49])).
% 1.64/1.39 thf(f30,plain,(
% 1.64/1.39 ( ! [X2 : b > a,X3 : a > a > a,X0 : g > $o,X1 : g > b,X4 : g > g > g] : (((sP0 @ X4 @ X3 @ X2 @ X1 @ X0) != $true) | ((X3 @ (X2 @ (X1 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0))) @ (X2 @ (X1 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0)))) != (X2 @ (X1 @ (X4 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0) @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0)))))) )),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f18])).
% 1.64/1.39 thf(f102,plain,(
% 1.64/1.39 spl17_2 | ~spl17_6),
% 1.64/1.39 inference(avatar_contradiction_clause,[status(thm)],[f101])).
% 1.64/1.39 thf(f101,plain,(
% 1.64/1.39 $false | (spl17_2 | ~spl17_6)),
% 1.64/1.39 inference(subsumption_resolution,[status(thm)],[f100,f71])).
% 1.64/1.39 thf(f71,plain,(
% 1.64/1.39 ($true = (sK13 @ sK16)) | ~spl17_6),
% 1.64/1.39 inference(avatar_component_clause,[status(thm)],[f69])).
% 1.64/1.39 thf(f69,definition,(
% 1.64/1.39 spl17_6 <=> ($true = (sK13 @ sK16))),
% 1.64/1.39 introduced(definition,[new_symbols(naming,[spl17_6])],[avatar_definition])).
% 1.64/1.39 thf(f100,plain,(
% 1.64/1.39 ($true != (sK13 @ sK16)) | spl17_2),
% 1.64/1.39 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 1.64/1.39 thf(f99,plain,(
% 1.64/1.39 ($true != (sK13 @ sK16)) | ($true != $true) | spl17_2),
% 1.64/1.39 inference(superposition,[status(thm)],[f98,f41])).
% 1.64/1.39 thf(f98,plain,(
% 1.64/1.39 ((sK8 @ (sK11 @ sK16)) != $true) | spl17_2),
% 1.64/1.39 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.64/1.39 thf(f97,plain,(
% 1.64/1.39 ((sK8 @ (sK11 @ sK16)) != $true) | ($true != $true) | spl17_2),
% 1.64/1.39 inference(superposition,[status(thm)],[f53,f40])).
% 1.64/1.39 thf(f40,plain,(
% 1.64/1.39 ( ! [X17 : b] : (((sK7 @ (sK9 @ X17)) = $true) | ($true != (sK8 @ X17))) )),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f23])).
% 1.64/1.39 thf(f53,plain,(
% 1.64/1.39 ((sK7 @ (sK9 @ (sK11 @ sK16))) != $true) | spl17_2),
% 1.64/1.39 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.64/1.39 thf(f51,definition,(
% 1.64/1.39 spl17_2 <=> ((sK7 @ (sK9 @ (sK11 @ sK16))) = $true)),
% 1.64/1.39 introduced(definition,[new_symbols(naming,[spl17_2])],[avatar_definition])).
% 1.64/1.39 thf(f96,plain,(
% 1.64/1.39 ~spl17_4 | spl17_8),
% 1.64/1.39 inference(avatar_split_clause,[status(thm)],[f93,f84,f59])).
% 1.64/1.39 thf(f84,definition,(
% 1.64/1.39 spl17_8 <=> ((sK13 @ (sK2 @ sK13 @ sK12)) = $true)),
% 1.64/1.39 introduced(definition,[new_symbols(naming,[spl17_8])],[avatar_definition])).
% 1.64/1.39 thf(f93,plain,(
% 1.64/1.39 ((sP1 @ sK13 @ sK12) != $true) | spl17_8),
% 1.64/1.39 inference(trivial_inequality_removal,[status(thm)],[f92])).
% 1.64/1.39 thf(f92,plain,(
% 1.64/1.39 ($true != $true) | ((sP1 @ sK13 @ sK12) != $true) | spl17_8),
% 1.64/1.39 inference(superposition,[status(thm)],[f86,f25])).
% 1.64/1.39 thf(f25,plain,(
% 1.64/1.39 ( ! [X0 : g > g > g,X1 : g > $o] : (($true = (X1 @ (sK2 @ X1 @ X0))) | ((sP1 @ X1 @ X0) != $true)) )),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f14])).
% 1.64/1.39 thf(f86,plain,(
% 1.64/1.39 ((sK13 @ (sK2 @ sK13 @ sK12)) != $true) | spl17_8),
% 1.64/1.39 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.64/1.39 thf(f91,plain,(
% 1.64/1.39 ~spl17_8 | ~spl17_9 | ~spl17_4),
% 1.64/1.39 inference(avatar_split_clause,[status(thm)],[f82,f59,f88,f84])).
% 1.64/1.39 thf(f82,plain,(
% 1.64/1.39 ((sK13 @ (sK3 @ sK13 @ sK12)) != $true) | ((sK13 @ (sK2 @ sK13 @ sK12)) != $true) | ~spl17_4),
% 1.64/1.39 inference(subsumption_resolution,[status(thm)],[f81,f61])).
% 1.64/1.39 thf(f81,plain,(
% 1.64/1.39 ((sK13 @ (sK3 @ sK13 @ sK12)) != $true) | ((sP1 @ sK13 @ sK12) != $true) | ((sK13 @ (sK2 @ sK13 @ sK12)) != $true)),
% 1.64/1.39 inference(trivial_inequality_removal,[status(thm)],[f80])).
