%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SYO225^5 : TPTP v9.2.1. Released v4.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% Computer : n019.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:53:42 AM UTC 2026
% Result : Theorem 1.75s 1.48s
% Output : Refutation 1.75s
% Verified :
% SZS Type : Refutation
% Derivation depth : 17
% Number of leaves : 21
% Syntax : Number of formulae : 123 ( 1 unt; 0 typ; 13 def)
% Number of atoms : 1315 ( 479 equ; 0 cnn)
% Maximal formula atoms : 54 ( 10 avg)
% Number of connectives : 2443 ( 257 ~; 261 |; 226 &;1616 @)
% ( 13 <=>; 70 =>; 0 <=; 0 <~>)
% Maximal formula depth : 28 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 220 ( 220 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 18 con; 0-5 aty)
% Number of variables : 392 ( 0 ^; 307 !; 85 ?; 392 :)
% 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 > a > a ) > ( a > $o ) > $o ).
thf(func_def_8,type,
sK2: ( a > a > a ) > ( a > $o ) > a ).
thf(func_def_9,type,
sK3: ( a > a > a ) > ( a > $o ) > 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 > b > b ).
thf(func_def_13,type,
sK7: g > b ).
thf(func_def_14,type,
sK8: b > a ).
thf(func_def_15,type,
sK9: a > $o ).
thf(func_def_16,type,
sK10: g > $o ).
thf(func_def_17,type,
sK11: g > g > g ).
thf(func_def_18,type,
sK12: a > a > a ).
thf(func_def_19,type,
sK13: b > $o ).
thf(func_def_20,type,
sK14: g ).
thf(func_def_21,type,
sK15: g ).
thf(func_def_22,type,
sK16: g ).
thf(func_def_24,type,
ph18:
!>[X0: $tType] : X0 ).
thf(f185,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f63,f68,f73,f78,f79,f80,f96,f102,f124,f134,f144,f155,f165,f170,f181,f184]) ).
thf(f184,plain,
( ~ spl17_4
| ~ spl17_8 ),
inference(avatar_split_clause,[status(thm)],[f183,f85,f60]) ).
thf(f60,definition,
( spl17_4
<=> ( $true
= ( sP1 @ sK12 @ sK9 ) ) ),
introduced(definition,[new_symbols(naming,[spl17_4])],[avatar_definition]) ).
thf(f85,definition,
( spl17_8
<=> ( ( sK9 @ ( sK2 @ sK12 @ sK9 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_8])],[avatar_definition]) ).
thf(f183,plain,
( ( $true
!= ( sP1 @ sK12 @ sK9 ) )
| ~ spl17_8 ),
inference(subsumption_resolution,[status(thm)],[f182,f27]) ).
thf(f27,plain,
! [X0: a > $o,X1: a > a > a] :
( ( ( X0 @ ( sK3 @ X1 @ X0 ) )
= $true )
| ( $true
!= ( sP1 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f15,plain,
! [X0: a > $o,X1: a > a > a] :
( ( ( ( X0 @ ( sK3 @ X1 @ X0 ) )
= $true )
& ( $true
= ( X0 @ ( sK2 @ X1 @ X0 ) ) )
& ( ( X0 @ ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) ) )
!= $true ) )
| ( $true
!= ( sP1 @ X1 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f13,f14]) ).
thf(f14,plain,
! [X0: a > $o,X1: a > a > a] :
( ? [X2: a,X3: a] :
( ( ( X0 @ X3 )
= $true )
& ( ( X0 @ X2 )
= $true )
& ( $true
!= ( X0 @ ( X1 @ X2 @ X3 ) ) ) )
=> ( ( ( X0 @ ( sK3 @ X1 @ X0 ) )
= $true )
& ( $true
= ( X0 @ ( sK2 @ X1 @ X0 ) ) )
& ( ( X0 @ ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X0: a > $o,X1: a > a > a] :
( ? [X2: a,X3: a] :
( ( ( X0 @ X3 )
= $true )
& ( ( X0 @ X2 )
= $true )
& ( $true
!= ( X0 @ ( X1 @ X2 @ X3 ) ) ) )
| ( $true
!= ( sP1 @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
! [X2: a > $o,X7: a > a > a] :
( ? [X21: a,X20: a] :
( ( $true
= ( X2 @ X20 ) )
& ( $true
= ( X2 @ X21 ) )
& ( ( X2 @ ( X7 @ X21 @ X20 ) )
!= $true ) )
| ( ( sP1 @ X7 @ X2 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f10]) ).
thf(f10,plain,
! [X2: a > $o,X7: a > a > a] :
( ? [X21: a,X20: a] :
( ( $true
= ( X2 @ X20 ) )
& ( $true
= ( X2 @ X21 ) )
& ( ( X2 @ ( X7 @ X21 @ X20 ) )
!= $true ) )
| ( ( sP1 @ X7 @ X2 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f182,plain,
( ( $true
!= ( sP1 @ sK12 @ sK9 ) )
| ( $true
!= ( sK9 @ ( sK3 @ sK12 @ sK9 ) ) )
| ~ spl17_8 ),
inference(subsumption_resolution,[status(thm)],[f82,f86]) ).
thf(f86,plain,
( ( ( sK9 @ ( sK2 @ sK12 @ sK9 ) )
= $true )
| ~ spl17_8 ),
inference(avatar_component_clause,[status(thm)],[f85]) ).
thf(f82,plain,
( ( $true
!= ( sP1 @ sK12 @ sK9 ) )
| ( ( sK9 @ ( sK2 @ sK12 @ sK9 ) )
!= $true )
| ( $true
!= ( sK9 @ ( sK3 @ sK12 @ sK9 ) ) ) ),
inference(trivial_inequality_removal,[status(thm)],[f81]) ).
thf(f81,plain,
( ( $true
!= ( sP1 @ sK12 @ sK9 ) )
| ( $true
!= ( sK9 @ ( sK3 @ sK12 @ sK9 ) ) )
| ( ( sK9 @ ( sK2 @ sK12 @ sK9 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f25,f37]) ).
thf(f37,plain,
! [X16: a,X15: a] :
( ( $true
= ( sK9 @ ( sK12 @ X16 @ X15 ) ) )
| ( ( sK9 @ X15 )
!= $true )
| ( ( sK9 @ X16 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f24,plain,
( ! [X8: g] :
( ( ( sK13 @ ( sK7 @ X8 ) )
= $true )
| ( ( sK10 @ X8 )
!= $true ) )
& ! [X9: b,X10: b] :
( ( $true
!= ( sK13 @ X9 ) )
| ( ( sK8 @ ( sK6 @ X10 @ X9 ) )
= ( sK12 @ ( sK8 @ X10 ) @ ( sK8 @ X9 ) ) )
| ( $true
!= ( sK13 @ X10 ) ) )
& ( ( $true
= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) )
| ( ( $true
= ( sK10 @ sK14 ) )
& ( $true
!= ( sK9 @ ( sK8 @ ( sK7 @ sK14 ) ) ) ) )
| ( ( ( sK10 @ ( sK11 @ sK16 @ sK15 ) )
!= $true )
& ( $true
= ( sK10 @ sK15 ) )
& ( ( sK10 @ sK16 )
= $true ) )
| ( $true
= ( sP1 @ sK12 @ sK9 ) ) )
& ! [X14: b] :
( ( ( sK13 @ X14 )
!= $true )
| ( ( sK9 @ ( sK8 @ X14 ) )
= $true ) )
& ! [X15: a,X16: a] :
( ( $true
= ( sK9 @ ( sK12 @ X16 @ X15 ) ) )
| ( ( sK9 @ X15 )
!= $true )
| ( ( sK9 @ X16 )
!= $true ) )
& ! [X17: g] :
( ( ( sK10 @ X17 )
!= $true )
| ( ( sK13 @ ( sK7 @ X17 ) )
= $true ) )
& ! [X18: g,X19: g] :
( ( $true
!= ( sK10 @ X19 ) )
| ( ( sK7 @ ( sK11 @ X18 @ X19 ) )
= ( sK6 @ ( sK7 @ X18 ) @ ( sK7 @ X19 ) ) )
| ( $true
!= ( sK10 @ X18 ) ) )
& ! [X20: g] :
( ( ( sK10 @ X20 )
!= $true )
| ( $true
= ( sK13 @ ( sK7 @ X20 ) ) ) )
& ! [X21: g,X22: g] :
( ( $true
!= ( sK10 @ X21 ) )
| ( ( sK10 @ ( sK11 @ X22 @ X21 ) )
= $true )
| ( $true
!= ( sK10 @ X22 ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16])],[f20,f23,f22,f21]) ).
thf(f21,plain,
( ? [X0: b > b > b,X1: g > b,X2: b > a,X3: a > $o,X4: g > $o,X5: g > g > g,X6: a > a > a,X7: b > $o] :
( ! [X8: g] :
( ( $true
= ( X7 @ ( X1 @ X8 ) ) )
| ( ( X4 @ X8 )
!= $true ) )
& ! [X9: b,X10: b] :
( ( ( X7 @ X9 )
!= $true )
| ( ( X6 @ ( X2 @ X10 ) @ ( X2 @ X9 ) )
= ( X2 @ ( X0 @ X10 @ X9 ) ) )
| ( ( X7 @ X10 )
!= $true ) )
& ( ( $true
= ( sP0 @ X6 @ X2 @ X1 @ X5 @ X4 ) )
| ? [X11: g] :
( ( $true
= ( X4 @ X11 ) )
& ( $true
!= ( X3 @ ( X2 @ ( X1 @ X11 ) ) ) ) )
| ? [X12: g,X13: g] :
( ( ( X4 @ ( X5 @ X13 @ X12 ) )
!= $true )
& ( ( X4 @ X12 )
= $true )
& ( $true
= ( X4 @ X13 ) ) )
| ( ( sP1 @ X6 @ X3 )
= $true ) )
& ! [X14: b] :
( ( ( X7 @ X14 )
!= $true )
| ( ( X3 @ ( X2 @ X14 ) )
= $true ) )
& ! [X15: a,X16: a] :
( ( ( X3 @ ( X6 @ X16 @ X15 ) )
= $true )
| ( ( X3 @ X15 )
!= $true )
| ( $true
!= ( X3 @ X16 ) ) )
& ! [X17: g] :
( ( $true
!= ( X4 @ X17 ) )
| ( $true
= ( X7 @ ( X1 @ X17 ) ) ) )
& ! [X18: g,X19: g] :
( ( ( X4 @ X19 )
!= $true )
| ( ( X0 @ ( X1 @ X18 ) @ ( X1 @ X19 ) )
= ( X1 @ ( X5 @ X18 @ X19 ) ) )
| ( $true
!= ( X4 @ X18 ) ) )
& ! [X20: g] :
( ( $true
!= ( X4 @ X20 ) )
| ( $true
= ( X7 @ ( X1 @ X20 ) ) ) )
& ! [X21: g,X22: g] :
( ( ( X4 @ X21 )
!= $true )
| ( ( X4 @ ( X5 @ X22 @ X21 ) )
= $true )
| ( $true
!= ( X4 @ X22 ) ) ) )
=> ( ! [X8: g] :
( ( ( sK13 @ ( sK7 @ X8 ) )
= $true )
| ( ( sK10 @ X8 )
!= $true ) )
& ! [X10: b,X9: b] :
( ( $true
!= ( sK13 @ X9 ) )
| ( ( sK8 @ ( sK6 @ X10 @ X9 ) )
= ( sK12 @ ( sK8 @ X10 ) @ ( sK8 @ X9 ) ) )
| ( $true
!= ( sK13 @ X10 ) ) )
& ( ( $true
= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) )
| ? [X11: g] :
( ( ( sK10 @ X11 )
= $true )
& ( ( sK9 @ ( sK8 @ ( sK7 @ X11 ) ) )
!= $true ) )
| ? [X13: g,X12: g] :
( ( ( sK10 @ ( sK11 @ X13 @ X12 ) )
!= $true )
& ( $true
= ( sK10 @ X12 ) )
& ( ( sK10 @ X13 )
= $true ) )
| ( $true
= ( sP1 @ sK12 @ sK9 ) ) )
& ! [X14: b] :
( ( ( sK13 @ X14 )
!= $true )
| ( ( sK9 @ ( sK8 @ X14 ) )
= $true ) )
& ! [X16: a,X15: a] :
( ( $true
= ( sK9 @ ( sK12 @ X16 @ X15 ) ) )
| ( ( sK9 @ X15 )
!= $true )
| ( ( sK9 @ X16 )
!= $true ) )
& ! [X17: g] :
( ( ( sK10 @ X17 )
!= $true )
| ( ( sK13 @ ( sK7 @ X17 ) )
= $true ) )
& ! [X19: g,X18: g] :
( ( $true
!= ( sK10 @ X19 ) )
| ( ( sK7 @ ( sK11 @ X18 @ X19 ) )
= ( sK6 @ ( sK7 @ X18 ) @ ( sK7 @ X19 ) ) )
| ( $true
!= ( sK10 @ X18 ) ) )
& ! [X20: g] :
( ( ( sK10 @ X20 )
!= $true )
| ( $true
= ( sK13 @ ( sK7 @ X20 ) ) ) )
& ! [X22: g,X21: g] :
( ( $true
!= ( sK10 @ X21 ) )
| ( ( sK10 @ ( sK11 @ X22 @ X21 ) )
= $true )
| ( $true
!= ( sK10 @ X22 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X11: g] :
( ( ( sK10 @ X11 )
= $true )
& ( ( sK9 @ ( sK8 @ ( sK7 @ X11 ) ) )
!= $true ) )
=> ( ( $true
= ( sK10 @ sK14 ) )
& ( $true
!= ( sK9 @ ( sK8 @ ( sK7 @ sK14 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ? [X13: g,X12: g] :
( ( ( sK10 @ ( sK11 @ X13 @ X12 ) )
!= $true )
& ( $true
= ( sK10 @ X12 ) )
& ( ( sK10 @ X13 )
= $true ) )
=> ( ( ( sK10 @ ( sK11 @ sK16 @ sK15 ) )
!= $true )
& ( $true
= ( sK10 @ sK15 ) )
& ( ( sK10 @ sK16 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
? [X0: b > b > b,X1: g > b,X2: b > a,X3: a > $o,X4: g > $o,X5: g > g > g,X6: a > a > a,X7: b > $o] :
( ! [X8: g] :
( ( $true
= ( X7 @ ( X1 @ X8 ) ) )
| ( ( X4 @ X8 )
!= $true ) )
& ! [X9: b,X10: b] :
( ( ( X7 @ X9 )
!= $true )
| ( ( X6 @ ( X2 @ X10 ) @ ( X2 @ X9 ) )
= ( X2 @ ( X0 @ X10 @ X9 ) ) )
| ( ( X7 @ X10 )
!= $true ) )
& ( ( $true
= ( sP0 @ X6 @ X2 @ X1 @ X5 @ X4 ) )
| ? [X11: g] :
( ( $true
= ( X4 @ X11 ) )
& ( $true
!= ( X3 @ ( X2 @ ( X1 @ X11 ) ) ) ) )
| ? [X12: g,X13: g] :
( ( ( X4 @ ( X5 @ X13 @ X12 ) )
!= $true )
& ( ( X4 @ X12 )
= $true )
& ( $true
= ( X4 @ X13 ) ) )
| ( ( sP1 @ X6 @ X3 )
= $true ) )
& ! [X14: b] :
( ( ( X7 @ X14 )
!= $true )
| ( ( X3 @ ( X2 @ X14 ) )
= $true ) )
& ! [X15: a,X16: a] :
( ( ( X3 @ ( X6 @ X16 @ X15 ) )
= $true )
| ( ( X3 @ X15 )
!= $true )
| ( $true
!= ( X3 @ X16 ) ) )
& ! [X17: g] :
( ( $true
!= ( X4 @ X17 ) )
| ( $true
= ( X7 @ ( X1 @ X17 ) ) ) )
& ! [X18: g,X19: g] :
( ( ( X4 @ X19 )
!= $true )
| ( ( X0 @ ( X1 @ X18 ) @ ( X1 @ X19 ) )
= ( X1 @ ( X5 @ X18 @ X19 ) ) )
| ( $true
!= ( X4 @ X18 ) ) )
& ! [X20: g] :
( ( $true
!= ( X4 @ X20 ) )
| ( $true
= ( X7 @ ( X1 @ X20 ) ) ) )
& ! [X21: g,X22: g] :
( ( ( X4 @ X21 )
!= $true )
| ( ( X4 @ ( X5 @ X22 @ X21 ) )
= $true )
| ( $true
!= ( X4 @ X22 ) ) ) ),
inference(rectify,[status(thm)],[f11]) ).
