%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV009^5 : 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 : n026.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 1.52s 1.29s
% Output : Refutation 1.52s
% Verified :
% SZS Type : Refutation
% Derivation depth : 21
% Number of leaves : 21
% Syntax : Number of formulae : 157 ( 7 unt; 0 typ; 12 def)
% Number of atoms : 1731 ( 606 equ; 0 cnn)
% Maximal formula atoms : 46 ( 11 avg)
% Number of connectives : 1806 ( 439 ~; 495 |; 178 &; 658 @)
% ( 12 <=>; 24 =>; 0 <=; 0 <~>)
% Maximal formula depth : 15 ( 6 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 195 ( 195 >; 0 *; 0 +; 0 <<)
% Number of symbols : 28 ( 25 usr; 20 con; 0-2 aty)
% Number of variables : 269 ( 0 ^; 171 !; 98 ?; 269 :)
% 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 > a > $o ).
thf(func_def_7,type,
sK2: a ).
thf(func_def_8,type,
sK3: a ).
thf(func_def_9,type,
sK4: a ).
thf(func_def_10,type,
sK5: a > $o ).
thf(func_def_11,type,
sK6: a > $o ).
thf(func_def_12,type,
sK7: a ).
thf(func_def_13,type,
sK8: a ).
thf(func_def_14,type,
sK9: a > $o ).
thf(func_def_15,type,
sK10: a ).
thf(func_def_17,type,
ph12:
!>[X0: $tType] : X0 ).
thf(f284,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f88,f96,f101,f110,f111,f112,f113,f117,f122,f127,f128,f129,f130,f131,f132,f133,f138,f139,f140,f141,f142,f143,f144,f145,f146,f147,f148,f149,f156,f163,f283]) ).
thf(f283,plain,
( ~ spl11_3
| ~ spl11_4
| ~ spl11_8
| ~ spl11_9
| ~ spl11_10
| ~ spl11_11
| ~ spl11_12 ),
inference(avatar_contradiction_clause,[status(thm)],[f282]) ).
thf(f282,plain,
( $false
| ~ spl11_3
| ~ spl11_4
| ~ spl11_8
| ~ spl11_9
| ~ spl11_10
| ~ spl11_11
| ~ spl11_12 ),
inference(trivial_inequality_removal,[status(thm)],[f279]) ).
thf(f279,plain,
( ( $true != $true )
| ~ spl11_3
| ~ spl11_4
| ~ spl11_8
| ~ spl11_9
| ~ spl11_10
| ~ spl11_11
| ~ spl11_12 ),
inference(superposition,[status(thm)],[f202,f275]) ).
thf(f275,plain,
( ( ( sK6 @ sK3 )
= $true )
| ~ spl11_3
| ~ spl11_8
| ~ spl11_10
| ~ spl11_11
| ~ spl11_12 ),
inference(trivial_inequality_removal,[status(thm)],[f272]) ).
thf(f272,plain,
( ( ( sK6 @ sK3 )
= $true )
| ( $false = $true )
| ~ spl11_3
| ~ spl11_8
| ~ spl11_10
| ~ spl11_11
| ~ spl11_12 ),
inference(superposition,[status(thm)],[f109,f250]) ).
thf(f250,plain,
( ! [X1: a] :
( ( $false
= ( sK5 @ X1 ) )
| ( ( sK6 @ X1 )
= $true ) )
| ~ spl11_3
| ~ spl11_10
| ~ spl11_11
| ~ spl11_12 ),
inference(binary_proxy_clausification,[status(thm)],[f249]) ).
thf(f249,plain,
( ! [X1: a] :
( ( sK6 @ X1 )
= ( sK5 @ X1 ) )
| ~ spl11_3
| ~ spl11_10
| ~ spl11_11
| ~ spl11_12 ),
inference(argument_congruence,[status(thm)],[f241]) ).
thf(f241,plain,
( ( sK5 = sK6 )
| ~ spl11_3
| ~ spl11_10
| ~ spl11_11
| ~ spl11_12 ),
inference(backward_demodulation,[status(thm)],[f223,f226]) ).
thf(f226,plain,
( ( ( sK1 @ sK4 )
= sK5 )
| ~ spl11_10
| ~ spl11_12 ),
inference(trivial_inequality_removal,[status(thm)],[f225]) ).
thf(f225,plain,
( ( $true != $true )
| ( ( sK1 @ sK4 )
= sK5 )
| ~ spl11_10
| ~ spl11_12 ),
inference(superposition,[status(thm)],[f218,f137]) ).
thf(f137,plain,
( ( ( sK5 @ sK4 )
= $true )
| ~ spl11_12 ),
inference(avatar_component_clause,[status(thm)],[f135]) ).
thf(f135,definition,
( spl11_12
<=> ( ( sK5 @ sK4 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl11_12])],[avatar_definition]) ).
thf(f218,plain,
( ! [X0: a] :
( ( ( sK5 @ X0 )
!= $true )
| ( sK5
= ( sK1 @ X0 ) ) )
| ~ spl11_10 ),
inference(trivial_inequality_removal,[status(thm)],[f213]) ).
thf(f213,plain,
( ! [X0: a] :
( ( $true != $true )
| ( sK5
= ( sK1 @ X0 ) )
| ( ( sK5 @ X0 )
!= $true ) )
| ~ spl11_10 ),
inference(superposition,[status(thm)],[f46,f121]) ).
thf(f121,plain,
( ( ( sK0 @ sK5 )
= $true )
| ~ spl11_10 ),
inference(avatar_component_clause,[status(thm)],[f119]) ).
thf(f119,definition,
( spl11_10
<=> ( ( sK0 @ sK5 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl11_10])],[avatar_definition]) ).
thf(f46,plain,
! [X3: a > $o,X1: a] :
( ( ( sK0 @ X3 )
!= $true )
| ( ( sK1 @ X1 )
= X3 )
| ( ( X3 @ X1 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ! [X1: a] :
( ( $true
= ( sK1 @ X1 @ X1 ) )
& ( $true
= ( sK0 @ ( sK1 @ X1 ) ) )
& ! [X3: a > $o] :
( ( ( sK1 @ X1 )
= X3 )
| ( ( X3 @ X1 )
!= $true )
| ( ( sK0 @ X3 )
!= $true ) ) )
& ( ( ( ( sK5 @ sK3 )
= $true )
& ( ( sK0 @ sK5 )
= $true )
& ( ( sK5 @ sK4 )
= $true )
& ( $true
= ( sK6 @ sK4 ) )
& ( $true
= ( sK6 @ sK2 ) )
& ( $true
= ( sK0 @ sK6 ) )
& ! [X9: a > $o] :
( ( $true
!= ( X9 @ sK2 ) )
| ( ( X9 @ sK3 )
!= $true )
| ( ( sK0 @ X9 )
!= $true ) ) )
| ( ! [X12: a > $o] :
( ( ( X12 @ sK7 )
!= $true )
| ( ( X12 @ sK8 )
!= $true )
| ( ( sK0 @ X12 )
!= $true ) )
& ( $true
= ( sK9 @ sK8 ) )
& ( $true
= ( sK9 @ sK7 ) )
& ( ( sK0 @ sK9 )
= $true ) )
| ! [X15: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10])],[f8,f16,f15,f14,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: ( a > $o ) > $o] :
( ! [X1: a] :
? [X2: a > $o] :
( ( ( X2 @ X1 )
= $true )
& ( ( X0 @ X2 )
= $true )
& ! [X3: a > $o] :
( ( X2 = X3 )
| ( ( X3 @ X1 )
!= $true )
| ( ( X0 @ X3 )
!= $true ) ) )
& ( ? [X4: a,X5: a,X6: a] :
( ? [X7: a > $o] :
( ( $true
= ( X7 @ X5 ) )
& ( $true
= ( X0 @ X7 ) )
& ( ( X7 @ X6 )
= $true ) )
& ? [X8: a > $o] :
( ( ( X8 @ X6 )
= $true )
& ( $true
= ( X8 @ X4 ) )
& ( ( X0 @ X8 )
= $true ) )
& ! [X9: a > $o] :
( ( $true
!= ( X9 @ X4 ) )
| ( ( X9 @ X5 )
!= $true )
| ( ( X0 @ X9 )
!= $true ) ) )
| ? [X10: a,X11: a] :
( ! [X12: a > $o] :
( ( $true
!= ( X12 @ X10 ) )
| ( ( X12 @ X11 )
!= $true )
| ( ( X0 @ X12 )
!= $true ) )
& ? [X13: a > $o] :
( ( ( X13 @ X11 )
= $true )
& ( ( X13 @ X10 )
= $true )
& ( $true
= ( X0 @ X13 ) ) ) )
| ? [X14: a] :
! [X15: a > $o] :
( ( ( X15 @ X14 )
!= $true )
| ( ( X0 @ X15 )
!= $true )
| ( ( X15 @ X14 )
!= $true ) ) ) )
=> ( ! [X1: a] :
? [X2: a > $o] :
( ( ( X2 @ X1 )
= $true )
& ( ( sK0 @ X2 )
= $true )
& ! [X3: a > $o] :
( ( X2 = X3 )
| ( ( X3 @ X1 )
!= $true )
| ( ( sK0 @ X3 )
!= $true ) ) )
& ( ? [X6: a,X5: a,X4: a] :
( ? [X7: a > $o] :
( ( $true
= ( X7 @ X5 ) )
& ( $true
= ( sK0 @ X7 ) )
& ( ( X7 @ X6 )
= $true ) )
& ? [X8: a > $o] :
( ( ( X8 @ X6 )
= $true )
& ( $true
= ( X8 @ X4 ) )
& ( ( sK0 @ X8 )
= $true ) )
& ! [X9: a > $o] :
( ( $true
!= ( X9 @ X4 ) )
| ( ( X9 @ X5 )
!= $true )
| ( ( sK0 @ X9 )
!= $true ) ) )
| ? [X11: a,X10: a] :
( ! [X12: a > $o] :
( ( $true
!= ( X12 @ X10 ) )
| ( ( X12 @ X11 )
!= $true )
| ( ( sK0 @ X12 )
!= $true ) )
& ? [X13: a > $o] :
( ( ( X13 @ X11 )
= $true )
& ( ( X13 @ X10 )
= $true )
& ( ( sK0 @ X13 )
= $true ) ) )
| ? [X14: a] :
! [X15: a > $o] :
( ( ( X15 @ X14 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X15 @ X14 )
!= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X1: a] :
( ? [X2: a > $o] :
( ( ( X2 @ X1 )
= $true )
& ( ( sK0 @ X2 )
= $true )
& ! [X3: a > $o] :
( ( X2 = X3 )
| ( ( X3 @ X1 )
!= $true )
| ( ( sK0 @ X3 )
!= $true ) ) )
=> ( ( $true
= ( sK1 @ X1 @ X1 ) )
& ( $true
= ( sK0 @ ( sK1 @ X1 ) ) )
& ! [X3: a > $o] :
( ( ( sK1 @ X1 )
= X3 )
| ( ( X3 @ X1 )
!= $true )
| ( ( sK0 @ X3 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
( ? [X6: a,X5: a,X4: a] :
( ? [X7: a > $o] :
( ( $true
= ( X7 @ X5 ) )
& ( $true
= ( sK0 @ X7 ) )
& ( ( X7 @ X6 )
= $true ) )
& ? [X8: a > $o] :
( ( ( X8 @ X6 )
= $true )
& ( $true
= ( X8 @ X4 ) )
& ( ( sK0 @ X8 )
= $true ) )
& ! [X9: a > $o] :
( ( $true
!= ( X9 @ X4 ) )
| ( ( X9 @ X5 )
!= $true )
| ( ( sK0 @ X9 )
!= $true ) ) )
=> ( ? [X7: a > $o] :
( ( $true
= ( X7 @ sK3 ) )
& ( $true
= ( sK0 @ X7 ) )
& ( ( X7 @ sK4 )
= $true ) )
& ? [X8: a > $o] :
( ( ( X8 @ sK4 )
= $true )
& ( $true
= ( X8 @ sK2 ) )
& ( ( sK0 @ X8 )
= $true ) )
& ! [X9: a > $o] :
( ( $true
!= ( X9 @ sK2 ) )
| ( ( X9 @ sK3 )
!= $true )
| ( ( sK0 @ X9 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
( ? [X7: a > $o] :
( ( $true
= ( X7 @ sK3 ) )
& ( $true
= ( sK0 @ X7 ) )
& ( ( X7 @ sK4 )
= $true ) )
=> ( ( ( sK5 @ sK3 )
= $true )
& ( ( sK0 @ sK5 )
= $true )
& ( ( sK5 @ sK4 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
( ? [X8: a > $o] :
( ( ( X8 @ sK4 )
= $true )
& ( $true
= ( X8 @ sK2 ) )
& ( ( sK0 @ X8 )
= $true ) )
=> ( ( $true
= ( sK6 @ sK4 ) )
& ( $true
= ( sK6 @ sK2 ) )
& ( $true
= ( sK0 @ sK6 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
( ? [X11: a,X10: a] :
( ! [X12: a > $o] :
( ( $true
!= ( X12 @ X10 ) )
| ( ( X12 @ X11 )
!= $true )
| ( ( sK0 @ X12 )
!= $true ) )
& ? [X13: a > $o] :
( ( ( X13 @ X11 )
= $true )
& ( ( X13 @ X10 )
= $true )
& ( ( sK0 @ X13 )
= $true ) ) )
=> ( ! [X12: a > $o] :
( ( ( X12 @ sK7 )
!= $true )
| ( ( X12 @ sK8 )
!= $true )
| ( ( sK0 @ X12 )
!= $true ) )
& ? [X13: a > $o] :
( ( ( X13 @ sK8 )
= $true )
& ( $true
= ( X13 @ sK7 ) )
& ( ( sK0 @ X13 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
( ? [X13: a > $o] :
( ( ( X13 @ sK8 )
= $true )
& ( $true
= ( X13 @ sK7 ) )
& ( ( sK0 @ X13 )
= $true ) )
