%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV008^5 : 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 : n012.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 09:40:03 AM UTC 2026
% Result : Theorem 1.02s 0.94s
% Output : Refutation 1.02s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 22
% Syntax : Number of formulae : 158 ( 7 unt; 0 typ; 12 def)
% Number of atoms : 1767 ( 622 equ; 0 cnn)
% Maximal formula atoms : 50 ( 11 avg)
% Number of connectives : 1861 ( 447 ~; 503 |; 188 &; 682 @)
% ( 12 <=>; 29 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 206 ( 206 >; 0 *; 0 +; 0 <<)
% Number of symbols : 29 ( 26 usr; 20 con; 0-2 aty)
% Number of variables : 290 ( 0 ^; 182 !; 108 ?; 290 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_2,type,
vEPSILON:
!>[X0: $tType] : ( ( X0 > $o ) > X0 ) ).
thf(func_def_5,type,
sK0: ( a > $o ) > $o ).
thf(func_def_6,type,
sK1: ( a > $o ) > a ).
thf(func_def_7,type,
sK2: a > a > $o ).
thf(func_def_8,type,
sK3: a ).
thf(func_def_9,type,
sK4: a ).
thf(func_def_10,type,
sK5: a ).
thf(func_def_11,type,
sK6: a > $o ).
thf(func_def_12,type,
sK7: a > $o ).
thf(func_def_13,type,
sK8: a ).
thf(func_def_14,type,
sK9: a ).
thf(func_def_15,type,
sK10: a > $o ).
thf(func_def_16,type,
sK11: a ).
thf(func_def_18,type,
ph13:
!>[X0: $tType] : X0 ).
thf(f309,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f90,f95,f99,f107,f116,f121,f122,f123,f124,f125,f126,f127,f132,f133,f138,f139,f140,f141,f142,f143,f144,f145,f146,f147,f148,f149,f150,f151,f158,f167,f308]) ).
thf(f308,plain,
( ~ spl12_2
| ~ spl12_5
| ~ spl12_6
| ~ spl12_9
| ~ spl12_10
| ~ spl12_11
| ~ spl12_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f307]) ).
thf(f307,plain,
( $false
| ~ spl12_2
| ~ spl12_5
| ~ spl12_6
| ~ spl12_9
| ~ spl12_10
| ~ spl12_11
| ~ spl12_12 ),
inference(trivial_inequality_removal,[status(thm)],[f305]) ).
thf(f305,plain,
( ( $true = $false )
| ~ spl12_2
| ~ spl12_5
| ~ spl12_6
| ~ spl12_9
| ~ spl12_10
| ~ spl12_11
| ~ spl12_12 ),
inference(backward_demodulation,[status(thm)],[f86,f295]) ).
thf(f295,plain,
( ( ( sK6 @ sK4 )
= $false )
| ~ spl12_5
| ~ spl12_6
| ~ spl12_9
| ~ spl12_10
| ~ spl12_11
| ~ spl12_12 ),
inference(trivial_inequality_removal,[status(thm)],[f292]) ).
thf(f292,plain,
( ( ( sK6 @ sK4 )
= $false )
| ( $true != $true )
| ~ spl12_5
| ~ spl12_6
| ~ spl12_9
| ~ spl12_10
| ~ spl12_11
| ~ spl12_12 ),
inference(superposition,[status(thm)],[f208,f277]) ).
thf(f277,plain,
( ! [X1: a] :
( ( ( sK7 @ X1 )
= $true )
| ( ( sK6 @ X1 )
= $false ) )
| ~ spl12_9
| ~ spl12_10
| ~ spl12_11
| ~ spl12_12 ),
inference(binary_proxy_clausification,[status(thm)],[f276]) ).
thf(f276,plain,
( ! [X1: a] :
( ( sK7 @ X1 )
= ( sK6 @ X1 ) )
| ~ spl12_9
| ~ spl12_10
| ~ spl12_11
| ~ spl12_12 ),
inference(argument_congruence,[status(thm)],[f266]) ).
thf(f266,plain,
( ( sK6 = sK7 )
| ~ spl12_9
| ~ spl12_10
| ~ spl12_11
| ~ spl12_12 ),
inference(backward_demodulation,[status(thm)],[f234,f249]) ).
thf(f249,plain,
( ( sK6
= ( sK2 @ sK5 ) )
| ~ spl12_10
| ~ spl12_12 ),
inference(trivial_inequality_removal,[status(thm)],[f245]) ).
thf(f245,plain,
( ( sK6
= ( sK2 @ sK5 ) )
| ( $true != $true )
| ~ spl12_10
| ~ spl12_12 ),
inference(superposition,[status(thm)],[f225,f120]) ).
thf(f120,plain,
( ( ( sK6 @ sK5 )
= $true )
| ~ spl12_10 ),
inference(avatar_component_clause,[status(thm)],[f118]) ).
thf(f118,definition,
( spl12_10
<=> ( ( sK6 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl12_10])],[avatar_definition]) ).
thf(f225,plain,
( ! [X0: a] :
( ( $true
!= ( sK6 @ X0 ) )
| ( ( sK2 @ X0 )
= sK6 ) )
| ~ spl12_12 ),
inference(trivial_inequality_removal,[status(thm)],[f218]) ).
thf(f218,plain,
( ! [X0: a] :
( ( $true
!= ( sK6 @ X0 ) )
| ( $true != $true )
| ( ( sK2 @ X0 )
= sK6 ) )
| ~ spl12_12 ),
inference(superposition,[status(thm)],[f49,f137]) ).
thf(f137,plain,
( ( ( sK0 @ sK6 )
= $true )
| ~ spl12_12 ),
inference(avatar_component_clause,[status(thm)],[f135]) ).
thf(f135,definition,
( spl12_12
<=> ( ( sK0 @ sK6 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl12_12])],[avatar_definition]) ).
thf(f49,plain,
! [X3: a,X5: a > $o] :
( ( ( sK0 @ X5 )
!= $true )
| ( ( X5 @ X3 )
!= $true )
| ( ( sK2 @ X3 )
= X5 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f18,plain,
( ! [X1: a > $o] :
( ( $true
= ( X1 @ ( sK1 @ X1 ) ) )
| ( ( sK0 @ X1 )
!= $true ) )
& ! [X3: a] :
( ! [X5: a > $o] :
( ( ( sK2 @ X3 )
= X5 )
| ( ( sK0 @ X5 )
!= $true )
| ( ( X5 @ X3 )
!= $true ) )
& ( $true
= ( sK2 @ X3 @ X3 ) )
& ( ( sK0 @ ( sK2 @ X3 ) )
= $true ) )
& ( ( ( ( sK6 @ sK5 )
= $true )
& ( ( sK0 @ sK6 )
= $true )
& ( $true
= ( sK6 @ sK4 ) )
& ! [X10: a > $o] :
( ( ( X10 @ sK3 )
!= $true )
| ( ( X10 @ sK4 )
!= $true )
| ( $true
!= ( sK0 @ X10 ) ) )
& ( ( sK7 @ sK5 )
= $true )
& ( ( sK7 @ sK3 )
= $true )
& ( $true
= ( sK0 @ sK7 ) ) )
| ( ( ( sK10 @ sK8 )
= $true )
& ( $true
= ( sK0 @ sK10 ) )
& ( $true
= ( sK10 @ sK9 ) )
& ! [X15: a > $o] :
( ( ( X15 @ sK9 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X15 @ sK8 )
!= $true ) ) )
| ! [X17: a > $o] :
( ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( X17 @ sK11 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11])],[f8,f17,f16,f15,f14,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: ( a > $o ) > $o] :
( ! [X1: a > $o] :
( ? [X2: a] :
( ( X1 @ X2 )
= $true )
| ( ( X0 @ X1 )
!= $true ) )
& ! [X3: a] :
? [X4: a > $o] :
( ! [X5: a > $o] :
( ( X4 = X5 )
| ( ( X0 @ X5 )
!= $true )
| ( ( X5 @ X3 )
!= $true ) )
& ( ( X4 @ X3 )
= $true )
& ( ( X0 @ X4 )
= $true ) )
& ( ? [X6: a,X7: a,X8: a] :
( ? [X9: a > $o] :
( ( ( X9 @ X8 )
= $true )
& ( ( X0 @ X9 )
= $true )
& ( ( X9 @ X7 )
= $true ) )
& ! [X10: a > $o] :
( ( ( X10 @ X6 )
!= $true )
| ( ( X10 @ X7 )
!= $true )
| ( ( X0 @ X10 )
!= $true ) )
& ? [X11: a > $o] :
( ( $true
= ( X11 @ X8 ) )
& ( $true
= ( X11 @ X6 ) )
& ( $true
= ( X0 @ X11 ) ) ) )
| ? [X12: a,X13: a] :
( ? [X14: a > $o] :
( ( ( X14 @ X12 )
= $true )
& ( $true
= ( X0 @ X14 ) )
& ( ( X14 @ X13 )
= $true ) )
& ! [X15: a > $o] :
( ( $true
!= ( X15 @ X13 ) )
| ( $true
!= ( X0 @ X15 ) )
| ( $true
!= ( X15 @ X12 ) ) ) )
| ? [X16: a] :
! [X17: a > $o] :
( ( ( X0 @ X17 )
!= $true )
| ( $true
!= ( X17 @ X16 ) )
| ( $true
!= ( X17 @ X16 ) ) ) ) )
=> ( ! [X1: a > $o] :
( ? [X2: a] :
( ( X1 @ X2 )
= $true )
| ( ( sK0 @ X1 )
!= $true ) )
& ! [X3: a] :
? [X4: a > $o] :
( ! [X5: a > $o] :
( ( X4 = X5 )
| ( ( sK0 @ X5 )
!= $true )
| ( ( X5 @ X3 )
!= $true ) )
& ( ( X4 @ X3 )
= $true )
& ( ( sK0 @ X4 )
= $true ) )
& ( ? [X8: a,X7: a,X6: a] :
( ? [X9: a > $o] :
( ( ( X9 @ X8 )
= $true )
& ( $true
= ( sK0 @ X9 ) )
& ( ( X9 @ X7 )
= $true ) )
& ! [X10: a > $o] :
( ( ( X10 @ X6 )
!= $true )
| ( ( X10 @ X7 )
!= $true )
| ( $true
!= ( sK0 @ X10 ) ) )
& ? [X11: a > $o] :
( ( $true
= ( X11 @ X8 ) )
& ( $true
= ( X11 @ X6 ) )
& ( $true
= ( sK0 @ X11 ) ) ) )
| ? [X13: a,X12: a] :
( ? [X14: a > $o] :
( ( ( X14 @ X12 )
= $true )
& ( $true
= ( sK0 @ X14 ) )
& ( ( X14 @ X13 )
= $true ) )
& ! [X15: a > $o] :
( ( $true
!= ( X15 @ X13 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ X12 ) ) ) )
| ? [X16: a] :
! [X17: a > $o] :
( ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ X16 ) )
| ( $true
!= ( X17 @ X16 ) ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X1: a > $o] :
( ? [X2: a] :
( ( X1 @ X2 )
= $true )
=> ( $true
= ( X1 @ ( sK1 @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X3: a] :
( ? [X4: a > $o] :
( ! [X5: a > $o] :
( ( X4 = X5 )
| ( ( sK0 @ X5 )
!= $true )
| ( ( X5 @ X3 )
!= $true ) )
& ( ( X4 @ X3 )
= $true )
& ( ( sK0 @ X4 )
= $true ) )
=> ( ! [X5: a > $o] :
( ( ( sK2 @ X3 )
= X5 )
| ( ( sK0 @ X5 )
!= $true )
| ( ( X5 @ X3 )
!= $true ) )
& ( $true
= ( sK2 @ X3 @ X3 ) )
& ( ( sK0 @ ( sK2 @ X3 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X8: a,X7: a,X6: a] :
( ? [X9: a > $o] :
( ( ( X9 @ X8 )
= $true )
& ( $true
= ( sK0 @ X9 ) )
& ( ( X9 @ X7 )
= $true ) )
& ! [X10: a > $o] :
( ( ( X10 @ X6 )
!= $true )
| ( ( X10 @ X7 )
!= $true )
| ( $true
!= ( sK0 @ X10 ) ) )
& ? [X11: a > $o] :
( ( $true
= ( X11 @ X8 ) )
& ( $true
= ( X11 @ X6 ) )
& ( $true
= ( sK0 @ X11 ) ) ) )
=> ( ? [X9: a > $o] :
( ( ( X9 @ sK5 )
= $true )
& ( $true
= ( sK0 @ X9 ) )
& ( $true
= ( X9 @ sK4 ) ) )
& ! [X10: a > $o] :
( ( ( X10 @ sK3 )
!= $true )
| ( ( X10 @ sK4 )
!= $true )
| ( $true
!= ( sK0 @ X10 ) ) )
& ? [X11: a > $o] :
( ( $true
= ( X11 @ sK5 ) )
& ( $true
= ( X11 @ sK3 ) )
& ( $true
= ( sK0 @ X11 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X9: a > $o] :
( ( ( X9 @ sK5 )
= $true )
& ( $true
= ( sK0 @ X9 ) )
& ( $true
= ( X9 @ sK4 ) ) )
=> ( ( ( sK6 @ sK5 )
= $true )
& ( ( sK0 @ sK6 )
= $true )
& ( $true
= ( sK6 @ sK4 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X11: a > $o] :
( ( $true
= ( X11 @ sK5 ) )
& ( $true
= ( X11 @ sK3 ) )
& ( $true
= ( sK0 @ X11 ) ) )
=> ( ( ( sK7 @ sK5 )
= $true )
& ( ( sK7 @ sK3 )
= $true )
& ( $true
= ( sK0 @ sK7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X13: a,X12: a] :
( ? [X14: a > $o] :
( ( ( X14 @ X12 )
= $true )
& ( $true
= ( sK0 @ X14 ) )
& ( ( X14 @ X13 )
= $true ) )
& ! [X15: a > $o] :
( ( $true
!= ( X15 @ X13 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ X12 ) ) ) )
=> ( ? [X14: a > $o] :
( ( $true