thf(f11,plain,
? [X0: b > b > b,X5: g > b,X4: b > a,X2: a > $o,X1: g > $o,X3: g > g > g,X7: a > a > a,X6: b > $o] :
( ! [X13: g] :
( ( ( X6 @ ( X5 @ X13 ) )
= $true )
| ( ( X1 @ X13 )
!= $true ) )
& ! [X14: b,X15: b] :
( ( $true
!= ( X6 @ X14 ) )
| ( ( X7 @ ( X4 @ X15 ) @ ( X4 @ X14 ) )
= ( X4 @ ( X0 @ X15 @ X14 ) ) )
| ( $true
!= ( X6 @ X15 ) ) )
& ( ( ( sP0 @ X7 @ X4 @ X5 @ X3 @ X1 )
= $true )
| ? [X24: g] :
( ( ( X1 @ X24 )
= $true )
& ( ( X2 @ ( X4 @ ( X5 @ X24 ) ) )
!= $true ) )
| ? [X22: g,X23: g] :
( ( $true
!= ( X1 @ ( X3 @ X23 @ X22 ) ) )
& ( $true
= ( X1 @ X22 ) )
& ( $true
= ( X1 @ X23 ) ) )
| ( ( sP1 @ X7 @ X2 )
= $true ) )
& ! [X19: b] :
( ( ( X6 @ X19 )
!= $true )
| ( ( X2 @ ( X4 @ X19 ) )
= $true ) )
& ! [X8: a,X9: a] :
( ( ( X2 @ ( X7 @ X9 @ X8 ) )
= $true )
| ( ( X2 @ X8 )
!= $true )
| ( ( X2 @ X9 )
!= $true ) )
& ! [X12: g] :
( ( ( X1 @ X12 )
!= $true )
| ( $true
= ( X6 @ ( X5 @ X12 ) ) ) )
& ! [X17: g,X16: g] :
( ( $true
!= ( X1 @ X16 ) )
| ( ( X5 @ ( X3 @ X17 @ X16 ) )
= ( X0 @ ( X5 @ X17 ) @ ( X5 @ X16 ) ) )
| ( ( X1 @ X17 )
!= $true ) )
& ! [X18: g] :
( ( $true
!= ( X1 @ X18 ) )
| ( $true
= ( X6 @ ( X5 @ X18 ) ) ) )
& ! [X10: g,X11: g] :
( ( $true
!= ( X1 @ X10 ) )
| ( ( X1 @ ( X3 @ X11 @ X10 ) )
= $true )
| ( ( X1 @ X11 )
!= $true ) ) ),
inference(definition_folding,[status(thm)],[f8,f10,f9]) ).
thf(f9,plain,
! [X1: g > $o,X3: g > g > g,X5: g > b,X4: b > a,X7: a > a > a] :
( ? [X25: g,X26: g] :
( ( $true
= ( X1 @ X25 ) )
& ( ( X7 @ ( X4 @ ( X5 @ X25 ) ) @ ( X4 @ ( X5 @ X26 ) ) )
!= ( X4 @ ( X5 @ ( X3 @ X25 @ X26 ) ) ) )
& ( $true
= ( X1 @ X25 ) )
& ( $true
= ( X1 @ X26 ) )
& ( $true
= ( X1 @ X26 ) ) )
| ( ( sP0 @ X7 @ X4 @ X5 @ X3 @ X1 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f8,plain,
? [X0: b > b > b,X5: g > b,X4: b > a,X2: a > $o,X1: g > $o,X3: g > g > g,X7: a > a > a,X6: b > $o] :
( ! [X13: g] :
( ( ( X6 @ ( X5 @ X13 ) )
= $true )
| ( ( X1 @ X13 )
!= $true ) )
& ! [X14: b,X15: b] :
( ( $true
!= ( X6 @ X14 ) )
| ( ( X7 @ ( X4 @ X15 ) @ ( X4 @ X14 ) )
= ( X4 @ ( X0 @ X15 @ X14 ) ) )
| ( $true
!= ( X6 @ X15 ) ) )
& ( ? [X25: g,X26: g] :
( ( $true
= ( X1 @ X25 ) )
& ( ( X7 @ ( X4 @ ( X5 @ X25 ) ) @ ( X4 @ ( X5 @ X26 ) ) )
!= ( X4 @ ( X5 @ ( X3 @ X25 @ X26 ) ) ) )
& ( $true
= ( X1 @ X25 ) )
& ( $true
= ( X1 @ X26 ) )
& ( $true
= ( X1 @ X26 ) ) )
| ? [X24: g] :
( ( ( X1 @ X24 )
= $true )
& ( ( X2 @ ( X4 @ ( X5 @ X24 ) ) )
!= $true ) )
| ? [X22: g,X23: g] :
( ( $true
!= ( X1 @ ( X3 @ X23 @ X22 ) ) )
& ( $true
= ( X1 @ X22 ) )
& ( $true
= ( X1 @ X23 ) ) )
| ? [X21: a,X20: a] :
( ( $true
= ( X2 @ X20 ) )
& ( $true
= ( X2 @ X21 ) )
& ( ( X2 @ ( X7 @ X21 @ X20 ) )
!= $true ) ) )
& ! [X19: b] :
( ( ( X6 @ X19 )
!= $true )
| ( ( X2 @ ( X4 @ X19 ) )
= $true ) )
& ! [X8: a,X9: a] :
( ( ( X2 @ ( X7 @ X9 @ X8 ) )
= $true )
| ( ( X2 @ X8 )
!= $true )
| ( ( X2 @ X9 )
!= $true ) )
& ! [X12: g] :
( ( ( X1 @ X12 )
!= $true )
| ( $true
= ( X6 @ ( X5 @ X12 ) ) ) )
& ! [X17: g,X16: g] :
( ( $true
!= ( X1 @ X16 ) )
| ( ( X5 @ ( X3 @ X17 @ X16 ) )
= ( X0 @ ( X5 @ X17 ) @ ( X5 @ X16 ) ) )
| ( ( X1 @ X17 )
!= $true ) )
& ! [X18: g] :
( ( $true
!= ( X1 @ X18 ) )
| ( $true
= ( X6 @ ( X5 @ X18 ) ) ) )
& ! [X10: g,X11: g] :
( ( $true
!= ( X1 @ X10 ) )
| ( ( X1 @ ( X3 @ X11 @ X10 ) )
= $true )
| ( ( X1 @ X11 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: b > b > b,X2: a > $o,X7: a > a > a,X5: g > b,X6: b > $o,X4: b > a,X3: g > g > g,X1: g > $o] :
( ( ? [X25: g,X26: g] :
( ( ( X7 @ ( X4 @ ( X5 @ X25 ) ) @ ( X4 @ ( X5 @ X26 ) ) )
!= ( X4 @ ( X5 @ ( X3 @ X25 @ X26 ) ) ) )
& ( $true
= ( X1 @ X26 ) )
& ( $true
= ( X1 @ X26 ) )
& ( $true
= ( X1 @ X25 ) )
& ( $true
= ( X1 @ X25 ) ) )
| ? [X20: a,X21: a] :
( ( ( X2 @ ( X7 @ X21 @ X20 ) )
!= $true )
& ( $true
= ( X2 @ X21 ) )
& ( $true
= ( X2 @ X20 ) ) )
| ? [X23: g,X22: g] :
( ( $true
!= ( X1 @ ( X3 @ X23 @ X22 ) ) )
& ( $true
= ( X1 @ X23 ) )
& ( $true
= ( X1 @ X22 ) ) )
| ? [X24: g] :
( ( ( X1 @ X24 )
= $true )
& ( ( X2 @ ( X4 @ ( X5 @ X24 ) ) )
!= $true ) ) )
& ! [X13: g] :
( ( ( X6 @ ( X5 @ X13 ) )
= $true )
| ( ( X1 @ X13 )
!= $true ) )
& ! [X9: a,X8: a] :
( ( ( X2 @ ( X7 @ X9 @ X8 ) )
= $true )
| ( ( X2 @ X8 )
!= $true )
| ( ( X2 @ X9 )
!= $true ) )
& ! [X17: g,X16: g] :
( ( ( X5 @ ( X3 @ X17 @ X16 ) )
= ( X0 @ ( X5 @ X17 ) @ ( X5 @ X16 ) ) )
| ( ( X1 @ X17 )
!= $true )
| ( $true
!= ( X1 @ X16 ) ) )
& ! [X18: g] :
( ( $true
!= ( X1 @ X18 ) )
| ( $true
= ( X6 @ ( X5 @ X18 ) ) ) )
& ! [X12: g] :
( ( ( X1 @ X12 )
!= $true )
| ( $true
= ( X6 @ ( X5 @ X12 ) ) ) )
& ! [X10: g,X11: g] :
( ( ( X1 @ ( X3 @ X11 @ X10 ) )
= $true )
| ( $true
!= ( X1 @ X10 ) )
| ( ( X1 @ X11 )
!= $true ) )
& ! [X15: b,X14: b] :
( ( ( X7 @ ( X4 @ X15 ) @ ( X4 @ X14 ) )
= ( X4 @ ( X0 @ X15 @ X14 ) ) )
| ( $true
!= ( X6 @ X15 ) )
| ( $true
!= ( X6 @ X14 ) ) )
& ! [X19: b] :
( ( ( X6 @ X19 )
!= $true )
| ( ( X2 @ ( X4 @ X19 ) )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f6]) ).
thf(f6,plain,
~ ! [X0: b > b > b,X2: a > $o,X7: a > a > a,X5: g > b,X6: b > $o,X4: b > a,X3: g > g > g,X1: g > $o] :
( ( ! [X13: g] :
( ( ( X1 @ X13 )
= $true )
=> ( ( X6 @ ( X5 @ X13 ) )
= $true ) )
& ! [X9: a,X8: a] :
( ( ( ( X2 @ X8 )
= $true )
& ( ( X2 @ X9 )
= $true ) )
=> ( ( X2 @ ( X7 @ X9 @ X8 ) )
= $true ) )
& ! [X17: g,X16: g] :
( ( ( ( X1 @ X17 )
= $true )
& ( $true
= ( X1 @ X16 ) ) )
=> ( ( X5 @ ( X3 @ X17 @ X16 ) )
= ( X0 @ ( X5 @ X17 ) @ ( X5 @ X16 ) ) ) )
& ! [X18: g] :
( ( $true
= ( X1 @ X18 ) )
=> ( $true
= ( X6 @ ( X5 @ X18 ) ) ) )
& ! [X12: g] :
( ( ( X1 @ X12 )
= $true )
=> ( $true
= ( X6 @ ( X5 @ X12 ) ) ) )
& ! [X10: g,X11: g] :
( ( ( $true
= ( X1 @ X10 ) )
& ( ( X1 @ X11 )
= $true ) )
=> ( ( X1 @ ( X3 @ X11 @ X10 ) )
= $true ) )
& ! [X15: b,X14: b] :
( ( ( $true
= ( X6 @ X15 ) )
& ( $true
= ( X6 @ X14 ) ) )
=> ( ( X7 @ ( X4 @ X15 ) @ ( X4 @ X14 ) )
= ( X4 @ ( X0 @ X15 @ X14 ) ) ) )
& ! [X19: b] :
( ( ( X6 @ X19 )
= $true )
=> ( ( X2 @ ( X4 @ X19 ) )
= $true ) ) )
=> ( ! [X25: g,X26: g] :
( ( ( $true
= ( X1 @ X26 ) )
& ( $true
= ( X1 @ X26 ) )
& ( $true
= ( X1 @ X25 ) )
& ( $true
= ( X1 @ X25 ) ) )
=> ( ( X7 @ ( X4 @ ( X5 @ X25 ) ) @ ( X4 @ ( X5 @ X26 ) ) )
= ( X4 @ ( X5 @ ( X3 @ X25 @ X26 ) ) ) ) )
& ! [X20: a,X21: a] :
( ( ( $true
= ( X2 @ X21 ) )
& ( $true
= ( X2 @ X20 ) ) )
=> ( ( X2 @ ( X7 @ X21 @ X20 ) )
= $true ) )
& ! [X23: g,X22: g] :
( ( ( $true
= ( X1 @ X23 ) )
& ( $true
= ( X1 @ X22 ) ) )
=> ( $true
= ( X1 @ ( X3 @ X23 @ X22 ) ) ) )
& ! [X24: g] :
( ( ( X1 @ X24 )
= $true )
=> ( ( X2 @ ( X4 @ ( X5 @ X24 ) ) )
= $true ) ) ) ),
inference(rectify,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: b > b > b,X2: g > $o,X4: a > $o,X5: g > g > g,X6: b > a,X8: g > b,X9: b > $o,X11: a > a > a] :
( ( ! [X14: a,X15: a] :
( ( ( ( X4 @ X15 )
= $true )
& ( ( X4 @ X14 )
= $true ) )
=> ( ( X4 @ ( X11 @ X15 @ X14 ) )
= $true ) )
& ! [X16: g,X17: g] :
( ( ( $true
= ( X2 @ X16 ) )
& ( $true
= ( X2 @ X17 ) ) )
=> ( ( X2 @ ( X5 @ X17 @ X16 ) )
= $true ) )
& ! [X18: g] :
( ( ( X2 @ X18 )
= $true )
=> ( ( X9 @ ( X8 @ X18 ) )
= $true ) )
& ! [X19: g] :
( ( ( X2 @ X19 )
= $true )
=> ( ( X9 @ ( X8 @ X19 ) )
= $true ) )
& ! [X20: b,X21: b] :
( ( ( ( X9 @ X20 )
= $true )
& ( $true
= ( X9 @ X21 ) ) )
=> ( ( X6 @ ( X0 @ X21 @ X20 ) )
= ( X11 @ ( X6 @ X21 ) @ ( X6 @ X20 ) ) ) )
& ! [X22: g,X23: g] :
( ( ( ( X2 @ X22 )
= $true )
& ( $true
= ( X2 @ X23 ) ) )
=> ( ( X8 @ ( X5 @ X23 @ X22 ) )
= ( X0 @ ( X8 @ X23 ) @ ( X8 @ X22 ) ) ) )
& ! [X24: g] :
( ( ( X2 @ X24 )
= $true )
=> ( ( X9 @ ( X8 @ X24 ) )
= $true ) )
& ! [X25: b] :
( ( ( X9 @ X25 )
= $true )
=> ( ( X4 @ ( X6 @ X25 ) )
= $true ) ) )
=> ( ! [X26: a,X27: a] :
( ( ( ( X4 @ X27 )
= $true )
& ( ( X4 @ X26 )
= $true ) )
=> ( $true
= ( X4 @ ( X11 @ X27 @ X26 ) ) ) )
& ! [X28: g,X29: g] :
( ( ( $true
= ( X2 @ X29 ) )
& ( ( X2 @ X28 )
= $true ) )
=> ( ( X2 @ ( X5 @ X29 @ X28 ) )
= $true ) )
& ! [X30: g] :
( ( ( X2 @ X30 )
= $true )
=> ( ( X4 @ ( X6 @ ( X8 @ X30 ) ) )
= $true ) )
& ! [X31: g,X32: g] :
( ( ( ( X2 @ X32 )
= $true )
& ( ( X2 @ X32 )
= $true )
& ( $true
= ( X2 @ X31 ) )
& ( $true
= ( X2 @ X31 ) ) )
=> ( ( X11 @ ( X6 @ ( X8 @ X31 ) ) @ ( X6 @ ( X8 @ X32 ) ) )
= ( X6 @ ( X8 @ ( X5 @ X31 @ X32 ) ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: b > b > b,X2: g > $o,X4: a > $o,X5: g > g > g,X6: b > a,X8: g > b,X9: b > $o,X11: a > a > a] :
( ( ! [X14: a,X15: a] :
( ( ( X4 @ X15 )
& ( X4 @ X14 ) )
=> ( X4 @ ( X11 @ X15 @ X14 ) ) )
& ! [X16: g,X17: g] :
( ( ( X2 @ X16 )
& ( X2 @ X17 ) )
=> ( X2 @ ( X5 @ X17 @ X16 ) ) )
& ! [X18: g] :
( ( X2 @ X18 )
=> ( X9 @ ( X8 @ X18 ) ) )
& ! [X19: g] :
( ( X2 @ X19 )
=> ( X9 @ ( X8 @ X19 ) ) )
& ! [X20: b,X21: b] :
( ( ( X9 @ X20 )
& ( X9 @ X21 ) )
=> ( ( X6 @ ( X0 @ X21 @ X20 ) )
= ( X11 @ ( X6 @ X21 ) @ ( X6 @ X20 ) ) ) )
& ! [X22: g,X23: g] :
( ( ( X2 @ X22 )
& ( X2 @ X23 ) )
=> ( ( X8 @ ( X5 @ X23 @ X22 ) )
= ( X0 @ ( X8 @ X23 ) @ ( X8 @ X22 ) ) ) )
& ! [X24: g] :
( ( X2 @ X24 )
=> ( X9 @ ( X8 @ X24 ) ) )
& ! [X25: b] :
( ( X9 @ X25 )
=> ( X4 @ ( X6 @ X25 ) ) ) )
=> ( ! [X26: a,X27: a] :
( ( ( X4 @ X27 )
& ( X4 @ X26 ) )
=> ( X4 @ ( X11 @ X27 @ X26 ) ) )
& ! [X28: g,X29: g] :
( ( ( X2 @ X29 )
& ( X2 @ X28 ) )
=> ( X2 @ ( X5 @ X29 @ X28 ) ) )
& ! [X30: g] :
( ( X2 @ X30 )
=> ( X4 @ ( X6 @ ( X8 @ X30 ) ) ) )
& ! [X31: g,X32: g] :
( ( ( X2 @ X32 )
& ( X2 @ X32 )
& ( X2 @ X31 )
& ( X2 @ X31 ) )
=> ( ( X11 @ ( X6 @ ( X8 @ X31 ) ) @ ( X6 @ ( X8 @ X32 ) ) )
= ( X6 @ ( X8 @ ( X5 @ X31 @ X32 ) ) ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X11: b > b > b,X0: g > b,X8: g > $o,X4: b > $o,X12: a > $o,X9: g > g > g,X7: b > a,X1: b > a,X6: g > b,X10: b > $o,X3: g > g > g,X13: a > a > a,X5: b > b > b,X2: g > $o] :
( ( ! [X15: a,X14: a] :
( ( ( X12 @ X14 )
& ( X12 @ X15 ) )
=> ( X12 @ ( X13 @ X14 @ X15 ) ) )
& ! [X15: g,X14: g] :
( ( ( X8 @ X15 )
& ( X8 @ X14 ) )
=> ( X8 @ ( X9 @ X14 @ X15 ) ) )
& ! [X14: g] :
( ( X8 @ X14 )
=> ( X10 @ ( X6 @ X14 ) ) )
& ! [X14: g] :
( ( X8 @ X14 )
=> ( X10 @ ( X6 @ X14 ) ) )
& ! [X15: b,X14: b] :
( ( ( X10 @ X15 )
& ( X10 @ X14 ) )
=> ( ( X7 @ ( X11 @ X14 @ X15 ) )
= ( X13 @ ( X7 @ X14 ) @ ( X7 @ X15 ) ) ) )
& ! [X15: g,X14: g] :
( ( ( X8 @ X15 )
& ( X8 @ X14 ) )
=> ( ( X6 @ ( X9 @ X14 @ X15 ) )
= ( X11 @ ( X6 @ X14 ) @ ( X6 @ X15 ) ) ) )
& ! [X14: g] :
( ( X8 @ X14 )
=> ( X10 @ ( X6 @ X14 ) ) )
& ! [X14: b] :
( ( X10 @ X14 )
=> ( X12 @ ( X7 @ X14 ) ) ) )
=> ( ! [X15: a,X14: a] :
( ( ( X12 @ X14 )
& ( X12 @ X15 ) )
=> ( X12 @ ( X13 @ X14 @ X15 ) ) )
& ! [X15: g,X14: g] :
( ( ( X8 @ X14 )
& ( X8 @ X15 ) )
=> ( X8 @ ( X9 @ X14 @ X15 ) ) )
& ! [X14: g] :
( ( X8 @ X14 )
=> ( X12 @ ( X7 @ ( X6 @ X14 ) ) ) )
& ! [X14: g,X15: g] :
( ( ( X8 @ X15 )
& ( X8 @ X15 )
& ( X8 @ X14 )
& ( X8 @ X14 ) )
=> ( ( X7 @ ( X6 @ ( X9 @ X14 @ X15 ) ) )
= ( X13 @ ( X7 @ ( X6 @ X14 ) ) @ ( X7 @ ( X6 @ X15 ) ) ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X11: b > b > b,X0: g > b,X8: g > $o,X4: b > $o,X12: a > $o,X9: g > g > g,X7: b > a,X1: b > a,X6: g > b,X10: b > $o,X3: g > g > g,X13: a > a > a,X5: b > b > b,X2: g > $o] :
( ( ! [X15: a,X14: a] :
( ( ( X12 @ X14 )
& ( X12 @ X15 ) )
=> ( X12 @ ( X13 @ X14 @ X15 ) ) )
& ! [X15: g,X14: g] :
( ( ( X8 @ X15 )
& ( X8 @ X14 ) )
=> ( X8 @ ( X9 @ X14 @ X15 ) ) )
& ! [X14: g] :
( ( X8 @ X14 )
=> ( X10 @ ( X6 @ X14 ) ) )
& ! [X14: g] :
( ( X8 @ X14 )
=> ( X10 @ ( X6 @ X14 ) ) )
& ! [X15: b,X14: b] :
( ( ( X10 @ X15 )
& ( X10 @ X14 ) )
=> ( ( X7 @ ( X11 @ X14 @ X15 ) )
= ( X13 @ ( X7 @ X14 ) @ ( X7 @ X15 ) ) ) )
& ! [X15: g,X14: g] :
( ( ( X8 @ X15 )
