%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV149^5 : 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 : n020.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 09:40:24 AM UTC 2026
% Result : Theorem 1.69s 1.40s
% Output : Refutation 1.69s
% Verified :
% SZS Type : Refutation
% Derivation depth : 28
% Number of leaves : 13
% Syntax : Number of formulae : 105 ( 6 unt; 0 typ; 4 def)
% Number of atoms : 1634 ( 637 equ; 0 cnn)
% Maximal formula atoms : 72 ( 15 avg)
% Number of connectives : 2224 ( 363 ~; 410 |; 190 &;1173 @)
% ( 4 <=>; 84 =>; 0 <=; 0 <~>)
% Maximal formula depth : 24 ( 7 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 141 ( 141 >; 0 *; 0 +; 0 <<)
% Number of symbols : 20 ( 17 usr; 8 con; 0-3 aty)
% Number of variables : 441 ( 26 ^; 343 !; 72 ?; 441 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_4,type,
sK0: a > a > $o ).
thf(func_def_5,type,
sK1: a ).
thf(func_def_6,type,
sK2: a > a > $o ).
thf(func_def_7,type,
sK3: a ).
thf(func_def_8,type,
sK4: a > $o ).
thf(func_def_9,type,
sK5: a > a > $o ).
thf(func_def_10,type,
sK6: a > a > $o ).
thf(func_def_11,type,
sK7: a > a > a > $o ).
thf(func_def_12,type,
sK8: a > a > a > $o ).
thf(func_def_13,type,
sK9: ( a > $o ) > a ).
thf(func_def_14,type,
sK10: ( a > $o ) > a ).
thf(func_def_15,type,
sK11: ( a > $o ) > a ).
thf(func_def_18,type,
ph13:
!>[X0: $tType] : X0 ).
thf(f1246,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f210,f779,f1192,f1229,f1245]) ).
thf(f1245,plain,
( ~ spl12_14
| ~ spl12_42 ),
inference(avatar_contradiction_clause,[status(thm)],[f1244]) ).
thf(f1244,plain,
( $false
| ~ spl12_14
| ~ spl12_42 ),
inference(subsumption_resolution,[status(thm)],[f1243,f36]) ).
thf(f36,plain,
( ( sK4 @ sK3 )
!= $true ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
( ( ( sK4 @ sK3 )
!= $true )
& ! [X5: a] :
( ( ( sK4 @ X5 )
= $true )
| ( ! [X7: a,X8: a] :
( ( ( sK5 @ X5 @ X7 )
= $true )
| ( ( sK0 @ X8 @ X7 )
!= $true )
| ( ( sK5 @ X5 @ X8 )
!= $true ) )
& ( ( sK5 @ X5 @ X5 )
!= $true )
& ! [X9: a] :
( ( $true
!= ( sK0 @ sK1 @ X9 ) )
| ( ( sK5 @ X5 @ X9 )
= $true ) )
& ( ( sK6 @ X5 @ X5 )
!= $true )
& ! [X11: a,X12: a] :
( ( ( sK2 @ X11 @ X12 )
!= $true )
| ( ( sK6 @ X5 @ X12 )
= $true )
| ( ( sK6 @ X5 @ X11 )
!= $true ) )
& ! [X13: a] :
( ( ( sK6 @ X5 @ X13 )
= $true )
| ( ( sK2 @ sK1 @ X13 )
!= $true ) ) ) )
& ! [X14: a,X15: a] :
( ( ( sK4 @ X14 )
!= $true )
| ( ! [X17: a] :
( ( ( sK7 @ X15 @ X14 @ X17 )
= $true )
| ( ( sK2 @ X14 @ X17 )
!= $true ) )
& ! [X18: a,X19: a] :
( ( ( sK2 @ X19 @ X18 )
!= $true )
| ( ( sK7 @ X15 @ X14 @ X19 )
!= $true )
| ( ( sK7 @ X15 @ X14 @ X18 )
= $true ) )
& ( ( sK7 @ X15 @ X14 @ X15 )
!= $true )
& ( ( sK8 @ X15 @ X14 @ X15 )
!= $true )
& ! [X21: a,X22: a] :
( ( ( sK8 @ X15 @ X14 @ X21 )
= $true )
| ( ( sK0 @ X22 @ X21 )
!= $true )
| ( ( sK8 @ X15 @ X14 @ X22 )
!= $true ) )
& ! [X23: a] :
( ( ( sK0 @ X14 @ X23 )
!= $true )
| ( ( sK8 @ X15 @ X14 @ X23 )
= $true ) ) )
| ( ( sK4 @ X15 )
= $true ) )
& ! [X24: a > $o] :
( ( ( X24 @ sK3 )
= $true )
| ( ( ( X24 @ ( sK9 @ X24 ) )
!= $true )
& ( ( ( sK2 @ ( sK10 @ X24 ) @ ( sK9 @ X24 ) )
= $true )
| ( ( sK0 @ ( sK10 @ X24 ) @ ( sK9 @ X24 ) )
= $true ) )
& ( ( X24 @ ( sK10 @ X24 ) )
= $true ) )
| ( ( ( ( sK0 @ sK1 @ ( sK11 @ X24 ) )
= $true )
| ( ( sK2 @ sK1 @ ( sK11 @ X24 ) )
= $true ) )
& ( ( X24 @ ( sK11 @ X24 ) )
!= $true ) ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11])],[f8,f16,f15,f14,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
( ? [X0: a > a > $o,X1: a,X2: a > a > $o,X3: a] :
( ? [X4: a > $o] :
( ( ( X4 @ X3 )
!= $true )
& ! [X5: a] :
( ( ( X4 @ X5 )
= $true )
| ( ? [X6: a > $o] :
( ! [X7: a,X8: a] :
( ( ( X6 @ X7 )
= $true )
| ( ( X0 @ X8 @ X7 )
!= $true )
| ( ( X6 @ X8 )
!= $true ) )
& ( ( X6 @ X5 )
!= $true )
& ! [X9: a] :
( ( ( X0 @ X1 @ X9 )
!= $true )
| ( ( X6 @ X9 )
= $true ) ) )
& ? [X10: a > $o] :
( ( ( X10 @ X5 )
!= $true )
& ! [X11: a,X12: a] :
( ( ( X2 @ X11 @ X12 )
!= $true )
| ( $true
= ( X10 @ X12 ) )
| ( $true
!= ( X10 @ X11 ) ) )
& ! [X13: a] :
