%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU905^5 : 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 : n022.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 1.31s 1.19s
% Output : Refutation 1.31s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 20
% Syntax : Number of formulae : 115 ( 3 unt; 0 typ; 12 def)
% Number of atoms : 1227 ( 438 equ; 0 cnn)
% Maximal formula atoms : 58 ( 10 avg)
% Number of connectives : 2391 ( 274 ~; 267 |; 191 &;1590 @)
% ( 12 <=>; 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 : 33 ( 30 usr; 17 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 > $o ).
thf(func_def_13,type,
sK7: b > b > b ).
thf(func_def_14,type,
sK8: a > $o ).
thf(func_def_15,type,
sK9: g > b ).
thf(func_def_16,type,
sK10: g > $o ).
thf(func_def_17,type,
sK11: a > a > a ).
thf(func_def_18,type,
sK12: b > a ).
thf(func_def_19,type,
sK13: g > g > g ).
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(f161,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f60,f69,f70,f71,f76,f77,f82,f114,f120,f129,f132,f143,f148,f153,f160]) ).
thf(f160,plain,
( ~ spl17_3
| spl17_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f159]) ).
thf(f159,plain,
( $false
| ~ spl17_3
| spl17_12 ),
inference(subsumption_resolution,[status(thm)],[f158,f55]) ).
thf(f55,plain,
( ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
= $true )
| ~ spl17_3 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f53,definition,
( spl17_3
<=> ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_3])],[avatar_definition]) ).
thf(f158,plain,
( ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
!= $true )
| spl17_12 ),
inference(trivial_inequality_removal,[status(thm)],[f157]) ).
thf(f157,plain,
( ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
!= $true )
| ( $true != $true )
| spl17_12 ),
inference(superposition,[status(thm)],[f142,f27]) ).
thf(f27,plain,
! [X2: g > b,X3: b > a,X0: g > $o,X1: g > g > g,X4: a > a > a] :
( ( ( X0 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
= $true )
| ( ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 )
!= $true ) ),
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] :
( ( ( ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
= $true )
& ( ( 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 ) ) ) ) )
& ( ( X0 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
= $true ) )
| ( ( 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 > g > g,X2: g > b,X3: b > a,X4: a > a > a] :
( ? [X5: g,X6: g] :
( ( ( X0 @ X5 )
= $true )
& ( ( X4 @ ( X3 @ ( X2 @ X5 ) ) @ ( X3 @ ( X2 @ X6 ) ) )
!= ( X3 @ ( X2 @ ( X1 @ X5 @ X6 ) ) ) )
& ( ( X0 @ X6 )
= $true ) )
=> ( ( ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
= $true )
& ( ( 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 ) ) ) ) )
& ( ( X0 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
= $true ) ) ),
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] :
( ( ( X0 @ X5 )
= $true )
& ( ( X4 @ ( X3 @ ( X2 @ X5 ) ) @ ( X3 @ ( X2 @ X6 ) ) )
!= ( X3 @ ( X2 @ ( X1 @ X5 @ X6 ) ) ) )
& ( ( X0 @ X6 )
= $true ) )
| ( ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f15]) ).
thf(f15,plain,
! [X1: g > $o,X4: g > g > g,X0: g > b,X2: b > a,X7: a > a > a] :
( ? [X11: g,X10: g] :
( ( ( X1 @ X11 )
= $true )
& ( ( X7 @ ( X2 @ ( X0 @ X11 ) ) @ ( X2 @ ( X0 @ X10 ) ) )
!= ( X2 @ ( X0 @ ( X4 @ X11 @ X10 ) ) ) )
& ( ( X1 @ X10 )
= $true ) )
| ( ( sP0 @ X7 @ X2 @ X0 @ X4 @ X1 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f8,plain,
! [X1: g > $o,X4: g > g > g,X0: g > b,X2: b > a,X7: a > a > a] :
( ? [X11: g,X10: g] :
( ( ( X1 @ X11 )
= $true )
& ( ( X7 @ ( X2 @ ( X0 @ X11 ) ) @ ( X2 @ ( X0 @ X10 ) ) )
!= ( X2 @ ( X0 @ ( X4 @ X11 @ X10 ) ) ) )
& ( ( X1 @ X10 )
= $true ) )
| ( ( sP0 @ X7 @ X2 @ X0 @ X4 @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f142,plain,
( ( $true
!= ( sK10 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) )
| spl17_12 ),
inference(avatar_component_clause,[status(thm)],[f140]) ).
thf(f140,definition,
( spl17_12
<=> ( $true
= ( sK10 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_12])],[avatar_definition]) ).
thf(f153,plain,
( ~ spl17_2
| spl17_5
| ~ spl17_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f152]) ).
thf(f152,plain,
( $false
| ~ spl17_2
| spl17_5
| ~ spl17_7 ),
inference(subsumption_resolution,[status(thm)],[f151,f51]) ).
thf(f51,plain,
( ( ( sK10 @ sK14 )
= $true )
| ~ spl17_2 ),
inference(avatar_component_clause,[status(thm)],[f49]) ).
thf(f49,definition,
( spl17_2
<=> ( ( sK10 @ sK14 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_2])],[avatar_definition]) ).
thf(f151,plain,
( ( ( sK10 @ sK14 )
!= $true )
| spl17_5
| ~ spl17_7 ),
inference(subsumption_resolution,[status(thm)],[f150,f75]) ).
thf(f75,plain,
( ( ( sK10 @ sK15 )
= $true )
| ~ spl17_7 ),
inference(avatar_component_clause,[status(thm)],[f73]) ).
thf(f73,definition,
( spl17_7
<=> ( ( sK10 @ sK15 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_7])],[avatar_definition]) ).
thf(f150,plain,
( ( ( sK10 @ sK15 )
!= $true )
| ( ( sK10 @ sK14 )
!= $true )
| spl17_5 ),
inference(trivial_inequality_removal,[status(thm)],[f149]) ).
thf(f149,plain,
( ( ( sK10 @ sK14 )
!= $true )
| ( ( sK10 @ sK15 )
!= $true )
| ( $true != $true )
| spl17_5 ),
inference(superposition,[status(thm)],[f64,f42]) ).
thf(f42,plain,
! [X10: g,X11: g] :
( ( ( sK10 @ ( sK13 @ X11 @ X10 ) )
= $true )
| ( ( sK10 @ X10 )
!= $true )
| ( ( sK10 @ X11 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f23,plain,
( ! [X8: b,X9: b] :
( ( ( sK6 @ X9 )
!= $true )
| ( ( sK6 @ X8 )
!= $true )
| ( $true
= ( sK6 @ ( sK7 @ X8 @ X9 ) ) ) )
& ! [X10: g,X11: g] :
( ( ( sK10 @ ( sK13 @ X11 @ X10 ) )
= $true )
| ( ( sK10 @ X10 )
!= $true )
| ( ( sK10 @ X11 )
!= $true ) )
& ! [X12: g,X13: g] :
( ( ( sK10 @ X12 )
!= $true )
| ( $true
!= ( sK10 @ X13 ) )
| ( ( sK9 @ ( sK13 @ X12 @ X13 ) )
= ( sK7 @ ( sK9 @ X12 ) @ ( sK9 @ X13 ) ) ) )
& ! [X14: g] :
( ( $true
= ( sK6 @ ( sK9 @ X14 ) ) )
| ( ( sK10 @ X14 )
!= $true ) )
& ! [X15: b] :
( ( ( sK6 @ X15 )
!= $true )
| ( ( sK8 @ ( sK12 @ X15 ) )
= $true ) )
& ( ( ( ( sK10 @ sK14 )
= $true )
& ( ( sK10 @ sK15 )
= $true )
& ( ( sK10 @ ( sK13 @ sK14 @ sK15 ) )
!= $true ) )
| ( $true
= ( sP1 @ sK8 @ sK11 ) )
| ( ( ( sK8 @ ( sK12 @ ( sK9 @ sK16 ) ) )
!= $true )
& ( ( sK10 @ sK16 )
= $true ) )
| ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
= $true ) )
& ! [X19: a,X20: a] :
( ( ( sK8 @ X19 )
!= $true )
| ( ( sK8 @ ( sK11 @ X20 @ X19 ) )
= $true )
| ( ( sK8 @ X20 )
!= $true ) )
& ! [X21: b,X22: b] :
( ( $true
= ( sK6 @ ( sK7 @ X22 @ X21 ) ) )
| ( $true
!= ( sK6 @ X21 ) )
| ( ( sK6 @ X22 )
!= $true ) )
& ! [X23: b,X24: b] :
( ( $true
!= ( sK6 @ X23 ) )
| ( ( sK6 @ X24 )
!= $true )
| ( ( sK11 @ ( sK12 @ X23 ) @ ( sK12 @ X24 ) )
= ( sK12 @ ( sK7 @ 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 > $o,X1: b > b > b,X2: a > $o,X3: g > b,X4: g > $o,X5: a > a > a,X6: b > a,X7: g > g > g] :
( ! [X8: b,X9: b] :
( ( ( X0 @ X9 )
!= $true )
| ( ( X0 @ X8 )
!= $true )
| ( $true
= ( X0 @ ( X1 @ X8 @ X9 ) ) ) )
& ! [X10: g,X11: g] :
( ( ( X4 @ ( X7 @ X11 @ X10 ) )
= $true )
| ( ( X4 @ X10 )
!= $true )
| ( ( X4 @ X11 )
!= $true ) )
& ! [X12: g,X13: g] :
( ( ( X4 @ X12 )
!= $true )
| ( ( X4 @ X13 )
!= $true )
| ( ( X1 @ ( X3 @ X12 ) @ ( X3 @ X13 ) )
= ( X3 @ ( X7 @ X12 @ X13 ) ) ) )
& ! [X14: g] :
( ( ( X0 @ ( X3 @ X14 ) )
= $true )
| ( ( X4 @ X14 )
!= $true ) )
& ! [X15: b] :
( ( ( X0 @ X15 )
!= $true )
| ( ( X2 @ ( X6 @ X15 ) )
= $true ) )
& ( ? [X16: g,X17: g] :
( ( ( X4 @ X16 )
= $true )
& ( $true
= ( X4 @ X17 ) )
& ( ( X4 @ ( X7 @ X16 @ X17 ) )
!= $true ) )
| ( ( sP1 @ X2 @ X5 )
= $true )
| ? [X18: g] :
( ( $true
!= ( X2 @ ( X6 @ ( X3 @ X18 ) ) ) )
& ( ( X4 @ X18 )
= $true ) )
| ( ( sP0 @ X5 @ X6 @ X3 @ X7 @ X4 )
= $true ) )
& ! [X19: a,X20: a] :
( ( ( X2 @ X19 )
!= $true )
| ( ( X2 @ ( X5 @ X20 @ X19 ) )
= $true )
| ( $true
!= ( X2 @ X20 ) ) )
& ! [X21: b,X22: b] :
( ( ( X0 @ ( X1 @ X22 @ X21 ) )
= $true )
| ( ( X0 @ X21 )
!= $true )
| ( ( X0 @ X22 )
!= $true ) )
& ! [X23: b,X24: b] :
( ( ( X0 @ X23 )
!= $true )
| ( ( X0 @ X24 )
!= $true )
| ( ( X5 @ ( X6 @ X23 ) @ ( X6 @ X24 ) )
= ( X6 @ ( X1 @ X23 @ X24 ) ) ) ) )
=> ( ! [X9: b,X8: b] :
( ( ( sK6 @ X9 )
!= $true )
| ( ( sK6 @ X8 )
!= $true )
| ( $true
= ( sK6 @ ( sK7 @ X8 @ X9 ) ) ) )
& ! [X11: g,X10: g] :
( ( ( sK10 @ ( sK13 @ X11 @ X10 ) )
= $true )
| ( ( sK10 @ X10 )
!= $true )
| ( ( sK10 @ X11 )
!= $true ) )
& ! [X13: g,X12: g] :
( ( ( sK10 @ X12 )
!= $true )
| ( $true
!= ( sK10 @ X13 ) )
| ( ( sK9 @ ( sK13 @ X12 @ X13 ) )
= ( sK7 @ ( sK9 @ X12 ) @ ( sK9 @ X13 ) ) ) )
& ! [X14: g] :
( ( $true
= ( sK6 @ ( sK9 @ X14 ) ) )
| ( ( sK10 @ X14 )
!= $true ) )
& ! [X15: b] :
( ( ( sK6 @ X15 )
!= $true )
| ( ( sK8 @ ( sK12 @ X15 ) )
= $true ) )
& ( ? [X17: g,X16: g] :
( ( $true
= ( sK10 @ X16 ) )
& ( $true
= ( sK10 @ X17 ) )
& ( ( sK10 @ ( sK13 @ X16 @ X17 ) )
!= $true ) )
| ( $true
= ( sP1 @ sK8 @ sK11 ) )
| ? [X18: g] :
( ( $true
!= ( sK8 @ ( sK12 @ ( sK9 @ X18 ) ) ) )
& ( ( sK10 @ X18 )
= $true ) )
| ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
= $true ) )
& ! [X20: a,X19: a] :
( ( ( sK8 @ X19 )
!= $true )
| ( ( sK8 @ ( sK11 @ X20 @ X19 ) )
= $true )
| ( ( sK8 @ X20 )
!= $true ) )
& ! [X22: b,X21: b] :
( ( $true
= ( sK6 @ ( sK7 @ X22 @ X21 ) ) )
| ( $true
!= ( sK6 @ X21 ) )
| ( ( sK6 @ X22 )
!= $true ) )
& ! [X24: b,X23: b] :
( ( $true
!= ( sK6 @ X23 ) )
| ( ( sK6 @ X24 )
!= $true )
| ( ( sK11 @ ( sK12 @ X23 ) @ ( sK12 @ X24 ) )
= ( sK12 @ ( sK7 @ X23 @ X24 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X17: g,X16: g] :
( ( $true
= ( sK10 @ X16 ) )
& ( $true
= ( sK10 @ X17 ) )
& ( ( sK10 @ ( sK13 @ X16 @ X17 ) )
!= $true ) )
=> ( ( ( sK10 @ sK14 )
= $true )
& ( ( sK10 @ sK15 )
= $true )
& ( ( sK10 @ ( sK13 @ sK14 @ sK15 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X18: g] :
( ( $true
!= ( sK8 @ ( sK12 @ ( sK9 @ X18 ) ) ) )
& ( ( sK10 @ X18 )
= $true ) )
=> ( ( ( sK8 @ ( sK12 @ ( sK9 @ sK16 ) ) )
!= $true )
& ( ( sK10 @ sK16 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f19,plain,
? [X0: b > $o,X1: b > b > b,X2: a > $o,X3: g > b,X4: g > $o,X5: a > a > a,X6: b > a,X7: g > g > g] :
( ! [X8: b,X9: b] :
( ( ( X0 @ X9 )
!= $true )
| ( ( X0 @ X8 )
!= $true )
| ( $true
= ( X0 @ ( X1 @ X8 @ X9 ) ) ) )
& ! [X10: g,X11: g] :
( ( ( X4 @ ( X7 @ X11 @ X10 ) )
= $true )
| ( ( X4 @ X10 )
!= $true )
| ( ( X4 @ X11 )
!= $true ) )
& ! [X12: g,X13: g] :
( ( ( X4 @ X12 )
!= $true )
| ( ( X4 @ X13 )
!= $true )
| ( ( X1 @ ( X3 @ X12 ) @ ( X3 @ X13 ) )
= ( X3 @ ( X7 @ X12 @ X13 ) ) ) )
& ! [X14: g] :
( ( ( X0 @ ( X3 @ X14 ) )
= $true )
| ( ( X4 @ X14 )
!= $true ) )
& ! [X15: b] :
( ( ( X0 @ X15 )
!= $true )
| ( ( X2 @ ( X6 @ X15 ) )
= $true ) )
& ( ? [X16: g,X17: g] :
( ( ( X4 @ X16 )
= $true )
& ( $true
= ( X4 @ X17 ) )
& ( ( X4 @ ( X7 @ X16 @ X17 ) )
!= $true ) )
| ( ( sP1 @ X2 @ X5 )
= $true )
| ? [X18: g] :
( ( $true
!= ( X2 @ ( X6 @ ( X3 @ X18 ) ) ) )
& ( ( X4 @ X18 )
= $true ) )
| ( ( sP0 @ X5 @ X6 @ X3 @ X7 @ X4 )
= $true ) )
& ! [X19: a,X20: a] :
( ( ( X2 @ X19 )
!= $true )
| ( ( X2 @ ( X5 @ X20 @ X19 ) )
= $true )
| ( $true
!= ( X2 @ X20 ) ) )
& ! [X21: b,X22: b] :
( ( ( X0 @ ( X1 @ X22 @ X21 ) )
= $true )
| ( ( X0 @ X21 )
!= $true )
| ( ( X0 @ X22 )
!= $true ) )
& ! [X23: b,X24: b] :
( ( ( X0 @ X23 )
!= $true )
| ( ( X0 @ X24 )
!= $true )
| ( ( X5 @ ( X6 @ X23 ) @ ( X6 @ X24 ) )
= ( X6 @ ( X1 @ X23 @ X24 ) ) ) ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
? [X5: b > $o,X3: b > b > b,X6: a > $o,X0: g > b,X1: g > $o,X7: a > a > a,X2: b > a,X4: g > g > g] :
( ! [X19: b,X20: b] :
( ( ( X5 @ X20 )
!= $true )
| ( ( X5 @ X19 )
!= $true )
| ( ( X5 @ ( X3 @ X19 @ X20 ) )
= $true ) )
& ! [X18: g,X17: g] :
( ( $true
= ( X1 @ ( X4 @ X17 @ X18 ) ) )
| ( ( X1 @ X18 )
!= $true )
| ( ( X1 @ X17 )
!= $true ) )
& ! [X26: g,X27: g] :
( ( ( X1 @ X26 )
!= $true )
| ( ( X1 @ X27 )
!= $true )
| ( ( X3 @ ( X0 @ X26 ) @ ( X0 @ X27 ) )
= ( X0 @ ( X4 @ X26 @ X27 ) ) ) )
& ! [X28: g] :
( ( $true
= ( X5 @ ( X0 @ X28 ) ) )
| ( ( X1 @ X28 )
!= $true ) )
& ! [X21: b] :
( ( ( X5 @ X21 )
!= $true )
| ( ( X6 @ ( X2 @ X21 ) )
= $true ) )
& ( ? [X9: g,X8: g] :
( ( ( X1 @ X9 )
= $true )
& ( ( X1 @ X8 )
= $true )
& ( ( X1 @ ( X4 @ X9 @ X8 ) )
!= $true ) )
| ( ( sP1 @ X6 @ X7 )
= $true )
| ? [X14: g] :
( ( ( X6 @ ( X2 @ ( X0 @ X14 ) ) )
!= $true )
& ( ( X1 @ X14 )
= $true ) )
| ( ( sP0 @ X7 @ X2 @ X0 @ X4 @ X1 )
= $true ) )
& ! [X16: a,X15: a] :
( ( $true
!= ( X6 @ X16 ) )
| ( $true
= ( X6 @ ( X7 @ X15 @ X16 ) ) )
| ( $true
!= ( X6 @ X15 ) ) )
& ! [X22: b,X23: b] :
( ( $true
= ( X5 @ ( X3 @ X23 @ X22 ) ) )
| ( ( X5 @ X22 )
!= $true )
| ( ( X5 @ X23 )
!= $true ) )
& ! [X25: b,X24: b] :
( ( ( X5 @ X25 )
!= $true )
| ( ( X5 @ X24 )
!= $true )
| ( ( X7 @ ( X2 @ X25 ) @ ( X2 @ X24 ) )
= ( X2 @ ( X3 @ X25 @ X24 ) ) ) ) ),
inference(definition_folding,[status(thm)],[f7,f9,f8]) ).