& ( X8 @ X14 ) )
=> ( ( X6 @ ( X9 @ X14 @ X15 ) )
= ( X11 @ ( X6 @ X14 ) @ ( X6 @ X15 ) ) ) )
& ! [X14: g] :
( ( X8 @ X14 )
=> ( X10 @ ( X6 @ X14 ) ) )
& ! [X14: b] :
( ( X10 @ X14 )
=> ( X12 @ ( X7 @ X14 ) ) ) )
=> ( ! [X15: a,X14: a] :
( ( ( X12 @ X14 )
& ( X12 @ X15 ) )
=> ( X12 @ ( X13 @ X14 @ X15 ) ) )
& ! [X15: g,X14: g] :
( ( ( X8 @ X14 )
& ( X8 @ X15 ) )
=> ( X8 @ ( X9 @ X14 @ X15 ) ) )
& ! [X14: g] :
( ( X8 @ X14 )
=> ( X12 @ ( X7 @ ( X6 @ X14 ) ) ) )
& ! [X14: g,X15: g] :
( ( ( X8 @ X15 )
& ( X8 @ X15 )
& ( X8 @ X14 )
& ( X8 @ X14 ) )
=> ( ( X7 @ ( X6 @ ( X9 @ X14 @ X15 ) ) )
= ( X13 @ ( X7 @ ( X6 @ X14 ) ) @ ( X7 @ ( X6 @ X15 ) ) ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.1ZAPm39mWR/DTF2THF_21330.p',cTHM126_CORRECTED_pme) ).
thf(f25,plain,
! [X0: a > $o,X1: a > a > a] :
( ( ( X0 @ ( X1 @ ( sK2 @ X1 @ X0 ) @ ( sK3 @ X1 @ X0 ) ) )
!= $true )
| ( $true
!= ( sP1 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f181,plain,
( ~ spl17_1
| spl17_14 ),
inference(avatar_contradiction_clause,[status(thm)],[f180]) ).
thf(f180,plain,
( $false
| ~ spl17_1
| spl17_14 ),
inference(subsumption_resolution,[status(thm)],[f176,f50]) ).
thf(f50,plain,
( ( $true
= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) )
| ~ spl17_1 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl17_1
<=> ( $true
= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ),
introduced(definition,[new_symbols(naming,[spl17_1])],[avatar_definition]) ).
thf(f176,plain,
( ( $true
!= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) )
| spl17_14 ),
inference(trivial_inequality_removal,[status(thm)],[f175]) ).
thf(f175,plain,
( ( $true
!= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) )
| ( $true != $true )
| spl17_14 ),
inference(superposition,[status(thm)],[f154,f32]) ).
thf(f32,plain,
! [X2: g > b,X3: b > a,X0: g > $o,X1: g > g > g,X4: a > a > a] :
( ( $true
= ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) )
| ( $true
!= ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
! [X0: g > $o,X1: g > g > g,X2: g > b,X3: b > a,X4: a > a > a] :
( ( ( $true
= ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) )
& ( ( X4 @ ( X3 @ ( X2 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) @ ( X3 @ ( X2 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) )
!= ( X3 @ ( X2 @ ( X1 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) )
& ( $true
= ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) )
& ( ( X0 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
= $true )
& ( ( X0 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
= $true ) )
| ( $true
!= ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f17,f18]) ).
thf(f18,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 @ X5 )
= $true )
& ( $true
= ( X0 @ X6 ) )
& ( $true
= ( X0 @ X6 ) ) )
=> ( ( $true
= ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) )
& ( ( X4 @ ( X3 @ ( X2 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) @ ( X3 @ ( X2 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) )
!= ( X3 @ ( X2 @ ( X1 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) )
& ( $true
= ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) )
& ( ( X0 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
= $true )
& ( ( X0 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
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 @ X5 )
= $true )
& ( $true
= ( X0 @ X6 ) )
& ( $true
= ( X0 @ X6 ) ) )
| ( $true
!= ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(rectify,[status(thm)],[f16]) ).
thf(f16,plain,
! [X1: g > $o,X3: g > g > g,X5: g > b,X4: b > a,X7: a > a > a] :
( ? [X25: g,X26: g] :
( ( $true
= ( X1 @ X25 ) )
& ( ( X7 @ ( X4 @ ( X5 @ X25 ) ) @ ( X4 @ ( X5 @ X26 ) ) )
!= ( X4 @ ( X5 @ ( X3 @ X25 @ X26 ) ) ) )
& ( $true
= ( X1 @ X25 ) )
& ( $true
= ( X1 @ X26 ) )
& ( $true
= ( X1 @ X26 ) ) )
| ( ( sP0 @ X7 @ X4 @ X5 @ X3 @ X1 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f9]) ).
thf(f154,plain,
( ( $true
!= ( sK10 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) )
| spl17_14 ),
inference(avatar_component_clause,[status(thm)],[f152]) ).
thf(f152,definition,
( spl17_14
<=> ( $true
= ( sK10 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_14])],[avatar_definition]) ).
thf(f170,plain,
( ~ spl17_3
| spl17_5
| ~ spl17_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f169]) ).
thf(f169,plain,
( $false
| ~ spl17_3
| spl17_5
| ~ spl17_6 ),
inference(subsumption_resolution,[status(thm)],[f168,f58]) ).
thf(f58,plain,
( ( $true
= ( sK10 @ sK15 ) )
| ~ spl17_3 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f56,definition,
( spl17_3
<=> ( $true
= ( sK10 @ sK15 ) ) ),
introduced(definition,[new_symbols(naming,[spl17_3])],[avatar_definition]) ).
thf(f168,plain,
( ( $true
!= ( sK10 @ sK15 ) )
| spl17_5
| ~ spl17_6 ),
inference(subsumption_resolution,[status(thm)],[f167,f72]) ).
thf(f72,plain,
( ( ( sK10 @ sK16 )
= $true )
| ~ spl17_6 ),
inference(avatar_component_clause,[status(thm)],[f70]) ).
thf(f70,definition,
( spl17_6
<=> ( ( sK10 @ sK16 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_6])],[avatar_definition]) ).
thf(f167,plain,
( ( ( sK10 @ sK16 )
!= $true )
| ( $true
!= ( sK10 @ sK15 ) )
| spl17_5 ),
inference(trivial_inequality_removal,[status(thm)],[f166]) ).
thf(f166,plain,
( ( ( sK10 @ sK16 )
!= $true )
| ( $true != $true )
| ( $true
!= ( sK10 @ sK15 ) )
| spl17_5 ),
inference(superposition,[status(thm)],[f67,f33]) ).
thf(f33,plain,
! [X21: g,X22: g] :
( ( ( sK10 @ ( sK11 @ X22 @ X21 ) )
= $true )
| ( $true
!= ( sK10 @ X22 ) )
| ( $true
!= ( sK10 @ X21 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f67,plain,
( ( ( sK10 @ ( sK11 @ sK16 @ sK15 ) )
!= $true )
| spl17_5 ),
inference(avatar_component_clause,[status(thm)],[f65]) ).
thf(f65,definition,
( spl17_5
<=> ( ( sK10 @ ( sK11 @ sK16 @ sK15 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_5])],[avatar_definition]) ).
thf(f165,plain,
( ~ spl17_1
| spl17_13 ),
inference(avatar_split_clause,[status(thm)],[f158,f148,f48]) ).
thf(f148,definition,
( spl17_13
<=> ( $true
= ( sK10 @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_13])],[avatar_definition]) ).
thf(f158,plain,
( ( $true
!= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) )
| spl17_13 ),
inference(trivial_inequality_removal,[status(thm)],[f156]) ).
thf(f156,plain,
( ( $true != $true )
| ( $true
!= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) )
| spl17_13 ),
inference(superposition,[status(thm)],[f150,f29]) ).
thf(f29,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 )
| ( $true
!= ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f150,plain,
( ( $true
!= ( sK10 @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) )
| spl17_13 ),
inference(avatar_component_clause,[status(thm)],[f148]) ).
thf(f155,plain,
( ~ spl17_13
| ~ spl17_14
| spl17_11 ),
inference(avatar_split_clause,[status(thm)],[f146,f117,f152,f148]) ).
thf(f117,definition,
( spl17_11
<=> ( ( sK8 @ ( sK6 @ ( sK7 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) @ ( sK7 @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) )
= ( sK8 @ ( sK7 @ ( sK11 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_11])],[avatar_definition]) ).
thf(f146,plain,
( ( $true
!= ( sK10 @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) )
| ( $true
!= ( sK10 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) )
| spl17_11 ),
inference(trivial_inequality_removal,[status(thm)],[f145]) ).
thf(f145,plain,
( ( ( sK8 @ ( sK7 @ ( sK11 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) )
!= ( sK8 @ ( sK7 @ ( sK11 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) ) )
| ( $true
!= ( sK10 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) )
| ( $true
!= ( sK10 @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) )
| spl17_11 ),
inference(superposition,[status(thm)],[f119,f35]) ).
thf(f35,plain,
! [X18: g,X19: g] :
( ( ( sK7 @ ( sK11 @ X18 @ X19 ) )
= ( sK6 @ ( sK7 @ X18 ) @ ( sK7 @ X19 ) ) )
| ( $true
!= ( sK10 @ X19 ) )
| ( $true
!= ( sK10 @ X18 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f119,plain,
( ( ( sK8 @ ( sK6 @ ( sK7 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) @ ( sK7 @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) )
!= ( sK8 @ ( sK7 @ ( sK11 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) ) )
| spl17_11 ),
inference(avatar_component_clause,[status(thm)],[f117]) ).
thf(f144,plain,
( ~ spl17_1
| spl17_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f143]) ).
thf(f143,plain,
( $false
| ~ spl17_1
| spl17_12 ),
inference(subsumption_resolution,[status(thm)],[f139,f50]) ).
thf(f139,plain,
( ( $true
!= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) )
| spl17_12 ),
inference(trivial_inequality_removal,[status(thm)],[f138]) ).
thf(f138,plain,
( ( $true != $true )
| ( $true
!= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) )
| spl17_12 ),
inference(superposition,[status(thm)],[f136,f28]) ).
thf(f28,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 )
| ( $true
!= ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f136,plain,
( ( $true
!= ( sK10 @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) )
| spl17_12 ),
inference(trivial_inequality_removal,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $true
!= ( sK10 @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) )
| ( $true != $true )
| spl17_12 ),
inference(superposition,[status(thm)],[f123,f34]) ).
thf(f34,plain,
! [X20: g] :
( ( $true
= ( sK13 @ ( sK7 @ X20 ) ) )
| ( ( sK10 @ X20 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f123,plain,
( ( ( sK13 @ ( sK7 @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) )
!= $true )
| spl17_12 ),
inference(avatar_component_clause,[status(thm)],[f121]) ).
thf(f121,definition,
( spl17_12
<=> ( ( sK13 @ ( sK7 @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl17_12])],[avatar_definition]) ).
thf(f134,plain,
( ~ spl17_1
| spl17_10 ),
inference(avatar_contradiction_clause,[status(thm)],[f133]) ).
thf(f133,plain,
( $false
| ~ spl17_1
| spl17_10 ),
inference(subsumption_resolution,[status(thm)],[f129,f50]) ).
thf(f129,plain,
( ( $true
!= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) )
| spl17_10 ),
inference(trivial_inequality_removal,[status(thm)],[f127]) ).
thf(f127,plain,
( ( $true
!= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) )
| ( $true != $true )
| spl17_10 ),
inference(superposition,[status(thm)],[f126,f30]) ).
thf(f30,plain,
! [X2: g > b,X3: b > a,X0: g > $o,X1: g > g > g,X4: a > a > a] :
( ( $true
= ( X0 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) )
| ( $true
!= ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f126,plain,
( ( $true
!= ( sK10 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) )
| spl17_10 ),
inference(trivial_inequality_removal,[status(thm)],[f125]) ).
thf(f125,plain,
( ( $true != $true )
| ( $true
!= ( sK10 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) )
| spl17_10 ),
inference(superposition,[status(thm)],[f115,f34]) ).
thf(f115,plain,
( ( $true
!= ( sK13 @ ( sK7 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) )
| spl17_10 ),
inference(avatar_component_clause,[status(thm)],[f113]) ).
thf(f113,definition,
( spl17_10
<=> ( $true
= ( sK13 @ ( sK7 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_10])],[avatar_definition]) ).
thf(f124,plain,
( ~ spl17_10
| ~ spl17_11
| ~ spl17_12
| ~ spl17_1 ),
inference(avatar_split_clause,[status(thm)],[f111,f48,f121,f117,f113]) ).