= ( X14 @ sK8 ) )
& ( $true
= ( sK0 @ X14 ) )
& ( ( X14 @ sK9 )
= $true ) )
& ! [X15: a > $o] :
( ( ( X15 @ sK9 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X15 @ sK8 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X14: a > $o] :
( ( $true
= ( X14 @ sK8 ) )
& ( $true
= ( sK0 @ X14 ) )
& ( ( X14 @ sK9 )
= $true ) )
=> ( ( ( sK10 @ sK8 )
= $true )
& ( $true
= ( sK0 @ sK10 ) )
& ( $true
= ( sK10 @ sK9 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X16: a] :
! [X17: a > $o] :
( ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ X16 ) )
| ( $true
!= ( X17 @ X16 ) ) )
=> ! [X17: a > $o] :
( ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( X17 @ sK11 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: ( a > $o ) > $o] :
( ! [X1: a > $o] :
( ? [X2: a] :
( ( X1 @ X2 )
= $true )
| ( ( X0 @ X1 )
!= $true ) )
& ! [X3: a] :
? [X4: a > $o] :
( ! [X5: a > $o] :
( ( X4 = X5 )
| ( ( X0 @ X5 )
!= $true )
| ( ( X5 @ X3 )
!= $true ) )
& ( ( X4 @ X3 )
= $true )
& ( ( X0 @ X4 )
= $true ) )
& ( ? [X6: a,X7: a,X8: a] :
( ? [X9: a > $o] :
( ( ( X9 @ X8 )
= $true )
& ( ( X0 @ X9 )
= $true )
& ( ( X9 @ X7 )
= $true ) )
& ! [X10: a > $o] :
( ( ( X10 @ X6 )
!= $true )
| ( ( X10 @ X7 )
!= $true )
| ( ( X0 @ X10 )
!= $true ) )
& ? [X11: a > $o] :
( ( $true
= ( X11 @ X8 ) )
& ( $true
= ( X11 @ X6 ) )
& ( $true
= ( X0 @ X11 ) ) ) )
| ? [X12: a,X13: a] :
( ? [X14: a > $o] :
( ( ( X14 @ X12 )
= $true )
& ( $true
= ( X0 @ X14 ) )
& ( ( X14 @ X13 )
= $true ) )
& ! [X15: a > $o] :
( ( $true
!= ( X15 @ X13 ) )
| ( $true
!= ( X0 @ X15 ) )
| ( $true
!= ( X15 @ X12 ) ) ) )
| ? [X16: a] :
! [X17: a > $o] :
( ( ( X0 @ X17 )
!= $true )
| ( $true
!= ( X17 @ X16 ) )
| ( $true
!= ( X17 @ X16 ) ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: ( a > $o ) > $o] :
( ! [X1: a > $o] :
( ? [X2: a] :
( ( X1 @ X2 )
= $true )
| ( ( X0 @ X1 )
!= $true ) )
& ! [X3: a] :
? [X4: a > $o] :
( ! [X5: a > $o] :
( ( X4 = X5 )
| ( ( X0 @ X5 )
!= $true )
| ( ( X5 @ X3 )
!= $true ) )
& ( ( X4 @ X3 )
= $true )
& ( ( X0 @ X4 )
= $true ) )
& ( ? [X13: a,X12: a,X14: a] :
( ? [X16: a > $o] :
( ( $true
= ( X16 @ X14 ) )
& ( $true
= ( X0 @ X16 ) )
& ( ( X16 @ X12 )
= $true ) )
& ! [X17: a > $o] :
( ( ( X17 @ X13 )
!= $true )
| ( $true
!= ( X17 @ X12 ) )
| ( ( X0 @ X17 )
!= $true ) )
& ? [X15: a > $o] :
( ( $true
= ( X15 @ X14 ) )
& ( $true
= ( X15 @ X13 ) )
& ( $true
= ( X0 @ X15 ) ) ) )
| ? [X7: a,X6: a] :
( ? [X8: a > $o] :
( ( $true
= ( X8 @ X7 ) )
& ( $true
= ( X0 @ X8 ) )
& ( ( X8 @ X6 )
= $true ) )
& ! [X9: a > $o] :
( ( $true
!= ( X9 @ X6 ) )
| ( ( X0 @ X9 )
!= $true )
| ( ( X9 @ X7 )
!= $true ) ) )
| ? [X10: a] :
! [X11: a > $o] :
( ( $true
!= ( X0 @ X11 ) )
| ( ( X11 @ X10 )
!= $true )
| ( ( X11 @ X10 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: ( a > $o ) > $o] :
( ( ? [X7: a,X6: a] :
( ? [X8: a > $o] :
( ( $true
= ( X8 @ X7 ) )
& ( $true
= ( X0 @ X8 ) )
& ( ( X8 @ X6 )
= $true ) )
& ! [X9: a > $o] :
( ( $true
!= ( X9 @ X6 ) )
| ( ( X0 @ X9 )
!= $true )
| ( ( X9 @ X7 )
!= $true ) ) )
| ? [X13: a,X14: a,X12: a] :
( ! [X17: a > $o] :
( ( ( X17 @ X13 )
!= $true )
| ( $true
!= ( X17 @ X12 ) )
| ( ( X0 @ X17 )
!= $true ) )
& ? [X16: a > $o] :
( ( $true
= ( X16 @ X14 ) )
& ( $true
= ( X0 @ X16 ) )
& ( ( X16 @ X12 )
= $true ) )
& ? [X15: a > $o] :
( ( $true
= ( X15 @ X14 ) )
& ( $true
= ( X15 @ X13 ) )
& ( $true
= ( X0 @ X15 ) ) ) )
| ? [X10: a] :
! [X11: a > $o] :
( ( $true
!= ( X0 @ X11 ) )
| ( ( X11 @ X10 )
!= $true )
| ( ( X11 @ X10 )
!= $true ) ) )
& ! [X1: a > $o] :
( ? [X2: a] :
( ( X1 @ X2 )
= $true )
| ( ( X0 @ X1 )
!= $true ) )
& ! [X3: a] :
? [X4: a > $o] :
( ! [X5: a > $o] :
( ( X4 = X5 )
| ( ( X0 @ X5 )
!= $true )
| ( ( X5 @ X3 )
!= $true ) )
& ( ( X4 @ X3 )
= $true )
& ( ( X0 @ X4 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( a > $o ) > $o] :
( ( ! [X1: a > $o] :
( ( ( X0 @ X1 )
= $true )
=> ? [X2: a] :
( ( X1 @ X2 )
= $true ) )
& ! [X3: a] :
? [X4: a > $o] :
( ! [X5: a > $o] :
( ( ( ( X0 @ X5 )
= $true )
& ( ( X5 @ X3 )
= $true ) )
=> ( X4 = X5 ) )
& ( ( X4 @ X3 )
= $true )
& ( ( X0 @ X4 )
= $true ) ) )
=> ( ! [X7: a,X6: a] :
( ? [X8: a > $o] :
( ( $true
= ( X8 @ X7 ) )
& ( $true
= ( X0 @ X8 ) )
& ( ( X8 @ X6 )
= $true ) )
=> ? [X9: a > $o] :
( ( ( X0 @ X9 )
= $true )
& ( $true
= ( X9 @ X6 ) )
& ( ( X9 @ X7 )
= $true ) ) )
& ! [X13: a,X14: a,X12: a] :
( ( ? [X16: a > $o] :
( ( $true
= ( X16 @ X14 ) )
& ( $true
= ( X0 @ X16 ) )
& ( ( X16 @ X12 )
= $true ) )
& ? [X15: a > $o] :
( ( $true
= ( X15 @ X14 ) )
& ( $true
= ( X15 @ X13 ) )
& ( $true
= ( X0 @ X15 ) ) ) )
=> ? [X17: a > $o] :
( ( $true
= ( X17 @ X12 ) )
& ( ( X17 @ X13 )
= $true )
& ( ( X0 @ X17 )
= $true ) ) )
& ! [X10: a] :
? [X11: a > $o] :
( ( $true
= ( X0 @ X11 ) )
& ( ( X11 @ X10 )
= $true )
& ( ( X11 @ X10 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( a > $o ) > $o] :
( ( ! [X1: a > $o] :
( ( X0 @ X1 )
=> ? [X2: a] : ( X1 @ X2 ) )
& ! [X3: a] :
? [X4: a > $o] :
( ( X4 @ X3 )
& ! [X5: a > $o] :
( ( ( X5 @ X3 )
& ( X0 @ X5 ) )
=> ( X4 = X5 ) )
& ( X0 @ X4 ) ) )
=> ( ! [X6: a,X7: a] :
( ? [X8: a > $o] :
( ( X8 @ X7 )
& ( X8 @ X6 )
& ( X0 @ X8 ) )
=> ? [X9: a > $o] :
( ( X9 @ X6 )
& ( X0 @ X9 )
& ( X9 @ X7 ) ) )
& ! [X10: a] :
? [X11: a > $o] :
( ( X11 @ X10 )
& ( X11 @ X10 )
& ( X0 @ X11 ) )
& ! [X12: a,X13: a,X14: a] :
( ( ? [X15: a > $o] :
( ( X15 @ X14 )
& ( X0 @ X15 )
& ( X15 @ X13 ) )
& ? [X16: a > $o] :
( ( X16 @ X12 )
& ( X0 @ X16 )
& ( X16 @ X14 ) ) )
=> ? [X17: a > $o] :
( ( X17 @ X12 )
& ( X0 @ X17 )
& ( X17 @ X13 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > $o ) > $o] :
( ( ! [X1: a > $o] :
( ( X0 @ X1 )
=> ? [X2: a] : ( X1 @ X2 ) )
& ! [X3: a] :
? [X1: a > $o] :
( ( X1 @ X3 )
& ! [X4: a > $o] :
( ( ( X4 @ X3 )
& ( X0 @ X4 ) )
=> ( X1 = X4 ) )
& ( X0 @ X1 ) ) )
=> ( ! [X3: a,X6: a] :
( ? [X5: a > $o] :
( ( X5 @ X6 )
& ( X5 @ X3 )
& ( X0 @ X5 ) )
=> ? [X5: a > $o] :
( ( X5 @ X3 )
& ( X0 @ X5 )
& ( X5 @ X6 ) ) )
& ! [X3: a] :
? [X5: a > $o] :
( ( X5 @ X3 )
& ( X5 @ X3 )
& ( X0 @ X5 ) )
& ! [X2: a,X3: a,X6: a] :
( ( ? [X5: a > $o] :
( ( X5 @ X6 )
& ( X0 @ X5 )
& ( X5 @ X3 ) )
& ? [X5: a > $o] :
( ( X5 @ X2 )
& ( X0 @ X5 )
& ( X5 @ X6 ) ) )
=> ? [X5: a > $o] :
( ( X5 @ X2 )
& ( X0 @ X5 )
& ( X5 @ X3 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( a > $o ) > $o] :
( ( ! [X1: a > $o] :
( ( X0 @ X1 )
=> ? [X2: a] : ( X1 @ X2 ) )
& ! [X3: a] :
? [X1: a > $o] :
( ( X1 @ X3 )
& ! [X4: a > $o] :
( ( ( X4 @ X3 )
& ( X0 @ X4 ) )
=> ( X1 = X4 ) )
& ( X0 @ X1 ) ) )
=> ( ! [X3: a,X6: a] :
( ? [X5: a > $o] :
( ( X5 @ X6 )
& ( X5 @ X3 )
& ( X0 @ X5 ) )
=> ? [X5: a > $o] :
( ( X5 @ X3 )
& ( X0 @ X5 )
& ( X5 @ X6 ) ) )
& ! [X3: a] :
? [X5: a > $o] :
( ( X5 @ X3 )
& ( X5 @ X3 )
& ( X0 @ X5 ) )
& ! [X2: a,X3: a,X6: a] :
( ( ? [X5: a > $o] :
( ( X5 @ X6 )
& ( X0 @ X5 )
& ( X5 @ X3 ) )
& ? [X5: a > $o] :
( ( X5 @ X2 )
& ( X0 @ X5 )
& ( X5 @ X6 ) ) )
=> ? [X5: a > $o] :
( ( X5 @ X2 )
& ( X0 @ X5 )
& ( X5 @ X3 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.SKX2tX6vzu/DTF2THF_7140.p',cTHM261_pme) ).
thf(f234,plain,
( ( ( sK2 @ sK5 )
= sK7 )
| ~ spl12_9
| ~ spl12_11 ),
inference(trivial_inequality_removal,[status(thm)],[f231]) ).
thf(f231,plain,
( ( ( sK2 @ sK5 )
= sK7 )
| ( $true != $true )
| ~ spl12_9
| ~ spl12_11 ),
inference(superposition,[status(thm)],[f224,f131]) ).
thf(f131,plain,
( ( ( sK7 @ sK5 )
= $true )
| ~ spl12_11 ),
inference(avatar_component_clause,[status(thm)],[f129]) ).
thf(f129,definition,
( spl12_11
<=> ( ( sK7 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl12_11])],[avatar_definition]) ).
thf(f224,plain,
( ! [X0: a] :
( ( $true
!= ( sK7 @ X0 ) )
| ( ( sK2 @ X0 )
= sK7 ) )
| ~ spl12_9 ),
inference(trivial_inequality_removal,[status(thm)],[f219]) ).
thf(f219,plain,
( ! [X0: a] :
( ( ( sK2 @ X0 )
= sK7 )
| ( $true
!= ( sK7 @ X0 ) )
| ( $true != $true ) )
| ~ spl12_9 ),
inference(superposition,[status(thm)],[f49,f115]) ).
thf(f115,plain,
( ( $true
= ( sK0 @ sK7 ) )
| ~ spl12_9 ),
inference(avatar_component_clause,[status(thm)],[f113]) ).
thf(f113,definition,
( spl12_9
<=> ( $true
= ( sK0 @ sK7 ) ) ),
introduced(definition,[new_symbols(naming,[spl12_9])],[avatar_definition]) ).
thf(f208,plain,
( ( $true
!= ( sK7 @ sK4 ) )
| ~ spl12_5
| ~ spl12_6
| ~ spl12_9 ),
inference(trivial_inequality_removal,[status(thm)],[f207]) ).
thf(f207,plain,
( ( $true
!= ( sK7 @ sK4 ) )
| ( $true != $true )
| ~ spl12_5
| ~ spl12_6
| ~ spl12_9 ),
inference(forward_demodulation,[status(thm)],[f199,f103]) ).
thf(f103,plain,
( ( ( sK7 @ sK3 )
= $true )
| ~ spl12_6 ),
inference(avatar_component_clause,[status(thm)],[f101]) ).
thf(f101,definition,
( spl12_6
<=> ( ( sK7 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl12_6])],[avatar_definition]) ).
thf(f199,plain,
( ( $true
!= ( sK7 @ sK4 ) )
| ( ( sK7 @ sK3 )
!= $true )
| ~ spl12_5
| ~ spl12_9 ),
inference(trivial_inequality_removal,[status(thm)],[f195]) ).
thf(f195,plain,
( ( $true
!= ( sK7 @ sK4 ) )
| ( $true != $true )
| ( ( sK7 @ sK3 )
!= $true )
| ~ spl12_5
| ~ spl12_9 ),
inference(superposition,[status(thm)],[f98,f115]) ).
thf(f98,plain,
( ! [X10: a > $o] :
( ( $true
!= ( sK0 @ X10 ) )
| ( ( X10 @ sK4 )
!= $true )
| ( ( X10 @ sK3 )
!= $true ) )
| ~ spl12_5 ),
inference(avatar_component_clause,[status(thm)],[f97]) ).