thf(f9,plain,
! [X7: a > a > a,X6: a > $o] :
( ? [X12: a,X13: a] :
( ( ( X6 @ ( X7 @ X13 @ X12 ) )
!= $true )
& ( ( X6 @ X13 )
= $true )
& ( ( X6 @ X12 )
= $true ) )
| ( ( sP1 @ X6 @ X7 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f7,plain,
? [X5: b > $o,X3: b > b > b,X6: a > $o,X0: g > b,X1: g > $o,X7: a > a > a,X2: b > a,X4: g > g > g] :
( ! [X19: b,X20: b] :
( ( ( X5 @ X20 )
!= $true )
| ( ( X5 @ X19 )
!= $true )
| ( ( X5 @ ( X3 @ X19 @ X20 ) )
= $true ) )
& ! [X18: g,X17: g] :
( ( $true
= ( X1 @ ( X4 @ X17 @ X18 ) ) )
| ( ( X1 @ X18 )
!= $true )
| ( ( X1 @ X17 )
!= $true ) )
& ! [X26: g,X27: g] :
( ( ( X1 @ X26 )
!= $true )
| ( ( X1 @ X27 )
!= $true )
| ( ( X3 @ ( X0 @ X26 ) @ ( X0 @ X27 ) )
= ( X0 @ ( X4 @ X26 @ X27 ) ) ) )
& ! [X28: g] :
( ( $true
= ( X5 @ ( X0 @ X28 ) ) )
| ( ( X1 @ X28 )
!= $true ) )
& ! [X21: b] :
( ( ( X5 @ X21 )
!= $true )
| ( ( X6 @ ( X2 @ X21 ) )
= $true ) )
& ( ? [X9: g,X8: g] :
( ( ( X1 @ X9 )
= $true )
& ( ( X1 @ X8 )
= $true )
& ( ( X1 @ ( X4 @ X9 @ X8 ) )
!= $true ) )
| ? [X12: a,X13: a] :
( ( ( X6 @ ( X7 @ X13 @ X12 ) )
!= $true )
& ( ( X6 @ X13 )
= $true )
& ( ( X6 @ X12 )
= $true ) )
| ? [X14: g] :
( ( ( X6 @ ( X2 @ ( X0 @ X14 ) ) )
!= $true )
& ( ( X1 @ X14 )
= $true ) )
| ? [X11: g,X10: g] :
( ( ( X1 @ X11 )
= $true )
& ( ( X7 @ ( X2 @ ( X0 @ X11 ) ) @ ( X2 @ ( X0 @ X10 ) ) )
!= ( X2 @ ( X0 @ ( X4 @ X11 @ X10 ) ) ) )
& ( ( X1 @ X10 )
= $true ) ) )
& ! [X16: a,X15: a] :
( ( $true
!= ( X6 @ X16 ) )
| ( $true
= ( X6 @ ( X7 @ X15 @ X16 ) ) )
| ( $true
!= ( X6 @ X15 ) ) )
& ! [X22: b,X23: b] :
( ( $true
= ( X5 @ ( X3 @ X23 @ X22 ) ) )
| ( ( X5 @ X22 )
!= $true )
| ( ( X5 @ X23 )
!= $true ) )
& ! [X25: b,X24: b] :
( ( ( X5 @ X25 )
!= $true )
| ( ( X5 @ X24 )
!= $true )
| ( ( X7 @ ( X2 @ X25 ) @ ( X2 @ X24 ) )
= ( X2 @ ( X3 @ X25 @ X24 ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X6: a > $o,X2: b > a,X3: b > b > b,X1: g > $o,X5: b > $o,X7: a > a > a,X4: g > g > g,X0: g > b] :
( ! [X23: b,X22: b] :
( ( $true
= ( X5 @ ( X3 @ X23 @ X22 ) ) )
| ( ( X5 @ X22 )
!= $true )
| ( ( X5 @ X23 )
!= $true ) )
& ! [X21: b] :
( ( ( X5 @ X21 )
!= $true )
| ( ( X6 @ ( X2 @ X21 ) )
= $true ) )
& ! [X27: g,X26: g] :
( ( ( X3 @ ( X0 @ X26 ) @ ( X0 @ X27 ) )
= ( X0 @ ( X4 @ X26 @ X27 ) ) )
| ( ( X1 @ X27 )
!= $true )
| ( ( X1 @ X26 )
!= $true ) )
& ! [X18: g,X17: g] :
( ( $true
= ( X1 @ ( X4 @ X17 @ X18 ) ) )
| ( ( X1 @ X18 )
!= $true )
| ( ( X1 @ X17 )
!= $true ) )
& ! [X28: g] :
( ( $true
= ( X5 @ ( X0 @ X28 ) ) )
| ( ( X1 @ X28 )
!= $true ) )
& ! [X15: a,X16: a] :
( ( $true
= ( X6 @ ( X7 @ X15 @ X16 ) ) )
| ( $true
!= ( X6 @ X15 ) )
| ( $true
!= ( X6 @ X16 ) ) )
& ! [X24: b,X25: b] :
( ( ( X7 @ ( X2 @ X25 ) @ ( X2 @ X24 ) )
= ( X2 @ ( X3 @ X25 @ X24 ) ) )
| ( ( X5 @ X25 )
!= $true )
| ( ( X5 @ X24 )
!= $true ) )
& ! [X20: b,X19: b] :
( ( ( X5 @ ( X3 @ X19 @ X20 ) )
= $true )
| ( ( X5 @ X19 )
!= $true )
| ( ( X5 @ X20 )
!= $true ) )
& ( ? [X8: g,X9: g] :
( ( ( X1 @ ( X4 @ X9 @ X8 ) )
!= $true )
& ( ( X1 @ X8 )
= $true )
& ( ( X1 @ X9 )
= $true ) )
| ? [X13: a,X12: a] :
( ( ( X6 @ ( X7 @ X13 @ X12 ) )
!= $true )
& ( ( X6 @ X12 )
= $true )
& ( ( X6 @ X13 )
= $true ) )
| ? [X10: g,X11: g] :
( ( ( X7 @ ( X2 @ ( X0 @ X11 ) ) @ ( X2 @ ( X0 @ X10 ) ) )
!= ( X2 @ ( X0 @ ( X4 @ X11 @ X10 ) ) ) )
& ( ( X1 @ X11 )
= $true )
& ( ( X1 @ X10 )
= $true ) )
| ? [X14: g] :
( ( ( X6 @ ( X2 @ ( X0 @ X14 ) ) )
!= $true )
& ( ( X1 @ X14 )
= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X6: a > $o,X2: b > a,X3: b > b > b,X1: g > $o,X5: b > $o,X7: a > a > a,X4: g > g > g,X0: g > b] :
( ~ ( ! [X8: g,X9: g] :
( ( ( ( X1 @ X8 )
= $true )
& ( ( X1 @ X9 )
= $true ) )
=> ( ( X1 @ ( X4 @ X9 @ X8 ) )
= $true ) )
& ! [X13: a,X12: a] :
( ( ( ( X6 @ X12 )
= $true )
& ( ( X6 @ X13 )
= $true ) )
=> ( ( X6 @ ( X7 @ X13 @ X12 ) )
= $true ) )
& ! [X10: g,X11: g] :
( ( ( ( X1 @ X11 )
= $true )
& ( ( X1 @ X10 )
= $true ) )
=> ( ( X7 @ ( X2 @ ( X0 @ X11 ) ) @ ( X2 @ ( X0 @ X10 ) ) )
= ( X2 @ ( X0 @ ( X4 @ X11 @ X10 ) ) ) ) )
& ! [X14: g] :
( ( ( X1 @ X14 )
= $true )
=> ( ( X6 @ ( X2 @ ( X0 @ X14 ) ) )
= $true ) ) )
=> ~ ( ! [X23: b,X22: b] :
( ( ( ( X5 @ X22 )
= $true )
& ( ( X5 @ X23 )
= $true ) )
=> ( $true
= ( X5 @ ( X3 @ X23 @ X22 ) ) ) )
& ! [X21: b] :
( ( ( X5 @ X21 )
= $true )
=> ( ( X6 @ ( X2 @ X21 ) )
= $true ) )
& ! [X27: g,X26: g] :
( ( ( ( X1 @ X27 )
= $true )
& ( ( X1 @ X26 )
= $true ) )
=> ( ( X3 @ ( X0 @ X26 ) @ ( X0 @ X27 ) )
= ( X0 @ ( X4 @ X26 @ X27 ) ) ) )
& ! [X18: g,X17: g] :
( ( ( ( X1 @ X18 )
= $true )
& ( ( X1 @ X17 )
= $true ) )
=> ( $true
= ( X1 @ ( X4 @ X17 @ X18 ) ) ) )
& ! [X28: g] :
( ( ( X1 @ X28 )
= $true )
=> ( $true
= ( X5 @ ( X0 @ X28 ) ) ) )
& ! [X15: a,X16: a] :
( ( ( $true
= ( X6 @ X15 ) )
& ( $true
= ( X6 @ X16 ) ) )
=> ( $true
= ( X6 @ ( X7 @ X15 @ X16 ) ) ) )
& ! [X24: b,X25: b] :
( ( ( ( X5 @ X25 )
= $true )
& ( ( X5 @ X24 )
= $true ) )
=> ( ( X7 @ ( X2 @ X25 ) @ ( X2 @ X24 ) )
= ( X2 @ ( X3 @ X25 @ X24 ) ) ) )
& ! [X20: b,X19: b] :
( ( ( ( X5 @ X19 )
= $true )
& ( ( X5 @ X20 )
= $true ) )
=> ( ( X5 @ ( X3 @ X19 @ X20 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: g > b,X1: g > $o,X2: b > a,X3: b > b > b,X4: g > g > g,X5: b > $o,X6: a > $o,X7: a > a > a] :
( ~ ( ! [X8: g,X9: g] :
( ( ( X1 @ X9 )
& ( X1 @ X8 ) )
=> ( X1 @ ( X4 @ X9 @ X8 ) ) )
& ! [X10: g,X11: g] :
( ( ( X1 @ X10 )
& ( X1 @ X11 ) )
=> ( ( X7 @ ( X2 @ ( X0 @ X11 ) ) @ ( X2 @ ( X0 @ X10 ) ) )
= ( X2 @ ( X0 @ ( X4 @ X11 @ X10 ) ) ) ) )
& ! [X12: a,X13: a] :
( ( ( X6 @ X12 )
& ( X6 @ X13 ) )
=> ( X6 @ ( X7 @ X13 @ X12 ) ) )
& ! [X14: g] :
( ( X1 @ X14 )
=> ( X6 @ ( X2 @ ( X0 @ X14 ) ) ) ) )
=> ~ ( ! [X15: a,X16: a] :
( ( ( X6 @ X15 )
& ( X6 @ X16 ) )
=> ( X6 @ ( X7 @ X15 @ X16 ) ) )
& ! [X17: g,X18: g] :
( ( ( X1 @ X18 )
& ( X1 @ X17 ) )
=> ( X1 @ ( X4 @ X17 @ X18 ) ) )
& ! [X19: b,X20: b] :
( ( ( X5 @ X19 )
& ( X5 @ X20 ) )
=> ( X5 @ ( X3 @ X19 @ X20 ) ) )
& ! [X21: b] :
( ( X5 @ X21 )
=> ( X6 @ ( X2 @ X21 ) ) )
& ! [X22: b,X23: b] :
( ( ( X5 @ X23 )
& ( X5 @ X22 ) )
=> ( X5 @ ( X3 @ X23 @ X22 ) ) )
& ! [X24: b,X25: b] :
( ( ( X5 @ X25 )
& ( X5 @ X24 ) )
=> ( ( X7 @ ( X2 @ X25 ) @ ( X2 @ X24 ) )
= ( X2 @ ( X3 @ X25 @ X24 ) ) ) )
& ! [X26: g,X27: g] :
( ( ( X1 @ X26 )
& ( X1 @ X27 ) )
=> ( ( X3 @ ( X0 @ X26 ) @ ( X0 @ X27 ) )
= ( X0 @ ( X4 @ X26 @ X27 ) ) ) )
& ! [X28: g] :
( ( X1 @ X28 )
=> ( X5 @ ( X0 @ X28 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: g > b,X2: g > $o,X1: b > a,X5: b > b > b,X3: g > g > g,X4: b > $o,X6: a > $o,X7: a > a > a] :
( ~ ( ! [X9: g,X8: g] :
( ( ( X2 @ X8 )
& ( X2 @ X9 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) )
& ! [X9: g,X8: g] :
( ( ( X2 @ X9 )
& ( X2 @ X8 ) )
=> ( ( X1 @ ( X0 @ ( X3 @ X8 @ X9 ) ) )
= ( X7 @ ( X1 @ ( X0 @ X8 ) ) @ ( X1 @ ( X0 @ X9 ) ) ) ) )
& ! [X9: a,X8: a] :
( ( ( X6 @ X9 )
& ( X6 @ X8 ) )
=> ( X6 @ ( X7 @ X8 @ 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 @ X9 )
& ( X2 @ X8 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) )
& ! [X8: b,X9: b] :
( ( ( X4 @ X8 )
& ( X4 @ X9 ) )
=> ( X4 @ ( X5 @ X8 @ X9 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) )
& ! [X9: b,X8: b] :
( ( ( X4 @ X8 )
& ( X4 @ X9 ) )
=> ( X4 @ ( X5 @ X8 @ X9 ) ) )
& ! [X9: b,X8: b] :
( ( ( X4 @ X8 )
& ( X4 @ X9 ) )
=> ( ( X1 @ ( X5 @ X8 @ X9 ) )
= ( X7 @ ( X1 @ X8 ) @ ( X1 @ X9 ) ) ) )
& ! [X8: g,X9: g] :
( ( ( X2 @ X8 )
& ( X2 @ X9 ) )
=> ( ( X0 @ ( X3 @ X8 @ X9 ) )
= ( X5 @ ( X0 @ X8 ) @ ( X0 @ X9 ) ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( X0 @ X8 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: g > b,X2: g > $o,X1: b > a,X5: b > b > b,X3: g > g > g,X4: b > $o,X6: a > $o,X7: a > a > a] :
( ~ ( ! [X9: g,X8: g] :
( ( ( X2 @ X8 )
& ( X2 @ X9 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) )
& ! [X9: g,X8: g] :
( ( ( X2 @ X9 )
& ( X2 @ X8 ) )
=> ( ( X1 @ ( X0 @ ( X3 @ X8 @ X9 ) ) )
= ( X7 @ ( X1 @ ( X0 @ X8 ) ) @ ( X1 @ ( X0 @ X9 ) ) ) ) )
& ! [X9: a,X8: a] :
( ( ( X6 @ X9 )
& ( X6 @ X8 ) )
=> ( X6 @ ( X7 @ X8 @ 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 @ X9 )
& ( X2 @ X8 ) )
=> ( X2 @ ( X3 @ X8 @ X9 ) ) )
& ! [X8: b,X9: b] :
( ( ( X4 @ X8 )
& ( X4 @ X9 ) )
=> ( X4 @ ( X5 @ X8 @ X9 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) )
& ! [X9: b,X8: b] :
( ( ( X4 @ X8 )
& ( X4 @ X9 ) )
=> ( X4 @ ( X5 @ X8 @ X9 ) ) )
& ! [X9: b,X8: b] :
( ( ( X4 @ X8 )
& ( X4 @ X9 ) )
=> ( ( X1 @ ( X5 @ X8 @ X9 ) )
= ( X7 @ ( X1 @ X8 ) @ ( X1 @ X9 ) ) ) )
& ! [X8: g,X9: g] :
( ( ( X2 @ X8 )
& ( X2 @ X9 ) )
=> ( ( X0 @ ( X3 @ X8 @ X9 ) )
= ( X5 @ ( X0 @ X8 ) @ ( X0 @ X9 ) ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( X0 @ X8 ) ) ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.lSDDNiAfOX/DTF2THF_5824.p',cTHM126A_pme) ).
