%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEU903^5 : 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 : n006.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Wed Feb 25 09:37:42 AM UTC 2026
% Result : Theorem 1.67s 1.35s
% Output : Refutation 1.67s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 16
% Syntax : Number of formulae : 81 ( 3 unt; 0 typ; 9 def)
% Number of atoms : 799 ( 311 equ; 0 cnn)
% Maximal formula atoms : 46 ( 9 avg)
% Number of connectives : 1281 ( 170 ~; 174 |; 131 &; 740 @)
% ( 9 <=>; 57 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 6 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 86 ( 86 >; 0 *; 0 +; 0 <<)
% Number of symbols : 26 ( 23 usr; 14 con; 0-2 aty)
% Number of variables : 223 ( 0 ^; 156 !; 67 ?; 223 :)
% 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 > $o ) > $o ).
thf(func_def_7,type,
sK1: ( a > a ) > ( a > $o ) > a ).
thf(func_def_8,type,
sK2: b > b ).
thf(func_def_9,type,
sK3: g > g ).
thf(func_def_10,type,
sK4: b > $o ).
thf(func_def_11,type,
sK5: a > a ).
thf(func_def_12,type,
sK6: g > b ).
thf(func_def_13,type,
sK7: b > a ).
thf(func_def_14,type,
sK8: g > $o ).
thf(func_def_15,type,
sK9: a > $o ).
thf(func_def_16,type,
sK10: g ).
thf(func_def_17,type,
sK11: g ).
thf(func_def_18,type,
sK12: g ).
thf(func_def_20,type,
ph14:
!>[X0: $tType] : X0 ).
thf(f112,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f54,f63,f68,f69,f70,f71,f72,f73,f76,f80,f96,f101,f107,f111]) ).
thf(f111,plain,
( ~ spl13_3
| spl13_9 ),
inference(avatar_contradiction_clause,[status(thm)],[f110]) ).
thf(f110,plain,
( $false
| ~ spl13_3
| spl13_9 ),
inference(subsumption_resolution,[status(thm)],[f109,f49]) ).
thf(f49,plain,
( ( ( sK8 @ sK11 )
= $true )
| ~ spl13_3 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f47,definition,
( spl13_3
<=> ( ( sK8 @ sK11 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_3])],[avatar_definition]) ).
thf(f109,plain,
( ( ( sK8 @ sK11 )
!= $true )
| spl13_9 ),
inference(trivial_inequality_removal,[status(thm)],[f108]) ).
thf(f108,plain,
( ( ( sK7 @ ( sK6 @ ( sK3 @ sK11 ) ) )
!= ( sK7 @ ( sK6 @ ( sK3 @ sK11 ) ) ) )
| ( ( sK8 @ sK11 )
!= $true )
| spl13_9 ),
inference(superposition,[status(thm)],[f95,f22]) ).
thf(f22,plain,
! [X18: g] :
( ( ( sK6 @ ( sK3 @ X18 ) )
= ( sK2 @ ( sK6 @ X18 ) ) )
| ( ( sK8 @ X18 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X8: b] :
( ( ( sK4 @ X8 )
!= $true )
| ( ( sK7 @ ( sK2 @ X8 ) )
= ( sK5 @ ( sK7 @ X8 ) ) ) )
& ! [X9: a] :
( ( ( sK9 @ ( sK5 @ X9 ) )
= $true )
| ( ( sK9 @ X9 )
!= $true ) )
& ! [X10: b] :
( ( ( sK9 @ ( sK7 @ X10 ) )
= $true )
| ( ( sK4 @ X10 )
!= $true ) )
& ! [X11: b] :
( ( ( sK4 @ X11 )
!= $true )
| ( ( sK4 @ ( sK2 @ X11 ) )
= $true ) )
& ! [X12: b] :
( ( ( sK4 @ ( sK2 @ X12 ) )
= $true )
| ( ( sK4 @ X12 )
!= $true ) )
& ! [X13: g] :
( ( ( sK4 @ ( sK6 @ X13 ) )
= $true )
| ( ( sK8 @ X13 )
!= $true ) )
& ! [X14: g] :
( ( ( sK8 @ X14 )
!= $true )
| ( ( sK8 @ ( sK3 @ X14 ) )
= $true ) )
& ( ( ( ( sK8 @ ( sK3 @ sK10 ) )
!= $true )
& ( ( sK8 @ sK10 )
= $true ) )
| ( ( ( sK7 @ ( sK6 @ ( sK3 @ sK11 ) ) )
!= ( sK5 @ ( sK7 @ ( sK6 @ sK11 ) ) ) )
& ( ( sK8 @ sK11 )
= $true ) )
| ( ( ( sK9 @ ( sK7 @ ( sK6 @ sK12 ) ) )
!= $true )
& ( ( sK8 @ sK12 )
= $true ) )
| ( ( sP0 @ sK5 @ sK9 )
= $true ) )
& ! [X18: g] :
( ( ( sK8 @ X18 )
!= $true )
| ( ( sK6 @ ( sK3 @ X18 ) )
= ( sK2 @ ( sK6 @ X18 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12])],[f14,f18,f17,f16,f15]) ).
thf(f15,plain,
( ? [X0: b > b,X1: g > g,X2: b > $o,X3: a > a,X4: g > b,X5: b > a,X6: g > $o,X7: a > $o] :
( ! [X8: b] :
( ( ( X2 @ X8 )
!= $true )
| ( ( X3 @ ( X5 @ X8 ) )
= ( X5 @ ( X0 @ X8 ) ) ) )
& ! [X9: a] :
( ( ( X7 @ ( X3 @ X9 ) )
= $true )
| ( ( X7 @ X9 )
!= $true ) )
& ! [X10: b] :
( ( ( X7 @ ( X5 @ X10 ) )
= $true )
| ( ( X2 @ X10 )
!= $true ) )
& ! [X11: b] :
( ( ( X2 @ X11 )
!= $true )
| ( ( X2 @ ( X0 @ X11 ) )
= $true ) )
& ! [X12: b] :
( ( ( X2 @ ( X0 @ X12 ) )
= $true )
| ( ( X2 @ X12 )
!= $true ) )
& ! [X13: g] :
( ( ( X2 @ ( X4 @ X13 ) )
= $true )
| ( ( X6 @ X13 )
!= $true ) )
& ! [X14: g] :
( ( ( X6 @ X14 )
!= $true )
| ( ( X6 @ ( X1 @ X14 ) )
= $true ) )
& ( ? [X15: g] :
( ( ( X6 @ ( X1 @ X15 ) )
!= $true )
& ( ( X6 @ X15 )
= $true ) )
| ? [X16: g] :
( ( ( X3 @ ( X5 @ ( X4 @ X16 ) ) )
!= ( X5 @ ( X4 @ ( X1 @ X16 ) ) ) )
& ( ( X6 @ X16 )
= $true ) )
| ? [X17: g] :
( ( ( X7 @ ( X5 @ ( X4 @ X17 ) ) )
!= $true )
& ( ( X6 @ X17 )
= $true ) )
| ( ( sP0 @ X3 @ X7 )
= $true ) )
& ! [X18: g] :
( ( ( X6 @ X18 )
!= $true )
| ( ( X4 @ ( X1 @ X18 ) )
= ( X0 @ ( X4 @ X18 ) ) ) ) )
=> ( ! [X8: b] :
( ( ( sK4 @ X8 )
!= $true )
| ( ( sK7 @ ( sK2 @ X8 ) )
= ( sK5 @ ( sK7 @ X8 ) ) ) )
& ! [X9: a] :
( ( ( sK9 @ ( sK5 @ X9 ) )
= $true )
| ( ( sK9 @ X9 )
!= $true ) )
& ! [X10: b] :
( ( ( sK9 @ ( sK7 @ X10 ) )
= $true )
| ( ( sK4 @ X10 )
!= $true ) )
& ! [X11: b] :
( ( ( sK4 @ X11 )
!= $true )
| ( ( sK4 @ ( sK2 @ X11 ) )
= $true ) )
& ! [X12: b] :
( ( ( sK4 @ ( sK2 @ X12 ) )
= $true )
| ( ( sK4 @ X12 )
!= $true ) )
& ! [X13: g] :
( ( ( sK4 @ ( sK6 @ X13 ) )
= $true )
| ( ( sK8 @ X13 )
!= $true ) )
& ! [X14: g] :
( ( ( sK8 @ X14 )
!= $true )
| ( ( sK8 @ ( sK3 @ X14 ) )
= $true ) )
& ( ? [X15: g] :
( ( ( sK8 @ ( sK3 @ X15 ) )
!= $true )
& ( ( sK8 @ X15 )
= $true ) )
| ? [X16: g] :
( ( ( sK7 @ ( sK6 @ ( sK3 @ X16 ) ) )
!= ( sK5 @ ( sK7 @ ( sK6 @ X16 ) ) ) )
& ( ( sK8 @ X16 )
= $true ) )
| ? [X17: g] :
( ( ( sK9 @ ( sK7 @ ( sK6 @ X17 ) ) )
!= $true )
& ( ( sK8 @ X17 )
= $true ) )
| ( ( sP0 @ sK5 @ sK9 )
= $true ) )
& ! [X18: g] :
( ( ( sK8 @ X18 )
!= $true )
| ( ( sK6 @ ( sK3 @ X18 ) )
= ( sK2 @ ( sK6 @ X18 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X15: g] :
( ( ( sK8 @ ( sK3 @ X15 ) )
!= $true )
& ( ( sK8 @ X15 )
= $true ) )
=> ( ( ( sK8 @ ( sK3 @ sK10 ) )
!= $true )
& ( ( sK8 @ sK10 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X16: g] :
( ( ( sK7 @ ( sK6 @ ( sK3 @ X16 ) ) )
!= ( sK5 @ ( sK7 @ ( sK6 @ X16 ) ) ) )
& ( ( sK8 @ X16 )
= $true ) )
=> ( ( ( sK7 @ ( sK6 @ ( sK3 @ sK11 ) ) )
!= ( sK5 @ ( sK7 @ ( sK6 @ sK11 ) ) ) )
& ( ( sK8 @ sK11 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X17: g] :
( ( ( sK9 @ ( sK7 @ ( sK6 @ X17 ) ) )
!= $true )
& ( ( sK8 @ X17 )
= $true ) )
=> ( ( ( sK9 @ ( sK7 @ ( sK6 @ sK12 ) ) )
!= $true )
& ( ( sK8 @ sK12 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
? [X0: b > b,X1: g > g,X2: b > $o,X3: a > a,X4: g > b,X5: b > a,X6: g > $o,X7: a > $o] :
( ! [X8: b] :
( ( ( X2 @ X8 )
!= $true )
| ( ( X3 @ ( X5 @ X8 ) )
= ( X5 @ ( X0 @ X8 ) ) ) )
& ! [X9: a] :
( ( ( X7 @ ( X3 @ X9 ) )
= $true )
| ( ( X7 @ X9 )
!= $true ) )
& ! [X10: b] :
( ( ( X7 @ ( X5 @ X10 ) )
= $true )
| ( ( X2 @ X10 )
!= $true ) )
& ! [X11: b] :
( ( ( X2 @ X11 )
!= $true )
| ( ( X2 @ ( X0 @ X11 ) )
= $true ) )
& ! [X12: b] :
( ( ( X2 @ ( X0 @ X12 ) )
= $true )
| ( ( X2 @ X12 )
!= $true ) )
& ! [X13: g] :
( ( ( X2 @ ( X4 @ X13 ) )
= $true )
| ( ( X6 @ X13 )
!= $true ) )
& ! [X14: g] :
( ( ( X6 @ X14 )
!= $true )
| ( ( X6 @ ( X1 @ X14 ) )
= $true ) )
& ( ? [X15: g] :
( ( ( X6 @ ( X1 @ X15 ) )
!= $true )
& ( ( X6 @ X15 )
= $true ) )
| ? [X16: g] :
( ( ( X3 @ ( X5 @ ( X4 @ X16 ) ) )
!= ( X5 @ ( X4 @ ( X1 @ X16 ) ) ) )
& ( ( X6 @ X16 )
= $true ) )
| ? [X17: g] :
( ( ( X7 @ ( X5 @ ( X4 @ X17 ) ) )
!= $true )
& ( ( X6 @ X17 )
= $true ) )
| ( ( sP0 @ X3 @ X7 )
= $true ) )
& ! [X18: g] :
( ( ( X6 @ X18 )
!= $true )
| ( ( X4 @ ( X1 @ X18 ) )
= ( X0 @ ( X4 @ X18 ) ) ) ) ),
inference(rectify,[status(thm)],[f9]) ).