=> ( ( $true
= ( sK9 @ sK8 ) )
& ( $true
= ( sK9 @ sK7 ) )
& ( ( sK0 @ sK9 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X14: a] :
! [X15: a > $o] :
( ( ( X15 @ X14 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X15 @ X14 )
!= $true ) )
=> ! [X15: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: ( a > $o ) > $o] :
( ! [X1: a] :
? [X2: a > $o] :
( ( ( X2 @ X1 )
= $true )
& ( ( X0 @ X2 )
= $true )
& ! [X3: a > $o] :
( ( X2 = X3 )
| ( ( X3 @ X1 )
!= $true )
| ( ( X0 @ X3 )
!= $true ) ) )
& ( ? [X4: a,X5: a,X6: a] :
( ? [X7: a > $o] :
( ( $true
= ( X7 @ X5 ) )
& ( $true
= ( X0 @ X7 ) )
& ( ( X7 @ X6 )
= $true ) )
& ? [X8: a > $o] :
( ( ( X8 @ X6 )
= $true )
& ( $true
= ( X8 @ X4 ) )
& ( ( X0 @ X8 )
= $true ) )
& ! [X9: a > $o] :
( ( $true
!= ( X9 @ X4 ) )
| ( ( X9 @ X5 )
!= $true )
| ( ( X0 @ X9 )
!= $true ) ) )
| ? [X10: a,X11: a] :
( ! [X12: a > $o] :
( ( $true
!= ( X12 @ X10 ) )
| ( ( X12 @ X11 )
!= $true )
| ( ( X0 @ X12 )
!= $true ) )
& ? [X13: a > $o] :
( ( ( X13 @ X11 )
= $true )
& ( ( X13 @ X10 )
= $true )
& ( $true
= ( X0 @ X13 ) ) ) )
| ? [X14: a] :
! [X15: a > $o] :
( ( ( X15 @ X14 )
!= $true )
| ( ( X0 @ X15 )
!= $true )
| ( ( X15 @ X14 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: ( a > $o ) > $o] :
( ! [X1: a] :
? [X2: a > $o] :
( ( ( X2 @ X1 )
= $true )
& ( ( X0 @ X2 )
= $true )
& ! [X3: a > $o] :
( ( X2 = X3 )
| ( ( X3 @ X1 )
!= $true )
| ( ( X0 @ X3 )
!= $true ) ) )
& ( ? [X7: a,X8: a,X6: a] :
( ? [X10: a > $o] :
( ( ( X10 @ X8 )
= $true )
& ( ( X0 @ X10 )
= $true )
& ( ( X10 @ X6 )
= $true ) )
& ? [X9: a > $o] :
( ( $true
= ( X9 @ X6 ) )
& ( ( X9 @ X7 )
= $true )
& ( ( X0 @ X9 )
= $true ) )
& ! [X11: a > $o] :
( ( ( X11 @ X7 )
!= $true )
| ( ( X11 @ X8 )
!= $true )
| ( ( X0 @ X11 )
!= $true ) ) )
| ? [X12: a,X13: a] :
( ! [X15: a > $o] :
( ( $true
!= ( X15 @ X12 ) )
| ( ( X15 @ X13 )
!= $true )
| ( ( X0 @ X15 )
!= $true ) )
& ? [X14: a > $o] :
( ( ( X14 @ X13 )
= $true )
& ( $true
= ( X14 @ X12 ) )
& ( ( X0 @ X14 )
= $true ) ) )
| ? [X4: a] :
! [X5: a > $o] :
( ( $true
!= ( X5 @ X4 ) )
| ( ( X0 @ X5 )
!= $true )
| ( $true
!= ( X5 @ X4 ) ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X0: ( a > $o ) > $o] :
( ( ? [X4: a] :
! [X5: a > $o] :
( ( $true
!= ( X5 @ X4 ) )
| ( ( X0 @ X5 )
!= $true )
| ( $true
!= ( X5 @ X4 ) ) )
| ? [X6: a,X7: a,X8: a] :
( ! [X11: a > $o] :
( ( ( X11 @ X7 )
!= $true )
| ( ( X11 @ X8 )
!= $true )
| ( ( X0 @ X11 )
!= $true ) )
& ? [X9: a > $o] :
( ( $true
= ( X9 @ X6 ) )
& ( ( X9 @ X7 )
= $true )
& ( ( X0 @ X9 )
= $true ) )
& ? [X10: a > $o] :
( ( ( X10 @ X8 )
= $true )
& ( ( X0 @ X10 )
= $true )
& ( ( X10 @ X6 )
= $true ) ) )
| ? [X12: a,X13: a] :
( ! [X15: a > $o] :
( ( $true
!= ( X15 @ X12 ) )
| ( ( X15 @ X13 )
!= $true )
| ( ( X0 @ X15 )
!= $true ) )
& ? [X14: a > $o] :
( ( ( X14 @ X13 )
= $true )
& ( $true
= ( X14 @ X12 ) )
& ( ( X0 @ X14 )
= $true ) ) ) )
& ! [X1: a] :
? [X2: a > $o] :
( ( ( X0 @ X2 )
= $true )
& ( ( X2 @ X1 )
= $true )
& ! [X3: a > $o] :
( ( X2 = X3 )
| ( ( X3 @ X1 )
!= $true )
| ( ( X0 @ X3 )
!= $true ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X0: ( a > $o ) > $o] :
( ! [X1: a] :
? [X2: a > $o] :
( ( ( X0 @ X2 )
= $true )
& ( ( X2 @ X1 )
= $true )
& ! [X3: a > $o] :
( ( ( ( X3 @ X1 )
= $true )
& ( ( X0 @ X3 )
= $true ) )
=> ( X2 = X3 ) ) )
=> ( ! [X4: a] :
? [X5: a > $o] :
( ( $true
= ( X5 @ X4 ) )
& ( $true
= ( X5 @ X4 ) )
& ( ( X0 @ X5 )
= $true ) )
& ! [X6: a,X7: a,X8: a] :
( ( ? [X9: a > $o] :
( ( $true
= ( X9 @ X6 ) )
& ( ( X9 @ X7 )
= $true )
& ( ( X0 @ X9 )
= $true ) )
& ? [X10: a > $o] :
( ( ( X10 @ X8 )
= $true )
& ( ( X0 @ X10 )
= $true )
& ( ( X10 @ X6 )
= $true ) ) )
=> ? [X11: a > $o] :
( ( ( X11 @ X7 )
= $true )
& ( ( X11 @ X8 )
= $true )
& ( ( X0 @ X11 )
= $true ) ) )
& ! [X12: a,X13: a] :
( ? [X14: a > $o] :
( ( ( X14 @ X13 )
= $true )
& ( $true
= ( X14 @ X12 ) )
& ( ( X0 @ X14 )
= $true ) )
=> ? [X15: a > $o] :
( ( ( X15 @ X13 )
= $true )
& ( ( X0 @ X15 )
= $true )
& ( $true
= ( X15 @ X12 ) ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: ( a > $o ) > $o] :
( ! [X1: a] :
? [X2: a > $o] :
( ( X0 @ X2 )
& ( X2 @ X1 )
& ! [X3: a > $o] :
( ( ( X0 @ X3 )
& ( X3 @ X1 ) )
=> ( X2 = X3 ) ) )
=> ( ! [X4: a] :
? [X5: a > $o] :
( ( X5 @ X4 )
& ( X0 @ X5 )
& ( X5 @ X4 ) )
& ! [X6: a,X7: a,X8: a] :
( ( ? [X9: a > $o] :
( ( X9 @ X6 )
& ( X9 @ X7 )
& ( X0 @ X9 ) )
& ? [X10: a > $o] :
( ( X10 @ X8 )
& ( X0 @ X10 )
& ( X10 @ X6 ) ) )
=> ? [X11: a > $o] :
( ( X0 @ X11 )
& ( X11 @ X7 )
& ( X11 @ X8 ) ) )
& ! [X12: a,X13: a] :
( ? [X14: a > $o] :
( ( X0 @ X14 )
& ( X14 @ X12 )
& ( X14 @ X13 ) )
=> ? [X15: a > $o] :
( ( X15 @ X13 )
& ( X15 @ X12 )
& ( X0 @ X15 ) ) ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: ( a > $o ) > $o] :
( ! [X1: a] :
? [X2: a > $o] :
( ( X0 @ X2 )
& ( X2 @ X1 )
& ! [X3: a > $o] :
( ( ( X0 @ X3 )
& ( X3 @ X1 ) )
=> ( X2 = X3 ) ) )
=> ( ! [X1: a] :
? [X4: a > $o] :
( ( X4 @ X1 )
& ( X0 @ X4 )
& ( X4 @ X1 ) )
& ! [X5: a,X6: a,X1: a] :
( ( ? [X4: a > $o] :
( ( X4 @ X5 )
& ( X4 @ X6 )
& ( X0 @ X4 ) )
& ? [X4: a > $o] :
( ( X4 @ X1 )
& ( X0 @ X4 )
& ( X4 @ X5 ) ) )
=> ? [X4: a > $o] :
( ( X0 @ X4 )
& ( X4 @ X6 )
& ( X4 @ X1 ) ) )
& ! [X5: a,X1: a] :
( ? [X4: a > $o] :
( ( X0 @ X4 )
& ( X4 @ X5 )
& ( X4 @ X1 ) )
=> ? [X4: a > $o] :
( ( X4 @ X1 )
& ( X4 @ X5 )
& ( X0 @ X4 ) ) ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: ( a > $o ) > $o] :
( ! [X1: a] :
? [X2: a > $o] :
( ( X0 @ X2 )
& ( X2 @ X1 )
& ! [X3: a > $o] :
( ( ( X0 @ X3 )
& ( X3 @ X1 ) )
=> ( X2 = X3 ) ) )
=> ( ! [X1: a] :
? [X4: a > $o] :
( ( X4 @ X1 )
& ( X0 @ X4 )
& ( X4 @ X1 ) )
& ! [X5: a,X6: a,X1: a] :
( ( ? [X4: a > $o] :
( ( X4 @ X5 )
& ( X4 @ X6 )
& ( X0 @ X4 ) )
& ? [X4: a > $o] :
( ( X4 @ X1 )
& ( X0 @ X4 )
& ( X4 @ X5 ) ) )
=> ? [X4: a > $o] :
( ( X0 @ X4 )
& ( X4 @ X6 )
& ( X4 @ X1 ) ) )
& ! [X5: a,X1: a] :
( ? [X4: a > $o] :
( ( X0 @ X4 )
& ( X4 @ X5 )
& ( X4 @ X1 ) )
=> ? [X4: a > $o] :
( ( X4 @ X1 )
& ( X4 @ X5 )
& ( X0 @ X4 ) ) ) ) ),
file('/export/starexec/sandbox/tmp/tmp.dpvmUEDf38/DTF2THF_10697.p',cTHM261_B_pme) ).
thf(f223,plain,
( ( ( sK1 @ sK4 )
= sK6 )
| ~ spl11_3
| ~ spl11_11 ),
inference(trivial_inequality_removal,[status(thm)],[f220]) ).
thf(f220,plain,
( ( $true != $true )
| ( ( sK1 @ sK4 )
= sK6 )
| ~ spl11_3
| ~ spl11_11 ),
inference(superposition,[status(thm)],[f216,f87]) ).
thf(f87,plain,
( ( $true
= ( sK6 @ sK4 ) )
| ~ spl11_3 ),
inference(avatar_component_clause,[status(thm)],[f85]) ).
thf(f85,definition,
( spl11_3
<=> ( $true
= ( sK6 @ sK4 ) ) ),
introduced(definition,[new_symbols(naming,[spl11_3])],[avatar_definition]) ).
thf(f216,plain,
( ! [X0: a] :
( ( ( sK6 @ X0 )
!= $true )
| ( sK6
= ( sK1 @ X0 ) ) )
| ~ spl11_11 ),
inference(trivial_inequality_removal,[status(thm)],[f212]) ).
thf(f212,plain,
( ! [X0: a] :
( ( sK6
= ( sK1 @ X0 ) )
| ( ( sK6 @ X0 )
!= $true )
| ( $true != $true ) )
| ~ spl11_11 ),
inference(superposition,[status(thm)],[f46,f126]) ).
thf(f126,plain,
( ( $true
= ( sK0 @ sK6 ) )
| ~ spl11_11 ),
inference(avatar_component_clause,[status(thm)],[f124]) ).
thf(f124,definition,
( spl11_11
<=> ( $true
= ( sK0 @ sK6 ) ) ),
introduced(definition,[new_symbols(naming,[spl11_11])],[avatar_definition]) ).
thf(f109,plain,
( ( ( sK5 @ sK3 )
= $true )
| ~ spl11_8 ),
inference(avatar_component_clause,[status(thm)],[f107]) ).
thf(f107,definition,
( spl11_8
<=> ( ( sK5 @ sK3 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl11_8])],[avatar_definition]) ).
thf(f202,plain,
( ( ( sK6 @ sK3 )
!= $true )
| ~ spl11_4
| ~ spl11_9
| ~ spl11_11 ),
inference(trivial_inequality_removal,[status(thm)],[f201]) ).
thf(f201,plain,
( ( $true != $true )
| ( ( sK6 @ sK3 )
!= $true )
| ~ spl11_4
| ~ spl11_9
| ~ spl11_11 ),
inference(forward_demodulation,[status(thm)],[f194,f92]) ).
thf(f92,plain,
( ( $true
= ( sK6 @ sK2 ) )
| ~ spl11_4 ),
inference(avatar_component_clause,[status(thm)],[f90]) ).
thf(f90,definition,
( spl11_4
<=> ( $true
= ( sK6 @ sK2 ) ) ),
introduced(definition,[new_symbols(naming,[spl11_4])],[avatar_definition]) ).
thf(f194,plain,
( ( ( sK6 @ sK3 )
!= $true )
| ( $true
!= ( sK6 @ sK2 ) )
| ~ spl11_9
| ~ spl11_11 ),
inference(trivial_inequality_removal,[status(thm)],[f188]) ).
thf(f188,plain,
( ( ( sK6 @ sK3 )
!= $true )
| ( $true != $true )
| ( $true
!= ( sK6 @ sK2 ) )
| ~ spl11_9
| ~ spl11_11 ),
inference(superposition,[status(thm)],[f116,f126]) ).
thf(f116,plain,
( ! [X9: a > $o] :
( ( ( sK0 @ X9 )
!= $true )
| ( $true
!= ( X9 @ sK2 ) )
| ( ( X9 @ sK3 )
!= $true ) )
| ~ spl11_9 ),
inference(avatar_component_clause,[status(thm)],[f115]) ).
thf(f115,definition,
( spl11_9
<=> ! [X9: a > $o] :
( ( ( X9 @ sK3 )
!= $true )
| ( $true
!= ( X9 @ sK2 ) )
| ( ( sK0 @ X9 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl11_9])],[avatar_definition]) ).
thf(f163,plain,
~ spl11_1,
inference(avatar_contradiction_clause,[status(thm)],[f162]) ).
