%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU904^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n008.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 09:37:42 AM UTC 2026
% Result : Theorem 1.67s 1.38s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 117 ( 1 unt; 0 typ; 13 def)
% Number of atoms : 1230 ( 438 equ; 0 cnn)
% Maximal formula atoms : 58 ( 10 avg)
% Number of connectives : 2317 ( 264 ~; 268 |; 191 &;1524 @)
% ( 13 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 179 ( 179 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 18 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: ( a > a > a ) > ( b > a ) > ( g > b ) > ( g > g > g ) > ( g > $o ) > $o ).
thf(func_def_7,type,
sP1: ( a > $o ) > ( a > a > a ) > $o ).
thf(func_def_8,type,
sK2: ( a > $o ) > ( a > a > a ) > a ).
thf(func_def_9,type,
sK3: ( a > $o ) > ( a > a > a ) > a ).
thf(func_def_10,type,
sK4: ( a > a > a ) > ( b > a ) > ( g > b ) > ( g > g > g ) > ( g > $o ) > g ).
thf(func_def_11,type,
sK5: ( a > a > a ) > ( b > a ) > ( g > b ) > ( g > g > g ) > ( g > $o ) > g ).
thf(func_def_12,type,
sK6: b > a ).
thf(func_def_13,type,
sK7: a > a > a ).
thf(func_def_14,type,
sK8: b > $o ).
thf(func_def_15,type,
sK9: g > b ).
thf(func_def_16,type,
sK10: b > b > b ).
thf(func_def_17,type,
sK11: g > g > g ).
thf(func_def_18,type,
sK12: g > $o ).
thf(func_def_19,type,
sK13: a > $o ).
thf(func_def_20,type,
sK14: g ).
thf(func_def_21,type,
sK15: g ).
thf(func_def_22,type,
sK16: g ).
thf(func_def_24,type,
ph18:
!>[X0: $tType] : X0 ).
thf(f171,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f60,f65,f70,f75,f76,f77,f93,f106,f125,f131,f137,f148,f152,f157,f163,f170]) ).
thf(f170,plain,
( ~ spl17_1
| spl17_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f169]) ).
thf(f169,plain,
( $false
| ~ spl17_1
| spl17_14 ),
inference(subsumption_resolution,[status(thm)],[f168,f47]) ).
thf(f47,plain,
( ( $true
= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
| ~ spl17_1 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl17_1
<=> ( $true
= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ),
introduced(definition,[new_symbols(naming,[spl17_1])],[avatar_definition]) ).
thf(f168,plain,
( ( $true
!= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
| spl17_14 ),
inference(trivial_inequality_removal,[status(thm)],[f167]) ).
thf(f167,plain,
( ( $true
!= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
| ( $true != $true )
| spl17_14 ),
inference(superposition,[status(thm)],[f147,f29]) ).
thf(f29,plain,
! [X2: g > b,X3: b > a,X0: g > $o,X1: g > g > g,X4: a > a > a] :
( ( $true
= ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) )
| ( $true
!= ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X0: g > $o,X1: g > g > g,X2: g > b,X3: b > a,X4: a > a > a] :
( ( ( $true
= ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) )
& ( ( X3 @ ( X2 @ ( X1 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) )
!= ( X4 @ ( X3 @ ( X2 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) @ ( X3 @ ( X2 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) )
& ( $true
= ( X0 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) )
| ( $true
!= ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f16,f17]) ).
thf(f17,plain,
! [X0: g > $o,X1: g > g > g,X2: g > b,X3: b > a,X4: a > a > a] :
( ? [X5: g,X6: g] :
( ( $true
= ( X0 @ X5 ) )
& ( ( X4 @ ( X3 @ ( X2 @ X5 ) ) @ ( X3 @ ( X2 @ X6 ) ) )
!= ( X3 @ ( X2 @ ( X1 @ X5 @ X6 ) ) ) )
& ( $true
= ( X0 @ X6 ) ) )
=> ( ( $true
= ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) )
& ( ( X3 @ ( X2 @ ( X1 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) )
!= ( X4 @ ( X3 @ ( X2 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) @ ( X3 @ ( X2 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) )
& ( $true
= ( X0 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
! [X0: g > $o,X1: g > g > g,X2: g > b,X3: b > a,X4: a > a > a] :
( ? [X5: g,X6: g] :
( ( $true
= ( X0 @ X5 ) )
& ( ( X4 @ ( X3 @ ( X2 @ X5 ) ) @ ( X3 @ ( X2 @ X6 ) ) )
!= ( X3 @ ( X2 @ ( X1 @ X5 @ X6 ) ) ) )
& ( $true
= ( X0 @ X6 ) ) )
| ( $true
!= ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,plain,
! [X3: g > $o,X7: g > g > g,X5: g > b,X4: b > a,X2: a > a > a] :
( ? [X22: g,X23: g] :
( ( $true
= ( X3 @ X22 ) )
& ( ( X2 @ ( X4 @ ( X5 @ X22 ) ) @ ( X4 @ ( X5 @ X23 ) ) )
!= ( X4 @ ( X5 @ ( X7 @ X22 @ X23 ) ) ) )
& ( $true
= ( X3 @ X23 ) ) )
| ( $true
!= ( sP0 @ X2 @ X4 @ X5 @ X7 @ X3 ) ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X3: g > $o,X7: g > g > g,X5: g > b,X4: b > a,X2: a > a > a] :
( ? [X22: g,X23: g] :
( ( $true
= ( X3 @ X22 ) )
& ( ( X2 @ ( X4 @ ( X5 @ X22 ) ) @ ( X4 @ ( X5 @ X23 ) ) )
!= ( X4 @ ( X5 @ ( X7 @ X22 @ X23 ) ) ) )
& ( $true
= ( X3 @ X23 ) ) )
| ( $true
!= ( sP0 @ X2 @ X4 @ X5 @ X7 @ X3 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f147,plain,
( ( $true
!= ( sK12 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) )
| spl17_14 ),
inference(avatar_component_clause,[status(thm)],[f145]) ).
thf(f145,definition,
( spl17_14
<=> ( $true
= ( sK12 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_14])],[avatar_definition]) ).
thf(f163,plain,
( ~ spl17_2
| spl17_5
| ~ spl17_6 ),
inference(avatar_split_clause,[status(thm)],[f160,f67,f62,f49]) ).
thf(f49,definition,
( spl17_2
<=> ( ( sK12 @ sK15 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_2])],[avatar_definition]) ).
thf(f62,definition,
( spl17_5
<=> ( $true
= ( sK12 @ ( sK11 @ sK14 @ sK15 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_5])],[avatar_definition]) ).
thf(f67,definition,
( spl17_6
<=> ( $true
= ( sK12 @ sK14 ) ) ),
introduced(definition,[new_symbols(naming,[spl17_6])],[avatar_definition]) ).
thf(f160,plain,
( ( ( sK12 @ sK15 )
!= $true )
| spl17_5
| ~ spl17_6 ),
inference(subsumption_resolution,[status(thm)],[f159,f69]) ).
thf(f69,plain,
( ( $true
= ( sK12 @ sK14 ) )
| ~ spl17_6 ),
inference(avatar_component_clause,[status(thm)],[f67]) ).
thf(f159,plain,
( ( $true
!= ( sK12 @ sK14 ) )
| ( ( sK12 @ sK15 )
!= $true )
| spl17_5 ),
inference(trivial_inequality_removal,[status(thm)],[f158]) ).
thf(f158,plain,
( ( ( sK12 @ sK15 )
!= $true )
| ( $true
!= ( sK12 @ sK14 ) )
| ( $true != $true )
| spl17_5 ),
inference(superposition,[status(thm)],[f64,f30]) ).
thf(f30,plain,
! [X24: g,X23: g] :
( ( $true
= ( sK12 @ ( sK11 @ X23 @ X24 ) ) )
| ( $true
!= ( sK12 @ X23 ) )
| ( $true
!= ( sK12 @ X24 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ! [X8: b] :
( ( $true
= ( sK13 @ ( sK6 @ X8 ) ) )
| ( $true
!= ( sK8 @ X8 ) ) )
& ! [X9: a,X10: a] :
( ( $true
= ( sK13 @ ( sK7 @ X9 @ X10 ) ) )
| ( ( sK13 @ X10 )
!= $true )
| ( $true
!= ( sK13 @ X9 ) ) )
& ! [X11: g] :
( ( $true
!= ( sK12 @ X11 ) )
| ( $true
= ( sK8 @ ( sK9 @ X11 ) ) ) )
& ! [X12: b,X13: b] :
( ( $true
!= ( sK8 @ X12 ) )
| ( $true
!= ( sK8 @ X13 ) )
| ( ( sK6 @ ( sK10 @ X12 @ X13 ) )
= ( sK7 @ ( sK6 @ X12 ) @ ( sK6 @ X13 ) ) ) )
& ! [X14: b,X15: b] :
( ( ( sK8 @ X15 )
!= $true )
| ( $true
!= ( sK8 @ X14 ) )
| ( $true
= ( sK8 @ ( sK10 @ X15 @ X14 ) ) ) )
& ! [X16: g,X17: g] :
( ( $true
!= ( sK12 @ X17 ) )
| ( $true
!= ( sK12 @ X16 ) )
| ( ( sK10 @ ( sK9 @ X16 ) @ ( sK9 @ X17 ) )
= ( sK9 @ ( sK11 @ X16 @ X17 ) ) ) )
& ( ( ( $true
= ( sK12 @ sK14 ) )
& ( ( sK12 @ sK15 )
= $true )
& ( $true
!= ( sK12 @ ( sK11 @ sK14 @ sK15 ) ) ) )
| ( ( $true
= ( sK12 @ sK16 ) )
& ( $true
!= ( sK13 @ ( sK6 @ ( sK9 @ sK16 ) ) ) ) )
| ( ( sP1 @ sK13 @ sK7 )
= $true )
| ( $true
= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) )
& ! [X21: b,X22: b] :
( ( $true
!= ( sK8 @ X22 ) )
| ( ( sK8 @ ( sK10 @ X21 @ X22 ) )
= $true )
| ( $true
!= ( sK8 @ X21 ) ) )
& ! [X23: g,X24: g] :
( ( $true
!= ( sK12 @ X24 ) )
| ( $true
!= ( sK12 @ X23 ) )
| ( $true
= ( sK12 @ ( sK11 @ X23 @ X24 ) ) ) ) ),
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: b > a,X1: a > a > a,X2: b > $o,X3: g > b,X4: b > b > b,X5: g > g > g,X6: g > $o,X7: a > $o] :
( ! [X8: b] :
( ( $true
= ( X7 @ ( X0 @ X8 ) ) )
| ( $true
!= ( X2 @ X8 ) ) )
& ! [X9: a,X10: a] :
( ( ( X7 @ ( X1 @ X9 @ X10 ) )
= $true )
| ( $true
!= ( X7 @ X10 ) )
| ( $true
!= ( X7 @ X9 ) ) )
& ! [X11: g] :
( ( $true
!= ( X6 @ X11 ) )
| ( $true
= ( X2 @ ( X3 @ X11 ) ) ) )
& ! [X12: b,X13: b] :
( ( $true
!= ( X2 @ X12 ) )
| ( $true
!= ( X2 @ X13 ) )
| ( ( X1 @ ( X0 @ X12 ) @ ( X0 @ X13 ) )
= ( X0 @ ( X4 @ X12 @ X13 ) ) ) )
& ! [X14: b,X15: b] :
( ( $true
!= ( X2 @ X15 ) )
| ( $true
!= ( X2 @ X14 ) )
| ( $true
= ( X2 @ ( X4 @ X15 @ X14 ) ) ) )
& ! [X16: g,X17: g] :
( ( $true
!= ( X6 @ X17 ) )
| ( ( X6 @ X16 )
!= $true )
| ( ( X4 @ ( X3 @ X16 ) @ ( X3 @ X17 ) )
= ( X3 @ ( X5 @ X16 @ X17 ) ) ) )
& ( ? [X18: g,X19: g] :
( ( ( X6 @ X18 )
= $true )
& ( $true
= ( X6 @ X19 ) )
& ( ( X6 @ ( X5 @ X18 @ X19 ) )
!= $true ) )
| ? [X20: g] :
( ( $true
= ( X6 @ X20 ) )
& ( ( X7 @ ( X0 @ ( X3 @ X20 ) ) )
!= $true ) )
| ( $true
= ( sP1 @ X7 @ X1 ) )
| ( $true
= ( sP0 @ X1 @ X0 @ X3 @ X5 @ X6 ) ) )
& ! [X21: b,X22: b] :
( ( $true
!= ( X2 @ X22 ) )
| ( $true
= ( X2 @ ( X4 @ X21 @ X22 ) ) )
| ( $true
!= ( X2 @ X21 ) ) )
& ! [X23: g,X24: g] :
( ( $true
!= ( X6 @ X24 ) )
| ( $true
!= ( X6 @ X23 ) )
| ( $true
= ( X6 @ ( X5 @ X23 @ X24 ) ) ) ) )
=> ( ! [X8: b] :
( ( $true
= ( sK13 @ ( sK6 @ X8 ) ) )
| ( $true
!= ( sK8 @ X8 ) ) )
& ! [X10: a,X9: a] :
( ( $true
= ( sK13 @ ( sK7 @ X9 @ X10 ) ) )
| ( ( sK13 @ X10 )
!= $true )
| ( $true
!= ( sK13 @ X9 ) ) )
& ! [X11: g] :
( ( $true
!= ( sK12 @ X11 ) )
| ( $true
= ( sK8 @ ( sK9 @ X11 ) ) ) )
& ! [X13: b,X12: b] :
( ( $true
!= ( sK8 @ X12 ) )
| ( $true
!= ( sK8 @ X13 ) )
| ( ( sK6 @ ( sK10 @ X12 @ X13 ) )
= ( sK7 @ ( sK6 @ X12 ) @ ( sK6 @ X13 ) ) ) )
& ! [X15: b,X14: b] :
( ( ( sK8 @ X15 )
!= $true )
| ( $true
!= ( sK8 @ X14 ) )
| ( $true
= ( sK8 @ ( sK10 @ X15 @ X14 ) ) ) )
& ! [X17: g,X16: g] :
( ( $true
!= ( sK12 @ X17 ) )
| ( $true
!= ( sK12 @ X16 ) )
| ( ( sK10 @ ( sK9 @ X16 ) @ ( sK9 @ X17 ) )
= ( sK9 @ ( sK11 @ X16 @ X17 ) ) ) )
& ( ? [X19: g,X18: g] :
( ( $true
= ( sK12 @ X18 ) )
& ( $true
= ( sK12 @ X19 ) )
& ( $true
!= ( sK12 @ ( sK11 @ X18 @ X19 ) ) ) )
| ? [X20: g] :
( ( $true
= ( sK12 @ X20 ) )
& ( $true
!= ( sK13 @ ( sK6 @ ( sK9 @ X20 ) ) ) ) )
| ( ( sP1 @ sK13 @ sK7 )
= $true )
| ( $true
= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) )
& ! [X22: b,X21: b] :
( ( $true
!= ( sK8 @ X22 ) )
| ( ( sK8 @ ( sK10 @ X21 @ X22 ) )
= $true )
| ( $true
!= ( sK8 @ X21 ) ) )
& ! [X24: g,X23: g] :
( ( $true
!= ( sK12 @ X24 ) )
| ( $true
!= ( sK12 @ X23 ) )
| ( $true