thf(f9,plain,
? [X6: b > b,X5: g > g,X2: b > $o,X1: a > a,X7: g > b,X3: b > a,X0: g > $o,X4: a > $o] :
( ! [X11: b] :
( ( ( X2 @ X11 )
!= $true )
| ( ( X1 @ ( X3 @ X11 ) )
= ( X3 @ ( X6 @ X11 ) ) ) )
& ! [X14: a] :
( ( ( X4 @ ( X1 @ X14 ) )
= $true )
| ( ( X4 @ X14 )
!= $true ) )
& ! [X8: b] :
( ( ( X4 @ ( X3 @ X8 ) )
= $true )
| ( ( X2 @ X8 )
!= $true ) )
& ! [X10: b] :
( ( ( X2 @ X10 )
!= $true )
| ( ( X2 @ ( X6 @ X10 ) )
= $true ) )
& ! [X13: b] :
( ( ( X2 @ ( X6 @ X13 ) )
= $true )
| ( ( X2 @ X13 )
!= $true ) )
& ! [X15: g] :
( ( ( X2 @ ( X7 @ X15 ) )
= $true )
| ( ( X0 @ X15 )
!= $true ) )
& ! [X9: g] :
( ( ( X0 @ X9 )
!= $true )
| ( ( X0 @ ( X5 @ X9 ) )
= $true ) )
& ( ? [X19: g] :
( ( ( X0 @ ( X5 @ X19 ) )
!= $true )
& ( ( X0 @ X19 )
= $true ) )
| ? [X17: g] :
( ( ( X1 @ ( X3 @ ( X7 @ X17 ) ) )
!= ( X3 @ ( X7 @ ( X5 @ X17 ) ) ) )
& ( ( X0 @ X17 )
= $true ) )
| ? [X16: g] :
( ( ( X4 @ ( X3 @ ( X7 @ X16 ) ) )
!= $true )
& ( ( X0 @ X16 )
= $true ) )
| ( ( sP0 @ X1 @ X4 )
= $true ) )
& ! [X12: g] :
( ( ( X0 @ X12 )
!= $true )
| ( ( X6 @ ( X7 @ X12 ) )
= ( X7 @ ( X5 @ X12 ) ) ) ) ),
inference(definition_folding,[status(thm)],[f7,f8]) ).
thf(f8,plain,
! [X4: a > $o,X1: a > a] :
( ? [X18: a] :
( ( ( X4 @ X18 )
= $true )
& ( ( X4 @ ( X1 @ X18 ) )
!= $true ) )
| ( ( sP0 @ X1 @ X4 )
!= $true ) ),
introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction]) ).
thf(f7,plain,
? [X6: b > b,X5: g > g,X2: b > $o,X1: a > a,X7: g > b,X3: b > a,X0: g > $o,X4: a > $o] :
( ! [X11: b] :
( ( ( X2 @ X11 )
!= $true )
| ( ( X1 @ ( X3 @ X11 ) )
= ( X3 @ ( X6 @ X11 ) ) ) )
& ! [X14: a] :
( ( ( X4 @ ( X1 @ X14 ) )
= $true )
| ( ( X4 @ X14 )
!= $true ) )
& ! [X8: b] :
( ( ( X4 @ ( X3 @ X8 ) )
= $true )
| ( ( X2 @ X8 )
!= $true ) )
& ! [X10: b] :
( ( ( X2 @ X10 )
!= $true )
| ( ( X2 @ ( X6 @ X10 ) )
= $true ) )
& ! [X13: b] :
( ( ( X2 @ ( X6 @ X13 ) )
= $true )
| ( ( X2 @ X13 )
!= $true ) )
& ! [X15: g] :
( ( ( X2 @ ( X7 @ X15 ) )
= $true )
| ( ( X0 @ X15 )
!= $true ) )
& ! [X9: g] :
( ( ( X0 @ X9 )
!= $true )
| ( ( X0 @ ( X5 @ X9 ) )
= $true ) )
& ( ? [X19: g] :
( ( ( X0 @ ( X5 @ X19 ) )
!= $true )
& ( ( X0 @ X19 )
= $true ) )
| ? [X17: g] :
( ( ( X1 @ ( X3 @ ( X7 @ X17 ) ) )
!= ( X3 @ ( X7 @ ( X5 @ X17 ) ) ) )
& ( ( X0 @ X17 )
= $true ) )
| ? [X16: g] :
( ( ( X4 @ ( X3 @ ( X7 @ X16 ) ) )
!= $true )
& ( ( X0 @ X16 )
= $true ) )
| ? [X18: a] :
( ( ( X4 @ X18 )
= $true )
& ( ( X4 @ ( X1 @ X18 ) )
!= $true ) ) )
& ! [X12: g] :
( ( ( X0 @ X12 )
!= $true )
| ( ( X6 @ ( X7 @ X12 ) )
= ( X7 @ ( X5 @ X12 ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: g > $o,X5: g > g,X1: a > a,X6: b > b,X3: b > a,X2: b > $o,X4: a > $o,X7: g > b] :
( ( ? [X19: g] :
( ( ( X0 @ ( X5 @ X19 ) )
!= $true )
& ( ( X0 @ X19 )
= $true ) )
| ? [X17: g] :
( ( ( X1 @ ( X3 @ ( X7 @ X17 ) ) )
!= ( X3 @ ( X7 @ ( X5 @ X17 ) ) ) )
& ( ( X0 @ X17 )
= $true ) )
| ? [X16: g] :
( ( ( X4 @ ( X3 @ ( X7 @ X16 ) ) )
!= $true )
& ( ( X0 @ X16 )
= $true ) )
| ? [X18: a] :
( ( ( X4 @ X18 )
= $true )
& ( ( X4 @ ( X1 @ X18 ) )
!= $true ) ) )
& ! [X15: g] :
( ( ( X2 @ ( X7 @ X15 ) )
= $true )
| ( ( X0 @ X15 )
!= $true ) )
& ! [X11: b] :
( ( ( X2 @ X11 )
!= $true )
| ( ( X1 @ ( X3 @ X11 ) )
= ( X3 @ ( X6 @ X11 ) ) ) )
& ! [X12: g] :
( ( ( X0 @ X12 )
!= $true )
| ( ( X6 @ ( X7 @ X12 ) )
= ( X7 @ ( X5 @ X12 ) ) ) )
& ! [X10: b] :
( ( ( X2 @ X10 )
!= $true )
| ( ( X2 @ ( X6 @ X10 ) )
= $true ) )
& ! [X9: g] :
( ( ( X0 @ X9 )
!= $true )
| ( ( X0 @ ( X5 @ X9 ) )
= $true ) )
& ! [X8: b] :
( ( ( X4 @ ( X3 @ X8 ) )
= $true )
| ( ( X2 @ X8 )
!= $true ) )
& ! [X14: a] :
( ( ( X4 @ ( X1 @ X14 ) )
= $true )
| ( ( X4 @ X14 )
!= $true ) )
& ! [X13: b] :
( ( ( X2 @ ( X6 @ X13 ) )
= $true )
| ( ( X2 @ X13 )
!= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: g > $o,X5: g > g,X1: a > a,X6: b > b,X3: b > a,X2: b > $o,X4: a > $o,X7: g > b] :
( ( ! [X15: g] :
( ( ( X0 @ X15 )
= $true )
=> ( ( X2 @ ( X7 @ X15 ) )
= $true ) )
& ! [X11: b] :
( ( ( X2 @ X11 )
= $true )
=> ( ( X1 @ ( X3 @ X11 ) )
= ( X3 @ ( X6 @ X11 ) ) ) )
& ! [X12: g] :
( ( ( X0 @ X12 )
= $true )
=> ( ( X6 @ ( X7 @ X12 ) )
= ( X7 @ ( X5 @ X12 ) ) ) )
& ! [X10: b] :
( ( ( X2 @ X10 )
= $true )
=> ( ( X2 @ ( X6 @ X10 ) )
= $true ) )
& ! [X9: g] :
( ( ( X0 @ X9 )
= $true )
=> ( ( X0 @ ( X5 @ X9 ) )
= $true ) )
& ! [X8: b] :
( ( ( X2 @ X8 )
= $true )
=> ( ( X4 @ ( X3 @ X8 ) )
= $true ) )
& ! [X14: a] :
( ( ( X4 @ X14 )
= $true )
=> ( ( X4 @ ( X1 @ X14 ) )
= $true ) )
& ! [X13: b] :
( ( ( X2 @ X13 )
= $true )
=> ( ( X2 @ ( X6 @ X13 ) )
= $true ) ) )
=> ( ! [X18: a] :
( ( ( X4 @ X18 )
= $true )
=> ( ( X4 @ ( X1 @ X18 ) )
= $true ) )
& ! [X17: g] :
( ( ( X0 @ X17 )
= $true )
=> ( ( X1 @ ( X3 @ ( X7 @ X17 ) ) )
= ( X3 @ ( X7 @ ( X5 @ X17 ) ) ) ) )
& ! [X16: g] :
( ( ( X0 @ X16 )
= $true )
=> ( ( X4 @ ( X3 @ ( X7 @ X16 ) ) )
= $true ) )
& ! [X19: g] :
( ( ( X0 @ X19 )
= $true )
=> ( ( X0 @ ( X5 @ X19 ) )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: g > $o,X1: a > a,X2: b > $o,X3: b > a,X4: a > $o,X5: g > g,X6: b > b,X7: g > b] :
( ( ! [X8: b] :
( ( X2 @ X8 )
=> ( X4 @ ( X3 @ X8 ) ) )
& ! [X9: g] :
( ( X0 @ X9 )
=> ( X0 @ ( X5 @ X9 ) ) )
& ! [X10: b] :
( ( X2 @ X10 )
=> ( X2 @ ( X6 @ X10 ) ) )
& ! [X11: b] :
( ( X2 @ X11 )
=> ( ( X1 @ ( X3 @ X11 ) )
= ( X3 @ ( X6 @ X11 ) ) ) )
& ! [X12: g] :
( ( X0 @ X12 )
=> ( ( X6 @ ( X7 @ X12 ) )
= ( X7 @ ( X5 @ X12 ) ) ) )
& ! [X13: b] :
( ( X2 @ X13 )
=> ( X2 @ ( X6 @ X13 ) ) )
& ! [X14: a] :
( ( X4 @ X14 )
=> ( X4 @ ( X1 @ X14 ) ) )
& ! [X15: g] :
( ( X0 @ X15 )
=> ( X2 @ ( X7 @ X15 ) ) ) )
=> ( ! [X16: g] :
( ( X0 @ X16 )
=> ( X4 @ ( X3 @ ( X7 @ X16 ) ) ) )
& ! [X17: g] :
( ( X0 @ X17 )
=> ( ( X1 @ ( X3 @ ( X7 @ X17 ) ) )
= ( X3 @ ( X7 @ ( X5 @ X17 ) ) ) ) )
& ! [X18: a] :
( ( X4 @ X18 )
=> ( X4 @ ( X1 @ X18 ) ) )
& ! [X19: g] :
( ( X0 @ X19 )
=> ( X0 @ ( X5 @ X19 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X2: g > $o,X7: a > a,X4: b > $o,X1: b > a,X6: a > $o,X3: g > g,X5: b > b,X0: g > b] :
( ( ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X2 @ ( X3 @ X8 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( ( X1 @ ( X5 @ X8 ) )
= ( X7 @ ( X1 @ X8 ) ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( ( X0 @ ( X3 @ X8 ) )
= ( X5 @ ( X0 @ X8 ) ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) )
& ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X7 @ X8 ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( X0 @ X8 ) ) ) )
=> ( ! [X8: g] :
( ( X2 @ X8 )
=> ( X6 @ ( X1 @ ( X0 @ X8 ) ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( ( X1 @ ( X0 @ ( X3 @ X8 ) ) )
= ( X7 @ ( X1 @ ( X0 @ X8 ) ) ) ) )
& ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X7 @ X8 ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X2 @ ( X3 @ X8 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X2: g > $o,X7: a > a,X4: b > $o,X1: b > a,X6: a > $o,X3: g > g,X5: b > b,X0: g > b] :
( ( ! [X8: b] :
( ( X4 @ X8 )
=> ( X6 @ ( X1 @ X8 ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X2 @ ( X3 @ X8 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( ( X1 @ ( X5 @ X8 ) )
= ( X7 @ ( X1 @ X8 ) ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( ( X0 @ ( X3 @ X8 ) )
= ( X5 @ ( X0 @ X8 ) ) ) )
& ! [X8: b] :
( ( X4 @ X8 )
=> ( X4 @ ( X5 @ X8 ) ) )
& ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X7 @ X8 ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X4 @ ( X0 @ X8 ) ) ) )
=> ( ! [X8: g] :
( ( X2 @ X8 )
=> ( X6 @ ( X1 @ ( X0 @ X8 ) ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( ( X1 @ ( X0 @ ( X3 @ X8 ) ) )
= ( X7 @ ( X1 @ ( X0 @ X8 ) ) ) ) )
& ! [X8: a] :
( ( X6 @ X8 )
=> ( X6 @ ( X7 @ X8 ) ) )
& ! [X8: g] :
( ( X2 @ X8 )
=> ( X2 @ ( X3 @ X8 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SPacvdwNQA/DTF2THF_26355.p',cTHM131_pme) ).