( ( ( X10 @ X13 )
= $true )
| ( ( X2 @ X1 @ X13 )
!= $true ) ) ) ) )
& ! [X14: a,X15: a] :
( ( ( X4 @ X14 )
!= $true )
| ( ? [X16: a > $o] :
( ! [X17: a] :
( ( ( X16 @ X17 )
= $true )
| ( ( X2 @ X14 @ X17 )
!= $true ) )
& ! [X18: a,X19: a] :
( ( ( X2 @ X19 @ X18 )
!= $true )
| ( ( X16 @ X19 )
!= $true )
| ( ( X16 @ X18 )
= $true ) )
& ( ( X16 @ X15 )
!= $true ) )
& ? [X20: a > $o] :
( ( ( X20 @ X15 )
!= $true )
& ! [X21: a,X22: a] :
( ( ( X20 @ X21 )
= $true )
| ( ( X0 @ X22 @ X21 )
!= $true )
| ( ( X20 @ X22 )
!= $true ) )
& ! [X23: a] :
( ( ( X0 @ X14 @ X23 )
!= $true )
| ( ( X20 @ X23 )
= $true ) ) ) )
| ( ( X4 @ X15 )
= $true ) ) )
& ! [X24: a > $o] :
( ( ( X24 @ X3 )
= $true )
| ? [X25: a,X26: a] :
( ( ( X24 @ X25 )
!= $true )
& ( ( ( X2 @ X26 @ X25 )
= $true )
| ( ( X0 @ X26 @ X25 )
= $true ) )
& ( ( X24 @ X26 )
= $true ) )
| ? [X27: a] :
( ( ( ( X0 @ X1 @ X27 )
= $true )
| ( ( X2 @ X1 @ X27 )
= $true ) )
& ( ( X24 @ X27 )
!= $true ) ) ) )
=> ( ? [X4: a > $o] :
( ( ( X4 @ sK3 )
!= $true )
& ! [X5: a] :
( ( ( X4 @ X5 )
= $true )
| ( ? [X6: a > $o] :
( ! [X8: a,X7: a] :
( ( ( X6 @ X7 )
= $true )
| ( ( sK0 @ X8 @ X7 )
!= $true )
| ( ( X6 @ X8 )
!= $true ) )
& ( ( X6 @ X5 )
!= $true )
& ! [X9: a] :
( ( $true
!= ( sK0 @ sK1 @ X9 ) )
| ( ( X6 @ X9 )
= $true ) ) )
& ? [X10: a > $o] :
( ( ( X10 @ X5 )
!= $true )
& ! [X12: a,X11: a] :
( ( ( sK2 @ X11 @ X12 )
!= $true )
| ( $true
= ( X10 @ X12 ) )
| ( $true
!= ( X10 @ X11 ) ) )
& ! [X13: a] :
( ( ( X10 @ X13 )
= $true )
| ( ( sK2 @ sK1 @ X13 )
!= $true ) ) ) ) )
& ! [X15: a,X14: a] :
( ( ( X4 @ X14 )
!= $true )
| ( ? [X16: a > $o] :
( ! [X17: a] :
( ( ( X16 @ X17 )
= $true )
| ( ( sK2 @ X14 @ X17 )
!= $true ) )
& ! [X19: a,X18: a] :
( ( ( sK2 @ X19 @ X18 )
!= $true )
| ( ( X16 @ X19 )
!= $true )
| ( ( X16 @ X18 )
= $true ) )
& ( ( X16 @ X15 )
!= $true ) )
& ? [X20: a > $o] :
( ( ( X20 @ X15 )
!= $true )
& ! [X22: a,X21: a] :
( ( ( X20 @ X21 )
= $true )
| ( ( sK0 @ X22 @ X21 )
!= $true )
| ( ( X20 @ X22 )
!= $true ) )
& ! [X23: a] :
( ( ( sK0 @ X14 @ X23 )
!= $true )
| ( ( X20 @ X23 )
= $true ) ) ) )
| ( ( X4 @ X15 )
= $true ) ) )
& ! [X24: a > $o] :
( ( ( X24 @ sK3 )
= $true )
| ? [X26: a,X25: a] :
( ( ( X24 @ X25 )
!= $true )
& ( ( ( sK2 @ X26 @ X25 )
= $true )
| ( ( sK0 @ X26 @ X25 )
= $true ) )
& ( ( X24 @ X26 )
= $true ) )
| ? [X27: a] :
( ( ( ( sK0 @ sK1 @ X27 )
= $true )
| ( $true
= ( sK2 @ sK1 @ X27 ) ) )
& ( ( X24 @ X27 )
!= $true ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
( ? [X4: a > $o] :
( ( ( X4 @ sK3 )
!= $true )
& ! [X5: a] :
( ( ( X4 @ X5 )
= $true )
| ( ? [X6: a > $o] :
( ! [X8: a,X7: a] :
( ( ( X6 @ X7 )
= $true )
| ( ( sK0 @ X8 @ X7 )
!= $true )
| ( ( X6 @ X8 )
!= $true ) )
& ( ( X6 @ X5 )
!= $true )
& ! [X9: a] :
( ( $true
!= ( sK0 @ sK1 @ X9 ) )
| ( ( X6 @ X9 )
= $true ) ) )
& ? [X10: a > $o] :
( ( ( X10 @ X5 )
!= $true )
& ! [X12: a,X11: a] :
( ( ( sK2 @ X11 @ X12 )
!= $true )
| ( $true
= ( X10 @ X12 ) )
| ( $true
!= ( X10 @ X11 ) ) )
& ! [X13: a] :
( ( ( X10 @ X13 )
= $true )
| ( ( sK2 @ sK1 @ X13 )
!= $true ) ) ) ) )
& ! [X15: a,X14: a] :
( ( ( X4 @ X14 )
!= $true )
| ( ? [X16: a > $o] :
( ! [X17: a] :
( ( ( X16 @ X17 )
= $true )
| ( ( sK2 @ X14 @ X17 )
!= $true ) )
& ! [X19: a,X18: a] :
( ( ( sK2 @ X19 @ X18 )
!= $true )
| ( ( X16 @ X19 )
!= $true )
| ( ( X16 @ X18 )
= $true ) )
& ( ( X16 @ X15 )
!= $true ) )
& ? [X20: a > $o] :
( ( ( X20 @ X15 )
!= $true )
& ! [X22: a,X21: a] :
( ( ( X20 @ X21 )
= $true )
| ( ( sK0 @ X22 @ X21 )
!= $true )
| ( ( X20 @ X22 )
!= $true ) )
& ! [X23: a] :
( ( ( sK0 @ X14 @ X23 )
!= $true )
| ( ( X20 @ X23 )
= $true ) ) ) )
| ( ( X4 @ X15 )
= $true ) ) )
=> ( ( ( sK4 @ sK3 )
!= $true )
& ! [X5: a] :
( ( ( sK4 @ X5 )
= $true )
| ( ? [X6: a > $o] :
( ! [X8: a,X7: a] :
( ( ( X6 @ X7 )
= $true )
| ( ( sK0 @ X8 @ X7 )
!= $true )
| ( ( X6 @ X8 )
!= $true ) )
& ( ( X6 @ X5 )
!= $true )
& ! [X9: a] :
( ( $true
!= ( sK0 @ sK1 @ X9 ) )
| ( ( X6 @ X9 )
= $true ) ) )
& ? [X10: a > $o] :
( ( ( X10 @ X5 )
!= $true )
& ! [X12: a,X11: a] :
( ( ( sK2 @ X11 @ X12 )