thf(f64,plain,
( ( ( sK10 @ ( sK13 @ sK14 @ sK15 ) )
!= $true )
| spl17_5 ),
inference(avatar_component_clause,[status(thm)],[f62]) ).
thf(f62,definition,
( spl17_5
<=> ( ( sK10 @ ( sK13 @ sK14 @ sK15 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_5])],[avatar_definition]) ).
thf(f148,plain,
( ~ spl17_3
| spl17_11 ),
inference(avatar_split_clause,[status(thm)],[f145,f136,f53]) ).
thf(f136,definition,
( spl17_11
<=> ( ( sK10 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_11])],[avatar_definition]) ).
thf(f145,plain,
( ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
!= $true )
| spl17_11 ),
inference(trivial_inequality_removal,[status(thm)],[f144]) ).
thf(f144,plain,
( ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
!= $true )
| ( $true != $true )
| spl17_11 ),
inference(superposition,[status(thm)],[f138,f29]) ).
thf(f29,plain,
! [X2: g > b,X3: b > a,X0: g > $o,X1: g > g > g,X4: a > a > a] :
( ( ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
= $true )
| ( ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f138,plain,
( ( ( sK10 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) )
!= $true )
| spl17_11 ),
inference(avatar_component_clause,[status(thm)],[f136]) ).
thf(f143,plain,
( ~ spl17_11
| ~ spl17_12
| spl17_10 ),
inference(avatar_split_clause,[status(thm)],[f134,f104,f140,f136]) ).
thf(f104,definition,
( spl17_10
<=> ( ( sK12 @ ( sK7 @ ( sK9 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) @ ( sK9 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) )
= ( sK12 @ ( sK9 @ ( sK13 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_10])],[avatar_definition]) ).
thf(f134,plain,
( ( $true
!= ( sK10 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) )
| ( ( sK10 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) )
!= $true )
| spl17_10 ),
inference(trivial_inequality_removal,[status(thm)],[f133]) ).
thf(f133,plain,
( ( $true
!= ( sK10 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) )
| ( ( sK12 @ ( sK9 @ ( sK13 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) )
!= ( sK12 @ ( sK9 @ ( sK13 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) ) )
| ( ( sK10 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) )
!= $true )
| spl17_10 ),
inference(superposition,[status(thm)],[f106,f41]) ).
thf(f41,plain,
! [X12: g,X13: g] :
( ( ( sK9 @ ( sK13 @ X12 @ X13 ) )
= ( sK7 @ ( sK9 @ X12 ) @ ( sK9 @ X13 ) ) )
| ( ( sK10 @ X12 )
!= $true )
| ( $true
!= ( sK10 @ X13 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f106,plain,
( ( ( sK12 @ ( sK7 @ ( sK9 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) @ ( sK9 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) )
!= ( sK12 @ ( sK9 @ ( sK13 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) ) )
| spl17_10 ),
inference(avatar_component_clause,[status(thm)],[f104]) ).
thf(f132,plain,
( ~ spl17_10
| ~ spl17_3
| ~ spl17_8
| ~ spl17_9 ),
inference(avatar_split_clause,[status(thm)],[f131,f100,f96,f53,f104]) ).
thf(f96,definition,
( spl17_8
<=> ( ( sK6 @ ( sK9 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_8])],[avatar_definition]) ).
thf(f100,definition,
( spl17_9
<=> ( ( sK6 @ ( sK9 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_9])],[avatar_definition]) ).
thf(f131,plain,
( ( ( sK12 @ ( sK7 @ ( sK9 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) @ ( sK9 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) )
!= ( sK12 @ ( sK9 @ ( sK13 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) ) )
| ~ spl17_3
| ~ spl17_8
| ~ spl17_9 ),
inference(subsumption_resolution,[status(thm)],[f130,f101]) ).
thf(f101,plain,
( ( ( sK6 @ ( sK9 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) )
= $true )
| ~ spl17_9 ),
inference(avatar_component_clause,[status(thm)],[f100]) ).
thf(f130,plain,
( ( ( sK6 @ ( sK9 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) )
!= $true )
| ( ( sK12 @ ( sK7 @ ( sK9 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) @ ( sK9 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) )
!= ( sK12 @ ( sK9 @ ( sK13 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) ) )
| ~ spl17_3
| ~ spl17_8 ),
inference(subsumption_resolution,[status(thm)],[f123,f97]) ).
thf(f97,plain,
( ( ( sK6 @ ( sK9 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) )
= $true )
| ~ spl17_8 ),
inference(avatar_component_clause,[status(thm)],[f96]) ).
thf(f123,plain,
( ( ( sK12 @ ( sK7 @ ( sK9 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) @ ( sK9 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) )
!= ( sK12 @ ( sK9 @ ( sK13 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) ) )
| ( ( sK6 @ ( sK9 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) )
!= $true )
| ( ( sK6 @ ( sK9 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) )
!= $true )
| ~ spl17_3 ),
inference(superposition,[status(thm)],[f122,f30]) ).
thf(f30,plain,
! [X24: b,X23: b] :
( ( ( sK11 @ ( sK12 @ X23 ) @ ( sK12 @ X24 ) )
= ( sK12 @ ( sK7 @ X23 @ X24 ) ) )
| ( $true
!= ( sK6 @ X23 ) )
| ( ( sK6 @ X24 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f122,plain,
( ( ( sK11 @ ( sK12 @ ( sK9 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) @ ( sK12 @ ( sK9 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) )
!= ( sK12 @ ( sK9 @ ( sK13 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) ) )
| ~ spl17_3 ),
inference(trivial_inequality_removal,[status(thm)],[f121]) ).
thf(f121,plain,
( ( $true != $true )
| ( ( sK11 @ ( sK12 @ ( sK9 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) @ ( sK12 @ ( sK9 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) )
!= ( sK12 @ ( sK9 @ ( sK13 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) ) ) )
| ~ spl17_3 ),
inference(superposition,[status(thm)],[f28,f55]) ).
thf(f28,plain,
! [X2: g > b,X3: b > a,X0: g > $o,X1: g > g > g,X4: a > a > a] :
( ( ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 )
!= $true )
| ( ( 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(f129,plain,
( ~ spl17_3
| spl17_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f128]) ).
thf(f128,plain,
( $false
| ~ spl17_3
| spl17_9 ),
inference(subsumption_resolution,[status(thm)],[f127,f55]) ).
thf(f127,plain,
( ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
!= $true )
| spl17_9 ),
inference(trivial_inequality_removal,[status(thm)],[f126]) ).
thf(f126,plain,
( ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
!= $true )
| ( $true != $true )
| spl17_9 ),
inference(superposition,[status(thm)],[f125,f27]) ).
thf(f125,plain,
( ( $true
!= ( sK10 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) )
| spl17_9 ),
inference(trivial_inequality_removal,[status(thm)],[f124]) ).
thf(f124,plain,
( ( $true != $true )
| ( $true
!= ( sK10 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) )
| spl17_9 ),
inference(superposition,[status(thm)],[f102,f40]) ).
thf(f40,plain,
! [X14: g] :
( ( $true
= ( sK6 @ ( sK9 @ X14 ) ) )
| ( ( sK10 @ X14 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f102,plain,
( ( ( sK6 @ ( sK9 @ ( sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) )
!= $true )
| spl17_9 ),
inference(avatar_component_clause,[status(thm)],[f100]) ).
thf(f120,plain,
( ~ spl17_1
| spl17_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f119]) ).
thf(f119,plain,
( $false
| ~ spl17_1
| spl17_6 ),
inference(subsumption_resolution,[status(thm)],[f118,f47]) ).
thf(f47,plain,
( ( ( sK10 @ sK16 )
= $true )
| ~ spl17_1 ),
inference(avatar_component_clause,[status(thm)],[f45]) ).
thf(f45,definition,
( spl17_1
<=> ( ( sK10 @ sK16 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_1])],[avatar_definition]) ).
thf(f118,plain,
( ( ( sK10 @ sK16 )
!= $true )
| spl17_6 ),
inference(trivial_inequality_removal,[status(thm)],[f117]) ).
thf(f117,plain,
( ( ( sK10 @ sK16 )
!= $true )
| ( $true != $true )
| spl17_6 ),
inference(superposition,[status(thm)],[f116,f40]) ).
thf(f116,plain,
( ( $true
!= ( sK6 @ ( sK9 @ sK16 ) ) )
| spl17_6 ),
inference(trivial_inequality_removal,[status(thm)],[f115]) ).
thf(f115,plain,
( ( $true
!= ( sK6 @ ( sK9 @ sK16 ) ) )
| ( $true != $true )
| spl17_6 ),
inference(superposition,[status(thm)],[f68,f39]) ).
thf(f39,plain,
! [X15: b] :
( ( ( sK8 @ ( sK12 @ X15 ) )
= $true )
| ( ( sK6 @ X15 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f68,plain,
( ( ( sK8 @ ( sK12 @ ( sK9 @ sK16 ) ) )
!= $true )
| spl17_6 ),
inference(avatar_component_clause,[status(thm)],[f66]) ).
thf(f66,definition,
( spl17_6
<=> ( ( sK8 @ ( sK12 @ ( sK9 @ sK16 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_6])],[avatar_definition]) ).
thf(f114,plain,
( ~ spl17_3
| spl17_8 ),
inference(avatar_split_clause,[status(thm)],[f111,f96,f53]) ).
thf(f111,plain,
( ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
!= $true )
| spl17_8 ),
inference(trivial_inequality_removal,[status(thm)],[f110]) ).
thf(f110,plain,
( ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
!= $true )
| ( $true != $true )
| spl17_8 ),
inference(superposition,[status(thm)],[f109,f29]) ).
thf(f109,plain,
( ( ( sK10 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) )
!= $true )
| spl17_8 ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
( ( ( sK10 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) )
!= $true )
| ( $true != $true )
| spl17_8 ),
inference(superposition,[status(thm)],[f98,f40]) ).
thf(f98,plain,
( ( ( sK6 @ ( sK9 @ ( sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 ) ) )
!= $true )
| spl17_8 ),
inference(avatar_component_clause,[status(thm)],[f96]) ).
thf(f82,plain,
~ spl17_4,
inference(avatar_split_clause,[status(thm)],[f81,f57]) ).
thf(f57,definition,
( spl17_4
<=> ( $true
= ( sP1 @ sK8 @ sK11 ) ) ),
introduced(definition,[new_symbols(naming,[spl17_4])],[avatar_definition]) ).
thf(f81,plain,
( $true
!= ( sP1 @ sK8 @ sK11 ) ),
inference(subsumption_resolution,[status(thm)],[f80,f25]) ).