thf(f95,plain,
( ( ( sK7 @ ( sK2 @ ( sK6 @ sK11 ) ) )
!= ( sK7 @ ( sK6 @ ( sK3 @ sK11 ) ) ) )
| spl13_9 ),
inference(avatar_component_clause,[status(thm)],[f93]) ).
thf(f93,definition,
( spl13_9
<=> ( ( sK7 @ ( sK2 @ ( sK6 @ sK11 ) ) )
= ( sK7 @ ( sK6 @ ( sK3 @ sK11 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl13_9])],[avatar_definition]) ).
thf(f107,plain,
( ~ spl13_1
| spl13_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f106]) ).
thf(f106,plain,
( $false
| ~ spl13_1
| spl13_5 ),
inference(subsumption_resolution,[status(thm)],[f105,f41]) ).
thf(f41,plain,
( ( ( sK8 @ sK12 )
= $true )
| ~ spl13_1 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl13_1
<=> ( ( sK8 @ sK12 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_1])],[avatar_definition]) ).
thf(f105,plain,
( ( ( sK8 @ sK12 )
!= $true )
| spl13_5 ),
inference(trivial_inequality_removal,[status(thm)],[f104]) ).
thf(f104,plain,
( ( $true != $true )
| ( ( sK8 @ sK12 )
!= $true )
| spl13_5 ),
inference(superposition,[status(thm)],[f103,f32]) ).
thf(f32,plain,
! [X13: g] :
( ( ( sK4 @ ( sK6 @ X13 ) )
= $true )
| ( ( sK8 @ X13 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f103,plain,
( ( ( sK4 @ ( sK6 @ sK12 ) )
!= $true )
| spl13_5 ),
inference(trivial_inequality_removal,[status(thm)],[f102]) ).
thf(f102,plain,
( ( ( sK4 @ ( sK6 @ sK12 ) )
!= $true )
| ( $true != $true )
| spl13_5 ),
inference(superposition,[status(thm)],[f58,f35]) ).
thf(f35,plain,
! [X10: b] :
( ( ( sK9 @ ( sK7 @ X10 ) )
= $true )
| ( ( sK4 @ X10 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f58,plain,
( ( ( sK9 @ ( sK7 @ ( sK6 @ sK12 ) ) )
!= $true )
| spl13_5 ),
inference(avatar_component_clause,[status(thm)],[f56]) ).
thf(f56,definition,
( spl13_5
<=> ( ( sK9 @ ( sK7 @ ( sK6 @ sK12 ) ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_5])],[avatar_definition]) ).
thf(f101,plain,
( ~ spl13_3
| spl13_8 ),
inference(avatar_split_clause,[status(thm)],[f98,f89,f47]) ).
thf(f89,definition,
( spl13_8
<=> ( ( sK4 @ ( sK6 @ sK11 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_8])],[avatar_definition]) ).
thf(f98,plain,
( ( ( sK8 @ sK11 )
!= $true )
| spl13_8 ),
inference(trivial_inequality_removal,[status(thm)],[f97]) ).
thf(f97,plain,
( ( $true != $true )
| ( ( sK8 @ sK11 )
!= $true )
| spl13_8 ),
inference(superposition,[status(thm)],[f91,f32]) ).
thf(f91,plain,
( ( ( sK4 @ ( sK6 @ sK11 ) )
!= $true )
| spl13_8 ),
inference(avatar_component_clause,[status(thm)],[f89]) ).
thf(f96,plain,
( ~ spl13_8
| ~ spl13_9
| spl13_6 ),
inference(avatar_split_clause,[status(thm)],[f87,f60,f93,f89]) ).
thf(f60,definition,
( spl13_6
<=> ( ( sK7 @ ( sK6 @ ( sK3 @ sK11 ) ) )
= ( sK5 @ ( sK7 @ ( sK6 @ sK11 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl13_6])],[avatar_definition]) ).
thf(f87,plain,
( ( ( sK7 @ ( sK2 @ ( sK6 @ sK11 ) ) )
!= ( sK7 @ ( sK6 @ ( sK3 @ sK11 ) ) ) )
| ( ( sK4 @ ( sK6 @ sK11 ) )
!= $true )
| spl13_6 ),
inference(superposition,[status(thm)],[f62,f37]) ).
thf(f37,plain,
! [X8: b] :
( ( ( sK7 @ ( sK2 @ X8 ) )
= ( sK5 @ ( sK7 @ X8 ) ) )
| ( ( sK4 @ X8 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f62,plain,
( ( ( sK7 @ ( sK6 @ ( sK3 @ sK11 ) ) )
!= ( sK5 @ ( sK7 @ ( sK6 @ sK11 ) ) ) )
| spl13_6 ),
inference(avatar_component_clause,[status(thm)],[f60]) ).
thf(f80,plain,
~ spl13_4,
inference(avatar_split_clause,[status(thm)],[f79,f51]) ).
thf(f51,definition,
( spl13_4
<=> ( ( sP0 @ sK5 @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_4])],[avatar_definition]) ).
thf(f79,plain,
( ( sP0 @ sK5 @ sK9 )
!= $true ),
inference(subsumption_resolution,[status(thm)],[f78,f21]) ).
thf(f21,plain,
! [X0: a > $o,X1: a > a] :
( ( ( X0 @ ( sK1 @ X1 @ X0 ) )
= $true )
| ( ( sP0 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f13,plain,
! [X0: a > $o,X1: a > a] :
( ( ( ( X0 @ ( sK1 @ X1 @ X0 ) )
= $true )
& ( ( X0 @ ( X1 @ ( sK1 @ X1 @ X0 ) ) )
!= $true ) )
| ( ( sP0 @ X1 @ X0 )
!= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f11,f12]) ).
thf(f12,plain,
! [X0: a > $o,X1: a > a] :
( ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ( ( X0 @ ( X1 @ X2 ) )
!= $true ) )
=> ( ( ( X0 @ ( sK1 @ X1 @ X0 ) )
= $true )
& ( ( X0 @ ( X1 @ ( sK1 @ X1 @ X0 ) ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X0: a > $o,X1: a > a] :
( ? [X2: a] :
( ( ( X0 @ X2 )
= $true )
& ( ( X0 @ ( X1 @ X2 ) )
!= $true ) )
| ( ( sP0 @ X1 @ X0 )
!= $true ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
! [X4: a > $o,X1: a > a] :
( ? [X18: a] :
( ( ( X4 @ X18 )
= $true )
& ( ( X4 @ ( X1 @ X18 ) )
!= $true ) )
| ( ( sP0 @ X1 @ X4 )
!= $true ) ),
inference(nnf_transformation,[status(thm)],[f8]) ).
thf(f78,plain,
( ( ( sK9 @ ( sK1 @ sK5 @ sK9 ) )
!= $true )
| ( ( sP0 @ sK5 @ sK9 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f77]) ).
thf(f77,plain,
( ( ( sP0 @ sK5 @ sK9 )
!= $true )
| ( ( sK9 @ ( sK1 @ sK5 @ sK9 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f20,f36]) ).
thf(f36,plain,
! [X9: a] :
( ( ( sK9 @ ( sK5 @ X9 ) )
= $true )
| ( ( sK9 @ X9 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f20,plain,
! [X0: a > $o,X1: a > a] :
( ( ( X0 @ ( X1 @ ( sK1 @ X1 @ X0 ) ) )
!= $true )
| ( ( sP0 @ X1 @ X0 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f13]) ).
thf(f76,plain,
( ~ spl13_7
| spl13_2 ),
inference(avatar_split_clause,[status(thm)],[f75,f43,f65]) ).
thf(f65,definition,
( spl13_7
<=> ( ( sK8 @ sK10 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_7])],[avatar_definition]) ).
thf(f43,definition,
( spl13_2
<=> ( ( sK8 @ ( sK3 @ sK10 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_2])],[avatar_definition]) ).
thf(f75,plain,
( ( ( sK8 @ sK10 )
!= $true )
| spl13_2 ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
( ( ( sK8 @ sK10 )
!= $true )
| ( $true != $true )
| spl13_2 ),
inference(superposition,[status(thm)],[f45,f31]) ).