= ( sK12 @ ( sK11 @ X23 @ X24 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X19: g,X18: g] :
( ( $true
= ( sK12 @ X18 ) )
& ( $true
= ( sK12 @ X19 ) )
& ( $true
!= ( sK12 @ ( sK11 @ X18 @ X19 ) ) ) )
=> ( ( $true
= ( sK12 @ sK14 ) )
& ( ( sK12 @ sK15 )
= $true )
& ( $true
!= ( sK12 @ ( sK11 @ sK14 @ sK15 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X20: g] :
( ( $true
= ( sK12 @ X20 ) )
& ( $true
!= ( sK13 @ ( sK6 @ ( sK9 @ X20 ) ) ) ) )
=> ( ( $true
= ( sK12 @ sK16 ) )
& ( $true
!= ( sK13 @ ( sK6 @ ( sK9 @ sK16 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
? [X0: b > a,X1: a > a > a,X2: b > $o,X3: g > b,X4: b > b > b,X5: g > g > g,X6: g > $o,X7: a > $o] :
( ! [X8: b] :
( ( $true
= ( X7 @ ( X0 @ X8 ) ) )
| ( $true
!= ( X2 @ X8 ) ) )
& ! [X9: a,X10: a] :
( ( ( X7 @ ( X1 @ X9 @ X10 ) )
= $true )
| ( $true
!= ( X7 @ X10 ) )
| ( $true
!= ( X7 @ X9 ) ) )
& ! [X11: g] :
( ( $true
!= ( X6 @ X11 ) )
| ( $true
= ( X2 @ ( X3 @ X11 ) ) ) )
& ! [X12: b,X13: b] :
( ( $true
!= ( X2 @ X12 ) )
| ( $true
!= ( X2 @ X13 ) )
| ( ( X1 @ ( X0 @ X12 ) @ ( X0 @ X13 ) )
= ( X0 @ ( X4 @ X12 @ X13 ) ) ) )
& ! [X14: b,X15: b] :
( ( $true
!= ( X2 @ X15 ) )
| ( $true
!= ( X2 @ X14 ) )
| ( $true
= ( X2 @ ( X4 @ X15 @ X14 ) ) ) )
& ! [X16: g,X17: g] :
( ( $true
!= ( X6 @ X17 ) )
| ( ( X6 @ X16 )
!= $true )
| ( ( X4 @ ( X3 @ X16 ) @ ( X3 @ X17 ) )
= ( X3 @ ( X5 @ X16 @ X17 ) ) ) )
& ( ? [X18: g,X19: g] :
( ( ( X6 @ X18 )
= $true )
& ( $true
= ( X6 @ X19 ) )
& ( ( X6 @ ( X5 @ X18 @ X19 ) )
!= $true ) )
| ? [X20: g] :
( ( $true
= ( X6 @ X20 ) )
& ( ( X7 @ ( X0 @ ( X3 @ X20 ) ) )
!= $true ) )
| ( $true
= ( sP1 @ X7 @ X1 ) )
| ( $true
= ( sP0 @ X1 @ X0 @ X3 @ X5 @ X6 ) ) )
& ! [X21: b,X22: b] :
( ( $true
!= ( X2 @ X22 ) )
| ( $true
= ( X2 @ ( X4 @ X21 @ X22 ) ) )
| ( $true
!= ( X2 @ X21 ) ) )
& ! [X23: g,X24: g] :
( ( $true
!= ( X6 @ X24 ) )
| ( $true
!= ( X6 @ X23 ) )
| ( $true
= ( X6 @ ( X5 @ X23 @ X24 ) ) ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
? [X4: b > a,X2: a > a > a,X1: b > $o,X5: g > b,X6: b > b > b,X7: g > g > g,X3: g > $o,X0: a > $o] :
( ! [X13: b] :
( ( $true
= ( X0 @ ( X4 @ X13 ) ) )
| ( $true
!= ( X1 @ X13 ) ) )
& ! [X12: a,X11: a] :
( ( $true
= ( X0 @ ( X2 @ X12 @ X11 ) ) )
| ( $true
!= ( X0 @ X11 ) )
| ( $true
!= ( X0 @ X12 ) ) )
& ! [X8: g] :
( ( $true
!= ( X3 @ X8 ) )
| ( $true
= ( X1 @ ( X5 @ X8 ) ) ) )
& ! [X19: b,X18: b] :
( ( $true
!= ( X1 @ X19 ) )
| ( $true
!= ( X1 @ X18 ) )
| ( ( X4 @ ( X6 @ X19 @ X18 ) )
= ( X2 @ ( X4 @ X19 ) @ ( X4 @ X18 ) ) ) )
& ! [X14: b,X15: b] :
( ( $true
!= ( X1 @ X15 ) )
| ( $true
!= ( X1 @ X14 ) )
| ( $true
= ( X1 @ ( X6 @ X15 @ X14 ) ) ) )
& ! [X17: g,X16: g] :
( ( ( X3 @ X16 )
!= $true )
| ( $true
!= ( X3 @ X17 ) )
| ( ( X5 @ ( X7 @ X17 @ X16 ) )
= ( X6 @ ( X5 @ X17 ) @ ( X5 @ X16 ) ) ) )
& ( ? [X24: g,X25: g] :
( ( ( X3 @ X24 )
= $true )
& ( $true
= ( X3 @ X25 ) )
& ( $true
!= ( X3 @ ( X7 @ X24 @ X25 ) ) ) )
| ? [X26: g] :
( ( $true
= ( X3 @ X26 ) )
& ( $true
!= ( X0 @ ( X4 @ ( X5 @ X26 ) ) ) ) )
| ( $true
= ( sP1 @ X0 @ X2 ) )
| ( $true
= ( sP0 @ X2 @ X4 @ X5 @ X7 @ X3 ) ) )
& ! [X20: b,X21: b] :
( ( $true
!= ( X1 @ X21 ) )
| ( ( X1 @ ( X6 @ X20 @ X21 ) )
= $true )
| ( ( X1 @ X20 )
!= $true ) )
& ! [X10: g,X9: g] :
( ( $true
!= ( X3 @ X9 ) )
| ( $true
!= ( X3 @ X10 ) )
| ( $true
= ( X3 @ ( X7 @ X10 @ X9 ) ) ) ) ),
inference(definition_folding,[status(thm)],[f7,f9,f8]) ).
thf(f9,plain,
! [X2: a > a > a,X0: a > $o] :
( ? [X27: a,X28: a] :
( ( $true
!= ( X0 @ ( X2 @ X28 @ X27 ) ) )
& ( $true
= ( X0 @ X28 ) )
& ( $true
= ( X0 @ X27 ) ) )
| ( $true
!= ( sP1 @ X0 @ X2 ) ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f7,plain,
? [X4: b > a,X2: a > a > a,X1: b > $o,X5: g > b,X6: b > b > b,X7: g > g > g,X3: g > $o,X0: a > $o] :
( ! [X13: b] :
( ( $true
= ( X0 @ ( X4 @ X13 ) ) )
| ( $true
!= ( X1 @ X13 ) ) )
& ! [X12: a,X11: a] :
( ( $true
= ( X0 @ ( X2 @ X12 @ X11 ) ) )
| ( $true
!= ( X0 @ X11 ) )
| ( $true
!= ( X0 @ X12 ) ) )
& ! [X8: g] :
( ( $true
!= ( X3 @ X8 ) )
| ( $true
= ( X1 @ ( X5 @ X8 ) ) ) )
& ! [X19: b,X18: b] :
( ( $true
!= ( X1 @ X19 ) )
| ( $true
!= ( X1 @ X18 ) )
| ( ( X4 @ ( X6 @ X19 @ X18 ) )
= ( X2 @ ( X4 @ X19 ) @ ( X4 @ X18 ) ) ) )
& ! [X14: b,X15: b] :
( ( $true
!= ( X1 @ X15 ) )
| ( $true
!= ( X1 @ X14 ) )
| ( $true
= ( X1 @ ( X6 @ X15 @ X14 ) ) ) )
& ! [X17: g,X16: g] :
( ( ( X3 @ X16 )
!= $true )
| ( $true
!= ( X3 @ X17 ) )
| ( ( X5 @ ( X7 @ X17 @ X16 ) )
= ( X6 @ ( X5 @ X17 ) @ ( X5 @ X16 ) ) ) )
& ( ? [X24: g,X25: g] :
( ( ( X3 @ X24 )
= $true )
& ( $true
= ( X3 @ X25 ) )
& ( $true
!= ( X3 @ ( X7 @ X24 @ X25 ) ) ) )
| ? [X26: g] :
( ( $true
= ( X3 @ X26 ) )
& ( $true
!= ( X0 @ ( X4 @ ( X5 @ X26 ) ) ) ) )
| ? [X27: a,X28: a] :
( ( $true
!= ( X0 @ ( X2 @ X28 @ X27 ) ) )
& ( $true
= ( X0 @ X28 ) )
& ( $true
= ( X0 @ X27 ) ) )
| ? [X22: g,X23: g] :
( ( $true
= ( X3 @ X22 ) )
& ( ( X2 @ ( X4 @ ( X5 @ X22 ) ) @ ( X4 @ ( X5 @ X23 ) ) )
!= ( X4 @ ( X5 @ ( X7 @ X22 @ X23 ) ) ) )
& ( $true
= ( X3 @ X23 ) ) ) )
& ! [X20: b,X21: b] :
( ( $true
!= ( X1 @ X21 ) )
| ( ( X1 @ ( X6 @ X20 @ X21 ) )
= $true )
| ( ( X1 @ X20 )
!= $true ) )
& ! [X10: g,X9: g] :
( ( $true
!= ( X3 @ X9 ) )
| ( $true
!= ( X3 @ X10 ) )
| ( $true
= ( X3 @ ( X7 @ X10 @ X9 ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X6: b > b > b,X3: g > $o,X4: b > a,X5: g > b,X1: b > $o,X0: a > $o,X7: g > g > g,X2: a > a > a] :
( ( ? [X25: g,X24: g] :
( ( $true
!= ( X3 @ ( X7 @ X24 @ X25 ) ) )
& ( ( X3 @ X24 )
= $true )
& ( $true
= ( X3 @ X25 ) ) )
| ? [X27: a,X28: a] :
( ( $true
!= ( X0 @ ( X2 @ X28 @ X27 ) ) )
& ( $true
= ( X0 @ X28 ) )
& ( $true
= ( X0 @ X27 ) ) )
| ? [X23: g,X22: g] :
( ( ( X2 @ ( X4 @ ( X5 @ X22 ) ) @ ( X4 @ ( X5 @ X23 ) ) )
!= ( X4 @ ( X5 @ ( X7 @ X22 @ X23 ) ) ) )
& ( $true
= ( X3 @ X23 ) )
& ( $true
= ( X3 @ X22 ) ) )
| ? [X26: g] :
( ( $true
= ( X3 @ X26 ) )
& ( $true
!= ( X0 @ ( X4 @ ( X5 @ X26 ) ) ) ) ) )
& ! [X11: a,X12: a] :
( ( $true
= ( X0 @ ( X2 @ X12 @ X11 ) ) )
| ( $true
!= ( X0 @ X11 ) )
| ( $true
!= ( X0 @ X12 ) ) )
& ! [X13: b] :
( ( $true
= ( X0 @ ( X4 @ X13 ) ) )
| ( $true
!= ( X1 @ X13 ) ) )
& ! [X14: b,X15: b] :
( ( $true
= ( X1 @ ( X6 @ X15 @ X14 ) ) )
| ( $true
!= ( X1 @ X14 ) )
| ( $true
!= ( X1 @ X15 ) ) )
& ! [X18: b,X19: b] :
( ( ( X4 @ ( X6 @ X19 @ X18 ) )
= ( X2 @ ( X4 @ X19 ) @ ( X4 @ X18 ) ) )
| ( $true
!= ( X1 @ X19 ) )
| ( $true
!= ( X1 @ X18 ) ) )
& ! [X9: g,X10: g] :
( ( $true
= ( X3 @ ( X7 @ X10 @ X9 ) ) )
| ( $true
!= ( X3 @ X10 ) )
| ( $true
!= ( X3 @ X9 ) ) )
& ! [X16: g,X17: g] :
( ( ( X5 @ ( X7 @ X17 @ X16 ) )
= ( X6 @ ( X5 @ X17 ) @ ( X5 @ X16 ) ) )
| ( ( X3 @ X16 )
!= $true )
| ( $true
!= ( X3 @ X17 ) ) )
& ! [X20: b,X21: b] :
( ( ( X1 @ ( X6 @ X20 @ X21 ) )
= $true )
| ( $true
!= ( X1 @ X21 ) )
| ( ( X1 @ X20 )
!= $true ) )
& ! [X8: g] :
( ( $true
!= ( X3 @ X8 ) )
| ( $true
= ( X1 @ ( X5 @ X8 ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X6: b > b > b,X3: g > $o,X4: b > a,X5: g > b,X1: b > $o,X0: a > $o,X7: g > g > g,X2: a > a > a] :
( ( ! [X11: a,X12: a] :
( ( ( $true
= ( X0 @ X11 ) )
& ( $true
= ( X0 @ X12 ) ) )
=> ( $true
= ( X0 @ ( X2 @ X12 @ X11 ) ) ) )
& ! [X13: b] :
( ( $true
= ( X1 @ X13 ) )
=> ( $true
= ( X0 @ ( X4 @ X13 ) ) ) )
& ! [X14: b,X15: b] :
( ( ( $true
= ( X1 @ X14 ) )
& ( $true
= ( X1 @ X15 ) ) )
=> ( $true
= ( X1 @ ( X6 @ X15 @ X14 ) ) ) )
& ! [X18: b,X19: b] :
( ( ( $true
= ( X1 @ X19 ) )
& ( $true
= ( X1 @ X18 ) ) )
=> ( ( X4 @ ( X6 @ X19 @ X18 ) )
= ( X2 @ ( X4 @ X19 ) @ ( X4 @ X18 ) ) ) )
& ! [X9: g,X10: g] :
( ( ( $true
= ( X3 @ X10 ) )
& ( $true
= ( X3 @ X9 ) ) )
=> ( $true
= ( X3 @ ( X7 @ X10 @ X9 ) ) ) )
& ! [X16: g,X17: g] :
( ( ( ( X3 @ X16 )
= $true )
& ( $true
= ( X3 @ X17 ) ) )
=> ( ( X5 @ ( X7 @ X17 @ X16 ) )
= ( X6 @ ( X5 @ X17 ) @ ( X5 @ X16 ) ) ) )
& ! [X20: b,X21: b] :
( ( ( $true
= ( X1 @ X21 ) )
& ( ( X1 @ X20 )
= $true ) )
=> ( ( X1 @ ( X6 @ X20 @ X21 ) )
= $true ) )
& ! [X8: g] :
( ( $true
= ( X3 @ X8 ) )
=> ( $true
= ( X1 @ ( X5 @ X8 ) ) ) ) )
=> ( ! [X25: g,X24: g] :
( ( ( ( X3 @ X24 )
= $true )
& ( $true
= ( X3 @ X25 ) ) )
=> ( $true
= ( X3 @ ( X7 @ X24 @ X25 ) ) ) )
& ! [X27: a,X28: a] :
( ( ( $true
= ( X0 @ X28 ) )
& ( $true
= ( X0 @ X27 ) ) )
=> ( $true
= ( X0 @ ( X2 @ X28 @ X27 ) ) ) )
& ! [X23: g,X22: g] :
( ( ( $true
= ( X3 @ X23 ) )
& ( $true
= ( X3 @ X22 ) ) )
=> ( ( X2 @ ( X4 @ ( X5 @ X22 ) ) @ ( X4 @ ( X5 @ X23 ) ) )
= ( X4 @ ( X5 @ ( X7 @ X22 @ X23 ) ) ) ) )
& ! [X26: g] :
( ( $true
= ( X3 @ X26 ) )
=> ( $true
= ( X0 @ ( X4 @ ( X5 @ X26 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > $o,X1: b > $o,X2: a > a > a,X3: g > $o,X4: b > a,X5: g > b,X6: b > b > b,X7: g > g > g] :
( ( ! [X8: g] :
( ( X3 @ X8 )
=> ( X1 @ ( X5 @ X8 ) ) )
& ! [X9: g,X10: g] :
( ( ( X3 @ X9 )
& ( X3 @ X10 ) )
=> ( X3 @ ( X7 @ X10 @ X9 ) ) )
& ! [X11: a,X12: a] :
( ( ( X0 @ X12 )
& ( X0 @ X11 ) )
=> ( X0 @ ( X2 @ X12 @ X11 ) ) )
& ! [X13: b] :
( ( X1 @ X13 )
=> ( X0 @ ( X4 @ X13 ) ) )
& ! [X14: b,X15: b] :
( ( ( X1 @ X15 )
& ( X1 @ X14 ) )
=> ( X1 @ ( X6 @ X15 @ X14 ) ) )
& ! [X16: g,X17: g] :
( ( ( X3 @ X16 )
& ( X3 @ X17 ) )
=> ( ( X5 @ ( X7 @ X17 @ X16 ) )
= ( X6 @ ( X5 @ X17 ) @ ( X5 @ X16 ) ) ) )
& ! [X18: b,X19: b] :
( ( ( X1 @ X19 )
& ( X1 @ X18 ) )
=> ( ( X4 @ ( X6 @ X19 @ X18 ) )
= ( X2 @ ( X4 @ X19 ) @ ( X4 @ X18 ) ) ) )
& ! [X20: b,X21: b] :
( ( ( X1 @ X21 )
& ( X1 @ X20 ) )
=> ( X1 @ ( X6 @ X20 @ X21 ) ) ) )
=> ( ! [X22: g,X23: g] :
( ( ( X3 @ X23 )
& ( X3 @ X22 ) )
=> ( ( X2 @ ( X4 @ ( X5 @ X22 ) ) @ ( X4 @ ( X5 @ X23 ) ) )
= ( X4 @ ( X5 @ ( X7 @ X22 @ X23 ) ) ) ) )
& ! [X24: g,X25: g] :
( ( ( X3 @ X24 )
& ( X3 @ X25 ) )
=> ( X3 @ ( X7 @ X24 @ X25 ) ) )
& ! [X26: g] :
( ( X3 @ X26 )
=> ( X0 @ ( X4 @ ( X5 @ X26 ) ) ) )
& ! [X27: a,X28: a] :
( ( ( X0 @ X27 )
& ( X0 @ X28 ) )
=> ( X0 @ ( X2 @ X28 @ X27 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X6: a > $o,X4: b > $o,X7: a > a > a,X2: g > $o,X1: b > a,X0: g > b,X5: b > b > b,X3: g > g > g] :
( ( ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( X0 @ X8 ) ) )
& ! [X9: g,X8: g] :
( ( ( X2 @ X9 )
& ( X2 @ X8 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) )
& ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( X6 @ X9 ) )
=> ( X6 @ ( X7 @ X8 @ X9 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) )
& ! [X9: b,X8: b] :
( ( ( X4 @ X8 )
& ( X4 @ X9 ) )
=> ( X4 @ ( X5 @ X8 @ X9 ) ) )
& ! [X9: g,X8: g] :
( ( ( X2 @ X9 )
& ( X2 @ X8 ) )
=> ( ( X0 @ ( X3 @ X8 @ X9 ) )
= ( X5 @ ( X0 @ X8 ) @ ( X0 @ 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: g,X9: g] :