thf(f162,plain,
( $false
| ~ spl11_1 ),
inference(trivial_inequality_removal,[status(thm)],[f161]) ).
thf(f161,plain,
( ( $true != $true )
| ~ spl11_1 ),
inference(superposition,[status(thm)],[f160,f48]) ).
thf(f48,plain,
! [X1: a] :
( $true
= ( sK1 @ X1 @ X1 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f160,plain,
( ! [X0: a] :
( ( sK1 @ X0 @ sK10 )
!= $true )
| ~ spl11_1 ),
inference(trivial_inequality_removal,[status(thm)],[f157]) ).
thf(f157,plain,
( ! [X0: a] :
( ( ( sK1 @ X0 @ sK10 )
!= $true )
| ( $true != $true ) )
| ~ spl11_1 ),
inference(superposition,[status(thm)],[f79,f47]) ).
thf(f47,plain,
! [X1: a] :
( $true
= ( sK0 @ ( sK1 @ X1 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f79,plain,
( ! [X15: a > $o] :
( ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) )
| ~ spl11_1 ),
inference(avatar_component_clause,[status(thm)],[f78]) ).
thf(f78,definition,
( spl11_1
<=> ! [X15: a > $o] :
( ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl11_1])],[avatar_definition]) ).
thf(f156,plain,
( ~ spl11_6
| ~ spl11_2
| ~ spl11_5
| ~ spl11_7 ),
inference(avatar_split_clause,[status(thm)],[f155,f103,f94,f81,f98]) ).
thf(f98,definition,
( spl11_6
<=> ( $true
= ( sK9 @ sK8 ) ) ),
introduced(definition,[new_symbols(naming,[spl11_6])],[avatar_definition]) ).
thf(f81,definition,
( spl11_2
<=> ( $true
= ( sK9 @ sK7 ) ) ),
introduced(definition,[new_symbols(naming,[spl11_2])],[avatar_definition]) ).
thf(f94,definition,
( spl11_5
<=> ! [X12: a > $o] :
( ( ( X12 @ sK8 )
!= $true )
| ( ( sK0 @ X12 )
!= $true )
| ( ( X12 @ sK7 )
!= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl11_5])],[avatar_definition]) ).
thf(f103,definition,
( spl11_7
<=> ( ( sK0 @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl11_7])],[avatar_definition]) ).
thf(f155,plain,
( ( $true
!= ( sK9 @ sK8 ) )
| ~ spl11_2
| ~ spl11_5
| ~ spl11_7 ),
inference(trivial_inequality_removal,[status(thm)],[f154]) ).
thf(f154,plain,
( ( $true != $true )
| ( $true
!= ( sK9 @ sK8 ) )
| ~ spl11_2
| ~ spl11_5
| ~ spl11_7 ),
inference(forward_demodulation,[status(thm)],[f152,f83]) ).
thf(f83,plain,
( ( $true
= ( sK9 @ sK7 ) )
| ~ spl11_2 ),
inference(avatar_component_clause,[status(thm)],[f81]) ).
thf(f152,plain,
( ( $true
!= ( sK9 @ sK8 ) )
| ( $true
!= ( sK9 @ sK7 ) )
| ~ spl11_5
| ~ spl11_7 ),
inference(trivial_inequality_removal,[status(thm)],[f151]) ).
thf(f151,plain,
( ( $true
!= ( sK9 @ sK8 ) )
| ( $true != $true )
| ( $true
!= ( sK9 @ sK7 ) )
| ~ spl11_5
| ~ spl11_7 ),
inference(superposition,[status(thm)],[f95,f105]) ).
thf(f105,plain,
( ( ( sK0 @ sK9 )
= $true )
| ~ spl11_7 ),
inference(avatar_component_clause,[status(thm)],[f103]) ).
thf(f95,plain,
( ! [X12: a > $o] :
( ( ( sK0 @ X12 )
!= $true )
| ( ( X12 @ sK7 )
!= $true )
| ( ( X12 @ sK8 )
!= $true ) )
| ~ spl11_5 ),
inference(avatar_component_clause,[status(thm)],[f94]) ).
thf(f149,plain,
( spl11_6
| spl11_10
| spl11_1 ),
inference(avatar_split_clause,[status(thm)],[f49,f78,f119,f98]) ).
thf(f49,plain,
! [X15: a > $o] :
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
= ( sK9 @ sK8 ) )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f40]) ).
thf(f40,plain,
! [X15: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK9 @ sK8 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f148,plain,
( spl11_1
| spl11_7
| spl11_9 ),
inference(avatar_split_clause,[status(thm)],[f50,f115,f103,f78]) ).
thf(f50,plain,
! [X9: a > $o,X15: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ sK9 )
= $true )
| ( ( sK0 @ X9 )
!= $true )
| ( ( X9 @ sK3 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X9 @ sK2 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f18]) ).
thf(f18,plain,
! [X9: a > $o,X15: a > $o] :
( ( ( sK0 @ sK9 )
= $true )
| ( $true
!= ( X9 @ sK2 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( X9 @ sK3 )
!= $true )
| ( ( sK0 @ X9 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f147,plain,
( spl11_6
| spl11_12
| spl11_1 ),
inference(avatar_split_clause,[status(thm)],[f51,f78,f135,f98]) ).
thf(f51,plain,
! [X15: a > $o] :
( ( ( sK0 @ X15 )
!= $true )
| ( ( sK5 @ sK4 )
= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( $true
= ( sK9 @ sK8 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f36]) ).
thf(f36,plain,
! [X15: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK5 @ sK4 )
= $true )
| ( $true
= ( sK9 @ sK8 ) )
| ( ( sK0 @ X15 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f146,plain,
( spl11_12
| spl11_5
| spl11_1 ),
inference(avatar_split_clause,[status(thm)],[f52,f78,f94,f135]) ).
thf(f52,plain,
! [X15: a > $o,X12: a > $o] :
( ( ( X12 @ sK8 )
!= $true )
| ( ( sK5 @ sK4 )
= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X12 @ sK7 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X12 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f37]) ).
thf(f37,plain,
! [X15: a > $o,X12: a > $o] :
( ( ( sK0 @ X12 )
!= $true )
| ( ( sK5 @ sK4 )
= $true )
| ( ( X12 @ sK7 )
!= $true )
| ( ( X12 @ sK8 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f145,plain,
( spl11_6
| spl11_1
| spl11_8 ),
inference(avatar_split_clause,[status(thm)],[f53,f107,f78,f98]) ).
thf(f53,plain,
! [X15: a > $o] :
( ( $true
= ( sK9 @ sK8 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK5 @ sK3 )
= $true )
| ( ( sK0 @ X15 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f44]) ).
thf(f44,plain,
! [X15: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( ( sK5 @ sK3 )
= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( $true
= ( sK9 @ sK8 ) )
| ( ( sK0 @ X15 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f144,plain,
( spl11_7
| spl11_4
| spl11_1 ),
inference(avatar_split_clause,[status(thm)],[f54,f78,f90,f103]) ).
thf(f54,plain,
! [X15: a > $o] :
( ( $true
= ( sK6 @ sK2 ) )
| ( ( sK0 @ sK9 )
= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f26]) ).
thf(f26,plain,
! [X15: a > $o] :
( ( ( sK0 @ sK9 )
= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( $true
= ( sK6 @ sK2 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f143,plain,
( spl11_2
| spl11_1
| spl11_10 ),
inference(avatar_split_clause,[status(thm)],[f55,f119,f78,f81]) ).
thf(f55,plain,
! [X15: a > $o] :
( ( ( sK0 @ X15 )
!= $true )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
= ( sK9 @ sK7 ) )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f39]) ).
thf(f39,plain,
! [X15: a > $o] :
( ( $true
= ( sK9 @ sK7 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f142,plain,
( spl11_7
| spl11_1
| spl11_12 ),
inference(avatar_split_clause,[status(thm)],[f56,f135,f78,f103]) ).
thf(f56,plain,
! [X15: a > $o] :
( ( ( sK0 @ sK9 )
= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( ( sK5 @ sK4 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f34]) ).
thf(f34,plain,
! [X15: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( ( sK5 @ sK4 )
= $true )
| ( ( sK0 @ sK9 )
= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f141,plain,
( spl11_1
| spl11_6
| spl11_11 ),
inference(avatar_split_clause,[status(thm)],[f57,f124,f98,f78]) ).
thf(f57,plain,
! [X15: a > $o] :
( ( $true
= ( sK9 @ sK8 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
= ( sK0 @ sK6 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f24]) ).
thf(f24,plain,
! [X15: a > $o] :
( ( $true
= ( sK0 @ sK6 ) )
| ( $true
= ( sK9 @ sK8 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f140,plain,
( spl11_1
| spl11_2
| spl11_9 ),
inference(avatar_split_clause,[status(thm)],[f58,f115,f81,f78]) ).
thf(f58,plain,
! [X9: a > $o,X15: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X9 @ sK3 )
!= $true )
| ( ( sK0 @ X9 )
!= $true )
| ( $true
!= ( X9 @ sK2 ) )
| ( $true
= ( sK9 @ sK7 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f19]) ).
thf(f19,plain,
! [X9: a > $o,X15: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X9 )
!= $true )
| ( ( X9 @ sK3 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( $true
!= ( X9 @ sK2 ) )
| ( $true
= ( sK9 @ sK7 ) )
| ( ( sK0 @ X15 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f139,plain,
( spl11_11
| spl11_1
| spl11_7 ),
inference(avatar_split_clause,[status(thm)],[f59,f103,f78,f124]) ).
thf(f59,plain,
! [X15: a > $o] :
( ( ( sK0 @ X15 )
!= $true )
| ( $true
= ( sK0 @ sK6 ) )
| ( ( sK0 @ sK9 )
= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f22]) ).
thf(f22,plain,
! [X15: a > $o] :
( ( ( sK0 @ X15 )
!= $true )
| ( $true
= ( sK0 @ sK6 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ sK9 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f138,plain,
( spl11_1
| spl11_2
| spl11_12 ),
inference(avatar_split_clause,[status(thm)],[f60,f135,f81,f78]) ).
thf(f60,plain,
! [X15: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( ( sK5 @ sK4 )
= $true )
| ( $true
= ( sK9 @ sK7 ) )
| ( ( sK0 @ X15 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f35]) ).
thf(f35,plain,
! [X15: a > $o] :
( ( ( sK5 @ sK4 )
= $true )
| ( $true
= ( sK9 @ sK7 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f133,plain,
( spl11_11
| spl11_1
| spl11_5 ),
inference(avatar_split_clause,[status(thm)],[f61,f94,f78,f124]) ).
thf(f61,plain,
! [X15: a > $o,X12: a > $o] :
( ( ( X12 @ sK8 )
!= $true )
| ( $true
= ( sK0 @ sK6 ) )
| ( ( sK0 @ X12 )
!= $true )
| ( ( X12 @ sK7 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f25]) ).
thf(f25,plain,
! [X15: a > $o,X12: a > $o] :
( ( ( sK0 @ X15 )
!= $true )
| ( ( X12 @ sK7 )
!= $true )
| ( ( sK0 @ X12 )
!= $true )
| ( ( X12 @ sK8 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( $true
= ( sK0 @ sK6 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f132,plain,
( spl11_5
| spl11_8
| spl11_1 ),
inference(avatar_split_clause,[status(thm)],[f62,f78,f107,f94]) ).
thf(f62,plain,
! [X15: a > $o,X12: a > $o] :
( ( ( X12 @ sK8 )
!= $true )
| ( ( X12 @ sK7 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK5 @ sK3 )
= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( ( sK0 @ X12 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f45]) ).
thf(f45,plain,
! [X15: a > $o,X12: a > $o] :
( ( ( X12 @ sK7 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( X12 @ sK8 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK5 @ sK3 )
= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( ( sK0 @ X12 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f131,plain,
( spl11_4
| spl11_1
| spl11_2 ),
inference(avatar_split_clause,[status(thm)],[f63,f81,f78,f90]) ).
thf(f63,plain,
! [X15: a > $o] :
( ( $true
= ( sK6 @ sK2 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
= ( sK9 @ sK7 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f27]) ).
thf(f27,plain,
! [X15: a > $o] :
( ( $true
= ( sK9 @ sK7 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( $true
= ( sK6 @ sK2 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f130,plain,
( spl11_5
| spl11_9
| spl11_1 ),
inference(avatar_split_clause,[status(thm)],[f64,f78,f115,f94]) ).
thf(f64,plain,
! [X9: a > $o,X15: a > $o,X12: a > $o] :
( ( ( X12 @ sK8 )
!= $true )
| ( ( X9 @ sK3 )
!= $true )
| ( ( X12 @ sK7 )
!= $true )
| ( ( sK0 @ X9 )
!= $true )
| ( $true
!= ( X9 @ sK2 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( ( sK0 @ X12 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f21]) ).
thf(f21,plain,
! [X9: a > $o,X15: a > $o,X12: a > $o] :
( ( $true
!= ( X9 @ sK2 ) )
| ( ( sK0 @ X12 )
!= $true )
| ( ( sK0 @ X9 )
!= $true )
| ( ( X12 @ sK7 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X9 @ sK3 )
!= $true )
| ( ( X12 @ sK8 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f129,plain,
( spl11_5
| spl11_1
| spl11_3 ),
inference(avatar_split_clause,[status(thm)],[f65,f85,f78,f94]) ).
thf(f65,plain,
! [X15: a > $o,X12: a > $o] :
( ( ( sK0 @ X15 )
!= $true )
| ( ( sK0 @ X12 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( $true
= ( sK6 @ sK4 ) )
| ( ( X12 @ sK8 )
!= $true )
| ( ( X12 @ sK7 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f33]) ).
thf(f33,plain,
! [X15: a > $o,X12: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( ( X12 @ sK7 )
!= $true )
| ( $true
= ( sK6 @ sK4 ) )
| ( ( sK0 @ X12 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X12 @ sK8 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f128,plain,
( spl11_1
| spl11_10
| spl11_7 ),
inference(avatar_split_clause,[status(thm)],[f66,f103,f119,f78]) ).
thf(f66,plain,
! [X15: a > $o] :
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( ( sK0 @ sK9 )
= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f38]) ).
thf(f38,plain,
! [X15: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ sK9 )
= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ X15 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f127,plain,
( spl11_11
| spl11_2
| spl11_1 ),
inference(avatar_split_clause,[status(thm)],[f67,f78,f81,f124]) ).
thf(f67,plain,
! [X15: a > $o] :
( ( $true
= ( sK0 @ sK6 ) )
| ( $true
= ( sK9 @ sK7 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f23]) ).