!= $true )
| ( $true
= ( X10 @ X12 ) )
| ( $true
!= ( X10 @ X11 ) ) )
& ! [X13: a] :
( ( ( X10 @ X13 )
= $true )
| ( ( sK2 @ sK1 @ X13 )
!= $true ) ) ) ) )
& ! [X15: a,X14: a] :
( ( ( sK4 @ X14 )
!= $true )
| ( ? [X16: a > $o] :
( ! [X17: a] :
( ( ( X16 @ X17 )
= $true )
| ( ( sK2 @ X14 @ X17 )
!= $true ) )
& ! [X19: a,X18: a] :
( ( ( sK2 @ X19 @ X18 )
!= $true )
| ( ( X16 @ X19 )
!= $true )
| ( ( X16 @ X18 )
= $true ) )
& ( ( X16 @ X15 )
!= $true ) )
& ? [X20: a > $o] :
( ( ( X20 @ X15 )
!= $true )
& ! [X22: a,X21: a] :
( ( ( X20 @ X21 )
= $true )
| ( ( sK0 @ X22 @ X21 )
!= $true )
| ( ( X20 @ X22 )
!= $true ) )
& ! [X23: a] :
( ( ( sK0 @ X14 @ X23 )
!= $true )
| ( ( X20 @ X23 )
= $true ) ) ) )
| ( ( sK4 @ X15 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X5: a] :
( ? [X6: a > $o] :
( ! [X8: a,X7: a] :
( ( ( X6 @ X7 )
= $true )
| ( ( sK0 @ X8 @ X7 )
!= $true )
| ( ( X6 @ X8 )
!= $true ) )
& ( ( X6 @ X5 )
!= $true )
& ! [X9: a] :
( ( $true
!= ( sK0 @ sK1 @ X9 ) )
| ( ( X6 @ X9 )
= $true ) ) )
=> ( ! [X8: a,X7: a] :
( ( ( sK5 @ X5 @ X7 )
= $true )
| ( ( sK0 @ X8 @ X7 )
!= $true )
| ( ( sK5 @ X5 @ X8 )
!= $true ) )
& ( ( sK5 @ X5 @ X5 )
!= $true )
& ! [X9: a] :
( ( $true
!= ( sK0 @ sK1 @ X9 ) )
| ( ( sK5 @ X5 @ X9 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X5: a] :
( ? [X10: a > $o] :
( ( ( X10 @ X5 )
!= $true )
& ! [X12: a,X11: a] :
( ( ( sK2 @ X11 @ X12 )
!= $true )
| ( $true
= ( X10 @ X12 ) )
| ( $true
!= ( X10 @ X11 ) ) )
& ! [X13: a] :
( ( ( X10 @ X13 )
= $true )
| ( ( sK2 @ sK1 @ X13 )
!= $true ) ) )
=> ( ( ( sK6 @ X5 @ X5 )
!= $true )
& ! [X12: a,X11: a] :
( ( ( sK2 @ X11 @ X12 )
!= $true )
| ( ( sK6 @ X5 @ X12 )
= $true )
| ( ( sK6 @ X5 @ X11 )
!= $true ) )
& ! [X13: a] :
( ( ( sK6 @ X5 @ X13 )
= $true )
| ( ( sK2 @ sK1 @ X13 )
!= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X14: a,X15: a] :
( ? [X16: a > $o] :
( ! [X17: a] :
( ( ( X16 @ X17 )
= $true )
| ( ( sK2 @ X14 @ X17 )
!= $true ) )
& ! [X19: a,X18: a] :
( ( ( sK2 @ X19 @ X18 )
!= $true )
| ( ( X16 @ X19 )
!= $true )
| ( ( X16 @ X18 )
= $true ) )
& ( ( X16 @ X15 )
!= $true ) )
=> ( ! [X17: a] :
( ( ( sK7 @ X15 @ X14 @ X17 )
= $true )
| ( ( sK2 @ X14 @ X17 )
!= $true ) )
& ! [X19: a,X18: a] :
( ( ( sK2 @ X19 @ X18 )
!= $true )
| ( ( sK7 @ X15 @ X14 @ X19 )
!= $true )
| ( ( sK7 @ X15 @ X14 @ X18 )
= $true ) )
& ( ( sK7 @ X15 @ X14 @ X15 )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
! [X14: a,X15: a] :
( ? [X20: a > $o] :
( ( ( X20 @ X15 )
!= $true )
& ! [X22: a,X21: a] :
( ( ( X20 @ X21 )
= $true )
| ( ( sK0 @ X22 @ X21 )
!= $true )
| ( ( X20 @ X22 )
!= $true ) )
& ! [X23: a] :
( ( ( sK0 @ X14 @ X23 )
!= $true )
| ( ( X20 @ X23 )
= $true ) ) )
=> ( ( ( sK8 @ X15 @ X14 @ X15 )
!= $true )
& ! [X22: a,X21: a] :
( ( ( sK8 @ X15 @ X14 @ X21 )
= $true )
| ( ( sK0 @ X22 @ X21 )
!= $true )
| ( ( sK8 @ X15 @ X14 @ X22 )
!= $true ) )
& ! [X23: a] :
( ( ( sK0 @ X14 @ X23 )
!= $true )
| ( ( sK8 @ X15 @ X14 @ X23 )
= $true ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X24: a > $o] :
( ? [X26: a,X25: a] :
( ( ( X24 @ X25 )
!= $true )
& ( ( ( sK2 @ X26 @ X25 )
= $true )
| ( ( sK0 @ X26 @ X25 )
= $true ) )
& ( ( X24 @ X26 )
= $true ) )
=> ( ( ( X24 @ ( sK9 @ X24 ) )
!= $true )
& ( ( ( sK2 @ ( sK10 @ X24 ) @ ( sK9 @ X24 ) )
= $true )
| ( ( sK0 @ ( sK10 @ X24 ) @ ( sK9 @ X24 ) )
= $true ) )
& ( ( X24 @ ( sK10 @ X24 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
! [X24: a > $o] :
( ? [X27: a] :
( ( ( ( sK0 @ sK1 @ X27 )
= $true )
| ( $true
= ( sK2 @ sK1 @ X27 ) ) )
& ( ( X24 @ X27 )
!= $true ) )
=> ( ( ( ( sK0 @ sK1 @ ( sK11 @ X24 ) )
= $true )
| ( ( sK2 @ sK1 @ ( sK11 @ X24 ) )
= $true ) )
& ( ( X24 @ ( sK11 @ X24 ) )
!= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
? [X0: a > a > $o,X1: a,X2: a > a > $o,X3: a] :
( ? [X4: a > $o] :
( ( ( X4 @ X3 )
!= $true )
& ! [X5: a] :
( ( ( X4 @ X5 )
= $true )
| ( ? [X6: a > $o] :
( ! [X7: a,X8: a] :
( ( ( X6 @ X7 )
= $true )
| ( ( X0 @ X8 @ X7 )
!= $true )
| ( ( X6 @ X8 )
!= $true ) )
& ( ( X6 @ X5 )
!= $true )