( ( ( X2 @ X9 )
& ( X2 @ X8 ) )
=> ( ( X1 @ ( X0 @ ( X3 @ X8 @ X9 ) ) )
= ( X7 @ ( X1 @ ( X0 @ X8 ) ) @ ( X1 @ ( X0 @ X9 ) ) ) ) )
& ! [X8: g,X9: g] :
( ( ( X2 @ X8 )
& ( X2 @ X9 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X6 @ ( X1 @ ( X0 @ X8 ) ) ) )
& ! [X9: a,X8: a] :
( ( ( X6 @ X9 )
& ( X6 @ X8 ) )
=> ( X6 @ ( X7 @ X8 @ X9 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X6: a > $o,X4: b > $o,X7: a > a > a,X2: g > $o,X1: b > a,X0: g > b,X5: b > b > b,X3: g > g > g] :
( ( ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( X0 @ X8 ) ) )
& ! [X9: g,X8: g] :
( ( ( X2 @ X9 )
& ( X2 @ X8 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) )
& ! [X9: a,X8: a] :
( ( ( X6 @ X8 )
& ( X6 @ X9 ) )
=> ( X6 @ ( X7 @ X8 @ X9 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) )
& ! [X9: b,X8: b] :
( ( ( X4 @ X8 )
& ( X4 @ X9 ) )
=> ( X4 @ ( X5 @ X8 @ X9 ) ) )
& ! [X9: g,X8: g] :
( ( ( X2 @ X9 )
& ( X2 @ X8 ) )
=> ( ( X0 @ ( X3 @ X8 @ X9 ) )
= ( X5 @ ( X0 @ X8 ) @ ( X0 @ 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: g,X9: g] :
( ( ( X2 @ X9 )
& ( X2 @ X8 ) )
=> ( ( X1 @ ( X0 @ ( X3 @ X8 @ X9 ) ) )
= ( X7 @ ( X1 @ ( X0 @ X8 ) ) @ ( X1 @ ( X0 @ X9 ) ) ) ) )
& ! [X8: g,X9: g] :
( ( ( X2 @ X8 )
& ( X2 @ X9 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X6 @ ( X1 @ ( X0 @ X8 ) ) ) )
& ! [X9: a,X8: a] :
( ( ( X6 @ X9 )
& ( X6 @ X8 ) )
=> ( X6 @ ( X7 @ X8 @ X9 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.i62NXBbrIK/DTF2THF_26225.p',cTHM126_pme) ).
thf(f64,plain,
( ( $true
!= ( sK12 @ ( sK11 @ sK14 @ sK15 ) ) )
| spl17_5 ),
inference(avatar_component_clause,[status(thm)],[f62]) ).
thf(f157,plain,
( ~ spl17_4
| spl17_7 ),
inference(avatar_split_clause,[status(thm)],[f156,f72,f57]) ).
thf(f57,definition,
( spl17_4
<=> ( $true
= ( sK12 @ sK16 ) ) ),
introduced(definition,[new_symbols(naming,[spl17_4])],[avatar_definition]) ).
thf(f72,definition,
( spl17_7
<=> ( $true
= ( sK13 @ ( sK6 @ ( sK9 @ sK16 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_7])],[avatar_definition]) ).
thf(f156,plain,
( ( $true
!= ( sK12 @ sK16 ) )
| spl17_7 ),
inference(trivial_inequality_removal,[status(thm)],[f155]) ).
thf(f155,plain,
( ( $true
!= ( sK12 @ sK16 ) )
| ( $true != $true )
| spl17_7 ),
inference(superposition,[status(thm)],[f154,f41]) ).
thf(f41,plain,
! [X11: g] :
( ( $true
= ( sK8 @ ( sK9 @ X11 ) ) )
| ( $true
!= ( sK12 @ X11 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f154,plain,
( ( $true
!= ( sK8 @ ( sK9 @ sK16 ) ) )
| spl17_7 ),
inference(trivial_inequality_removal,[status(thm)],[f153]) ).
thf(f153,plain,
( ( $true
!= ( sK8 @ ( sK9 @ sK16 ) ) )
| ( $true != $true )
| spl17_7 ),
inference(superposition,[status(thm)],[f74,f43]) ).
thf(f43,plain,
! [X8: b] :
( ( $true
= ( sK13 @ ( sK6 @ X8 ) ) )
| ( $true
!= ( sK8 @ X8 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f74,plain,
( ( $true
!= ( sK13 @ ( sK6 @ ( sK9 @ sK16 ) ) ) )
| spl17_7 ),
inference(avatar_component_clause,[status(thm)],[f72]) ).
thf(f152,plain,
( ~ spl17_1
| spl17_13 ),
inference(avatar_contradiction_clause,[status(thm)],[f151]) ).
thf(f151,plain,
( $false
| ~ spl17_1
| spl17_13 ),
inference(subsumption_resolution,[status(thm)],[f150,f47]) ).
thf(f150,plain,
( ( $true
!= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
| spl17_13 ),
inference(trivial_inequality_removal,[status(thm)],[f149]) ).
thf(f149,plain,
( ( $true
!= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
| ( $true != $true )
| spl17_13 ),
inference(superposition,[status(thm)],[f143,f27]) ).
thf(f27,plain,
! [X2: g > b,X3: b > a,X0: g > $o,X1: g > g > g,X4: a > a > a] :
( ( $true
= ( X0 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) )
| ( $true
!= ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f143,plain,
( ( ( sK12 @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
!= $true )
| spl17_13 ),
inference(avatar_component_clause,[status(thm)],[f141]) ).
thf(f141,definition,
( spl17_13
<=> ( ( sK12 @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_13])],[avatar_definition]) ).
thf(f148,plain,
( ~ spl17_13
| ~ spl17_14
| spl17_11 ),
inference(avatar_split_clause,[status(thm)],[f139,f118,f145,f141]) ).
thf(f118,definition,
( spl17_11
<=> ( ( sK6 @ ( sK9 @ ( sK11 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) )
= ( sK6 @ ( sK10 @ ( sK9 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) @ ( sK9 @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_11])],[avatar_definition]) ).
thf(f139,plain,
( ( $true
!= ( sK12 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) )
| ( ( sK12 @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
!= $true )
| spl17_11 ),
inference(trivial_inequality_removal,[status(thm)],[f138]) ).
thf(f138,plain,
( ( ( sK12 @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
!= $true )
| ( ( sK6 @ ( sK9 @ ( sK11 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) )
!= ( sK6 @ ( sK9 @ ( sK11 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) ) )
| ( $true
!= ( sK12 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) )
| spl17_11 ),
inference(superposition,[status(thm)],[f120,f38]) ).
thf(f38,plain,
! [X16: g,X17: g] :
( ( ( sK10 @ ( sK9 @ X16 ) @ ( sK9 @ X17 ) )
= ( sK9 @ ( sK11 @ X16 @ X17 ) ) )
| ( $true
!= ( sK12 @ X17 ) )
| ( $true
!= ( sK12 @ X16 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f120,plain,
( ( ( sK6 @ ( sK9 @ ( sK11 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) )
!= ( sK6 @ ( sK10 @ ( sK9 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) @ ( sK9 @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) ) )
| spl17_11 ),
inference(avatar_component_clause,[status(thm)],[f118]) ).
thf(f137,plain,
( ~ spl17_1
| spl17_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f136]) ).
thf(f136,plain,
( $false
| ~ spl17_1
| spl17_12 ),
inference(subsumption_resolution,[status(thm)],[f135,f47]) ).
thf(f135,plain,
( ( $true
!= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
| spl17_12 ),
inference(trivial_inequality_removal,[status(thm)],[f134]) ).
thf(f134,plain,
( ( $true != $true )
| ( $true
!= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
| spl17_12 ),
inference(superposition,[status(thm)],[f133,f27]) ).
thf(f133,plain,
( ( ( sK12 @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
!= $true )
| spl17_12 ),
inference(trivial_inequality_removal,[status(thm)],[f132]) ).
thf(f132,plain,
( ( $true != $true )
| ( ( sK12 @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
!= $true )
| spl17_12 ),
inference(superposition,[status(thm)],[f124,f41]) ).
thf(f124,plain,
( ( $true
!= ( sK8 @ ( sK9 @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) )
| spl17_12 ),
inference(avatar_component_clause,[status(thm)],[f122]) ).
thf(f122,definition,
( spl17_12
<=> ( $true
= ( sK8 @ ( sK9 @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_12])],[avatar_definition]) ).
thf(f131,plain,
( ~ spl17_1
| spl17_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f130]) ).
thf(f130,plain,
( $false
| ~ spl17_1
| spl17_10 ),
inference(subsumption_resolution,[status(thm)],[f129,f47]) ).
thf(f129,plain,
( ( $true
!= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
| spl17_10 ),
inference(trivial_inequality_removal,[status(thm)],[f128]) ).
thf(f128,plain,
( ( $true != $true )
| ( $true
!= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
| spl17_10 ),
inference(superposition,[status(thm)],[f127,f29]) ).
thf(f127,plain,
( ( $true
!= ( sK12 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) )
| spl17_10 ),
inference(trivial_inequality_removal,[status(thm)],[f126]) ).
thf(f126,plain,
( ( $true
!= ( sK12 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) )
| ( $true != $true )
| spl17_10 ),
inference(superposition,[status(thm)],[f116,f41]) ).
thf(f116,plain,
( ( ( sK8 @ ( sK9 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) )
!= $true )
| spl17_10 ),
inference(avatar_component_clause,[status(thm)],[f114]) ).
thf(f114,definition,
( spl17_10
<=> ( ( sK8 @ ( sK9 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_10])],[avatar_definition]) ).
thf(f125,plain,
( ~ spl17_10
| ~ spl17_11
| ~ spl17_12
| ~ spl17_1 ),
inference(avatar_split_clause,[status(thm)],[f112,f45,f122,f118,f114]) ).
thf(f112,plain,
( ( $true
!= ( sK8 @ ( sK9 @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) )
| ( ( sK6 @ ( sK9 @ ( sK11 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) )
!= ( sK6 @ ( sK10 @ ( sK9 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) @ ( sK9 @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) ) )
| ( ( sK8 @ ( sK9 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) )
!= $true )
| ~ spl17_1 ),
inference(superposition,[status(thm)],[f108,f40]) ).
thf(f40,plain,
! [X12: b,X13: b] :
( ( ( sK6 @ ( sK10 @ X12 @ X13 ) )
= ( sK7 @ ( sK6 @ X12 ) @ ( sK6 @ X13 ) ) )
| ( $true
!= ( sK8 @ X13 ) )
| ( $true
!= ( sK8 @ X12 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f108,plain,
( ( ( sK6 @ ( sK9 @ ( sK11 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) )
!= ( sK7 @ ( sK6 @ ( sK9 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) @ ( sK6 @ ( sK9 @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) ) )
| ~ spl17_1 ),
inference(trivial_inequality_removal,[status(thm)],[f107]) ).
thf(f107,plain,
( ( ( sK6 @ ( sK9 @ ( sK11 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) )
!= ( sK7 @ ( sK6 @ ( sK9 @ ( sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) @ ( sK6 @ ( sK9 @ ( sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) ) ) ) )
| ( $true != $true )
| ~ spl17_1 ),
inference(superposition,[status(thm)],[f28,f47]) ).
thf(f28,plain,
! [X2: g > b,X3: b > a,X0: g > $o,X1: g > g > g,X4: a > a > a] :
( ( $true
!= ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
| ( ( X3 @ ( X2 @ ( X1 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) )
!= ( X4 @ ( X3 @ ( X2 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) @ ( X3 @ ( X2 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f106,plain,
( ~ spl17_3
| ~ spl17_8 ),
inference(avatar_split_clause,[status(thm)],[f105,f82,f53]) ).
thf(f53,definition,
( spl17_3
<=> ( ( sP1 @ sK13 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_3])],[avatar_definition]) ).
thf(f82,definition,
( spl17_8
<=> ( ( sK13 @ ( sK3 @ sK13 @ sK7 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_8])],[avatar_definition]) ).
thf(f105,plain,
( ( ( sP1 @ sK13 @ sK7 )
!= $true )
| ~ spl17_8 ),
inference(subsumption_resolution,[status(thm)],[f104,f24]) ).