thf(f23,plain,
! [X15: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
= ( sK0 @ sK6 ) )
| ( $true
= ( sK9 @ sK7 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f122,plain,
( spl11_5
| spl11_1
| spl11_10 ),
inference(avatar_split_clause,[status(thm)],[f68,f119,f78,f94]) ).
thf(f68,plain,
! [X15: a > $o,X12: a > $o] :
( ( ( sK0 @ sK5 )
= $true )
| ( ( X12 @ sK7 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X12 @ sK8 )
!= $true )
| ( ( sK0 @ X12 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f41]) ).
thf(f41,plain,
! [X15: a > $o,X12: a > $o] :
( ( ( sK0 @ sK5 )
= $true )
| ( ( sK0 @ X12 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( X12 @ sK7 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X12 @ sK8 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f117,plain,
( spl11_1
| spl11_6
| spl11_9 ),
inference(avatar_split_clause,[status(thm)],[f69,f115,f98,f78]) ).
thf(f69,plain,
! [X9: a > $o,X15: a > $o] :
( ( ( sK0 @ X15 )
!= $true )
| ( $true
= ( sK9 @ sK8 ) )
| ( ( X9 @ sK3 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X9 )
!= $true )
| ( $true
!= ( X9 @ sK2 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f20]) ).
thf(f20,plain,
! [X9: a > $o,X15: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( $true
!= ( X9 @ sK2 ) )
| ( $true
= ( sK9 @ sK8 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( ( X9 @ sK3 )
!= $true )
| ( ( sK0 @ X9 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f113,plain,
( spl11_3
| spl11_1
| spl11_7 ),
inference(avatar_split_clause,[status(thm)],[f70,f103,f78,f85]) ).
thf(f70,plain,
! [X15: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( $true
= ( sK6 @ sK4 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( ( sK0 @ sK9 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f30]) ).
thf(f30,plain,
! [X15: a > $o] :
( ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ sK9 )
= $true )
| ( $true
= ( sK6 @ sK4 ) )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f112,plain,
( spl11_8
| spl11_2
| spl11_1 ),
inference(avatar_split_clause,[status(thm)],[f71,f78,f81,f107]) ).
thf(f71,plain,
! [X15: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( $true
= ( sK9 @ sK7 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( ( sK5 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f43]) ).
thf(f43,plain,
! [X15: a > $o] :
( ( $true
!= ( X15 @ sK10 ) )
| ( $true
= ( sK9 @ sK7 ) )
| ( ( sK5 @ sK3 )
= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X15 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f111,plain,
( spl11_3
| spl11_6
| spl11_1 ),
inference(avatar_split_clause,[status(thm)],[f72,f78,f98,f85]) ).
thf(f72,plain,
! [X15: a > $o] :
( ( $true
= ( sK9 @ sK8 ) )
| ( $true
= ( sK6 @ sK4 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f32]) ).
thf(f32,plain,
! [X15: a > $o] :
( ( ( sK0 @ X15 )
!= $true )
| ( $true
= ( sK9 @ sK8 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( $true
= ( sK6 @ sK4 ) )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f110,plain,
( spl11_1
| spl11_7
| spl11_8 ),
inference(avatar_split_clause,[status(thm)],[f73,f107,f103,f78]) ).
thf(f73,plain,
! [X15: a > $o] :
( ( ( sK0 @ sK9 )
= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK5 @ sK3 )
= $true )
| ( ( sK0 @ X15 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f42]) ).
thf(f42,plain,
! [X15: a > $o] :
( ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK5 @ sK3 )
= $true )
| ( ( sK0 @ sK9 )
= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f101,plain,
( spl11_1
| spl11_4
| spl11_6 ),
inference(avatar_split_clause,[status(thm)],[f74,f98,f90,f78]) ).
thf(f74,plain,
! [X15: a > $o] :
( ( ( sK0 @ X15 )
!= $true )
| ( $true
= ( sK9 @ sK8 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( $true
= ( sK6 @ sK2 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f28]) ).
thf(f28,plain,
! [X15: a > $o] :
( ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( $true
= ( sK9 @ sK8 ) )
| ( $true
= ( sK6 @ sK2 ) )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f96,plain,
( spl11_4
| spl11_1
| spl11_5 ),
inference(avatar_split_clause,[status(thm)],[f75,f94,f78,f90]) ).
thf(f75,plain,
! [X15: a > $o,X12: a > $o] :
( ( ( X12 @ sK8 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
= ( sK6 @ sK2 ) )
| ( ( X12 @ sK7 )
!= $true )
| ( ( sK0 @ X12 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f29]) ).
thf(f29,plain,
! [X15: a > $o,X12: a > $o] :
( ( ( X12 @ sK7 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( ( sK0 @ X12 )
!= $true )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
= ( sK6 @ sK2 ) )
| ( ( X12 @ sK8 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f88,plain,
( spl11_1
| spl11_2
| spl11_3 ),
inference(avatar_split_clause,[status(thm)],[f76,f85,f81,f78]) ).
thf(f76,plain,
! [X15: a > $o] :
( ( $true
= ( sK6 @ sK4 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
= ( sK9 @ sK7 ) )
| ( $true
!= ( X15 @ sK10 ) ) ),
inference(duplicate_literal_removal,[status(thm)],[f31]) ).
thf(f31,plain,
! [X15: a > $o] :
( ( $true
= ( sK6 @ sK4 ) )
| ( ( sK0 @ X15 )
!= $true )
| ( $true
!= ( X15 @ sK10 ) )
| ( $true
!= ( X15 @ sK10 ) )
| ( $true
= ( sK9 @ sK7 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV009^5 : TPTP v9.2.1. Released v4.0.0.
% 0.11/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.33 % Computer : n026.cluster.edu
% 0.16/0.33 % Model : x86_64 x86_64
% 0.16/0.33 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.33 % Memory : 8042.1875MB
% 0.16/0.33 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.33 % CPULimit : 300
% 0.16/0.33 % WCLimit : 300
% 0.16/0.33 % DateTime : Tue Feb 24 12:38:40 EST 2026
% 0.16/0.33 % CPUTime :
% 0.16/0.33 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.30/0.45 ---- Original DTF file ---
% 0.30/0.45 thf(spec,logic,$$dhol).
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 % File : SEV009^5 : TPTP v9.2.1. Released v4.0.0.
% 0.30/0.45 % Domain : Set Theory (Relations)
% 0.30/0.45 % Problem : TPS problem THM261-B
% 0.30/0.45 % Version : Especial.
% 0.30/0.45 % English : A partition defines an equivalence relation.
% 0.30/0.45
% 0.30/0.45 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.30/0.45 % Source : [Bro09]
% 0.30/0.45 % Names : tps_0511 [Bro09]
% 0.30/0.45 % : THM261-B [TPS]
% 0.30/0.45
% 0.30/0.45 % Status : Theorem
% 0.30/0.45 % 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
% 0.30/0.45 % Syntax : Number of formulae : 2 ( 1 unt; 1 typ; 0 def)
% 0.30/0.45 % Number of atoms : 1 ( 1 equ; 0 cnn)
% 0.30/0.45 % Maximal formula atoms : 1 ( 1 avg)
% 0.30/0.45 % Number of connectives : 44 ( 0 ~; 0 |; 18 &; 22 @)
% 0.30/0.45 % ( 0 <=>; 4 =>; 0 <=; 0 <~>)
% 0.30/0.45 % Maximal formula depth : 14 ( 14 avg)
% 0.30/0.45 % Number of types : 2 ( 1 usr)
% 0.30/0.45 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.30/0.45 % Number of symbols : 1 ( 0 usr; 0 con; 2-2 aty)
% 0.30/0.45 % Number of variables : 16 ( 0 ^; 9 !; 7 ?; 16 :)
% 0.30/0.45 % SPC : TH0_THM_EQU_NAR
% 0.30/0.45
% 0.30/0.45 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.30/0.45 % project in the Department of Mathematical Sciences at Carnegie
% 0.30/0.45 % Mellon University. Distributed under the Creative Commons copyleft
% 0.30/0.45 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.30/0.45 % : Polymorphic definitions expanded.
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 thf(a_type,type,
% 0.30/0.45 a: $tType ).
% 0.30/0.45
% 0.30/0.45 thf(cTHM261_B_pme,conjecture,
% 0.30/0.45 ! [P: ( a > $o ) > $o] :
% 0.30/0.45 ( ! [Xx: a] :
% 0.30/0.45 ? [Xp: a > $o] :
% 0.30/0.45 ( ( P @ Xp )
% 0.30/0.45 & ( Xp @ Xx )
% 0.30/0.45 & ! [Xq: a > $o] :
% 0.30/0.45 ( ( ( P @ Xq )
% 0.30/0.45 & ( Xq @ Xx ) )
% 0.30/0.45 => ( Xq = Xp ) ) )
% 0.30/0.45 => ( ! [Xx: a] :
% 0.30/0.45 ? [S: a > $o] :
% 0.30/0.45 ( ( P @ S )
% 0.30/0.45 & ( S @ Xx )
% 0.30/0.45 & ( S @ Xx ) )
% 0.30/0.45 & ! [Xx: a,Xy: a] :
% 0.30/0.45 ( ? [S: a > $o] :
% 0.30/0.45 ( ( P @ S )
% 0.30/0.45 & ( S @ Xx )
% 0.30/0.45 & ( S @ Xy ) )
% 0.30/0.45 => ? [S: a > $o] :
% 0.30/0.45 ( ( P @ S )
% 0.30/0.45 & ( S @ Xy )
% 0.30/0.45 & ( S @ Xx ) ) )
% 0.30/0.45 & ! [Xx: a,Xy: a,Xz: a] :
% 0.30/0.45 ( ( ? [S: a > $o] :
% 0.30/0.45 ( ( P @ S )
% 0.30/0.45 & ( S @ Xx )
% 0.30/0.45 & ( S @ Xy ) )
% 0.30/0.45 & ? [S: a > $o] :
% 0.30/0.45 ( ( P @ S )
% 0.30/0.45 & ( S @ Xy )
% 0.30/0.45 & ( S @ Xz ) ) )
% 0.30/0.45 => ? [S: a > $o] :
% 0.30/0.45 ( ( P @ S )
% 0.30/0.45 & ( S @ Xx )
% 0.30/0.45 & ( S @ Xz ) ) ) ) ) ).
% 0.30/0.45
% 0.30/0.45 %------------------------------------------------------------------------------
% 0.30/0.45 ------------------------
% 1.52/1.23 ---- Embedded in THF ---
% 1.52/1.24 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.52/1.24 %%% Generated on Tue Feb 24 12:38:41 EST 2026
% 1.52/1.24 %%% using '$$dhol' embedding, version 1.3.0.
% 1.52/1.24 %%% Logic specification used:
% 1.52/1.24 %%% thf(spec, logic, $$dhol).
% 1.52/1.24
% 1.52/1.24 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.dpvmUEDf38/DTF2DTF10697.p
% See solution above
% 1.52/1.24 ------------------------
% 1.52/1.25 ---- Cleaned THF ---
% 1.52/1.25 thf(a_type,type,
% 1.52/1.25 a: $tType ).
% 1.52/1.25
% 1.52/1.25 thf(cTHM261_B_pme,conjecture,
% 1.52/1.25 ! [P: ( a > $o ) > $o] :
% 1.52/1.25 ( ! [Xx: a] :
% 1.52/1.25 ? [Xp: a > $o] :
% 1.52/1.25 ( ( P @ Xp )
% 1.52/1.25 & ( Xp @ Xx )
% 1.52/1.25 & ! [Xq: a > $o] :
% 1.52/1.25 ( ( ( P @ Xq )
% 1.52/1.25 & ( Xq @ Xx ) )
% 1.52/1.25 => ( Xq = Xp ) ) )
% 1.52/1.25 => ( ! [Xx: a] :
% 1.52/1.25 ? [S: a > $o] :
% 1.52/1.25 ( ( P @ S )
% 1.52/1.25 & ( S @ Xx )
% 1.52/1.25 & ( S @ Xx ) )
% 1.52/1.25 & ! [Xx: a,Xy: a] :
% 1.52/1.25 ( ? [S: a > $o] :
% 1.52/1.25 ( ( P @ S )
% 1.52/1.25 & ( S @ Xx )
% 1.52/1.25 & ( S @ Xy ) )
% 1.52/1.25 => ? [S: a > $o] :
% 1.52/1.25 ( ( P @ S )
% 1.52/1.25 & ( S @ Xy )
% 1.52/1.25 & ( S @ Xx ) ) )
% 1.52/1.25 & ! [Xx: a,Xy: a,Xz: a] :
% 1.52/1.25 ( ( ? [S: a > $o] :
% 1.52/1.25 ( ( P @ S )
% 1.52/1.25 & ( S @ Xx )
% 1.52/1.25 & ( S @ Xy ) )
% 1.52/1.25 & ? [S: a > $o] :
% 1.52/1.25 ( ( P @ S )
% 1.52/1.25 & ( S @ Xy )
% 1.52/1.25 & ( S @ Xz ) ) )
% 1.52/1.25 => ? [S: a > $o] :
% 1.52/1.25 ( ( P @ S )
% 1.52/1.25 & ( S @ Xx )
% 1.52/1.25 & ( S @ Xz ) ) ) ) ) ).
% 1.52/1.25 ------------------------
% 1.52/1.26 % (10990)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_10697 for (3000ds/2Mi)
% 1.52/1.26 % (10990)Instruction limit reached!
% 1.52/1.26 % (10990)------------------------------
% 1.52/1.26 % (10990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.26 % (10990)Termination reason: Unknown
% 1.52/1.26 % (10990)Termination phase: Saturation
% 1.52/1.26
% 1.52/1.26 % (10990)Memory used [KB]: 1023
% 1.52/1.26 % (10990)Time elapsed: 0.002 s
% 1.52/1.26 % (10990)Instructions burned: 3 (million)
% 1.52/1.26 % (10990)------------------------------
% 1.52/1.26 % (10990)------------------------------
% 1.52/1.27 % (10986)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_10697 for (3000ds/183Mi)
% 1.52/1.27 % (10987)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_10697 for (3000ds/4Mi)
% 1.52/1.27 % (10988)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_10697 for (3000ds/27Mi)
% 1.52/1.27 % (10989)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_10697 for (3000ds/2Mi)
% 1.52/1.27 % (10991)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_10697 for (3000ds/275Mi)
% 1.52/1.27 % (10992)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_10697 for (3000ds/18Mi)
% 1.52/1.27 % (10989)Instruction limit reached!