thf(f111,plain,
( ( ( sK13 @ ( sK7 @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) )
!= $true )
| ( ( sK8 @ ( sK6 @ ( sK7 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) @ ( sK7 @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) )
!= ( sK8 @ ( sK7 @ ( sK11 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) ) )
| ( $true
!= ( sK13 @ ( sK7 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) )
| ~ spl17_1 ),
inference(superposition,[status(thm)],[f107,f45]) ).
thf(f45,plain,
! [X10: b,X9: b] :
( ( ( sK8 @ ( sK6 @ X10 @ X9 ) )
= ( sK12 @ ( sK8 @ X10 ) @ ( sK8 @ X9 ) ) )
| ( $true
!= ( sK13 @ X9 ) )
| ( $true
!= ( sK13 @ X10 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f107,plain,
( ( ( sK12 @ ( sK8 @ ( sK7 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) @ ( sK8 @ ( sK7 @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) )
!= ( sK8 @ ( sK7 @ ( sK11 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) ) )
| ~ spl17_1 ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
( ( $true != $true )
| ( ( sK12 @ ( sK8 @ ( sK7 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) @ ( sK8 @ ( sK7 @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) )
!= ( sK8 @ ( sK7 @ ( sK11 @ ( sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) @ ( sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ) ) )
| ~ spl17_1 ),
inference(superposition,[status(thm)],[f31,f50]) ).
thf(f31,plain,
! [X2: g > b,X3: b > a,X0: g > $o,X1: g > g > g,X4: a > a > a] :
( ( $true
!= ( sP0 @ X4 @ X3 @ X2 @ X1 @ X0 ) )
| ( ( X4 @ ( X3 @ ( X2 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) @ ( X3 @ ( X2 @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) )
!= ( X3 @ ( X2 @ ( X1 @ ( sK4 @ X4 @ X3 @ X2 @ X1 @ X0 ) @ ( sK5 @ X4 @ X3 @ X2 @ X1 @ X0 ) ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f102,plain,
( spl17_2
| ~ spl17_7 ),
inference(avatar_contradiction_clause,[status(thm)],[f101]) ).
thf(f101,plain,
( $false
| spl17_2
| ~ spl17_7 ),
inference(subsumption_resolution,[status(thm)],[f100,f77]) ).
thf(f77,plain,
( ( $true
= ( sK10 @ sK14 ) )
| ~ spl17_7 ),
inference(avatar_component_clause,[status(thm)],[f75]) ).
thf(f75,definition,
( spl17_7
<=> ( $true
= ( sK10 @ sK14 ) ) ),
introduced(definition,[new_symbols(naming,[spl17_7])],[avatar_definition]) ).
thf(f100,plain,
( ( $true
!= ( sK10 @ sK14 ) )
| spl17_2 ),
inference(trivial_inequality_removal,[status(thm)],[f99]) ).
thf(f99,plain,
( ( $true != $true )
| ( $true
!= ( sK10 @ sK14 ) )
| spl17_2 ),
inference(superposition,[status(thm)],[f98,f34]) ).
thf(f98,plain,
( ( $true
!= ( sK13 @ ( sK7 @ sK14 ) ) )
| spl17_2 ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $true
!= ( sK13 @ ( sK7 @ sK14 ) ) )
| ( $true != $true )
| spl17_2 ),
inference(superposition,[status(thm)],[f54,f38]) ).
thf(f38,plain,
! [X14: b] :
( ( ( sK9 @ ( sK8 @ X14 ) )
= $true )
| ( ( sK13 @ X14 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f54,plain,
( ( $true
!= ( sK9 @ ( sK8 @ ( sK7 @ sK14 ) ) ) )
| spl17_2 ),
inference(avatar_component_clause,[status(thm)],[f52]) ).
thf(f52,definition,
( spl17_2
<=> ( $true
= ( sK9 @ ( sK8 @ ( sK7 @ sK14 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl17_2])],[avatar_definition]) ).
thf(f96,plain,
( ~ spl17_4
| spl17_8 ),
inference(avatar_contradiction_clause,[status(thm)],[f95]) ).
thf(f95,plain,
( $false
| ~ spl17_4
| spl17_8 ),
inference(subsumption_resolution,[status(thm)],[f94,f62]) ).
thf(f62,plain,
( ( $true
= ( sP1 @ sK12 @ sK9 ) )
| ~ spl17_4 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f94,plain,
( ( $true
!= ( sP1 @ sK12 @ sK9 ) )
| spl17_8 ),
inference(trivial_inequality_removal,[status(thm)],[f93]) ).
thf(f93,plain,
( ( $true != $true )
| ( $true
!= ( sP1 @ sK12 @ sK9 ) )
| spl17_8 ),
inference(superposition,[status(thm)],[f87,f26]) ).
thf(f26,plain,
! [X0: a > $o,X1: a > a > a] :
( ( $true
= ( X0 @ ( sK2 @ X1 @ X0 ) ) )
| ( $true
!= ( sP1 @ X1 @ X0 ) ) ),
inference(cnf_transformation,[status(thm)],[f15]) ).
thf(f87,plain,
( ( ( sK9 @ ( sK2 @ sK12 @ sK9 ) )
!= $true )
| spl17_8 ),
inference(avatar_component_clause,[status(thm)],[f85]) ).
thf(f80,plain,
( spl17_4
| spl17_7
| ~ spl17_5
| spl17_1 ),
inference(avatar_split_clause,[status(thm)],[f44,f48,f65,f75,f60]) ).
thf(f44,plain,
( ( $true
= ( sK10 @ sK14 ) )
| ( $true
= ( sP1 @ sK12 @ sK9 ) )
| ( ( sK10 @ ( sK11 @ sK16 @ sK15 ) )
!= $true )
| ( $true
= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f79,plain,
( spl17_7
| spl17_4
| spl17_1
| spl17_3 ),
inference(avatar_split_clause,[status(thm)],[f43,f56,f48,f60,f75]) ).
thf(f43,plain,
( ( $true
= ( sK10 @ sK15 ) )
| ( $true
= ( sK10 @ sK14 ) )
| ( $true
= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) )
| ( $true
= ( sP1 @ sK12 @ sK9 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f78,plain,
( spl17_7
| spl17_4
| spl17_1
| spl17_6 ),
inference(avatar_split_clause,[status(thm)],[f42,f70,f48,f60,f75]) ).
thf(f42,plain,
( ( $true
= ( sK10 @ sK14 ) )
| ( $true
= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) )
| ( $true
= ( sP1 @ sK12 @ sK9 ) )
| ( ( sK10 @ sK16 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f73,plain,
( ~ spl17_2
| spl17_1
| spl17_6
| spl17_4 ),
inference(avatar_split_clause,[status(thm)],[f39,f60,f70,f48,f52]) ).
thf(f39,plain,
( ( $true
!= ( sK9 @ ( sK8 @ ( sK7 @ sK14 ) ) ) )
| ( ( sK10 @ sK16 )
= $true )
| ( $true
= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) )
| ( $true
= ( sP1 @ sK12 @ sK9 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f68,plain,
( spl17_1
| ~ spl17_2
| ~ spl17_5
| spl17_4 ),
inference(avatar_split_clause,[status(thm)],[f41,f60,f65,f52,f48]) ).
thf(f41,plain,
( ( $true
!= ( sK9 @ ( sK8 @ ( sK7 @ sK14 ) ) ) )
| ( $true
= ( sP1 @ sK12 @ sK9 ) )
| ( ( sK10 @ ( sK11 @ sK16 @ sK15 ) )
!= $true )
| ( $true
= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
thf(f63,plain,
( spl17_1
| ~ spl17_2
| spl17_3
| spl17_4 ),
inference(avatar_split_clause,[status(thm)],[f40,f60,f56,f52,f48]) ).
thf(f40,plain,
( ( $true
!= ( sK9 @ ( sK8 @ ( sK7 @ sK14 ) ) ) )
| ( $true
= ( sP1 @ sK12 @ sK9 ) )
| ( $true
= ( sK10 @ sK15 ) )
| ( $true
= ( sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f24]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SYO225^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n019.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 14:26:24 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.46 ---- Original DTF file ---
% 0.19/0.46 thf(spec,logic,$$dhol).
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 % File : SYO225^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.46 % Domain : Syntactic
% 0.19/0.46 % Problem : TPS problem THM126-CORRECTED
% 0.19/0.46 % Version : Especial.
% 0.19/0.46 % English :
% 0.19/0.46
% 0.19/0.46 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.46 % Source : [Bro09]
% 0.19/0.46 % Names : tps_0504 [Bro09]
% 0.19/0.46 % : THM126-CORRECTED [TPS]
% 0.19/0.46
% 0.19/0.46 % Status : Theorem
% 0.19/0.46 % Rating : 0.11 v9.1.0, 0.25 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.19/0.46 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.19/0.46 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.19/0.46 % Maximal formula atoms : 3 ( 3 avg)
% 0.19/0.46 % Number of connectives : 100 ( 0 ~; 0 |; 19 &; 68 @)
% 0.19/0.46 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.19/0.46 % Maximal formula depth : 28 ( 28 avg)
% 0.19/0.46 % Number of types : 4 ( 3 usr)
% 0.19/0.46 % Number of type conns : 19 ( 19 >; 0 *; 0 +; 0 <<)
% 0.19/0.46 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.19/0.46 % Number of variables : 33 ( 0 ^; 33 !; 0 ?; 33 :)
% 0.19/0.46 % SPC : TH0_THM_EQU_NAR
% 0.19/0.46
% 0.19/0.46 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.46 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.46 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.46 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.46 % : Polymorphic definitions expanded.
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 thf(g_type,type,
% 0.19/0.46 g: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(b_type,type,
% 0.19/0.46 b: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(a_type,type,
% 0.19/0.46 a: $tType ).
% 0.19/0.46
% 0.19/0.46 thf(cTHM126_CORRECTED_pme,conjecture,
% 0.19/0.46 ! [Xh1: g > b,Xh2: b > a,Xs1: g > $o,Xf1: g > g > g,Xs2: b > $o,Xf2: b > b > b,Xh10: g > b,Xh20: b > a,Xs10: g > $o,Xf10: g > g > g,Xs20: b > $o,Xf20: b > b > b,Xs3: a > $o,Xf3: a > a > a] :
% 0.19/0.46 ( ( ! [Xx: g,Xy: g] :
% 0.19/0.46 ( ( ( Xs10 @ Xx )
% 0.19/0.46 & ( Xs10 @ Xy ) )
% 0.19/0.46 => ( Xs10 @ ( Xf10 @ Xx @ Xy ) ) )
% 0.19/0.46 & ! [Xx: g] :
% 0.19/0.46 ( ( Xs10 @ Xx )
% 0.19/0.46 => ( Xs20 @ ( Xh10 @ Xx ) ) )
% 0.19/0.46 & ! [Xx: g] :
% 0.19/0.46 ( ( Xs10 @ Xx )
% 0.19/0.46 => ( Xs20 @ ( Xh10 @ Xx ) ) )
% 0.19/0.46 & ! [Xx: g] :
% 0.19/0.46 ( ( Xs10 @ Xx )
% 0.19/0.46 => ( Xs20 @ ( Xh10 @ Xx ) ) )
% 0.19/0.46 & ! [Xx: g,Xy: g] :
% 0.19/0.46 ( ( ( Xs10 @ Xx )
% 0.19/0.46 & ( Xs10 @ Xy ) )
% 0.19/0.46 => ( ( Xh10 @ ( Xf10 @ Xx @ Xy ) )
% 0.19/0.46 = ( Xf20 @ ( Xh10 @ Xx ) @ ( Xh10 @ Xy ) ) ) )
% 0.19/0.46 & ! [Xx: a,Xy: a] :
% 0.19/0.46 ( ( ( Xs3 @ Xx )
% 0.19/0.46 & ( Xs3 @ Xy ) )
% 0.19/0.46 => ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
% 0.19/0.46 & ! [Xx: b] :
% 0.19/0.46 ( ( Xs20 @ Xx )
% 0.19/0.46 => ( Xs3 @ ( Xh20 @ Xx ) ) )
% 0.19/0.46 & ! [Xx: b,Xy: b] :
% 0.19/0.46 ( ( ( Xs20 @ Xx )
% 0.19/0.46 & ( Xs20 @ Xy ) )
% 0.19/0.46 => ( ( Xh20 @ ( Xf20 @ Xx @ Xy ) )
% 0.19/0.46 = ( Xf3 @ ( Xh20 @ Xx ) @ ( Xh20 @ Xy ) ) ) ) )
% 0.19/0.46 => ( ! [Xx: g,Xy: g] :
% 0.19/0.46 ( ( ( Xs10 @ Xx )
% 0.19/0.46 & ( Xs10 @ Xy ) )
% 0.19/0.46 => ( Xs10 @ ( Xf10 @ Xx @ Xy ) ) )
% 0.19/0.46 & ! [Xx: a,Xy: a] :
% 0.19/0.46 ( ( ( Xs3 @ Xx )
% 0.19/0.46 & ( Xs3 @ Xy ) )
% 0.19/0.46 => ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
% 0.19/0.46 & ! [Xx: g] :
% 0.19/0.46 ( ( Xs10 @ Xx )
% 0.19/0.46 => ( Xs3 @ ( Xh20 @ ( Xh10 @ Xx ) ) ) )
% 0.19/0.46 & ! [Xx: g,Xy: g] :
% 0.19/0.46 ( ( ( Xs10 @ Xx )
% 0.19/0.46 & ( Xs10 @ Xy )
% 0.19/0.46 & ( Xs10 @ Xx )
% 0.19/0.46 & ( Xs10 @ Xy ) )
% 0.19/0.46 => ( ( Xh20 @ ( Xh10 @ ( Xf10 @ Xx @ Xy ) ) )
% 0.19/0.46 = ( Xf3 @ ( Xh20 @ ( Xh10 @ Xx ) ) @ ( Xh20 @ ( Xh10 @ Xy ) ) ) ) ) ) ) ).
% 0.19/0.46
% 0.19/0.46 %------------------------------------------------------------------------------
% 0.19/0.46 ------------------------
% 1.75/1.43 ---- Embedded in THF ---
% 1.75/1.43 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.75/1.43 %%% Generated on Tue Feb 24 14:26:25 EST 2026
% 1.75/1.43 %%% using '$$dhol' embedding, version 1.3.0.
% 1.75/1.43 %%% Logic specification used:
% 1.75/1.43 %%% thf(spec, logic, $$dhol).
% 1.75/1.43
% 1.75/1.43 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.1ZAPm39mWR/DTF2DTF21330.p
% See solution above
% 1.75/1.43 ------------------------
% 1.75/1.44 ---- Cleaned THF ---
% 1.75/1.44 thf(g_type,type,
% 1.75/1.44 g: $tType ).
% 1.75/1.44
% 1.75/1.44 thf(b_type,type,
% 1.75/1.44 b: $tType ).
% 1.75/1.44
% 1.75/1.44 thf(a_type,type,
% 1.75/1.44 a: $tType ).