thf(f31,plain,
! [X14: g] :
( ( ( sK8 @ ( sK3 @ X14 ) )
= $true )
| ( ( sK8 @ X14 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f45,plain,
( ( ( sK8 @ ( sK3 @ sK10 ) )
!= $true )
| spl13_2 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f73,plain,
( ~ spl13_5
| spl13_7
| ~ spl13_6
| spl13_4 ),
inference(avatar_split_clause,[status(thm)],[f26,f51,f60,f65,f56]) ).
thf(f26,plain,
( ( ( sP0 @ sK5 @ sK9 )
= $true )
| ( ( sK8 @ sK10 )
= $true )
| ( ( sK9 @ ( sK7 @ ( sK6 @ sK12 ) ) )
!= $true )
| ( ( sK7 @ ( sK6 @ ( sK3 @ sK11 ) ) )
!= ( sK5 @ ( sK7 @ ( sK6 @ sK11 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f72,plain,
( ~ spl13_5
| spl13_3
| spl13_4
| spl13_7 ),
inference(avatar_split_clause,[status(thm)],[f24,f65,f51,f47,f56]) ).
thf(f24,plain,
( ( ( sK8 @ sK11 )
= $true )
| ( ( sP0 @ sK5 @ sK9 )
= $true )
| ( ( sK8 @ sK10 )
= $true )
| ( ( sK9 @ ( sK7 @ ( sK6 @ sK12 ) ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f71,plain,
( spl13_3
| ~ spl13_2
| ~ spl13_5
| spl13_4 ),
inference(avatar_split_clause,[status(thm)],[f28,f51,f56,f43,f47]) ).
thf(f28,plain,
( ( ( sK8 @ ( sK3 @ sK10 ) )
!= $true )
| ( ( sK8 @ sK11 )
= $true )
| ( ( sK9 @ ( sK7 @ ( sK6 @ sK12 ) ) )
!= $true )
| ( ( sP0 @ sK5 @ sK9 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f70,plain,
( ~ spl13_2
| spl13_4
| ~ spl13_6
| spl13_1 ),
inference(avatar_split_clause,[status(thm)],[f29,f39,f60,f51,f43]) ).
thf(f29,plain,
( ( ( sK8 @ sK12 )
= $true )
| ( ( sP0 @ sK5 @ sK9 )
= $true )
| ( ( sK8 @ ( sK3 @ sK10 ) )
!= $true )
| ( ( sK7 @ ( sK6 @ ( sK3 @ sK11 ) ) )
!= ( sK5 @ ( sK7 @ ( sK6 @ sK11 ) ) ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f69,plain,
( spl13_7
| spl13_3
| spl13_1
| spl13_4 ),
inference(avatar_split_clause,[status(thm)],[f23,f51,f39,f47,f65]) ).
thf(f23,plain,
( ( ( sK8 @ sK12 )
= $true )
| ( ( sK8 @ sK10 )
= $true )
| ( ( sP0 @ sK5 @ sK9 )
= $true )
| ( ( sK8 @ sK11 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f68,plain,
( spl13_1
| ~ spl13_6
| spl13_4
| spl13_7 ),
inference(avatar_split_clause,[status(thm)],[f25,f65,f51,f60,f39]) ).
thf(f25,plain,
( ( ( sK7 @ ( sK6 @ ( sK3 @ sK11 ) ) )
!= ( sK5 @ ( sK7 @ ( sK6 @ sK11 ) ) ) )
| ( ( sK8 @ sK12 )
= $true )
| ( ( sP0 @ sK5 @ sK9 )
= $true )
| ( ( sK8 @ sK10 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f63,plain,
( ~ spl13_2
| ~ spl13_5
| spl13_4
| ~ spl13_6 ),
inference(avatar_split_clause,[status(thm)],[f30,f60,f51,f56,f43]) ).
thf(f30,plain,
( ( ( sK9 @ ( sK7 @ ( sK6 @ sK12 ) ) )
!= $true )
| ( ( sK8 @ ( sK3 @ sK10 ) )
!= $true )
| ( ( sK7 @ ( sK6 @ ( sK3 @ sK11 ) ) )
!= ( sK5 @ ( sK7 @ ( sK6 @ sK11 ) ) ) )
| ( ( sP0 @ sK5 @ sK9 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f54,plain,
( spl13_1
| ~ spl13_2
| spl13_3
| spl13_4 ),
inference(avatar_split_clause,[status(thm)],[f27,f51,f47,f43,f39]) ).
thf(f27,plain,
( ( ( sK8 @ sK11 )
= $true )
| ( ( sK8 @ ( sK3 @ sK10 ) )
!= $true )
| ( ( sP0 @ sK5 @ sK9 )
= $true )
| ( ( sK8 @ sK12 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEU903^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n006.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:36:15 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
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : SEU903^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.45 % Domain : Set Theory
% 0.30/0.45 % Problem : TPS problem THM131
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English :
% 0.30/0.45
% 0.30/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Bro09]
% 0.30/0.45 % Names : tps_0520 [Bro09]
% 0.30/0.45 % : THM131 [TPS]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % Rating : 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.12 v7.0.0, 0.14 v6.4.0, 0.17 v6.3.0, 0.20 v6.2.0, 0.00 v6.1.0, 0.14 v5.5.0, 0.17 v5.4.0, 0.20 v5.3.0, 0.40 v5.2.0, 0.20 v5.1.0, 0.40 v5.0.0, 0.20 v4.1.0, 0.00 v4.0.0
% 0.30/0.45 % Syntax : Number of formulae : 4 ( 0 unt; 3 typ; 0 def)
% 0.30/0.45 % Number of atoms : 3 ( 3 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 3 ( 3 avg)
% 0.30/0.45 % Number of connectives : 68 ( 0 ~; 0 |; 10 &; 45 @)
% 0.30/0.45 % ( 0 <=>; 13 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 21 ( 21 avg)
% 0.30/0.45 % Number of types : 4 ( 3 usr)
% 0.30/0.45 % Number of type conns : 8 ( 8 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.30/0.45 % Number of variables : 20 ( 0 ^; 20 !; 0 ?; 20 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.45 % : Polymorphic definitions expanded.
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(g_type,type,
% 0.30/0.45 g: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(b_type,type,
% 0.30/0.45 b: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(a_type,type,
% 0.30/0.45 a: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(cTHM131_pme,conjecture,
% 0.30/0.45 ! [Xh1: g > b,Xh2: b > a,Xs1: g > $o,Xf1: g > g,Xs2: b > $o,Xf2: b > b,Xs3: a > $o,Xf3: a > a] :
% 0.30/0.45 ( ( ! [Xx: g] :
% 0.30/0.45 ( ( Xs1 @ Xx )
% 0.30/0.45 => ( Xs1 @ ( Xf1 @ Xx ) ) )
% 0.30/0.45 & ! [Xx: b] :
% 0.30/0.45 ( ( Xs2 @ Xx )
% 0.30/0.45 => ( Xs2 @ ( Xf2 @ Xx ) ) )
% 0.30/0.45 & ! [Xx: g] :
% 0.30/0.45 ( ( Xs1 @ Xx )
% 0.30/0.45 => ( Xs2 @ ( Xh1 @ Xx ) ) )
% 0.30/0.45 & ! [Xx: g] :
% 0.30/0.45 ( ( Xs1 @ Xx )
% 0.30/0.45 => ( ( Xh1 @ ( Xf1 @ Xx ) )
% 0.30/0.45 = ( Xf2 @ ( Xh1 @ Xx ) ) ) )
% 0.30/0.45 & ! [Xx: b] :
% 0.30/0.45 ( ( Xs2 @ Xx )
% 0.30/0.45 => ( Xs2 @ ( Xf2 @ Xx ) ) )
% 0.30/0.45 & ! [Xx: a] :
% 0.30/0.45 ( ( Xs3 @ Xx )
% 0.30/0.45 => ( Xs3 @ ( Xf3 @ Xx ) ) )
% 0.30/0.45 & ! [Xx: b] :
% 0.30/0.45 ( ( Xs2 @ Xx )
% 0.30/0.45 => ( Xs3 @ ( Xh2 @ Xx ) ) )
% 0.30/0.45 & ! [Xx: b] :
% 0.30/0.45 ( ( Xs2 @ Xx )
% 0.30/0.45 => ( ( Xh2 @ ( Xf2 @ Xx ) )
% 0.30/0.45 = ( Xf3 @ ( Xh2 @ Xx ) ) ) ) )
% 0.30/0.45 => ( ! [Xx: g] :
% 0.30/0.45 ( ( Xs1 @ Xx )
% 0.30/0.45 => ( Xs1 @ ( Xf1 @ Xx ) ) )
% 0.30/0.45 & ! [Xx: a] :
% 0.30/0.45 ( ( Xs3 @ Xx )
% 0.30/0.45 => ( Xs3 @ ( Xf3 @ Xx ) ) )
% 0.30/0.45 & ! [Xx: g] :
% 0.30/0.45 ( ( Xs1 @ Xx )
% 0.30/0.45 => ( Xs3 @ ( Xh2 @ ( Xh1 @ Xx ) ) ) )
% 0.30/0.45 & ! [Xx: g] :
% 0.30/0.45 ( ( Xs1 @ Xx )
% 0.30/0.45 => ( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx ) ) )
% 0.30/0.45 = ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.67/1.30 ---- Embedded in THF ---
% 1.67/1.31 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.67/1.31 %%% Generated on Tue Feb 24 12:36:16 EST 2026
% 1.67/1.31 %%% using '$$dhol' embedding, version 1.3.0.
% 1.67/1.31 %%% Logic specification used:
% 1.67/1.31 %%% thf(spec, logic, $$dhol).
% 1.67/1.31
% 1.67/1.31 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.SPacvdwNQA/DTF2DTF26355.p
% See solution above
% 1.67/1.31 ------------------------
% 1.67/1.32 ---- Cleaned THF ---
% 1.67/1.32 thf(g_type,type,
% 1.67/1.32 g: $tType ).
% 1.67/1.32
% 1.67/1.32 thf(b_type,type,
% 1.67/1.32 b: $tType ).
% 1.67/1.32
% 1.67/1.32 thf(a_type,type,
% 1.67/1.32 a: $tType ).