& ! [X9: a] :
( ( ( X0 @ X1 @ X9 )
!= $true )
| ( ( X6 @ X9 )
= $true ) ) )
& ? [X10: a > $o] :
( ( ( X10 @ X5 )
!= $true )
& ! [X11: a,X12: a] :
( ( ( X2 @ X11 @ X12 )
!= $true )
| ( $true
= ( X10 @ X12 ) )
| ( $true
!= ( X10 @ X11 ) ) )
& ! [X13: a] :
( ( ( X10 @ X13 )
= $true )
| ( ( X2 @ X1 @ X13 )
!= $true ) ) ) ) )
& ! [X14: a,X15: a] :
( ( ( X4 @ X14 )
!= $true )
| ( ? [X16: a > $o] :
( ! [X17: a] :
( ( ( X16 @ X17 )
= $true )
| ( ( X2 @ X14 @ X17 )
!= $true ) )
& ! [X18: a,X19: a] :
( ( ( X2 @ X19 @ X18 )
!= $true )
| ( ( X16 @ X19 )
!= $true )
| ( ( X16 @ X18 )
= $true ) )
& ( ( X16 @ X15 )
!= $true ) )
& ? [X20: a > $o] :
( ( ( X20 @ X15 )
!= $true )
& ! [X21: a,X22: a] :
( ( ( X20 @ X21 )
= $true )
| ( ( X0 @ X22 @ X21 )
!= $true )
| ( ( X20 @ X22 )
!= $true ) )
& ! [X23: a] :
( ( ( X0 @ X14 @ X23 )
!= $true )
| ( ( X20 @ X23 )
= $true ) ) ) )
| ( ( X4 @ X15 )
= $true ) ) )
& ! [X24: a > $o] :
( ( ( X24 @ X3 )
= $true )
| ? [X25: a,X26: a] :
( ( ( X24 @ X25 )
!= $true )
& ( ( ( X2 @ X26 @ X25 )
= $true )
| ( ( X0 @ X26 @ X25 )
= $true ) )
& ( ( X24 @ X26 )
= $true ) )
| ? [X27: a] :
( ( ( ( X0 @ X1 @ X27 )
= $true )
| ( ( X2 @ X1 @ X27 )
= $true ) )
& ( ( X24 @ X27 )
!= $true ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
? [X0: a > a > $o,X2: a,X1: a > a > $o,X3: a] :
( ? [X8: a > $o] :
( ( ( X8 @ X3 )
!= $true )
& ! [X19: a] :
( ( ( X8 @ X19 )
= $true )
| ( ? [X24: a > $o] :
( ! [X26: a,X25: a] :
( ( ( X24 @ X26 )
= $true )
| ( ( X0 @ X25 @ X26 )
!= $true )
| ( ( X24 @ X25 )
!= $true ) )
& ( ( X24 @ X19 )
!= $true )
& ! [X27: a] :
( ( ( X0 @ X2 @ X27 )
!= $true )
| ( ( X24 @ X27 )
= $true ) ) )
& ? [X20: a > $o] :
( ( ( X20 @ X19 )
!= $true )
& ! [X22: a,X21: a] :
( ( ( X1 @ X22 @ X21 )
!= $true )
| ( ( X20 @ X21 )
= $true )
| ( ( X20 @ X22 )
!= $true ) )
& ! [X23: a] :
( ( ( X20 @ X23 )
= $true )
| ( ( X1 @ X2 @ X23 )
!= $true ) ) ) ) )
& ! [X9: a,X10: a] :
( ( ( X8 @ X9 )
!= $true )
| ( ? [X11: a > $o] :
( ! [X12: a] :
( ( ( X11 @ X12 )
= $true )
| ( ( X1 @ X9 @ X12 )
!= $true ) )
& ! [X13: a,X14: a] :
( ( ( X1 @ X14 @ X13 )
!= $true )
| ( ( X11 @ X14 )
!= $true )
| ( ( X11 @ X13 )
= $true ) )
& ( $true
!= ( X11 @ X10 ) ) )
& ? [X15: a > $o] :
( ( ( X15 @ X10 )
!= $true )
& ! [X17: a,X16: a] :
( ( ( X15 @ X17 )
= $true )
| ( ( X0 @ X16 @ X17 )
!= $true )
| ( ( X15 @ X16 )
!= $true ) )
& ! [X18: a] :
( ( ( X0 @ X9 @ X18 )
!= $true )
| ( ( X15 @ X18 )
= $true ) ) ) )
| ( ( X8 @ X10 )
= $true ) ) )
& ! [X4: a > $o] :
( ( ( X4 @ X3 )
= $true )
| ? [X6: a,X5: a] :
( ( ( X4 @ X6 )
!= $true )
& ( ( ( X1 @ X5 @ X6 )
= $true )
| ( ( X0 @ X5 @ X6 )
= $true ) )
& ( ( X4 @ X5 )
= $true ) )
| ? [X7: a] :
( ( ( ( X0 @ X2 @ X7 )
= $true )
| ( ( X1 @ X2 @ X7 )
= $true ) )
& ( ( X4 @ X7 )
!= $true ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
? [X2: a,X0: a > a > $o,X3: a,X1: a > a > $o] :
( ? [X8: a > $o] :
( ( ( X8 @ X3 )
!= $true )
& ! [X19: a] :
( ( ( X8 @ X19 )
= $true )
| ( ? [X24: a > $o] :
( ( ( X24 @ X19 )
!= $true )
& ! [X27: a] :
( ( ( X0 @ X2 @ X27 )
!= $true )
| ( ( X24 @ X27 )
= $true ) )
& ! [X26: a,X25: a] :
( ( ( X24 @ X26 )
= $true )
| ( ( X24 @ X25 )
!= $true )
| ( ( X0 @ X25 @ X26 )
!= $true ) ) )
& ? [X20: a > $o] :
( ( ( X20 @ X19 )
!= $true )
& ! [X23: a] :
( ( ( X20 @ X23 )
= $true )
| ( ( X1 @ X2 @ X23 )
!= $true ) )
& ! [X21: a,X22: a] :
( ( ( X20 @ X21 )
= $true )
| ( ( X20 @ X22 )
!= $true )
| ( ( X1 @ X22 @ X21 )
!= $true ) ) ) ) )
& ! [X10: a,X9: a] :
( ( ( X8 @ X10 )
= $true )
| ( ( X8 @ X9 )
!= $true )
| ( ? [X15: a > $o] :
( ( ( X15 @ X10 )
!= $true )
& ! [X18: a] :
( ( ( X0 @ X9 @ X18 )
!= $true )
| ( ( X15 @ X18 )
= $true ) )
& ! [X16: a,X17: a] :
( ( ( X15 @ X17 )
= $true )
| ( ( X15 @ X16 )
!= $true )
| ( ( X0 @ X16 @ X17 )
!= $true ) ) )
& ? [X11: a > $o] :
( ( $true
!= ( X11 @ X10 ) )
& ! [X14: a,X13: a] :
( ( ( X11 @ X13 )
= $true )
| ( ( X11 @ X14 )
!= $true )
| ( ( X1 @ X14 @ X13 )
!= $true ) )
& ! [X12: a] :
( ( ( X11 @ X12 )
= $true )
| ( ( X1 @ X9 @ X12 )
!= $true ) ) ) ) ) )
& ! [X4: a > $o] :