thf(f25,plain,
! [X0: a > a > a,X1: a > $o] :
( ( ( X1 @ ( sK3 @ X1 @ X0 ) )
= $true )
| ( ( sP1 @ X1 @ X0 )
!= $true ) ),
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 )
& ( ( X1 @ ( sK3 @ X1 @ X0 ) )
= $true )
& ( ( X1 @ ( sK2 @ X1 @ X0 ) )
= $true ) )
| ( ( sP1 @ X1 @ X0 )
!= $true ) ),
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] :
( ( ( X1 @ ( X0 @ X3 @ X2 ) )
!= $true )
& ( ( X1 @ X3 )
= $true )
& ( $true
= ( X1 @ X2 ) ) )
=> ( ( ( X1 @ ( X0 @ ( sK3 @ X1 @ X0 ) @ ( sK2 @ X1 @ X0 ) ) )
!= $true )
& ( ( X1 @ ( sK3 @ X1 @ X0 ) )
= $true )
& ( ( X1 @ ( sK2 @ X1 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X0: a > a > a,X1: a > $o] :
( ? [X2: a,X3: a] :
( ( ( X1 @ ( X0 @ X3 @ X2 ) )
!= $true )
& ( ( X1 @ X3 )
= $true )
& ( $true
= ( X1 @ X2 ) ) )
| ( ( sP1 @ X1 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
! [X7: a > a > a,X6: a > $o] :
( ? [X12: a,X13: a] :
( ( ( X6 @ ( X7 @ X13 @ X12 ) )
!= $true )
& ( ( X6 @ X13 )
= $true )
& ( ( X6 @ X12 )
= $true ) )
| ( ( sP1 @ X6 @ X7 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f80,plain,
( ( $true
!= ( sK8 @ ( sK3 @ sK8 @ sK11 ) ) )
| ( $true
!= ( sP1 @ sK8 @ sK11 ) ) ),
inference(subsumption_resolution,[status(thm)],[f79,f24]) ).
thf(f24,plain,
! [X0: a > a > a,X1: a > $o] :
( ( ( X1 @ ( sK2 @ X1 @ X0 ) )
= $true )
| ( ( sP1 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f79,plain,
( ( ( sK8 @ ( sK2 @ sK8 @ sK11 ) )
!= $true )
| ( $true
!= ( sP1 @ sK8 @ sK11 ) )
| ( $true
!= ( sK8 @ ( sK3 @ sK8 @ sK11 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f78]) ).
thf(f78,plain,
( ( $true
!= ( sP1 @ sK8 @ sK11 ) )
| ( $true
!= ( sK8 @ ( sK3 @ sK8 @ sK11 ) ) )
| ( ( sK8 @ ( sK2 @ sK8 @ sK11 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f26,f32]) ).
thf(f32,plain,
! [X19: a,X20: a] :
( ( ( sK8 @ ( sK11 @ X20 @ X19 ) )
= $true )
| ( ( sK8 @ X19 )
!= $true )
| ( ( sK8 @ X20 )
!= $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 )
| ( ( sP1 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f14]) ).
thf(f77,plain,
( spl17_1
| spl17_4
| spl17_7
| spl17_3 ),
inference(avatar_split_clause,[status(thm)],[f35,f53,f73,f57,f45]) ).
thf(f35,plain,
( ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
= $true )
| ( ( sK10 @ sK15 )
= $true )
| ( ( sK10 @ sK16 )
= $true )
| ( $true
= ( sP1 @ sK8 @ sK11 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f76,plain,
( spl17_7
| spl17_3
| spl17_4
| ~ spl17_6 ),
inference(avatar_split_clause,[status(thm)],[f36,f66,f57,f53,f73]) ).
thf(f36,plain,
( ( ( sK8 @ ( sK12 @ ( sK9 @ sK16 ) ) )
!= $true )
| ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
= $true )
| ( ( sK10 @ sK15 )
= $true )
| ( $true
= ( sP1 @ sK8 @ sK11 ) ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f71,plain,
( spl17_1
| ~ spl17_5
| spl17_3
| spl17_4 ),
inference(avatar_split_clause,[status(thm)],[f33,f57,f53,f62,f45]) ).
thf(f33,plain,
( ( ( sK10 @ sK16 )
= $true )
| ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
= $true )
| ( $true
= ( sP1 @ sK8 @ sK11 ) )
| ( ( sK10 @ ( sK13 @ sK14 @ sK15 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f70,plain,
( ~ spl17_6
| spl17_4
| spl17_2
| spl17_3 ),
inference(avatar_split_clause,[status(thm)],[f38,f53,f49,f57,f66]) ).
thf(f38,plain,
( ( $true
= ( sP1 @ sK8 @ sK11 ) )
| ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
= $true )
| ( ( sK8 @ ( sK12 @ ( sK9 @ sK16 ) ) )
!= $true )
| ( ( sK10 @ sK14 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f69,plain,
( spl17_4
| ~ spl17_5
| spl17_3
| ~ spl17_6 ),
inference(avatar_split_clause,[status(thm)],[f34,f66,f53,f62,f57]) ).
thf(f34,plain,
( ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
= $true )
| ( ( sK10 @ ( sK13 @ sK14 @ sK15 ) )
!= $true )
| ( $true
= ( sP1 @ sK8 @ sK11 ) )
| ( ( sK8 @ ( sK12 @ ( sK9 @ sK16 ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
thf(f60,plain,
( spl17_1
| spl17_2
| spl17_3
| spl17_4 ),
inference(avatar_split_clause,[status(thm)],[f37,f57,f53,f49,f45]) ).
thf(f37,plain,
( ( $true
= ( sP1 @ sK8 @ sK11 ) )
| ( ( sK10 @ sK14 )
= $true )
| ( ( sK10 @ sK16 )
= $true )
| ( ( sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f23]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.13 % Problem : SEU905^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.14 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.14/0.34 % Computer : n022.cluster.edu
% 0.14/0.34 % Model : x86_64 x86_64
% 0.14/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.34 % Memory : 8042.1875MB
% 0.14/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.34 % CPULimit : 300
% 0.14/0.34 % WCLimit : 300
% 0.14/0.34 % DateTime : Tue Feb 24 12:36:21 EST 2026
% 0.14/0.34 % CPUTime :
% 0.14/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.44 ---- Original DTF file ---
% 0.16/0.44 thf(spec,logic,$$dhol).
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 % File : SEU905^5 : TPTP v9.2.1. Released v4.0.0.
% 0.16/0.44 % Domain : Set Theory
% 0.16/0.44 % Problem : TPS problem THM126A
% 0.16/0.44 % Version : Especial.
% 0.16/0.44 % English :
% 0.16/0.44
% 0.16/0.44 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.16/0.44 % Source : [Bro09]
% 0.16/0.44 % Names : tps_0523 [Bro09]
% 0.16/0.44 % : THM126A [TPS]
% 0.16/0.44
% 0.16/0.44 % Status : Theorem
% 0.16/0.44 % Rating : 0.00 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 v4.0.1, 0.33 v4.0.0
% 0.16/0.44 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.16/0.44 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.16/0.44 % Maximal formula atoms : 3 ( 3 avg)
% 0.16/0.44 % Number of connectives : 104 ( 2 ~; 0 |; 19 &; 70 @)
% 0.16/0.44 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.16/0.44 % Maximal formula depth : 23 ( 23 avg)
% 0.16/0.44 % Number of types : 4 ( 3 usr)
% 0.16/0.44 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.16/0.44 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.16/0.44 % Number of variables : 29 ( 0 ^; 29 !; 0 ?; 29 :)
% 0.16/0.44 % SPC : TH0_THM_EQU_NAR
% 0.16/0.44
% 0.16/0.44 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.16/0.44 % project in the Department of Mathematical Sciences at Carnegie
% 0.16/0.44 % Mellon University. Distributed under the Creative Commons copyleft
% 0.16/0.44 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.16/0.44 % : Polymorphic definitions expanded.
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 thf(g_type,type,
% 0.16/0.44 g: $tType ).
% 0.16/0.44
% 0.16/0.44 thf(b_type,type,
% 0.16/0.44 b: $tType ).
% 0.16/0.44
% 0.16/0.44 thf(a_type,type,
% 0.16/0.44 a: $tType ).
% 0.16/0.44
% 0.16/0.44 thf(cTHM126A_pme,conjecture,
% 0.16/0.44 ! [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] :
% 0.16/0.44 ( ~ ( ! [Xx: g,Xy: g] :
% 0.16/0.44 ( ( ( Xs1 @ Xx )
% 0.16/0.44 & ( Xs1 @ Xy ) )
% 0.16/0.44 => ( Xs1 @ ( Xf1 @ Xx @ Xy ) ) )
% 0.16/0.44 & ! [Xx: a,Xy: a] :
% 0.16/0.44 ( ( ( Xs3 @ Xx )
% 0.16/0.44 & ( Xs3 @ Xy ) )
% 0.16/0.44 => ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
% 0.16/0.44 & ! [Xx: g] :
% 0.16/0.44 ( ( Xs1 @ Xx )
% 0.16/0.44 => ( Xs3 @ ( Xh2 @ ( Xh1 @ Xx ) ) ) )
% 0.16/0.44 & ! [Xx: g,Xy: g] :
% 0.16/0.44 ( ( ( Xs1 @ Xx )
% 0.16/0.44 & ( Xs1 @ Xy ) )
% 0.16/0.44 => ( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx @ Xy ) ) )
% 0.16/0.44 = ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) @ ( Xh2 @ ( Xh1 @ Xy ) ) ) ) ) )
% 0.16/0.44 => ~ ( ! [Xx: g,Xy: g] :
% 0.16/0.44 ( ( ( Xs1 @ Xx )
% 0.16/0.44 & ( Xs1 @ Xy ) )
% 0.16/0.44 => ( Xs1 @ ( Xf1 @ Xx @ Xy ) ) )
% 0.16/0.44 & ! [Xx: b,Xy: b] :
% 0.16/0.44 ( ( ( Xs2 @ Xx )
% 0.16/0.44 & ( Xs2 @ Xy ) )
% 0.16/0.44 => ( Xs2 @ ( Xf2 @ Xx @ Xy ) ) )
% 0.16/0.44 & ! [Xx: g] :
% 0.16/0.44 ( ( Xs1 @ Xx )
% 0.16/0.44 => ( Xs2 @ ( Xh1 @ Xx ) ) )
% 0.16/0.44 & ! [Xx: g,Xy: g] :
% 0.16/0.44 ( ( ( Xs1 @ Xx )
% 0.16/0.44 & ( Xs1 @ Xy ) )
% 0.16/0.44 => ( ( Xh1 @ ( Xf1 @ Xx @ Xy ) )
% 0.16/0.44 = ( Xf2 @ ( Xh1 @ Xx ) @ ( Xh1 @ Xy ) ) ) )
% 0.16/0.44 & ! [Xx: b,Xy: b] :
% 0.16/0.44 ( ( ( Xs2 @ Xx )
% 0.16/0.44 & ( Xs2 @ Xy ) )
% 0.16/0.44 => ( Xs2 @ ( Xf2 @ Xx @ Xy ) ) )
% 0.16/0.44 & ! [Xx: a,Xy: a] :
% 0.16/0.44 ( ( ( Xs3 @ Xx )
% 0.16/0.44 & ( Xs3 @ Xy ) )
% 0.16/0.44 => ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
% 0.16/0.44 & ! [Xx: b] :
% 0.16/0.44 ( ( Xs2 @ Xx )
% 0.16/0.44 => ( Xs3 @ ( Xh2 @ Xx ) ) )
% 0.16/0.44 & ! [Xx: b,Xy: b] :
% 0.16/0.44 ( ( ( Xs2 @ Xx )
% 0.16/0.44 & ( Xs2 @ Xy ) )
% 0.16/0.44 => ( ( Xh2 @ ( Xf2 @ Xx @ Xy ) )
% 0.16/0.44 = ( Xf3 @ ( Xh2 @ Xx ) @ ( Xh2 @ Xy ) ) ) ) ) ) ).
% 0.16/0.44
% 0.16/0.44 %------------------------------------------------------------------------------
% 0.16/0.44 ------------------------
% 1.31/1.14 ---- Embedded in THF ---
% 1.31/1.14 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.31/1.14 %%% Generated on Tue Feb 24 12:36:22 EST 2026
% 1.31/1.14 %%% using '$$dhol' embedding, version 1.3.0.
% 1.31/1.14 %%% Logic specification used:
% 1.31/1.14 %%% thf(spec, logic, $$dhol).
% 1.31/1.14
% 1.31/1.14 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.lSDDNiAfOX/DTF2DTF5824.p
% See solution above
% 1.31/1.14 ------------------------
% 1.31/1.14 ---- Cleaned THF ---
% 1.31/1.15 thf(g_type,type,
% 1.31/1.15 g: $tType ).
% 1.31/1.15
% 1.31/1.15 thf(b_type,type,
% 1.31/1.15 b: $tType ).
% 1.31/1.15
% 1.31/1.15 thf(a_type,type,
% 1.31/1.15 a: $tType ).
% 1.31/1.15
% 1.31/1.15 thf(cTHM126A_pme,conjecture,
% 1.31/1.15 ! [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] :
% 1.31/1.15 ( ~ ( ! [Xx: g,Xy: g] :
% 1.31/1.15 ( ( ( Xs1 @ Xx )
% 1.31/1.15 & ( Xs1 @ Xy ) )
% 1.31/1.15 => ( Xs1 @ ( Xf1 @ Xx @ Xy ) ) )
% 1.31/1.15 & ! [Xx: a,Xy: a] :
% 1.31/1.15 ( ( ( Xs3 @ Xx )
% 1.31/1.15 & ( Xs3 @ Xy ) )
% 1.31/1.15 => ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
% 1.31/1.15 & ! [Xx: g] :
% 1.31/1.15 ( ( Xs1 @ Xx )
% 1.31/1.15 => ( Xs3 @ ( Xh2 @ ( Xh1 @ Xx ) ) ) )
% 1.31/1.15 & ! [Xx: g,Xy: g] :
% 1.31/1.15 ( ( ( Xs1 @ Xx )
% 1.31/1.15 & ( Xs1 @ Xy ) )
% 1.31/1.15 => ( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx @ Xy ) ) )
% 1.31/1.15 = ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) @ ( Xh2 @ ( Xh1 @ Xy ) ) ) ) ) )
% 1.31/1.15 => ~ ( ! [Xx: g,Xy: g] :
% 1.31/1.15 ( ( ( Xs1 @ Xx )
% 1.31/1.15 & ( Xs1 @ Xy ) )
% 1.31/1.15 => ( Xs1 @ ( Xf1 @ Xx @ Xy ) ) )
% 1.31/1.15 & ! [Xx: b,Xy: b] :
% 1.31/1.15 ( ( ( Xs2 @ Xx )
% 1.31/1.15 & ( Xs2 @ Xy ) )
% 1.31/1.15 => ( Xs2 @ ( Xf2 @ Xx @ Xy ) ) )
% 1.31/1.15 & ! [Xx: g] :
% 1.31/1.15 ( ( Xs1 @ Xx )
% 1.31/1.15 => ( Xs2 @ ( Xh1 @ Xx ) ) )
% 1.31/1.15 & ! [Xx: g,Xy: g] :
% 1.31/1.15 ( ( ( Xs1 @ Xx )
% 1.31/1.15 & ( Xs1 @ Xy ) )
% 1.31/1.15 => ( ( Xh1 @ ( Xf1 @ Xx @ Xy ) )
% 1.31/1.15 = ( Xf2 @ ( Xh1 @ Xx ) @ ( Xh1 @ Xy ) ) ) )
% 1.31/1.15 & ! [Xx: b,Xy: b] :
% 1.31/1.15 ( ( ( Xs2 @ Xx )
% 1.31/1.15 & ( Xs2 @ Xy ) )
% 1.31/1.15 => ( Xs2 @ ( Xf2 @ Xx @ Xy ) ) )
% 1.31/1.15 & ! [Xx: a,Xy: a] :
% 1.31/1.15 ( ( ( Xs3 @ Xx )
% 1.31/1.15 & ( Xs3 @ Xy ) )
% 1.31/1.15 => ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
% 1.31/1.15 & ! [Xx: b] :
% 1.31/1.15 ( ( Xs2 @ Xx )
% 1.31/1.15 => ( Xs3 @ ( Xh2 @ Xx ) ) )
% 1.31/1.15 & ! [Xx: b,Xy: b] :
% 1.31/1.15 ( ( ( Xs2 @ Xx )
% 1.31/1.15 & ( Xs2 @ Xy ) )
% 1.31/1.15 => ( ( Xh2 @ ( Xf2 @ Xx @ Xy ) )
% 1.31/1.15 = ( Xf3 @ ( Xh2 @ Xx ) @ ( Xh2 @ Xy ) ) ) ) ) ) ).