% 1.52/1.27 % (10989)------------------------------
% 1.52/1.27 % (10989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.27 % (10989)Termination reason: Unknown
% 1.52/1.27 % (10989)Termination phase: Preprocessing 3
% 1.52/1.27
% 1.52/1.27 % (10989)Memory used [KB]: 895
% 1.52/1.27 % (10989)Time elapsed: 0.003 s
% 1.52/1.27 % (10989)Instructions burned: 2 (million)
% 1.52/1.27 % (10989)------------------------------
% 1.52/1.27 % (10989)------------------------------
% 1.52/1.27 % (10987)Instruction limit reached!
% 1.52/1.27 % (10987)------------------------------
% 1.52/1.27 % (10987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.27 % (10987)Termination reason: Unknown
% 1.52/1.27 % (10987)Termination phase: Saturation
% 1.52/1.27
% 1.52/1.27 % (10987)Memory used [KB]: 5500
% 1.52/1.27 % (10987)Time elapsed: 0.005 s
% 1.52/1.27 % (10987)Instructions burned: 4 (million)
% 1.52/1.27 % (10987)------------------------------
% 1.52/1.27 % (10987)------------------------------
% 1.52/1.27 % (10993)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10697 for (2999ds/3Mi)
% 1.52/1.27 % (10993)Instruction limit reached!
% 1.52/1.27 % (10993)------------------------------
% 1.52/1.27 % (10993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.27 % (10993)Termination reason: Unknown
% 1.52/1.27 % (10993)Termination phase: Saturation
% 1.52/1.27
% 1.52/1.27 % (10993)Memory used [KB]: 5500
% 1.52/1.27 % (10993)Time elapsed: 0.003 s
% 1.52/1.27 % (10993)Instructions burned: 3 (million)
% 1.52/1.27 % (10993)------------------------------
% 1.52/1.27 % (10993)------------------------------
% 1.52/1.28 % (10992)Instruction limit reached!
% 1.52/1.28 % (10992)------------------------------
% 1.52/1.28 % (10992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.28 % (10992)Termination reason: Unknown
% 1.52/1.28 % (10992)Termination phase: Saturation
% 1.52/1.28
% 1.52/1.28 % (10992)Memory used [KB]: 5628
% 1.52/1.28 % (10992)Time elapsed: 0.014 s
% 1.52/1.28 % (10992)Instructions burned: 18 (million)
% 1.52/1.28 % (10992)------------------------------
% 1.52/1.28 % (10992)------------------------------
% 1.52/1.28 % (10988)First to succeed.
% 1.52/1.28 % (10996)dis+21_1:1_cbe=off:cnfonf=off:fs=off:fsr=off:hud=1:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_10697 for (2999ds/3Mi)
% 1.52/1.28 % (10996)Instruction limit reached!
% 1.52/1.28 % (10996)------------------------------
% 1.52/1.28 % (10996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.28 % (10996)Termination reason: Unknown
% 1.52/1.28 % (10996)Termination phase: Saturation
% 1.52/1.28
% 1.52/1.28 % (10996)Memory used [KB]: 5500
% 1.52/1.28 % (10996)Time elapsed: 0.003 s
% 1.52/1.28 % (10996)Instructions burned: 3 (million)
% 1.52/1.28 % (10996)------------------------------
% 1.52/1.28 % (10996)------------------------------
% 1.52/1.28 % (10994)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_10697 for (2999ds/37Mi)
% 1.52/1.29 % (10988)Refutation found. Thanks to Tanya!
% 1.52/1.29 % SZS status Theorem for DTF2THF_10697
% 1.52/1.29 % SZS output start Proof for DTF2THF_10697
% 1.52/1.29 thf(type_def_5, type, a: $tType).
% 1.52/1.29 thf(func_def_0, type, a: $tType).
% 1.52/1.29 thf(func_def_2, type, vEPSILON: !>[X0: $tType]:((X0 > $o) > X0)).
% 1.52/1.29 thf(func_def_5, type, sK0: (a > $o) > $o).
% 1.52/1.29 thf(func_def_6, type, sK1: a > a > $o).
% 1.52/1.29 thf(func_def_7, type, sK2: a).
% 1.52/1.29 thf(func_def_8, type, sK3: a).
% 1.52/1.29 thf(func_def_9, type, sK4: a).
% 1.52/1.29 thf(func_def_10, type, sK5: a > $o).
% 1.52/1.29 thf(func_def_11, type, sK6: a > $o).
% 1.52/1.29 thf(func_def_12, type, sK7: a).
% 1.52/1.29 thf(func_def_13, type, sK8: a).
% 1.52/1.29 thf(func_def_14, type, sK9: a > $o).
% 1.52/1.29 thf(func_def_15, type, sK10: a).
% 1.52/1.29 thf(func_def_17, type, ph12: !>[X0: $tType]:(X0)).
% 1.52/1.29 thf(f284,plain,(
% 1.52/1.29 $false),
% 1.52/1.29 inference(avatar_sat_refutation,[status(thm)],[f88,f96,f101,f110,f111,f112,f113,f117,f122,f127,f128,f129,f130,f131,f132,f133,f138,f139,f140,f141,f142,f143,f144,f145,f146,f147,f148,f149,f156,f163,f283])).
% 1.52/1.29 thf(f283,plain,(
% 1.52/1.29 ~spl11_3 | ~spl11_4 | ~spl11_8 | ~spl11_9 | ~spl11_10 | ~spl11_11 | ~spl11_12),
% 1.52/1.29 inference(avatar_contradiction_clause,[status(thm)],[f282])).
% 1.52/1.29 thf(f282,plain,(
% 1.52/1.29 $false | (~spl11_3 | ~spl11_4 | ~spl11_8 | ~spl11_9 | ~spl11_10 | ~spl11_11 | ~spl11_12)),
% 1.52/1.29 inference(trivial_inequality_removal,[status(thm)],[f279])).
% 1.52/1.29 thf(f279,plain,(
% 1.52/1.29 ($true != $true) | (~spl11_3 | ~spl11_4 | ~spl11_8 | ~spl11_9 | ~spl11_10 | ~spl11_11 | ~spl11_12)),
% 1.52/1.29 inference(superposition,[status(thm)],[f202,f275])).
% 1.52/1.29 thf(f275,plain,(
% 1.52/1.29 ((sK6 @ sK3) = $true) | (~spl11_3 | ~spl11_8 | ~spl11_10 | ~spl11_11 | ~spl11_12)),
% 1.52/1.29 inference(trivial_inequality_removal,[status(thm)],[f272])).
% 1.52/1.29 thf(f272,plain,(
% 1.52/1.29 ((sK6 @ sK3) = $true) | ($false = $true) | (~spl11_3 | ~spl11_8 | ~spl11_10 | ~spl11_11 | ~spl11_12)),
% 1.52/1.29 inference(superposition,[status(thm)],[f109,f250])).
% 1.52/1.29 thf(f250,plain,(
% 1.52/1.29 ( ! [X1 : a] : (($false = (sK5 @ X1)) | ((sK6 @ X1) = $true)) ) | (~spl11_3 | ~spl11_10 | ~spl11_11 | ~spl11_12)),
% 1.52/1.29 inference(binary_proxy_clausification,[status(thm)],[f249])).
% 1.52/1.29 thf(f249,plain,(
% 1.52/1.29 ( ! [X1 : a] : (((sK6 @ X1) = (sK5 @ X1))) ) | (~spl11_3 | ~spl11_10 | ~spl11_11 | ~spl11_12)),
% 1.52/1.29 inference(argument_congruence,[status(thm)],[f241])).
% 1.52/1.29 thf(f241,plain,(
% 1.52/1.29 (sK5 = sK6) | (~spl11_3 | ~spl11_10 | ~spl11_11 | ~spl11_12)),
% 1.52/1.29 inference(backward_demodulation,[status(thm)],[f223,f226])).
% 1.52/1.29 thf(f226,plain,(
% 1.52/1.29 ((sK1 @ sK4) = sK5) | (~spl11_10 | ~spl11_12)),
% 1.52/1.29 inference(trivial_inequality_removal,[status(thm)],[f225])).
% 1.52/1.29 thf(f225,plain,(
% 1.52/1.29 ($true != $true) | ((sK1 @ sK4) = sK5) | (~spl11_10 | ~spl11_12)),
% 1.52/1.29 inference(superposition,[status(thm)],[f218,f137])).
% 1.52/1.29 thf(f137,plain,(
% 1.52/1.29 ((sK5 @ sK4) = $true) | ~spl11_12),
% 1.52/1.29 inference(avatar_component_clause,[status(thm)],[f135])).
% 1.52/1.29 thf(f135,definition,(
% 1.52/1.29 spl11_12 <=> ((sK5 @ sK4) = $true)),
% 1.52/1.29 introduced(definition,[new_symbols(naming,[spl11_12])],[avatar_definition])).
% 1.52/1.29 thf(f218,plain,(
% 1.52/1.29 ( ! [X0 : a] : (((sK5 @ X0) != $true) | (sK5 = (sK1 @ X0))) ) | ~spl11_10),
% 1.52/1.29 inference(trivial_inequality_removal,[status(thm)],[f213])).
% 1.52/1.29 thf(f213,plain,(
% 1.52/1.29 ( ! [X0 : a] : (($true != $true) | (sK5 = (sK1 @ X0)) | ((sK5 @ X0) != $true)) ) | ~spl11_10),
% 1.52/1.29 inference(superposition,[status(thm)],[f46,f121])).
% 1.52/1.29 thf(f121,plain,(
% 1.52/1.29 ((sK0 @ sK5) = $true) | ~spl11_10),
% 1.52/1.29 inference(avatar_component_clause,[status(thm)],[f119])).
% 1.52/1.29 thf(f119,definition,(
% 1.52/1.29 spl11_10 <=> ((sK0 @ sK5) = $true)),
% 1.52/1.29 introduced(definition,[new_symbols(naming,[spl11_10])],[avatar_definition])).
% 1.52/1.29 thf(f46,plain,(
% 1.52/1.29 ( ! [X3 : a > $o,X1 : a] : (((sK0 @ X3) != $true) | ((sK1 @ X1) = X3) | ((X3 @ X1) != $true)) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f17,plain,(
% 1.52/1.29 ! [X1 : a] : (($true = (sK1 @ X1 @ X1)) & ($true = (sK0 @ (sK1 @ X1))) & ! [X3 : a > $o] : (((sK1 @ X1) = X3) | ((X3 @ X1) != $true) | ((sK0 @ X3) != $true))) & (((((sK5 @ sK3) = $true) & ((sK0 @ sK5) = $true) & ((sK5 @ sK4) = $true)) & (($true = (sK6 @ sK4)) & ($true = (sK6 @ sK2)) & ($true = (sK0 @ sK6))) & ! [X9 : a > $o] : (($true != (X9 @ sK2)) | ((X9 @ sK3) != $true) | ((sK0 @ X9) != $true))) | (! [X12 : a > $o] : (((X12 @ sK7) != $true) | ((X12 @ sK8) != $true) | ((sK0 @ X12) != $true)) & (($true = (sK9 @ sK8)) & ($true = (sK9 @ sK7)) & ((sK0 @ sK9) = $true))) | ! [X15 : a > $o] : (($true != (X15 @ sK10)) | ((sK0 @ X15) != $true) | ($true != (X15 @ sK10))))),
% 1.52/1.29 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10])],[f8,f16,f15,f14,f13,f12,f11,f10,f9])).
% 1.52/1.29 thf(f9,plain,(
% 1.52/1.29 ? [X0 : (a > $o) > $o] : (! [X1 : a] : ? [X2 : a > $o] : (((X2 @ X1) = $true) & ((X0 @ X2) = $true) & ! [X3 : a > $o] : ((X2 = X3) | ((X3 @ X1) != $true) | ((X0 @ X3) != $true))) & (? [X4 : a,X5 : a,X6 : a] : (? [X7 : a > $o] : (($true = (X7 @ X5)) & ($true = (X0 @ X7)) & ((X7 @ X6) = $true)) & ? [X8 : a > $o] : (((X8 @ X6) = $true) & ($true = (X8 @ X4)) & ((X0 @ X8) = $true)) & ! [X9 : a > $o] : (($true != (X9 @ X4)) | ((X9 @ X5) != $true) | ((X0 @ X9) != $true))) | ? [X10 : a,X11 : a] : (! [X12 : a > $o] : (($true != (X12 @ X10)) | ((X12 @ X11) != $true) | ((X0 @ X12) != $true)) & ? [X13 : a > $o] : (((X13 @ X11) = $true) & ((X13 @ X10) = $true) & ($true = (X0 @ X13)))) | ? [X14 : a] : ! [X15 : a > $o] : (((X15 @ X14) != $true) | ((X0 @ X15) != $true) | ((X15 @ X14) != $true)))) => (! [X1 : a] : ? [X2 : a > $o] : (((X2 @ X1) = $true) & ((sK0 @ X2) = $true) & ! [X3 : a > $o] : ((X2 = X3) | ((X3 @ X1) != $true) | ((sK0 @ X3) != $true))) & (? [X6 : a,X5 : a,X4 : a] : (? [X7 : a > $o] : (($true = (X7 @ X5)) & ($true = (sK0 @ X7)) & ((X7 @ X6) = $true)) & ? [X8 : a > $o] : (((X8 @ X6) = $true) & ($true = (X8 @ X4)) & ((sK0 @ X8) = $true)) & ! [X9 : a > $o] : (($true != (X9 @ X4)) | ((X9 @ X5) != $true) | ((sK0 @ X9) != $true))) | ? [X11 : a,X10 : a] : (! [X12 : a > $o] : (($true != (X12 @ X10)) | ((X12 @ X11) != $true) | ((sK0 @ X12) != $true)) & ? [X13 : a > $o] : (((X13 @ X11) = $true) & ((X13 @ X10) = $true) & ((sK0 @ X13) = $true))) | ? [X14 : a] : ! [X15 : a > $o] : (((X15 @ X14) != $true) | ((sK0 @ X15) != $true) | ((X15 @ X14) != $true))))),
% 1.52/1.29 introduced(definition,[],[choice_axiom])).
% 1.52/1.29 thf(f10,plain,(
% 1.52/1.29 ! [X1 : a] : (? [X2 : a > $o] : (((X2 @ X1) = $true) & ((sK0 @ X2) = $true) & ! [X3 : a > $o] : ((X2 = X3) | ((X3 @ X1) != $true) | ((sK0 @ X3) != $true))) => (($true = (sK1 @ X1 @ X1)) & ($true = (sK0 @ (sK1 @ X1))) & ! [X3 : a > $o] : (((sK1 @ X1) = X3) | ((X3 @ X1) != $true) | ((sK0 @ X3) != $true))))),
% 1.52/1.29 introduced(definition,[],[choice_axiom])).