( ( ( X4 @ X3 )
= $true )
| ? [X7: a] :
( ( ( ( X0 @ X2 @ X7 )
= $true )
| ( ( X1 @ X2 @ X7 )
= $true ) )
& ( ( X4 @ X7 )
!= $true ) )
| ? [X6: a,X5: a] :
( ( ( X4 @ X6 )
!= $true )
& ( ( X4 @ X5 )
= $true )
& ( ( ( X1 @ X5 @ X6 )
= $true )
| ( ( X0 @ X5 @ X6 )
= $true ) ) ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ! [X2: a,X0: a > a > $o,X3: a,X1: a > a > $o] :
( ! [X4: a > $o] :
( ( ! [X7: a] :
( ( ( ( X0 @ X2 @ X7 )
= $true )
| ( ( X1 @ X2 @ X7 )
= $true ) )
=> ( ( X4 @ X7 )
= $true ) )
& ! [X6: a,X5: a] :
( ( ( ( X4 @ X5 )
= $true )
& ( ( ( X1 @ X5 @ X6 )
= $true )
| ( ( X0 @ X5 @ X6 )
= $true ) ) )
=> ( ( X4 @ X6 )
= $true ) ) )
=> ( ( X4 @ X3 )
= $true ) )
=> ! [X8: a > $o] :
( ( ! [X19: a] :
( ( ! [X24: a > $o] :
( ( ! [X27: a] :
( ( ( X0 @ X2 @ X27 )
= $true )
=> ( ( X24 @ X27 )
= $true ) )
& ! [X26: a,X25: a] :
( ( ( ( X24 @ X25 )
= $true )
& ( ( X0 @ X25 @ X26 )
= $true ) )
=> ( ( X24 @ X26 )
= $true ) ) )
=> ( ( X24 @ X19 )
= $true ) )
| ! [X20: a > $o] :
( ( ! [X23: a] :
( ( ( X1 @ X2 @ X23 )
= $true )
=> ( ( X20 @ X23 )
= $true ) )
& ! [X21: a,X22: a] :
( ( ( ( X20 @ X22 )
= $true )
& ( ( X1 @ X22 @ X21 )
= $true ) )
=> ( ( X20 @ X21 )
= $true ) ) )
=> ( ( X20 @ X19 )
= $true ) ) )
=> ( ( X8 @ X19 )
= $true ) )
& ! [X10: a,X9: a] :
( ( ( ( X8 @ X9 )
= $true )
& ( ! [X15: a > $o] :
( ( ! [X18: a] :
( ( ( X0 @ X9 @ X18 )
= $true )
=> ( ( X15 @ X18 )
= $true ) )
& ! [X16: a,X17: a] :
( ( ( ( X15 @ X16 )
= $true )
& ( ( X0 @ X16 @ X17 )
= $true ) )
=> ( ( X15 @ X17 )
= $true ) ) )
=> ( ( X15 @ X10 )
= $true ) )
| ! [X11: a > $o] :
( ( ! [X14: a,X13: a] :
( ( ( ( X11 @ X14 )
= $true )
& ( ( X1 @ X14 @ X13 )
= $true ) )
=> ( ( X11 @ X13 )
= $true ) )
& ! [X12: a] :
( ( ( X1 @ X9 @ X12 )
= $true )
=> ( ( X11 @ X12 )
= $true ) ) )
=> ( $true
= ( X11 @ X10 ) ) ) ) )
=> ( ( X8 @ X10 )
= $true ) ) )
=> ( ( X8 @ X3 )
= $true ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ! [X0: a > a > $o,X1: a > a > $o,X2: a,X3: a] :
( ! [X4: a > $o] :
( ( ! [X5: a,X6: a] :
( ( ( ( X0 @ X5 @ X6 )
| ( X1 @ X5 @ X6 ) )
& ( X4 @ X5 ) )
=> ( X4 @ X6 ) )
& ! [X7: a] :
( ( ( X0 @ X2 @ X7 )
| ( X1 @ X2 @ X7 ) )
=> ( X4 @ X7 ) ) )
=> ( X4 @ X3 ) )
=> ! [X8: a > $o] :
( ( ! [X9: a,X10: a] :
( ( ( ! [X11: a > $o] :
( ( ! [X12: a] :
( ( X1 @ X9 @ X12 )
=> ( X11 @ X12 ) )
& ! [X13: a,X14: a] :
( ( ( X11 @ X14 )
& ( X1 @ X14 @ X13 ) )
=> ( X11 @ X13 ) ) )
=> ( X11 @ X10 ) )
| ! [X15: a > $o] :
( ( ! [X16: a,X17: a] :
( ( ( X15 @ X16 )
& ( X0 @ X16 @ X17 ) )
=> ( X15 @ X17 ) )
& ! [X18: a] :
( ( X0 @ X9 @ X18 )
=> ( X15 @ X18 ) ) )
=> ( X15 @ X10 ) ) )
& ( X8 @ X9 ) )
=> ( X8 @ X10 ) )
& ! [X19: a] :
( ( ! [X20: a > $o] :
( ( ! [X21: a,X22: a] :
( ( ( X1 @ X22 @ X21 )
& ( X20 @ X22 ) )
=> ( X20 @ X21 ) )
& ! [X23: a] :
( ( X1 @ X2 @ X23 )
=> ( X20 @ X23 ) ) )
=> ( X20 @ X19 ) )
| ! [X24: a > $o] :
( ( ! [X25: a,X26: a] :
( ( ( X24 @ X25 )
& ( X0 @ X25 @ X26 ) )
=> ( X24 @ X26 ) )
& ! [X27: a] :
( ( X0 @ X2 @ X27 )
=> ( X24 @ X27 ) ) )
=> ( X24 @ X19 ) ) )
=> ( X8 @ X19 ) ) )
=> ( X8 @ X3 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ! [X0: a > a > $o,X1: a > a > $o,X2: a,X3: a] :
( ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( ! [X8: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X6 @ X5 )
=> ( X8 @ X5 ) )
& ! [X11: a,X10: a] :
( ( ( X8 @ X10 )
& ( X1 @ X10 @ X11 ) )
=> ( X8 @ X11 ) ) )
=> ( X8 @ X7 ) )
| ! [X8: a > $o] :
( ( ! [X10: a,X11: a] :
( ( ( X8 @ X10 )
& ( X0 @ X10 @ X11 ) )
=> ( X8 @ X11 ) )
& ! [X5: a] :
( ( X0 @ X6 @ X5 )
=> ( X8 @ X5 ) ) )
=> ( X8 @ X7 ) ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ! [X8: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( X1 @ X6 @ X7 )
& ( X8 @ X6 ) )
=> ( X8 @ X7 ) )
& ! [X9: a] :
( ( X1 @ X2 @ X9 )
=> ( X8 @ X9 ) ) )
=> ( X8 @ X5 ) )
| ! [X8: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( X8 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X8 @ X7 ) )
& ! [X9: a] :
( ( X0 @ X2 @ X9 )
=> ( X8 @ X9 ) ) )
=> ( X8 @ X5 ) ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