% 1.31/1.15 ------------------------
% 1.31/1.16 % (5924)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5824 for (2999ds/183Mi)
% 1.31/1.16 % (5925)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_5824 for (2999ds/4Mi)
% 1.31/1.16 % (5929)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_5824 for (2999ds/275Mi)
% 1.31/1.17 % (5926)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_5824 for (2999ds/27Mi)
% 1.31/1.17 % (5927)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5824 for (2999ds/2Mi)
% 1.31/1.17 % (5928)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_5824 for (2999ds/2Mi)
% 1.31/1.17 % (5930)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5824 for (2999ds/18Mi)
% 1.31/1.17 % (5928)Instruction limit reached!
% 1.31/1.17 % (5928)------------------------------
% 1.31/1.17 % (5928)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.17 % (5928)Termination reason: Unknown
% 1.31/1.17 % (5928)Termination phase: shuffling
% 1.31/1.17
% 1.31/1.17 % (5928)Memory used [KB]: 1023
% 1.31/1.17 % (5928)Time elapsed: 0.002 s
% 1.31/1.17 % (5928)Instructions burned: 2 (million)
% 1.31/1.17 % (5928)------------------------------
% 1.31/1.17 % (5928)------------------------------
% 1.31/1.17 % (5927)Instruction limit reached!
% 1.31/1.17 % (5927)------------------------------
% 1.31/1.17 % (5927)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.17 % (5927)Termination reason: Unknown
% 1.31/1.17 % (5927)Termination phase: Preprocessing 3
% 1.31/1.17
% 1.31/1.17 % (5927)Memory used [KB]: 1023
% 1.31/1.17 % (5927)Time elapsed: 0.003 s
% 1.31/1.17 % (5927)Instructions burned: 3 (million)
% 1.31/1.17 % (5927)------------------------------
% 1.31/1.17 % (5927)------------------------------
% 1.31/1.17 % (5925)Instruction limit reached!
% 1.31/1.17 % (5925)------------------------------
% 1.31/1.17 % (5925)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.17 % (5925)Termination reason: Unknown
% 1.31/1.17 % (5925)Termination phase: Property scanning
% 1.31/1.17
% 1.31/1.17 % (5925)Memory used [KB]: 1023
% 1.31/1.17 % (5925)Time elapsed: 0.003 s
% 1.31/1.17 % (5925)Instructions burned: 4 (million)
% 1.31/1.17 % (5925)------------------------------
% 1.31/1.17 % (5925)------------------------------
% 1.31/1.17 % (5930)Instruction limit reached!
% 1.31/1.17 % (5930)------------------------------
% 1.31/1.17 % (5930)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.17 % (5930)Termination reason: Unknown
% 1.31/1.17 % (5930)Termination phase: Saturation
% 1.31/1.17
% 1.31/1.17 % (5930)Memory used [KB]: 5756
% 1.31/1.17 % (5930)Time elapsed: 0.011 s
% 1.31/1.17 % (5930)Instructions burned: 18 (million)
% 1.31/1.17 % (5930)------------------------------
% 1.31/1.17 % (5930)------------------------------
% 1.31/1.18 % (5926)Instruction limit reached!
% 1.31/1.18 % (5926)------------------------------
% 1.31/1.18 % (5926)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.18 % (5926)Termination reason: Unknown
% 1.31/1.18 % (5926)Termination phase: Saturation
% 1.31/1.18
% 1.31/1.18 % (5926)Memory used [KB]: 5756
% 1.31/1.18 % (5926)Time elapsed: 0.016 s
% 1.31/1.18 % (5926)Instructions burned: 28 (million)
% 1.31/1.18 % (5926)------------------------------
% 1.31/1.18 % (5926)------------------------------
% 1.31/1.18 % (5933)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_5824 for (2999ds/15Mi)
% 1.31/1.18 % (5931)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5824 for (2999ds/3Mi)
% 1.31/1.18 % (5929)First to succeed.
% 1.31/1.18 % (5932)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_5824 for (2999ds/37Mi)
% 1.31/1.18 % (5931)Instruction limit reached!
% 1.31/1.18 % (5931)------------------------------
% 1.31/1.18 % (5931)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.18 % (5931)Termination reason: Unknown
% 1.31/1.18 % (5931)Termination phase: Preprocessing 3
% 1.31/1.18
% 1.31/1.18 % (5931)Memory used [KB]: 1023
% 1.31/1.18 % (5931)Time elapsed: 0.003 s
% 1.31/1.18 % (5931)Instructions burned: 4 (million)
% 1.31/1.18 % (5931)------------------------------
% 1.31/1.18 % (5931)------------------------------
% 1.31/1.19 % (5933)Instruction limit reached!
% 1.31/1.19 % (5933)------------------------------
% 1.31/1.19 % (5933)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.19 % (5933)Termination reason: Unknown
% 1.31/1.19 % (5933)Termination phase: Saturation
% 1.31/1.19
% 1.31/1.19 % (5933)Memory used [KB]: 5756
% 1.31/1.19 % (5933)Time elapsed: 0.006 s
% 1.31/1.19 % (5933)Instructions burned: 15 (million)
% 1.31/1.19 % (5933)------------------------------
% 1.31/1.19 % (5933)------------------------------
% 1.31/1.19 % (5929)Refutation found. Thanks to Tanya!
% 1.31/1.19 % SZS status Theorem for DTF2THF_5824
% 1.31/1.19 % SZS output start Proof for DTF2THF_5824
% 1.31/1.19 thf(type_def_5, type, g: $tType).
% 1.31/1.19 thf(type_def_6, type, b: $tType).
% 1.31/1.19 thf(type_def_8, type, a: $tType).
% 1.31/1.19 thf(func_def_0, type, g: $tType).
% 1.31/1.19 thf(func_def_1, type, b: $tType).
% 1.31/1.19 thf(func_def_2, type, a: $tType).
% 1.31/1.19 thf(func_def_6, type, sP0: (a > a > a) > (b > a) > (g > b) > (g > g > g) > (g > $o) > $o).
% 1.31/1.19 thf(func_def_7, type, sP1: (a > $o) > (a > a > a) > $o).
% 1.31/1.19 thf(func_def_8, type, sK2: (a > $o) > (a > a > a) > a).
% 1.31/1.19 thf(func_def_9, type, sK3: (a > $o) > (a > a > a) > a).
% 1.31/1.19 thf(func_def_10, type, sK4: (a > a > a) > (b > a) > (g > b) > (g > g > g) > (g > $o) > g).
% 1.31/1.19 thf(func_def_11, type, sK5: (a > a > a) > (b > a) > (g > b) > (g > g > g) > (g > $o) > g).
% 1.31/1.19 thf(func_def_12, type, sK6: b > $o).
% 1.31/1.19 thf(func_def_13, type, sK7: b > b > b).
% 1.31/1.19 thf(func_def_14, type, sK8: a > $o).
% 1.31/1.19 thf(func_def_15, type, sK9: g > b).
% 1.31/1.19 thf(func_def_16, type, sK10: g > $o).
% 1.31/1.19 thf(func_def_17, type, sK11: a > a > a).
% 1.31/1.19 thf(func_def_18, type, sK12: b > a).
% 1.31/1.19 thf(func_def_19, type, sK13: g > g > g).
% 1.31/1.19 thf(func_def_20, type, sK14: g).
% 1.31/1.19 thf(func_def_21, type, sK15: g).
% 1.31/1.19 thf(func_def_22, type, sK16: g).
% 1.31/1.19 thf(func_def_24, type, ph18: !>[X0: $tType]:(X0)).
% 1.31/1.19 thf(f161,plain,(
% 1.31/1.19 $false),
% 1.31/1.19 inference(avatar_sat_refutation,[status(thm)],[f60,f69,f70,f71,f76,f77,f82,f114,f120,f129,f132,f143,f148,f153,f160])).
% 1.31/1.19 thf(f160,plain,(
% 1.31/1.19 ~spl17_3 | spl17_12),
% 1.31/1.19 inference(avatar_contradiction_clause,[status(thm)],[f159])).
% 1.31/1.19 thf(f159,plain,(
% 1.31/1.19 $false | (~spl17_3 | spl17_12)),
% 1.31/1.19 inference(subsumption_resolution,[status(thm)],[f158,f55])).
% 1.31/1.19 thf(f55,plain,(
% 1.31/1.19 ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) = $true) | ~spl17_3),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f53])).
% 1.31/1.19 thf(f53,definition,(
% 1.31/1.19 spl17_3 <=> ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) = $true)),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl17_3])],[avatar_definition])).
% 1.31/1.19 thf(f158,plain,(
% 1.31/1.19 ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) != $true) | spl17_12),
% 1.31/1.19 inference(trivial_inequality_removal,[status(thm)],[f157])).
% 1.31/1.19 thf(f157,plain,(
% 1.31/1.19 ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) != $true) | ($true != $true) | spl17_12),
% 1.31/1.19 inference(superposition,[status(thm)],[f142,f27])).
% 1.31/1.19 thf(f27,plain,(
% 1.31/1.19 ( ! [X2 : g > b,X3 : b > a,X0 : g > $o,X1 : g > g > g,X4 : a > a > a] : (((X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true) | ((sP0 @ X4 @ X3 @ X2 @ X1 @ X0) != $true)) )),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f18])).
% 1.31/1.19 thf(f18,plain,(
% 1.31/1.19 ! [X0 : g > $o,X1 : g > g > g,X2 : g > b,X3 : b > a,X4 : a > a > a] : ((((X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true) & ((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))))) & ((X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true)) | ((sP0 @ X4 @ X3 @ X2 @ X1 @ X0) != $true))),
% 1.31/1.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f16,f17])).
% 1.31/1.19 thf(f17,plain,(
% 1.31/1.19 ! [X0 : g > $o,X1 : g > g > g,X2 : g > b,X3 : b > a,X4 : a > a > a] : (? [X5 : g,X6 : g] : (((X0 @ X5) = $true) & ((X4 @ (X3 @ (X2 @ X5)) @ (X3 @ (X2 @ X6))) != (X3 @ (X2 @ (X1 @ X5 @ X6)))) & ((X0 @ X6) = $true)) => (((X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true) & ((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))))) & ((X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true)))),
% 1.31/1.19 introduced(definition,[],[choice_axiom])).
% 1.31/1.19 thf(f16,plain,(
% 1.31/1.19 ! [X0 : g > $o,X1 : g > g > g,X2 : g > b,X3 : b > a,X4 : a > a > a] : (? [X5 : g,X6 : g] : (((X0 @ X5) = $true) & ((X4 @ (X3 @ (X2 @ X5)) @ (X3 @ (X2 @ X6))) != (X3 @ (X2 @ (X1 @ X5 @ X6)))) & ((X0 @ X6) = $true)) | ((sP0 @ X4 @ X3 @ X2 @ X1 @ X0) != $true))),
% 1.31/1.19 inference(rectify,[status(thm)],[f15])).
% 1.31/1.19 thf(f15,plain,(
% 1.31/1.19 ! [X1 : g > $o,X4 : g > g > g,X0 : g > b,X2 : b > a,X7 : a > a > a] : (? [X11 : g,X10 : g] : (((X1 @ X11) = $true) & ((X7 @ (X2 @ (X0 @ X11)) @ (X2 @ (X0 @ X10))) != (X2 @ (X0 @ (X4 @ X11 @ X10)))) & ((X1 @ X10) = $true)) | ((sP0 @ X7 @ X2 @ X0 @ X4 @ X1) != $true))),
% 1.31/1.19 inference(nnf_transformation,[status(thm)],[f8])).
% 1.31/1.19 thf(f8,plain,(
% 1.31/1.19 ! [X1 : g > $o,X4 : g > g > g,X0 : g > b,X2 : b > a,X7 : a > a > a] : (? [X11 : g,X10 : g] : (((X1 @ X11) = $true) & ((X7 @ (X2 @ (X0 @ X11)) @ (X2 @ (X0 @ X10))) != (X2 @ (X0 @ (X4 @ X11 @ X10)))) & ((X1 @ X10) = $true)) | ~((sP0 @ X7 @ X2 @ X0 @ X4 @ X1) = $true))),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.31/1.19 thf(f142,plain,(
% 1.31/1.19 ($true != (sK10 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))) | spl17_12),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f140])).
% 1.31/1.19 thf(f140,definition,(
% 1.31/1.19 spl17_12 <=> ($true = (sK10 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)))),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl17_12])],[avatar_definition])).
% 1.31/1.19 thf(f153,plain,(
% 1.31/1.19 ~spl17_2 | spl17_5 | ~spl17_7),
% 1.31/1.19 inference(avatar_contradiction_clause,[status(thm)],[f152])).
% 1.31/1.19 thf(f152,plain,(
% 1.31/1.19 $false | (~spl17_2 | spl17_5 | ~spl17_7)),
% 1.31/1.19 inference(subsumption_resolution,[status(thm)],[f151,f51])).
% 1.31/1.19 thf(f51,plain,(
% 1.31/1.19 ((sK10 @ sK14) = $true) | ~spl17_2),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f49])).
% 1.31/1.19 thf(f49,definition,(
% 1.31/1.19 spl17_2 <=> ((sK10 @ sK14) = $true)),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl17_2])],[avatar_definition])).
% 1.31/1.19 thf(f151,plain,(
% 1.31/1.19 ((sK10 @ sK14) != $true) | (spl17_5 | ~spl17_7)),
% 1.31/1.19 inference(subsumption_resolution,[status(thm)],[f150,f75])).
% 1.31/1.19 thf(f75,plain,(
% 1.31/1.19 ((sK10 @ sK15) = $true) | ~spl17_7),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f73])).
% 1.31/1.19 thf(f73,definition,(
% 1.31/1.19 spl17_7 <=> ((sK10 @ sK15) = $true)),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl17_7])],[avatar_definition])).
% 1.31/1.19 thf(f150,plain,(
% 1.31/1.19 ((sK10 @ sK15) != $true) | ((sK10 @ sK14) != $true) | spl17_5),
% 1.31/1.19 inference(trivial_inequality_removal,[status(thm)],[f149])).
% 1.31/1.19 thf(f149,plain,(
% 1.31/1.19 ((sK10 @ sK14) != $true) | ((sK10 @ sK15) != $true) | ($true != $true) | spl17_5),
% 1.31/1.19 inference(superposition,[status(thm)],[f64,f42])).
% 1.31/1.19 thf(f42,plain,(
% 1.31/1.19 ( ! [X10 : g,X11 : g] : (((sK10 @ (sK13 @ X11 @ X10)) = $true) | ((sK10 @ X10) != $true) | ((sK10 @ X11) != $true)) )),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f23])).