thf(f24,plain,
! [X0: a > a > a,X1: a > $o] :
( ( $true
= ( X1 @ ( sK2 @ X1 @ X0 ) ) )
| ( $true
!= ( sP1 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f14,plain,
! [X0: a > a > a,X1: a > $o] :
( ( ( ( X1 @ ( X0 @ ( sK3 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) ) )
!= $true )
& ( $true
= ( X1 @ ( sK3 @ X1 @ X0 ) ) )
& ( $true
= ( X1 @ ( sK2 @ X1 @ X0 ) ) ) )
| ( $true
!= ( sP1 @ X1 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f12,f13]) ).
thf(f13,plain,
! [X0: a > a > a,X1: a > $o] :
( ? [X2: a,X3: a] :
( ( $true
!= ( X1 @ ( X0 @ X3 @ X2 ) ) )
& ( $true
= ( X1 @ X3 ) )
& ( $true
= ( X1 @ X2 ) ) )
=> ( ( ( X1 @ ( X0 @ ( sK3 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) ) )
!= $true )
& ( $true
= ( X1 @ ( sK3 @ X1 @ X0 ) ) )
& ( $true
= ( X1 @ ( sK2 @ X1 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X0: a > a > a,X1: a > $o] :
( ? [X2: a,X3: a] :
( ( $true
!= ( X1 @ ( X0 @ X3 @ X2 ) ) )
& ( $true
= ( X1 @ X3 ) )
& ( $true
= ( X1 @ X2 ) ) )
| ( $true
!= ( sP1 @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
! [X2: a > a > a,X0: a > $o] :
( ? [X27: a,X28: a] :
( ( $true
!= ( X0 @ ( X2 @ X28 @ X27 ) ) )
& ( $true
= ( X0 @ X28 ) )
& ( $true
= ( X0 @ X27 ) ) )
| ( $true
!= ( sP1 @ X0 @ X2 ) ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f104,plain,
( ( $true
!= ( sK13 @ ( sK2 @ sK13 @ sK7 ) ) )
| ( ( sP1 @ sK13 @ sK7 )
!= $true )
| ~ spl17_8 ),
inference(subsumption_resolution,[status(thm)],[f79,f83]) ).
thf(f83,plain,
( ( ( sK13 @ ( sK3 @ sK13 @ sK7 ) )
= $true )
| ~ spl17_8 ),
inference(avatar_component_clause,[status(thm)],[f82]) ).
thf(f79,plain,
( ( ( sP1 @ sK13 @ sK7 )
!= $true )
| ( $true
!= ( sK13 @ ( sK2 @ sK13 @ sK7 ) ) )
| ( ( sK13 @ ( sK3 @ sK13 @ sK7 ) )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ( $true
!= ( sK13 @ ( sK2 @ sK13 @ sK7 ) ) )
| ( ( sP1 @ sK13 @ sK7 )
!= $true )
| ( ( sK13 @ ( sK3 @ sK13 @ sK7 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f26,f42]) ).
thf(f42,plain,
! [X10: a,X9: a] :
( ( $true
= ( sK13 @ ( sK7 @ X9 @ X10 ) ) )
| ( $true
!= ( sK13 @ X9 ) )
| ( ( sK13 @ X10 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f26,plain,
! [X0: a > a > a,X1: a > $o] :
( ( ( X1 @ ( X0 @ ( sK3 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) ) )
!= $true )
| ( $true
!= ( sP1 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f93,plain,
( ~ spl17_3
| spl17_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f92]) ).
thf(f92,plain,
( $false
| ~ spl17_3
| spl17_8 ),
inference(subsumption_resolution,[status(thm)],[f91,f55]) ).
thf(f55,plain,
( ( ( sP1 @ sK13 @ sK7 )
= $true )
| ~ spl17_3 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f91,plain,
( ( ( sP1 @ sK13 @ sK7 )
!= $true )
| spl17_8 ),
inference(trivial_inequality_removal,[status(thm)],[f90]) ).
thf(f90,plain,
( ( $true != $true )
| ( ( sP1 @ sK13 @ sK7 )
!= $true )
| spl17_8 ),
inference(superposition,[status(thm)],[f84,f25]) ).
thf(f25,plain,
! [X0: a > a > a,X1: a > $o] :
( ( $true
= ( X1 @ ( sK3 @ X1 @ X0 ) ) )
| ( $true
!= ( sP1 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f84,plain,
( ( ( sK13 @ ( sK3 @ sK13 @ sK7 ) )
!= $true )
| spl17_8 ),
inference(avatar_component_clause,[status(thm)],[f82]) ).
thf(f77,plain,
( ~ spl17_7
| spl17_1
| spl17_3
| ~ spl17_5 ),
inference(avatar_split_clause,[status(thm)],[f32,f62,f53,f45,f72]) ).
thf(f32,plain,
( ( $true
= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
| ( ( sP1 @ sK13 @ sK7 )
= $true )
| ( $true
!= ( sK13 @ ( sK6 @ ( sK9 @ sK16 ) ) ) )
| ( $true
!= ( sK12 @ ( sK11 @ sK14 @ sK15 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f76,plain,
( spl17_3
| spl17_2
| spl17_1
| ~ spl17_7 ),
inference(avatar_split_clause,[status(thm)],[f34,f72,f45,f49,f53]) ).
thf(f34,plain,
( ( $true
!= ( sK13 @ ( sK6 @ ( sK9 @ sK16 ) ) ) )
| ( $true
= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
| ( ( sK12 @ sK15 )
= $true )
| ( ( sP1 @ sK13 @ sK7 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f75,plain,
( spl17_3
| ~ spl17_7
| spl17_6
| spl17_1 ),
inference(avatar_split_clause,[status(thm)],[f36,f45,f67,f72,f53]) ).
thf(f36,plain,
( ( $true
!= ( sK13 @ ( sK6 @ ( sK9 @ sK16 ) ) ) )
| ( $true
= ( sK12 @ sK14 ) )
| ( $true
= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
| ( ( sP1 @ sK13 @ sK7 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f70,plain,
( spl17_6
| spl17_1
| spl17_3
| spl17_4 ),
inference(avatar_split_clause,[status(thm)],[f37,f57,f53,f45,f67]) ).
thf(f37,plain,
( ( $true
= ( sK12 @ sK16 ) )
| ( $true
= ( sK12 @ sK14 ) )
| ( $true
= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
| ( ( sP1 @ sK13 @ sK7 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f65,plain,
( spl17_1
| spl17_3
| spl17_4
| ~ spl17_5 ),
inference(avatar_split_clause,[status(thm)],[f33,f62,f57,f53,f45]) ).
thf(f33,plain,
( ( $true
= ( sK12 @ sK16 ) )
| ( $true
= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
| ( ( sP1 @ sK13 @ sK7 )
= $true )
| ( $true
!= ( sK12 @ ( sK11 @ sK14 @ sK15 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f60,plain,
( spl17_1
| spl17_2
| spl17_3
| spl17_4 ),
inference(avatar_split_clause,[status(thm)],[f35,f57,f53,f49,f45]) ).
thf(f35,plain,
( ( $true
= ( sK12 @ sK16 ) )
| ( $true
= ( sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12 ) )
| ( ( sP1 @ sK13 @ sK7 )
= $true )
| ( ( sK12 @ sK15 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU904^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n008.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:36:24 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.27/0.47 ---- Original DTF file ---
% 0.27/0.47 thf(spec,logic,$$dhol).
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 % File : SEU904^5 : TPTP v9.2.1. Released v4.0.0.
% 0.27/0.47 % Domain : Set Theory
% 0.27/0.47 % Problem : TPS problem THM126
% 0.27/0.47 % Version : Especial.
% 0.27/0.47 % English : The composition of homomorphisms of binary operators is a
% 0.27/0.47 % homomorphism. Suggested by [BL+86].
% 0.27/0.47
% 0.27/0.47 % Refs : [BL+86] Boyer et al. (1986), Set Theory in First-Order Logic:
% 0.27/0.47 % : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.27/0.47 % Source : [Bro09]
% 0.27/0.47 % Names : tps_0521 [Bro09]
% 0.27/0.47 % : THM126 [TPS]
% 0.27/0.47
% 0.27/0.47 % Status : Theorem
% 0.27/0.47 % Rating : 0.11 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, 0.14 v6.1.0, 0.29 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 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
% 0.27/0.47 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.27/0.47 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.27/0.47 % Maximal formula atoms : 3 ( 3 avg)
% 0.27/0.47 % Number of connectives : 102 ( 0 ~; 0 |; 19 &; 70 @)
% 0.27/0.47 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.27/0.47 % Maximal formula depth : 22 ( 22 avg)
% 0.27/0.47 % Number of types : 4 ( 3 usr)
% 0.27/0.47 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.27/0.47 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.27/0.47 % Number of variables : 29 ( 0 ^; 29 !; 0 ?; 29 :)
% 0.27/0.47 % SPC : TH0_THM_EQU_NAR
% 0.27/0.47
% 0.27/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.27/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.27/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.27/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.27/0.47 % : Polymorphic definitions expanded.
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 thf(g_type,type,
% 0.27/0.47 g: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(b_type,type,
% 0.27/0.47 b: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(a_type,type,
% 0.27/0.47 a: $tType ).
% 0.27/0.47
% 0.27/0.47 thf(cTHM126_pme,conjecture,
% 0.27/0.47 ! [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] :
% 0.27/0.47 ( ( ! [Xx: g,Xy: g] :
% 0.27/0.47 ( ( ( Xs1 @ Xx )
% 0.27/0.47 & ( Xs1 @ Xy ) )
% 0.27/0.47 => ( Xs1 @ ( Xf1 @ Xx @ Xy ) ) )
% 0.27/0.47 & ! [Xx: b,Xy: b] :
% 0.27/0.47 ( ( ( Xs2 @ Xx )
% 0.27/0.47 & ( Xs2 @ Xy ) )
% 0.27/0.47 => ( Xs2 @ ( Xf2 @ Xx @ Xy ) ) )
% 0.27/0.47 & ! [Xx: g] :
% 0.27/0.47 ( ( Xs1 @ Xx )
% 0.27/0.47 => ( Xs2 @ ( Xh1 @ Xx ) ) )
% 0.27/0.47 & ! [Xx: g,Xy: g] :
% 0.27/0.47 ( ( ( Xs1 @ Xx )
% 0.27/0.47 & ( Xs1 @ Xy ) )
% 0.27/0.47 => ( ( Xh1 @ ( Xf1 @ Xx @ Xy ) )
% 0.27/0.47 = ( Xf2 @ ( Xh1 @ Xx ) @ ( Xh1 @ Xy ) ) ) )
% 0.27/0.47 & ! [Xx: b,Xy: b] :
% 0.27/0.47 ( ( ( Xs2 @ Xx )
% 0.27/0.47 & ( Xs2 @ Xy ) )
% 0.27/0.47 => ( Xs2 @ ( Xf2 @ Xx @ Xy ) ) )
% 0.27/0.47 & ! [Xx: a,Xy: a] :
% 0.27/0.47 ( ( ( Xs3 @ Xx )
% 0.27/0.47 & ( Xs3 @ Xy ) )
% 0.27/0.47 => ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
% 0.27/0.47 & ! [Xx: b] :
% 0.27/0.47 ( ( Xs2 @ Xx )
% 0.27/0.47 => ( Xs3 @ ( Xh2 @ Xx ) ) )
% 0.27/0.47 & ! [Xx: b,Xy: b] :
% 0.27/0.47 ( ( ( Xs2 @ Xx )
% 0.27/0.47 & ( Xs2 @ Xy ) )
% 0.27/0.47 => ( ( Xh2 @ ( Xf2 @ Xx @ Xy ) )
% 0.27/0.47 = ( Xf3 @ ( Xh2 @ Xx ) @ ( Xh2 @ Xy ) ) ) ) )
% 0.27/0.47 => ( ! [Xx: g,Xy: g] :
% 0.27/0.47 ( ( ( Xs1 @ Xx )
% 0.27/0.47 & ( Xs1 @ Xy ) )
% 0.27/0.47 => ( Xs1 @ ( Xf1 @ Xx @ Xy ) ) )
% 0.27/0.47 & ! [Xx: a,Xy: a] :
% 0.27/0.47 ( ( ( Xs3 @ Xx )
% 0.27/0.47 & ( Xs3 @ Xy ) )
% 0.27/0.47 => ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
% 0.27/0.47 & ! [Xx: g] :
% 0.27/0.47 ( ( Xs1 @ Xx )
% 0.27/0.47 => ( Xs3 @ ( Xh2 @ ( Xh1 @ Xx ) ) ) )
% 0.27/0.47 & ! [Xx: g,Xy: g] :
% 0.27/0.47 ( ( ( Xs1 @ Xx )
% 0.27/0.47 & ( Xs1 @ Xy ) )
% 0.27/0.47 => ( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx @ Xy ) ) )
% 0.27/0.47 = ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) @ ( Xh2 @ ( Xh1 @ Xy ) ) ) ) ) ) ) ).
% 0.27/0.47
% 0.27/0.47 %------------------------------------------------------------------------------
% 0.27/0.47 ------------------------
% 1.67/1.32 ---- Embedded in THF ---
% 1.67/1.32 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.32 %%% Generated on Tue Feb 24 12:36:25 EST 2026
% 1.67/1.32 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.32 %%% Logic specification used:
% 1.67/1.32 %%% thf(spec, logic, $$dhol).
% 1.67/1.32
% 1.67/1.32 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.i62NXBbrIK/DTF2DTF26225.p
% See solution above
% 1.67/1.32 ------------------------
% 1.67/1.33 ---- Cleaned THF ---
% 1.67/1.33 thf(g_type,type,
% 1.67/1.33 g: $tType ).
% 1.67/1.33
% 1.67/1.33 thf(b_type,type,
% 1.67/1.33 b: $tType ).
% 1.67/1.33
% 1.67/1.33 thf(a_type,type,
% 1.67/1.33 a: $tType ).