thf(f97,definition,
( spl12_5
<=> ! [X10: a > $o] :
( ( ( X10 @ sK4 )
!= $true )
| ( ( X10 @ sK3 )
!= $true )
| ( $true
!= ( sK0 @ X10 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl12_5])],[avatar_definition]) ).
thf(f86,plain,
( ( $true
= ( sK6 @ sK4 ) )
| ~ spl12_2 ),
inference(avatar_component_clause,[status(thm)],[f84]) ).
thf(f84,definition,
( spl12_2
<=> ( $true
= ( sK6 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl12_2])],[avatar_definition]) ).
thf(f167,plain,
( ~ spl12_8
| ~ spl12_1
| ~ spl12_4
| ~ spl12_7 ),
inference(avatar_split_clause,[status(thm)],[f166,f105,f92,f80,f109]) ).
thf(f109,definition,
( spl12_8
<=> ( $true
= ( sK10 @ sK9 ) ) ),
introduced(definition,[new_symbols(naming,[spl12_8])],[avatar_definition]) ).
thf(f80,definition,
( spl12_1
<=> ( ( sK10 @ sK8 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl12_1])],[avatar_definition]) ).
thf(f92,definition,
( spl12_4
<=> ( $true
= ( sK0 @ sK10 ) ) ),
introduced(definition,[new_symbols(naming,[spl12_4])],[avatar_definition]) ).
thf(f105,definition,
( spl12_7
<=> ! [X15: a > $o] :
( ( ( X15 @ sK8 )
!= $true )
| ( ( X15 @ sK9 )
!= $true )
| ( ( sK0 @ X15 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl12_7])],[avatar_definition]) ).
thf(f166,plain,
( ( $true
!= ( sK10 @ sK9 ) )
| ~ spl12_1
| ~ spl12_4
| ~ spl12_7 ),
inference(trivial_inequality_removal,[status(thm)],[f165]) ).
thf(f165,plain,
( ( $true != $true )
| ( $true
!= ( sK10 @ sK9 ) )
| ~ spl12_1
| ~ spl12_4
| ~ spl12_7 ),
inference(forward_demodulation,[status(thm)],[f163,f82]) ).
thf(f82,plain,
( ( ( sK10 @ sK8 )
= $true )
| ~ spl12_1 ),
inference(avatar_component_clause,[status(thm)],[f80]) ).
thf(f163,plain,
( ( $true
!= ( sK10 @ sK9 ) )
| ( ( sK10 @ sK8 )
!= $true )
| ~ spl12_4
| ~ spl12_7 ),
inference(trivial_inequality_removal,[status(thm)],[f161]) ).
thf(f161,plain,
( ( ( sK10 @ sK8 )
!= $true )
| ( $true != $true )
| ( $true
!= ( sK10 @ sK9 ) )
| ~ spl12_4
| ~ spl12_7 ),
inference(superposition,[status(thm)],[f106,f94]) ).
thf(f94,plain,
( ( $true
= ( sK0 @ sK10 ) )
| ~ spl12_4 ),
inference(avatar_component_clause,[status(thm)],[f92]) ).
thf(f106,plain,
( ! [X15: a > $o] :
( ( ( sK0 @ X15 )
!= $true )
| ( ( X15 @ sK9 )
!= $true )
| ( ( X15 @ sK8 )
!= $true ) )
| ~ spl12_7 ),
inference(avatar_component_clause,[status(thm)],[f105]) ).
thf(f158,plain,
~ spl12_3,
inference(avatar_contradiction_clause,[status(thm)],[f157]) ).
thf(f157,plain,
( $false
| ~ spl12_3 ),
inference(trivial_inequality_removal,[status(thm)],[f156]) ).
thf(f156,plain,
( ( $true != $true )
| ~ spl12_3 ),
inference(superposition,[status(thm)],[f153,f48]) ).
thf(f48,plain,
! [X3: a] :
( $true
= ( sK2 @ X3 @ X3 ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f153,plain,
( ! [X0: a] :
( ( sK2 @ X0 @ sK11 )
!= $true )
| ~ spl12_3 ),
inference(trivial_inequality_removal,[status(thm)],[f152]) ).
thf(f152,plain,
( ! [X0: a] :
( ( ( sK2 @ X0 @ sK11 )
!= $true )
| ( $true != $true ) )
| ~ spl12_3 ),
inference(superposition,[status(thm)],[f89,f47]) ).
thf(f47,plain,
! [X3: a] :
( ( sK0 @ ( sK2 @ X3 ) )
= $true ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f89,plain,
( ! [X17: a > $o] :
( ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ sK11 ) ) )
| ~ spl12_3 ),
inference(avatar_component_clause,[status(thm)],[f88]) ).
thf(f88,definition,
( spl12_3
<=> ! [X17: a > $o] :
( ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl12_3])],[avatar_definition]) ).
thf(f151,plain,
( spl12_4
| spl12_3
| spl12_12 ),
inference(avatar_split_clause,[status(thm)],[f51,f135,f88,f92]) ).
thf(f51,plain,
! [X17: a > $o] :
( ( $true
!= ( sK0 @ X17 ) )
| ( $true
= ( sK0 @ sK10 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK0 @ sK6 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X17: a > $o] :
( ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( ( sK0 @ sK6 )
= $true )
| ( $true
= ( sK0 @ sK10 ) )
| ( $true
!= ( X17 @ sK11 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f150,plain,
( spl12_5
| spl12_3
| spl12_1 ),
inference(avatar_split_clause,[status(thm)],[f52,f80,f88,f97]) ).
thf(f52,plain,
! [X10: a > $o,X17: a > $o] :
( ( ( X10 @ sK3 )
!= $true )
| ( $true
!= ( sK0 @ X17 ) )
| ( ( X10 @ sK4 )
!= $true )
| ( ( sK10 @ sK8 )
= $true )
| ( $true
!= ( sK0 @ X10 ) )
| ( $true
!= ( X17 @ sK11 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f34]) ).
thf(f34,plain,
! [X10: a > $o,X17: a > $o] :
( ( $true
!= ( sK0 @ X10 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( X10 @ sK3 )
!= $true )
| ( ( X10 @ sK4 )
!= $true )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK10 @ sK8 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f149,plain,
( spl12_10
| spl12_3
| spl12_7 ),
inference(avatar_split_clause,[status(thm)],[f53,f105,f88,f118]) ).
thf(f53,plain,
! [X17: a > $o,X15: a > $o] :
( ( ( X15 @ sK8 )
!= $true )
| ( ( sK6 @ sK5 )
= $true )
| ( ( X15 @ sK9 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( ( sK0 @ X15 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X17: a > $o,X15: a > $o] :
( ( ( X15 @ sK8 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( X15 @ sK9 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( ( sK6 @ sK5 )
= $true )
| ( $true
!= ( sK0 @ X17 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f148,plain,
( spl12_3
| spl12_1
| spl12_6 ),
inference(avatar_split_clause,[status(thm)],[f54,f101,f80,f88]) ).
thf(f54,plain,
! [X17: a > $o] :
( ( ( sK7 @ sK3 )
= $true )
| ( ( sK10 @ sK8 )
= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f26]) ).
thf(f26,plain,
! [X17: a > $o] :
( ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( ( sK7 @ sK3 )
= $true )
| ( ( sK10 @ sK8 )
= $true )
| ( $true
!= ( X17 @ sK11 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f147,plain,
( spl12_7
| spl12_3
| spl12_11 ),
inference(avatar_split_clause,[status(thm)],[f55,f129,f88,f105]) ).
thf(f55,plain,
! [X17: a > $o,X15: a > $o] :
( ( ( X15 @ sK9 )
!= $true )
| ( ( X15 @ sK8 )
!= $true )
| ( ( sK7 @ sK5 )
= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f27]) ).
thf(f27,plain,
! [X17: a > $o,X15: a > $o] :
( ( ( X15 @ sK8 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X15 @ sK9 )
!= $true )
| ( ( sK7 @ sK5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f146,plain,
( spl12_3
| spl12_8
| spl12_5 ),
inference(avatar_split_clause,[status(thm)],[f56,f97,f109,f88]) ).
thf(f56,plain,
! [X10: a > $o,X17: a > $o] :
( ( ( X10 @ sK3 )
!= $true )
| ( $true
= ( sK10 @ sK9 ) )
| ( $true
!= ( sK0 @ X10 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( X10 @ sK4 )
!= $true )
| ( $true
!= ( sK0 @ X17 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X10: a > $o,X17: a > $o] :
( ( ( X10 @ sK4 )
!= $true )
| ( $true
= ( sK10 @ sK9 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( sK0 @ X10 ) )
| ( ( X10 @ sK3 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f145,plain,
( spl12_11
| spl12_3
| spl12_1 ),
inference(avatar_split_clause,[status(thm)],[f57,f80,f88,f129]) ).
thf(f57,plain,
! [X17: a > $o] :
( ( ( sK10 @ sK8 )
= $true )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK7 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f30]) ).
thf(f30,plain,
! [X17: a > $o] :
( ( $true
!= ( sK0 @ X17 ) )
| ( ( sK10 @ sK8 )
= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK7 @ sK5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f144,plain,
( spl12_12
| spl12_7
| spl12_3 ),
inference(avatar_split_clause,[status(thm)],[f58,f88,f105,f135]) ).
thf(f58,plain,
! [X17: a > $o,X15: a > $o] :
( ( $true
!= ( sK0 @ X17 ) )
| ( ( X15 @ sK9 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X15 @ sK8 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK0 @ sK6 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f39]) ).
thf(f39,plain,
! [X17: a > $o,X15: a > $o] :
( ( ( X15 @ sK8 )
!= $true )
| ( ( sK0 @ sK6 )
= $true )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( X15 @ sK9 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f143,plain,
( spl12_8
| spl12_6
| spl12_3 ),
inference(avatar_split_clause,[status(thm)],[f59,f88,f101,f109]) ).
thf(f59,plain,
! [X17: a > $o] :
( ( $true
!= ( sK0 @ X17 ) )
| ( $true
= ( sK10 @ sK9 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK7 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f24]) ).
thf(f24,plain,
! [X17: a > $o] :
( ( ( sK7 @ sK3 )
= $true )
| ( $true
= ( sK10 @ sK9 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ sK11 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f142,plain,
( spl12_3
| spl12_5
| spl12_7 ),
inference(avatar_split_clause,[status(thm)],[f60,f105,f97,f88]) ).
thf(f60,plain,
! [X10: a > $o,X17: a > $o,X15: a > $o] :
( ( ( X15 @ sK8 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X10 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( ( X10 @ sK4 )
!= $true )
| ( ( X10 @ sK3 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X15 @ sK9 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f31]) ).
thf(f31,plain,
! [X10: a > $o,X17: a > $o,X15: a > $o] :
( ( $true
!= ( X17 @ sK11 ) )
| ( ( X15 @ sK8 )
!= $true )
| ( $true
!= ( sK0 @ X10 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( ( X10 @ sK4 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X10 @ sK3 )
!= $true )
| ( ( X15 @ sK9 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f141,plain,
( spl12_4
| spl12_11
| spl12_3 ),
inference(avatar_split_clause,[status(thm)],[f61,f88,f129,f92]) ).
thf(f61,plain,
! [X17: a > $o] :
( ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK7 @ sK5 )
= $true )
| ( $true
= ( sK0 @ sK10 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f29]) ).
thf(f29,plain,
! [X17: a > $o] :
( ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK7 @ sK5 )
= $true )
| ( $true
= ( sK0 @ sK10 ) )
| ( $true
!= ( sK0 @ X17 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f140,plain,
( spl12_3
| spl12_8
| spl12_2 ),
inference(avatar_split_clause,[status(thm)],[f62,f84,f109,f88]) ).
thf(f62,plain,
! [X17: a > $o] :
( ( $true
= ( sK6 @ sK4 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
= ( sK10 @ sK9 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f36]) ).
thf(f36,plain,
! [X17: a > $o] :
( ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
= ( sK10 @ sK9 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
= ( sK6 @ sK4 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f139,plain,
( spl12_12
| spl12_3
| spl12_1 ),
inference(avatar_split_clause,[status(thm)],[f63,f80,f88,f135]) ).
thf(f63,plain,
! [X17: a > $o] :
( ( ( sK0 @ sK6 )
= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK10 @ sK8 )
= $true )
| ( $true
!= ( sK0 @ X17 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f42]) ).
thf(f42,plain,
! [X17: a > $o] :
( ( ( sK0 @ sK6 )
= $true )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK10 @ sK8 )
= $true )
| ( $true
!= ( X17 @ sK11 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f138,plain,
( spl12_3
| spl12_8
| spl12_12 ),
inference(avatar_split_clause,[status(thm)],[f64,f135,f109,f88]) ).
thf(f64,plain,
! [X17: a > $o] :
( ( $true
!= ( X17 @ sK11 ) )
| ( ( sK0 @ sK6 )
= $true )
| ( $true
= ( sK10 @ sK9 ) )
| ( $true
!= ( sK0 @ X17 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f40]) ).
thf(f40,plain,
! [X17: a > $o] :
( ( $true
= ( sK10 @ sK9 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK0 @ sK6 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f133,plain,
( spl12_3
| spl12_4
| spl12_10 ),
inference(avatar_split_clause,[status(thm)],[f65,f118,f92,f88]) ).
thf(f65,plain,
! [X17: a > $o] :
( ( $true
!= ( sK0 @ X17 ) )
| ( $true
= ( sK0 @ sK10 ) )
| ( ( sK6 @ sK5 )
= $true )
| ( $true
!= ( X17 @ sK11 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f45]) ).
thf(f45,plain,
! [X17: a > $o] :
( ( $true
= ( sK0 @ sK10 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK6 @ sK5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f132,plain,
( spl12_8
| spl12_3
| spl12_11 ),
inference(avatar_split_clause,[status(thm)],[f66,f129,f88,f109]) ).
thf(f66,plain,
! [X17: a > $o] :
( ( $true
!= ( sK0 @ X17 ) )
| ( $true
= ( sK10 @ sK9 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK7 @ sK5 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f28]) ).
thf(f28,plain,
! [X17: a > $o] :
( ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK7 @ sK5 )
= $true )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
= ( sK10 @ sK9 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f127,plain,
( spl12_3
| spl12_2
| spl12_7 ),
inference(avatar_split_clause,[status(thm)],[f67,f105,f84,f88]) ).
thf(f67,plain,
! [X17: a > $o,X15: a > $o] :
( ( ( sK0 @ X15 )
!= $true )
| ( ( X15 @ sK8 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( X15 @ sK9 )
!= $true )
| ( $true
= ( sK6 @ sK4 ) )
| ( $true
!= ( sK0 @ X17 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f35]) ).