% 1.52/1.29 thf(f11,plain,(
% 1.52/1.29 ? [X6 : a,X5 : a,X4 : a] : (? [X7 : a > $o] : (($true = (X7 @ X5)) & ($true = (sK0 @ X7)) & ((X7 @ X6) = $true)) & ? [X8 : a > $o] : (((X8 @ X6) = $true) & ($true = (X8 @ X4)) & ((sK0 @ X8) = $true)) & ! [X9 : a > $o] : (($true != (X9 @ X4)) | ((X9 @ X5) != $true) | ((sK0 @ X9) != $true))) => (? [X7 : a > $o] : (($true = (X7 @ sK3)) & ($true = (sK0 @ X7)) & ((X7 @ sK4) = $true)) & ? [X8 : a > $o] : (((X8 @ sK4) = $true) & ($true = (X8 @ sK2)) & ((sK0 @ X8) = $true)) & ! [X9 : a > $o] : (($true != (X9 @ sK2)) | ((X9 @ sK3) != $true) | ((sK0 @ X9) != $true)))),
% 1.52/1.29 introduced(definition,[],[choice_axiom])).
% 1.52/1.29 thf(f12,plain,(
% 1.52/1.29 ? [X7 : a > $o] : (($true = (X7 @ sK3)) & ($true = (sK0 @ X7)) & ((X7 @ sK4) = $true)) => (((sK5 @ sK3) = $true) & ((sK0 @ sK5) = $true) & ((sK5 @ sK4) = $true))),
% 1.52/1.29 introduced(definition,[],[choice_axiom])).
% 1.52/1.29 thf(f13,plain,(
% 1.52/1.29 ? [X8 : a > $o] : (((X8 @ sK4) = $true) & ($true = (X8 @ sK2)) & ((sK0 @ X8) = $true)) => (($true = (sK6 @ sK4)) & ($true = (sK6 @ sK2)) & ($true = (sK0 @ sK6)))),
% 1.52/1.29 introduced(definition,[],[choice_axiom])).
% 1.52/1.29 thf(f14,plain,(
% 1.52/1.29 ? [X11 : a,X10 : a] : (! [X12 : a > $o] : (($true != (X12 @ X10)) | ((X12 @ X11) != $true) | ((sK0 @ X12) != $true)) & ? [X13 : a > $o] : (((X13 @ X11) = $true) & ((X13 @ X10) = $true) & ((sK0 @ X13) = $true))) => (! [X12 : a > $o] : (((X12 @ sK7) != $true) | ((X12 @ sK8) != $true) | ((sK0 @ X12) != $true)) & ? [X13 : a > $o] : (((X13 @ sK8) = $true) & ($true = (X13 @ sK7)) & ((sK0 @ X13) = $true)))),
% 1.52/1.29 introduced(definition,[],[choice_axiom])).
% 1.52/1.29 thf(f15,plain,(
% 1.52/1.29 ? [X13 : a > $o] : (((X13 @ sK8) = $true) & ($true = (X13 @ sK7)) & ((sK0 @ X13) = $true)) => (($true = (sK9 @ sK8)) & ($true = (sK9 @ sK7)) & ((sK0 @ sK9) = $true))),
% 1.52/1.29 introduced(definition,[],[choice_axiom])).
% 1.52/1.29 thf(f16,plain,(
% 1.52/1.29 ? [X14 : a] : ! [X15 : a > $o] : (((X15 @ X14) != $true) | ((sK0 @ X15) != $true) | ((X15 @ X14) != $true)) => ! [X15 : a > $o] : (($true != (X15 @ sK10)) | ((sK0 @ X15) != $true) | ($true != (X15 @ sK10)))),
% 1.52/1.29 introduced(definition,[],[choice_axiom])).
% 1.52/1.29 thf(f8,plain,(
% 1.52/1.29 ? [X0 : (a > $o) > $o] : (! [X1 : a] : ? [X2 : a > $o] : (((X2 @ X1) = $true) & ((X0 @ X2) = $true) & ! [X3 : a > $o] : ((X2 = X3) | ((X3 @ X1) != $true) | ((X0 @ X3) != $true))) & (? [X4 : a,X5 : a,X6 : a] : (? [X7 : a > $o] : (($true = (X7 @ X5)) & ($true = (X0 @ X7)) & ((X7 @ X6) = $true)) & ? [X8 : a > $o] : (((X8 @ X6) = $true) & ($true = (X8 @ X4)) & ((X0 @ X8) = $true)) & ! [X9 : a > $o] : (($true != (X9 @ X4)) | ((X9 @ X5) != $true) | ((X0 @ X9) != $true))) | ? [X10 : a,X11 : a] : (! [X12 : a > $o] : (($true != (X12 @ X10)) | ((X12 @ X11) != $true) | ((X0 @ X12) != $true)) & ? [X13 : a > $o] : (((X13 @ X11) = $true) & ((X13 @ X10) = $true) & ($true = (X0 @ X13)))) | ? [X14 : a] : ! [X15 : a > $o] : (((X15 @ X14) != $true) | ((X0 @ X15) != $true) | ((X15 @ X14) != $true))))),
% 1.52/1.29 inference(rectify,[status(thm)],[f7])).
% 1.52/1.29 thf(f7,plain,(
% 1.52/1.29 ? [X0 : (a > $o) > $o] : (! [X1 : a] : ? [X2 : a > $o] : (((X2 @ X1) = $true) & ((X0 @ X2) = $true) & ! [X3 : a > $o] : ((X2 = X3) | ((X3 @ X1) != $true) | ((X0 @ X3) != $true))) & (? [X7 : a,X8 : a,X6 : a] : (? [X10 : a > $o] : (((X10 @ X8) = $true) & ((X0 @ X10) = $true) & ((X10 @ X6) = $true)) & ? [X9 : a > $o] : (($true = (X9 @ X6)) & ((X9 @ X7) = $true) & ((X0 @ X9) = $true)) & ! [X11 : a > $o] : (((X11 @ X7) != $true) | ((X11 @ X8) != $true) | ((X0 @ X11) != $true))) | ? [X12 : a,X13 : a] : (! [X15 : a > $o] : (($true != (X15 @ X12)) | ((X15 @ X13) != $true) | ((X0 @ X15) != $true)) & ? [X14 : a > $o] : (((X14 @ X13) = $true) & ($true = (X14 @ X12)) & ((X0 @ X14) = $true))) | ? [X4 : a] : ! [X5 : a > $o] : (($true != (X5 @ X4)) | ((X0 @ X5) != $true) | ($true != (X5 @ X4)))))),
% 1.52/1.29 inference(flattening,[status(thm)],[f6])).
% 1.52/1.29 thf(f6,plain,(
% 1.52/1.29 ? [X0 : (a > $o) > $o] : ((? [X4 : a] : ! [X5 : a > $o] : (($true != (X5 @ X4)) | ((X0 @ X5) != $true) | ($true != (X5 @ X4))) | ? [X6 : a,X7 : a,X8 : a] : (! [X11 : a > $o] : (((X11 @ X7) != $true) | ((X11 @ X8) != $true) | ((X0 @ X11) != $true)) & (? [X9 : a > $o] : (($true = (X9 @ X6)) & ((X9 @ X7) = $true) & ((X0 @ X9) = $true)) & ? [X10 : a > $o] : (((X10 @ X8) = $true) & ((X0 @ X10) = $true) & ((X10 @ X6) = $true)))) | ? [X12 : a,X13 : a] : (! [X15 : a > $o] : (($true != (X15 @ X12)) | ((X15 @ X13) != $true) | ((X0 @ X15) != $true)) & ? [X14 : a > $o] : (((X14 @ X13) = $true) & ($true = (X14 @ X12)) & ((X0 @ X14) = $true)))) & ! [X1 : a] : ? [X2 : a > $o] : (((X0 @ X2) = $true) & ((X2 @ X1) = $true) & ! [X3 : a > $o] : ((X2 = X3) | (((X3 @ X1) != $true) | ((X0 @ X3) != $true)))))),
% 1.52/1.29 inference(ennf_transformation,[status(thm)],[f5])).
% 1.52/1.29 thf(f5,plain,(
% 1.52/1.29 ~! [X0 : (a > $o) > $o] : (! [X1 : a] : ? [X2 : a > $o] : (((X0 @ X2) = $true) & ((X2 @ X1) = $true) & ! [X3 : a > $o] : ((((X3 @ X1) = $true) & ((X0 @ X3) = $true)) => (X2 = X3))) => (! [X4 : a] : ? [X5 : a > $o] : (($true = (X5 @ X4)) & ($true = (X5 @ X4)) & ((X0 @ X5) = $true)) & ! [X6 : a,X7 : a,X8 : a] : ((? [X9 : a > $o] : (($true = (X9 @ X6)) & ((X9 @ X7) = $true) & ((X0 @ X9) = $true)) & ? [X10 : a > $o] : (((X10 @ X8) = $true) & ((X0 @ X10) = $true) & ((X10 @ X6) = $true))) => ? [X11 : a > $o] : (((X11 @ X7) = $true) & ((X11 @ X8) = $true) & ((X0 @ X11) = $true))) & ! [X12 : a,X13 : a] : (? [X14 : a > $o] : (((X14 @ X13) = $true) & ($true = (X14 @ X12)) & ((X0 @ X14) = $true)) => ? [X15 : a > $o] : (((X15 @ X13) = $true) & ((X0 @ X15) = $true) & ($true = (X15 @ X12))))))),
% 1.52/1.29 inference(fool_elimination,[status(thm)],[f4])).
% 1.52/1.29 thf(f4,plain,(
% 1.52/1.29 ~! [X0 : (a > $o) > $o] : (! [X1 : a] : ? [X2 : a > $o] : ((X0 @ X2) & (X2 @ X1) & ! [X3 : a > $o] : (((X0 @ X3) & (X3 @ X1)) => (X2 = X3))) => (! [X4 : a] : ? [X5 : a > $o] : ((X5 @ X4) & (X0 @ X5) & (X5 @ X4)) & ! [X6 : a,X7 : a,X8 : a] : ((? [X9 : a > $o] : ((X9 @ X6) & (X9 @ X7) & (X0 @ X9)) & ? [X10 : a > $o] : ((X10 @ X8) & (X0 @ X10) & (X10 @ X6))) => ? [X11 : a > $o] : ((X0 @ X11) & (X11 @ X7) & (X11 @ X8))) & ! [X12 : a,X13 : a] : (? [X14 : a > $o] : ((X0 @ X14) & (X14 @ X12) & (X14 @ X13)) => ? [X15 : a > $o] : ((X15 @ X13) & (X15 @ X12) & (X0 @ X15)))))),
% 1.52/1.29 inference(rectify,[status(thm)],[f2])).
% 1.52/1.29 thf(f2,negated_conjecture,(
% 1.52/1.29 ~! [X0 : (a > $o) > $o] : (! [X1 : a] : ? [X2 : a > $o] : ((X0 @ X2) & (X2 @ X1) & ! [X3 : a > $o] : (((X0 @ X3) & (X3 @ X1)) => (X2 = X3))) => (! [X1 : a] : ? [X4 : a > $o] : ((X4 @ X1) & (X0 @ X4) & (X4 @ X1)) & ! [X5 : a,X6 : a,X1 : a] : ((? [X4 : a > $o] : ((X4 @ X5) & (X4 @ X6) & (X0 @ X4)) & ? [X4 : a > $o] : ((X4 @ X1) & (X0 @ X4) & (X4 @ X5))) => ? [X4 : a > $o] : ((X0 @ X4) & (X4 @ X6) & (X4 @ X1))) & ! [X5 : a,X1 : a] : (? [X4 : a > $o] : ((X0 @ X4) & (X4 @ X5) & (X4 @ X1)) => ? [X4 : a > $o] : ((X4 @ X1) & (X4 @ X5) & (X0 @ X4)))))),
% 1.52/1.29 inference(negated_conjecture,[status(cth)],[f1])).
% 1.52/1.29 thf(f1,conjecture,(
% 1.52/1.29 ! [X0 : (a > $o) > $o] : (! [X1 : a] : ? [X2 : a > $o] : ((X0 @ X2) & (X2 @ X1) & ! [X3 : a > $o] : (((X0 @ X3) & (X3 @ X1)) => (X2 = X3))) => (! [X1 : a] : ? [X4 : a > $o] : ((X4 @ X1) & (X0 @ X4) & (X4 @ X1)) & ! [X5 : a,X6 : a,X1 : a] : ((? [X4 : a > $o] : ((X4 @ X5) & (X4 @ X6) & (X0 @ X4)) & ? [X4 : a > $o] : ((X4 @ X1) & (X0 @ X4) & (X4 @ X5))) => ? [X4 : a > $o] : ((X0 @ X4) & (X4 @ X6) & (X4 @ X1))) & ! [X5 : a,X1 : a] : (? [X4 : a > $o] : ((X0 @ X4) & (X4 @ X5) & (X4 @ X1)) => ? [X4 : a > $o] : ((X4 @ X1) & (X4 @ X5) & (X0 @ X4)))))),
% 1.52/1.29 file('/export/starexec/sandbox/tmp/tmp.dpvmUEDf38/DTF2THF_10697.p',cTHM261_B_pme)).
% 1.52/1.29 thf(f223,plain,(
% 1.52/1.29 ((sK1 @ sK4) = sK6) | (~spl11_3 | ~spl11_11)),
% 1.52/1.29 inference(trivial_inequality_removal,[status(thm)],[f220])).
% 1.52/1.29 thf(f220,plain,(
% 1.52/1.29 ($true != $true) | ((sK1 @ sK4) = sK6) | (~spl11_3 | ~spl11_11)),
% 1.52/1.29 inference(superposition,[status(thm)],[f216,f87])).
% 1.52/1.29 thf(f87,plain,(
% 1.52/1.29 ($true = (sK6 @ sK4)) | ~spl11_3),
% 1.52/1.29 inference(avatar_component_clause,[status(thm)],[f85])).
% 1.52/1.29 thf(f85,definition,(
% 1.52/1.29 spl11_3 <=> ($true = (sK6 @ sK4))),
% 1.52/1.29 introduced(definition,[new_symbols(naming,[spl11_3])],[avatar_definition])).