% 1.67/1.32
% 1.67/1.32 thf(cTHM131_pme,conjecture,
% 1.67/1.32 ! [Xh1: g > b,Xh2: b > a,Xs1: g > $o,Xf1: g > g,Xs2: b > $o,Xf2: b > b,Xs3: a > $o,Xf3: a > a] :
% 1.67/1.32 ( ( ! [Xx: g] :
% 1.67/1.32 ( ( Xs1 @ Xx )
% 1.67/1.32 => ( Xs1 @ ( Xf1 @ Xx ) ) )
% 1.67/1.32 & ! [Xx: b] :
% 1.67/1.32 ( ( Xs2 @ Xx )
% 1.67/1.32 => ( Xs2 @ ( Xf2 @ Xx ) ) )
% 1.67/1.32 & ! [Xx: g] :
% 1.67/1.32 ( ( Xs1 @ Xx )
% 1.67/1.32 => ( Xs2 @ ( Xh1 @ Xx ) ) )
% 1.67/1.32 & ! [Xx: g] :
% 1.67/1.32 ( ( Xs1 @ Xx )
% 1.67/1.32 => ( ( Xh1 @ ( Xf1 @ Xx ) )
% 1.67/1.32 = ( Xf2 @ ( Xh1 @ Xx ) ) ) )
% 1.67/1.32 & ! [Xx: b] :
% 1.67/1.32 ( ( Xs2 @ Xx )
% 1.67/1.32 => ( Xs2 @ ( Xf2 @ Xx ) ) )
% 1.67/1.32 & ! [Xx: a] :
% 1.67/1.32 ( ( Xs3 @ Xx )
% 1.67/1.32 => ( Xs3 @ ( Xf3 @ Xx ) ) )
% 1.67/1.32 & ! [Xx: b] :
% 1.67/1.32 ( ( Xs2 @ Xx )
% 1.67/1.32 => ( Xs3 @ ( Xh2 @ Xx ) ) )
% 1.67/1.32 & ! [Xx: b] :
% 1.67/1.32 ( ( Xs2 @ Xx )
% 1.67/1.32 => ( ( Xh2 @ ( Xf2 @ Xx ) )
% 1.67/1.32 = ( Xf3 @ ( Xh2 @ Xx ) ) ) ) )
% 1.67/1.32 => ( ! [Xx: g] :
% 1.67/1.32 ( ( Xs1 @ Xx )
% 1.67/1.32 => ( Xs1 @ ( Xf1 @ Xx ) ) )
% 1.67/1.32 & ! [Xx: a] :
% 1.67/1.32 ( ( Xs3 @ Xx )
% 1.67/1.32 => ( Xs3 @ ( Xf3 @ Xx ) ) )
% 1.67/1.32 & ! [Xx: g] :
% 1.67/1.32 ( ( Xs1 @ Xx )
% 1.67/1.32 => ( Xs3 @ ( Xh2 @ ( Xh1 @ Xx ) ) ) )
% 1.67/1.32 & ! [Xx: g] :
% 1.67/1.32 ( ( Xs1 @ Xx )
% 1.67/1.32 => ( ( Xh2 @ ( Xh1 @ ( Xf1 @ Xx ) ) )
% 1.67/1.32 = ( Xf3 @ ( Xh2 @ ( Xh1 @ Xx ) ) ) ) ) ) ) ).
% 1.67/1.32 ------------------------
% 1.67/1.33 % (26548)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_26355 for (3000ds/2Mi)
% 1.67/1.33 % (26548)Instruction limit reached!
% 1.67/1.33 % (26548)------------------------------
% 1.67/1.33 % (26548)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (26548)Termination reason: Unknown
% 1.67/1.33 % (26548)Termination phase: Property scanning
% 1.67/1.33
% 1.67/1.33 % (26548)Memory used [KB]: 1023
% 1.67/1.33 % (26548)Time elapsed: 0.002 s
% 1.67/1.33 % (26548)Instructions burned: 3 (million)
% 1.67/1.33 % (26548)------------------------------
% 1.67/1.33 % (26548)------------------------------
% 1.67/1.33 % (26547)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_26355 for (3000ds/2Mi)
% 1.67/1.33 % (26550)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_26355 for (3000ds/18Mi)
% 1.67/1.33 % (26547)Instruction limit reached!
% 1.67/1.33 % (26547)------------------------------
% 1.67/1.33 % (26547)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.33 % (26547)Termination reason: Unknown
% 1.67/1.33 % (26547)Termination phase: Preprocessing 3
% 1.67/1.33
% 1.67/1.33 % (26547)Memory used [KB]: 1023
% 1.67/1.33 % (26547)Time elapsed: 0.003 s
% 1.67/1.33 % (26547)Instructions burned: 3 (million)
% 1.67/1.33 % (26547)------------------------------
% 1.67/1.33 % (26547)------------------------------
% 1.67/1.34 % (26544)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_26355 for (3000ds/183Mi)
% 1.67/1.34 % (26546)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_26355 for (3000ds/27Mi)
% 1.67/1.34 % (26545)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_26355 for (3000ds/4Mi)
% 1.67/1.34 % (26549)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_26355 for (3000ds/275Mi)
% 1.67/1.34 % (26545)Instruction limit reached!
% 1.67/1.34 % (26545)------------------------------
% 1.67/1.34 % (26545)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (26545)Termination reason: Unknown
% 1.67/1.34 % (26545)Termination phase: Property scanning
% 1.67/1.34
% 1.67/1.34 % (26545)Memory used [KB]: 1023
% 1.67/1.34 % (26545)Time elapsed: 0.004 s
% 1.67/1.34 % (26545)Instructions burned: 4 (million)
% 1.67/1.34 % (26545)------------------------------
% 1.67/1.34 % (26545)------------------------------
% 1.67/1.34 % (26550)Instruction limit reached!
% 1.67/1.34 % (26550)------------------------------
% 1.67/1.34 % (26550)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.34 % (26550)Termination reason: Unknown
% 1.67/1.34 % (26550)Termination phase: Saturation
% 1.67/1.34
% 1.67/1.34 % (26550)Memory used [KB]: 5628
% 1.67/1.34 % (26550)Time elapsed: 0.008 s
% 1.67/1.34 % (26550)Instructions burned: 19 (million)
% 1.67/1.34 % (26550)------------------------------
% 1.67/1.34 % (26550)------------------------------
% 1.67/1.34 % (26551)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_26355 for (2999ds/3Mi)
% 1.67/1.35 % (26549)First to succeed.
% 1.67/1.35 % (26551)Instruction limit reached!
% 1.67/1.35 % (26551)------------------------------
% 1.67/1.35 % (26551)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (26551)Termination reason: Unknown
% 1.67/1.35 % (26551)Termination phase: Saturation
% 1.67/1.35
% 1.67/1.35 % (26551)Memory used [KB]: 5500
% 1.67/1.35 % (26551)Time elapsed: 0.003 s
% 1.67/1.35 % (26551)Instructions burned: 5 (million)
% 1.67/1.35 % (26551)------------------------------
% 1.67/1.35 % (26551)------------------------------
% 1.67/1.35 % (26552)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_26355 for (2999ds/37Mi)
% 1.67/1.35 % (26546)Also succeeded, but the first one will report.
% 1.67/1.35 % (26549)Refutation found. Thanks to Tanya!
% 1.67/1.35 % SZS status Theorem for DTF2THF_26355
% 1.67/1.35 % SZS output start Proof for DTF2THF_26355
% 1.67/1.35 thf(type_def_5, type, g: $tType).
% 1.67/1.35 thf(type_def_6, type, b: $tType).
% 1.67/1.35 thf(type_def_8, type, a: $tType).
% 1.67/1.35 thf(func_def_0, type, g: $tType).
% 1.67/1.35 thf(func_def_1, type, b: $tType).
% 1.67/1.35 thf(func_def_2, type, a: $tType).
% 1.67/1.35 thf(func_def_6, type, sP0: (a > a) > (a > $o) > $o).
% 1.67/1.35 thf(func_def_7, type, sK1: (a > a) > (a > $o) > a).
% 1.67/1.35 thf(func_def_8, type, sK2: b > b).
% 1.67/1.35 thf(func_def_9, type, sK3: g > g).
% 1.67/1.35 thf(func_def_10, type, sK4: b > $o).
% 1.67/1.35 thf(func_def_11, type, sK5: a > a).
% 1.67/1.35 thf(func_def_12, type, sK6: g > b).
% 1.67/1.35 thf(func_def_13, type, sK7: b > a).
% 1.67/1.35 thf(func_def_14, type, sK8: g > $o).
% 1.67/1.35 thf(func_def_15, type, sK9: a > $o).
% 1.67/1.35 thf(func_def_16, type, sK10: g).
% 1.67/1.35 thf(func_def_17, type, sK11: g).
% 1.67/1.35 thf(func_def_18, type, sK12: g).
% 1.67/1.35 thf(func_def_20, type, ph14: !>[X0: $tType]:(X0)).
% 1.67/1.35 thf(f112,plain,(
% 1.67/1.35 $false),
% 1.67/1.35 inference(avatar_sat_refutation,[status(thm)],[f54,f63,f68,f69,f70,f71,f72,f73,f76,f80,f96,f101,f107,f111])).
% 1.67/1.35 thf(f111,plain,(
% 1.67/1.35 ~spl13_3 | spl13_9),
% 1.67/1.35 inference(avatar_contradiction_clause,[status(thm)],[f110])).
% 1.67/1.35 thf(f110,plain,(
% 1.67/1.35 $false | (~spl13_3 | spl13_9)),
% 1.67/1.35 inference(subsumption_resolution,[status(thm)],[f109,f49])).
% 1.67/1.35 thf(f49,plain,(
% 1.67/1.35 ((sK8 @ sK11) = $true) | ~spl13_3),
% 1.67/1.35 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.67/1.35 thf(f47,definition,(
% 1.67/1.35 spl13_3 <=> ((sK8 @ sK11) = $true)),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl13_3])],[avatar_definition])).
% 1.67/1.35 thf(f109,plain,(
% 1.67/1.35 ((sK8 @ sK11) != $true) | spl13_9),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f108])).
% 1.67/1.35 thf(f108,plain,(
% 1.67/1.35 ((sK7 @ (sK6 @ (sK3 @ sK11))) != (sK7 @ (sK6 @ (sK3 @ sK11)))) | ((sK8 @ sK11) != $true) | spl13_9),
% 1.67/1.35 inference(superposition,[status(thm)],[f95,f22])).
% 1.67/1.35 thf(f22,plain,(
% 1.67/1.35 ( ! [X18 : g] : (((sK6 @ (sK3 @ X18)) = (sK2 @ (sK6 @ X18))) | ((sK8 @ X18) != $true)) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.35 thf(f19,plain,(
% 1.67/1.35 ! [X8 : b] : (((sK4 @ X8) != $true) | ((sK7 @ (sK2 @ X8)) = (sK5 @ (sK7 @ X8)))) & ! [X9 : a] : (((sK9 @ (sK5 @ X9)) = $true) | ((sK9 @ X9) != $true)) & ! [X10 : b] : (((sK9 @ (sK7 @ X10)) = $true) | ((sK4 @ X10) != $true)) & ! [X11 : b] : (((sK4 @ X11) != $true) | ((sK4 @ (sK2 @ X11)) = $true)) & ! [X12 : b] : (((sK4 @ (sK2 @ X12)) = $true) | ((sK4 @ X12) != $true)) & ! [X13 : g] : (((sK4 @ (sK6 @ X13)) = $true) | ((sK8 @ X13) != $true)) & ! [X14 : g] : (((sK8 @ X14) != $true) | ((sK8 @ (sK3 @ X14)) = $true)) & ((((sK8 @ (sK3 @ sK10)) != $true) & ((sK8 @ sK10) = $true)) | (((sK7 @ (sK6 @ (sK3 @ sK11))) != (sK5 @ (sK7 @ (sK6 @ sK11)))) & ((sK8 @ sK11) = $true)) | (((sK9 @ (sK7 @ (sK6 @ sK12))) != $true) & ((sK8 @ sK12) = $true)) | ((sP0 @ sK5 @ sK9) = $true)) & ! [X18 : g] : (((sK8 @ X18) != $true) | ((sK6 @ (sK3 @ X18)) = (sK2 @ (sK6 @ X18))))),
% 1.67/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12])],[f14,f18,f17,f16,f15])).