thf(f35,plain,
! [X17: a > $o,X15: a > $o] :
( ( $true
!= ( sK0 @ X17 ) )
| ( $true
= ( sK6 @ sK4 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( X15 @ sK8 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( X15 @ sK9 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f126,plain,
( spl12_1
| spl12_10
| spl12_3 ),
inference(avatar_split_clause,[status(thm)],[f68,f88,f118,f80]) ).
thf(f68,plain,
! [X17: a > $o] :
( ( ( sK6 @ sK5 )
= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK10 @ sK8 )
= $true )
| ( $true
!= ( sK0 @ X17 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f46]) ).
thf(f46,plain,
! [X17: a > $o] :
( ( $true
!= ( X17 @ sK11 ) )
| ( ( sK10 @ sK8 )
= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( ( sK6 @ sK5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f125,plain,
( spl12_3
| spl12_9
| spl12_1 ),
inference(avatar_split_clause,[status(thm)],[f69,f80,f113,f88]) ).
thf(f69,plain,
! [X17: a > $o] :
( ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK10 @ sK8 )
= $true )
| ( $true
= ( sK0 @ sK7 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f22]) ).
thf(f22,plain,
! [X17: a > $o] :
( ( $true
= ( sK0 @ sK7 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( sK10 @ sK8 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f124,plain,
( spl12_4
| spl12_3
| spl12_6 ),
inference(avatar_split_clause,[status(thm)],[f70,f101,f88,f92]) ).
thf(f70,plain,
! [X17: a > $o] :
( ( $true
= ( sK0 @ sK10 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( ( sK7 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f25]) ).
thf(f25,plain,
! [X17: a > $o] :
( ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( ( sK7 @ sK3 )
= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
= ( sK0 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f123,plain,
( spl12_9
| spl12_3
| spl12_7 ),
inference(avatar_split_clause,[status(thm)],[f71,f105,f88,f113]) ).
thf(f71,plain,
! [X17: a > $o,X15: a > $o] :
( ( $true
= ( sK0 @ sK7 ) )
| ( ( X15 @ sK8 )
!= $true )
| ( $true
!= ( sK0 @ X17 ) )
| ( ( X15 @ sK9 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f19]) ).
thf(f19,plain,
! [X17: a > $o,X15: a > $o] :
( ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( ( X15 @ sK9 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( X15 @ sK8 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
= ( sK0 @ sK7 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f122,plain,
( spl12_4
| spl12_9
| spl12_3 ),
inference(avatar_split_clause,[status(thm)],[f72,f88,f113,f92]) ).
thf(f72,plain,
! [X17: a > $o] :
( ( $true
!= ( X17 @ sK11 ) )
| ( $true
= ( sK0 @ sK7 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
= ( sK0 @ sK10 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f21]) ).
thf(f21,plain,
! [X17: a > $o] :
( ( $true
= ( sK0 @ sK10 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
= ( sK0 @ sK7 ) )
| ( $true
!= ( sK0 @ X17 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f121,plain,
( spl12_8
| spl12_10
| spl12_3 ),
inference(avatar_split_clause,[status(thm)],[f73,f88,f118,f109]) ).
thf(f73,plain,
! [X17: a > $o] :
( ( $true
!= ( sK0 @ X17 ) )
| ( $true
= ( sK10 @ sK9 ) )
| ( ( sK6 @ sK5 )
= $true )
| ( $true
!= ( X17 @ sK11 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f44]) ).
thf(f44,plain,
! [X17: a > $o] :
( ( $true
!= ( sK0 @ X17 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
= ( sK10 @ sK9 ) )
| ( ( sK6 @ sK5 )
= $true )
| ( $true
!= ( X17 @ sK11 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f116,plain,
( spl12_8
| spl12_9
| spl12_3 ),
inference(avatar_split_clause,[status(thm)],[f74,f88,f113,f109]) ).
thf(f74,plain,
! [X17: a > $o] :
( ( $true
= ( sK10 @ sK9 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
= ( sK0 @ sK7 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f20]) ).
thf(f20,plain,
! [X17: a > $o] :
( ( $true
= ( sK10 @ sK9 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
= ( sK0 @ sK7 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f107,plain,
( spl12_6
| spl12_7
| spl12_3 ),
inference(avatar_split_clause,[status(thm)],[f75,f88,f105,f101]) ).
thf(f75,plain,
! [X17: a > $o,X15: a > $o] :
( ( ( X15 @ sK8 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X15 @ sK9 )
!= $true )
| ( ( sK7 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f23]) ).
thf(f23,plain,
! [X17: a > $o,X15: a > $o] :
( ( ( sK7 @ sK3 )
= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X15 @ sK9 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( ( X15 @ sK8 )
!= $true )
| ( $true
!= ( sK0 @ X17 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f99,plain,
( spl12_4
| spl12_5
| spl12_3 ),
inference(avatar_split_clause,[status(thm)],[f76,f88,f97,f92]) ).
thf(f76,plain,
! [X10: a > $o,X17: a > $o] :
( ( ( X10 @ sK4 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X10 ) )
| ( $true
= ( sK0 @ sK10 ) )
| ( ( X10 @ sK3 )
!= $true )
| ( $true
!= ( sK0 @ X17 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f33]) ).
thf(f33,plain,
! [X10: a > $o,X17: a > $o] :
( ( ( X10 @ sK3 )
!= $true )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X10 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
= ( sK0 @ sK10 ) )
| ( ( X10 @ sK4 )
!= $true )
| ( $true
!= ( sK0 @ X17 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f95,plain,
( spl12_3
| spl12_4
| spl12_2 ),
inference(avatar_split_clause,[status(thm)],[f77,f84,f92,f88]) ).
thf(f77,plain,
! [X17: a > $o] :
( ( $true
= ( sK6 @ sK4 ) )
| ( $true
= ( sK0 @ sK10 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f37]) ).
thf(f37,plain,
! [X17: a > $o] :
( ( $true
= ( sK6 @ sK4 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( $true
= ( sK0 @ sK10 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( X17 @ sK11 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
thf(f90,plain,
( spl12_1
| spl12_2
| spl12_3 ),
inference(avatar_split_clause,[status(thm)],[f78,f88,f84,f80]) ).
thf(f78,plain,
! [X17: a > $o] :
( ( $true
= ( sK6 @ sK4 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) )
| ( ( sK10 @ sK8 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f38]) ).
thf(f38,plain,
! [X17: a > $o] :
( ( ( sK10 @ sK8 )
= $true )
| ( $true
= ( sK6 @ sK4 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( X17 @ sK11 ) )
| ( $true
!= ( sK0 @ X17 ) ) ),
inference(cnf_transformation,[status(thm)],[f18]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.06 % Problem : SEV008^5 : TPTP v9.2.1. Released v4.0.0.
% 0.00/0.07 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.25 % Computer : n012.cluster.edu
% 0.07/0.25 % Model : x86_64 x86_64
% 0.07/0.25 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.07/0.25 % Memory : 8042.1875MB
% 0.07/0.25 % OS : Linux 3.10.0-693.el7.x86_64
% 0.07/0.25 % CPULimit : 300
% 0.07/0.25 % WCLimit : 300
% 0.07/0.25 % DateTime : Tue Feb 24 12:38:15 EST 2026
% 0.07/0.25 % CPUTime :
% 0.07/0.25 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.07/0.32 ---- Original DTF file ---
% 0.07/0.32 thf(spec,logic,$$dhol).
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 % File : SEV008^5 : TPTP v9.2.1. Released v4.0.0.
% 0.07/0.32 % Domain : Set Theory (Relations)
% 0.07/0.32 % Problem : TPS problem THM261
% 0.07/0.32 % Version : Especial.
% 0.07/0.32 % English : A partition defines an equivalence relation.
% 0.07/0.32
% 0.07/0.32 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.07/0.32 % Source : [Bro09]
% 0.07/0.32 % Names : tps_0491 [Bro09]
% 0.07/0.32 % : THM261 [TPS]
% 0.07/0.32
% 0.07/0.32 % Status : Theorem
% 0.07/0.32 % Rating : 0.00 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.00 v7.4.0, 0.11 v7.2.0, 0.00 v7.1.0, 0.25 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 v4.0.1, 0.67 v4.0.0
% 0.07/0.32 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.07/0.32 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.07/0.32 % Maximal formula atoms : 1 ( 1 avg)
% 0.07/0.32 % Number of connectives : 48 ( 0 ~; 0 |; 19 &; 24 @)
% 0.07/0.32 % ( 0 <=>; 5 =>; 0 <=; 0 <~>)
% 0.07/0.32 % Maximal formula depth : 14 ( 14 avg)
% 0.07/0.32 % Number of types : 2 ( 1 usr)
% 0.07/0.32 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.07/0.32 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.07/0.32 % Number of variables : 18 ( 0 ^; 10 !; 8 ?; 18 :)
% 0.07/0.32 % SPC : TH0_THM_EQU_NAR
% 0.07/0.32
% 0.07/0.32 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.07/0.32 % project in the Department of Mathematical Sciences at Carnegie
% 0.07/0.32 % Mellon University. Distributed under the Creative Commons copyleft
% 0.07/0.32 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.07/0.32 % : Polymorphic definitions expanded.
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 thf(a_type,type,
% 0.07/0.32 a: $tType ).
% 0.07/0.32
% 0.07/0.32 thf(cTHM261_pme,conjecture,
% 0.07/0.32 ! [P: ( a > $o ) > $o] :
% 0.07/0.32 ( ( ! [Xp: a > $o] :
% 0.07/0.32 ( ( P @ Xp )
% 0.07/0.32 => ? [Xz: a] : ( Xp @ Xz ) )
% 0.07/0.32 & ! [Xx: a] :
% 0.07/0.32 ? [Xp: a > $o] :
% 0.07/0.32 ( ( P @ Xp )
% 0.07/0.32 & ( Xp @ Xx )
% 0.07/0.32 & ! [Xq: a > $o] :
% 0.07/0.32 ( ( ( P @ Xq )
% 0.07/0.32 & ( Xq @ Xx ) )
% 0.07/0.32 => ( Xq = Xp ) ) ) )
% 0.07/0.32 => ( ! [Xx: a] :
% 0.07/0.32 ? [S: a > $o] :
% 0.07/0.32 ( ( P @ S )
% 0.07/0.32 & ( S @ Xx )
% 0.07/0.32 & ( S @ Xx ) )
% 0.07/0.32 & ! [Xx: a,Xy: a] :
% 0.07/0.32 ( ? [S: a > $o] :
% 0.07/0.32 ( ( P @ S )
% 0.07/0.32 & ( S @ Xx )
% 0.07/0.32 & ( S @ Xy ) )
% 0.07/0.32 => ? [S: a > $o] :
% 0.07/0.32 ( ( P @ S )
% 0.07/0.32 & ( S @ Xy )
% 0.07/0.32 & ( S @ Xx ) ) )
% 0.07/0.32 & ! [Xx: a,Xy: a,Xz: a] :
% 0.07/0.32 ( ( ? [S: a > $o] :
% 0.07/0.32 ( ( P @ S )
% 0.07/0.32 & ( S @ Xx )
% 0.07/0.32 & ( S @ Xy ) )
% 0.07/0.32 & ? [S: a > $o] :
% 0.07/0.32 ( ( P @ S )
% 0.07/0.32 & ( S @ Xy )
% 0.07/0.32 & ( S @ Xz ) ) )
% 0.07/0.32 => ? [S: a > $o] :
% 0.07/0.32 ( ( P @ S )
% 0.07/0.32 & ( S @ Xx )
% 0.07/0.32 & ( S @ Xz ) ) ) ) ) ).
% 0.07/0.32
% 0.07/0.32 %------------------------------------------------------------------------------
% 0.07/0.32 ------------------------
% 1.02/0.91 ---- Embedded in THF ---
% 1.02/0.91 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.02/0.91 %%% Generated on Tue Feb 24 12:38:16 EST 2026
% 1.02/0.91 %%% using '$$dhol' embedding, version 1.3.0.
% 1.02/0.91 %%% Logic specification used:
% 1.02/0.91 %%% thf(spec, logic, $$dhol).
% 1.02/0.91
% 1.02/0.91 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.SKX2tX6vzu/DTF2DTF7140.p
% See solution above
% 1.02/0.91 ------------------------
% 1.02/0.91 ---- Cleaned THF ---
% 1.02/0.92 thf(a_type,type,
% 1.02/0.92 a: $tType ).
% 1.02/0.92
% 1.02/0.92 thf(cTHM261_pme,conjecture,
% 1.02/0.92 ! [P: ( a > $o ) > $o] :
% 1.02/0.92 ( ( ! [Xp: a > $o] :
% 1.02/0.92 ( ( P @ Xp )
% 1.02/0.92 => ? [Xz: a] : ( Xp @ Xz ) )
% 1.02/0.92 & ! [Xx: a] :
% 1.02/0.92 ? [Xp: a > $o] :
% 1.02/0.92 ( ( P @ Xp )
% 1.02/0.92 & ( Xp @ Xx )
% 1.02/0.92 & ! [Xq: a > $o] :
% 1.02/0.92 ( ( ( P @ Xq )
% 1.02/0.92 & ( Xq @ Xx ) )
% 1.02/0.92 => ( Xq = Xp ) ) ) )
% 1.02/0.92 => ( ! [Xx: a] :
% 1.02/0.92 ? [S: a > $o] :
% 1.02/0.92 ( ( P @ S )
% 1.02/0.92 & ( S @ Xx )
% 1.02/0.92 & ( S @ Xx ) )
% 1.02/0.92 & ! [Xx: a,Xy: a] :
% 1.02/0.92 ( ? [S: a > $o] :
% 1.02/0.92 ( ( P @ S )
% 1.02/0.92 & ( S @ Xx )
% 1.02/0.92 & ( S @ Xy ) )
% 1.02/0.92 => ? [S: a > $o] :
% 1.02/0.92 ( ( P @ S )
% 1.02/0.92 & ( S @ Xy )
% 1.02/0.92 & ( S @ Xx ) ) )
% 1.02/0.92 & ! [Xx: a,Xy: a,Xz: a] :
% 1.02/0.92 ( ( ? [S: a > $o] :
% 1.02/0.92 ( ( P @ S )
% 1.02/0.92 & ( S @ Xx )
% 1.02/0.92 & ( S @ Xy ) )
% 1.02/0.92 & ? [S: a > $o] :
% 1.02/0.92 ( ( P @ S )
% 1.02/0.92 & ( S @ Xy )
% 1.02/0.92 & ( S @ Xz ) ) )
% 1.02/0.92 => ? [S: a > $o] :
% 1.02/0.92 ( ( P @ S )
% 1.02/0.92 & ( S @ Xx )
% 1.02/0.92 & ( S @ Xz ) ) ) ) ) ).