! [X0: a > a > $o,X1: a > a > $o,X2: a,X3: a] :
( ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( ( X0 @ X6 @ X7 )
| ( X1 @ X6 @ X7 ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ( X0 @ X2 @ X5 )
| ( X1 @ X2 @ X5 ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) )
=> ! [X4: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( ! [X8: a > $o] :
( ( ! [X5: a] :
( ( X1 @ X6 @ X5 )
=> ( X8 @ X5 ) )
& ! [X11: a,X10: a] :
( ( ( X8 @ X10 )
& ( X1 @ X10 @ X11 ) )
=> ( X8 @ X11 ) ) )
=> ( X8 @ X7 ) )
| ! [X8: a > $o] :
( ( ! [X10: a,X11: a] :
( ( ( X8 @ X10 )
& ( X0 @ X10 @ X11 ) )
=> ( X8 @ X11 ) )
& ! [X5: a] :
( ( X0 @ X6 @ X5 )
=> ( X8 @ X5 ) ) )
=> ( X8 @ X7 ) ) )
& ( X4 @ X6 ) )
=> ( X4 @ X7 ) )
& ! [X5: a] :
( ( ! [X8: a > $o] :
( ( ! [X7: a,X6: a] :
( ( ( X1 @ X6 @ X7 )
& ( X8 @ X6 ) )
=> ( X8 @ X7 ) )
& ! [X9: a] :
( ( X1 @ X2 @ X9 )
=> ( X8 @ X9 ) ) )
=> ( X8 @ X5 ) )
| ! [X8: a > $o] :
( ( ! [X6: a,X7: a] :
( ( ( X8 @ X6 )
& ( X0 @ X6 @ X7 ) )
=> ( X8 @ X7 ) )
& ! [X9: a] :
( ( X0 @ X2 @ X9 )
=> ( X8 @ X9 ) ) )
=> ( X8 @ X5 ) ) )
=> ( X4 @ X5 ) ) )
=> ( X4 @ X3 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.Ma74ZRMDgU/DTF2THF_9795.p',cTHM251B_pme) ).
thf(f1243,plain,
( ( ( sK4 @ sK3 )
= $true )
| ~ spl12_14
| ~ spl12_42 ),
inference(subsumption_resolution,[status(thm)],[f607,f596]) ).
thf(f596,plain,
( ( ( sK4 @ ( sK9 @ sK4 ) )
= $true )
| ~ spl12_42 ),
inference(avatar_component_clause,[status(thm)],[f595]) ).
thf(f595,definition,
( spl12_42
<=> ( ( sK4 @ ( sK9 @ sK4 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl12_42])],[avatar_definition]) ).
thf(f607,plain,
( ( ( sK4 @ ( sK9 @ sK4 ) )
!= $true )
| ( ( sK4 @ sK3 )
= $true )
| ~ spl12_14 ),
inference(trivial_inequality_removal,[status(thm)],[f606]) ).
thf(f606,plain,
( ( ( sK4 @ sK3 )
= $true )
| ( ( sK4 @ ( sK9 @ sK4 ) )
!= $true )
| ( $true != $true )
| ~ spl12_14 ),
inference(duplicate_literal_removal,[status(thm)],[f605]) ).
thf(f605,plain,
( ( ( sK4 @ ( sK9 @ sK4 ) )
!= $true )
| ( ( sK4 @ sK3 )
= $true )
| ( ( sK4 @ ( sK9 @ sK4 ) )
!= $true )
| ( $true != $true )
| ( ( sK4 @ sK3 )
= $true )
| ~ spl12_14 ),
inference(superposition,[status(thm)],[f22,f203]) ).
thf(f203,plain,
( ! [X0: a > $o] :
( ( ( sK4 @ ( sK11 @ X0 ) )
= $true )
| ( ( X0 @ ( sK9 @ X0 ) )
!= $true )
| ( ( X0 @ sK3 )
= $true ) )
| ~ spl12_14 ),
inference(avatar_component_clause,[status(thm)],[f202]) ).
thf(f202,definition,
( spl12_14
<=> ! [X0: a > $o] :
( ( ( X0 @ sK3 )
= $true )
| ( ( X0 @ ( sK9 @ X0 ) )
!= $true )
| ( ( sK4 @ ( sK11 @ X0 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl12_14])],[avatar_definition]) ).
thf(f22,plain,
! [X24: a > $o] :
( ( ( X24 @ ( sK11 @ X24 ) )
!= $true )
| ( ( X24 @ sK3 )
= $true )
| ( ( X24 @ ( sK9 @ X24 ) )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f1229,plain,
( spl12_42
| ~ spl12_43
| ~ spl12_62 ),
inference(avatar_contradiction_clause,[status(thm)],[f1228]) ).
thf(f1228,plain,
( $false
| spl12_42
| ~ spl12_43
| ~ spl12_62 ),
inference(subsumption_resolution,[status(thm)],[f1227,f597]) ).
thf(f597,plain,
( ( ( sK4 @ ( sK9 @ sK4 ) )
!= $true )
| spl12_42 ),
inference(avatar_component_clause,[status(thm)],[f595]) ).
thf(f1227,plain,
( ( ( sK4 @ ( sK9 @ sK4 ) )
= $true )
| spl12_42
| ~ spl12_43
| ~ spl12_62 ),
inference(subsumption_resolution,[status(thm)],[f1226,f36]) ).
thf(f1226,plain,
( ( ( sK4 @ sK3 )
= $true )
| ( ( sK4 @ ( sK9 @ sK4 ) )
= $true )
| spl12_42
| ~ spl12_43
| ~ spl12_62 ),
inference(subsumption_resolution,[status(thm)],[f1211,f601]) ).
thf(f601,plain,
( ( ( sK4 @ ( sK10 @ sK4 ) )
= $true )
| ~ spl12_43 ),
inference(avatar_component_clause,[status(thm)],[f599]) ).
thf(f599,definition,
( spl12_43
<=> ( ( sK4 @ ( sK10 @ sK4 ) )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl12_43])],[avatar_definition]) ).
thf(f1211,plain,
( ( ( sK4 @ ( sK10 @ sK4 ) )
!= $true )
| ( ( sK4 @ sK3 )
= $true )
| ( ( sK4 @ ( sK9 @ sK4 ) )
= $true )
| spl12_42
| ~ spl12_43
| ~ spl12_62 ),
inference(trivial_inequality_removal,[status(thm)],[f1207]) ).