% 1.31/1.19 thf(f23,plain,(
% 1.31/1.19 ! [X8 : b,X9 : b] : (((sK6 @ X9) != $true) | ((sK6 @ X8) != $true) | ($true = (sK6 @ (sK7 @ X8 @ X9)))) & ! [X10 : g,X11 : g] : (((sK10 @ (sK13 @ X11 @ X10)) = $true) | ((sK10 @ X10) != $true) | ((sK10 @ X11) != $true)) & ! [X12 : g,X13 : g] : (((sK10 @ X12) != $true) | ($true != (sK10 @ X13)) | ((sK9 @ (sK13 @ X12 @ X13)) = (sK7 @ (sK9 @ X12) @ (sK9 @ X13)))) & ! [X14 : g] : (($true = (sK6 @ (sK9 @ X14))) | ((sK10 @ X14) != $true)) & ! [X15 : b] : (((sK6 @ X15) != $true) | ((sK8 @ (sK12 @ X15)) = $true)) & ((((sK10 @ sK14) = $true) & ((sK10 @ sK15) = $true) & ((sK10 @ (sK13 @ sK14 @ sK15)) != $true)) | ($true = (sP1 @ sK8 @ sK11)) | (((sK8 @ (sK12 @ (sK9 @ sK16))) != $true) & ((sK10 @ sK16) = $true)) | ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) = $true)) & ! [X19 : a,X20 : a] : (((sK8 @ X19) != $true) | ((sK8 @ (sK11 @ X20 @ X19)) = $true) | ((sK8 @ X20) != $true)) & ! [X21 : b,X22 : b] : (($true = (sK6 @ (sK7 @ X22 @ X21))) | ($true != (sK6 @ X21)) | ((sK6 @ X22) != $true)) & ! [X23 : b,X24 : b] : (($true != (sK6 @ X23)) | ((sK6 @ X24) != $true) | ((sK11 @ (sK12 @ X23) @ (sK12 @ X24)) = (sK12 @ (sK7 @ X23 @ X24))))),
% 1.31/1.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16])],[f19,f22,f21,f20])).
% 1.31/1.19 thf(f20,plain,(
% 1.31/1.19 ? [X0 : b > $o,X1 : b > b > b,X2 : a > $o,X3 : g > b,X4 : g > $o,X5 : a > a > a,X6 : b > a,X7 : g > g > g] : (! [X8 : b,X9 : b] : (((X0 @ X9) != $true) | ((X0 @ X8) != $true) | ($true = (X0 @ (X1 @ X8 @ X9)))) & ! [X10 : g,X11 : g] : (((X4 @ (X7 @ X11 @ X10)) = $true) | ((X4 @ X10) != $true) | ((X4 @ X11) != $true)) & ! [X12 : g,X13 : g] : (((X4 @ X12) != $true) | ((X4 @ X13) != $true) | ((X1 @ (X3 @ X12) @ (X3 @ X13)) = (X3 @ (X7 @ X12 @ X13)))) & ! [X14 : g] : (((X0 @ (X3 @ X14)) = $true) | ((X4 @ X14) != $true)) & ! [X15 : b] : (((X0 @ X15) != $true) | ((X2 @ (X6 @ X15)) = $true)) & (? [X16 : g,X17 : g] : (((X4 @ X16) = $true) & ($true = (X4 @ X17)) & ((X4 @ (X7 @ X16 @ X17)) != $true)) | ((sP1 @ X2 @ X5) = $true) | ? [X18 : g] : (($true != (X2 @ (X6 @ (X3 @ X18)))) & ((X4 @ X18) = $true)) | ((sP0 @ X5 @ X6 @ X3 @ X7 @ X4) = $true)) & ! [X19 : a,X20 : a] : (((X2 @ X19) != $true) | ((X2 @ (X5 @ X20 @ X19)) = $true) | ($true != (X2 @ X20))) & ! [X21 : b,X22 : b] : (((X0 @ (X1 @ X22 @ X21)) = $true) | ((X0 @ X21) != $true) | ((X0 @ X22) != $true)) & ! [X23 : b,X24 : b] : (((X0 @ X23) != $true) | ((X0 @ X24) != $true) | ((X5 @ (X6 @ X23) @ (X6 @ X24)) = (X6 @ (X1 @ X23 @ X24))))) => (! [X9 : b,X8 : b] : (((sK6 @ X9) != $true) | ((sK6 @ X8) != $true) | ($true = (sK6 @ (sK7 @ X8 @ X9)))) & ! [X11 : g,X10 : g] : (((sK10 @ (sK13 @ X11 @ X10)) = $true) | ((sK10 @ X10) != $true) | ((sK10 @ X11) != $true)) & ! [X13 : g,X12 : g] : (((sK10 @ X12) != $true) | ($true != (sK10 @ X13)) | ((sK9 @ (sK13 @ X12 @ X13)) = (sK7 @ (sK9 @ X12) @ (sK9 @ X13)))) & ! [X14 : g] : (($true = (sK6 @ (sK9 @ X14))) | ((sK10 @ X14) != $true)) & ! [X15 : b] : (((sK6 @ X15) != $true) | ((sK8 @ (sK12 @ X15)) = $true)) & (? [X17 : g,X16 : g] : (($true = (sK10 @ X16)) & ($true = (sK10 @ X17)) & ((sK10 @ (sK13 @ X16 @ X17)) != $true)) | ($true = (sP1 @ sK8 @ sK11)) | ? [X18 : g] : (($true != (sK8 @ (sK12 @ (sK9 @ X18)))) & ((sK10 @ X18) = $true)) | ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) = $true)) & ! [X20 : a,X19 : a] : (((sK8 @ X19) != $true) | ((sK8 @ (sK11 @ X20 @ X19)) = $true) | ((sK8 @ X20) != $true)) & ! [X22 : b,X21 : b] : (($true = (sK6 @ (sK7 @ X22 @ X21))) | ($true != (sK6 @ X21)) | ((sK6 @ X22) != $true)) & ! [X24 : b,X23 : b] : (($true != (sK6 @ X23)) | ((sK6 @ X24) != $true) | ((sK11 @ (sK12 @ X23) @ (sK12 @ X24)) = (sK12 @ (sK7 @ X23 @ X24)))))),
% 1.31/1.19 introduced(definition,[],[choice_axiom])).
% 1.31/1.19 thf(f21,plain,(
% 1.31/1.19 ? [X17 : g,X16 : g] : (($true = (sK10 @ X16)) & ($true = (sK10 @ X17)) & ((sK10 @ (sK13 @ X16 @ X17)) != $true)) => (((sK10 @ sK14) = $true) & ((sK10 @ sK15) = $true) & ((sK10 @ (sK13 @ sK14 @ sK15)) != $true))),
% 1.31/1.19 introduced(definition,[],[choice_axiom])).
% 1.31/1.19 thf(f22,plain,(
% 1.31/1.19 ? [X18 : g] : (($true != (sK8 @ (sK12 @ (sK9 @ X18)))) & ((sK10 @ X18) = $true)) => (((sK8 @ (sK12 @ (sK9 @ sK16))) != $true) & ((sK10 @ sK16) = $true))),
% 1.31/1.19 introduced(definition,[],[choice_axiom])).
% 1.31/1.19 thf(f19,plain,(
% 1.31/1.19 ? [X0 : b > $o,X1 : b > b > b,X2 : a > $o,X3 : g > b,X4 : g > $o,X5 : a > a > a,X6 : b > a,X7 : g > g > g] : (! [X8 : b,X9 : b] : (((X0 @ X9) != $true) | ((X0 @ X8) != $true) | ($true = (X0 @ (X1 @ X8 @ X9)))) & ! [X10 : g,X11 : g] : (((X4 @ (X7 @ X11 @ X10)) = $true) | ((X4 @ X10) != $true) | ((X4 @ X11) != $true)) & ! [X12 : g,X13 : g] : (((X4 @ X12) != $true) | ((X4 @ X13) != $true) | ((X1 @ (X3 @ X12) @ (X3 @ X13)) = (X3 @ (X7 @ X12 @ X13)))) & ! [X14 : g] : (((X0 @ (X3 @ X14)) = $true) | ((X4 @ X14) != $true)) & ! [X15 : b] : (((X0 @ X15) != $true) | ((X2 @ (X6 @ X15)) = $true)) & (? [X16 : g,X17 : g] : (((X4 @ X16) = $true) & ($true = (X4 @ X17)) & ((X4 @ (X7 @ X16 @ X17)) != $true)) | ((sP1 @ X2 @ X5) = $true) | ? [X18 : g] : (($true != (X2 @ (X6 @ (X3 @ X18)))) & ((X4 @ X18) = $true)) | ((sP0 @ X5 @ X6 @ X3 @ X7 @ X4) = $true)) & ! [X19 : a,X20 : a] : (((X2 @ X19) != $true) | ((X2 @ (X5 @ X20 @ X19)) = $true) | ($true != (X2 @ X20))) & ! [X21 : b,X22 : b] : (((X0 @ (X1 @ X22 @ X21)) = $true) | ((X0 @ X21) != $true) | ((X0 @ X22) != $true)) & ! [X23 : b,X24 : b] : (((X0 @ X23) != $true) | ((X0 @ X24) != $true) | ((X5 @ (X6 @ X23) @ (X6 @ X24)) = (X6 @ (X1 @ X23 @ X24)))))),
% 1.31/1.19 inference(rectify,[status(thm)],[f10])).
% 1.31/1.19 thf(f10,plain,(
% 1.31/1.19 ? [X5 : b > $o,X3 : b > b > b,X6 : a > $o,X0 : g > b,X1 : g > $o,X7 : a > a > a,X2 : b > a,X4 : g > g > g] : (! [X19 : b,X20 : b] : (((X5 @ X20) != $true) | ((X5 @ X19) != $true) | ((X5 @ (X3 @ X19 @ X20)) = $true)) & ! [X18 : g,X17 : g] : (($true = (X1 @ (X4 @ X17 @ X18))) | ((X1 @ X18) != $true) | ((X1 @ X17) != $true)) & ! [X26 : g,X27 : g] : (((X1 @ X26) != $true) | ((X1 @ X27) != $true) | ((X3 @ (X0 @ X26) @ (X0 @ X27)) = (X0 @ (X4 @ X26 @ X27)))) & ! [X28 : g] : (($true = (X5 @ (X0 @ X28))) | ((X1 @ X28) != $true)) & ! [X21 : b] : (((X5 @ X21) != $true) | ((X6 @ (X2 @ X21)) = $true)) & (? [X9 : g,X8 : g] : (((X1 @ X9) = $true) & ((X1 @ X8) = $true) & ((X1 @ (X4 @ X9 @ X8)) != $true)) | ((sP1 @ X6 @ X7) = $true) | ? [X14 : g] : (((X6 @ (X2 @ (X0 @ X14))) != $true) & ((X1 @ X14) = $true)) | ((sP0 @ X7 @ X2 @ X0 @ X4 @ X1) = $true)) & ! [X16 : a,X15 : a] : (($true != (X6 @ X16)) | ($true = (X6 @ (X7 @ X15 @ X16))) | ($true != (X6 @ X15))) & ! [X22 : b,X23 : b] : (($true = (X5 @ (X3 @ X23 @ X22))) | ((X5 @ X22) != $true) | ((X5 @ X23) != $true)) & ! [X25 : b,X24 : b] : (((X5 @ X25) != $true) | ((X5 @ X24) != $true) | ((X7 @ (X2 @ X25) @ (X2 @ X24)) = (X2 @ (X3 @ X25 @ X24)))))),
% 1.31/1.19 inference(definition_folding,[status(thm)],[f7,f9,f8])).
% 1.31/1.19 thf(f9,plain,(
% 1.31/1.19 ! [X7 : a > a > a,X6 : a > $o] : (? [X12 : a,X13 : a] : (((X6 @ (X7 @ X13 @ X12)) != $true) & ((X6 @ X13) = $true) & ((X6 @ X12) = $true)) | ~((sP1 @ X6 @ X7) = $true))),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.31/1.19 thf(f7,plain,(
% 1.31/1.19 ? [X5 : b > $o,X3 : b > b > b,X6 : a > $o,X0 : g > b,X1 : g > $o,X7 : a > a > a,X2 : b > a,X4 : g > g > g] : (! [X19 : b,X20 : b] : (((X5 @ X20) != $true) | ((X5 @ X19) != $true) | ((X5 @ (X3 @ X19 @ X20)) = $true)) & ! [X18 : g,X17 : g] : (($true = (X1 @ (X4 @ X17 @ X18))) | ((X1 @ X18) != $true) | ((X1 @ X17) != $true)) & ! [X26 : g,X27 : g] : (((X1 @ X26) != $true) | ((X1 @ X27) != $true) | ((X3 @ (X0 @ X26) @ (X0 @ X27)) = (X0 @ (X4 @ X26 @ X27)))) & ! [X28 : g] : (($true = (X5 @ (X0 @ X28))) | ((X1 @ X28) != $true)) & ! [X21 : b] : (((X5 @ X21) != $true) | ((X6 @ (X2 @ X21)) = $true)) & (? [X9 : g,X8 : g] : (((X1 @ X9) = $true) & ((X1 @ X8) = $true) & ((X1 @ (X4 @ X9 @ X8)) != $true)) | ? [X12 : a,X13 : a] : (((X6 @ (X7 @ X13 @ X12)) != $true) & ((X6 @ X13) = $true) & ((X6 @ X12) = $true)) | ? [X14 : g] : (((X6 @ (X2 @ (X0 @ X14))) != $true) & ((X1 @ X14) = $true)) | ? [X11 : g,X10 : g] : (((X1 @ X11) = $true) & ((X7 @ (X2 @ (X0 @ X11)) @ (X2 @ (X0 @ X10))) != (X2 @ (X0 @ (X4 @ X11 @ X10)))) & ((X1 @ X10) = $true))) & ! [X16 : a,X15 : a] : (($true != (X6 @ X16)) | ($true = (X6 @ (X7 @ X15 @ X16))) | ($true != (X6 @ X15))) & ! [X22 : b,X23 : b] : (($true = (X5 @ (X3 @ X23 @ X22))) | ((X5 @ X22) != $true) | ((X5 @ X23) != $true)) & ! [X25 : b,X24 : b] : (((X5 @ X25) != $true) | ((X5 @ X24) != $true) | ((X7 @ (X2 @ X25) @ (X2 @ X24)) = (X2 @ (X3 @ X25 @ X24)))))),
% 1.31/1.19 inference(flattening,[status(thm)],[f6])).
% 1.31/1.19 thf(f6,plain,(
% 1.31/1.19 ? [X6 : a > $o,X2 : b > a,X3 : b > b > b,X1 : g > $o,X5 : b > $o,X7 : a > a > a,X4 : g > g > g,X0 : g > b] : ((! [X23 : b,X22 : b] : (($true = (X5 @ (X3 @ X23 @ X22))) | (((X5 @ X22) != $true) | ((X5 @ X23) != $true))) & ! [X21 : b] : (((X5 @ X21) != $true) | ((X6 @ (X2 @ X21)) = $true)) & ! [X27 : g,X26 : g] : (((X3 @ (X0 @ X26) @ (X0 @ X27)) = (X0 @ (X4 @ X26 @ X27))) | (((X1 @ X27) != $true) | ((X1 @ X26) != $true))) & ! [X18 : g,X17 : g] : (($true = (X1 @ (X4 @ X17 @ X18))) | (((X1 @ X18) != $true) | ((X1 @ X17) != $true))) & ! [X28 : g] : (($true = (X5 @ (X0 @ X28))) | ((X1 @ X28) != $true)) & ! [X15 : a,X16 : a] : (($true = (X6 @ (X7 @ X15 @ X16))) | (($true != (X6 @ X15)) | ($true != (X6 @ X16)))) & ! [X24 : b,X25 : b] : (((X7 @ (X2 @ X25) @ (X2 @ X24)) = (X2 @ (X3 @ X25 @ X24))) | (((X5 @ X25) != $true) | ((X5 @ X24) != $true))) & ! [X20 : b,X19 : b] : (((X5 @ (X3 @ X19 @ X20)) = $true) | (((X5 @ X19) != $true) | ((X5 @ X20) != $true)))) & (? [X8 : g,X9 : g] : (((X1 @ (X4 @ X9 @ X8)) != $true) & (((X1 @ X8) = $true) & ((X1 @ X9) = $true))) | ? [X13 : a,X12 : a] : (((X6 @ (X7 @ X13 @ X12)) != $true) & (((X6 @ X12) = $true) & ((X6 @ X13) = $true))) | ? [X10 : g,X11 : g] : (((X7 @ (X2 @ (X0 @ X11)) @ (X2 @ (X0 @ X10))) != (X2 @ (X0 @ (X4 @ X11 @ X10)))) & (((X1 @ X11) = $true) & ((X1 @ X10) = $true))) | ? [X14 : g] : (((X6 @ (X2 @ (X0 @ X14))) != $true) & ((X1 @ X14) = $true))))),
% 1.31/1.19 inference(ennf_transformation,[status(thm)],[f5])).