% 1.02/0.92 ------------------------
% 1.02/0.93 % (7334)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_7140 for (3000ds/275Mi)
% 1.02/0.93 % (7330)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_7140 for (3000ds/4Mi)
% 1.02/0.93 % (7329)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_7140 for (3000ds/183Mi)
% 1.02/0.93 % (7333)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_7140 for (3000ds/2Mi)
% 1.02/0.93 % (7335)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_7140 for (3000ds/18Mi)
% 1.02/0.93 % (7331)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_7140 for (3000ds/27Mi)
% 1.02/0.93 % (7333)Instruction limit reached!
% 1.02/0.93 % (7333)------------------------------
% 1.02/0.93 % (7333)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.93 % (7333)Termination reason: Unknown
% 1.02/0.93 % (7333)Termination phase: Saturation
% 1.02/0.93
% 1.02/0.93 % (7333)Memory used [KB]: 1023
% 1.02/0.93 % (7333)Time elapsed: 0.002 s
% 1.02/0.93 % (7333)Instructions burned: 3 (million)
% 1.02/0.93 % (7333)------------------------------
% 1.02/0.93 % (7333)------------------------------
% 1.02/0.93 % (7330)Instruction limit reached!
% 1.02/0.93 % (7330)------------------------------
% 1.02/0.93 % (7330)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.93 % (7330)Termination reason: Unknown
% 1.02/0.93 % (7330)Termination phase: Saturation
% 1.02/0.93
% 1.02/0.93 % (7330)Memory used [KB]: 5500
% 1.02/0.93 % (7330)Time elapsed: 0.003 s
% 1.02/0.93 % (7330)Instructions burned: 5 (million)
% 1.02/0.93 % (7330)------------------------------
% 1.02/0.93 % (7330)------------------------------
% 1.02/0.93 % (7332)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_7140 for (3000ds/2Mi)
% 1.02/0.93 % (7332)Instruction limit reached!
% 1.02/0.93 % (7332)------------------------------
% 1.02/0.93 % (7332)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.93 % (7332)Termination reason: Unknown
% 1.02/0.93 % (7332)Termination phase: Preprocessing 3
% 1.02/0.93
% 1.02/0.93 % (7332)Memory used [KB]: 1023
% 1.02/0.93 % (7332)Time elapsed: 0.002 s
% 1.02/0.93 % (7332)Instructions burned: 2 (million)
% 1.02/0.93 % (7332)------------------------------
% 1.02/0.93 % (7332)------------------------------
% 1.02/0.93 % (7335)Instruction limit reached!
% 1.02/0.93 % (7335)------------------------------
% 1.02/0.93 % (7335)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.93 % (7335)Termination reason: Unknown
% 1.02/0.93 % (7335)Termination phase: Saturation
% 1.02/0.93
% 1.02/0.93 % (7335)Memory used [KB]: 5628
% 1.02/0.93 % (7335)Time elapsed: 0.008 s
% 1.02/0.93 % (7335)Instructions burned: 20 (million)
% 1.02/0.93 % (7335)------------------------------
% 1.02/0.93 % (7335)------------------------------
% 1.02/0.94 % (7336)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_7140 for (2999ds/3Mi)
% 1.02/0.94 % (7336)Instruction limit reached!
% 1.02/0.94 % (7336)------------------------------
% 1.02/0.94 % (7336)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.94 % (7336)Termination reason: Unknown
% 1.02/0.94 % (7336)Termination phase: Saturation
% 1.02/0.94
% 1.02/0.94 % (7336)Memory used [KB]: 5500
% 1.02/0.94 % (7336)Time elapsed: 0.002 s
% 1.02/0.94 % (7336)Instructions burned: 3 (million)
% 1.02/0.94 % (7336)------------------------------
% 1.02/0.94 % (7336)------------------------------
% 1.02/0.94 % (7338)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_7140 for (2999ds/15Mi)
% 1.02/0.94 % (7331)First to succeed.
% 1.02/0.94 % (7337)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_7140 for (2999ds/37Mi)
% 1.02/0.94 % (7331)Refutation found. Thanks to Tanya!
% 1.02/0.94 % SZS status Theorem for DTF2THF_7140
% 1.02/0.94 % SZS output start Proof for DTF2THF_7140
% 1.02/0.94 thf(type_def_5, type, a: $tType).
% 1.02/0.94 thf(func_def_0, type, a: $tType).
% 1.02/0.94 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.02/0.94 thf(func_def_5, type, sK0: (a > $o) > $o).
% 1.02/0.94 thf(func_def_6, type, sK1: (a > $o) > a).
% 1.02/0.94 thf(func_def_7, type, sK2: a > a > $o).
% 1.02/0.94 thf(func_def_8, type, sK3: a).
% 1.02/0.94 thf(func_def_9, type, sK4: a).
% 1.02/0.94 thf(func_def_10, type, sK5: a).
% 1.02/0.94 thf(func_def_11, type, sK6: a > $o).
% 1.02/0.94 thf(func_def_12, type, sK7: a > $o).
% 1.02/0.94 thf(func_def_13, type, sK8: a).
% 1.02/0.94 thf(func_def_14, type, sK9: a).
% 1.02/0.94 thf(func_def_15, type, sK10: a > $o).
% 1.02/0.94 thf(func_def_16, type, sK11: a).
% 1.02/0.94 thf(func_def_18, type, ph13: !>[X0: $tType]:(X0)).
% 1.02/0.94 thf(f309,plain,(
% 1.02/0.94 $false),
% 1.02/0.94 inference(avatar_sat_refutation,[status(thm)],[f90,f95,f99,f107,f116,f121,f122,f123,f124,f125,f126,f127,f132,f133,f138,f139,f140,f141,f142,f143,f144,f145,f146,f147,f148,f149,f150,f151,f158,f167,f308])).
% 1.02/0.94 thf(f308,plain,(
% 1.02/0.94 ~spl12_2 | ~spl12_5 | ~spl12_6 | ~spl12_9 | ~spl12_10 | ~spl12_11 | ~spl12_12),
% 1.02/0.94 inference(avatar_contradiction_clause,[status(thm)],[f307])).
% 1.02/0.94 thf(f307,plain,(
% 1.02/0.94 $false | (~spl12_2 | ~spl12_5 | ~spl12_6 | ~spl12_9 | ~spl12_10 | ~spl12_11 | ~spl12_12)),
% 1.02/0.94 inference(trivial_inequality_removal,[status(thm)],[f305])).
% 1.02/0.94 thf(f305,plain,(
% 1.02/0.94 ($true = $false) | (~spl12_2 | ~spl12_5 | ~spl12_6 | ~spl12_9 | ~spl12_10 | ~spl12_11 | ~spl12_12)),
% 1.02/0.94 inference(backward_demodulation,[status(thm)],[f86,f295])).
% 1.02/0.94 thf(f295,plain,(
% 1.02/0.94 ((sK6 @ sK4) = $false) | (~spl12_5 | ~spl12_6 | ~spl12_9 | ~spl12_10 | ~spl12_11 | ~spl12_12)),
% 1.02/0.94 inference(trivial_inequality_removal,[status(thm)],[f292])).
% 1.02/0.94 thf(f292,plain,(
% 1.02/0.94 ((sK6 @ sK4) = $false) | ($true != $true) | (~spl12_5 | ~spl12_6 | ~spl12_9 | ~spl12_10 | ~spl12_11 | ~spl12_12)),
% 1.02/0.94 inference(superposition,[status(thm)],[f208,f277])).
% 1.02/0.94 thf(f277,plain,(
% 1.02/0.94 ( ! [X1 : a] : (((sK7 @ X1) = $true) | ((sK6 @ X1) = $false)) ) | (~spl12_9 | ~spl12_10 | ~spl12_11 | ~spl12_12)),
% 1.02/0.94 inference(binary_proxy_clausification,[status(thm)],[f276])).
% 1.02/0.94 thf(f276,plain,(
% 1.02/0.94 ( ! [X1 : a] : (((sK7 @ X1) = (sK6 @ X1))) ) | (~spl12_9 | ~spl12_10 | ~spl12_11 | ~spl12_12)),
% 1.02/0.94 inference(argument_congruence,[status(thm)],[f266])).
% 1.02/0.94 thf(f266,plain,(
% 1.02/0.94 (sK6 = sK7) | (~spl12_9 | ~spl12_10 | ~spl12_11 | ~spl12_12)),
% 1.02/0.94 inference(backward_demodulation,[status(thm)],[f234,f249])).
% 1.02/0.94 thf(f249,plain,(
% 1.02/0.94 (sK6 = (sK2 @ sK5)) | (~spl12_10 | ~spl12_12)),
% 1.02/0.94 inference(trivial_inequality_removal,[status(thm)],[f245])).
% 1.02/0.94 thf(f245,plain,(
% 1.02/0.94 (sK6 = (sK2 @ sK5)) | ($true != $true) | (~spl12_10 | ~spl12_12)),
% 1.02/0.94 inference(superposition,[status(thm)],[f225,f120])).
% 1.02/0.94 thf(f120,plain,(
% 1.02/0.94 ((sK6 @ sK5) = $true) | ~spl12_10),
% 1.02/0.94 inference(avatar_component_clause,[status(thm)],[f118])).
% 1.02/0.94 thf(f118,definition,(
% 1.02/0.94 spl12_10 <=> ((sK6 @ sK5) = $true)),
% 1.02/0.94 introduced(definition,[new_symbols(naming,[spl12_10])],[avatar_definition])).
% 1.02/0.94 thf(f225,plain,(
% 1.02/0.94 ( ! [X0 : a] : (($true != (sK6 @ X0)) | ((sK2 @ X0) = sK6)) ) | ~spl12_12),
% 1.02/0.94 inference(trivial_inequality_removal,[status(thm)],[f218])).
% 1.02/0.94 thf(f218,plain,(
% 1.02/0.94 ( ! [X0 : a] : (($true != (sK6 @ X0)) | ($true != $true) | ((sK2 @ X0) = sK6)) ) | ~spl12_12),
% 1.02/0.94 inference(superposition,[status(thm)],[f49,f137])).
% 1.02/0.94 thf(f137,plain,(
% 1.02/0.94 ((sK0 @ sK6) = $true) | ~spl12_12),
% 1.02/0.94 inference(avatar_component_clause,[status(thm)],[f135])).
% 1.02/0.94 thf(f135,definition,(
% 1.02/0.94 spl12_12 <=> ((sK0 @ sK6) = $true)),
% 1.02/0.94 introduced(definition,[new_symbols(naming,[spl12_12])],[avatar_definition])).
% 1.02/0.94 thf(f49,plain,(
% 1.02/0.94 ( ! [X3 : a,X5 : a > $o] : (((sK0 @ X5) != $true) | ((X5 @ X3) != $true) | ((sK2 @ X3) = X5)) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f18,plain,(
% 1.02/0.94 ! [X1 : a > $o] : (($true = (X1 @ (sK1 @ X1))) | ((sK0 @ X1) != $true)) & ! [X3 : a] : (! [X5 : a > $o] : (((sK2 @ X3) = X5) | ((sK0 @ X5) != $true) | ((X5 @ X3) != $true)) & ($true = (sK2 @ X3 @ X3)) & ((sK0 @ (sK2 @ X3)) = $true)) & (((((sK6 @ sK5) = $true) & ((sK0 @ sK6) = $true) & ($true = (sK6 @ sK4))) & ! [X10 : a > $o] : (((X10 @ sK3) != $true) | ((X10 @ sK4) != $true) | ($true != (sK0 @ X10))) & (((sK7 @ sK5) = $true) & ((sK7 @ sK3) = $true) & ($true = (sK0 @ sK7)))) | ((((sK10 @ sK8) = $true) & ($true = (sK0 @ sK10)) & ($true = (sK10 @ sK9))) & ! [X15 : a > $o] : (((X15 @ sK9) != $true) | ((sK0 @ X15) != $true) | ((X15 @ sK8) != $true))) | ! [X17 : a > $o] : (($true != (sK0 @ X17)) | ($true != (X17 @ sK11)) | ($true != (X17 @ sK11))))),
% 1.02/0.94 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11])],[f8,f17,f16,f15,f14,f13,f12,f11,f10,f9])).
% 1.02/0.94 thf(f9,plain,(
% 1.02/0.94 ? [X0 : (a > $o) > $o] : (! [X1 : a > $o] : (? [X2 : a] : ((X1 @ X2) = $true) | ((X0 @ X1) != $true)) & ! [X3 : a] : ? [X4 : a > $o] : (! [X5 : a > $o] : ((X4 = X5) | ((X0 @ X5) != $true) | ((X5 @ X3) != $true)) & ((X4 @ X3) = $true) & ((X0 @ X4) = $true)) & (? [X6 : a,X7 : a,X8 : a] : (? [X9 : a > $o] : (((X9 @ X8) = $true) & ((X0 @ X9) = $true) & ((X9 @ X7) = $true)) & ! [X10 : a > $o] : (((X10 @ X6) != $true) | ((X10 @ X7) != $true) | ((X0 @ X10) != $true)) & ? [X11 : a > $o] : (($true = (X11 @ X8)) & ($true = (X11 @ X6)) & ($true = (X0 @ X11)))) | ? [X12 : a,X13 : a] : (? [X14 : a > $o] : (((X14 @ X12) = $true) & ($true = (X0 @ X14)) & ((X14 @ X13) = $true)) & ! [X15 : a > $o] : (($true != (X15 @ X13)) | ($true != (X0 @ X15)) | ($true != (X15 @ X12)))) | ? [X16 : a] : ! [X17 : a > $o] : (((X0 @ X17) != $true) | ($true != (X17 @ X16)) | ($true != (X17 @ X16))))) => (! [X1 : a > $o] : (? [X2 : a] : ((X1 @ X2) = $true) | ((sK0 @ X1) != $true)) & ! [X3 : a] : ? [X4 : a > $o] : (! [X5 : a > $o] : ((X4 = X5) | ((sK0 @ X5) != $true) | ((X5 @ X3) != $true)) & ((X4 @ X3) = $true) & ((sK0 @ X4) = $true)) & (? [X8 : a,X7 : a,X6 : a] : (? [X9 : a > $o] : (((X9 @ X8) = $true) & ($true = (sK0 @ X9)) & ((X9 @ X7) = $true)) & ! [X10 : a > $o] : (((X10 @ X6) != $true) | ((X10 @ X7) != $true) | ($true != (sK0 @ X10))) & ? [X11 : a > $o] : (($true = (X11 @ X8)) & ($true = (X11 @ X6)) & ($true = (sK0 @ X11)))) | ? [X13 : a,X12 : a] : (? [X14 : a > $o] : (((X14 @ X12) = $true) & ($true = (sK0 @ X14)) & ((X14 @ X13) = $true)) & ! [X15 : a > $o] : (($true != (X15 @ X13)) | ((sK0 @ X15) != $true) | ($true != (X15 @ X12)))) | ? [X16 : a] : ! [X17 : a > $o] : (($true != (sK0 @ X17)) | ($true != (X17 @ X16)) | ($true != (X17 @ X16)))))),
% 1.02/0.94 introduced(definition,[],[choice_axiom])).