% 1.52/1.29 thf(f216,plain,(
% 1.52/1.29 ( ! [X0 : a] : (((sK6 @ X0) != $true) | (sK6 = (sK1 @ X0))) ) | ~spl11_11),
% 1.52/1.29 inference(trivial_inequality_removal,[status(thm)],[f212])).
% 1.52/1.29 thf(f212,plain,(
% 1.52/1.29 ( ! [X0 : a] : ((sK6 = (sK1 @ X0)) | ((sK6 @ X0) != $true) | ($true != $true)) ) | ~spl11_11),
% 1.52/1.29 inference(superposition,[status(thm)],[f46,f126])).
% 1.52/1.29 thf(f126,plain,(
% 1.52/1.29 ($true = (sK0 @ sK6)) | ~spl11_11),
% 1.52/1.29 inference(avatar_component_clause,[status(thm)],[f124])).
% 1.52/1.29 thf(f124,definition,(
% 1.52/1.29 spl11_11 <=> ($true = (sK0 @ sK6))),
% 1.52/1.29 introduced(definition,[new_symbols(naming,[spl11_11])],[avatar_definition])).
% 1.52/1.29 thf(f109,plain,(
% 1.52/1.29 ((sK5 @ sK3) = $true) | ~spl11_8),
% 1.52/1.29 inference(avatar_component_clause,[status(thm)],[f107])).
% 1.52/1.29 thf(f107,definition,(
% 1.52/1.29 spl11_8 <=> ((sK5 @ sK3) = $true)),
% 1.52/1.29 introduced(definition,[new_symbols(naming,[spl11_8])],[avatar_definition])).
% 1.52/1.29 thf(f202,plain,(
% 1.52/1.29 ((sK6 @ sK3) != $true) | (~spl11_4 | ~spl11_9 | ~spl11_11)),
% 1.52/1.29 inference(trivial_inequality_removal,[status(thm)],[f201])).
% 1.52/1.29 thf(f201,plain,(
% 1.52/1.29 ($true != $true) | ((sK6 @ sK3) != $true) | (~spl11_4 | ~spl11_9 | ~spl11_11)),
% 1.52/1.29 inference(forward_demodulation,[status(thm)],[f194,f92])).
% 1.52/1.29 thf(f92,plain,(
% 1.52/1.29 ($true = (sK6 @ sK2)) | ~spl11_4),
% 1.52/1.29 inference(avatar_component_clause,[status(thm)],[f90])).
% 1.52/1.29 thf(f90,definition,(
% 1.52/1.29 spl11_4 <=> ($true = (sK6 @ sK2))),
% 1.52/1.29 introduced(definition,[new_symbols(naming,[spl11_4])],[avatar_definition])).
% 1.52/1.29 thf(f194,plain,(
% 1.52/1.29 ((sK6 @ sK3) != $true) | ($true != (sK6 @ sK2)) | (~spl11_9 | ~spl11_11)),
% 1.52/1.29 inference(trivial_inequality_removal,[status(thm)],[f188])).
% 1.52/1.29 thf(f188,plain,(
% 1.52/1.29 ((sK6 @ sK3) != $true) | ($true != $true) | ($true != (sK6 @ sK2)) | (~spl11_9 | ~spl11_11)),
% 1.52/1.29 inference(superposition,[status(thm)],[f116,f126])).
% 1.52/1.29 thf(f116,plain,(
% 1.52/1.29 ( ! [X9 : a > $o] : (((sK0 @ X9) != $true) | ($true != (X9 @ sK2)) | ((X9 @ sK3) != $true)) ) | ~spl11_9),
% 1.52/1.29 inference(avatar_component_clause,[status(thm)],[f115])).
% 1.52/1.29 thf(f115,definition,(
% 1.52/1.29 spl11_9 <=> ! [X9 : a > $o] : (((X9 @ sK3) != $true) | ($true != (X9 @ sK2)) | ((sK0 @ X9) != $true))),
% 1.52/1.29 introduced(definition,[new_symbols(naming,[spl11_9])],[avatar_definition])).
% 1.52/1.29 thf(f163,plain,(
% 1.52/1.29 ~spl11_1),
% 1.52/1.29 inference(avatar_contradiction_clause,[status(thm)],[f162])).
% 1.52/1.29 thf(f162,plain,(
% 1.52/1.29 $false | ~spl11_1),
% 1.52/1.29 inference(trivial_inequality_removal,[status(thm)],[f161])).
% 1.52/1.29 thf(f161,plain,(
% 1.52/1.29 ($true != $true) | ~spl11_1),
% 1.52/1.29 inference(superposition,[status(thm)],[f160,f48])).
% 1.52/1.29 thf(f48,plain,(
% 1.52/1.29 ( ! [X1 : a] : (($true = (sK1 @ X1 @ X1))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f160,plain,(
% 1.52/1.29 ( ! [X0 : a] : (((sK1 @ X0 @ sK10) != $true)) ) | ~spl11_1),
% 1.52/1.29 inference(trivial_inequality_removal,[status(thm)],[f157])).
% 1.52/1.29 thf(f157,plain,(
% 1.52/1.29 ( ! [X0 : a] : (((sK1 @ X0 @ sK10) != $true) | ($true != $true)) ) | ~spl11_1),
% 1.52/1.29 inference(superposition,[status(thm)],[f79,f47])).
% 1.52/1.29 thf(f47,plain,(
% 1.52/1.29 ( ! [X1 : a] : (($true = (sK0 @ (sK1 @ X1)))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f79,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (((sK0 @ X15) != $true) | ($true != (X15 @ sK10))) ) | ~spl11_1),
% 1.52/1.29 inference(avatar_component_clause,[status(thm)],[f78])).
% 1.52/1.29 thf(f78,definition,(
% 1.52/1.29 spl11_1 <=> ! [X15 : a > $o] : (((sK0 @ X15) != $true) | ($true != (X15 @ sK10)))),
% 1.52/1.29 introduced(definition,[new_symbols(naming,[spl11_1])],[avatar_definition])).
% 1.52/1.29 thf(f156,plain,(
% 1.52/1.29 ~spl11_6 | ~spl11_2 | ~spl11_5 | ~spl11_7),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f155,f103,f94,f81,f98])).
% 1.52/1.29 thf(f98,definition,(
% 1.52/1.29 spl11_6 <=> ($true = (sK9 @ sK8))),
% 1.52/1.29 introduced(definition,[new_symbols(naming,[spl11_6])],[avatar_definition])).
% 1.52/1.29 thf(f81,definition,(
% 1.52/1.29 spl11_2 <=> ($true = (sK9 @ sK7))),
% 1.52/1.29 introduced(definition,[new_symbols(naming,[spl11_2])],[avatar_definition])).
% 1.52/1.29 thf(f94,definition,(
% 1.52/1.29 spl11_5 <=> ! [X12 : a > $o] : (((X12 @ sK8) != $true) | ((sK0 @ X12) != $true) | ((X12 @ sK7) != $true))),
% 1.52/1.29 introduced(definition,[new_symbols(naming,[spl11_5])],[avatar_definition])).
% 1.52/1.29 thf(f103,definition,(
% 1.52/1.29 spl11_7 <=> ((sK0 @ sK9) = $true)),
% 1.52/1.29 introduced(definition,[new_symbols(naming,[spl11_7])],[avatar_definition])).
% 1.52/1.29 thf(f155,plain,(
% 1.52/1.29 ($true != (sK9 @ sK8)) | (~spl11_2 | ~spl11_5 | ~spl11_7)),
% 1.52/1.29 inference(trivial_inequality_removal,[status(thm)],[f154])).
% 1.52/1.29 thf(f154,plain,(
% 1.52/1.29 ($true != $true) | ($true != (sK9 @ sK8)) | (~spl11_2 | ~spl11_5 | ~spl11_7)),
% 1.52/1.29 inference(forward_demodulation,[status(thm)],[f152,f83])).
% 1.52/1.29 thf(f83,plain,(
% 1.52/1.29 ($true = (sK9 @ sK7)) | ~spl11_2),
% 1.52/1.29 inference(avatar_component_clause,[status(thm)],[f81])).
% 1.52/1.29 thf(f152,plain,(
% 1.52/1.29 ($true != (sK9 @ sK8)) | ($true != (sK9 @ sK7)) | (~spl11_5 | ~spl11_7)),
% 1.52/1.29 inference(trivial_inequality_removal,[status(thm)],[f151])).
% 1.52/1.29 thf(f151,plain,(
% 1.52/1.29 ($true != (sK9 @ sK8)) | ($true != $true) | ($true != (sK9 @ sK7)) | (~spl11_5 | ~spl11_7)),
% 1.52/1.29 inference(superposition,[status(thm)],[f95,f105])).
% 1.52/1.29 thf(f105,plain,(
% 1.52/1.29 ((sK0 @ sK9) = $true) | ~spl11_7),
% 1.52/1.29 inference(avatar_component_clause,[status(thm)],[f103])).
% 1.52/1.29 thf(f95,plain,(
% 1.52/1.29 ( ! [X12 : a > $o] : (((sK0 @ X12) != $true) | ((X12 @ sK7) != $true) | ((X12 @ sK8) != $true)) ) | ~spl11_5),
% 1.52/1.29 inference(avatar_component_clause,[status(thm)],[f94])).
% 1.52/1.29 thf(f149,plain,(
% 1.52/1.29 spl11_6 | spl11_10 | spl11_1),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f49,f78,f119,f98])).
% 1.52/1.29 thf(f49,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (((sK0 @ sK5) = $true) | ((sK0 @ X15) != $true) | ($true = (sK9 @ sK8)) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f40])).
% 1.52/1.29 thf(f40,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true != (X15 @ sK10)) | ($true != (X15 @ sK10)) | ((sK0 @ X15) != $true) | ((sK0 @ sK5) = $true) | ($true = (sK9 @ sK8))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f148,plain,(
% 1.52/1.29 spl11_1 | spl11_7 | spl11_9),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f50,f115,f103,f78])).
% 1.52/1.29 thf(f50,plain,(
% 1.52/1.29 ( ! [X9 : a > $o,X15 : a > $o] : (($true != (X15 @ sK10)) | ((sK0 @ sK9) = $true) | ((sK0 @ X9) != $true) | ((X9 @ sK3) != $true) | ((sK0 @ X15) != $true) | ($true != (X9 @ sK2))) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f18])).
% 1.52/1.29 thf(f18,plain,(
% 1.52/1.29 ( ! [X9 : a > $o,X15 : a > $o] : (((sK0 @ sK9) = $true) | ($true != (X9 @ sK2)) | ((sK0 @ X15) != $true) | ($true != (X15 @ sK10)) | ((X9 @ sK3) != $true) | ((sK0 @ X9) != $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f147,plain,(
% 1.52/1.29 spl11_6 | spl11_12 | spl11_1),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f51,f78,f135,f98])).
% 1.52/1.29 thf(f51,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (((sK0 @ X15) != $true) | ((sK5 @ sK4) = $true) | ($true != (X15 @ sK10)) | ($true = (sK9 @ sK8))) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f36])).
% 1.52/1.29 thf(f36,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true != (X15 @ sK10)) | ($true != (X15 @ sK10)) | ((sK5 @ sK4) = $true) | ($true = (sK9 @ sK8)) | ((sK0 @ X15) != $true)) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f146,plain,(
% 1.52/1.29 spl11_12 | spl11_5 | spl11_1),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f52,f78,f94,f135])).
% 1.52/1.29 thf(f52,plain,(
% 1.52/1.29 ( ! [X15 : a > $o,X12 : a > $o] : (((X12 @ sK8) != $true) | ((sK5 @ sK4) = $true) | ((sK0 @ X15) != $true) | ((X12 @ sK7) != $true) | ($true != (X15 @ sK10)) | ((sK0 @ X12) != $true)) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f37])).
% 1.52/1.29 thf(f37,plain,(
% 1.52/1.29 ( ! [X15 : a > $o,X12 : a > $o] : (((sK0 @ X12) != $true) | ((sK5 @ sK4) = $true) | ((X12 @ sK7) != $true) | ((X12 @ sK8) != $true) | ($true != (X15 @ sK10)) | ((sK0 @ X15) != $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f145,plain,(
% 1.52/1.29 spl11_6 | spl11_1 | spl11_8),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f53,f107,f78,f98])).
% 1.52/1.29 thf(f53,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true = (sK9 @ sK8)) | ($true != (X15 @ sK10)) | ((sK5 @ sK3) = $true) | ((sK0 @ X15) != $true)) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f44])).
% 1.52/1.29 thf(f44,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true != (X15 @ sK10)) | ((sK5 @ sK3) = $true) | ($true != (X15 @ sK10)) | ($true = (sK9 @ sK8)) | ((sK0 @ X15) != $true)) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f144,plain,(
% 1.52/1.29 spl11_7 | spl11_4 | spl11_1),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f54,f78,f90,f103])).
% 1.52/1.29 thf(f54,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true = (sK6 @ sK2)) | ((sK0 @ sK9) = $true) | ((sK0 @ X15) != $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f26])).
% 1.52/1.29 thf(f26,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (((sK0 @ sK9) = $true) | ($true != (X15 @ sK10)) | ($true = (sK6 @ sK2)) | ((sK0 @ X15) != $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f143,plain,(
% 1.52/1.29 spl11_2 | spl11_1 | spl11_10),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f55,f119,f78,f81])).
% 1.52/1.29 thf(f55,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (((sK0 @ X15) != $true) | ((sK0 @ sK5) = $true) | ($true = (sK9 @ sK7)) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f39])).
% 1.52/1.29 thf(f39,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true = (sK9 @ sK7)) | ((sK0 @ sK5) = $true) | ($true != (X15 @ sK10)) | ((sK0 @ X15) != $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f142,plain,(
% 1.52/1.29 spl11_7 | spl11_1 | spl11_12),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f56,f135,f78,f103])).
% 1.52/1.29 thf(f56,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (((sK0 @ sK9) = $true) | ($true != (X15 @ sK10)) | ((sK0 @ X15) != $true) | ((sK5 @ sK4) = $true)) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f34])).
% 1.52/1.29 thf(f34,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true != (X15 @ sK10)) | ((sK5 @ sK4) = $true) | ((sK0 @ sK9) = $true) | ($true != (X15 @ sK10)) | ((sK0 @ X15) != $true)) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f141,plain,(
% 1.52/1.29 spl11_1 | spl11_6 | spl11_11),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f57,f124,f98,f78])).
% 1.52/1.29 thf(f57,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true = (sK9 @ sK8)) | ($true != (X15 @ sK10)) | ((sK0 @ X15) != $true) | ($true = (sK0 @ sK6))) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f24])).