% 1.31/1.19 thf(f5,plain,(
% 1.31/1.19 ~! [X6 : a > $o,X2 : b > a,X3 : b > b > b,X1 : g > $o,X5 : b > $o,X7 : a > a > a,X4 : g > g > g,X0 : g > b] : (~(! [X8 : g,X9 : g] : ((((X1 @ X8) = $true) & ((X1 @ X9) = $true)) => ((X1 @ (X4 @ X9 @ X8)) = $true)) & ! [X13 : a,X12 : a] : ((((X6 @ X12) = $true) & ((X6 @ X13) = $true)) => ((X6 @ (X7 @ X13 @ X12)) = $true)) & ! [X10 : g,X11 : g] : ((((X1 @ X11) = $true) & ((X1 @ X10) = $true)) => ((X7 @ (X2 @ (X0 @ X11)) @ (X2 @ (X0 @ X10))) = (X2 @ (X0 @ (X4 @ X11 @ X10))))) & ! [X14 : g] : (((X1 @ X14) = $true) => ((X6 @ (X2 @ (X0 @ X14))) = $true))) => ~(! [X23 : b,X22 : b] : ((((X5 @ X22) = $true) & ((X5 @ X23) = $true)) => ($true = (X5 @ (X3 @ X23 @ X22)))) & ! [X21 : b] : (((X5 @ X21) = $true) => ((X6 @ (X2 @ X21)) = $true)) & ! [X27 : g,X26 : g] : ((((X1 @ X27) = $true) & ((X1 @ X26) = $true)) => ((X3 @ (X0 @ X26) @ (X0 @ X27)) = (X0 @ (X4 @ X26 @ X27)))) & ! [X18 : g,X17 : g] : ((((X1 @ X18) = $true) & ((X1 @ X17) = $true)) => ($true = (X1 @ (X4 @ X17 @ X18)))) & ! [X28 : g] : (((X1 @ X28) = $true) => ($true = (X5 @ (X0 @ X28)))) & ! [X15 : a,X16 : a] : ((($true = (X6 @ X15)) & ($true = (X6 @ X16))) => ($true = (X6 @ (X7 @ X15 @ X16)))) & ! [X24 : b,X25 : b] : ((((X5 @ X25) = $true) & ((X5 @ X24) = $true)) => ((X7 @ (X2 @ X25) @ (X2 @ X24)) = (X2 @ (X3 @ X25 @ X24)))) & ! [X20 : b,X19 : b] : ((((X5 @ X19) = $true) & ((X5 @ X20) = $true)) => ((X5 @ (X3 @ X19 @ X20)) = $true))))),
% 1.31/1.19 inference(fool_elimination,[status(thm)],[f4])).
% 1.31/1.19 thf(f4,plain,(
% 1.31/1.19 ~! [X0 : g > b,X1 : g > $o,X2 : b > a,X3 : b > b > b,X4 : g > g > g,X5 : b > $o,X6 : a > $o,X7 : a > a > a] : (~(! [X8 : g,X9 : g] : (((X1 @ X9) & (X1 @ X8)) => (X1 @ (X4 @ X9 @ X8))) & ! [X10 : g,X11 : g] : (((X1 @ X10) & (X1 @ X11)) => ((X7 @ (X2 @ (X0 @ X11)) @ (X2 @ (X0 @ X10))) = (X2 @ (X0 @ (X4 @ X11 @ X10))))) & ! [X12 : a,X13 : a] : (((X6 @ X12) & (X6 @ X13)) => (X6 @ (X7 @ X13 @ X12))) & ! [X14 : g] : ((X1 @ X14) => (X6 @ (X2 @ (X0 @ X14))))) => ~(! [X15 : a,X16 : a] : (((X6 @ X15) & (X6 @ X16)) => (X6 @ (X7 @ X15 @ X16))) & ! [X17 : g,X18 : g] : (((X1 @ X18) & (X1 @ X17)) => (X1 @ (X4 @ X17 @ X18))) & ! [X19 : b,X20 : b] : (((X5 @ X19) & (X5 @ X20)) => (X5 @ (X3 @ X19 @ X20))) & ! [X21 : b] : ((X5 @ X21) => (X6 @ (X2 @ X21))) & ! [X22 : b,X23 : b] : (((X5 @ X23) & (X5 @ X22)) => (X5 @ (X3 @ X23 @ X22))) & ! [X24 : b,X25 : b] : (((X5 @ X25) & (X5 @ X24)) => ((X7 @ (X2 @ X25) @ (X2 @ X24)) = (X2 @ (X3 @ X25 @ X24)))) & ! [X26 : g,X27 : g] : (((X1 @ X26) & (X1 @ X27)) => ((X3 @ (X0 @ X26) @ (X0 @ X27)) = (X0 @ (X4 @ X26 @ X27)))) & ! [X28 : g] : ((X1 @ X28) => (X5 @ (X0 @ X28)))))),
% 1.31/1.19 inference(rectify,[status(thm)],[f2])).
% 1.31/1.19 thf(f2,negated_conjecture,(
% 1.31/1.19 ~! [X0 : g > b,X2 : g > $o,X1 : b > a,X5 : b > b > b,X3 : g > g > g,X4 : b > $o,X6 : a > $o,X7 : a > a > a] : (~(! [X9 : g,X8 : g] : (((X2 @ X8) & (X2 @ X9)) => (X2 @ (X3 @ X8 @ X9))) & ! [X9 : g,X8 : g] : (((X2 @ X9) & (X2 @ X8)) => ((X1 @ (X0 @ (X3 @ X8 @ X9))) = (X7 @ (X1 @ (X0 @ X8)) @ (X1 @ (X0 @ X9))))) & ! [X9 : a,X8 : a] : (((X6 @ X9) & (X6 @ X8)) => (X6 @ (X7 @ X8 @ 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 @ X9) & (X2 @ X8)) => (X2 @ (X3 @ X8 @ X9))) & ! [X8 : b,X9 : b] : (((X4 @ X8) & (X4 @ X9)) => (X4 @ (X5 @ X8 @ X9))) & ! [X8 : b] : ((X4 @ X8) => (X6 @ (X1 @ X8))) & ! [X9 : b,X8 : b] : (((X4 @ X8) & (X4 @ X9)) => (X4 @ (X5 @ X8 @ X9))) & ! [X9 : b,X8 : b] : (((X4 @ X8) & (X4 @ X9)) => ((X1 @ (X5 @ X8 @ X9)) = (X7 @ (X1 @ X8) @ (X1 @ X9)))) & ! [X8 : g,X9 : g] : (((X2 @ X8) & (X2 @ X9)) => ((X0 @ (X3 @ X8 @ X9)) = (X5 @ (X0 @ X8) @ (X0 @ X9)))) & ! [X8 : g] : ((X2 @ X8) => (X4 @ (X0 @ X8)))))),
% 1.31/1.19 inference(negated_conjecture,[status(cth)],[f1])).
% 1.31/1.19 thf(f1,conjecture,(
% 1.31/1.19 ! [X0 : g > b,X2 : g > $o,X1 : b > a,X5 : b > b > b,X3 : g > g > g,X4 : b > $o,X6 : a > $o,X7 : a > a > a] : (~(! [X9 : g,X8 : g] : (((X2 @ X8) & (X2 @ X9)) => (X2 @ (X3 @ X8 @ X9))) & ! [X9 : g,X8 : g] : (((X2 @ X9) & (X2 @ X8)) => ((X1 @ (X0 @ (X3 @ X8 @ X9))) = (X7 @ (X1 @ (X0 @ X8)) @ (X1 @ (X0 @ X9))))) & ! [X9 : a,X8 : a] : (((X6 @ X9) & (X6 @ X8)) => (X6 @ (X7 @ X8 @ 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 @ X9) & (X2 @ X8)) => (X2 @ (X3 @ X8 @ X9))) & ! [X8 : b,X9 : b] : (((X4 @ X8) & (X4 @ X9)) => (X4 @ (X5 @ X8 @ X9))) & ! [X8 : b] : ((X4 @ X8) => (X6 @ (X1 @ X8))) & ! [X9 : b,X8 : b] : (((X4 @ X8) & (X4 @ X9)) => (X4 @ (X5 @ X8 @ X9))) & ! [X9 : b,X8 : b] : (((X4 @ X8) & (X4 @ X9)) => ((X1 @ (X5 @ X8 @ X9)) = (X7 @ (X1 @ X8) @ (X1 @ X9)))) & ! [X8 : g,X9 : g] : (((X2 @ X8) & (X2 @ X9)) => ((X0 @ (X3 @ X8 @ X9)) = (X5 @ (X0 @ X8) @ (X0 @ X9)))) & ! [X8 : g] : ((X2 @ X8) => (X4 @ (X0 @ X8)))))),
% 1.31/1.19 file('/export/starexec/sandbox2/tmp/tmp.lSDDNiAfOX/DTF2THF_5824.p',cTHM126A_pme)).
% 1.31/1.19 thf(f64,plain,(
% 1.31/1.19 ((sK10 @ (sK13 @ sK14 @ sK15)) != $true) | spl17_5),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f62])).
% 1.31/1.19 thf(f62,definition,(
% 1.31/1.19 spl17_5 <=> ((sK10 @ (sK13 @ sK14 @ sK15)) = $true)),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl17_5])],[avatar_definition])).
% 1.31/1.19 thf(f148,plain,(
% 1.31/1.19 ~spl17_3 | spl17_11),
% 1.31/1.19 inference(avatar_split_clause,[status(thm)],[f145,f136,f53])).
% 1.31/1.19 thf(f136,definition,(
% 1.31/1.19 spl17_11 <=> ((sK10 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)) = $true)),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl17_11])],[avatar_definition])).
% 1.31/1.19 thf(f145,plain,(
% 1.31/1.19 ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) != $true) | spl17_11),
% 1.31/1.19 inference(trivial_inequality_removal,[status(thm)],[f144])).
% 1.31/1.19 thf(f144,plain,(
% 1.31/1.19 ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) != $true) | ($true != $true) | spl17_11),
% 1.31/1.19 inference(superposition,[status(thm)],[f138,f29])).
% 1.31/1.19 thf(f29,plain,(
% 1.31/1.19 ( ! [X2 : g > b,X3 : b > a,X0 : g > $o,X1 : g > g > g,X4 : a > a > a] : (((X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true) | ((sP0 @ X4 @ X3 @ X2 @ X1 @ X0) != $true)) )),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f18])).
% 1.31/1.19 thf(f138,plain,(
% 1.31/1.19 ((sK10 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)) != $true) | spl17_11),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f136])).
% 1.31/1.19 thf(f143,plain,(
% 1.31/1.19 ~spl17_11 | ~spl17_12 | spl17_10),
% 1.31/1.19 inference(avatar_split_clause,[status(thm)],[f134,f104,f140,f136])).
% 1.31/1.19 thf(f104,definition,(
% 1.31/1.19 spl17_10 <=> ((sK12 @ (sK7 @ (sK9 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)) @ (sK9 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)))) = (sK12 @ (sK9 @ (sK13 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)))))),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl17_10])],[avatar_definition])).
% 1.31/1.19 thf(f134,plain,(
% 1.31/1.19 ($true != (sK10 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))) | ((sK10 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)) != $true) | spl17_10),
% 1.31/1.19 inference(trivial_inequality_removal,[status(thm)],[f133])).
% 1.31/1.19 thf(f133,plain,(
% 1.31/1.19 ($true != (sK10 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))) | ((sK12 @ (sK9 @ (sK13 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)))) != (sK12 @ (sK9 @ (sK13 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))))) | ((sK10 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)) != $true) | spl17_10),
% 1.31/1.19 inference(superposition,[status(thm)],[f106,f41])).
% 1.31/1.19 thf(f41,plain,(
% 1.31/1.19 ( ! [X12 : g,X13 : g] : (((sK9 @ (sK13 @ X12 @ X13)) = (sK7 @ (sK9 @ X12) @ (sK9 @ X13))) | ((sK10 @ X12) != $true) | ($true != (sK10 @ X13))) )),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f23])).
% 1.31/1.19 thf(f106,plain,(
% 1.31/1.19 ((sK12 @ (sK7 @ (sK9 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)) @ (sK9 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)))) != (sK12 @ (sK9 @ (sK13 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))))) | spl17_10),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f104])).
% 1.31/1.19 thf(f132,plain,(
% 1.31/1.19 ~spl17_10 | ~spl17_3 | ~spl17_8 | ~spl17_9),
% 1.31/1.19 inference(avatar_split_clause,[status(thm)],[f131,f100,f96,f53,f104])).
% 1.31/1.19 thf(f96,definition,(
% 1.31/1.19 spl17_8 <=> ((sK6 @ (sK9 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))) = $true)),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl17_8])],[avatar_definition])).
% 1.31/1.19 thf(f100,definition,(
% 1.31/1.19 spl17_9 <=> ((sK6 @ (sK9 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))) = $true)),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl17_9])],[avatar_definition])).
% 1.31/1.19 thf(f131,plain,(
% 1.31/1.19 ((sK12 @ (sK7 @ (sK9 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)) @ (sK9 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)))) != (sK12 @ (sK9 @ (sK13 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))))) | (~spl17_3 | ~spl17_8 | ~spl17_9)),
% 1.31/1.19 inference(subsumption_resolution,[status(thm)],[f130,f101])).
% 1.31/1.19 thf(f101,plain,(
% 1.31/1.19 ((sK6 @ (sK9 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))) = $true) | ~spl17_9),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f100])).
% 1.31/1.19 thf(f130,plain,(
% 1.31/1.19 ((sK6 @ (sK9 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))) != $true) | ((sK12 @ (sK7 @ (sK9 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)) @ (sK9 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)))) != (sK12 @ (sK9 @ (sK13 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))))) | (~spl17_3 | ~spl17_8)),
% 1.31/1.19 inference(subsumption_resolution,[status(thm)],[f123,f97])).
% 1.31/1.19 thf(f97,plain,(
% 1.31/1.19 ((sK6 @ (sK9 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))) = $true) | ~spl17_8),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f96])).
% 1.31/1.19 thf(f123,plain,(
% 1.31/1.19 ((sK12 @ (sK7 @ (sK9 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)) @ (sK9 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)))) != (sK12 @ (sK9 @ (sK13 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))))) | ((sK6 @ (sK9 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))) != $true) | ((sK6 @ (sK9 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))) != $true) | ~spl17_3),
% 1.31/1.19 inference(superposition,[status(thm)],[f122,f30])).