% 1.02/0.94 thf(f10,plain,(
% 1.02/0.94 ! [X1 : a > $o] : (? [X2 : a] : ((X1 @ X2) = $true) => ($true = (X1 @ (sK1 @ X1))))),
% 1.02/0.94 introduced(definition,[],[choice_axiom])).
% 1.02/0.94 thf(f11,plain,(
% 1.02/0.94 ! [X3 : a] : (? [X4 : a > $o] : (! [X5 : a > $o] : ((X4 = X5) | ((sK0 @ X5) != $true) | ((X5 @ X3) != $true)) & ((X4 @ X3) = $true) & ((sK0 @ X4) = $true)) => (! [X5 : a > $o] : (((sK2 @ X3) = X5) | ((sK0 @ X5) != $true) | ((X5 @ X3) != $true)) & ($true = (sK2 @ X3 @ X3)) & ((sK0 @ (sK2 @ X3)) = $true)))),
% 1.02/0.94 introduced(definition,[],[choice_axiom])).
% 1.02/0.94 thf(f12,plain,(
% 1.02/0.94 ? [X8 : a,X7 : a,X6 : a] : (? [X9 : a > $o] : (((X9 @ X8) = $true) & ($true = (sK0 @ X9)) & ((X9 @ X7) = $true)) & ! [X10 : a > $o] : (((X10 @ X6) != $true) | ((X10 @ X7) != $true) | ($true != (sK0 @ X10))) & ? [X11 : a > $o] : (($true = (X11 @ X8)) & ($true = (X11 @ X6)) & ($true = (sK0 @ X11)))) => (? [X9 : a > $o] : (((X9 @ sK5) = $true) & ($true = (sK0 @ X9)) & ($true = (X9 @ sK4))) & ! [X10 : a > $o] : (((X10 @ sK3) != $true) | ((X10 @ sK4) != $true) | ($true != (sK0 @ X10))) & ? [X11 : a > $o] : (($true = (X11 @ sK5)) & ($true = (X11 @ sK3)) & ($true = (sK0 @ X11))))),
% 1.02/0.94 introduced(definition,[],[choice_axiom])).
% 1.02/0.94 thf(f13,plain,(
% 1.02/0.94 ? [X9 : a > $o] : (((X9 @ sK5) = $true) & ($true = (sK0 @ X9)) & ($true = (X9 @ sK4))) => (((sK6 @ sK5) = $true) & ((sK0 @ sK6) = $true) & ($true = (sK6 @ sK4)))),
% 1.02/0.94 introduced(definition,[],[choice_axiom])).
% 1.02/0.94 thf(f14,plain,(
% 1.02/0.94 ? [X11 : a > $o] : (($true = (X11 @ sK5)) & ($true = (X11 @ sK3)) & ($true = (sK0 @ X11))) => (((sK7 @ sK5) = $true) & ((sK7 @ sK3) = $true) & ($true = (sK0 @ sK7)))),
% 1.02/0.94 introduced(definition,[],[choice_axiom])).
% 1.02/0.94 thf(f15,plain,(
% 1.02/0.94 ? [X13 : a,X12 : a] : (? [X14 : a > $o] : (((X14 @ X12) = $true) & ($true = (sK0 @ X14)) & ((X14 @ X13) = $true)) & ! [X15 : a > $o] : (($true != (X15 @ X13)) | ((sK0 @ X15) != $true) | ($true != (X15 @ X12)))) => (? [X14 : a > $o] : (($true = (X14 @ sK8)) & ($true = (sK0 @ X14)) & ((X14 @ sK9) = $true)) & ! [X15 : a > $o] : (((X15 @ sK9) != $true) | ((sK0 @ X15) != $true) | ((X15 @ sK8) != $true)))),
% 1.02/0.94 introduced(definition,[],[choice_axiom])).
% 1.02/0.94 thf(f16,plain,(
% 1.02/0.94 ? [X14 : a > $o] : (($true = (X14 @ sK8)) & ($true = (sK0 @ X14)) & ((X14 @ sK9) = $true)) => (((sK10 @ sK8) = $true) & ($true = (sK0 @ sK10)) & ($true = (sK10 @ sK9)))),
% 1.02/0.94 introduced(definition,[],[choice_axiom])).
% 1.02/0.94 thf(f17,plain,(
% 1.02/0.94 ? [X16 : a] : ! [X17 : a > $o] : (($true != (sK0 @ X17)) | ($true != (X17 @ X16)) | ($true != (X17 @ X16))) => ! [X17 : a > $o] : (($true != (sK0 @ X17)) | ($true != (X17 @ sK11)) | ($true != (X17 @ sK11)))),
% 1.02/0.94 introduced(definition,[],[choice_axiom])).
% 1.02/0.94 thf(f8,plain,(
% 1.02/0.94 ? [X0 : (a > $o) > $o] : (! [X1 : a > $o] : (? [X2 : a] : ((X1 @ X2) = $true) | ((X0 @ X1) != $true)) & ! [X3 : a] : ? [X4 : a > $o] : (! [X5 : a > $o] : ((X4 = X5) | ((X0 @ X5) != $true) | ((X5 @ X3) != $true)) & ((X4 @ X3) = $true) & ((X0 @ X4) = $true)) & (? [X6 : a,X7 : a,X8 : a] : (? [X9 : a > $o] : (((X9 @ X8) = $true) & ((X0 @ X9) = $true) & ((X9 @ X7) = $true)) & ! [X10 : a > $o] : (((X10 @ X6) != $true) | ((X10 @ X7) != $true) | ((X0 @ X10) != $true)) & ? [X11 : a > $o] : (($true = (X11 @ X8)) & ($true = (X11 @ X6)) & ($true = (X0 @ X11)))) | ? [X12 : a,X13 : a] : (? [X14 : a > $o] : (((X14 @ X12) = $true) & ($true = (X0 @ X14)) & ((X14 @ X13) = $true)) & ! [X15 : a > $o] : (($true != (X15 @ X13)) | ($true != (X0 @ X15)) | ($true != (X15 @ X12)))) | ? [X16 : a] : ! [X17 : a > $o] : (((X0 @ X17) != $true) | ($true != (X17 @ X16)) | ($true != (X17 @ X16)))))),
% 1.02/0.94 inference(rectify,[status(thm)],[f7])).
% 1.02/0.94 thf(f7,plain,(
% 1.02/0.94 ? [X0 : (a > $o) > $o] : (! [X1 : a > $o] : (? [X2 : a] : ((X1 @ X2) = $true) | ((X0 @ X1) != $true)) & ! [X3 : a] : ? [X4 : a > $o] : (! [X5 : a > $o] : ((X4 = X5) | ((X0 @ X5) != $true) | ((X5 @ X3) != $true)) & ((X4 @ X3) = $true) & ((X0 @ X4) = $true)) & (? [X13 : a,X12 : a,X14 : a] : (? [X16 : a > $o] : (($true = (X16 @ X14)) & ($true = (X0 @ X16)) & ((X16 @ X12) = $true)) & ! [X17 : a > $o] : (((X17 @ X13) != $true) | ($true != (X17 @ X12)) | ((X0 @ X17) != $true)) & ? [X15 : a > $o] : (($true = (X15 @ X14)) & ($true = (X15 @ X13)) & ($true = (X0 @ X15)))) | ? [X7 : a,X6 : a] : (? [X8 : a > $o] : (($true = (X8 @ X7)) & ($true = (X0 @ X8)) & ((X8 @ X6) = $true)) & ! [X9 : a > $o] : (($true != (X9 @ X6)) | ((X0 @ X9) != $true) | ((X9 @ X7) != $true))) | ? [X10 : a] : ! [X11 : a > $o] : (($true != (X0 @ X11)) | ((X11 @ X10) != $true) | ((X11 @ X10) != $true))))),
% 1.02/0.94 inference(flattening,[status(thm)],[f6])).
% 1.02/0.94 thf(f6,plain,(
% 1.02/0.94 ? [X0 : (a > $o) > $o] : ((? [X7 : a,X6 : a] : (? [X8 : a > $o] : (($true = (X8 @ X7)) & ($true = (X0 @ X8)) & ((X8 @ X6) = $true)) & ! [X9 : a > $o] : (($true != (X9 @ X6)) | ((X0 @ X9) != $true) | ((X9 @ X7) != $true))) | ? [X13 : a,X14 : a,X12 : a] : (! [X17 : a > $o] : (((X17 @ X13) != $true) | ($true != (X17 @ X12)) | ((X0 @ X17) != $true)) & (? [X16 : a > $o] : (($true = (X16 @ X14)) & ($true = (X0 @ X16)) & ((X16 @ X12) = $true)) & ? [X15 : a > $o] : (($true = (X15 @ X14)) & ($true = (X15 @ X13)) & ($true = (X0 @ X15))))) | ? [X10 : a] : ! [X11 : a > $o] : (($true != (X0 @ X11)) | ((X11 @ X10) != $true) | ((X11 @ X10) != $true))) & (! [X1 : a > $o] : (? [X2 : a] : ((X1 @ X2) = $true) | ((X0 @ X1) != $true)) & ! [X3 : a] : ? [X4 : a > $o] : (! [X5 : a > $o] : ((X4 = X5) | (((X0 @ X5) != $true) | ((X5 @ X3) != $true))) & ((X4 @ X3) = $true) & ((X0 @ X4) = $true))))),
% 1.02/0.94 inference(ennf_transformation,[status(thm)],[f5])).
% 1.02/0.94 thf(f5,plain,(
% 1.02/0.94 ~! [X0 : (a > $o) > $o] : ((! [X1 : a > $o] : (((X0 @ X1) = $true) => ? [X2 : a] : ((X1 @ X2) = $true)) & ! [X3 : a] : ? [X4 : a > $o] : (! [X5 : a > $o] : ((((X0 @ X5) = $true) & ((X5 @ X3) = $true)) => (X4 = X5)) & ((X4 @ X3) = $true) & ((X0 @ X4) = $true))) => (! [X7 : a,X6 : a] : (? [X8 : a > $o] : (($true = (X8 @ X7)) & ($true = (X0 @ X8)) & ((X8 @ X6) = $true)) => ? [X9 : a > $o] : (((X0 @ X9) = $true) & ($true = (X9 @ X6)) & ((X9 @ X7) = $true))) & ! [X13 : a,X14 : a,X12 : a] : ((? [X16 : a > $o] : (($true = (X16 @ X14)) & ($true = (X0 @ X16)) & ((X16 @ X12) = $true)) & ? [X15 : a > $o] : (($true = (X15 @ X14)) & ($true = (X15 @ X13)) & ($true = (X0 @ X15)))) => ? [X17 : a > $o] : (($true = (X17 @ X12)) & ((X17 @ X13) = $true) & ((X0 @ X17) = $true))) & ! [X10 : a] : ? [X11 : a > $o] : (($true = (X0 @ X11)) & ((X11 @ X10) = $true) & ((X11 @ X10) = $true))))),
% 1.02/0.94 inference(fool_elimination,[status(thm)],[f4])).
% 1.02/0.94 thf(f4,plain,(
% 1.02/0.94 ~! [X0 : (a > $o) > $o] : ((! [X1 : a > $o] : ((X0 @ X1) => ? [X2 : a] : (X1 @ X2)) & ! [X3 : a] : ? [X4 : a > $o] : ((X4 @ X3) & ! [X5 : a > $o] : (((X5 @ X3) & (X0 @ X5)) => (X4 = X5)) & (X0 @ X4))) => (! [X6 : a,X7 : a] : (? [X8 : a > $o] : ((X8 @ X7) & (X8 @ X6) & (X0 @ X8)) => ? [X9 : a > $o] : ((X9 @ X6) & (X0 @ X9) & (X9 @ X7))) & ! [X10 : a] : ? [X11 : a > $o] : ((X11 @ X10) & (X11 @ X10) & (X0 @ X11)) & ! [X12 : a,X13 : a,X14 : a] : ((? [X15 : a > $o] : ((X15 @ X14) & (X0 @ X15) & (X15 @ X13)) & ? [X16 : a > $o] : ((X16 @ X12) & (X0 @ X16) & (X16 @ X14))) => ? [X17 : a > $o] : ((X17 @ X12) & (X0 @ X17) & (X17 @ X13)))))),
% 1.02/0.94 inference(rectify,[status(thm)],[f2])).
% 1.02/0.94 thf(f2,negated_conjecture,(
% 1.02/0.94 ~! [X0 : (a > $o) > $o] : ((! [X1 : a > $o] : ((X0 @ X1) => ? [X2 : a] : (X1 @ X2)) & ! [X3 : a] : ? [X1 : a > $o] : ((X1 @ X3) & ! [X4 : a > $o] : (((X4 @ X3) & (X0 @ X4)) => (X1 = X4)) & (X0 @ X1))) => (! [X3 : a,X6 : a] : (? [X5 : a > $o] : ((X5 @ X6) & (X5 @ X3) & (X0 @ X5)) => ? [X5 : a > $o] : ((X5 @ X3) & (X0 @ X5) & (X5 @ X6))) & ! [X3 : a] : ? [X5 : a > $o] : ((X5 @ X3) & (X5 @ X3) & (X0 @ X5)) & ! [X2 : a,X3 : a,X6 : a] : ((? [X5 : a > $o] : ((X5 @ X6) & (X0 @ X5) & (X5 @ X3)) & ? [X5 : a > $o] : ((X5 @ X2) & (X0 @ X5) & (X5 @ X6))) => ? [X5 : a > $o] : ((X5 @ X2) & (X0 @ X5) & (X5 @ X3)))))),
% 1.02/0.94 inference(negated_conjecture,[status(cth)],[f1])).
% 1.02/0.94 thf(f1,conjecture,(
% 1.02/0.94 ! [X0 : (a > $o) > $o] : ((! [X1 : a > $o] : ((X0 @ X1) => ? [X2 : a] : (X1 @ X2)) & ! [X3 : a] : ? [X1 : a > $o] : ((X1 @ X3) & ! [X4 : a > $o] : (((X4 @ X3) & (X0 @ X4)) => (X1 = X4)) & (X0 @ X1))) => (! [X3 : a,X6 : a] : (? [X5 : a > $o] : ((X5 @ X6) & (X5 @ X3) & (X0 @ X5)) => ? [X5 : a > $o] : ((X5 @ X3) & (X0 @ X5) & (X5 @ X6))) & ! [X3 : a] : ? [X5 : a > $o] : ((X5 @ X3) & (X5 @ X3) & (X0 @ X5)) & ! [X2 : a,X3 : a,X6 : a] : ((? [X5 : a > $o] : ((X5 @ X6) & (X0 @ X5) & (X5 @ X3)) & ? [X5 : a > $o] : ((X5 @ X2) & (X0 @ X5) & (X5 @ X6))) => ? [X5 : a > $o] : ((X5 @ X2) & (X0 @ X5) & (X5 @ X3)))))),
% 1.02/0.94 file('/export/starexec/sandbox/tmp/tmp.SKX2tX6vzu/DTF2THF_7140.p',cTHM261_pme)).