% 1.67/1.35 thf(f15,plain,(
% 1.67/1.35 ? [X0 : b > b,X1 : g > g,X2 : b > $o,X3 : a > a,X4 : g > b,X5 : b > a,X6 : g > $o,X7 : a > $o] : (! [X8 : b] : (((X2 @ X8) != $true) | ((X3 @ (X5 @ X8)) = (X5 @ (X0 @ X8)))) & ! [X9 : a] : (((X7 @ (X3 @ X9)) = $true) | ((X7 @ X9) != $true)) & ! [X10 : b] : (((X7 @ (X5 @ X10)) = $true) | ((X2 @ X10) != $true)) & ! [X11 : b] : (((X2 @ X11) != $true) | ((X2 @ (X0 @ X11)) = $true)) & ! [X12 : b] : (((X2 @ (X0 @ X12)) = $true) | ((X2 @ X12) != $true)) & ! [X13 : g] : (((X2 @ (X4 @ X13)) = $true) | ((X6 @ X13) != $true)) & ! [X14 : g] : (((X6 @ X14) != $true) | ((X6 @ (X1 @ X14)) = $true)) & (? [X15 : g] : (((X6 @ (X1 @ X15)) != $true) & ((X6 @ X15) = $true)) | ? [X16 : g] : (((X3 @ (X5 @ (X4 @ X16))) != (X5 @ (X4 @ (X1 @ X16)))) & ((X6 @ X16) = $true)) | ? [X17 : g] : (((X7 @ (X5 @ (X4 @ X17))) != $true) & ((X6 @ X17) = $true)) | ((sP0 @ X3 @ X7) = $true)) & ! [X18 : g] : (((X6 @ X18) != $true) | ((X4 @ (X1 @ X18)) = (X0 @ (X4 @ X18))))) => (! [X8 : b] : (((sK4 @ X8) != $true) | ((sK7 @ (sK2 @ X8)) = (sK5 @ (sK7 @ X8)))) & ! [X9 : a] : (((sK9 @ (sK5 @ X9)) = $true) | ((sK9 @ X9) != $true)) & ! [X10 : b] : (((sK9 @ (sK7 @ X10)) = $true) | ((sK4 @ X10) != $true)) & ! [X11 : b] : (((sK4 @ X11) != $true) | ((sK4 @ (sK2 @ X11)) = $true)) & ! [X12 : b] : (((sK4 @ (sK2 @ X12)) = $true) | ((sK4 @ X12) != $true)) & ! [X13 : g] : (((sK4 @ (sK6 @ X13)) = $true) | ((sK8 @ X13) != $true)) & ! [X14 : g] : (((sK8 @ X14) != $true) | ((sK8 @ (sK3 @ X14)) = $true)) & (? [X15 : g] : (((sK8 @ (sK3 @ X15)) != $true) & ((sK8 @ X15) = $true)) | ? [X16 : g] : (((sK7 @ (sK6 @ (sK3 @ X16))) != (sK5 @ (sK7 @ (sK6 @ X16)))) & ((sK8 @ X16) = $true)) | ? [X17 : g] : (((sK9 @ (sK7 @ (sK6 @ X17))) != $true) & ((sK8 @ X17) = $true)) | ((sP0 @ sK5 @ sK9) = $true)) & ! [X18 : g] : (((sK8 @ X18) != $true) | ((sK6 @ (sK3 @ X18)) = (sK2 @ (sK6 @ X18)))))),
% 1.67/1.35 introduced(definition,[],[choice_axiom])).
% 1.67/1.35 thf(f16,plain,(
% 1.67/1.35 ? [X15 : g] : (((sK8 @ (sK3 @ X15)) != $true) & ((sK8 @ X15) = $true)) => (((sK8 @ (sK3 @ sK10)) != $true) & ((sK8 @ sK10) = $true))),
% 1.67/1.35 introduced(definition,[],[choice_axiom])).
% 1.67/1.35 thf(f17,plain,(
% 1.67/1.35 ? [X16 : g] : (((sK7 @ (sK6 @ (sK3 @ X16))) != (sK5 @ (sK7 @ (sK6 @ X16)))) & ((sK8 @ X16) = $true)) => (((sK7 @ (sK6 @ (sK3 @ sK11))) != (sK5 @ (sK7 @ (sK6 @ sK11)))) & ((sK8 @ sK11) = $true))),
% 1.67/1.35 introduced(definition,[],[choice_axiom])).
% 1.67/1.35 thf(f18,plain,(
% 1.67/1.35 ? [X17 : g] : (((sK9 @ (sK7 @ (sK6 @ X17))) != $true) & ((sK8 @ X17) = $true)) => (((sK9 @ (sK7 @ (sK6 @ sK12))) != $true) & ((sK8 @ sK12) = $true))),
% 1.67/1.35 introduced(definition,[],[choice_axiom])).
% 1.67/1.35 thf(f14,plain,(
% 1.67/1.35 ? [X0 : b > b,X1 : g > g,X2 : b > $o,X3 : a > a,X4 : g > b,X5 : b > a,X6 : g > $o,X7 : a > $o] : (! [X8 : b] : (((X2 @ X8) != $true) | ((X3 @ (X5 @ X8)) = (X5 @ (X0 @ X8)))) & ! [X9 : a] : (((X7 @ (X3 @ X9)) = $true) | ((X7 @ X9) != $true)) & ! [X10 : b] : (((X7 @ (X5 @ X10)) = $true) | ((X2 @ X10) != $true)) & ! [X11 : b] : (((X2 @ X11) != $true) | ((X2 @ (X0 @ X11)) = $true)) & ! [X12 : b] : (((X2 @ (X0 @ X12)) = $true) | ((X2 @ X12) != $true)) & ! [X13 : g] : (((X2 @ (X4 @ X13)) = $true) | ((X6 @ X13) != $true)) & ! [X14 : g] : (((X6 @ X14) != $true) | ((X6 @ (X1 @ X14)) = $true)) & (? [X15 : g] : (((X6 @ (X1 @ X15)) != $true) & ((X6 @ X15) = $true)) | ? [X16 : g] : (((X3 @ (X5 @ (X4 @ X16))) != (X5 @ (X4 @ (X1 @ X16)))) & ((X6 @ X16) = $true)) | ? [X17 : g] : (((X7 @ (X5 @ (X4 @ X17))) != $true) & ((X6 @ X17) = $true)) | ((sP0 @ X3 @ X7) = $true)) & ! [X18 : g] : (((X6 @ X18) != $true) | ((X4 @ (X1 @ X18)) = (X0 @ (X4 @ X18)))))),
% 1.67/1.35 inference(rectify,[status(thm)],[f9])).
% 1.67/1.35 thf(f9,plain,(
% 1.67/1.35 ? [X6 : b > b,X5 : g > g,X2 : b > $o,X1 : a > a,X7 : g > b,X3 : b > a,X0 : g > $o,X4 : a > $o] : (! [X11 : b] : (((X2 @ X11) != $true) | ((X1 @ (X3 @ X11)) = (X3 @ (X6 @ X11)))) & ! [X14 : a] : (((X4 @ (X1 @ X14)) = $true) | ((X4 @ X14) != $true)) & ! [X8 : b] : (((X4 @ (X3 @ X8)) = $true) | ((X2 @ X8) != $true)) & ! [X10 : b] : (((X2 @ X10) != $true) | ((X2 @ (X6 @ X10)) = $true)) & ! [X13 : b] : (((X2 @ (X6 @ X13)) = $true) | ((X2 @ X13) != $true)) & ! [X15 : g] : (((X2 @ (X7 @ X15)) = $true) | ((X0 @ X15) != $true)) & ! [X9 : g] : (((X0 @ X9) != $true) | ((X0 @ (X5 @ X9)) = $true)) & (? [X19 : g] : (((X0 @ (X5 @ X19)) != $true) & ((X0 @ X19) = $true)) | ? [X17 : g] : (((X1 @ (X3 @ (X7 @ X17))) != (X3 @ (X7 @ (X5 @ X17)))) & ((X0 @ X17) = $true)) | ? [X16 : g] : (((X4 @ (X3 @ (X7 @ X16))) != $true) & ((X0 @ X16) = $true)) | ((sP0 @ X1 @ X4) = $true)) & ! [X12 : g] : (((X0 @ X12) != $true) | ((X6 @ (X7 @ X12)) = (X7 @ (X5 @ X12)))))),
% 1.67/1.35 inference(definition_folding,[status(thm)],[f7,f8])).
% 1.67/1.35 thf(f8,plain,(
% 1.67/1.35 ! [X4 : a > $o,X1 : a > a] : (? [X18 : a] : (((X4 @ X18) = $true) & ((X4 @ (X1 @ X18)) != $true)) | ~((sP0 @ X1 @ X4) = $true))),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[=])],[predicate_definition_introduction])).
% 1.67/1.35 thf(f7,plain,(
% 1.67/1.35 ? [X6 : b > b,X5 : g > g,X2 : b > $o,X1 : a > a,X7 : g > b,X3 : b > a,X0 : g > $o,X4 : a > $o] : (! [X11 : b] : (((X2 @ X11) != $true) | ((X1 @ (X3 @ X11)) = (X3 @ (X6 @ X11)))) & ! [X14 : a] : (((X4 @ (X1 @ X14)) = $true) | ((X4 @ X14) != $true)) & ! [X8 : b] : (((X4 @ (X3 @ X8)) = $true) | ((X2 @ X8) != $true)) & ! [X10 : b] : (((X2 @ X10) != $true) | ((X2 @ (X6 @ X10)) = $true)) & ! [X13 : b] : (((X2 @ (X6 @ X13)) = $true) | ((X2 @ X13) != $true)) & ! [X15 : g] : (((X2 @ (X7 @ X15)) = $true) | ((X0 @ X15) != $true)) & ! [X9 : g] : (((X0 @ X9) != $true) | ((X0 @ (X5 @ X9)) = $true)) & (? [X19 : g] : (((X0 @ (X5 @ X19)) != $true) & ((X0 @ X19) = $true)) | ? [X17 : g] : (((X1 @ (X3 @ (X7 @ X17))) != (X3 @ (X7 @ (X5 @ X17)))) & ((X0 @ X17) = $true)) | ? [X16 : g] : (((X4 @ (X3 @ (X7 @ X16))) != $true) & ((X0 @ X16) = $true)) | ? [X18 : a] : (((X4 @ X18) = $true) & ((X4 @ (X1 @ X18)) != $true))) & ! [X12 : g] : (((X0 @ X12) != $true) | ((X6 @ (X7 @ X12)) = (X7 @ (X5 @ X12)))))),
% 1.67/1.35 inference(flattening,[status(thm)],[f6])).
% 1.67/1.35 thf(f6,plain,(
% 1.67/1.35 ? [X0 : g > $o,X5 : g > g,X1 : a > a,X6 : b > b,X3 : b > a,X2 : b > $o,X4 : a > $o,X7 : g > b] : ((? [X19 : g] : (((X0 @ (X5 @ X19)) != $true) & ((X0 @ X19) = $true)) | ? [X17 : g] : (((X1 @ (X3 @ (X7 @ X17))) != (X3 @ (X7 @ (X5 @ X17)))) & ((X0 @ X17) = $true)) | ? [X16 : g] : (((X4 @ (X3 @ (X7 @ X16))) != $true) & ((X0 @ X16) = $true)) | ? [X18 : a] : (((X4 @ X18) = $true) & ((X4 @ (X1 @ X18)) != $true))) & (! [X15 : g] : (((X2 @ (X7 @ X15)) = $true) | ((X0 @ X15) != $true)) & ! [X11 : b] : (((X2 @ X11) != $true) | ((X1 @ (X3 @ X11)) = (X3 @ (X6 @ X11)))) & ! [X12 : g] : (((X0 @ X12) != $true) | ((X6 @ (X7 @ X12)) = (X7 @ (X5 @ X12)))) & ! [X10 : b] : (((X2 @ X10) != $true) | ((X2 @ (X6 @ X10)) = $true)) & ! [X9 : g] : (((X0 @ X9) != $true) | ((X0 @ (X5 @ X9)) = $true)) & ! [X8 : b] : (((X4 @ (X3 @ X8)) = $true) | ((X2 @ X8) != $true)) & ! [X14 : a] : (((X4 @ (X1 @ X14)) = $true) | ((X4 @ X14) != $true)) & ! [X13 : b] : (((X2 @ (X6 @ X13)) = $true) | ((X2 @ X13) != $true))))),
% 1.67/1.35 inference(ennf_transformation,[status(thm)],[f5])).