% 1.67/1.33
% 1.67/1.33 thf(cTHM126_pme,conjecture,
% 1.67/1.33 ! [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] :
% 1.67/1.33 ( ( ! [Xx: g,Xy: g] :
% 1.67/1.33 ( ( ( Xs1 @ Xx )
% 1.67/1.33 & ( Xs1 @ Xy ) )
% 1.67/1.33 => ( Xs1 @ ( Xf1 @ Xx @ Xy ) ) )
% 1.67/1.33 & ! [Xx: b,Xy: b] :
% 1.67/1.33 ( ( ( Xs2 @ Xx )
% 1.67/1.33 & ( Xs2 @ Xy ) )
% 1.67/1.33 => ( Xs2 @ ( Xf2 @ Xx @ Xy ) ) )
% 1.67/1.33 & ! [Xx: g] :
% 1.67/1.33 ( ( Xs1 @ Xx )
% 1.67/1.33 => ( Xs2 @ ( Xh1 @ Xx ) ) )
% 1.67/1.33 & ! [Xx: g,Xy: g] :
% 1.67/1.33 ( ( ( Xs1 @ Xx )
% 1.67/1.33 & ( Xs1 @ Xy ) )
% 1.67/1.33 => ( ( Xh1 @ ( Xf1 @ Xx @ Xy ) )
% 1.67/1.33 = ( Xf2 @ ( Xh1 @ Xx ) @ ( Xh1 @ Xy ) ) ) )
% 1.67/1.33 & ! [Xx: b,Xy: b] :
% 1.67/1.33 ( ( ( Xs2 @ Xx )
% 1.67/1.33 & ( Xs2 @ Xy ) )
% 1.67/1.33 => ( Xs2 @ ( Xf2 @ Xx @ Xy ) ) )
% 1.67/1.33 & ! [Xx: a,Xy: a] :
% 1.67/1.33 ( ( ( Xs3 @ Xx )
% 1.67/1.33 & ( Xs3 @ Xy ) )
% 1.67/1.33 => ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
% 1.67/1.33 & ! [Xx: b] :
% 1.67/1.33 ( ( Xs2 @ Xx )
% 1.67/1.33 => ( Xs3 @ ( Xh2 @ Xx ) ) )
% 1.67/1.33 & ! [Xx: b,Xy: b] :
% 1.67/1.33 ( ( ( Xs2 @ Xx )
% 1.67/1.33 & ( Xs2 @ Xy ) )
% 1.67/1.33 => ( ( Xh2 @ ( Xf2 @ Xx @ Xy ) )
% 1.67/1.33 = ( Xf3 @ ( Xh2 @ Xx ) @ ( Xh2 @ Xy ) ) ) ) )
% 1.67/1.33 => ( ! [Xx: g,Xy: g] :
% 1.67/1.33 ( ( ( Xs1 @ Xx )
% 1.67/1.33 & ( Xs1 @ Xy ) )
% 1.67/1.33 => ( Xs1 @ ( Xf1 @ Xx @ Xy ) ) )
% 1.67/1.33 & ! [Xx: a,Xy: a] :
% 1.67/1.33 ( ( ( Xs3 @ Xx )
% 1.67/1.33 & ( Xs3 @ Xy ) )
% 1.67/1.33 => ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
% 1.67/1.33 & ! [Xx: g] :
% 1.67/1.33 ( ( Xs1 @ Xx )
% 1.67/1.33 => ( Xs3 @ ( Xh2 @ ( Xh1 @ Xx ) ) ) )
% 1.67/1.33 & ! [Xx: g,Xy: g] :
% 1.67/1.33 ( ( ( Xs1 @ Xx )
% 1.67/1.33 & ( Xs1 @ Xy ) )
% 1.67/1.33 => ( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx @ Xy ) ) )
% 1.67/1.33 = ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) @ ( Xh2 @ ( Xh1 @ Xy ) ) ) ) ) ) ) ).
% 1.67/1.33 ------------------------
% 1.67/1.35 % (26509)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_26225 for (2999ds/2Mi)
% 1.67/1.35 % (26505)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26225 for (2999ds/183Mi)
% 1.67/1.35 % (26509)Instruction limit reached!
% 1.67/1.35 % (26509)------------------------------
% 1.67/1.35 % (26509)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (26509)Termination reason: Unknown
% 1.67/1.35 % (26509)Termination phase: shuffling
% 1.67/1.35
% 1.67/1.35 % (26509)Memory used [KB]: 1023
% 1.67/1.35 % (26509)Time elapsed: 0.002 s
% 1.67/1.35 % (26509)Instructions burned: 3 (million)
% 1.67/1.35 % (26509)------------------------------
% 1.67/1.35 % (26509)------------------------------
% 1.67/1.35 % (26506)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_26225 for (2999ds/4Mi)
% 1.67/1.35 % (26507)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_26225 for (2999ds/27Mi)
% 1.67/1.35 % (26508)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26225 for (2999ds/2Mi)
% 1.67/1.35 % (26511)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26225 for (2999ds/18Mi)
% 1.67/1.35 % (26510)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_26225 for (2999ds/275Mi)
% 1.67/1.35 % (26508)Instruction limit reached!
% 1.67/1.35 % (26508)------------------------------
% 1.67/1.35 % (26508)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (26508)Termination reason: Unknown
% 1.67/1.35 % (26508)Termination phase: Property scanning
% 1.67/1.35
% 1.67/1.35 % (26508)Memory used [KB]: 1023
% 1.67/1.35 % (26508)Time elapsed: 0.003 s
% 1.67/1.35 % (26508)Instructions burned: 2 (million)
% 1.67/1.35 % (26508)------------------------------
% 1.67/1.35 % (26508)------------------------------
% 1.67/1.35 % (26506)Instruction limit reached!
% 1.67/1.35 % (26506)------------------------------
% 1.67/1.35 % (26506)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (26506)Termination reason: Unknown
% 1.67/1.35 % (26506)Termination phase: Preprocessing 3
% 1.67/1.35
% 1.67/1.35 % (26506)Memory used [KB]: 1023
% 1.67/1.35 % (26506)Time elapsed: 0.004 s
% 1.67/1.35 % (26506)Instructions burned: 4 (million)
% 1.67/1.35 % (26506)------------------------------
% 1.67/1.35 % (26506)------------------------------
% 1.67/1.36 % (26512)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26225 for (2999ds/3Mi)
% 1.67/1.37 % (26511)Instruction limit reached!
% 1.67/1.37 % (26511)------------------------------
% 1.67/1.37 % (26511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (26511)Termination reason: Unknown
% 1.67/1.37 % (26511)Termination phase: Saturation
% 1.67/1.37
% 1.67/1.37 % (26511)Memory used [KB]: 5756
% 1.67/1.37 % (26511)Time elapsed: 0.014 s
% 1.67/1.37 % (26511)Instructions burned: 19 (million)
% 1.67/1.37 % (26511)------------------------------
% 1.67/1.37 % (26511)------------------------------
% 1.67/1.37 % (26512)Instruction limit reached!
% 1.67/1.37 % (26512)------------------------------
% 1.67/1.37 % (26512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (26512)Termination reason: Unknown
% 1.67/1.37 % (26512)Termination phase: Preprocessing 3
% 1.67/1.37
% 1.67/1.37 % (26512)Memory used [KB]: 1023
% 1.67/1.37 % (26512)Time elapsed: 0.004 s
% 1.67/1.37 % (26512)Instructions burned: 4 (million)
% 1.67/1.37 % (26512)------------------------------
% 1.67/1.37 % (26512)------------------------------
% 1.67/1.37 % (26507)Instruction limit reached!
% 1.67/1.37 % (26507)------------------------------
% 1.67/1.37 % (26507)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.37 % (26507)Termination reason: Unknown
% 1.67/1.37 % (26507)Termination phase: Saturation
% 1.67/1.37
% 1.67/1.37 % (26507)Memory used [KB]: 5756
% 1.67/1.37 % (26507)Time elapsed: 0.019 s
% 1.67/1.37 % (26507)Instructions burned: 27 (million)
% 1.67/1.37 % (26507)------------------------------
% 1.67/1.37 % (26507)------------------------------
% 1.67/1.37 % (26513)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_26225 for (2999ds/37Mi)
% 1.67/1.37 % (26514)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_26225 for (2999ds/15Mi)
% 1.67/1.37 % (26510)First to succeed.
% 1.67/1.38 % (26510)Refutation found. Thanks to Tanya!
% 1.67/1.38 % SZS status Theorem for DTF2THF_26225
% 1.67/1.38 % SZS output start Proof for DTF2THF_26225
% 1.67/1.38 thf(type_def_5, type, g: $tType).
% 1.67/1.38 thf(type_def_6, type, b: $tType).
% 1.67/1.38 thf(type_def_8, type, a: $tType).
% 1.67/1.38 thf(func_def_0, type, g: $tType).
% 1.67/1.38 thf(func_def_1, type, b: $tType).
% 1.67/1.38 thf(func_def_2, type, a: $tType).
% 1.67/1.38 thf(func_def_6, type, sP0: (a > a > a) > (b > a) > (g > b) > (g > g > g) > (g > $o) > $o).
% 1.67/1.38 thf(func_def_7, type, sP1: (a > $o) > (a > a > a) > $o).
% 1.67/1.38 thf(func_def_8, type, sK2: (a > $o) > (a > a > a) > a).
% 1.67/1.38 thf(func_def_9, type, sK3: (a > $o) > (a > a > a) > a).
% 1.67/1.38 thf(func_def_10, type, sK4: (a > a > a) > (b > a) > (g > b) > (g > g > g) > (g > $o) > g).
% 1.67/1.38 thf(func_def_11, type, sK5: (a > a > a) > (b > a) > (g > b) > (g > g > g) > (g > $o) > g).
% 1.67/1.38 thf(func_def_12, type, sK6: b > a).
% 1.67/1.38 thf(func_def_13, type, sK7: a > a > a).
% 1.67/1.38 thf(func_def_14, type, sK8: b > $o).
% 1.67/1.38 thf(func_def_15, type, sK9: g > b).
% 1.67/1.38 thf(func_def_16, type, sK10: b > b > b).
% 1.67/1.38 thf(func_def_17, type, sK11: g > g > g).
% 1.67/1.38 thf(func_def_18, type, sK12: g > $o).
% 1.67/1.38 thf(func_def_19, type, sK13: a > $o).
% 1.67/1.38 thf(func_def_20, type, sK14: g).
% 1.67/1.38 thf(func_def_21, type, sK15: g).
% 1.67/1.38 thf(func_def_22, type, sK16: g).
% 1.67/1.38 thf(func_def_24, type, ph18: !>[X0: $tType]:(X0)).
% 1.67/1.38 thf(f171,plain,(
% 1.67/1.38 $false),
% 1.67/1.38 inference(avatar_sat_refutation,[status(thm)],[f60,f65,f70,f75,f76,f77,f93,f106,f125,f131,f137,f148,f152,f157,f163,f170])).
% 1.67/1.38 thf(f170,plain,(
% 1.67/1.38 ~spl17_1 | spl17_14),
% 1.67/1.38 inference(avatar_contradiction_clause,[status(thm)],[f169])).
% 1.67/1.38 thf(f169,plain,(
% 1.67/1.38 $false | (~spl17_1 | spl17_14)),
% 1.67/1.38 inference(subsumption_resolution,[status(thm)],[f168,f47])).
% 1.67/1.38 thf(f47,plain,(
% 1.67/1.38 ($true = (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) | ~spl17_1),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.67/1.38 thf(f45,definition,(
% 1.67/1.38 spl17_1 <=> ($true = (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl17_1])],[avatar_definition])).
% 1.67/1.38 thf(f168,plain,(
% 1.67/1.38 ($true != (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) | spl17_14),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f167])).
% 1.67/1.38 thf(f167,plain,(
% 1.67/1.38 ($true != (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) | ($true != $true) | spl17_14),
% 1.67/1.38 inference(superposition,[status(thm)],[f147,f29])).
% 1.67/1.38 thf(f29,plain,(
% 1.67/1.38 ( ! [X2 : g > b,X3 : b > a,X0 : g > $o,X1 : g > g > g,X4 : a > a > a] : (($true = (X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) | ($true != (sP0 @ X4 @ X3 @ X2 @ X1 @ X0))) )),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f18])).
% 1.67/1.38 thf(f18,plain,(
% 1.67/1.38 ! [X0 : g > $o,X1 : g > g > g,X2 : g > b,X3 : b > a,X4 : a > a > a] : ((($true = (X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) & ((X3 @ (X2 @ (X1 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0) @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)))) != (X4 @ (X3 @ (X2 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) @ (X3 @ (X2 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0))))) & ($true = (X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)))) | ($true != (sP0 @ X4 @ X3 @ X2 @ X1 @ X0)))),
% 1.67/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f16,f17])).
% 1.67/1.38 thf(f17,plain,(
% 1.67/1.38 ! [X0 : g > $o,X1 : g > g > g,X2 : g > b,X3 : b > a,X4 : a > a > a] : (? [X5 : g,X6 : g] : (($true = (X0 @ X5)) & ((X4 @ (X3 @ (X2 @ X5)) @ (X3 @ (X2 @ X6))) != (X3 @ (X2 @ (X1 @ X5 @ X6)))) & ($true = (X0 @ X6))) => (($true = (X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) & ((X3 @ (X2 @ (X1 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0) @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)))) != (X4 @ (X3 @ (X2 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) @ (X3 @ (X2 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0))))) & ($true = (X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)))))),
% 1.67/1.38 introduced(definition,[],[choice_axiom])).
% 1.67/1.38 thf(f16,plain,(
% 1.67/1.38 ! [X0 : g > $o,X1 : g > g > g,X2 : g > b,X3 : b > a,X4 : a > a > a] : (? [X5 : g,X6 : g] : (($true = (X0 @ X5)) & ((X4 @ (X3 @ (X2 @ X5)) @ (X3 @ (X2 @ X6))) != (X3 @ (X2 @ (X1 @ X5 @ X6)))) & ($true = (X0 @ X6))) | ($true != (sP0 @ X4 @ X3 @ X2 @ X1 @ X0)))),
% 1.67/1.38 inference(rectify,[status(thm)],[f15])).
% 1.67/1.38 thf(f15,plain,(
% 1.67/1.38 ! [X3 : g > $o,X7 : g > g > g,X5 : g > b,X4 : b > a,X2 : a > a > a] : (? [X22 : g,X23 : g] : (($true = (X3 @ X22)) & ((X2 @ (X4 @ (X5 @ X22)) @ (X4 @ (X5 @ X23))) != (X4 @ (X5 @ (X7 @ X22 @ X23)))) & ($true = (X3 @ X23))) | ($true != (sP0 @ X2 @ X4 @ X5 @ X7 @ X3)))),
% 1.67/1.38 inference(nnf_transformation,[status(thm)],[f8])).
% 1.67/1.38 thf(f8,plain,(
% 1.67/1.38 ! [X3 : g > $o,X7 : g > g > g,X5 : g > b,X4 : b > a,X2 : a > a > a] : (? [X22 : g,X23 : g] : (($true = (X3 @ X22)) & ((X2 @ (X4 @ (X5 @ X22)) @ (X4 @ (X5 @ X23))) != (X4 @ (X5 @ (X7 @ X22 @ X23)))) & ($true = (X3 @ X23))) | ~($true = (sP0 @ X2 @ X4 @ X5 @ X7 @ X3)))),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.67/1.38 thf(f147,plain,(
% 1.67/1.38 ($true != (sK12 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))) | spl17_14),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f145])).
% 1.67/1.38 thf(f145,definition,(
% 1.67/1.38 spl17_14 <=> ($true = (sK12 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)))),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl17_14])],[avatar_definition])).
% 1.67/1.38 thf(f163,plain,(
% 1.67/1.38 ~spl17_2 | spl17_5 | ~spl17_6),
% 1.67/1.38 inference(avatar_split_clause,[status(thm)],[f160,f67,f62,f49])).
% 1.67/1.38 thf(f49,definition,(
% 1.67/1.38 spl17_2 <=> ((sK12 @ sK15) = $true)),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl17_2])],[avatar_definition])).
% 1.67/1.38 thf(f62,definition,(
% 1.67/1.38 spl17_5 <=> ($true = (sK12 @ (sK11 @ sK14 @ sK15)))),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl17_5])],[avatar_definition])).
% 1.67/1.38 thf(f67,definition,(
% 1.67/1.38 spl17_6 <=> ($true = (sK12 @ sK14))),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl17_6])],[avatar_definition])).
% 1.67/1.38 thf(f160,plain,(
% 1.67/1.38 ((sK12 @ sK15) != $true) | (spl17_5 | ~spl17_6)),
% 1.67/1.38 inference(subsumption_resolution,[status(thm)],[f159,f69])).
% 1.67/1.38 thf(f69,plain,(
% 1.67/1.38 ($true = (sK12 @ sK14)) | ~spl17_6),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f67])).
% 1.67/1.38 thf(f159,plain,(
% 1.67/1.38 ($true != (sK12 @ sK14)) | ((sK12 @ sK15) != $true) | spl17_5),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f158])).
% 1.67/1.38 thf(f158,plain,(
% 1.67/1.38 ((sK12 @ sK15) != $true) | ($true != (sK12 @ sK14)) | ($true != $true) | spl17_5),
% 1.67/1.38 inference(superposition,[status(thm)],[f64,f30])).