% 1.02/0.94 thf(f234,plain,(
% 1.02/0.94 ((sK2 @ sK5) = sK7) | (~spl12_9 | ~spl12_11)),
% 1.02/0.94 inference(trivial_inequality_removal,[status(thm)],[f231])).
% 1.02/0.94 thf(f231,plain,(
% 1.02/0.94 ((sK2 @ sK5) = sK7) | ($true != $true) | (~spl12_9 | ~spl12_11)),
% 1.02/0.94 inference(superposition,[status(thm)],[f224,f131])).
% 1.02/0.94 thf(f131,plain,(
% 1.02/0.94 ((sK7 @ sK5) = $true) | ~spl12_11),
% 1.02/0.94 inference(avatar_component_clause,[status(thm)],[f129])).
% 1.02/0.94 thf(f129,definition,(
% 1.02/0.94 spl12_11 <=> ((sK7 @ sK5) = $true)),
% 1.02/0.94 introduced(definition,[new_symbols(naming,[spl12_11])],[avatar_definition])).
% 1.02/0.94 thf(f224,plain,(
% 1.02/0.94 ( ! [X0 : a] : (($true != (sK7 @ X0)) | ((sK2 @ X0) = sK7)) ) | ~spl12_9),
% 1.02/0.94 inference(trivial_inequality_removal,[status(thm)],[f219])).
% 1.02/0.94 thf(f219,plain,(
% 1.02/0.94 ( ! [X0 : a] : (((sK2 @ X0) = sK7) | ($true != (sK7 @ X0)) | ($true != $true)) ) | ~spl12_9),
% 1.02/0.94 inference(superposition,[status(thm)],[f49,f115])).
% 1.02/0.94 thf(f115,plain,(
% 1.02/0.94 ($true = (sK0 @ sK7)) | ~spl12_9),
% 1.02/0.94 inference(avatar_component_clause,[status(thm)],[f113])).
% 1.02/0.94 thf(f113,definition,(
% 1.02/0.94 spl12_9 <=> ($true = (sK0 @ sK7))),
% 1.02/0.94 introduced(definition,[new_symbols(naming,[spl12_9])],[avatar_definition])).
% 1.02/0.94 thf(f208,plain,(
% 1.02/0.94 ($true != (sK7 @ sK4)) | (~spl12_5 | ~spl12_6 | ~spl12_9)),
% 1.02/0.94 inference(trivial_inequality_removal,[status(thm)],[f207])).
% 1.02/0.94 thf(f207,plain,(
% 1.02/0.94 ($true != (sK7 @ sK4)) | ($true != $true) | (~spl12_5 | ~spl12_6 | ~spl12_9)),
% 1.02/0.94 inference(forward_demodulation,[status(thm)],[f199,f103])).
% 1.02/0.94 thf(f103,plain,(
% 1.02/0.94 ((sK7 @ sK3) = $true) | ~spl12_6),
% 1.02/0.94 inference(avatar_component_clause,[status(thm)],[f101])).
% 1.02/0.94 thf(f101,definition,(
% 1.02/0.94 spl12_6 <=> ((sK7 @ sK3) = $true)),
% 1.02/0.94 introduced(definition,[new_symbols(naming,[spl12_6])],[avatar_definition])).
% 1.02/0.94 thf(f199,plain,(
% 1.02/0.94 ($true != (sK7 @ sK4)) | ((sK7 @ sK3) != $true) | (~spl12_5 | ~spl12_9)),
% 1.02/0.94 inference(trivial_inequality_removal,[status(thm)],[f195])).
% 1.02/0.94 thf(f195,plain,(
% 1.02/0.94 ($true != (sK7 @ sK4)) | ($true != $true) | ((sK7 @ sK3) != $true) | (~spl12_5 | ~spl12_9)),
% 1.02/0.94 inference(superposition,[status(thm)],[f98,f115])).
% 1.02/0.94 thf(f98,plain,(
% 1.02/0.94 ( ! [X10 : a > $o] : (($true != (sK0 @ X10)) | ((X10 @ sK4) != $true) | ((X10 @ sK3) != $true)) ) | ~spl12_5),
% 1.02/0.94 inference(avatar_component_clause,[status(thm)],[f97])).
% 1.02/0.94 thf(f97,definition,(
% 1.02/0.94 spl12_5 <=> ! [X10 : a > $o] : (((X10 @ sK4) != $true) | ((X10 @ sK3) != $true) | ($true != (sK0 @ X10)))),
% 1.02/0.94 introduced(definition,[new_symbols(naming,[spl12_5])],[avatar_definition])).
% 1.02/0.94 thf(f86,plain,(
% 1.02/0.94 ($true = (sK6 @ sK4)) | ~spl12_2),
% 1.02/0.94 inference(avatar_component_clause,[status(thm)],[f84])).
% 1.02/0.94 thf(f84,definition,(
% 1.02/0.94 spl12_2 <=> ($true = (sK6 @ sK4))),
% 1.02/0.94 introduced(definition,[new_symbols(naming,[spl12_2])],[avatar_definition])).
% 1.02/0.94 thf(f167,plain,(
% 1.02/0.94 ~spl12_8 | ~spl12_1 | ~spl12_4 | ~spl12_7),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f166,f105,f92,f80,f109])).
% 1.02/0.94 thf(f109,definition,(
% 1.02/0.94 spl12_8 <=> ($true = (sK10 @ sK9))),
% 1.02/0.94 introduced(definition,[new_symbols(naming,[spl12_8])],[avatar_definition])).
% 1.02/0.94 thf(f80,definition,(
% 1.02/0.94 spl12_1 <=> ((sK10 @ sK8) = $true)),
% 1.02/0.94 introduced(definition,[new_symbols(naming,[spl12_1])],[avatar_definition])).
% 1.02/0.94 thf(f92,definition,(
% 1.02/0.94 spl12_4 <=> ($true = (sK0 @ sK10))),
% 1.02/0.94 introduced(definition,[new_symbols(naming,[spl12_4])],[avatar_definition])).
% 1.02/0.94 thf(f105,definition,(
% 1.02/0.94 spl12_7 <=> ! [X15 : a > $o] : (((X15 @ sK8) != $true) | ((X15 @ sK9) != $true) | ((sK0 @ X15) != $true))),
% 1.02/0.94 introduced(definition,[new_symbols(naming,[spl12_7])],[avatar_definition])).
% 1.02/0.94 thf(f166,plain,(
% 1.02/0.94 ($true != (sK10 @ sK9)) | (~spl12_1 | ~spl12_4 | ~spl12_7)),
% 1.02/0.94 inference(trivial_inequality_removal,[status(thm)],[f165])).
% 1.02/0.94 thf(f165,plain,(
% 1.02/0.94 ($true != $true) | ($true != (sK10 @ sK9)) | (~spl12_1 | ~spl12_4 | ~spl12_7)),
% 1.02/0.94 inference(forward_demodulation,[status(thm)],[f163,f82])).
% 1.02/0.94 thf(f82,plain,(
% 1.02/0.94 ((sK10 @ sK8) = $true) | ~spl12_1),
% 1.02/0.94 inference(avatar_component_clause,[status(thm)],[f80])).
% 1.02/0.94 thf(f163,plain,(
% 1.02/0.94 ($true != (sK10 @ sK9)) | ((sK10 @ sK8) != $true) | (~spl12_4 | ~spl12_7)),
% 1.02/0.94 inference(trivial_inequality_removal,[status(thm)],[f161])).
% 1.02/0.94 thf(f161,plain,(
% 1.02/0.94 ((sK10 @ sK8) != $true) | ($true != $true) | ($true != (sK10 @ sK9)) | (~spl12_4 | ~spl12_7)),
% 1.02/0.94 inference(superposition,[status(thm)],[f106,f94])).
% 1.02/0.94 thf(f94,plain,(
% 1.02/0.94 ($true = (sK0 @ sK10)) | ~spl12_4),
% 1.02/0.94 inference(avatar_component_clause,[status(thm)],[f92])).
% 1.02/0.94 thf(f106,plain,(
% 1.02/0.94 ( ! [X15 : a > $o] : (((sK0 @ X15) != $true) | ((X15 @ sK9) != $true) | ((X15 @ sK8) != $true)) ) | ~spl12_7),
% 1.02/0.94 inference(avatar_component_clause,[status(thm)],[f105])).
% 1.02/0.94 thf(f158,plain,(
% 1.02/0.94 ~spl12_3),
% 1.02/0.94 inference(avatar_contradiction_clause,[status(thm)],[f157])).
% 1.02/0.94 thf(f157,plain,(
% 1.02/0.94 $false | ~spl12_3),
% 1.02/0.94 inference(trivial_inequality_removal,[status(thm)],[f156])).
% 1.02/0.94 thf(f156,plain,(
% 1.02/0.94 ($true != $true) | ~spl12_3),
% 1.02/0.94 inference(superposition,[status(thm)],[f153,f48])).
% 1.02/0.94 thf(f48,plain,(
% 1.02/0.94 ( ! [X3 : a] : (($true = (sK2 @ X3 @ X3))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f153,plain,(
% 1.02/0.94 ( ! [X0 : a] : (((sK2 @ X0 @ sK11) != $true)) ) | ~spl12_3),
% 1.02/0.94 inference(trivial_inequality_removal,[status(thm)],[f152])).
% 1.02/0.94 thf(f152,plain,(
% 1.02/0.94 ( ! [X0 : a] : (((sK2 @ X0 @ sK11) != $true) | ($true != $true)) ) | ~spl12_3),
% 1.02/0.94 inference(superposition,[status(thm)],[f89,f47])).
% 1.02/0.94 thf(f47,plain,(
% 1.02/0.94 ( ! [X3 : a] : (((sK0 @ (sK2 @ X3)) = $true)) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f89,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (sK0 @ X17)) | ($true != (X17 @ sK11))) ) | ~spl12_3),
% 1.02/0.94 inference(avatar_component_clause,[status(thm)],[f88])).
% 1.02/0.94 thf(f88,definition,(
% 1.02/0.94 spl12_3 <=> ! [X17 : a > $o] : (($true != (X17 @ sK11)) | ($true != (sK0 @ X17)))),
% 1.02/0.94 introduced(definition,[new_symbols(naming,[spl12_3])],[avatar_definition])).
% 1.02/0.94 thf(f151,plain,(
% 1.02/0.94 spl12_4 | spl12_3 | spl12_12),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f51,f135,f88,f92])).
% 1.02/0.94 thf(f51,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (sK0 @ X17)) | ($true = (sK0 @ sK10)) | ($true != (X17 @ sK11)) | ((sK0 @ sK6) = $true)) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f41])).
% 1.02/0.94 thf(f41,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ((sK0 @ sK6) = $true) | ($true = (sK0 @ sK10)) | ($true != (X17 @ sK11))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f150,plain,(
% 1.02/0.94 spl12_5 | spl12_3 | spl12_1),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f52,f80,f88,f97])).
% 1.02/0.94 thf(f52,plain,(
% 1.02/0.94 ( ! [X10 : a > $o,X17 : a > $o] : (((X10 @ sK3) != $true) | ($true != (sK0 @ X17)) | ((X10 @ sK4) != $true) | ((sK10 @ sK8) = $true) | ($true != (sK0 @ X10)) | ($true != (X17 @ sK11))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f34])).
% 1.02/0.94 thf(f34,plain,(
% 1.02/0.94 ( ! [X10 : a > $o,X17 : a > $o] : (($true != (sK0 @ X10)) | ($true != (X17 @ sK11)) | ((X10 @ sK3) != $true) | ((X10 @ sK4) != $true) | ($true != (sK0 @ X17)) | ($true != (X17 @ sK11)) | ((sK10 @ sK8) = $true)) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f149,plain,(
% 1.02/0.94 spl12_10 | spl12_3 | spl12_7),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f53,f105,f88,f118])).
% 1.02/0.94 thf(f53,plain,(
% 1.02/0.94 ( ! [X17 : a > $o,X15 : a > $o] : (((X15 @ sK8) != $true) | ((sK6 @ sK5) = $true) | ((X15 @ sK9) != $true) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ((sK0 @ X15) != $true)) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f43])).
% 1.02/0.94 thf(f43,plain,(
% 1.02/0.94 ( ! [X17 : a > $o,X15 : a > $o] : (((X15 @ sK8) != $true) | ($true != (X17 @ sK11)) | ($true != (X17 @ sK11)) | ((X15 @ sK9) != $true) | ((sK0 @ X15) != $true) | ((sK6 @ sK5) = $true) | ($true != (sK0 @ X17))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f148,plain,(
% 1.02/0.94 spl12_3 | spl12_1 | spl12_6),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f54,f101,f80,f88])).
% 1.02/0.94 thf(f54,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (((sK7 @ sK3) = $true) | ((sK10 @ sK8) = $true) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f26])).
% 1.02/0.94 thf(f26,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ((sK7 @ sK3) = $true) | ((sK10 @ sK8) = $true) | ($true != (X17 @ sK11))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f147,plain,(
% 1.02/0.94 spl12_7 | spl12_3 | spl12_11),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f55,f129,f88,f105])).
% 1.02/0.94 thf(f55,plain,(
% 1.02/0.94 ( ! [X17 : a > $o,X15 : a > $o] : (((X15 @ sK9) != $true) | ((X15 @ sK8) != $true) | ((sK7 @ sK5) = $true) | ((sK0 @ X15) != $true) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f27])).
% 1.02/0.94 thf(f27,plain,(
% 1.02/0.94 ( ! [X17 : a > $o,X15 : a > $o] : (((X15 @ sK8) != $true) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ($true != (X17 @ sK11)) | ((sK0 @ X15) != $true) | ((X15 @ sK9) != $true) | ((sK7 @ sK5) = $true)) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f146,plain,(
% 1.02/0.94 spl12_3 | spl12_8 | spl12_5),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f56,f97,f109,f88])).
% 1.02/0.94 thf(f56,plain,(
% 1.02/0.94 ( ! [X10 : a > $o,X17 : a > $o] : (((X10 @ sK3) != $true) | ($true = (sK10 @ sK9)) | ($true != (sK0 @ X10)) | ($true != (X17 @ sK11)) | ((X10 @ sK4) != $true) | ($true != (sK0 @ X17))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f32])).