% 1.75/1.44
% 1.75/1.44 thf(cTHM126_CORRECTED_pme,conjecture,
% 1.75/1.44 ! [Xh1: g > b,Xh2: b > a,Xs1: g > $o,Xf1: g > g > g,Xs2: b > $o,Xf2: b > b > b,Xh10: g > b,Xh20: b > a,Xs10: g > $o,Xf10: g > g > g,Xs20: b > $o,Xf20: b > b > b,Xs3: a > $o,Xf3: a > a > a] :
% 1.75/1.44 ( ( ! [Xx: g,Xy: g] :
% 1.75/1.44 ( ( ( Xs10 @ Xx )
% 1.75/1.44 & ( Xs10 @ Xy ) )
% 1.75/1.44 => ( Xs10 @ ( Xf10 @ Xx @ Xy ) ) )
% 1.75/1.44 & ! [Xx: g] :
% 1.75/1.44 ( ( Xs10 @ Xx )
% 1.75/1.44 => ( Xs20 @ ( Xh10 @ Xx ) ) )
% 1.75/1.44 & ! [Xx: g] :
% 1.75/1.44 ( ( Xs10 @ Xx )
% 1.75/1.44 => ( Xs20 @ ( Xh10 @ Xx ) ) )
% 1.75/1.44 & ! [Xx: g] :
% 1.75/1.44 ( ( Xs10 @ Xx )
% 1.75/1.44 => ( Xs20 @ ( Xh10 @ Xx ) ) )
% 1.75/1.44 & ! [Xx: g,Xy: g] :
% 1.75/1.44 ( ( ( Xs10 @ Xx )
% 1.75/1.44 & ( Xs10 @ Xy ) )
% 1.75/1.44 => ( ( Xh10 @ ( Xf10 @ Xx @ Xy ) )
% 1.75/1.44 = ( Xf20 @ ( Xh10 @ Xx ) @ ( Xh10 @ Xy ) ) ) )
% 1.75/1.44 & ! [Xx: a,Xy: a] :
% 1.75/1.44 ( ( ( Xs3 @ Xx )
% 1.75/1.44 & ( Xs3 @ Xy ) )
% 1.75/1.44 => ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
% 1.75/1.44 & ! [Xx: b] :
% 1.75/1.44 ( ( Xs20 @ Xx )
% 1.75/1.44 => ( Xs3 @ ( Xh20 @ Xx ) ) )
% 1.75/1.44 & ! [Xx: b,Xy: b] :
% 1.75/1.44 ( ( ( Xs20 @ Xx )
% 1.75/1.44 & ( Xs20 @ Xy ) )
% 1.75/1.44 => ( ( Xh20 @ ( Xf20 @ Xx @ Xy ) )
% 1.75/1.44 = ( Xf3 @ ( Xh20 @ Xx ) @ ( Xh20 @ Xy ) ) ) ) )
% 1.75/1.44 => ( ! [Xx: g,Xy: g] :
% 1.75/1.44 ( ( ( Xs10 @ Xx )
% 1.75/1.44 & ( Xs10 @ Xy ) )
% 1.75/1.44 => ( Xs10 @ ( Xf10 @ Xx @ Xy ) ) )
% 1.75/1.44 & ! [Xx: a,Xy: a] :
% 1.75/1.44 ( ( ( Xs3 @ Xx )
% 1.75/1.44 & ( Xs3 @ Xy ) )
% 1.75/1.44 => ( Xs3 @ ( Xf3 @ Xx @ Xy ) ) )
% 1.75/1.44 & ! [Xx: g] :
% 1.75/1.44 ( ( Xs10 @ Xx )
% 1.75/1.44 => ( Xs3 @ ( Xh20 @ ( Xh10 @ Xx ) ) ) )
% 1.75/1.44 & ! [Xx: g,Xy: g] :
% 1.75/1.44 ( ( ( Xs10 @ Xx )
% 1.75/1.44 & ( Xs10 @ Xy )
% 1.75/1.44 & ( Xs10 @ Xx )
% 1.75/1.44 & ( Xs10 @ Xy ) )
% 1.75/1.44 => ( ( Xh20 @ ( Xh10 @ ( Xf10 @ Xx @ Xy ) ) )
% 1.75/1.44 = ( Xf3 @ ( Xh20 @ ( Xh10 @ Xx ) ) @ ( Xh20 @ ( Xh10 @ Xy ) ) ) ) ) ) ) ).
% 1.75/1.44 ------------------------
% 1.75/1.46 % (21428)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_21330 for (2999ds/4Mi)
% 1.75/1.46 % (21429)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_21330 for (2999ds/27Mi)
% 1.75/1.46 % (21430)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_21330 for (2999ds/2Mi)
% 1.75/1.46 % (21431)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_21330 for (2999ds/2Mi)
% 1.75/1.46 % (21432)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_21330 for (2999ds/275Mi)
% 1.75/1.46 % (21433)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_21330 for (2999ds/18Mi)
% 1.75/1.46 % (21427)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_21330 for (2999ds/183Mi)
% 1.75/1.46 % (21430)Instruction limit reached!
% 1.75/1.46 % (21430)------------------------------
% 1.75/1.46 % (21430)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.46 % (21430)Termination reason: Unknown
% 1.75/1.46 % (21431)Instruction limit reached!
% 1.75/1.46 % (21431)------------------------------
% 1.75/1.46 % (21431)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.46 % (21431)Termination reason: Unknown
% 1.75/1.46 % (21431)Termination phase: Property scanning
% 1.75/1.46
% 1.75/1.46 % (21431)Memory used [KB]: 1023
% 1.75/1.46 % (21431)Time elapsed: 0.003 s
% 1.75/1.46 % (21431)Instructions burned: 3 (million)
% 1.75/1.46 % (21431)------------------------------
% 1.75/1.46 % (21431)------------------------------
% 1.75/1.46 % (21430)Termination phase: Preprocessing 3
% 1.75/1.46
% 1.75/1.46 % (21430)Memory used [KB]: 1023
% 1.75/1.46 % (21430)Time elapsed: 0.003 s
% 1.75/1.46 % (21430)Instructions burned: 3 (million)
% 1.75/1.46 % (21430)------------------------------
% 1.75/1.46 % (21430)------------------------------
% 1.75/1.46 % (21428)Instruction limit reached!
% 1.75/1.46 % (21428)------------------------------
% 1.75/1.46 % (21428)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.46 % (21428)Termination reason: Unknown
% 1.75/1.46 % (21428)Termination phase: Property scanning
% 1.75/1.46
% 1.75/1.46 % (21428)Memory used [KB]: 1023
% 1.75/1.46 % (21428)Time elapsed: 0.004 s
% 1.75/1.46 % (21428)Instructions burned: 5 (million)
% 1.75/1.46 % (21428)------------------------------
% 1.75/1.46 % (21428)------------------------------
% 1.75/1.47 % (21433)Instruction limit reached!
% 1.75/1.47 % (21433)------------------------------
% 1.75/1.47 % (21433)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.47 % (21433)Termination reason: Unknown
% 1.75/1.47 % (21433)Termination phase: Saturation
% 1.75/1.47
% 1.75/1.47 % (21433)Memory used [KB]: 5756
% 1.75/1.47 % (21433)Time elapsed: 0.011 s
% 1.75/1.47 % (21433)Instructions burned: 18 (million)
% 1.75/1.47 % (21433)------------------------------
% 1.75/1.47 % (21433)------------------------------
% 1.75/1.47 % (21429)Instruction limit reached!
% 1.75/1.47 % (21429)------------------------------
% 1.75/1.47 % (21429)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.47 % (21429)Termination reason: Unknown
% 1.75/1.47 % (21429)Termination phase: Saturation
% 1.75/1.47
% 1.75/1.47 % (21429)Memory used [KB]: 5756
% 1.75/1.47 % (21429)Time elapsed: 0.016 s
% 1.75/1.47 % (21429)Instructions burned: 28 (million)
% 1.75/1.47 % (21429)------------------------------
% 1.75/1.47 % (21429)------------------------------
% 1.75/1.47 % (21434)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_21330 for (2999ds/3Mi)
% 1.75/1.47 % (21435)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_21330 for (2999ds/37Mi)
% 1.75/1.47 % (21432)First to succeed.
% 1.75/1.48 % (21436)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_21330 for (2999ds/15Mi)
% 1.75/1.48 % (21434)Instruction limit reached!
% 1.75/1.48 % (21434)------------------------------
% 1.75/1.48 % (21434)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.48 % (21434)Termination reason: Unknown
% 1.75/1.48 % (21434)Termination phase: Preprocessing 3
% 1.75/1.48
% 1.75/1.48 % (21434)Memory used [KB]: 1023
% 1.75/1.48 % (21434)Time elapsed: 0.003 s
% 1.75/1.48 % (21434)Instructions burned: 3 (million)
% 1.75/1.48 % (21434)------------------------------
% 1.75/1.48 % (21434)------------------------------
% 1.75/1.48 % (21432)Refutation found. Thanks to Tanya!
% 1.75/1.48 % SZS status Theorem for DTF2THF_21330
% 1.75/1.48 % SZS output start Proof for DTF2THF_21330
% 1.75/1.48 thf(type_def_5, type, g: $tType).
% 1.75/1.48 thf(type_def_6, type, b: $tType).
% 1.75/1.48 thf(type_def_8, type, a: $tType).
% 1.75/1.48 thf(func_def_0, type, g: $tType).
% 1.75/1.48 thf(func_def_1, type, b: $tType).
% 1.75/1.48 thf(func_def_2, type, a: $tType).
% 1.75/1.48 thf(func_def_6, type, sP0: (a > a > a) > (b > a) > (g > b) > (g > g > g) > (g > $o) > $o).
% 1.75/1.48 thf(func_def_7, type, sP1: (a > a > a) > (a > $o) > $o).
% 1.75/1.48 thf(func_def_8, type, sK2: (a > a > a) > (a > $o) > a).
% 1.75/1.48 thf(func_def_9, type, sK3: (a > a > a) > (a > $o) > a).
% 1.75/1.48 thf(func_def_10, type, sK4: (a > a > a) > (b > a) > (g > b) > (g > g > g) > (g > $o) > g).
% 1.75/1.48 thf(func_def_11, type, sK5: (a > a > a) > (b > a) > (g > b) > (g > g > g) > (g > $o) > g).
% 1.75/1.48 thf(func_def_12, type, sK6: b > b > b).
% 1.75/1.48 thf(func_def_13, type, sK7: g > b).
% 1.75/1.48 thf(func_def_14, type, sK8: b > a).
% 1.75/1.48 thf(func_def_15, type, sK9: a > $o).
% 1.75/1.48 thf(func_def_16, type, sK10: g > $o).
% 1.75/1.48 thf(func_def_17, type, sK11: g > g > g).
% 1.75/1.48 thf(func_def_18, type, sK12: a > a > a).
% 1.75/1.48 thf(func_def_19, type, sK13: b > $o).
% 1.75/1.48 thf(func_def_20, type, sK14: g).
% 1.75/1.48 thf(func_def_21, type, sK15: g).
% 1.75/1.48 thf(func_def_22, type, sK16: g).
% 1.75/1.48 thf(func_def_24, type, ph18: !>[X0: $tType]:(X0)).
% 1.75/1.48 thf(f185,plain,(
% 1.75/1.48 $false),
% 1.75/1.48 inference(avatar_sat_refutation,[status(thm)],[f63,f68,f73,f78,f79,f80,f96,f102,f124,f134,f144,f155,f165,f170,f181,f184])).
% 1.75/1.48 thf(f184,plain,(
% 1.75/1.48 ~spl17_4 | ~spl17_8),
% 1.75/1.48 inference(avatar_split_clause,[status(thm)],[f183,f85,f60])).
% 1.75/1.48 thf(f60,definition,(
% 1.75/1.48 spl17_4 <=> ($true = (sP1 @ sK12 @ sK9))),
% 1.75/1.48 introduced(definition,[new_symbols(naming,[spl17_4])],[avatar_definition])).
% 1.75/1.48 thf(f85,definition,(
% 1.75/1.48 spl17_8 <=> ((sK9 @ (sK2 @ sK12 @ sK9)) = $true)),
% 1.75/1.48 introduced(definition,[new_symbols(naming,[spl17_8])],[avatar_definition])).
% 1.75/1.48 thf(f183,plain,(
% 1.75/1.48 ($true != (sP1 @ sK12 @ sK9)) | ~spl17_8),
% 1.75/1.48 inference(subsumption_resolution,[status(thm)],[f182,f27])).
% 1.75/1.48 thf(f27,plain,(
% 1.75/1.48 ( ! [X0 : a > $o,X1 : a > a > a] : (((X0 @ (sK3 @ X1 @ X0)) = $true) | ($true != (sP1 @ X1 @ X0))) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f15])).
% 1.75/1.48 thf(f15,plain,(
% 1.75/1.48 ! [X0 : a > $o,X1 : a > a > a] : ((((X0 @ (sK3 @ X1 @ X0)) = $true) & ($true = (X0 @ (sK2 @ X1 @ X0))) & ((X0 @ (X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) != $true)) | ($true != (sP1 @ X1 @ X0)))),
% 1.75/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3])],[f13,f14])).
% 1.75/1.48 thf(f14,plain,(
% 1.75/1.48 ! [X0 : a > $o,X1 : a > a > a] : (? [X2 : a,X3 : a] : (((X0 @ X3) = $true) & ((X0 @ X2) = $true) & ($true != (X0 @ (X1 @ X2 @ X3)))) => (((X0 @ (sK3 @ X1 @ X0)) = $true) & ($true = (X0 @ (sK2 @ X1 @ X0))) & ((X0 @ (X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) != $true)))),
% 1.75/1.48 introduced(definition,[],[choice_axiom])).
% 1.75/1.48 thf(f13,plain,(
% 1.75/1.48 ! [X0 : a > $o,X1 : a > a > a] : (? [X2 : a,X3 : a] : (((X0 @ X3) = $true) & ((X0 @ X2) = $true) & ($true != (X0 @ (X1 @ X2 @ X3)))) | ($true != (sP1 @ X1 @ X0)))),
% 1.75/1.48 inference(rectify,[status(thm)],[f12])).
% 1.75/1.48 thf(f12,plain,(
% 1.75/1.48 ! [X2 : a > $o,X7 : a > a > a] : (? [X21 : a,X20 : a] : (($true = (X2 @ X20)) & ($true = (X2 @ X21)) & ((X2 @ (X7 @ X21 @ X20)) != $true)) | ((sP1 @ X7 @ X2) != $true))),
% 1.75/1.48 inference(nnf_transformation,[status(thm)],[f10])).
% 1.75/1.48 thf(f10,plain,(
% 1.75/1.48 ! [X2 : a > $o,X7 : a > a > a] : (? [X21 : a,X20 : a] : (($true = (X2 @ X20)) & ($true = (X2 @ X21)) & ((X2 @ (X7 @ X21 @ X20)) != $true)) | ~((sP1 @ X7 @ X2) = $true))),
% 1.75/1.48 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.75/1.48 thf(f182,plain,(
% 1.75/1.48 ($true != (sP1 @ sK12 @ sK9)) | ($true != (sK9 @ (sK3 @ sK12 @ sK9))) | ~spl17_8),
% 1.75/1.48 inference(subsumption_resolution,[status(thm)],[f82,f86])).
% 1.75/1.48 thf(f86,plain,(
% 1.75/1.48 ((sK9 @ (sK2 @ sK12 @ sK9)) = $true) | ~spl17_8),
% 1.75/1.48 inference(avatar_component_clause,[status(thm)],[f85])).
% 1.75/1.48 thf(f82,plain,(
% 1.75/1.48 ($true != (sP1 @ sK12 @ sK9)) | ((sK9 @ (sK2 @ sK12 @ sK9)) != $true) | ($true != (sK9 @ (sK3 @ sK12 @ sK9)))),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f81])).
% 1.75/1.48 thf(f81,plain,(
% 1.75/1.48 ($true != (sP1 @ sK12 @ sK9)) | ($true != (sK9 @ (sK3 @ sK12 @ sK9))) | ((sK9 @ (sK2 @ sK12 @ sK9)) != $true) | ($true != $true)),
% 1.75/1.48 inference(superposition,[status(thm)],[f25,f37])).
% 1.75/1.48 thf(f37,plain,(
% 1.75/1.48 ( ! [X16 : a,X15 : a] : (($true = (sK9 @ (sK12 @ X16 @ X15))) | ((sK9 @ X15) != $true) | ((sK9 @ X16) != $true)) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f24])).
% 1.75/1.48 thf(f24,plain,(
% 1.75/1.48 ! [X8 : g] : (((sK13 @ (sK7 @ X8)) = $true) | ((sK10 @ X8) != $true)) & ! [X9 : b,X10 : b] : (($true != (sK13 @ X9)) | ((sK8 @ (sK6 @ X10 @ X9)) = (sK12 @ (sK8 @ X10) @ (sK8 @ X9))) | ($true != (sK13 @ X10))) & (($true = (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) | (($true = (sK10 @ sK14)) & ($true != (sK9 @ (sK8 @ (sK7 @ sK14))))) | (((sK10 @ (sK11 @ sK16 @ sK15)) != $true) & ($true = (sK10 @ sK15)) & ((sK10 @ sK16) = $true)) | ($true = (sP1 @ sK12 @ sK9))) & ! [X14 : b] : (((sK13 @ X14) != $true) | ((sK9 @ (sK8 @ X14)) = $true)) & ! [X15 : a,X16 : a] : (($true = (sK9 @ (sK12 @ X16 @ X15))) | ((sK9 @ X15) != $true) | ((sK9 @ X16) != $true)) & ! [X17 : g] : (((sK10 @ X17) != $true) | ((sK13 @ (sK7 @ X17)) = $true)) & ! [X18 : g,X19 : g] : (($true != (sK10 @ X19)) | ((sK7 @ (sK11 @ X18 @ X19)) = (sK6 @ (sK7 @ X18) @ (sK7 @ X19))) | ($true != (sK10 @ X18))) & ! [X20 : g] : (((sK10 @ X20) != $true) | ($true = (sK13 @ (sK7 @ X20)))) & ! [X21 : g,X22 : g] : (($true != (sK10 @ X21)) | ((sK10 @ (sK11 @ X22 @ X21)) = $true) | ($true != (sK10 @ X22)))),
% 1.75/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16])],[f20,f23,f22,f21])).