thf(f1207,plain,
( ( ( sK4 @ ( sK10 @ sK4 ) )
!= $true )
| ( $true != $true )
| ( ( sK4 @ ( sK9 @ sK4 ) )
= $true )
| ( ( sK4 @ sK3 )
= $true )
| spl12_42
| ~ spl12_43
| ~ spl12_62 ),
inference(superposition,[status(thm)],[f963,f1184]) ).
thf(f1184,plain,
( ! [X0: a > $o] :
( ( ( sK4 @ ( sK11 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK9 @ X0 ) )
= $true )
| ( ( X0 @ sK3 )
= $true )
| ( ( sK4 @ ( sK10 @ X0 ) )
!= $true ) )
| ~ spl12_62 ),
inference(avatar_component_clause,[status(thm)],[f1183]) ).
thf(f1183,definition,
( spl12_62
<=> ! [X0: a > $o] :
( ( ( sK4 @ ( sK10 @ X0 ) )
!= $true )
| ( ( X0 @ sK3 )
= $true )
| ( ( sK4 @ ( sK9 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK11 @ X0 ) )
= $true ) ) ),
introduced(definition,[new_symbols(naming,[spl12_62])],[avatar_definition]) ).
thf(f963,plain,
( ( ( sK4 @ ( sK11 @ sK4 ) )
!= $true )
| spl12_42
| ~ spl12_43 ),
inference(subsumption_resolution,[status(thm)],[f962,f36]) ).
thf(f962,plain,
( ( ( sK4 @ ( sK11 @ sK4 ) )
!= $true )
| ( ( sK4 @ sK3 )
= $true )
| spl12_42
| ~ spl12_43 ),
inference(subsumption_resolution,[status(thm)],[f955,f601]) ).
thf(f955,plain,
( ( ( sK4 @ ( sK10 @ sK4 ) )
!= $true )
| ( ( sK4 @ ( sK11 @ sK4 ) )
!= $true )
| ( ( sK4 @ sK3 )
= $true )
| spl12_42 ),
inference(trivial_inequality_removal,[status(thm)],[f954]) ).
thf(f954,plain,
( ( ( sK4 @ ( sK11 @ sK4 ) )
!= $true )
| ( ( sK4 @ ( sK10 @ sK4 ) )
!= $true )
| ( $true != $true )
| ( ( sK4 @ sK3 )
= $true )
| spl12_42 ),
inference(superposition,[status(thm)],[f597,f240]) ).
thf(f240,plain,
! [X0: a > $o] :
( ( ( sK4 @ ( sK9 @ X0 ) )
= $true )
| ( ( X0 @ sK3 )
= $true )
| ( ( sK4 @ ( sK10 @ X0 ) )
!= $true )
| ( ( X0 @ ( sK11 @ X0 ) )
!= $true ) ),
inference(subsumption_resolution,[status(thm)],[f239,f135]) ).
thf(f135,plain,
! [X0: a,X1: a] :
( ( ( sK0 @ X1 @ X0 )
!= $true )
| ( ( sK4 @ X0 )
= $true )
| ( ( sK4 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f134]) ).
thf(f134,plain,
! [X0: a,X1: a] :
( ( ( sK0 @ X1 @ X0 )
!= $true )
| ( ( sK4 @ X0 )
= $true )
| ( $true != $true )
| ( ( sK4 @ X1 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f131]) ).
thf(f131,plain,
! [X0: a,X1: a] :
( ( ( sK4 @ X0 )
= $true )
| ( $true != $true )
| ( ( sK4 @ X1 )
!= $true )
| ( ( sK0 @ X1 @ X0 )
!= $true )
| ( ( sK4 @ X0 )
= $true )
| ( ( sK4 @ X1 )
!= $true ) ),
inference(superposition,[status(thm)],[f26,f24]) ).
thf(f24,plain,
! [X14: a,X15: a,X23: a] :
( ( ( sK8 @ X15 @ X14 @ X23 )
= $true )
| ( ( sK4 @ X15 )
= $true )
| ( ( sK0 @ X14 @ X23 )
!= $true )
| ( ( sK4 @ X14 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f26,plain,
! [X14: a,X15: a] :
( ( ( sK8 @ X15 @ X14 @ X15 )
!= $true )
| ( ( sK4 @ X14 )
!= $true )
| ( ( sK4 @ X15 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f239,plain,
! [X0: a > $o] :
( ( ( X0 @ ( sK11 @ X0 ) )
!= $true )
| ( ( sK0 @ ( sK10 @ X0 ) @ ( sK9 @ X0 ) )
= $true )
| ( ( X0 @ sK3 )
= $true )
| ( ( sK4 @ ( sK10 @ X0 ) )
!= $true )
| ( ( sK4 @ ( sK9 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f238]) ).
thf(f238,plain,
! [X0: a > $o] :
( ( ( X0 @ ( sK11 @ X0 ) )
!= $true )
| ( ( X0 @ sK3 )
= $true )
| ( ( sK0 @ ( sK10 @ X0 ) @ ( sK9 @ X0 ) )
= $true )
| ( $true != $true )
| ( ( sK4 @ ( sK10 @ X0 ) )
!= $true )
| ( ( sK4 @ ( sK9 @ X0 ) )
= $true ) ),
inference(superposition,[status(thm)],[f141,f20]) ).
thf(f20,plain,
! [X24: a > $o] :
( ( ( sK2 @ ( sK10 @ X24 ) @ ( sK9 @ X24 ) )
= $true )
| ( ( X24 @ ( sK11 @ X24 ) )
!= $true )
| ( ( X24 @ sK3 )
= $true )
| ( ( sK0 @ ( sK10 @ X24 ) @ ( sK9 @ X24 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f141,plain,
! [X0: a,X1: a] :
( ( ( sK2 @ X1 @ X0 )
!= $true )
| ( ( sK4 @ X1 )
!= $true )
| ( ( sK4 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f140]) ).
thf(f140,plain,
! [X0: a,X1: a] :
( ( ( sK4 @ X0 )
= $true )
| ( ( sK2 @ X1 @ X0 )
!= $true )
| ( $true != $true )
| ( ( sK4 @ X1 )
!= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f138]) ).
thf(f138,plain,
! [X0: a,X1: a] :
( ( ( sK4 @ X0 )
= $true )
| ( ( sK4 @ X1 )
!= $true )
| ( ( sK4 @ X1 )
!= $true )
| ( $true != $true )
| ( ( sK4 @ X0 )
= $true )
| ( ( sK2 @ X1 @ X0 )
!= $true ) ),
inference(superposition,[status(thm)],[f27,f29]) ).