% 1.02/0.94 thf(f32,plain,(
% 1.02/0.94 ( ! [X10 : a > $o,X17 : a > $o] : (((X10 @ sK4) != $true) | ($true = (sK10 @ sK9)) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ($true != (sK0 @ X10)) | ((X10 @ sK3) != $true) | ($true != (X17 @ sK11))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f145,plain,(
% 1.02/0.94 spl12_11 | spl12_3 | spl12_1),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f57,f80,f88,f129])).
% 1.02/0.94 thf(f57,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (((sK10 @ sK8) = $true) | ($true != (sK0 @ X17)) | ($true != (X17 @ sK11)) | ((sK7 @ sK5) = $true)) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f30])).
% 1.02/0.94 thf(f30,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (sK0 @ X17)) | ((sK10 @ sK8) = $true) | ($true != (X17 @ sK11)) | ($true != (X17 @ sK11)) | ((sK7 @ sK5) = $true)) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f144,plain,(
% 1.02/0.94 spl12_12 | spl12_7 | spl12_3),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f58,f88,f105,f135])).
% 1.02/0.94 thf(f58,plain,(
% 1.02/0.94 ( ! [X17 : a > $o,X15 : a > $o] : (($true != (sK0 @ X17)) | ((X15 @ sK9) != $true) | ((sK0 @ X15) != $true) | ((X15 @ sK8) != $true) | ($true != (X17 @ sK11)) | ((sK0 @ sK6) = $true)) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f39])).
% 1.02/0.94 thf(f39,plain,(
% 1.02/0.94 ( ! [X17 : a > $o,X15 : a > $o] : (((X15 @ sK8) != $true) | ((sK0 @ sK6) = $true) | ($true != (sK0 @ X17)) | ($true != (X17 @ sK11)) | ((X15 @ sK9) != $true) | ((sK0 @ X15) != $true) | ($true != (X17 @ sK11))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f143,plain,(
% 1.02/0.94 spl12_8 | spl12_6 | spl12_3),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f59,f88,f101,f109])).
% 1.02/0.94 thf(f59,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (sK0 @ X17)) | ($true = (sK10 @ sK9)) | ($true != (X17 @ sK11)) | ((sK7 @ sK3) = $true)) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f24])).
% 1.02/0.94 thf(f24,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (((sK7 @ sK3) = $true) | ($true = (sK10 @ sK9)) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ($true != (X17 @ sK11))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f142,plain,(
% 1.02/0.94 spl12_3 | spl12_5 | spl12_7),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f60,f105,f97,f88])).
% 1.02/0.94 thf(f60,plain,(
% 1.02/0.94 ( ! [X10 : a > $o,X17 : a > $o,X15 : a > $o] : (((X15 @ sK8) != $true) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X10)) | ($true != (sK0 @ X17)) | ((X10 @ sK4) != $true) | ((X10 @ sK3) != $true) | ((sK0 @ X15) != $true) | ((X15 @ sK9) != $true)) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f31])).
% 1.02/0.94 thf(f31,plain,(
% 1.02/0.94 ( ! [X10 : a > $o,X17 : a > $o,X15 : a > $o] : (($true != (X17 @ sK11)) | ((X15 @ sK8) != $true) | ($true != (sK0 @ X10)) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ((X10 @ sK4) != $true) | ((sK0 @ X15) != $true) | ((X10 @ sK3) != $true) | ((X15 @ sK9) != $true)) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f141,plain,(
% 1.02/0.94 spl12_4 | spl12_11 | spl12_3),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f61,f88,f129,f92])).
% 1.02/0.94 thf(f61,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (sK0 @ X17)) | ($true != (X17 @ sK11)) | ((sK7 @ sK5) = $true) | ($true = (sK0 @ sK10))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f29])).
% 1.02/0.94 thf(f29,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (X17 @ sK11)) | ($true != (X17 @ sK11)) | ((sK7 @ sK5) = $true) | ($true = (sK0 @ sK10)) | ($true != (sK0 @ X17))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f140,plain,(
% 1.02/0.94 spl12_3 | spl12_8 | spl12_2),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f62,f84,f109,f88])).
% 1.02/0.94 thf(f62,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true = (sK6 @ sK4)) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ($true = (sK10 @ sK9))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f36])).
% 1.02/0.94 thf(f36,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ($true = (sK10 @ sK9)) | ($true != (X17 @ sK11)) | ($true = (sK6 @ sK4))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f139,plain,(
% 1.02/0.94 spl12_12 | spl12_3 | spl12_1),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f63,f80,f88,f135])).
% 1.02/0.94 thf(f63,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (((sK0 @ sK6) = $true) | ($true != (X17 @ sK11)) | ((sK10 @ sK8) = $true) | ($true != (sK0 @ X17))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f42])).
% 1.02/0.94 thf(f42,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (((sK0 @ sK6) = $true) | ($true != (sK0 @ X17)) | ($true != (X17 @ sK11)) | ((sK10 @ sK8) = $true) | ($true != (X17 @ sK11))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f138,plain,(
% 1.02/0.94 spl12_3 | spl12_8 | spl12_12),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f64,f135,f109,f88])).
% 1.02/0.94 thf(f64,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (X17 @ sK11)) | ((sK0 @ sK6) = $true) | ($true = (sK10 @ sK9)) | ($true != (sK0 @ X17))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f40])).
% 1.02/0.94 thf(f40,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true = (sK10 @ sK9)) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ($true != (X17 @ sK11)) | ((sK0 @ sK6) = $true)) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f133,plain,(
% 1.02/0.94 spl12_3 | spl12_4 | spl12_10),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f65,f118,f92,f88])).
% 1.02/0.94 thf(f65,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (sK0 @ X17)) | ($true = (sK0 @ sK10)) | ((sK6 @ sK5) = $true) | ($true != (X17 @ sK11))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f45])).
% 1.02/0.94 thf(f45,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true = (sK0 @ sK10)) | ($true != (sK0 @ X17)) | ($true != (X17 @ sK11)) | ($true != (X17 @ sK11)) | ((sK6 @ sK5) = $true)) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f132,plain,(
% 1.02/0.94 spl12_8 | spl12_3 | spl12_11),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f66,f129,f88,f109])).
% 1.02/0.94 thf(f66,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (sK0 @ X17)) | ($true = (sK10 @ sK9)) | ($true != (X17 @ sK11)) | ((sK7 @ sK5) = $true)) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f28])).
% 1.02/0.94 thf(f28,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (X17 @ sK11)) | ($true != (X17 @ sK11)) | ((sK7 @ sK5) = $true) | ($true != (sK0 @ X17)) | ($true = (sK10 @ sK9))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f127,plain,(
% 1.02/0.94 spl12_3 | spl12_2 | spl12_7),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f67,f105,f84,f88])).
% 1.02/0.94 thf(f67,plain,(
% 1.02/0.94 ( ! [X17 : a > $o,X15 : a > $o] : (((sK0 @ X15) != $true) | ((X15 @ sK8) != $true) | ($true != (X17 @ sK11)) | ((X15 @ sK9) != $true) | ($true = (sK6 @ sK4)) | ($true != (sK0 @ X17))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f35])).
% 1.02/0.94 thf(f35,plain,(
% 1.02/0.94 ( ! [X17 : a > $o,X15 : a > $o] : (($true != (sK0 @ X17)) | ($true = (sK6 @ sK4)) | ((sK0 @ X15) != $true) | ($true != (X17 @ sK11)) | ((X15 @ sK8) != $true) | ($true != (X17 @ sK11)) | ((X15 @ sK9) != $true)) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f126,plain,(
% 1.02/0.94 spl12_1 | spl12_10 | spl12_3),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f68,f88,f118,f80])).
% 1.02/0.94 thf(f68,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (((sK6 @ sK5) = $true) | ($true != (X17 @ sK11)) | ((sK10 @ sK8) = $true) | ($true != (sK0 @ X17))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f46])).
% 1.02/0.94 thf(f46,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (X17 @ sK11)) | ((sK10 @ sK8) = $true) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ((sK6 @ sK5) = $true)) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f125,plain,(
% 1.02/0.94 spl12_3 | spl12_9 | spl12_1),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f69,f80,f113,f88])).
% 1.02/0.94 thf(f69,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (sK0 @ X17)) | ($true != (X17 @ sK11)) | ((sK10 @ sK8) = $true) | ($true = (sK0 @ sK7))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f22])).
% 1.02/0.94 thf(f22,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true = (sK0 @ sK7)) | ($true != (sK0 @ X17)) | ($true != (X17 @ sK11)) | ($true != (X17 @ sK11)) | ((sK10 @ sK8) = $true)) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f124,plain,(
% 1.02/0.94 spl12_4 | spl12_3 | spl12_6),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f70,f101,f88,f92])).
% 1.02/0.94 thf(f70,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true = (sK0 @ sK10)) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ((sK7 @ sK3) = $true)) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f25])).
% 1.02/0.94 thf(f25,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ((sK7 @ sK3) = $true) | ($true != (X17 @ sK11)) | ($true = (sK0 @ sK10))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f123,plain,(
% 1.02/0.94 spl12_9 | spl12_3 | spl12_7),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f71,f105,f88,f113])).
% 1.02/0.94 thf(f71,plain,(
% 1.02/0.94 ( ! [X17 : a > $o,X15 : a > $o] : (($true = (sK0 @ sK7)) | ((X15 @ sK8) != $true) | ($true != (sK0 @ X17)) | ((X15 @ sK9) != $true) | ((sK0 @ X15) != $true) | ($true != (X17 @ sK11))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f19])).
% 1.02/0.94 thf(f19,plain,(
% 1.02/0.94 ( ! [X17 : a > $o,X15 : a > $o] : (($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ((X15 @ sK9) != $true) | ($true != (X17 @ sK11)) | ((X15 @ sK8) != $true) | ((sK0 @ X15) != $true) | ($true = (sK0 @ sK7))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f122,plain,(
% 1.02/0.94 spl12_4 | spl12_9 | spl12_3),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f72,f88,f113,f92])).
% 1.02/0.94 thf(f72,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (X17 @ sK11)) | ($true = (sK0 @ sK7)) | ($true != (sK0 @ X17)) | ($true = (sK0 @ sK10))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f21])).
% 1.02/0.94 thf(f21,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true = (sK0 @ sK10)) | ($true != (X17 @ sK11)) | ($true != (X17 @ sK11)) | ($true = (sK0 @ sK7)) | ($true != (sK0 @ X17))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f121,plain,(
% 1.02/0.94 spl12_8 | spl12_10 | spl12_3),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f73,f88,f118,f109])).
% 1.02/0.94 thf(f73,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (sK0 @ X17)) | ($true = (sK10 @ sK9)) | ((sK6 @ sK5) = $true) | ($true != (X17 @ sK11))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f44])).
% 1.02/0.94 thf(f44,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true != (sK0 @ X17)) | ($true != (X17 @ sK11)) | ($true = (sK10 @ sK9)) | ((sK6 @ sK5) = $true) | ($true != (X17 @ sK11))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f116,plain,(
% 1.02/0.94 spl12_8 | spl12_9 | spl12_3),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f74,f88,f113,f109])).
% 1.02/0.94 thf(f74,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true = (sK10 @ sK9)) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ($true = (sK0 @ sK7))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f20])).
% 1.02/0.94 thf(f20,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true = (sK10 @ sK9)) | ($true != (X17 @ sK11)) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ($true = (sK0 @ sK7))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f107,plain,(
% 1.02/0.94 spl12_6 | spl12_7 | spl12_3),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f75,f88,f105,f101])).
% 1.02/0.94 thf(f75,plain,(
% 1.02/0.94 ( ! [X17 : a > $o,X15 : a > $o] : (((X15 @ sK8) != $true) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ((sK0 @ X15) != $true) | ((X15 @ sK9) != $true) | ((sK7 @ sK3) = $true)) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f23])).
% 1.02/0.94 thf(f23,plain,(
% 1.02/0.94 ( ! [X17 : a > $o,X15 : a > $o] : (((sK7 @ sK3) = $true) | ((sK0 @ X15) != $true) | ((X15 @ sK9) != $true) | ($true != (X17 @ sK11)) | ($true != (X17 @ sK11)) | ((X15 @ sK8) != $true) | ($true != (sK0 @ X17))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f99,plain,(
% 1.02/0.94 spl12_4 | spl12_5 | spl12_3),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f76,f88,f97,f92])).
% 1.02/0.94 thf(f76,plain,(
% 1.02/0.94 ( ! [X10 : a > $o,X17 : a > $o] : (((X10 @ sK4) != $true) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X10)) | ($true = (sK0 @ sK10)) | ((X10 @ sK3) != $true) | ($true != (sK0 @ X17))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f33])).
% 1.02/0.94 thf(f33,plain,(
% 1.02/0.94 ( ! [X10 : a > $o,X17 : a > $o] : (((X10 @ sK3) != $true) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X10)) | ($true != (X17 @ sK11)) | ($true = (sK0 @ sK10)) | ((X10 @ sK4) != $true) | ($true != (sK0 @ X17))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f95,plain,(
% 1.02/0.94 spl12_3 | spl12_4 | spl12_2),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f77,f84,f92,f88])).
% 1.02/0.94 thf(f77,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true = (sK6 @ sK4)) | ($true = (sK0 @ sK10)) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17))) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f37])).
% 1.02/0.94 thf(f37,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true = (sK6 @ sK4)) | ($true != (sK0 @ X17)) | ($true = (sK0 @ sK10)) | ($true != (X17 @ sK11)) | ($true != (X17 @ sK11))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 thf(f90,plain,(
% 1.02/0.94 spl12_1 | spl12_2 | spl12_3),
% 1.02/0.94 inference(avatar_split_clause,[status(thm)],[f78,f88,f84,f80])).
% 1.02/0.94 thf(f78,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (($true = (sK6 @ sK4)) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17)) | ((sK10 @ sK8) = $true)) )),
% 1.02/0.94 inference(duplicate_literal_removal,[status(thm)],[f38])).
% 1.02/0.94 thf(f38,plain,(
% 1.02/0.94 ( ! [X17 : a > $o] : (((sK10 @ sK8) = $true) | ($true = (sK6 @ sK4)) | ($true != (X17 @ sK11)) | ($true != (X17 @ sK11)) | ($true != (sK0 @ X17))) )),
% 1.02/0.94 inference(cnf_transformation,[status(thm)],[f18])).
% 1.02/0.94 % SZS output end Proof for DTF2THF_7140
% 1.02/0.94 % (7331)------------------------------
% 1.02/0.94 % (7331)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.02/0.94 % (7331)Termination reason: Refutation
% 1.02/0.94
% 1.02/0.94 % (7331)Memory used [KB]: 5756
% 1.02/0.94 % (7331)Time elapsed: 0.016 s
% 1.02/0.94 % (7331)Instructions burned: 25 (million)
% 1.02/0.94 % (7331)------------------------------
% 1.02/0.94 % (7331)------------------------------
% 1.02/0.94 % (7328)Success in time 0.017 s
%------------------------------------------------------------------------------