% 1.75/1.48 thf(f21,plain,(
% 1.75/1.48 ? [X0 : b > b > b,X1 : g > b,X2 : b > a,X3 : a > $o,X4 : g > $o,X5 : g > g > g,X6 : a > a > a,X7 : b > $o] : (! [X8 : g] : (($true = (X7 @ (X1 @ X8))) | ((X4 @ X8) != $true)) & ! [X9 : b,X10 : b] : (((X7 @ X9) != $true) | ((X6 @ (X2 @ X10) @ (X2 @ X9)) = (X2 @ (X0 @ X10 @ X9))) | ((X7 @ X10) != $true)) & (($true = (sP0 @ X6 @ X2 @ X1 @ X5 @ X4)) | ? [X11 : g] : (($true = (X4 @ X11)) & ($true != (X3 @ (X2 @ (X1 @ X11))))) | ? [X12 : g,X13 : g] : (((X4 @ (X5 @ X13 @ X12)) != $true) & ((X4 @ X12) = $true) & ($true = (X4 @ X13))) | ((sP1 @ X6 @ X3) = $true)) & ! [X14 : b] : (((X7 @ X14) != $true) | ((X3 @ (X2 @ X14)) = $true)) & ! [X15 : a,X16 : a] : (((X3 @ (X6 @ X16 @ X15)) = $true) | ((X3 @ X15) != $true) | ($true != (X3 @ X16))) & ! [X17 : g] : (($true != (X4 @ X17)) | ($true = (X7 @ (X1 @ X17)))) & ! [X18 : g,X19 : g] : (((X4 @ X19) != $true) | ((X0 @ (X1 @ X18) @ (X1 @ X19)) = (X1 @ (X5 @ X18 @ X19))) | ($true != (X4 @ X18))) & ! [X20 : g] : (($true != (X4 @ X20)) | ($true = (X7 @ (X1 @ X20)))) & ! [X21 : g,X22 : g] : (((X4 @ X21) != $true) | ((X4 @ (X5 @ X22 @ X21)) = $true) | ($true != (X4 @ X22)))) => (! [X8 : g] : (((sK13 @ (sK7 @ X8)) = $true) | ((sK10 @ X8) != $true)) & ! [X10 : b,X9 : b] : (($true != (sK13 @ X9)) | ((sK8 @ (sK6 @ X10 @ X9)) = (sK12 @ (sK8 @ X10) @ (sK8 @ X9))) | ($true != (sK13 @ X10))) & (($true = (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) | ? [X11 : g] : (((sK10 @ X11) = $true) & ((sK9 @ (sK8 @ (sK7 @ X11))) != $true)) | ? [X13 : g,X12 : g] : (((sK10 @ (sK11 @ X13 @ X12)) != $true) & ($true = (sK10 @ X12)) & ((sK10 @ X13) = $true)) | ($true = (sP1 @ sK12 @ sK9))) & ! [X14 : b] : (((sK13 @ X14) != $true) | ((sK9 @ (sK8 @ X14)) = $true)) & ! [X16 : a,X15 : a] : (($true = (sK9 @ (sK12 @ X16 @ X15))) | ((sK9 @ X15) != $true) | ((sK9 @ X16) != $true)) & ! [X17 : g] : (((sK10 @ X17) != $true) | ((sK13 @ (sK7 @ X17)) = $true)) & ! [X19 : g,X18 : g] : (($true != (sK10 @ X19)) | ((sK7 @ (sK11 @ X18 @ X19)) = (sK6 @ (sK7 @ X18) @ (sK7 @ X19))) | ($true != (sK10 @ X18))) & ! [X20 : g] : (((sK10 @ X20) != $true) | ($true = (sK13 @ (sK7 @ X20)))) & ! [X22 : g,X21 : g] : (($true != (sK10 @ X21)) | ((sK10 @ (sK11 @ X22 @ X21)) = $true) | ($true != (sK10 @ X22))))),
% 1.75/1.48 introduced(definition,[],[choice_axiom])).
% 1.75/1.48 thf(f22,plain,(
% 1.75/1.48 ? [X11 : g] : (((sK10 @ X11) = $true) & ((sK9 @ (sK8 @ (sK7 @ X11))) != $true)) => (($true = (sK10 @ sK14)) & ($true != (sK9 @ (sK8 @ (sK7 @ sK14)))))),
% 1.75/1.48 introduced(definition,[],[choice_axiom])).
% 1.75/1.48 thf(f23,plain,(
% 1.75/1.48 ? [X13 : g,X12 : g] : (((sK10 @ (sK11 @ X13 @ X12)) != $true) & ($true = (sK10 @ X12)) & ((sK10 @ X13) = $true)) => (((sK10 @ (sK11 @ sK16 @ sK15)) != $true) & ($true = (sK10 @ sK15)) & ((sK10 @ sK16) = $true))),
% 1.75/1.48 introduced(definition,[],[choice_axiom])).
% 1.75/1.48 thf(f20,plain,(
% 1.75/1.48 ? [X0 : b > b > b,X1 : g > b,X2 : b > a,X3 : a > $o,X4 : g > $o,X5 : g > g > g,X6 : a > a > a,X7 : b > $o] : (! [X8 : g] : (($true = (X7 @ (X1 @ X8))) | ((X4 @ X8) != $true)) & ! [X9 : b,X10 : b] : (((X7 @ X9) != $true) | ((X6 @ (X2 @ X10) @ (X2 @ X9)) = (X2 @ (X0 @ X10 @ X9))) | ((X7 @ X10) != $true)) & (($true = (sP0 @ X6 @ X2 @ X1 @ X5 @ X4)) | ? [X11 : g] : (($true = (X4 @ X11)) & ($true != (X3 @ (X2 @ (X1 @ X11))))) | ? [X12 : g,X13 : g] : (((X4 @ (X5 @ X13 @ X12)) != $true) & ((X4 @ X12) = $true) & ($true = (X4 @ X13))) | ((sP1 @ X6 @ X3) = $true)) & ! [X14 : b] : (((X7 @ X14) != $true) | ((X3 @ (X2 @ X14)) = $true)) & ! [X15 : a,X16 : a] : (((X3 @ (X6 @ X16 @ X15)) = $true) | ((X3 @ X15) != $true) | ($true != (X3 @ X16))) & ! [X17 : g] : (($true != (X4 @ X17)) | ($true = (X7 @ (X1 @ X17)))) & ! [X18 : g,X19 : g] : (((X4 @ X19) != $true) | ((X0 @ (X1 @ X18) @ (X1 @ X19)) = (X1 @ (X5 @ X18 @ X19))) | ($true != (X4 @ X18))) & ! [X20 : g] : (($true != (X4 @ X20)) | ($true = (X7 @ (X1 @ X20)))) & ! [X21 : g,X22 : g] : (((X4 @ X21) != $true) | ((X4 @ (X5 @ X22 @ X21)) = $true) | ($true != (X4 @ X22))))),
% 1.75/1.48 inference(rectify,[status(thm)],[f11])).
% 1.75/1.48 thf(f11,plain,(
% 1.75/1.48 ? [X0 : b > b > b,X5 : g > b,X4 : b > a,X2 : a > $o,X1 : g > $o,X3 : g > g > g,X7 : a > a > a,X6 : b > $o] : (! [X13 : g] : (((X6 @ (X5 @ X13)) = $true) | ((X1 @ X13) != $true)) & ! [X14 : b,X15 : b] : (($true != (X6 @ X14)) | ((X7 @ (X4 @ X15) @ (X4 @ X14)) = (X4 @ (X0 @ X15 @ X14))) | ($true != (X6 @ X15))) & (((sP0 @ X7 @ X4 @ X5 @ X3 @ X1) = $true) | ? [X24 : g] : (((X1 @ X24) = $true) & ((X2 @ (X4 @ (X5 @ X24))) != $true)) | ? [X22 : g,X23 : g] : (($true != (X1 @ (X3 @ X23 @ X22))) & ($true = (X1 @ X22)) & ($true = (X1 @ X23))) | ((sP1 @ X7 @ X2) = $true)) & ! [X19 : b] : (((X6 @ X19) != $true) | ((X2 @ (X4 @ X19)) = $true)) & ! [X8 : a,X9 : a] : (((X2 @ (X7 @ X9 @ X8)) = $true) | ((X2 @ X8) != $true) | ((X2 @ X9) != $true)) & ! [X12 : g] : (((X1 @ X12) != $true) | ($true = (X6 @ (X5 @ X12)))) & ! [X17 : g,X16 : g] : (($true != (X1 @ X16)) | ((X5 @ (X3 @ X17 @ X16)) = (X0 @ (X5 @ X17) @ (X5 @ X16))) | ((X1 @ X17) != $true)) & ! [X18 : g] : (($true != (X1 @ X18)) | ($true = (X6 @ (X5 @ X18)))) & ! [X10 : g,X11 : g] : (($true != (X1 @ X10)) | ((X1 @ (X3 @ X11 @ X10)) = $true) | ((X1 @ X11) != $true)))),
% 1.75/1.48 inference(definition_folding,[status(thm)],[f8,f10,f9])).
% 1.75/1.48 thf(f9,plain,(
% 1.75/1.48 ! [X1 : g > $o,X3 : g > g > g,X5 : g > b,X4 : b > a,X7 : a > a > a] : (? [X25 : g,X26 : g] : (($true = (X1 @ X25)) & ((X7 @ (X4 @ (X5 @ X25)) @ (X4 @ (X5 @ X26))) != (X4 @ (X5 @ (X3 @ X25 @ X26)))) & ($true = (X1 @ X25)) & ($true = (X1 @ X26)) & ($true = (X1 @ X26))) | ~((sP0 @ X7 @ X4 @ X5 @ X3 @ X1) = $true))),
% 1.75/1.48 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.75/1.48 thf(f8,plain,(
% 1.75/1.48 ? [X0 : b > b > b,X5 : g > b,X4 : b > a,X2 : a > $o,X1 : g > $o,X3 : g > g > g,X7 : a > a > a,X6 : b > $o] : (! [X13 : g] : (((X6 @ (X5 @ X13)) = $true) | ((X1 @ X13) != $true)) & ! [X14 : b,X15 : b] : (($true != (X6 @ X14)) | ((X7 @ (X4 @ X15) @ (X4 @ X14)) = (X4 @ (X0 @ X15 @ X14))) | ($true != (X6 @ X15))) & (? [X25 : g,X26 : g] : (($true = (X1 @ X25)) & ((X7 @ (X4 @ (X5 @ X25)) @ (X4 @ (X5 @ X26))) != (X4 @ (X5 @ (X3 @ X25 @ X26)))) & ($true = (X1 @ X25)) & ($true = (X1 @ X26)) & ($true = (X1 @ X26))) | ? [X24 : g] : (((X1 @ X24) = $true) & ((X2 @ (X4 @ (X5 @ X24))) != $true)) | ? [X22 : g,X23 : g] : (($true != (X1 @ (X3 @ X23 @ X22))) & ($true = (X1 @ X22)) & ($true = (X1 @ X23))) | ? [X21 : a,X20 : a] : (($true = (X2 @ X20)) & ($true = (X2 @ X21)) & ((X2 @ (X7 @ X21 @ X20)) != $true))) & ! [X19 : b] : (((X6 @ X19) != $true) | ((X2 @ (X4 @ X19)) = $true)) & ! [X8 : a,X9 : a] : (((X2 @ (X7 @ X9 @ X8)) = $true) | ((X2 @ X8) != $true) | ((X2 @ X9) != $true)) & ! [X12 : g] : (((X1 @ X12) != $true) | ($true = (X6 @ (X5 @ X12)))) & ! [X17 : g,X16 : g] : (($true != (X1 @ X16)) | ((X5 @ (X3 @ X17 @ X16)) = (X0 @ (X5 @ X17) @ (X5 @ X16))) | ((X1 @ X17) != $true)) & ! [X18 : g] : (($true != (X1 @ X18)) | ($true = (X6 @ (X5 @ X18)))) & ! [X10 : g,X11 : g] : (($true != (X1 @ X10)) | ((X1 @ (X3 @ X11 @ X10)) = $true) | ((X1 @ X11) != $true)))),
% 1.75/1.48 inference(flattening,[status(thm)],[f7])).
% 1.75/1.48 thf(f7,plain,(
% 1.75/1.48 ? [X0 : b > b > b,X2 : a > $o,X7 : a > a > a,X5 : g > b,X6 : b > $o,X4 : b > a,X3 : g > g > g,X1 : g > $o] : ((? [X25 : g,X26 : g] : (((X7 @ (X4 @ (X5 @ X25)) @ (X4 @ (X5 @ X26))) != (X4 @ (X5 @ (X3 @ X25 @ X26)))) & (($true = (X1 @ X26)) & ($true = (X1 @ X26)) & ($true = (X1 @ X25)) & ($true = (X1 @ X25)))) | ? [X20 : a,X21 : a] : (((X2 @ (X7 @ X21 @ X20)) != $true) & (($true = (X2 @ X21)) & ($true = (X2 @ X20)))) | ? [X23 : g,X22 : g] : (($true != (X1 @ (X3 @ X23 @ X22))) & (($true = (X1 @ X23)) & ($true = (X1 @ X22)))) | ? [X24 : g] : (((X1 @ X24) = $true) & ((X2 @ (X4 @ (X5 @ X24))) != $true))) & (! [X13 : g] : (((X6 @ (X5 @ X13)) = $true) | ((X1 @ X13) != $true)) & ! [X9 : a,X8 : a] : (((X2 @ (X7 @ X9 @ X8)) = $true) | (((X2 @ X8) != $true) | ((X2 @ X9) != $true))) & ! [X17 : g,X16 : g] : (((X5 @ (X3 @ X17 @ X16)) = (X0 @ (X5 @ X17) @ (X5 @ X16))) | (((X1 @ X17) != $true) | ($true != (X1 @ X16)))) & ! [X18 : g] : (($true != (X1 @ X18)) | ($true = (X6 @ (X5 @ X18)))) & ! [X12 : g] : (((X1 @ X12) != $true) | ($true = (X6 @ (X5 @ X12)))) & ! [X10 : g,X11 : g] : (((X1 @ (X3 @ X11 @ X10)) = $true) | (($true != (X1 @ X10)) | ((X1 @ X11) != $true))) & ! [X15 : b,X14 : b] : (((X7 @ (X4 @ X15) @ (X4 @ X14)) = (X4 @ (X0 @ X15 @ X14))) | (($true != (X6 @ X15)) | ($true != (X6 @ X14)))) & ! [X19 : b] : (((X6 @ X19) != $true) | ((X2 @ (X4 @ X19)) = $true))))),
% 1.75/1.48 inference(ennf_transformation,[status(thm)],[f6])).
% 1.75/1.48 thf(f6,plain,(
% 1.75/1.48 ~! [X0 : b > b > b,X2 : a > $o,X7 : a > a > a,X5 : g > b,X6 : b > $o,X4 : b > a,X3 : g > g > g,X1 : g > $o] : ((! [X13 : g] : (((X1 @ X13) = $true) => ((X6 @ (X5 @ X13)) = $true)) & ! [X9 : a,X8 : a] : ((((X2 @ X8) = $true) & ((X2 @ X9) = $true)) => ((X2 @ (X7 @ X9 @ X8)) = $true)) & ! [X17 : g,X16 : g] : ((((X1 @ X17) = $true) & ($true = (X1 @ X16))) => ((X5 @ (X3 @ X17 @ X16)) = (X0 @ (X5 @ X17) @ (X5 @ X16)))) & ! [X18 : g] : (($true = (X1 @ X18)) => ($true = (X6 @ (X5 @ X18)))) & ! [X12 : g] : (((X1 @ X12) = $true) => ($true = (X6 @ (X5 @ X12)))) & ! [X10 : g,X11 : g] : ((($true = (X1 @ X10)) & ((X1 @ X11) = $true)) => ((X1 @ (X3 @ X11 @ X10)) = $true)) & ! [X15 : b,X14 : b] : ((($true = (X6 @ X15)) & ($true = (X6 @ X14))) => ((X7 @ (X4 @ X15) @ (X4 @ X14)) = (X4 @ (X0 @ X15 @ X14)))) & ! [X19 : b] : (((X6 @ X19) = $true) => ((X2 @ (X4 @ X19)) = $true))) => (! [X25 : g,X26 : g] : ((($true = (X1 @ X26)) & ($true = (X1 @ X26)) & ($true = (X1 @ X25)) & ($true = (X1 @ X25))) => ((X7 @ (X4 @ (X5 @ X25)) @ (X4 @ (X5 @ X26))) = (X4 @ (X5 @ (X3 @ X25 @ X26))))) & ! [X20 : a,X21 : a] : ((($true = (X2 @ X21)) & ($true = (X2 @ X20))) => ((X2 @ (X7 @ X21 @ X20)) = $true)) & ! [X23 : g,X22 : g] : ((($true = (X1 @ X23)) & ($true = (X1 @ X22))) => ($true = (X1 @ (X3 @ X23 @ X22)))) & ! [X24 : g] : (((X1 @ X24) = $true) => ((X2 @ (X4 @ (X5 @ X24))) = $true))))),
% 1.75/1.48 inference(rectify,[status(thm)],[f5])).