% 1.64/1.39 thf(f80,plain,(
% 1.64/1.39 ((sP1 @ sK13 @ sK12) != $true) | ((sK13 @ (sK3 @ sK13 @ sK12)) != $true) | ((sK13 @ (sK2 @ sK13 @ sK12)) != $true) | ($true != $true)),
% 1.64/1.39 inference(superposition,[status(thm)],[f26,f39])).
% 1.64/1.39 thf(f39,plain,(
% 1.64/1.39 ( ! [X18 : g,X19 : g] : (((sK13 @ (sK12 @ X18 @ X19)) = $true) | ($true != (sK13 @ X18)) | ((sK13 @ X19) != $true)) )),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f23])).
% 1.64/1.39 thf(f26,plain,(
% 1.64/1.39 ( ! [X0 : g > g > g,X1 : g > $o] : (($true != (X1 @ (X0 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0)))) | ((sP1 @ X1 @ X0) != $true)) )),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f14])).
% 1.64/1.39 thf(f79,plain,(
% 1.64/1.39 spl17_5 | spl17_6 | spl17_4 | spl17_1),
% 1.64/1.39 inference(avatar_split_clause,[status(thm)],[f36,f47,f59,f69,f64])).
% 1.64/1.39 thf(f36,plain,(
% 1.64/1.39 ($true = (sK13 @ sK16)) | ((sK7 @ sK14) = $true) | ((sP1 @ sK13 @ sK12) = $true) | ($true = (sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13))),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f23])).
% 1.64/1.39 thf(f78,plain,(
% 1.64/1.39 spl17_1 | ~spl17_7 | spl17_4 | ~spl17_2),
% 1.64/1.39 inference(avatar_split_clause,[status(thm)],[f33,f51,f59,f74,f47])).
% 1.64/1.39 thf(f33,plain,(
% 1.64/1.39 ($true = (sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) | ((sK7 @ (sK9 @ (sK11 @ sK16))) != $true) | ((sP1 @ sK13 @ sK12) = $true) | ($true != (sK7 @ (sK6 @ sK14 @ sK15)))),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f23])).
% 1.64/1.39 thf(f77,plain,(
% 1.64/1.39 spl17_6 | ~spl17_7 | spl17_4 | spl17_1),
% 1.64/1.39 inference(avatar_split_clause,[status(thm)],[f32,f47,f59,f74,f69])).
% 1.64/1.39 thf(f32,plain,(
% 1.64/1.39 ((sP1 @ sK13 @ sK12) = $true) | ($true != (sK7 @ (sK6 @ sK14 @ sK15))) | ($true = (sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) | ($true = (sK13 @ sK16))),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f23])).
% 1.64/1.39 thf(f72,plain,(
% 1.64/1.39 spl17_4 | spl17_3 | spl17_1 | spl17_6),
% 1.64/1.39 inference(avatar_split_clause,[status(thm)],[f34,f69,f47,f55,f59])).
% 1.64/1.39 thf(f34,plain,(
% 1.64/1.39 ((sP1 @ sK13 @ sK12) = $true) | ($true = (sK13 @ sK16)) | ($true = (sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) | ((sK7 @ sK15) = $true)),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f23])).
% 1.64/1.39 thf(f67,plain,(
% 1.64/1.39 spl17_1 | spl17_4 | spl17_5 | ~spl17_2),
% 1.64/1.39 inference(avatar_split_clause,[status(thm)],[f37,f51,f64,f59,f47])).
% 1.64/1.39 thf(f37,plain,(
% 1.64/1.39 ((sK7 @ (sK9 @ (sK11 @ sK16))) != $true) | ($true = (sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) | ((sK7 @ sK14) = $true) | ((sP1 @ sK13 @ sK12) = $true)),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f23])).
% 1.64/1.39 thf(f62,plain,(
% 1.64/1.39 spl17_1 | ~spl17_2 | spl17_3 | spl17_4),
% 1.64/1.39 inference(avatar_split_clause,[status(thm)],[f35,f59,f55,f51,f47])).
% 1.64/1.39 thf(f35,plain,(
% 1.64/1.39 ((sK7 @ sK15) = $true) | ((sP1 @ sK13 @ sK12) = $true) | ($true = (sP0 @ sK12 @ sK6 @ sK9 @ sK11 @ sK13)) | ((sK7 @ (sK9 @ (sK11 @ sK16))) != $true)),
% 1.64/1.39 inference(cnf_transformation,[status(thm)],[f23])).
% 1.64/1.39 % SZS output end Proof for DTF2THF_1319
% 1.64/1.39 % (1422)------------------------------
% 1.64/1.39 % (1422)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.64/1.39 % (1422)Termination reason: Refutation
% 1.64/1.39
% 1.64/1.39 % (1422)Memory used [KB]: 5884
% 1.64/1.39 % (1422)Time elapsed: 0.027 s
% 1.64/1.39 % (1422)Instructions burned: 36 (million)
% 1.64/1.39 % (1422)------------------------------
% 1.64/1.39 % (1422)------------------------------
% 1.64/1.39 % (1416)Success in time 0.04 s
%------------------------------------------------------------------------------