% 1.67/1.38 thf(f30,plain,(
% 1.67/1.38 ( ! [X24 : g,X23 : g] : (($true = (sK12 @ (sK11 @ X23 @ X24))) | ($true != (sK12 @ X23)) | ($true != (sK12 @ X24))) )),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.38 thf(f23,plain,(
% 1.67/1.38 ! [X8 : b] : (($true = (sK13 @ (sK6 @ X8))) | ($true != (sK8 @ X8))) & ! [X9 : a,X10 : a] : (($true = (sK13 @ (sK7 @ X9 @ X10))) | ((sK13 @ X10) != $true) | ($true != (sK13 @ X9))) & ! [X11 : g] : (($true != (sK12 @ X11)) | ($true = (sK8 @ (sK9 @ X11)))) & ! [X12 : b,X13 : b] : (($true != (sK8 @ X12)) | ($true != (sK8 @ X13)) | ((sK6 @ (sK10 @ X12 @ X13)) = (sK7 @ (sK6 @ X12) @ (sK6 @ X13)))) & ! [X14 : b,X15 : b] : (((sK8 @ X15) != $true) | ($true != (sK8 @ X14)) | ($true = (sK8 @ (sK10 @ X15 @ X14)))) & ! [X16 : g,X17 : g] : (($true != (sK12 @ X17)) | ($true != (sK12 @ X16)) | ((sK10 @ (sK9 @ X16) @ (sK9 @ X17)) = (sK9 @ (sK11 @ X16 @ X17)))) & ((($true = (sK12 @ sK14)) & ((sK12 @ sK15) = $true) & ($true != (sK12 @ (sK11 @ sK14 @ sK15)))) | (($true = (sK12 @ sK16)) & ($true != (sK13 @ (sK6 @ (sK9 @ sK16))))) | ((sP1 @ sK13 @ sK7) = $true) | ($true = (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))) & ! [X21 : b,X22 : b] : (($true != (sK8 @ X22)) | ((sK8 @ (sK10 @ X21 @ X22)) = $true) | ($true != (sK8 @ X21))) & ! [X23 : g,X24 : g] : (($true != (sK12 @ X24)) | ($true != (sK12 @ X23)) | ($true = (sK12 @ (sK11 @ X23 @ X24))))),
% 1.67/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16])],[f19,f22,f21,f20])).
% 1.67/1.38 thf(f20,plain,(
% 1.67/1.38 ? [X0 : b > a,X1 : a > a > a,X2 : b > $o,X3 : g > b,X4 : b > b > b,X5 : g > g > g,X6 : g > $o,X7 : a > $o] : (! [X8 : b] : (($true = (X7 @ (X0 @ X8))) | ($true != (X2 @ X8))) & ! [X9 : a,X10 : a] : (((X7 @ (X1 @ X9 @ X10)) = $true) | ($true != (X7 @ X10)) | ($true != (X7 @ X9))) & ! [X11 : g] : (($true != (X6 @ X11)) | ($true = (X2 @ (X3 @ X11)))) & ! [X12 : b,X13 : b] : (($true != (X2 @ X12)) | ($true != (X2 @ X13)) | ((X1 @ (X0 @ X12) @ (X0 @ X13)) = (X0 @ (X4 @ X12 @ X13)))) & ! [X14 : b,X15 : b] : (($true != (X2 @ X15)) | ($true != (X2 @ X14)) | ($true = (X2 @ (X4 @ X15 @ X14)))) & ! [X16 : g,X17 : g] : (($true != (X6 @ X17)) | ((X6 @ X16) != $true) | ((X4 @ (X3 @ X16) @ (X3 @ X17)) = (X3 @ (X5 @ X16 @ X17)))) & (? [X18 : g,X19 : g] : (((X6 @ X18) = $true) & ($true = (X6 @ X19)) & ((X6 @ (X5 @ X18 @ X19)) != $true)) | ? [X20 : g] : (($true = (X6 @ X20)) & ((X7 @ (X0 @ (X3 @ X20))) != $true)) | ($true = (sP1 @ X7 @ X1)) | ($true = (sP0 @ X1 @ X0 @ X3 @ X5 @ X6))) & ! [X21 : b,X22 : b] : (($true != (X2 @ X22)) | ($true = (X2 @ (X4 @ X21 @ X22))) | ($true != (X2 @ X21))) & ! [X23 : g,X24 : g] : (($true != (X6 @ X24)) | ($true != (X6 @ X23)) | ($true = (X6 @ (X5 @ X23 @ X24))))) => (! [X8 : b] : (($true = (sK13 @ (sK6 @ X8))) | ($true != (sK8 @ X8))) & ! [X10 : a,X9 : a] : (($true = (sK13 @ (sK7 @ X9 @ X10))) | ((sK13 @ X10) != $true) | ($true != (sK13 @ X9))) & ! [X11 : g] : (($true != (sK12 @ X11)) | ($true = (sK8 @ (sK9 @ X11)))) & ! [X13 : b,X12 : b] : (($true != (sK8 @ X12)) | ($true != (sK8 @ X13)) | ((sK6 @ (sK10 @ X12 @ X13)) = (sK7 @ (sK6 @ X12) @ (sK6 @ X13)))) & ! [X15 : b,X14 : b] : (((sK8 @ X15) != $true) | ($true != (sK8 @ X14)) | ($true = (sK8 @ (sK10 @ X15 @ X14)))) & ! [X17 : g,X16 : g] : (($true != (sK12 @ X17)) | ($true != (sK12 @ X16)) | ((sK10 @ (sK9 @ X16) @ (sK9 @ X17)) = (sK9 @ (sK11 @ X16 @ X17)))) & (? [X19 : g,X18 : g] : (($true = (sK12 @ X18)) & ($true = (sK12 @ X19)) & ($true != (sK12 @ (sK11 @ X18 @ X19)))) | ? [X20 : g] : (($true = (sK12 @ X20)) & ($true != (sK13 @ (sK6 @ (sK9 @ X20))))) | ((sP1 @ sK13 @ sK7) = $true) | ($true = (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))) & ! [X22 : b,X21 : b] : (($true != (sK8 @ X22)) | ((sK8 @ (sK10 @ X21 @ X22)) = $true) | ($true != (sK8 @ X21))) & ! [X24 : g,X23 : g] : (($true != (sK12 @ X24)) | ($true != (sK12 @ X23)) | ($true = (sK12 @ (sK11 @ X23 @ X24)))))),
% 1.67/1.38 introduced(definition,[],[choice_axiom])).
% 1.67/1.38 thf(f21,plain,(
% 1.67/1.38 ? [X19 : g,X18 : g] : (($true = (sK12 @ X18)) & ($true = (sK12 @ X19)) & ($true != (sK12 @ (sK11 @ X18 @ X19)))) => (($true = (sK12 @ sK14)) & ((sK12 @ sK15) = $true) & ($true != (sK12 @ (sK11 @ sK14 @ sK15))))),
% 1.67/1.38 introduced(definition,[],[choice_axiom])).
% 1.67/1.38 thf(f22,plain,(
% 1.67/1.38 ? [X20 : g] : (($true = (sK12 @ X20)) & ($true != (sK13 @ (sK6 @ (sK9 @ X20))))) => (($true = (sK12 @ sK16)) & ($true != (sK13 @ (sK6 @ (sK9 @ sK16)))))),
% 1.67/1.38 introduced(definition,[],[choice_axiom])).
% 1.67/1.38 thf(f19,plain,(
% 1.67/1.38 ? [X0 : b > a,X1 : a > a > a,X2 : b > $o,X3 : g > b,X4 : b > b > b,X5 : g > g > g,X6 : g > $o,X7 : a > $o] : (! [X8 : b] : (($true = (X7 @ (X0 @ X8))) | ($true != (X2 @ X8))) & ! [X9 : a,X10 : a] : (((X7 @ (X1 @ X9 @ X10)) = $true) | ($true != (X7 @ X10)) | ($true != (X7 @ X9))) & ! [X11 : g] : (($true != (X6 @ X11)) | ($true = (X2 @ (X3 @ X11)))) & ! [X12 : b,X13 : b] : (($true != (X2 @ X12)) | ($true != (X2 @ X13)) | ((X1 @ (X0 @ X12) @ (X0 @ X13)) = (X0 @ (X4 @ X12 @ X13)))) & ! [X14 : b,X15 : b] : (($true != (X2 @ X15)) | ($true != (X2 @ X14)) | ($true = (X2 @ (X4 @ X15 @ X14)))) & ! [X16 : g,X17 : g] : (($true != (X6 @ X17)) | ((X6 @ X16) != $true) | ((X4 @ (X3 @ X16) @ (X3 @ X17)) = (X3 @ (X5 @ X16 @ X17)))) & (? [X18 : g,X19 : g] : (((X6 @ X18) = $true) & ($true = (X6 @ X19)) & ((X6 @ (X5 @ X18 @ X19)) != $true)) | ? [X20 : g] : (($true = (X6 @ X20)) & ((X7 @ (X0 @ (X3 @ X20))) != $true)) | ($true = (sP1 @ X7 @ X1)) | ($true = (sP0 @ X1 @ X0 @ X3 @ X5 @ X6))) & ! [X21 : b,X22 : b] : (($true != (X2 @ X22)) | ($true = (X2 @ (X4 @ X21 @ X22))) | ($true != (X2 @ X21))) & ! [X23 : g,X24 : g] : (($true != (X6 @ X24)) | ($true != (X6 @ X23)) | ($true = (X6 @ (X5 @ X23 @ X24)))))),
% 1.67/1.38 inference(rectify,[status(thm)],[f10])).
% 1.67/1.38 thf(f10,plain,(
% 1.67/1.38 ? [X4 : b > a,X2 : a > a > a,X1 : b > $o,X5 : g > b,X6 : b > b > b,X7 : g > g > g,X3 : g > $o,X0 : a > $o] : (! [X13 : b] : (($true = (X0 @ (X4 @ X13))) | ($true != (X1 @ X13))) & ! [X12 : a,X11 : a] : (($true = (X0 @ (X2 @ X12 @ X11))) | ($true != (X0 @ X11)) | ($true != (X0 @ X12))) & ! [X8 : g] : (($true != (X3 @ X8)) | ($true = (X1 @ (X5 @ X8)))) & ! [X19 : b,X18 : b] : (($true != (X1 @ X19)) | ($true != (X1 @ X18)) | ((X4 @ (X6 @ X19 @ X18)) = (X2 @ (X4 @ X19) @ (X4 @ X18)))) & ! [X14 : b,X15 : b] : (($true != (X1 @ X15)) | ($true != (X1 @ X14)) | ($true = (X1 @ (X6 @ X15 @ X14)))) & ! [X17 : g,X16 : g] : (((X3 @ X16) != $true) | ($true != (X3 @ X17)) | ((X5 @ (X7 @ X17 @ X16)) = (X6 @ (X5 @ X17) @ (X5 @ X16)))) & (? [X24 : g,X25 : g] : (((X3 @ X24) = $true) & ($true = (X3 @ X25)) & ($true != (X3 @ (X7 @ X24 @ X25)))) | ? [X26 : g] : (($true = (X3 @ X26)) & ($true != (X0 @ (X4 @ (X5 @ X26))))) | ($true = (sP1 @ X0 @ X2)) | ($true = (sP0 @ X2 @ X4 @ X5 @ X7 @ X3))) & ! [X20 : b,X21 : b] : (($true != (X1 @ X21)) | ((X1 @ (X6 @ X20 @ X21)) = $true) | ((X1 @ X20) != $true)) & ! [X10 : g,X9 : g] : (($true != (X3 @ X9)) | ($true != (X3 @ X10)) | ($true = (X3 @ (X7 @ X10 @ X9)))))),
% 1.67/1.38 inference(definition_folding,[status(thm)],[f7,f9,f8])).
% 1.67/1.38 thf(f9,plain,(
% 1.67/1.38 ! [X2 : a > a > a,X0 : a > $o] : (? [X27 : a,X28 : a] : (($true != (X0 @ (X2 @ X28 @ X27))) & ($true = (X0 @ X28)) & ($true = (X0 @ X27))) | ~($true = (sP1 @ X0 @ X2)))),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.67/1.38 thf(f7,plain,(
% 1.67/1.38 ? [X4 : b > a,X2 : a > a > a,X1 : b > $o,X5 : g > b,X6 : b > b > b,X7 : g > g > g,X3 : g > $o,X0 : a > $o] : (! [X13 : b] : (($true = (X0 @ (X4 @ X13))) | ($true != (X1 @ X13))) & ! [X12 : a,X11 : a] : (($true = (X0 @ (X2 @ X12 @ X11))) | ($true != (X0 @ X11)) | ($true != (X0 @ X12))) & ! [X8 : g] : (($true != (X3 @ X8)) | ($true = (X1 @ (X5 @ X8)))) & ! [X19 : b,X18 : b] : (($true != (X1 @ X19)) | ($true != (X1 @ X18)) | ((X4 @ (X6 @ X19 @ X18)) = (X2 @ (X4 @ X19) @ (X4 @ X18)))) & ! [X14 : b,X15 : b] : (($true != (X1 @ X15)) | ($true != (X1 @ X14)) | ($true = (X1 @ (X6 @ X15 @ X14)))) & ! [X17 : g,X16 : g] : (((X3 @ X16) != $true) | ($true != (X3 @ X17)) | ((X5 @ (X7 @ X17 @ X16)) = (X6 @ (X5 @ X17) @ (X5 @ X16)))) & (? [X24 : g,X25 : g] : (((X3 @ X24) = $true) & ($true = (X3 @ X25)) & ($true != (X3 @ (X7 @ X24 @ X25)))) | ? [X26 : g] : (($true = (X3 @ X26)) & ($true != (X0 @ (X4 @ (X5 @ X26))))) | ? [X27 : a,X28 : a] : (($true != (X0 @ (X2 @ X28 @ X27))) & ($true = (X0 @ X28)) & ($true = (X0 @ X27))) | ? [X22 : g,X23 : g] : (($true = (X3 @ X22)) & ((X2 @ (X4 @ (X5 @ X22)) @ (X4 @ (X5 @ X23))) != (X4 @ (X5 @ (X7 @ X22 @ X23)))) & ($true = (X3 @ X23)))) & ! [X20 : b,X21 : b] : (($true != (X1 @ X21)) | ((X1 @ (X6 @ X20 @ X21)) = $true) | ((X1 @ X20) != $true)) & ! [X10 : g,X9 : g] : (($true != (X3 @ X9)) | ($true != (X3 @ X10)) | ($true = (X3 @ (X7 @ X10 @ X9)))))),
% 1.67/1.38 inference(flattening,[status(thm)],[f6])).