% 1.75/1.48 thf(f5,plain,(
% 1.75/1.48 ~! [X0 : b > b > b,X2 : g > $o,X4 : a > $o,X5 : g > g > g,X6 : b > a,X8 : g > b,X9 : b > $o,X11 : a > a > a] : ((! [X14 : a,X15 : a] : ((((X4 @ X15) = $true) & ((X4 @ X14) = $true)) => ((X4 @ (X11 @ X15 @ X14)) = $true)) & ! [X16 : g,X17 : g] : ((($true = (X2 @ X16)) & ($true = (X2 @ X17))) => ((X2 @ (X5 @ X17 @ X16)) = $true)) & ! [X18 : g] : (((X2 @ X18) = $true) => ((X9 @ (X8 @ X18)) = $true)) & ! [X19 : g] : (((X2 @ X19) = $true) => ((X9 @ (X8 @ X19)) = $true)) & ! [X20 : b,X21 : b] : ((((X9 @ X20) = $true) & ($true = (X9 @ X21))) => ((X6 @ (X0 @ X21 @ X20)) = (X11 @ (X6 @ X21) @ (X6 @ X20)))) & ! [X22 : g,X23 : g] : ((((X2 @ X22) = $true) & ($true = (X2 @ X23))) => ((X8 @ (X5 @ X23 @ X22)) = (X0 @ (X8 @ X23) @ (X8 @ X22)))) & ! [X24 : g] : (((X2 @ X24) = $true) => ((X9 @ (X8 @ X24)) = $true)) & ! [X25 : b] : (((X9 @ X25) = $true) => ((X4 @ (X6 @ X25)) = $true))) => (! [X26 : a,X27 : a] : ((((X4 @ X27) = $true) & ((X4 @ X26) = $true)) => ($true = (X4 @ (X11 @ X27 @ X26)))) & ! [X28 : g,X29 : g] : ((($true = (X2 @ X29)) & ((X2 @ X28) = $true)) => ((X2 @ (X5 @ X29 @ X28)) = $true)) & ! [X30 : g] : (((X2 @ X30) = $true) => ((X4 @ (X6 @ (X8 @ X30))) = $true)) & ! [X31 : g,X32 : g] : ((((X2 @ X32) = $true) & ((X2 @ X32) = $true) & ($true = (X2 @ X31)) & ($true = (X2 @ X31))) => ((X11 @ (X6 @ (X8 @ X31)) @ (X6 @ (X8 @ X32))) = (X6 @ (X8 @ (X5 @ X31 @ X32)))))))),
% 1.75/1.48 inference(fool_elimination,[status(thm)],[f4])).
% 1.75/1.48 thf(f4,plain,(
% 1.75/1.48 ~! [X0 : b > b > b,X2 : g > $o,X4 : a > $o,X5 : g > g > g,X6 : b > a,X8 : g > b,X9 : b > $o,X11 : a > a > a] : ((! [X14 : a,X15 : a] : (((X4 @ X15) & (X4 @ X14)) => (X4 @ (X11 @ X15 @ X14))) & ! [X16 : g,X17 : g] : (((X2 @ X16) & (X2 @ X17)) => (X2 @ (X5 @ X17 @ X16))) & ! [X18 : g] : ((X2 @ X18) => (X9 @ (X8 @ X18))) & ! [X19 : g] : ((X2 @ X19) => (X9 @ (X8 @ X19))) & ! [X20 : b,X21 : b] : (((X9 @ X20) & (X9 @ X21)) => ((X6 @ (X0 @ X21 @ X20)) = (X11 @ (X6 @ X21) @ (X6 @ X20)))) & ! [X22 : g,X23 : g] : (((X2 @ X22) & (X2 @ X23)) => ((X8 @ (X5 @ X23 @ X22)) = (X0 @ (X8 @ X23) @ (X8 @ X22)))) & ! [X24 : g] : ((X2 @ X24) => (X9 @ (X8 @ X24))) & ! [X25 : b] : ((X9 @ X25) => (X4 @ (X6 @ X25)))) => (! [X26 : a,X27 : a] : (((X4 @ X27) & (X4 @ X26)) => (X4 @ (X11 @ X27 @ X26))) & ! [X28 : g,X29 : g] : (((X2 @ X29) & (X2 @ X28)) => (X2 @ (X5 @ X29 @ X28))) & ! [X30 : g] : ((X2 @ X30) => (X4 @ (X6 @ (X8 @ X30)))) & ! [X31 : g,X32 : g] : (((X2 @ X32) & (X2 @ X32) & (X2 @ X31) & (X2 @ X31)) => ((X11 @ (X6 @ (X8 @ X31)) @ (X6 @ (X8 @ X32))) = (X6 @ (X8 @ (X5 @ X31 @ X32)))))))),
% 1.75/1.48 inference(rectify,[status(thm)],[f2])).
% 1.75/1.48 thf(f2,negated_conjecture,(
% 1.75/1.48 ~! [X11 : b > b > b,X0 : g > b,X8 : g > $o,X4 : b > $o,X12 : a > $o,X9 : g > g > g,X7 : b > a,X1 : b > a,X6 : g > b,X10 : b > $o,X3 : g > g > g,X13 : a > a > a,X5 : b > b > b,X2 : g > $o] : ((! [X15 : a,X14 : a] : (((X12 @ X14) & (X12 @ X15)) => (X12 @ (X13 @ X14 @ X15))) & ! [X15 : g,X14 : g] : (((X8 @ X15) & (X8 @ X14)) => (X8 @ (X9 @ X14 @ X15))) & ! [X14 : g] : ((X8 @ X14) => (X10 @ (X6 @ X14))) & ! [X14 : g] : ((X8 @ X14) => (X10 @ (X6 @ X14))) & ! [X15 : b,X14 : b] : (((X10 @ X15) & (X10 @ X14)) => ((X7 @ (X11 @ X14 @ X15)) = (X13 @ (X7 @ X14) @ (X7 @ X15)))) & ! [X15 : g,X14 : g] : (((X8 @ X15) & (X8 @ X14)) => ((X6 @ (X9 @ X14 @ X15)) = (X11 @ (X6 @ X14) @ (X6 @ X15)))) & ! [X14 : g] : ((X8 @ X14) => (X10 @ (X6 @ X14))) & ! [X14 : b] : ((X10 @ X14) => (X12 @ (X7 @ X14)))) => (! [X15 : a,X14 : a] : (((X12 @ X14) & (X12 @ X15)) => (X12 @ (X13 @ X14 @ X15))) & ! [X15 : g,X14 : g] : (((X8 @ X14) & (X8 @ X15)) => (X8 @ (X9 @ X14 @ X15))) & ! [X14 : g] : ((X8 @ X14) => (X12 @ (X7 @ (X6 @ X14)))) & ! [X14 : g,X15 : g] : (((X8 @ X15) & (X8 @ X15) & (X8 @ X14) & (X8 @ X14)) => ((X7 @ (X6 @ (X9 @ X14 @ X15))) = (X13 @ (X7 @ (X6 @ X14)) @ (X7 @ (X6 @ X15)))))))),
% 1.75/1.48 inference(negated_conjecture,[status(cth)],[f1])).
% 1.75/1.48 thf(f1,conjecture,(
% 1.75/1.48 ! [X11 : b > b > b,X0 : g > b,X8 : g > $o,X4 : b > $o,X12 : a > $o,X9 : g > g > g,X7 : b > a,X1 : b > a,X6 : g > b,X10 : b > $o,X3 : g > g > g,X13 : a > a > a,X5 : b > b > b,X2 : g > $o] : ((! [X15 : a,X14 : a] : (((X12 @ X14) & (X12 @ X15)) => (X12 @ (X13 @ X14 @ X15))) & ! [X15 : g,X14 : g] : (((X8 @ X15) & (X8 @ X14)) => (X8 @ (X9 @ X14 @ X15))) & ! [X14 : g] : ((X8 @ X14) => (X10 @ (X6 @ X14))) & ! [X14 : g] : ((X8 @ X14) => (X10 @ (X6 @ X14))) & ! [X15 : b,X14 : b] : (((X10 @ X15) & (X10 @ X14)) => ((X7 @ (X11 @ X14 @ X15)) = (X13 @ (X7 @ X14) @ (X7 @ X15)))) & ! [X15 : g,X14 : g] : (((X8 @ X15) & (X8 @ X14)) => ((X6 @ (X9 @ X14 @ X15)) = (X11 @ (X6 @ X14) @ (X6 @ X15)))) & ! [X14 : g] : ((X8 @ X14) => (X10 @ (X6 @ X14))) & ! [X14 : b] : ((X10 @ X14) => (X12 @ (X7 @ X14)))) => (! [X15 : a,X14 : a] : (((X12 @ X14) & (X12 @ X15)) => (X12 @ (X13 @ X14 @ X15))) & ! [X15 : g,X14 : g] : (((X8 @ X14) & (X8 @ X15)) => (X8 @ (X9 @ X14 @ X15))) & ! [X14 : g] : ((X8 @ X14) => (X12 @ (X7 @ (X6 @ X14)))) & ! [X14 : g,X15 : g] : (((X8 @ X15) & (X8 @ X15) & (X8 @ X14) & (X8 @ X14)) => ((X7 @ (X6 @ (X9 @ X14 @ X15))) = (X13 @ (X7 @ (X6 @ X14)) @ (X7 @ (X6 @ X15)))))))),
% 1.75/1.48 file('/export/starexec/sandbox/tmp/tmp.1ZAPm39mWR/DTF2THF_21330.p',cTHM126_CORRECTED_pme)).
% 1.75/1.48 thf(f25,plain,(
% 1.75/1.48 ( ! [X0 : a > $o,X1 : a > a > a] : (((X0 @ (X1 @ (sK2 @ X1 @ X0) @ (sK3 @ X1 @ X0))) != $true) | ($true != (sP1 @ X1 @ X0))) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f15])).
% 1.75/1.48 thf(f181,plain,(
% 1.75/1.48 ~spl17_1 | spl17_14),
% 1.75/1.48 inference(avatar_contradiction_clause,[status(thm)],[f180])).
% 1.75/1.48 thf(f180,plain,(
% 1.75/1.48 $false | (~spl17_1 | spl17_14)),
% 1.75/1.48 inference(subsumption_resolution,[status(thm)],[f176,f50])).
% 1.75/1.48 thf(f50,plain,(
% 1.75/1.48 ($true = (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) | ~spl17_1),
% 1.75/1.48 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.75/1.48 thf(f48,definition,(
% 1.75/1.48 spl17_1 <=> ($true = (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))),
% 1.75/1.48 introduced(definition,[new_symbols(naming,[spl17_1])],[avatar_definition])).
% 1.75/1.48 thf(f176,plain,(
% 1.75/1.48 ($true != (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) | spl17_14),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f175])).
% 1.75/1.48 thf(f175,plain,(
% 1.75/1.48 ($true != (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) | ($true != $true) | spl17_14),
% 1.75/1.48 inference(superposition,[status(thm)],[f154,f32])).
% 1.75/1.48 thf(f32,plain,(
% 1.75/1.48 ( ! [X2 : g > b,X3 : b > a,X0 : g > $o,X1 : g > g > g,X4 : a > a > a] : (($true = (X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) | ($true != (sP0 @ X4 @ X3 @ X2 @ X1 @ X0))) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f19])).
% 1.75/1.48 thf(f19,plain,(
% 1.75/1.48 ! [X0 : g > $o,X1 : g > g > g,X2 : g > b,X3 : b > a,X4 : a > a > a] : ((($true = (X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) & ((X4 @ (X3 @ (X2 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) @ (X3 @ (X2 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)))) != (X3 @ (X2 @ (X1 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0) @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0))))) & ($true = (X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) & ((X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true) & ((X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true)) | ($true != (sP0 @ X4 @ X3 @ X2 @ X1 @ X0)))),
% 1.75/1.48 inference(skolemisation,[status(esa),new_symbols(skolem,[sK4,sK5])],[f17,f18])).
% 1.75/1.48 thf(f18,plain,(
% 1.75/1.48 ! [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 @ X5) = $true) & ($true = (X0 @ X6)) & ($true = (X0 @ X6))) => (($true = (X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) & ((X4 @ (X3 @ (X2 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) @ (X3 @ (X2 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)))) != (X3 @ (X2 @ (X1 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0) @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0))))) & ($true = (X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) & ((X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true) & ((X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true)))),
% 1.75/1.48 introduced(definition,[],[choice_axiom])).
% 1.75/1.48 thf(f17,plain,(
% 1.75/1.48 ! [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 @ X5) = $true) & ($true = (X0 @ X6)) & ($true = (X0 @ X6))) | ($true != (sP0 @ X4 @ X3 @ X2 @ X1 @ X0)))),
% 1.75/1.48 inference(rectify,[status(thm)],[f16])).
% 1.75/1.48 thf(f16,plain,(
% 1.75/1.48 ! [X1 : g > $o,X3 : g > g > g,X5 : g > b,X4 : b > a,X7 : a > a > a] : (? [X25 : g,X26 : g] : (($true = (X1 @ X25)) & ((X7 @ (X4 @ (X5 @ X25)) @ (X4 @ (X5 @ X26))) != (X4 @ (X5 @ (X3 @ X25 @ X26)))) & ($true = (X1 @ X25)) & ($true = (X1 @ X26)) & ($true = (X1 @ X26))) | ((sP0 @ X7 @ X4 @ X5 @ X3 @ X1) != $true))),
% 1.75/1.48 inference(nnf_transformation,[status(thm)],[f9])).
% 1.75/1.48 thf(f154,plain,(
% 1.75/1.48 ($true != (sK10 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))) | spl17_14),
% 1.75/1.48 inference(avatar_component_clause,[status(thm)],[f152])).
% 1.75/1.48 thf(f152,definition,(
% 1.75/1.48 spl17_14 <=> ($true = (sK10 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)))),
% 1.75/1.48 introduced(definition,[new_symbols(naming,[spl17_14])],[avatar_definition])).
% 1.75/1.48 thf(f170,plain,(
% 1.75/1.48 ~spl17_3 | spl17_5 | ~spl17_6),
% 1.75/1.48 inference(avatar_contradiction_clause,[status(thm)],[f169])).
% 1.75/1.48 thf(f169,plain,(
% 1.75/1.48 $false | (~spl17_3 | spl17_5 | ~spl17_6)),
% 1.75/1.48 inference(subsumption_resolution,[status(thm)],[f168,f58])).
% 1.75/1.48 thf(f58,plain,(
% 1.75/1.48 ($true = (sK10 @ sK15)) | ~spl17_3),
% 1.75/1.48 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.75/1.48 thf(f56,definition,(
% 1.75/1.48 spl17_3 <=> ($true = (sK10 @ sK15))),
% 1.75/1.48 introduced(definition,[new_symbols(naming,[spl17_3])],[avatar_definition])).
% 1.75/1.48 thf(f168,plain,(
% 1.75/1.48 ($true != (sK10 @ sK15)) | (spl17_5 | ~spl17_6)),
% 1.75/1.48 inference(subsumption_resolution,[status(thm)],[f167,f72])).
% 1.75/1.48 thf(f72,plain,(
% 1.75/1.48 ((sK10 @ sK16) = $true) | ~spl17_6),
% 1.75/1.48 inference(avatar_component_clause,[status(thm)],[f70])).
% 1.75/1.48 thf(f70,definition,(
% 1.75/1.48 spl17_6 <=> ((sK10 @ sK16) = $true)),
% 1.75/1.48 introduced(definition,[new_symbols(naming,[spl17_6])],[avatar_definition])).
% 1.75/1.48 thf(f167,plain,(
% 1.75/1.48 ((sK10 @ sK16) != $true) | ($true != (sK10 @ sK15)) | spl17_5),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f166])).
% 1.75/1.48 thf(f166,plain,(
% 1.75/1.48 ((sK10 @ sK16) != $true) | ($true != $true) | ($true != (sK10 @ sK15)) | spl17_5),
% 1.75/1.48 inference(superposition,[status(thm)],[f67,f33])).
% 1.75/1.48 thf(f33,plain,(
% 1.75/1.48 ( ! [X21 : g,X22 : g] : (((sK10 @ (sK11 @ X22 @ X21)) = $true) | ($true != (sK10 @ X22)) | ($true != (sK10 @ X21))) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f24])).
% 1.75/1.48 thf(f67,plain,(
% 1.75/1.48 ((sK10 @ (sK11 @ sK16 @ sK15)) != $true) | spl17_5),
% 1.75/1.48 inference(avatar_component_clause,[status(thm)],[f65])).
% 1.75/1.48 thf(f65,definition,(
% 1.75/1.48 spl17_5 <=> ((sK10 @ (sK11 @ sK16 @ sK15)) = $true)),
% 1.75/1.48 introduced(definition,[new_symbols(naming,[spl17_5])],[avatar_definition])).
% 1.75/1.48 thf(f165,plain,(
% 1.75/1.48 ~spl17_1 | spl17_13),
% 1.75/1.48 inference(avatar_split_clause,[status(thm)],[f158,f148,f48])).
% 1.75/1.48 thf(f148,definition,(
% 1.75/1.48 spl17_13 <=> ($true = (sK10 @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)))),
% 1.75/1.48 introduced(definition,[new_symbols(naming,[spl17_13])],[avatar_definition])).
% 1.75/1.48 thf(f158,plain,(
% 1.75/1.48 ($true != (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) | spl17_13),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f156])).
% 1.75/1.48 thf(f156,plain,(
% 1.75/1.48 ($true != $true) | ($true != (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) | spl17_13),
% 1.75/1.48 inference(superposition,[status(thm)],[f150,f29])).