% 1.52/1.29 thf(f24,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true = (sK0 @ sK6)) | ($true = (sK9 @ sK8)) | ($true != (X15 @ sK10)) | ((sK0 @ X15) != $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f140,plain,(
% 1.52/1.29 spl11_1 | spl11_2 | spl11_9),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f58,f115,f81,f78])).
% 1.52/1.29 thf(f58,plain,(
% 1.52/1.29 ( ! [X9 : a > $o,X15 : a > $o] : (($true != (X15 @ sK10)) | ((sK0 @ X15) != $true) | ((X9 @ sK3) != $true) | ((sK0 @ X9) != $true) | ($true != (X9 @ sK2)) | ($true = (sK9 @ sK7))) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f19])).
% 1.52/1.29 thf(f19,plain,(
% 1.52/1.29 ( ! [X9 : a > $o,X15 : a > $o] : (($true != (X15 @ sK10)) | ((sK0 @ X9) != $true) | ((X9 @ sK3) != $true) | ($true != (X15 @ sK10)) | ($true != (X9 @ sK2)) | ($true = (sK9 @ sK7)) | ((sK0 @ X15) != $true)) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f139,plain,(
% 1.52/1.29 spl11_11 | spl11_1 | spl11_7),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f59,f103,f78,f124])).
% 1.52/1.29 thf(f59,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (((sK0 @ X15) != $true) | ($true = (sK0 @ sK6)) | ((sK0 @ sK9) = $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f22])).
% 1.52/1.29 thf(f22,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (((sK0 @ X15) != $true) | ($true = (sK0 @ sK6)) | ($true != (X15 @ sK10)) | ($true != (X15 @ sK10)) | ((sK0 @ sK9) = $true)) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f138,plain,(
% 1.52/1.29 spl11_1 | spl11_2 | spl11_12),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f60,f135,f81,f78])).
% 1.52/1.29 thf(f60,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true != (X15 @ sK10)) | ((sK5 @ sK4) = $true) | ($true = (sK9 @ sK7)) | ((sK0 @ X15) != $true)) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f35])).
% 1.52/1.29 thf(f35,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (((sK5 @ sK4) = $true) | ($true = (sK9 @ sK7)) | ($true != (X15 @ sK10)) | ((sK0 @ X15) != $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f133,plain,(
% 1.52/1.29 spl11_11 | spl11_1 | spl11_5),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f61,f94,f78,f124])).
% 1.52/1.29 thf(f61,plain,(
% 1.52/1.29 ( ! [X15 : a > $o,X12 : a > $o] : (((X12 @ sK8) != $true) | ($true = (sK0 @ sK6)) | ((sK0 @ X12) != $true) | ((X12 @ sK7) != $true) | ((sK0 @ X15) != $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f25])).
% 1.52/1.29 thf(f25,plain,(
% 1.52/1.29 ( ! [X15 : a > $o,X12 : a > $o] : (((sK0 @ X15) != $true) | ((X12 @ sK7) != $true) | ((sK0 @ X12) != $true) | ((X12 @ sK8) != $true) | ($true != (X15 @ sK10)) | ($true != (X15 @ sK10)) | ($true = (sK0 @ sK6))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f132,plain,(
% 1.52/1.29 spl11_5 | spl11_8 | spl11_1),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f62,f78,f107,f94])).
% 1.52/1.29 thf(f62,plain,(
% 1.52/1.29 ( ! [X15 : a > $o,X12 : a > $o] : (((X12 @ sK8) != $true) | ((X12 @ sK7) != $true) | ($true != (X15 @ sK10)) | ((sK5 @ sK3) = $true) | ((sK0 @ X15) != $true) | ((sK0 @ X12) != $true)) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f45])).
% 1.52/1.29 thf(f45,plain,(
% 1.52/1.29 ( ! [X15 : a > $o,X12 : a > $o] : (((X12 @ sK7) != $true) | ($true != (X15 @ sK10)) | ((X12 @ sK8) != $true) | ($true != (X15 @ sK10)) | ((sK5 @ sK3) = $true) | ((sK0 @ X15) != $true) | ((sK0 @ X12) != $true)) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f131,plain,(
% 1.52/1.29 spl11_4 | spl11_1 | spl11_2),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f63,f81,f78,f90])).
% 1.52/1.29 thf(f63,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true = (sK6 @ sK2)) | ($true != (X15 @ sK10)) | ((sK0 @ X15) != $true) | ($true = (sK9 @ sK7))) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f27])).
% 1.52/1.29 thf(f27,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true = (sK9 @ sK7)) | ($true != (X15 @ sK10)) | ($true = (sK6 @ sK2)) | ((sK0 @ X15) != $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f130,plain,(
% 1.52/1.29 spl11_5 | spl11_9 | spl11_1),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f64,f78,f115,f94])).
% 1.52/1.29 thf(f64,plain,(
% 1.52/1.29 ( ! [X9 : a > $o,X15 : a > $o,X12 : a > $o] : (((X12 @ sK8) != $true) | ((X9 @ sK3) != $true) | ((X12 @ sK7) != $true) | ((sK0 @ X9) != $true) | ($true != (X9 @ sK2)) | ($true != (X15 @ sK10)) | ((sK0 @ X15) != $true) | ((sK0 @ X12) != $true)) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f21])).
% 1.52/1.29 thf(f21,plain,(
% 1.52/1.29 ( ! [X9 : a > $o,X15 : a > $o,X12 : a > $o] : (($true != (X9 @ sK2)) | ((sK0 @ X12) != $true) | ((sK0 @ X9) != $true) | ((X12 @ sK7) != $true) | ((sK0 @ X15) != $true) | ((X9 @ sK3) != $true) | ((X12 @ sK8) != $true) | ($true != (X15 @ sK10)) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f129,plain,(
% 1.52/1.29 spl11_5 | spl11_1 | spl11_3),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f65,f85,f78,f94])).
% 1.52/1.29 thf(f65,plain,(
% 1.52/1.29 ( ! [X15 : a > $o,X12 : a > $o] : (((sK0 @ X15) != $true) | ((sK0 @ X12) != $true) | ($true != (X15 @ sK10)) | ($true = (sK6 @ sK4)) | ((X12 @ sK8) != $true) | ((X12 @ sK7) != $true)) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f33])).
% 1.52/1.29 thf(f33,plain,(
% 1.52/1.29 ( ! [X15 : a > $o,X12 : a > $o] : (($true != (X15 @ sK10)) | ((X12 @ sK7) != $true) | ($true = (sK6 @ sK4)) | ((sK0 @ X12) != $true) | ((sK0 @ X15) != $true) | ((X12 @ sK8) != $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f128,plain,(
% 1.52/1.29 spl11_1 | spl11_10 | spl11_7),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f66,f103,f119,f78])).
% 1.52/1.29 thf(f66,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (((sK0 @ sK5) = $true) | ((sK0 @ X15) != $true) | ((sK0 @ sK9) = $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f38])).
% 1.52/1.29 thf(f38,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true != (X15 @ sK10)) | ((sK0 @ sK9) = $true) | ($true != (X15 @ sK10)) | ((sK0 @ sK5) = $true) | ((sK0 @ X15) != $true)) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f127,plain,(
% 1.52/1.29 spl11_11 | spl11_2 | spl11_1),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f67,f78,f81,f124])).
% 1.52/1.29 thf(f67,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true = (sK0 @ sK6)) | ($true = (sK9 @ sK7)) | ($true != (X15 @ sK10)) | ((sK0 @ X15) != $true)) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f23])).
% 1.52/1.29 thf(f23,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true != (X15 @ sK10)) | ($true != (X15 @ sK10)) | ((sK0 @ X15) != $true) | ($true = (sK0 @ sK6)) | ($true = (sK9 @ sK7))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f122,plain,(
% 1.52/1.29 spl11_5 | spl11_1 | spl11_10),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f68,f119,f78,f94])).
% 1.52/1.29 thf(f68,plain,(
% 1.52/1.29 ( ! [X15 : a > $o,X12 : a > $o] : (((sK0 @ sK5) = $true) | ((X12 @ sK7) != $true) | ($true != (X15 @ sK10)) | ((sK0 @ X15) != $true) | ((X12 @ sK8) != $true) | ((sK0 @ X12) != $true)) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f41])).
% 1.52/1.29 thf(f41,plain,(
% 1.52/1.29 ( ! [X15 : a > $o,X12 : a > $o] : (((sK0 @ sK5) = $true) | ((sK0 @ X12) != $true) | ($true != (X15 @ sK10)) | ((X12 @ sK7) != $true) | ($true != (X15 @ sK10)) | ((sK0 @ X15) != $true) | ((X12 @ sK8) != $true)) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f117,plain,(
% 1.52/1.29 spl11_1 | spl11_6 | spl11_9),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f69,f115,f98,f78])).
% 1.52/1.29 thf(f69,plain,(
% 1.52/1.29 ( ! [X9 : a > $o,X15 : a > $o] : (((sK0 @ X15) != $true) | ($true = (sK9 @ sK8)) | ((X9 @ sK3) != $true) | ($true != (X15 @ sK10)) | ((sK0 @ X9) != $true) | ($true != (X9 @ sK2))) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f20])).
% 1.52/1.29 thf(f20,plain,(
% 1.52/1.29 ( ! [X9 : a > $o,X15 : a > $o] : (($true != (X15 @ sK10)) | ($true != (X9 @ sK2)) | ($true = (sK9 @ sK8)) | ((sK0 @ X15) != $true) | ((X9 @ sK3) != $true) | ((sK0 @ X9) != $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f113,plain,(
% 1.52/1.29 spl11_3 | spl11_1 | spl11_7),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f70,f103,f78,f85])).
% 1.52/1.29 thf(f70,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true != (X15 @ sK10)) | ($true = (sK6 @ sK4)) | ((sK0 @ X15) != $true) | ((sK0 @ sK9) = $true)) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f30])).
% 1.52/1.29 thf(f30,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (((sK0 @ X15) != $true) | ($true != (X15 @ sK10)) | ((sK0 @ sK9) = $true) | ($true = (sK6 @ sK4)) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f112,plain,(
% 1.52/1.29 spl11_8 | spl11_2 | spl11_1),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f71,f78,f81,f107])).
% 1.52/1.29 thf(f71,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true != (X15 @ sK10)) | ($true = (sK9 @ sK7)) | ((sK0 @ X15) != $true) | ((sK5 @ sK3) = $true)) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f43])).
% 1.52/1.29 thf(f43,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true != (X15 @ sK10)) | ($true = (sK9 @ sK7)) | ((sK5 @ sK3) = $true) | ($true != (X15 @ sK10)) | ((sK0 @ X15) != $true)) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f111,plain,(
% 1.52/1.29 spl11_3 | spl11_6 | spl11_1),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f72,f78,f98,f85])).
% 1.52/1.29 thf(f72,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true = (sK9 @ sK8)) | ($true = (sK6 @ sK4)) | ((sK0 @ X15) != $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f32])).
% 1.52/1.29 thf(f32,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (((sK0 @ X15) != $true) | ($true = (sK9 @ sK8)) | ($true != (X15 @ sK10)) | ($true = (sK6 @ sK4)) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f110,plain,(
% 1.52/1.29 spl11_1 | spl11_7 | spl11_8),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f73,f107,f103,f78])).
% 1.52/1.29 thf(f73,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (((sK0 @ sK9) = $true) | ($true != (X15 @ sK10)) | ((sK5 @ sK3) = $true) | ((sK0 @ X15) != $true)) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f42])).
% 1.52/1.29 thf(f42,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (((sK0 @ X15) != $true) | ($true != (X15 @ sK10)) | ((sK5 @ sK3) = $true) | ((sK0 @ sK9) = $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f101,plain,(
% 1.52/1.29 spl11_1 | spl11_4 | spl11_6),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f74,f98,f90,f78])).
% 1.52/1.29 thf(f74,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (((sK0 @ X15) != $true) | ($true = (sK9 @ sK8)) | ($true != (X15 @ sK10)) | ($true = (sK6 @ sK2))) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f28])).
% 1.52/1.29 thf(f28,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (((sK0 @ X15) != $true) | ($true != (X15 @ sK10)) | ($true = (sK9 @ sK8)) | ($true = (sK6 @ sK2)) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f96,plain,(
% 1.52/1.29 spl11_4 | spl11_1 | spl11_5),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f75,f94,f78,f90])).
% 1.52/1.29 thf(f75,plain,(
% 1.52/1.29 ( ! [X15 : a > $o,X12 : a > $o] : (((X12 @ sK8) != $true) | ((sK0 @ X15) != $true) | ($true = (sK6 @ sK2)) | ((X12 @ sK7) != $true) | ((sK0 @ X12) != $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f29])).
% 1.52/1.29 thf(f29,plain,(
% 1.52/1.29 ( ! [X15 : a > $o,X12 : a > $o] : (((X12 @ sK7) != $true) | ($true != (X15 @ sK10)) | ((sK0 @ X12) != $true) | ((sK0 @ X15) != $true) | ($true = (sK6 @ sK2)) | ((X12 @ sK8) != $true) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 thf(f88,plain,(
% 1.52/1.29 spl11_1 | spl11_2 | spl11_3),
% 1.52/1.29 inference(avatar_split_clause,[status(thm)],[f76,f85,f81,f78])).
% 1.52/1.29 thf(f76,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true = (sK6 @ sK4)) | ((sK0 @ X15) != $true) | ($true = (sK9 @ sK7)) | ($true != (X15 @ sK10))) )),
% 1.52/1.29 inference(duplicate_literal_removal,[status(thm)],[f31])).
% 1.52/1.29 thf(f31,plain,(
% 1.52/1.29 ( ! [X15 : a > $o] : (($true = (sK6 @ sK4)) | ((sK0 @ X15) != $true) | ($true != (X15 @ sK10)) | ($true != (X15 @ sK10)) | ($true = (sK9 @ sK7))) )),
% 1.52/1.29 inference(cnf_transformation,[status(thm)],[f17])).
% 1.52/1.29 % SZS output end Proof for DTF2THF_10697
% 1.52/1.29 % (10988)------------------------------
% 1.52/1.29 % (10988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.52/1.29 % (10988)Termination reason: Refutation
% 1.52/1.29
% 1.52/1.29 % (10988)Memory used [KB]: 5756
% 1.52/1.29 % (10988)Time elapsed: 0.021 s
% 1.52/1.29 % (10988)Instructions burned: 20 (million)
% 1.52/1.29 % (10988)------------------------------
% 1.52/1.29 % (10988)------------------------------
% 1.52/1.29 % (10985)Success in time 0.033 s
%------------------------------------------------------------------------------