% 1.67/1.38 thf(f6,plain,(
% 1.67/1.38 ? [X6 : b > b > b,X3 : g > $o,X4 : b > a,X5 : g > b,X1 : b > $o,X0 : a > $o,X7 : g > g > g,X2 : a > a > a] : ((? [X25 : g,X24 : g] : (($true != (X3 @ (X7 @ X24 @ X25))) & (((X3 @ X24) = $true) & ($true = (X3 @ X25)))) | ? [X27 : a,X28 : a] : (($true != (X0 @ (X2 @ X28 @ X27))) & (($true = (X0 @ X28)) & ($true = (X0 @ X27)))) | ? [X23 : g,X22 : g] : (((X2 @ (X4 @ (X5 @ X22)) @ (X4 @ (X5 @ X23))) != (X4 @ (X5 @ (X7 @ X22 @ X23)))) & (($true = (X3 @ X23)) & ($true = (X3 @ X22)))) | ? [X26 : g] : (($true = (X3 @ X26)) & ($true != (X0 @ (X4 @ (X5 @ X26)))))) & (! [X11 : a,X12 : a] : (($true = (X0 @ (X2 @ X12 @ X11))) | (($true != (X0 @ X11)) | ($true != (X0 @ X12)))) & ! [X13 : b] : (($true = (X0 @ (X4 @ X13))) | ($true != (X1 @ X13))) & ! [X14 : b,X15 : b] : (($true = (X1 @ (X6 @ X15 @ X14))) | (($true != (X1 @ X14)) | ($true != (X1 @ X15)))) & ! [X18 : b,X19 : b] : (((X4 @ (X6 @ X19 @ X18)) = (X2 @ (X4 @ X19) @ (X4 @ X18))) | (($true != (X1 @ X19)) | ($true != (X1 @ X18)))) & ! [X9 : g,X10 : g] : (($true = (X3 @ (X7 @ X10 @ X9))) | (($true != (X3 @ X10)) | ($true != (X3 @ X9)))) & ! [X16 : g,X17 : g] : (((X5 @ (X7 @ X17 @ X16)) = (X6 @ (X5 @ X17) @ (X5 @ X16))) | (((X3 @ X16) != $true) | ($true != (X3 @ X17)))) & ! [X20 : b,X21 : b] : (((X1 @ (X6 @ X20 @ X21)) = $true) | (($true != (X1 @ X21)) | ((X1 @ X20) != $true))) & ! [X8 : g] : (($true != (X3 @ X8)) | ($true = (X1 @ (X5 @ X8))))))),
% 1.67/1.38 inference(ennf_transformation,[status(thm)],[f5])).
% 1.67/1.38 thf(f5,plain,(
% 1.67/1.38 ~! [X6 : b > b > b,X3 : g > $o,X4 : b > a,X5 : g > b,X1 : b > $o,X0 : a > $o,X7 : g > g > g,X2 : a > a > a] : ((! [X11 : a,X12 : a] : ((($true = (X0 @ X11)) & ($true = (X0 @ X12))) => ($true = (X0 @ (X2 @ X12 @ X11)))) & ! [X13 : b] : (($true = (X1 @ X13)) => ($true = (X0 @ (X4 @ X13)))) & ! [X14 : b,X15 : b] : ((($true = (X1 @ X14)) & ($true = (X1 @ X15))) => ($true = (X1 @ (X6 @ X15 @ X14)))) & ! [X18 : b,X19 : b] : ((($true = (X1 @ X19)) & ($true = (X1 @ X18))) => ((X4 @ (X6 @ X19 @ X18)) = (X2 @ (X4 @ X19) @ (X4 @ X18)))) & ! [X9 : g,X10 : g] : ((($true = (X3 @ X10)) & ($true = (X3 @ X9))) => ($true = (X3 @ (X7 @ X10 @ X9)))) & ! [X16 : g,X17 : g] : ((((X3 @ X16) = $true) & ($true = (X3 @ X17))) => ((X5 @ (X7 @ X17 @ X16)) = (X6 @ (X5 @ X17) @ (X5 @ X16)))) & ! [X20 : b,X21 : b] : ((($true = (X1 @ X21)) & ((X1 @ X20) = $true)) => ((X1 @ (X6 @ X20 @ X21)) = $true)) & ! [X8 : g] : (($true = (X3 @ X8)) => ($true = (X1 @ (X5 @ X8))))) => (! [X25 : g,X24 : g] : ((((X3 @ X24) = $true) & ($true = (X3 @ X25))) => ($true = (X3 @ (X7 @ X24 @ X25)))) & ! [X27 : a,X28 : a] : ((($true = (X0 @ X28)) & ($true = (X0 @ X27))) => ($true = (X0 @ (X2 @ X28 @ X27)))) & ! [X23 : g,X22 : g] : ((($true = (X3 @ X23)) & ($true = (X3 @ X22))) => ((X2 @ (X4 @ (X5 @ X22)) @ (X4 @ (X5 @ X23))) = (X4 @ (X5 @ (X7 @ X22 @ X23))))) & ! [X26 : g] : (($true = (X3 @ X26)) => ($true = (X0 @ (X4 @ (X5 @ X26)))))))),
% 1.67/1.38 inference(fool_elimination,[status(thm)],[f4])).
% 1.67/1.38 thf(f4,plain,(
% 1.67/1.38 ~! [X0 : a > $o,X1 : b > $o,X2 : a > a > a,X3 : g > $o,X4 : b > a,X5 : g > b,X6 : b > b > b,X7 : g > g > g] : ((! [X8 : g] : ((X3 @ X8) => (X1 @ (X5 @ X8))) & ! [X9 : g,X10 : g] : (((X3 @ X9) & (X3 @ X10)) => (X3 @ (X7 @ X10 @ X9))) & ! [X11 : a,X12 : a] : (((X0 @ X12) & (X0 @ X11)) => (X0 @ (X2 @ X12 @ X11))) & ! [X13 : b] : ((X1 @ X13) => (X0 @ (X4 @ X13))) & ! [X14 : b,X15 : b] : (((X1 @ X15) & (X1 @ X14)) => (X1 @ (X6 @ X15 @ X14))) & ! [X16 : g,X17 : g] : (((X3 @ X16) & (X3 @ X17)) => ((X5 @ (X7 @ X17 @ X16)) = (X6 @ (X5 @ X17) @ (X5 @ X16)))) & ! [X18 : b,X19 : b] : (((X1 @ X19) & (X1 @ X18)) => ((X4 @ (X6 @ X19 @ X18)) = (X2 @ (X4 @ X19) @ (X4 @ X18)))) & ! [X20 : b,X21 : b] : (((X1 @ X21) & (X1 @ X20)) => (X1 @ (X6 @ X20 @ X21)))) => (! [X22 : g,X23 : g] : (((X3 @ X23) & (X3 @ X22)) => ((X2 @ (X4 @ (X5 @ X22)) @ (X4 @ (X5 @ X23))) = (X4 @ (X5 @ (X7 @ X22 @ X23))))) & ! [X24 : g,X25 : g] : (((X3 @ X24) & (X3 @ X25)) => (X3 @ (X7 @ X24 @ X25))) & ! [X26 : g] : ((X3 @ X26) => (X0 @ (X4 @ (X5 @ X26)))) & ! [X27 : a,X28 : a] : (((X0 @ X27) & (X0 @ X28)) => (X0 @ (X2 @ X28 @ X27)))))),
% 1.67/1.38 inference(rectify,[status(thm)],[f2])).
% 1.67/1.38 thf(f2,negated_conjecture,(
% 1.67/1.38 ~! [X6 : a > $o,X4 : b > $o,X7 : a > a > a,X2 : g > $o,X1 : b > a,X0 : g > b,X5 : b > b > b,X3 : g > g > g] : ((! [X8 : g] : ((X2 @ X8) => (X4 @ (X0 @ X8))) & ! [X9 : g,X8 : g] : (((X2 @ X9) & (X2 @ X8)) => (X2 @ (X3 @ X8 @ X9))) & ! [X9 : a,X8 : a] : (((X6 @ X8) & (X6 @ X9)) => (X6 @ (X7 @ X8 @ X9))) & ! [X8 : b] : ((X4 @ X8) => (X6 @ (X1 @ X8))) & ! [X9 : b,X8 : b] : (((X4 @ X8) & (X4 @ X9)) => (X4 @ (X5 @ X8 @ X9))) & ! [X9 : g,X8 : g] : (((X2 @ X9) & (X2 @ X8)) => ((X0 @ (X3 @ X8 @ X9)) = (X5 @ (X0 @ X8) @ (X0 @ 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 : g,X9 : g] : (((X2 @ X9) & (X2 @ X8)) => ((X1 @ (X0 @ (X3 @ X8 @ X9))) = (X7 @ (X1 @ (X0 @ X8)) @ (X1 @ (X0 @ X9))))) & ! [X8 : g,X9 : g] : (((X2 @ X8) & (X2 @ X9)) => (X2 @ (X3 @ X8 @ X9))) & ! [X8 : g] : ((X2 @ X8) => (X6 @ (X1 @ (X0 @ X8)))) & ! [X9 : a,X8 : a] : (((X6 @ X9) & (X6 @ X8)) => (X6 @ (X7 @ X8 @ X9)))))),
% 1.67/1.38 inference(negated_conjecture,[status(cth)],[f1])).
% 1.67/1.38 thf(f1,conjecture,(
% 1.67/1.38 ! [X6 : a > $o,X4 : b > $o,X7 : a > a > a,X2 : g > $o,X1 : b > a,X0 : g > b,X5 : b > b > b,X3 : g > g > g] : ((! [X8 : g] : ((X2 @ X8) => (X4 @ (X0 @ X8))) & ! [X9 : g,X8 : g] : (((X2 @ X9) & (X2 @ X8)) => (X2 @ (X3 @ X8 @ X9))) & ! [X9 : a,X8 : a] : (((X6 @ X8) & (X6 @ X9)) => (X6 @ (X7 @ X8 @ X9))) & ! [X8 : b] : ((X4 @ X8) => (X6 @ (X1 @ X8))) & ! [X9 : b,X8 : b] : (((X4 @ X8) & (X4 @ X9)) => (X4 @ (X5 @ X8 @ X9))) & ! [X9 : g,X8 : g] : (((X2 @ X9) & (X2 @ X8)) => ((X0 @ (X3 @ X8 @ X9)) = (X5 @ (X0 @ X8) @ (X0 @ X9)))) & ! [X9 : b,X8 : b] : (((X4 @ X8) & (X4 @ X9)) => ((X1 @ (X5 @ X8 @ X9)) = (X7 @ (X1 @ X8) @ (X1 @ X9)))) & ! [X8 : b,X9 : b] : (((X4 @ X9) & (X4 @ X8)) => (X4 @ (X5 @ X8 @ X9)))) => (! [X8 : g,X9 : g] : (((X2 @ X9) & (X2 @ X8)) => ((X1 @ (X0 @ (X3 @ X8 @ X9))) = (X7 @ (X1 @ (X0 @ X8)) @ (X1 @ (X0 @ X9))))) & ! [X8 : g,X9 : g] : (((X2 @ X8) & (X2 @ X9)) => (X2 @ (X3 @ X8 @ X9))) & ! [X8 : g] : ((X2 @ X8) => (X6 @ (X1 @ (X0 @ X8)))) & ! [X9 : a,X8 : a] : (((X6 @ X9) & (X6 @ X8)) => (X6 @ (X7 @ X8 @ X9)))))),
% 1.67/1.38 file('/export/starexec/sandbox/tmp/tmp.i62NXBbrIK/DTF2THF_26225.p',cTHM126_pme)).
% 1.67/1.38 thf(f64,plain,(
% 1.67/1.38 ($true != (sK12 @ (sK11 @ sK14 @ sK15))) | spl17_5),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f62])).
% 1.67/1.38 thf(f157,plain,(
% 1.67/1.38 ~spl17_4 | spl17_7),
% 1.67/1.38 inference(avatar_split_clause,[status(thm)],[f156,f72,f57])).
% 1.67/1.38 thf(f57,definition,(
% 1.67/1.38 spl17_4 <=> ($true = (sK12 @ sK16))),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl17_4])],[avatar_definition])).
% 1.67/1.38 thf(f72,definition,(
% 1.67/1.38 spl17_7 <=> ($true = (sK13 @ (sK6 @ (sK9 @ sK16))))),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl17_7])],[avatar_definition])).
% 1.67/1.38 thf(f156,plain,(
% 1.67/1.38 ($true != (sK12 @ sK16)) | spl17_7),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f155])).
% 1.67/1.38 thf(f155,plain,(
% 1.67/1.38 ($true != (sK12 @ sK16)) | ($true != $true) | spl17_7),
% 1.67/1.38 inference(superposition,[status(thm)],[f154,f41])).
% 1.67/1.38 thf(f41,plain,(
% 1.67/1.38 ( ! [X11 : g] : (($true = (sK8 @ (sK9 @ X11))) | ($true != (sK12 @ X11))) )),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.38 thf(f154,plain,(
% 1.67/1.38 ($true != (sK8 @ (sK9 @ sK16))) | spl17_7),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f153])).
% 1.67/1.38 thf(f153,plain,(
% 1.67/1.38 ($true != (sK8 @ (sK9 @ sK16))) | ($true != $true) | spl17_7),
% 1.67/1.38 inference(superposition,[status(thm)],[f74,f43])).
% 1.67/1.38 thf(f43,plain,(
% 1.67/1.38 ( ! [X8 : b] : (($true = (sK13 @ (sK6 @ X8))) | ($true != (sK8 @ X8))) )),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.38 thf(f74,plain,(
% 1.67/1.38 ($true != (sK13 @ (sK6 @ (sK9 @ sK16)))) | spl17_7),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f72])).
% 1.67/1.38 thf(f152,plain,(
% 1.67/1.38 ~spl17_1 | spl17_13),
% 1.67/1.38 inference(avatar_contradiction_clause,[status(thm)],[f151])).
% 1.67/1.38 thf(f151,plain,(
% 1.67/1.38 $false | (~spl17_1 | spl17_13)),
% 1.67/1.38 inference(subsumption_resolution,[status(thm)],[f150,f47])).
% 1.67/1.38 thf(f150,plain,(
% 1.67/1.38 ($true != (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) | spl17_13),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f149])).
% 1.67/1.38 thf(f149,plain,(
% 1.67/1.38 ($true != (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) | ($true != $true) | spl17_13),
% 1.67/1.38 inference(superposition,[status(thm)],[f143,f27])).
% 1.67/1.38 thf(f27,plain,(
% 1.67/1.38 ( ! [X2 : g > b,X3 : b > a,X0 : g > $o,X1 : g > g > g,X4 : a > a > a] : (($true = (X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0))) | ($true != (sP0 @ X4 @ X3 @ X2 @ X1 @ X0))) )),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f18])).
% 1.67/1.38 thf(f143,plain,(
% 1.67/1.38 ((sK12 @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) != $true) | spl17_13),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f141])).
% 1.67/1.38 thf(f141,definition,(
% 1.67/1.38 spl17_13 <=> ((sK12 @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) = $true)),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl17_13])],[avatar_definition])).
% 1.67/1.38 thf(f148,plain,(
% 1.67/1.38 ~spl17_13 | ~spl17_14 | spl17_11),
% 1.67/1.38 inference(avatar_split_clause,[status(thm)],[f139,f118,f145,f141])).
% 1.67/1.38 thf(f118,definition,(
% 1.67/1.38 spl17_11 <=> ((sK6 @ (sK9 @ (sK11 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12) @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)))) = (sK6 @ (sK10 @ (sK9 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) @ (sK9 @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)))))),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl17_11])],[avatar_definition])).
% 1.67/1.38 thf(f139,plain,(
% 1.67/1.38 ($true != (sK12 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))) | ((sK12 @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) != $true) | spl17_11),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f138])).
% 1.67/1.38 thf(f138,plain,(
% 1.67/1.38 ((sK12 @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) != $true) | ((sK6 @ (sK9 @ (sK11 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12) @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)))) != (sK6 @ (sK9 @ (sK11 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12) @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))))) | ($true != (sK12 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))) | spl17_11),
% 1.67/1.38 inference(superposition,[status(thm)],[f120,f38])).
% 1.67/1.38 thf(f38,plain,(
% 1.67/1.38 ( ! [X16 : g,X17 : g] : (((sK10 @ (sK9 @ X16) @ (sK9 @ X17)) = (sK9 @ (sK11 @ X16 @ X17))) | ($true != (sK12 @ X17)) | ($true != (sK12 @ X16))) )),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.38 thf(f120,plain,(
% 1.67/1.38 ((sK6 @ (sK9 @ (sK11 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12) @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)))) != (sK6 @ (sK10 @ (sK9 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) @ (sK9 @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))))) | spl17_11),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f118])).