% 1.75/1.48 thf(f29,plain,(
% 1.75/1.48 ( ! [X2 : g > b,X3 : b > a,X0 : g > $o,X1 : g > g > g,X4 : a > a > a] : (((X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true) | ($true != (sP0 @ X4 @ X3 @ X2 @ X1 @ X0))) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f19])).
% 1.75/1.48 thf(f150,plain,(
% 1.75/1.48 ($true != (sK10 @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))) | spl17_13),
% 1.75/1.48 inference(avatar_component_clause,[status(thm)],[f148])).
% 1.75/1.48 thf(f155,plain,(
% 1.75/1.48 ~spl17_13 | ~spl17_14 | spl17_11),
% 1.75/1.48 inference(avatar_split_clause,[status(thm)],[f146,f117,f152,f148])).
% 1.75/1.48 thf(f117,definition,(
% 1.75/1.48 spl17_11 <=> ((sK8 @ (sK6 @ (sK7 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) @ (sK7 @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)))) = (sK8 @ (sK7 @ (sK11 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10) @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)))))),
% 1.75/1.48 introduced(definition,[new_symbols(naming,[spl17_11])],[avatar_definition])).
% 1.75/1.48 thf(f146,plain,(
% 1.75/1.48 ($true != (sK10 @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))) | ($true != (sK10 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))) | spl17_11),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f145])).
% 1.75/1.48 thf(f145,plain,(
% 1.75/1.48 ((sK8 @ (sK7 @ (sK11 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10) @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)))) != (sK8 @ (sK7 @ (sK11 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10) @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))))) | ($true != (sK10 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))) | ($true != (sK10 @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))) | spl17_11),
% 1.75/1.48 inference(superposition,[status(thm)],[f119,f35])).
% 1.75/1.48 thf(f35,plain,(
% 1.75/1.48 ( ! [X18 : g,X19 : g] : (((sK7 @ (sK11 @ X18 @ X19)) = (sK6 @ (sK7 @ X18) @ (sK7 @ X19))) | ($true != (sK10 @ X19)) | ($true != (sK10 @ X18))) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f24])).
% 1.75/1.48 thf(f119,plain,(
% 1.75/1.48 ((sK8 @ (sK6 @ (sK7 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) @ (sK7 @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)))) != (sK8 @ (sK7 @ (sK11 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10) @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))))) | spl17_11),
% 1.75/1.48 inference(avatar_component_clause,[status(thm)],[f117])).
% 1.75/1.48 thf(f144,plain,(
% 1.75/1.48 ~spl17_1 | spl17_12),
% 1.75/1.48 inference(avatar_contradiction_clause,[status(thm)],[f143])).
% 1.75/1.48 thf(f143,plain,(
% 1.75/1.48 $false | (~spl17_1 | spl17_12)),
% 1.75/1.48 inference(subsumption_resolution,[status(thm)],[f139,f50])).
% 1.75/1.48 thf(f139,plain,(
% 1.75/1.48 ($true != (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) | spl17_12),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f138])).
% 1.75/1.48 thf(f138,plain,(
% 1.75/1.48 ($true != $true) | ($true != (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) | spl17_12),
% 1.75/1.48 inference(superposition,[status(thm)],[f136,f28])).
% 1.75/1.48 thf(f28,plain,(
% 1.75/1.48 ( ! [X2 : g > b,X3 : b > a,X0 : g > $o,X1 : g > g > g,X4 : a > a > a] : (((X0 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)) = $true) | ($true != (sP0 @ X4 @ X3 @ X2 @ X1 @ X0))) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f19])).
% 1.75/1.48 thf(f136,plain,(
% 1.75/1.48 ($true != (sK10 @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))) | spl17_12),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f135])).
% 1.75/1.48 thf(f135,plain,(
% 1.75/1.48 ($true != (sK10 @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))) | ($true != $true) | spl17_12),
% 1.75/1.48 inference(superposition,[status(thm)],[f123,f34])).
% 1.75/1.48 thf(f34,plain,(
% 1.75/1.48 ( ! [X20 : g] : (($true = (sK13 @ (sK7 @ X20))) | ((sK10 @ X20) != $true)) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f24])).
% 1.75/1.48 thf(f123,plain,(
% 1.75/1.48 ((sK13 @ (sK7 @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))) != $true) | spl17_12),
% 1.75/1.48 inference(avatar_component_clause,[status(thm)],[f121])).
% 1.75/1.48 thf(f121,definition,(
% 1.75/1.48 spl17_12 <=> ((sK13 @ (sK7 @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))) = $true)),
% 1.75/1.48 introduced(definition,[new_symbols(naming,[spl17_12])],[avatar_definition])).
% 1.75/1.48 thf(f134,plain,(
% 1.75/1.48 ~spl17_1 | spl17_10),
% 1.75/1.48 inference(avatar_contradiction_clause,[status(thm)],[f133])).
% 1.75/1.48 thf(f133,plain,(
% 1.75/1.48 $false | (~spl17_1 | spl17_10)),
% 1.75/1.48 inference(subsumption_resolution,[status(thm)],[f129,f50])).
% 1.75/1.48 thf(f129,plain,(
% 1.75/1.48 ($true != (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) | spl17_10),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f127])).
% 1.75/1.48 thf(f127,plain,(
% 1.75/1.48 ($true != (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) | ($true != $true) | spl17_10),
% 1.75/1.48 inference(superposition,[status(thm)],[f126,f30])).
% 1.75/1.48 thf(f30,plain,(
% 1.75/1.48 ( ! [X2 : g > b,X3 : b > a,X0 : g > $o,X1 : g > g > g,X4 : a > a > a] : (($true = (X0 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) | ($true != (sP0 @ X4 @ X3 @ X2 @ X1 @ X0))) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f19])).
% 1.75/1.48 thf(f126,plain,(
% 1.75/1.48 ($true != (sK10 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))) | spl17_10),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f125])).
% 1.75/1.48 thf(f125,plain,(
% 1.75/1.48 ($true != $true) | ($true != (sK10 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))) | spl17_10),
% 1.75/1.48 inference(superposition,[status(thm)],[f115,f34])).
% 1.75/1.48 thf(f115,plain,(
% 1.75/1.48 ($true != (sK13 @ (sK7 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)))) | spl17_10),
% 1.75/1.48 inference(avatar_component_clause,[status(thm)],[f113])).
% 1.75/1.48 thf(f113,definition,(
% 1.75/1.48 spl17_10 <=> ($true = (sK13 @ (sK7 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))))),
% 1.75/1.48 introduced(definition,[new_symbols(naming,[spl17_10])],[avatar_definition])).
% 1.75/1.48 thf(f124,plain,(
% 1.75/1.48 ~spl17_10 | ~spl17_11 | ~spl17_12 | ~spl17_1),
% 1.75/1.48 inference(avatar_split_clause,[status(thm)],[f111,f48,f121,f117,f113])).
% 1.75/1.48 thf(f111,plain,(
% 1.75/1.48 ((sK13 @ (sK7 @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))) != $true) | ((sK8 @ (sK6 @ (sK7 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) @ (sK7 @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)))) != (sK8 @ (sK7 @ (sK11 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10) @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))))) | ($true != (sK13 @ (sK7 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)))) | ~spl17_1),
% 1.75/1.48 inference(superposition,[status(thm)],[f107,f45])).
% 1.75/1.48 thf(f45,plain,(
% 1.75/1.48 ( ! [X10 : b,X9 : b] : (((sK8 @ (sK6 @ X10 @ X9)) = (sK12 @ (sK8 @ X10) @ (sK8 @ X9))) | ($true != (sK13 @ X9)) | ($true != (sK13 @ X10))) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f24])).
% 1.75/1.48 thf(f107,plain,(
% 1.75/1.48 ((sK12 @ (sK8 @ (sK7 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))) @ (sK8 @ (sK7 @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)))) != (sK8 @ (sK7 @ (sK11 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10) @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))))) | ~spl17_1),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.75/1.48 thf(f106,plain,(
% 1.75/1.48 ($true != $true) | ((sK12 @ (sK8 @ (sK7 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))) @ (sK8 @ (sK7 @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)))) != (sK8 @ (sK7 @ (sK11 @ (sK4 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10) @ (sK5 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))))) | ~spl17_1),
% 1.75/1.48 inference(superposition,[status(thm)],[f31,f50])).
% 1.75/1.48 thf(f31,plain,(
% 1.75/1.48 ( ! [X2 : g > b,X3 : b > a,X0 : g > $o,X1 : g > g > g,X4 : a > a > a] : (($true != (sP0 @ X4 @ X3 @ X2 @ X1 @ X0)) | ((X4 @ (X3 @ (X2 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0))) @ (X3 @ (X2 @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)))) != (X3 @ (X2 @ (X1 @ (sK4 @ X4 @ X3 @ X2 @ X1 @ X0) @ (sK5 @ X4 @ X3 @ X2 @ X1 @ X0)))))) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f19])).
% 1.75/1.48 thf(f102,plain,(
% 1.75/1.48 spl17_2 | ~spl17_7),
% 1.75/1.48 inference(avatar_contradiction_clause,[status(thm)],[f101])).
% 1.75/1.48 thf(f101,plain,(
% 1.75/1.48 $false | (spl17_2 | ~spl17_7)),
% 1.75/1.48 inference(subsumption_resolution,[status(thm)],[f100,f77])).
% 1.75/1.48 thf(f77,plain,(
% 1.75/1.48 ($true = (sK10 @ sK14)) | ~spl17_7),
% 1.75/1.48 inference(avatar_component_clause,[status(thm)],[f75])).
% 1.75/1.48 thf(f75,definition,(
% 1.75/1.48 spl17_7 <=> ($true = (sK10 @ sK14))),
% 1.75/1.48 introduced(definition,[new_symbols(naming,[spl17_7])],[avatar_definition])).
% 1.75/1.48 thf(f100,plain,(
% 1.75/1.48 ($true != (sK10 @ sK14)) | spl17_2),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f99])).
% 1.75/1.48 thf(f99,plain,(
% 1.75/1.48 ($true != $true) | ($true != (sK10 @ sK14)) | spl17_2),
% 1.75/1.48 inference(superposition,[status(thm)],[f98,f34])).
% 1.75/1.48 thf(f98,plain,(
% 1.75/1.48 ($true != (sK13 @ (sK7 @ sK14))) | spl17_2),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.75/1.48 thf(f97,plain,(
% 1.75/1.48 ($true != (sK13 @ (sK7 @ sK14))) | ($true != $true) | spl17_2),
% 1.75/1.48 inference(superposition,[status(thm)],[f54,f38])).
% 1.75/1.48 thf(f38,plain,(
% 1.75/1.48 ( ! [X14 : b] : (((sK9 @ (sK8 @ X14)) = $true) | ((sK13 @ X14) != $true)) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f24])).
% 1.75/1.48 thf(f54,plain,(
% 1.75/1.48 ($true != (sK9 @ (sK8 @ (sK7 @ sK14)))) | spl17_2),
% 1.75/1.48 inference(avatar_component_clause,[status(thm)],[f52])).
% 1.75/1.48 thf(f52,definition,(
% 1.75/1.48 spl17_2 <=> ($true = (sK9 @ (sK8 @ (sK7 @ sK14))))),
% 1.75/1.48 introduced(definition,[new_symbols(naming,[spl17_2])],[avatar_definition])).
% 1.75/1.48 thf(f96,plain,(
% 1.75/1.48 ~spl17_4 | spl17_8),
% 1.75/1.48 inference(avatar_contradiction_clause,[status(thm)],[f95])).
% 1.75/1.48 thf(f95,plain,(
% 1.75/1.48 $false | (~spl17_4 | spl17_8)),
% 1.75/1.48 inference(subsumption_resolution,[status(thm)],[f94,f62])).
% 1.75/1.48 thf(f62,plain,(
% 1.75/1.48 ($true = (sP1 @ sK12 @ sK9)) | ~spl17_4),
% 1.75/1.48 inference(avatar_component_clause,[status(thm)],[f60])).
% 1.75/1.48 thf(f94,plain,(
% 1.75/1.48 ($true != (sP1 @ sK12 @ sK9)) | spl17_8),
% 1.75/1.48 inference(trivial_inequality_removal,[status(thm)],[f93])).
% 1.75/1.48 thf(f93,plain,(
% 1.75/1.48 ($true != $true) | ($true != (sP1 @ sK12 @ sK9)) | spl17_8),
% 1.75/1.48 inference(superposition,[status(thm)],[f87,f26])).
% 1.75/1.48 thf(f26,plain,(
% 1.75/1.48 ( ! [X0 : a > $o,X1 : a > a > a] : (($true = (X0 @ (sK2 @ X1 @ X0))) | ($true != (sP1 @ X1 @ X0))) )),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f15])).
% 1.75/1.48 thf(f87,plain,(
% 1.75/1.48 ((sK9 @ (sK2 @ sK12 @ sK9)) != $true) | spl17_8),
% 1.75/1.48 inference(avatar_component_clause,[status(thm)],[f85])).
% 1.75/1.48 thf(f80,plain,(
% 1.75/1.48 spl17_4 | spl17_7 | ~spl17_5 | spl17_1),
% 1.75/1.48 inference(avatar_split_clause,[status(thm)],[f44,f48,f65,f75,f60])).
% 1.75/1.48 thf(f44,plain,(
% 1.75/1.48 ($true = (sK10 @ sK14)) | ($true = (sP1 @ sK12 @ sK9)) | ((sK10 @ (sK11 @ sK16 @ sK15)) != $true) | ($true = (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f24])).
% 1.75/1.48 thf(f79,plain,(
% 1.75/1.48 spl17_7 | spl17_4 | spl17_1 | spl17_3),
% 1.75/1.48 inference(avatar_split_clause,[status(thm)],[f43,f56,f48,f60,f75])).
% 1.75/1.48 thf(f43,plain,(
% 1.75/1.48 ($true = (sK10 @ sK15)) | ($true = (sK10 @ sK14)) | ($true = (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) | ($true = (sP1 @ sK12 @ sK9))),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f24])).
% 1.75/1.48 thf(f78,plain,(
% 1.75/1.48 spl17_7 | spl17_4 | spl17_1 | spl17_6),
% 1.75/1.48 inference(avatar_split_clause,[status(thm)],[f42,f70,f48,f60,f75])).
% 1.75/1.48 thf(f42,plain,(
% 1.75/1.48 ($true = (sK10 @ sK14)) | ($true = (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) | ($true = (sP1 @ sK12 @ sK9)) | ((sK10 @ sK16) = $true)),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f24])).
% 1.75/1.48 thf(f73,plain,(
% 1.75/1.48 ~spl17_2 | spl17_1 | spl17_6 | spl17_4),
% 1.75/1.48 inference(avatar_split_clause,[status(thm)],[f39,f60,f70,f48,f52])).
% 1.75/1.48 thf(f39,plain,(
% 1.75/1.48 ($true != (sK9 @ (sK8 @ (sK7 @ sK14)))) | ((sK10 @ sK16) = $true) | ($true = (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10)) | ($true = (sP1 @ sK12 @ sK9))),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f24])).
% 1.75/1.48 thf(f68,plain,(
% 1.75/1.48 spl17_1 | ~spl17_2 | ~spl17_5 | spl17_4),
% 1.75/1.48 inference(avatar_split_clause,[status(thm)],[f41,f60,f65,f52,f48])).
% 1.75/1.48 thf(f41,plain,(
% 1.75/1.48 ($true != (sK9 @ (sK8 @ (sK7 @ sK14)))) | ($true = (sP1 @ sK12 @ sK9)) | ((sK10 @ (sK11 @ sK16 @ sK15)) != $true) | ($true = (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f24])).
% 1.75/1.48 thf(f63,plain,(
% 1.75/1.48 spl17_1 | ~spl17_2 | spl17_3 | spl17_4),
% 1.75/1.48 inference(avatar_split_clause,[status(thm)],[f40,f60,f56,f52,f48])).
% 1.75/1.48 thf(f40,plain,(
% 1.75/1.48 ($true != (sK9 @ (sK8 @ (sK7 @ sK14)))) | ($true = (sP1 @ sK12 @ sK9)) | ($true = (sK10 @ sK15)) | ($true = (sP0 @ sK12 @ sK8 @ sK7 @ sK11 @ sK10))),
% 1.75/1.48 inference(cnf_transformation,[status(thm)],[f24])).
% 1.75/1.48 % SZS output end Proof for DTF2THF_21330
% 1.75/1.48 % (21432)------------------------------
% 1.75/1.48 % (21432)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.75/1.48 % (21432)Termination reason: Refutation
% 1.75/1.48
% 1.75/1.48 % (21432)Memory used [KB]: 5884
% 1.75/1.48 % (21432)Time elapsed: 0.025 s
% 1.75/1.48 % (21432)Instructions burned: 34 (million)
% 1.75/1.48 % (21432)------------------------------
% 1.75/1.48 % (21432)------------------------------
% 1.75/1.48 % (21426)Success in time 0.038 s
%------------------------------------------------------------------------------