% 1.67/1.35 thf(f5,plain,(
% 1.67/1.35 ~! [X0 : g > $o,X5 : g > g,X1 : a > a,X6 : b > b,X3 : b > a,X2 : b > $o,X4 : a > $o,X7 : g > b] : ((! [X15 : g] : (((X0 @ X15) = $true) => ((X2 @ (X7 @ X15)) = $true)) & ! [X11 : b] : (((X2 @ X11) = $true) => ((X1 @ (X3 @ X11)) = (X3 @ (X6 @ X11)))) & ! [X12 : g] : (((X0 @ X12) = $true) => ((X6 @ (X7 @ X12)) = (X7 @ (X5 @ X12)))) & ! [X10 : b] : (((X2 @ X10) = $true) => ((X2 @ (X6 @ X10)) = $true)) & ! [X9 : g] : (((X0 @ X9) = $true) => ((X0 @ (X5 @ X9)) = $true)) & ! [X8 : b] : (((X2 @ X8) = $true) => ((X4 @ (X3 @ X8)) = $true)) & ! [X14 : a] : (((X4 @ X14) = $true) => ((X4 @ (X1 @ X14)) = $true)) & ! [X13 : b] : (((X2 @ X13) = $true) => ((X2 @ (X6 @ X13)) = $true))) => (! [X18 : a] : (((X4 @ X18) = $true) => ((X4 @ (X1 @ X18)) = $true)) & ! [X17 : g] : (((X0 @ X17) = $true) => ((X1 @ (X3 @ (X7 @ X17))) = (X3 @ (X7 @ (X5 @ X17))))) & ! [X16 : g] : (((X0 @ X16) = $true) => ((X4 @ (X3 @ (X7 @ X16))) = $true)) & ! [X19 : g] : (((X0 @ X19) = $true) => ((X0 @ (X5 @ X19)) = $true))))),
% 1.67/1.35 inference(fool_elimination,[status(thm)],[f4])).
% 1.67/1.35 thf(f4,plain,(
% 1.67/1.35 ~! [X0 : g > $o,X1 : a > a,X2 : b > $o,X3 : b > a,X4 : a > $o,X5 : g > g,X6 : b > b,X7 : g > b] : ((! [X8 : b] : ((X2 @ X8) => (X4 @ (X3 @ X8))) & ! [X9 : g] : ((X0 @ X9) => (X0 @ (X5 @ X9))) & ! [X10 : b] : ((X2 @ X10) => (X2 @ (X6 @ X10))) & ! [X11 : b] : ((X2 @ X11) => ((X1 @ (X3 @ X11)) = (X3 @ (X6 @ X11)))) & ! [X12 : g] : ((X0 @ X12) => ((X6 @ (X7 @ X12)) = (X7 @ (X5 @ X12)))) & ! [X13 : b] : ((X2 @ X13) => (X2 @ (X6 @ X13))) & ! [X14 : a] : ((X4 @ X14) => (X4 @ (X1 @ X14))) & ! [X15 : g] : ((X0 @ X15) => (X2 @ (X7 @ X15)))) => (! [X16 : g] : ((X0 @ X16) => (X4 @ (X3 @ (X7 @ X16)))) & ! [X17 : g] : ((X0 @ X17) => ((X1 @ (X3 @ (X7 @ X17))) = (X3 @ (X7 @ (X5 @ X17))))) & ! [X18 : a] : ((X4 @ X18) => (X4 @ (X1 @ X18))) & ! [X19 : g] : ((X0 @ X19) => (X0 @ (X5 @ X19)))))),
% 1.67/1.35 inference(rectify,[status(thm)],[f2])).
% 1.67/1.35 thf(f2,negated_conjecture,(
% 1.67/1.35 ~! [X2 : g > $o,X7 : a > a,X4 : b > $o,X1 : b > a,X6 : a > $o,X3 : g > g,X5 : b > b,X0 : g > b] : ((! [X8 : b] : ((X4 @ X8) => (X6 @ (X1 @ X8))) & ! [X8 : g] : ((X2 @ X8) => (X2 @ (X3 @ X8))) & ! [X8 : b] : ((X4 @ X8) => (X4 @ (X5 @ X8))) & ! [X8 : b] : ((X4 @ X8) => ((X1 @ (X5 @ X8)) = (X7 @ (X1 @ X8)))) & ! [X8 : g] : ((X2 @ X8) => ((X0 @ (X3 @ X8)) = (X5 @ (X0 @ X8)))) & ! [X8 : b] : ((X4 @ X8) => (X4 @ (X5 @ X8))) & ! [X8 : a] : ((X6 @ X8) => (X6 @ (X7 @ X8))) & ! [X8 : g] : ((X2 @ X8) => (X4 @ (X0 @ X8)))) => (! [X8 : g] : ((X2 @ X8) => (X6 @ (X1 @ (X0 @ X8)))) & ! [X8 : g] : ((X2 @ X8) => ((X1 @ (X0 @ (X3 @ X8))) = (X7 @ (X1 @ (X0 @ X8))))) & ! [X8 : a] : ((X6 @ X8) => (X6 @ (X7 @ X8))) & ! [X8 : g] : ((X2 @ X8) => (X2 @ (X3 @ X8)))))),
% 1.67/1.35 inference(negated_conjecture,[status(cth)],[f1])).
% 1.67/1.35 thf(f1,conjecture,(
% 1.67/1.35 ! [X2 : g > $o,X7 : a > a,X4 : b > $o,X1 : b > a,X6 : a > $o,X3 : g > g,X5 : b > b,X0 : g > b] : ((! [X8 : b] : ((X4 @ X8) => (X6 @ (X1 @ X8))) & ! [X8 : g] : ((X2 @ X8) => (X2 @ (X3 @ X8))) & ! [X8 : b] : ((X4 @ X8) => (X4 @ (X5 @ X8))) & ! [X8 : b] : ((X4 @ X8) => ((X1 @ (X5 @ X8)) = (X7 @ (X1 @ X8)))) & ! [X8 : g] : ((X2 @ X8) => ((X0 @ (X3 @ X8)) = (X5 @ (X0 @ X8)))) & ! [X8 : b] : ((X4 @ X8) => (X4 @ (X5 @ X8))) & ! [X8 : a] : ((X6 @ X8) => (X6 @ (X7 @ X8))) & ! [X8 : g] : ((X2 @ X8) => (X4 @ (X0 @ X8)))) => (! [X8 : g] : ((X2 @ X8) => (X6 @ (X1 @ (X0 @ X8)))) & ! [X8 : g] : ((X2 @ X8) => ((X1 @ (X0 @ (X3 @ X8))) = (X7 @ (X1 @ (X0 @ X8))))) & ! [X8 : a] : ((X6 @ X8) => (X6 @ (X7 @ X8))) & ! [X8 : g] : ((X2 @ X8) => (X2 @ (X3 @ X8)))))),
% 1.67/1.35 file('/export/starexec/sandbox/tmp/tmp.SPacvdwNQA/DTF2THF_26355.p',cTHM131_pme)).
% 1.67/1.35 thf(f95,plain,(
% 1.67/1.35 ((sK7 @ (sK2 @ (sK6 @ sK11))) != (sK7 @ (sK6 @ (sK3 @ sK11)))) | spl13_9),
% 1.67/1.35 inference(avatar_component_clause,[status(thm)],[f93])).
% 1.67/1.35 thf(f93,definition,(
% 1.67/1.35 spl13_9 <=> ((sK7 @ (sK2 @ (sK6 @ sK11))) = (sK7 @ (sK6 @ (sK3 @ sK11))))),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl13_9])],[avatar_definition])).
% 1.67/1.35 thf(f107,plain,(
% 1.67/1.35 ~spl13_1 | spl13_5),
% 1.67/1.35 inference(avatar_contradiction_clause,[status(thm)],[f106])).
% 1.67/1.35 thf(f106,plain,(
% 1.67/1.35 $false | (~spl13_1 | spl13_5)),
% 1.67/1.35 inference(subsumption_resolution,[status(thm)],[f105,f41])).
% 1.67/1.35 thf(f41,plain,(
% 1.67/1.35 ((sK8 @ sK12) = $true) | ~spl13_1),
% 1.67/1.35 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.67/1.35 thf(f39,definition,(
% 1.67/1.35 spl13_1 <=> ((sK8 @ sK12) = $true)),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl13_1])],[avatar_definition])).
% 1.67/1.35 thf(f105,plain,(
% 1.67/1.35 ((sK8 @ sK12) != $true) | spl13_5),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f104])).
% 1.67/1.35 thf(f104,plain,(
% 1.67/1.35 ($true != $true) | ((sK8 @ sK12) != $true) | spl13_5),
% 1.67/1.35 inference(superposition,[status(thm)],[f103,f32])).
% 1.67/1.35 thf(f32,plain,(
% 1.67/1.35 ( ! [X13 : g] : (((sK4 @ (sK6 @ X13)) = $true) | ((sK8 @ X13) != $true)) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.35 thf(f103,plain,(
% 1.67/1.35 ((sK4 @ (sK6 @ sK12)) != $true) | spl13_5),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f102])).
% 1.67/1.35 thf(f102,plain,(
% 1.67/1.35 ((sK4 @ (sK6 @ sK12)) != $true) | ($true != $true) | spl13_5),
% 1.67/1.35 inference(superposition,[status(thm)],[f58,f35])).
% 1.67/1.35 thf(f35,plain,(
% 1.67/1.35 ( ! [X10 : b] : (((sK9 @ (sK7 @ X10)) = $true) | ((sK4 @ X10) != $true)) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.35 thf(f58,plain,(
% 1.67/1.35 ((sK9 @ (sK7 @ (sK6 @ sK12))) != $true) | spl13_5),
% 1.67/1.35 inference(avatar_component_clause,[status(thm)],[f56])).
% 1.67/1.35 thf(f56,definition,(
% 1.67/1.35 spl13_5 <=> ((sK9 @ (sK7 @ (sK6 @ sK12))) = $true)),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl13_5])],[avatar_definition])).
% 1.67/1.35 thf(f101,plain,(
% 1.67/1.35 ~spl13_3 | spl13_8),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f98,f89,f47])).
% 1.67/1.35 thf(f89,definition,(
% 1.67/1.35 spl13_8 <=> ((sK4 @ (sK6 @ sK11)) = $true)),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl13_8])],[avatar_definition])).
% 1.67/1.35 thf(f98,plain,(
% 1.67/1.35 ((sK8 @ sK11) != $true) | spl13_8),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f97])).
% 1.67/1.35 thf(f97,plain,(
% 1.67/1.35 ($true != $true) | ((sK8 @ sK11) != $true) | spl13_8),
% 1.67/1.35 inference(superposition,[status(thm)],[f91,f32])).