% 1.67/1.38 thf(f137,plain,(
% 1.67/1.38 ~spl17_1 | spl17_12),
% 1.67/1.38 inference(avatar_contradiction_clause,[status(thm)],[f136])).
% 1.67/1.38 thf(f136,plain,(
% 1.67/1.38 $false | (~spl17_1 | spl17_12)),
% 1.67/1.38 inference(subsumption_resolution,[status(thm)],[f135,f47])).
% 1.67/1.38 thf(f135,plain,(
% 1.67/1.38 ($true != (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) | spl17_12),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f134])).
% 1.67/1.38 thf(f134,plain,(
% 1.67/1.38 ($true != $true) | ($true != (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) | spl17_12),
% 1.67/1.38 inference(superposition,[status(thm)],[f133,f27])).
% 1.67/1.38 thf(f133,plain,(
% 1.67/1.38 ((sK12 @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) != $true) | spl17_12),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f132])).
% 1.67/1.38 thf(f132,plain,(
% 1.67/1.38 ($true != $true) | ((sK12 @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) != $true) | spl17_12),
% 1.67/1.38 inference(superposition,[status(thm)],[f124,f41])).
% 1.67/1.38 thf(f124,plain,(
% 1.67/1.38 ($true != (sK8 @ (sK9 @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)))) | spl17_12),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f122])).
% 1.67/1.38 thf(f122,definition,(
% 1.67/1.38 spl17_12 <=> ($true = (sK8 @ (sK9 @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))))),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl17_12])],[avatar_definition])).
% 1.67/1.38 thf(f131,plain,(
% 1.67/1.38 ~spl17_1 | spl17_10),
% 1.67/1.38 inference(avatar_contradiction_clause,[status(thm)],[f130])).
% 1.67/1.38 thf(f130,plain,(
% 1.67/1.38 $false | (~spl17_1 | spl17_10)),
% 1.67/1.38 inference(subsumption_resolution,[status(thm)],[f129,f47])).
% 1.67/1.38 thf(f129,plain,(
% 1.67/1.38 ($true != (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) | spl17_10),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f128])).
% 1.67/1.38 thf(f128,plain,(
% 1.67/1.38 ($true != $true) | ($true != (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) | spl17_10),
% 1.67/1.38 inference(superposition,[status(thm)],[f127,f29])).
% 1.67/1.38 thf(f127,plain,(
% 1.67/1.38 ($true != (sK12 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))) | spl17_10),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f126])).
% 1.67/1.38 thf(f126,plain,(
% 1.67/1.38 ($true != (sK12 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))) | ($true != $true) | spl17_10),
% 1.67/1.38 inference(superposition,[status(thm)],[f116,f41])).
% 1.67/1.38 thf(f116,plain,(
% 1.67/1.38 ((sK8 @ (sK9 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))) != $true) | spl17_10),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f114])).
% 1.67/1.38 thf(f114,definition,(
% 1.67/1.38 spl17_10 <=> ((sK8 @ (sK9 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))) = $true)),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl17_10])],[avatar_definition])).
% 1.67/1.38 thf(f125,plain,(
% 1.67/1.38 ~spl17_10 | ~spl17_11 | ~spl17_12 | ~spl17_1),
% 1.67/1.38 inference(avatar_split_clause,[status(thm)],[f112,f45,f122,f118,f114])).
% 1.67/1.38 thf(f112,plain,(
% 1.67/1.38 ($true != (sK8 @ (sK9 @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)))) | ((sK6 @ (sK9 @ (sK11 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12) @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)))) != (sK6 @ (sK10 @ (sK9 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) @ (sK9 @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))))) | ((sK8 @ (sK9 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))) != $true) | ~spl17_1),
% 1.67/1.38 inference(superposition,[status(thm)],[f108,f40])).
% 1.67/1.38 thf(f40,plain,(
% 1.67/1.38 ( ! [X12 : b,X13 : b] : (((sK6 @ (sK10 @ X12 @ X13)) = (sK7 @ (sK6 @ X12) @ (sK6 @ X13))) | ($true != (sK8 @ X13)) | ($true != (sK8 @ X12))) )),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.38 thf(f108,plain,(
% 1.67/1.38 ((sK6 @ (sK9 @ (sK11 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12) @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)))) != (sK7 @ (sK6 @ (sK9 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))) @ (sK6 @ (sK9 @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))))) | ~spl17_1),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f107])).
% 1.67/1.38 thf(f107,plain,(
% 1.67/1.38 ((sK6 @ (sK9 @ (sK11 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12) @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)))) != (sK7 @ (sK6 @ (sK9 @ (sK4 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))) @ (sK6 @ (sK9 @ (sK5 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12))))) | ($true != $true) | ~spl17_1),
% 1.67/1.38 inference(superposition,[status(thm)],[f28,f47])).
% 1.67/1.38 thf(f28,plain,(
% 1.67/1.38 ( ! [X2 : g > b,X3 : b > a,X0 : g > $o,X1 : g > g > g,X4 : a > a > a] : (($true != (sP0 @ X4 @ X3 @ X2 @ X1 @ X0)) | ((X3 @ (X2 @ (X1 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0) @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)))) != (X4 @ (X3 @ (X2 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) @ (X3 @ (X2 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)))))) )),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f18])).
% 1.67/1.38 thf(f106,plain,(
% 1.67/1.38 ~spl17_3 | ~spl17_8),
% 1.67/1.38 inference(avatar_split_clause,[status(thm)],[f105,f82,f53])).
% 1.67/1.38 thf(f53,definition,(
% 1.67/1.38 spl17_3 <=> ((sP1 @ sK13 @ sK7) = $true)),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl17_3])],[avatar_definition])).
% 1.67/1.38 thf(f82,definition,(
% 1.67/1.38 spl17_8 <=> ((sK13 @ (sK3 @ sK13 @ sK7)) = $true)),
% 1.67/1.38 introduced(definition,[new_symbols(naming,[spl17_8])],[avatar_definition])).
% 1.67/1.38 thf(f105,plain,(
% 1.67/1.38 ((sP1 @ sK13 @ sK7) != $true) | ~spl17_8),
% 1.67/1.38 inference(subsumption_resolution,[status(thm)],[f104,f24])).
% 1.67/1.38 thf(f24,plain,(
% 1.67/1.38 ( ! [X0 : a > a > a,X1 : a > $o] : (($true = (X1 @ (sK2 @ X1 @ X0))) | ($true != (sP1 @ X1 @ X0))) )),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f14])).
% 1.67/1.38 thf(f14,plain,(
% 1.67/1.38 ! [X0 : a > a > a,X1 : a > $o] : ((((X1 @ (X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0))) != $true) & ($true = (X1 @ (sK3 @ X1 @ X0))) & ($true = (X1 @ (sK2 @ X1 @ X0)))) | ($true != (sP1 @ X1 @ X0)))),
% 1.67/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f12,f13])).
% 1.67/1.38 thf(f13,plain,(
% 1.67/1.38 ! [X0 : a > a > a,X1 : a > $o] : (? [X2 : a,X3 : a] : (($true != (X1 @ (X0 @ X3 @ X2))) & ($true = (X1 @ X3)) & ($true = (X1 @ X2))) => (((X1 @ (X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0))) != $true) & ($true = (X1 @ (sK3 @ X1 @ X0))) & ($true = (X1 @ (sK2 @ X1 @ X0)))))),
% 1.67/1.38 introduced(definition,[],[choice_axiom])).
% 1.67/1.38 thf(f12,plain,(
% 1.67/1.38 ! [X0 : a > a > a,X1 : a > $o] : (? [X2 : a,X3 : a] : (($true != (X1 @ (X0 @ X3 @ X2))) & ($true = (X1 @ X3)) & ($true = (X1 @ X2))) | ($true != (sP1 @ X1 @ X0)))),
% 1.67/1.38 inference(rectify,[status(thm)],[f11])).
% 1.67/1.38 thf(f11,plain,(
% 1.67/1.38 ! [X2 : a > a > a,X0 : a > $o] : (? [X27 : a,X28 : a] : (($true != (X0 @ (X2 @ X28 @ X27))) & ($true = (X0 @ X28)) & ($true = (X0 @ X27))) | ($true != (sP1 @ X0 @ X2)))),
% 1.67/1.38 inference(nnf_transformation,[status(thm)],[f9])).
% 1.67/1.38 thf(f104,plain,(
% 1.67/1.38 ($true != (sK13 @ (sK2 @ sK13 @ sK7))) | ((sP1 @ sK13 @ sK7) != $true) | ~spl17_8),
% 1.67/1.38 inference(subsumption_resolution,[status(thm)],[f79,f83])).
% 1.67/1.38 thf(f83,plain,(
% 1.67/1.38 ((sK13 @ (sK3 @ sK13 @ sK7)) = $true) | ~spl17_8),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f82])).
% 1.67/1.38 thf(f79,plain,(
% 1.67/1.38 ((sP1 @ sK13 @ sK7) != $true) | ($true != (sK13 @ (sK2 @ sK13 @ sK7))) | ((sK13 @ (sK3 @ sK13 @ sK7)) != $true)),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.67/1.38 thf(f78,plain,(
% 1.67/1.38 ($true != (sK13 @ (sK2 @ sK13 @ sK7))) | ((sP1 @ sK13 @ sK7) != $true) | ((sK13 @ (sK3 @ sK13 @ sK7)) != $true) | ($true != $true)),
% 1.67/1.38 inference(superposition,[status(thm)],[f26,f42])).
% 1.67/1.38 thf(f42,plain,(
% 1.67/1.38 ( ! [X10 : a,X9 : a] : (($true = (sK13 @ (sK7 @ X9 @ X10))) | ($true != (sK13 @ X9)) | ((sK13 @ X10) != $true)) )),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.38 thf(f26,plain,(
% 1.67/1.38 ( ! [X0 : a > a > a,X1 : a > $o] : (((X1 @ (X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0))) != $true) | ($true != (sP1 @ X1 @ X0))) )),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f14])).
% 1.67/1.38 thf(f93,plain,(
% 1.67/1.38 ~spl17_3 | spl17_8),
% 1.67/1.38 inference(avatar_contradiction_clause,[status(thm)],[f92])).
% 1.67/1.38 thf(f92,plain,(
% 1.67/1.38 $false | (~spl17_3 | spl17_8)),
% 1.67/1.38 inference(subsumption_resolution,[status(thm)],[f91,f55])).
% 1.67/1.38 thf(f55,plain,(
% 1.67/1.38 ((sP1 @ sK13 @ sK7) = $true) | ~spl17_3),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f53])).
% 1.67/1.38 thf(f91,plain,(
% 1.67/1.38 ((sP1 @ sK13 @ sK7) != $true) | spl17_8),
% 1.67/1.38 inference(trivial_inequality_removal,[status(thm)],[f90])).
% 1.67/1.38 thf(f90,plain,(
% 1.67/1.38 ($true != $true) | ((sP1 @ sK13 @ sK7) != $true) | spl17_8),
% 1.67/1.38 inference(superposition,[status(thm)],[f84,f25])).
% 1.67/1.38 thf(f25,plain,(
% 1.67/1.38 ( ! [X0 : a > a > a,X1 : a > $o] : (($true = (X1 @ (sK3 @ X1 @ X0))) | ($true != (sP1 @ X1 @ X0))) )),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f14])).
% 1.67/1.38 thf(f84,plain,(
% 1.67/1.38 ((sK13 @ (sK3 @ sK13 @ sK7)) != $true) | spl17_8),
% 1.67/1.38 inference(avatar_component_clause,[status(thm)],[f82])).
% 1.67/1.38 thf(f77,plain,(
% 1.67/1.38 ~spl17_7 | spl17_1 | spl17_3 | ~spl17_5),
% 1.67/1.38 inference(avatar_split_clause,[status(thm)],[f32,f62,f53,f45,f72])).
% 1.67/1.38 thf(f32,plain,(
% 1.67/1.38 ($true = (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) | ((sP1 @ sK13 @ sK7) = $true) | ($true != (sK13 @ (sK6 @ (sK9 @ sK16)))) | ($true != (sK12 @ (sK11 @ sK14 @ sK15)))),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.38 thf(f76,plain,(
% 1.67/1.38 spl17_3 | spl17_2 | spl17_1 | ~spl17_7),
% 1.67/1.38 inference(avatar_split_clause,[status(thm)],[f34,f72,f45,f49,f53])).
% 1.67/1.38 thf(f34,plain,(
% 1.67/1.38 ($true != (sK13 @ (sK6 @ (sK9 @ sK16)))) | ($true = (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) | ((sK12 @ sK15) = $true) | ((sP1 @ sK13 @ sK7) = $true)),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.38 thf(f75,plain,(
% 1.67/1.38 spl17_3 | ~spl17_7 | spl17_6 | spl17_1),
% 1.67/1.38 inference(avatar_split_clause,[status(thm)],[f36,f45,f67,f72,f53])).
% 1.67/1.38 thf(f36,plain,(
% 1.67/1.38 ($true != (sK13 @ (sK6 @ (sK9 @ sK16)))) | ($true = (sK12 @ sK14)) | ($true = (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) | ((sP1 @ sK13 @ sK7) = $true)),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.38 thf(f70,plain,(
% 1.67/1.38 spl17_6 | spl17_1 | spl17_3 | spl17_4),
% 1.67/1.38 inference(avatar_split_clause,[status(thm)],[f37,f57,f53,f45,f67])).
% 1.67/1.38 thf(f37,plain,(
% 1.67/1.38 ($true = (sK12 @ sK16)) | ($true = (sK12 @ sK14)) | ($true = (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) | ((sP1 @ sK13 @ sK7) = $true)),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.38 thf(f65,plain,(
% 1.67/1.38 spl17_1 | spl17_3 | spl17_4 | ~spl17_5),
% 1.67/1.38 inference(avatar_split_clause,[status(thm)],[f33,f62,f57,f53,f45])).
% 1.67/1.38 thf(f33,plain,(
% 1.67/1.38 ($true = (sK12 @ sK16)) | ($true = (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) | ((sP1 @ sK13 @ sK7) = $true) | ($true != (sK12 @ (sK11 @ sK14 @ sK15)))),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.38 thf(f60,plain,(
% 1.67/1.38 spl17_1 | spl17_2 | spl17_3 | spl17_4),
% 1.67/1.38 inference(avatar_split_clause,[status(thm)],[f35,f57,f53,f49,f45])).
% 1.67/1.38 thf(f35,plain,(
% 1.67/1.38 ($true = (sK12 @ sK16)) | ($true = (sP0 @ sK7 @ sK6 @ sK9 @ sK11 @ sK12)) | ((sP1 @ sK13 @ sK7) = $true) | ((sK12 @ sK15) = $true)),
% 1.67/1.38 inference(cnf_transformation,[status(thm)],[f23])).
% 1.67/1.38 % SZS output end Proof for DTF2THF_26225
% 1.67/1.38 % (26510)------------------------------
% 1.67/1.38 % (26510)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.38 % (26510)Termination reason: Refutation
% 1.67/1.38
% 1.67/1.38 % (26510)Memory used [KB]: 5884
% 1.67/1.38 % (26510)Time elapsed: 0.029 s
% 1.67/1.38 % (26510)Instructions burned: 32 (million)
% 1.67/1.38 % (26510)------------------------------
% 1.67/1.38 % (26510)------------------------------
% 1.67/1.38 % (26504)Success in time 0.043 s
%------------------------------------------------------------------------------