% 1.31/1.19 thf(f30,plain,(
% 1.31/1.19 ( ! [X24 : b,X23 : b] : (((sK11 @ (sK12 @ X23) @ (sK12 @ X24)) = (sK12 @ (sK7 @ X23 @ X24))) | ($true != (sK6 @ X23)) | ((sK6 @ X24) != $true)) )),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f23])).
% 1.31/1.19 thf(f122,plain,(
% 1.31/1.19 ((sK11 @ (sK12 @ (sK9 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))) @ (sK12 @ (sK9 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)))) != (sK12 @ (sK9 @ (sK13 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))))) | ~spl17_3),
% 1.31/1.19 inference(trivial_inequality_removal,[status(thm)],[f121])).
% 1.31/1.19 thf(f121,plain,(
% 1.31/1.19 ($true != $true) | ((sK11 @ (sK12 @ (sK9 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))) @ (sK12 @ (sK9 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)))) != (sK12 @ (sK9 @ (sK13 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))))) | ~spl17_3),
% 1.31/1.19 inference(superposition,[status(thm)],[f28,f55])).
% 1.31/1.19 thf(f28,plain,(
% 1.31/1.19 ( ! [X2 : g > b,X3 : b > a,X0 : g > $o,X1 : g > g > g,X4 : a > a > a] : (((sP0 @ X4 @ X3 @ X2 @ X1 @ X0) != $true) | ((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)))))) )),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f18])).
% 1.31/1.19 thf(f129,plain,(
% 1.31/1.19 ~spl17_3 | spl17_9),
% 1.31/1.19 inference(avatar_contradiction_clause,[status(thm)],[f128])).
% 1.31/1.19 thf(f128,plain,(
% 1.31/1.19 $false | (~spl17_3 | spl17_9)),
% 1.31/1.19 inference(subsumption_resolution,[status(thm)],[f127,f55])).
% 1.31/1.19 thf(f127,plain,(
% 1.31/1.19 ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) != $true) | spl17_9),
% 1.31/1.19 inference(trivial_inequality_removal,[status(thm)],[f126])).
% 1.31/1.19 thf(f126,plain,(
% 1.31/1.19 ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) != $true) | ($true != $true) | spl17_9),
% 1.31/1.19 inference(superposition,[status(thm)],[f125,f27])).
% 1.31/1.19 thf(f125,plain,(
% 1.31/1.19 ($true != (sK10 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))) | spl17_9),
% 1.31/1.19 inference(trivial_inequality_removal,[status(thm)],[f124])).
% 1.31/1.19 thf(f124,plain,(
% 1.31/1.19 ($true != $true) | ($true != (sK10 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))) | spl17_9),
% 1.31/1.19 inference(superposition,[status(thm)],[f102,f40])).
% 1.31/1.19 thf(f40,plain,(
% 1.31/1.19 ( ! [X14 : g] : (($true = (sK6 @ (sK9 @ X14))) | ((sK10 @ X14) != $true)) )),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f23])).
% 1.31/1.19 thf(f102,plain,(
% 1.31/1.19 ((sK6 @ (sK9 @ (sK5 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))) != $true) | spl17_9),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f100])).
% 1.31/1.19 thf(f120,plain,(
% 1.31/1.19 ~spl17_1 | spl17_6),
% 1.31/1.19 inference(avatar_contradiction_clause,[status(thm)],[f119])).
% 1.31/1.19 thf(f119,plain,(
% 1.31/1.19 $false | (~spl17_1 | spl17_6)),
% 1.31/1.19 inference(subsumption_resolution,[status(thm)],[f118,f47])).
% 1.31/1.19 thf(f47,plain,(
% 1.31/1.19 ((sK10 @ sK16) = $true) | ~spl17_1),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f45])).
% 1.31/1.19 thf(f45,definition,(
% 1.31/1.19 spl17_1 <=> ((sK10 @ sK16) = $true)),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl17_1])],[avatar_definition])).
% 1.31/1.19 thf(f118,plain,(
% 1.31/1.19 ((sK10 @ sK16) != $true) | spl17_6),
% 1.31/1.19 inference(trivial_inequality_removal,[status(thm)],[f117])).
% 1.31/1.19 thf(f117,plain,(
% 1.31/1.19 ((sK10 @ sK16) != $true) | ($true != $true) | spl17_6),
% 1.31/1.19 inference(superposition,[status(thm)],[f116,f40])).
% 1.31/1.19 thf(f116,plain,(
% 1.31/1.19 ($true != (sK6 @ (sK9 @ sK16))) | spl17_6),
% 1.31/1.19 inference(trivial_inequality_removal,[status(thm)],[f115])).
% 1.31/1.19 thf(f115,plain,(
% 1.31/1.19 ($true != (sK6 @ (sK9 @ sK16))) | ($true != $true) | spl17_6),
% 1.31/1.19 inference(superposition,[status(thm)],[f68,f39])).
% 1.31/1.19 thf(f39,plain,(
% 1.31/1.19 ( ! [X15 : b] : (((sK8 @ (sK12 @ X15)) = $true) | ((sK6 @ X15) != $true)) )),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f23])).
% 1.31/1.19 thf(f68,plain,(
% 1.31/1.19 ((sK8 @ (sK12 @ (sK9 @ sK16))) != $true) | spl17_6),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f66])).
% 1.31/1.19 thf(f66,definition,(
% 1.31/1.19 spl17_6 <=> ((sK8 @ (sK12 @ (sK9 @ sK16))) = $true)),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl17_6])],[avatar_definition])).
% 1.31/1.19 thf(f114,plain,(
% 1.31/1.19 ~spl17_3 | spl17_8),
% 1.31/1.19 inference(avatar_split_clause,[status(thm)],[f111,f96,f53])).
% 1.31/1.19 thf(f111,plain,(
% 1.31/1.19 ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) != $true) | spl17_8),
% 1.31/1.19 inference(trivial_inequality_removal,[status(thm)],[f110])).
% 1.31/1.19 thf(f110,plain,(
% 1.31/1.19 ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) != $true) | ($true != $true) | spl17_8),
% 1.31/1.19 inference(superposition,[status(thm)],[f109,f29])).
% 1.31/1.19 thf(f109,plain,(
% 1.31/1.19 ((sK10 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)) != $true) | spl17_8),
% 1.31/1.19 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.31/1.19 thf(f108,plain,(
% 1.31/1.19 ((sK10 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10)) != $true) | ($true != $true) | spl17_8),
% 1.31/1.19 inference(superposition,[status(thm)],[f98,f40])).
% 1.31/1.19 thf(f98,plain,(
% 1.31/1.19 ((sK6 @ (sK9 @ (sK4 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10))) != $true) | spl17_8),
% 1.31/1.19 inference(avatar_component_clause,[status(thm)],[f96])).
% 1.31/1.19 thf(f82,plain,(
% 1.31/1.19 ~spl17_4),
% 1.31/1.19 inference(avatar_split_clause,[status(thm)],[f81,f57])).
% 1.31/1.19 thf(f57,definition,(
% 1.31/1.19 spl17_4 <=> ($true = (sP1 @ sK8 @ sK11))),
% 1.31/1.19 introduced(definition,[new_symbols(naming,[spl17_4])],[avatar_definition])).
% 1.31/1.19 thf(f81,plain,(
% 1.31/1.19 ($true != (sP1 @ sK8 @ sK11))),
% 1.31/1.19 inference(subsumption_resolution,[status(thm)],[f80,f25])).
% 1.31/1.19 thf(f25,plain,(
% 1.31/1.19 ( ! [X0 : a > a > a,X1 : a > $o] : (((X1 @ (sK3 @ X1 @ X0)) = $true) | ((sP1 @ X1 @ X0) != $true)) )),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f14])).
% 1.31/1.19 thf(f14,plain,(
% 1.31/1.19 ! [X0 : a > a > a,X1 : a > $o] : ((((X1 @ (X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0))) != $true) & ((X1 @ (sK3 @ X1 @ X0)) = $true) & ((X1 @ (sK2 @ X1 @ X0)) = $true)) | ((sP1 @ X1 @ X0) != $true))),
% 1.31/1.19 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f12,f13])).
% 1.31/1.19 thf(f13,plain,(
% 1.31/1.19 ! [X0 : a > a > a,X1 : a > $o] : (? [X2 : a,X3 : a] : (((X1 @ (X0 @ X3 @ X2)) != $true) & ((X1 @ X3) = $true) & ($true = (X1 @ X2))) => (((X1 @ (X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0))) != $true) & ((X1 @ (sK3 @ X1 @ X0)) = $true) & ((X1 @ (sK2 @ X1 @ X0)) = $true)))),
% 1.31/1.19 introduced(definition,[],[choice_axiom])).
% 1.31/1.19 thf(f12,plain,(
% 1.31/1.19 ! [X0 : a > a > a,X1 : a > $o] : (? [X2 : a,X3 : a] : (((X1 @ (X0 @ X3 @ X2)) != $true) & ((X1 @ X3) = $true) & ($true = (X1 @ X2))) | ((sP1 @ X1 @ X0) != $true))),
% 1.31/1.19 inference(rectify,[status(thm)],[f11])).
% 1.31/1.19 thf(f11,plain,(
% 1.31/1.19 ! [X7 : a > a > a,X6 : a > $o] : (? [X12 : a,X13 : a] : (((X6 @ (X7 @ X13 @ X12)) != $true) & ((X6 @ X13) = $true) & ((X6 @ X12) = $true)) | ((sP1 @ X6 @ X7) != $true))),
% 1.31/1.19 inference(nnf_transformation,[status(thm)],[f9])).
% 1.31/1.19 thf(f80,plain,(
% 1.31/1.19 ($true != (sK8 @ (sK3 @ sK8 @ sK11))) | ($true != (sP1 @ sK8 @ sK11))),
% 1.31/1.19 inference(subsumption_resolution,[status(thm)],[f79,f24])).
% 1.31/1.19 thf(f24,plain,(
% 1.31/1.19 ( ! [X0 : a > a > a,X1 : a > $o] : (((X1 @ (sK2 @ X1 @ X0)) = $true) | ((sP1 @ X1 @ X0) != $true)) )),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f14])).
% 1.31/1.19 thf(f79,plain,(
% 1.31/1.19 ((sK8 @ (sK2 @ sK8 @ sK11)) != $true) | ($true != (sP1 @ sK8 @ sK11)) | ($true != (sK8 @ (sK3 @ sK8 @ sK11)))),
% 1.31/1.19 inference(trivial_inequality_removal,[status(thm)],[f78])).
% 1.31/1.19 thf(f78,plain,(
% 1.31/1.19 ($true != (sP1 @ sK8 @ sK11)) | ($true != (sK8 @ (sK3 @ sK8 @ sK11))) | ((sK8 @ (sK2 @ sK8 @ sK11)) != $true) | ($true != $true)),
% 1.31/1.19 inference(superposition,[status(thm)],[f26,f32])).
% 1.31/1.19 thf(f32,plain,(
% 1.31/1.19 ( ! [X19 : a,X20 : a] : (((sK8 @ (sK11 @ X20 @ X19)) = $true) | ((sK8 @ X19) != $true) | ((sK8 @ X20) != $true)) )),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f23])).
% 1.31/1.19 thf(f26,plain,(
% 1.31/1.19 ( ! [X0 : a > a > a,X1 : a > $o] : (((X1 @ (X0 @ (sK3 @ X1 @ X0) @ (sK2 @ X1 @ X0))) != $true) | ((sP1 @ X1 @ X0) != $true)) )),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f14])).
% 1.31/1.19 thf(f77,plain,(
% 1.31/1.19 spl17_1 | spl17_4 | spl17_7 | spl17_3),
% 1.31/1.19 inference(avatar_split_clause,[status(thm)],[f35,f53,f73,f57,f45])).
% 1.31/1.19 thf(f35,plain,(
% 1.31/1.19 ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) = $true) | ((sK10 @ sK15) = $true) | ((sK10 @ sK16) = $true) | ($true = (sP1 @ sK8 @ sK11))),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f23])).
% 1.31/1.19 thf(f76,plain,(
% 1.31/1.19 spl17_7 | spl17_3 | spl17_4 | ~spl17_6),
% 1.31/1.19 inference(avatar_split_clause,[status(thm)],[f36,f66,f57,f53,f73])).
% 1.31/1.19 thf(f36,plain,(
% 1.31/1.19 ((sK8 @ (sK12 @ (sK9 @ sK16))) != $true) | ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) = $true) | ((sK10 @ sK15) = $true) | ($true = (sP1 @ sK8 @ sK11))),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f23])).
% 1.31/1.19 thf(f71,plain,(
% 1.31/1.19 spl17_1 | ~spl17_5 | spl17_3 | spl17_4),
% 1.31/1.19 inference(avatar_split_clause,[status(thm)],[f33,f57,f53,f62,f45])).
% 1.31/1.19 thf(f33,plain,(
% 1.31/1.19 ((sK10 @ sK16) = $true) | ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) = $true) | ($true = (sP1 @ sK8 @ sK11)) | ((sK10 @ (sK13 @ sK14 @ sK15)) != $true)),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f23])).
% 1.31/1.19 thf(f70,plain,(
% 1.31/1.19 ~spl17_6 | spl17_4 | spl17_2 | spl17_3),
% 1.31/1.19 inference(avatar_split_clause,[status(thm)],[f38,f53,f49,f57,f66])).
% 1.31/1.19 thf(f38,plain,(
% 1.31/1.19 ($true = (sP1 @ sK8 @ sK11)) | ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) = $true) | ((sK8 @ (sK12 @ (sK9 @ sK16))) != $true) | ((sK10 @ sK14) = $true)),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f23])).
% 1.31/1.19 thf(f69,plain,(
% 1.31/1.19 spl17_4 | ~spl17_5 | spl17_3 | ~spl17_6),
% 1.31/1.19 inference(avatar_split_clause,[status(thm)],[f34,f66,f53,f62,f57])).
% 1.31/1.19 thf(f34,plain,(
% 1.31/1.19 ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) = $true) | ((sK10 @ (sK13 @ sK14 @ sK15)) != $true) | ($true = (sP1 @ sK8 @ sK11)) | ((sK8 @ (sK12 @ (sK9 @ sK16))) != $true)),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f23])).
% 1.31/1.19 thf(f60,plain,(
% 1.31/1.19 spl17_1 | spl17_2 | spl17_3 | spl17_4),
% 1.31/1.19 inference(avatar_split_clause,[status(thm)],[f37,f57,f53,f49,f45])).
% 1.31/1.19 thf(f37,plain,(
% 1.31/1.19 ($true = (sP1 @ sK8 @ sK11)) | ((sK10 @ sK14) = $true) | ((sK10 @ sK16) = $true) | ((sP0 @ sK11 @ sK12 @ sK9 @ sK13 @ sK10) = $true)),
% 1.31/1.19 inference(cnf_transformation,[status(thm)],[f23])).
% 1.31/1.19 % SZS output end Proof for DTF2THF_5824
% 1.31/1.19 % (5929)------------------------------
% 1.31/1.19 % (5929)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.31/1.19 % (5929)Termination reason: Refutation
% 1.31/1.19
% 1.31/1.19 % (5929)Memory used [KB]: 5756
% 1.31/1.19 % (5929)Time elapsed: 0.023 s
% 1.31/1.19 % (5929)Instructions burned: 34 (million)
% 1.31/1.19 % (5929)------------------------------
% 1.31/1.19 % (5929)------------------------------
% 1.31/1.19 % (5923)Success in time 0.036 s
%------------------------------------------------------------------------------