% 1.67/1.35 thf(f91,plain,(
% 1.67/1.35 ((sK4 @ (sK6 @ sK11)) != $true) | spl13_8),
% 1.67/1.35 inference(avatar_component_clause,[status(thm)],[f89])).
% 1.67/1.35 thf(f96,plain,(
% 1.67/1.35 ~spl13_8 | ~spl13_9 | spl13_6),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f87,f60,f93,f89])).
% 1.67/1.35 thf(f60,definition,(
% 1.67/1.35 spl13_6 <=> ((sK7 @ (sK6 @ (sK3 @ sK11))) = (sK5 @ (sK7 @ (sK6 @ sK11))))),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl13_6])],[avatar_definition])).
% 1.67/1.35 thf(f87,plain,(
% 1.67/1.35 ((sK7 @ (sK2 @ (sK6 @ sK11))) != (sK7 @ (sK6 @ (sK3 @ sK11)))) | ((sK4 @ (sK6 @ sK11)) != $true) | spl13_6),
% 1.67/1.35 inference(superposition,[status(thm)],[f62,f37])).
% 1.67/1.35 thf(f37,plain,(
% 1.67/1.35 ( ! [X8 : b] : (((sK7 @ (sK2 @ X8)) = (sK5 @ (sK7 @ X8))) | ((sK4 @ X8) != $true)) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.35 thf(f62,plain,(
% 1.67/1.35 ((sK7 @ (sK6 @ (sK3 @ sK11))) != (sK5 @ (sK7 @ (sK6 @ sK11)))) | spl13_6),
% 1.67/1.35 inference(avatar_component_clause,[status(thm)],[f60])).
% 1.67/1.35 thf(f80,plain,(
% 1.67/1.35 ~spl13_4),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f79,f51])).
% 1.67/1.35 thf(f51,definition,(
% 1.67/1.35 spl13_4 <=> ((sP0 @ sK5 @ sK9) = $true)),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl13_4])],[avatar_definition])).
% 1.67/1.35 thf(f79,plain,(
% 1.67/1.35 ((sP0 @ sK5 @ sK9) != $true)),
% 1.67/1.35 inference(subsumption_resolution,[status(thm)],[f78,f21])).
% 1.67/1.35 thf(f21,plain,(
% 1.67/1.35 ( ! [X0 : a > $o,X1 : a > a] : (((X0 @ (sK1 @ X1 @ X0)) = $true) | ((sP0 @ X1 @ X0) != $true)) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f13])).
% 1.67/1.35 thf(f13,plain,(
% 1.67/1.35 ! [X0 : a > $o,X1 : a > a] : ((((X0 @ (sK1 @ X1 @ X0)) = $true) & ((X0 @ (X1 @ (sK1 @ X1 @ X0))) != $true)) | ((sP0 @ X1 @ X0) != $true))),
% 1.67/1.35 inference(skolemisation,[status(esa),new_symbols(skolem,[sK1])],[f11,f12])).
% 1.67/1.35 thf(f12,plain,(
% 1.67/1.35 ! [X0 : a > $o,X1 : a > a] : (? [X2 : a] : (((X0 @ X2) = $true) & ((X0 @ (X1 @ X2)) != $true)) => (((X0 @ (sK1 @ X1 @ X0)) = $true) & ((X0 @ (X1 @ (sK1 @ X1 @ X0))) != $true)))),
% 1.67/1.35 introduced(definition,[],[choice_axiom])).
% 1.67/1.35 thf(f11,plain,(
% 1.67/1.35 ! [X0 : a > $o,X1 : a > a] : (? [X2 : a] : (((X0 @ X2) = $true) & ((X0 @ (X1 @ X2)) != $true)) | ((sP0 @ X1 @ X0) != $true))),
% 1.67/1.35 inference(rectify,[status(thm)],[f10])).
% 1.67/1.35 thf(f10,plain,(
% 1.67/1.35 ! [X4 : a > $o,X1 : a > a] : (? [X18 : a] : (((X4 @ X18) = $true) & ((X4 @ (X1 @ X18)) != $true)) | ((sP0 @ X1 @ X4) != $true))),
% 1.67/1.35 inference(nnf_transformation,[status(thm)],[f8])).
% 1.67/1.35 thf(f78,plain,(
% 1.67/1.35 ((sK9 @ (sK1 @ sK5 @ sK9)) != $true) | ((sP0 @ sK5 @ sK9) != $true)),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f77])).
% 1.67/1.35 thf(f77,plain,(
% 1.67/1.35 ((sP0 @ sK5 @ sK9) != $true) | ((sK9 @ (sK1 @ sK5 @ sK9)) != $true) | ($true != $true)),
% 1.67/1.35 inference(superposition,[status(thm)],[f20,f36])).
% 1.67/1.35 thf(f36,plain,(
% 1.67/1.35 ( ! [X9 : a] : (((sK9 @ (sK5 @ X9)) = $true) | ((sK9 @ X9) != $true)) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.35 thf(f20,plain,(
% 1.67/1.35 ( ! [X0 : a > $o,X1 : a > a] : (((X0 @ (X1 @ (sK1 @ X1 @ X0))) != $true) | ((sP0 @ X1 @ X0) != $true)) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f13])).
% 1.67/1.35 thf(f76,plain,(
% 1.67/1.35 ~spl13_7 | spl13_2),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f75,f43,f65])).
% 1.67/1.35 thf(f65,definition,(
% 1.67/1.35 spl13_7 <=> ((sK8 @ sK10) = $true)),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl13_7])],[avatar_definition])).
% 1.67/1.35 thf(f43,definition,(
% 1.67/1.35 spl13_2 <=> ((sK8 @ (sK3 @ sK10)) = $true)),
% 1.67/1.35 introduced(definition,[new_symbols(naming,[spl13_2])],[avatar_definition])).
% 1.67/1.35 thf(f75,plain,(
% 1.67/1.35 ((sK8 @ sK10) != $true) | spl13_2),
% 1.67/1.35 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.67/1.35 thf(f74,plain,(
% 1.67/1.35 ((sK8 @ sK10) != $true) | ($true != $true) | spl13_2),
% 1.67/1.35 inference(superposition,[status(thm)],[f45,f31])).
% 1.67/1.35 thf(f31,plain,(
% 1.67/1.35 ( ! [X14 : g] : (((sK8 @ (sK3 @ X14)) = $true) | ((sK8 @ X14) != $true)) )),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.35 thf(f45,plain,(
% 1.67/1.35 ((sK8 @ (sK3 @ sK10)) != $true) | spl13_2),
% 1.67/1.35 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.67/1.35 thf(f73,plain,(
% 1.67/1.35 ~spl13_5 | spl13_7 | ~spl13_6 | spl13_4),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f26,f51,f60,f65,f56])).
% 1.67/1.35 thf(f26,plain,(
% 1.67/1.35 ((sP0 @ sK5 @ sK9) = $true) | ((sK8 @ sK10) = $true) | ((sK9 @ (sK7 @ (sK6 @ sK12))) != $true) | ((sK7 @ (sK6 @ (sK3 @ sK11))) != (sK5 @ (sK7 @ (sK6 @ sK11))))),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.35 thf(f72,plain,(
% 1.67/1.35 ~spl13_5 | spl13_3 | spl13_4 | spl13_7),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f24,f65,f51,f47,f56])).
% 1.67/1.35 thf(f24,plain,(
% 1.67/1.35 ((sK8 @ sK11) = $true) | ((sP0 @ sK5 @ sK9) = $true) | ((sK8 @ sK10) = $true) | ((sK9 @ (sK7 @ (sK6 @ sK12))) != $true)),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.35 thf(f71,plain,(
% 1.67/1.35 spl13_3 | ~spl13_2 | ~spl13_5 | spl13_4),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f28,f51,f56,f43,f47])).
% 1.67/1.35 thf(f28,plain,(
% 1.67/1.35 ((sK8 @ (sK3 @ sK10)) != $true) | ((sK8 @ sK11) = $true) | ((sK9 @ (sK7 @ (sK6 @ sK12))) != $true) | ((sP0 @ sK5 @ sK9) = $true)),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.35 thf(f70,plain,(
% 1.67/1.35 ~spl13_2 | spl13_4 | ~spl13_6 | spl13_1),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f29,f39,f60,f51,f43])).
% 1.67/1.35 thf(f29,plain,(
% 1.67/1.35 ((sK8 @ sK12) = $true) | ((sP0 @ sK5 @ sK9) = $true) | ((sK8 @ (sK3 @ sK10)) != $true) | ((sK7 @ (sK6 @ (sK3 @ sK11))) != (sK5 @ (sK7 @ (sK6 @ sK11))))),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.35 thf(f69,plain,(
% 1.67/1.35 spl13_7 | spl13_3 | spl13_1 | spl13_4),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f23,f51,f39,f47,f65])).
% 1.67/1.35 thf(f23,plain,(
% 1.67/1.35 ((sK8 @ sK12) = $true) | ((sK8 @ sK10) = $true) | ((sP0 @ sK5 @ sK9) = $true) | ((sK8 @ sK11) = $true)),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.35 thf(f68,plain,(
% 1.67/1.35 spl13_1 | ~spl13_6 | spl13_4 | spl13_7),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f25,f65,f51,f60,f39])).
% 1.67/1.35 thf(f25,plain,(
% 1.67/1.35 ((sK7 @ (sK6 @ (sK3 @ sK11))) != (sK5 @ (sK7 @ (sK6 @ sK11)))) | ((sK8 @ sK12) = $true) | ((sP0 @ sK5 @ sK9) = $true) | ((sK8 @ sK10) = $true)),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.35 thf(f63,plain,(
% 1.67/1.35 ~spl13_2 | ~spl13_5 | spl13_4 | ~spl13_6),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f30,f60,f51,f56,f43])).
% 1.67/1.35 thf(f30,plain,(
% 1.67/1.35 ((sK9 @ (sK7 @ (sK6 @ sK12))) != $true) | ((sK8 @ (sK3 @ sK10)) != $true) | ((sK7 @ (sK6 @ (sK3 @ sK11))) != (sK5 @ (sK7 @ (sK6 @ sK11)))) | ((sP0 @ sK5 @ sK9) = $true)),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.35 thf(f54,plain,(
% 1.67/1.35 spl13_1 | ~spl13_2 | spl13_3 | spl13_4),
% 1.67/1.35 inference(avatar_split_clause,[status(thm)],[f27,f51,f47,f43,f39])).
% 1.67/1.35 thf(f27,plain,(
% 1.67/1.35 ((sK8 @ sK11) = $true) | ((sK8 @ (sK3 @ sK10)) != $true) | ((sP0 @ sK5 @ sK9) = $true) | ((sK8 @ sK12) = $true)),
% 1.67/1.35 inference(cnf_transformation,[status(thm)],[f19])).
% 1.67/1.35 % SZS output end Proof for DTF2THF_26355
% 1.67/1.35 % (26549)------------------------------
% 1.67/1.35 % (26549)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.67/1.35 % (26549)Termination reason: Refutation
% 1.67/1.35
% 1.67/1.35 % (26549)Memory used [KB]: 5628
% 1.67/1.35 % (26549)Time elapsed: 0.015 s
% 1.67/1.35 % (26549)Instructions burned: 13 (million)
% 1.67/1.35 % (26549)------------------------------
% 1.67/1.35 % (26549)------------------------------
% 1.67/1.35 % (26543)Success in time 0.022 s
%------------------------------------------------------------------------------