thf(f29,plain,
! [X14: a,X17: a,X15: a] :
( ( ( sK7 @ X15 @ X14 @ X17 )
= $true )
| ( ( sK4 @ X14 )
!= $true )
| ( ( sK2 @ X14 @ X17 )
!= $true )
| ( ( sK4 @ X15 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f27,plain,
! [X14: a,X15: a] :
( ( ( sK7 @ X15 @ X14 @ X15 )
!= $true )
| ( ( sK4 @ X15 )
= $true )
| ( ( sK4 @ X14 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f1192,plain,
spl12_62,
inference(avatar_split_clause,[status(thm)],[f1191,f1183]) ).
thf(f1191,plain,
! [X0: a > $o] :
( ( ( sK4 @ ( sK11 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK9 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK10 @ X0 ) )
!= $true )
| ( ( X0 @ sK3 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f1169,f95]) ).
thf(f95,plain,
! [X0: a] :
( ( ( sK0 @ sK1 @ X0 )
!= $true )
| ( ( sK4 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f94]) ).
thf(f94,plain,
! [X0: a] :
( ( ( sK4 @ X0 )
= $true )
| ( ( sK0 @ sK1 @ X0 )
!= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f92]) ).
thf(f92,plain,
! [X0: a] :
( ( ( sK0 @ sK1 @ X0 )
!= $true )
| ( ( sK4 @ X0 )
= $true )
| ( $true != $true )
| ( ( sK4 @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f34,f33]) ).
thf(f33,plain,
! [X9: a,X5: a] :
( ( ( sK5 @ X5 @ X9 )
= $true )
| ( $true
!= ( sK0 @ sK1 @ X9 ) )
| ( ( sK4 @ X5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f34,plain,
! [X5: a] :
( ( ( sK5 @ X5 @ X5 )
!= $true )
| ( ( sK4 @ X5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f1169,plain,
! [X0: a > $o] :
( ( ( sK4 @ ( sK9 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK10 @ X0 ) )
!= $true )
| ( ( sK4 @ ( sK11 @ X0 ) )
= $true )
| ( ( X0 @ sK3 )
= $true )
| ( ( sK0 @ sK1 @ ( sK11 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f1152]) ).
thf(f1152,plain,
! [X0: a > $o] :
( ( ( X0 @ sK3 )
= $true )
| ( ( sK4 @ ( sK11 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK9 @ X0 ) )
= $true )
| ( ( sK0 @ sK1 @ ( sK11 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK10 @ X0 ) )
!= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f75,f243]) ).
thf(f243,plain,
! [X0: a > $o] :
( ( ( sK2 @ sK1 @ ( sK11 @ X0 ) )
= $true )
| ( ( sK0 @ sK1 @ ( sK11 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK9 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK10 @ X0 ) )
!= $true )
| ( ( X0 @ sK3 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f242,f135]) ).
thf(f242,plain,
! [X0: a > $o] :
( ( ( X0 @ sK3 )
= $true )
| ( ( sK2 @ sK1 @ ( sK11 @ X0 ) )
= $true )
| ( ( sK0 @ ( sK10 @ X0 ) @ ( sK9 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK10 @ X0 ) )
!= $true )
| ( ( sK4 @ ( sK9 @ X0 ) )
= $true )
| ( ( sK0 @ sK1 @ ( sK11 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f241]) ).
thf(f241,plain,
! [X0: a > $o] :
( ( $true != $true )
| ( ( sK0 @ sK1 @ ( sK11 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK10 @ X0 ) )
!= $true )
| ( ( sK0 @ ( sK10 @ X0 ) @ ( sK9 @ X0 ) )
= $true )
| ( ( sK2 @ sK1 @ ( sK11 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK9 @ X0 ) )
= $true )
| ( ( X0 @ sK3 )
= $true ) ),
inference(superposition,[status(thm)],[f141,f21]) ).
thf(f21,plain,
! [X24: a > $o] :
( ( ( sK2 @ ( sK10 @ X24 ) @ ( sK9 @ X24 ) )
= $true )
| ( ( sK0 @ sK1 @ ( sK11 @ X24 ) )
= $true )
| ( ( sK2 @ sK1 @ ( sK11 @ X24 ) )
= $true )
| ( ( X24 @ sK3 )
= $true )
| ( ( sK0 @ ( sK10 @ X24 ) @ ( sK9 @ X24 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f75,plain,
! [X0: a] :
( ( ( sK2 @ sK1 @ X0 )
!= $true )
| ( ( sK4 @ X0 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f74]) ).
thf(f74,plain,
! [X0: a] :
( ( ( sK2 @ sK1 @ X0 )
!= $true )
| ( ( sK4 @ X0 )
= $true )
| ( $true != $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f72]) ).
thf(f72,plain,
! [X0: a] :
( ( $true != $true )
| ( ( sK4 @ X0 )
= $true )
| ( ( sK2 @ sK1 @ X0 )
!= $true )
| ( ( sK4 @ X0 )
= $true ) ),
inference(superposition,[status(thm)],[f32,f30]) ).
thf(f30,plain,
! [X5: a,X13: a] :
( ( ( sK6 @ X5 @ X13 )
= $true )
| ( ( sK2 @ sK1 @ X13 )
!= $true )
| ( ( sK4 @ X5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f32,plain,
! [X5: a] :
( ( ( sK6 @ X5 @ X5 )
!= $true )
| ( ( sK4 @ X5 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f779,plain,
spl12_43,
inference(avatar_split_clause,[status(thm)],[f778,f599]) ).
thf(f778,plain,
( ( sK4 @ ( sK10 @ sK4 ) )
= $true ),
inference(subsumption_resolution,[status(thm)],[f728,f36]) ).
thf(f728,plain,
( ( ( sK4 @ ( sK10 @ sK4 ) )
= $true )
| ( ( sK4 @ sK3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f727]) ).
thf(f727,plain,
( ( $false = $true )
| ( ( sK4 @ ( sK10 @ sK4 ) )
= $true )
| ( ( sK4 @ sK3 )
= $true ) ),
inference(duplicate_literal_removal,[status(thm)],[f704]) ).
thf(f704,plain,
( ( $false = $true )
| ( ( sK4 @ ( sK10 @ sK4 ) )
= $true )
| ( ( sK4 @ sK3 )
= $true )
| ( ( sK4 @ ( sK10 @ sK4 ) )
= $true )
| ( ( sK4 @ sK3 )
= $true ) ),
inference(superposition,[status(thm)],[f161,f338]) ).
thf(f338,plain,
! [X30: a > $o] :
( ( ( X30 @ ( sK11 @ X30 ) )
= $false )
| ( ( X30 @ ( sK10 @ X30 ) )
= $true )
| ( ( X30 @ sK3 )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f337]) ).
thf(f337,plain,
! [X30: a > $o] :
( ( ( X30 @ sK3 )
= $true )
| ( ( ~ ( X30 @ ( sK10 @ X30 ) ) )
= $false )
| ( ( X30 @ ( sK11 @ X30 ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f336]) ).
thf(f336,plain,
! [X30: a > $o] :
( ( ( ~ ( X30 @ ( sK11 @ X30 ) ) )
= $true )
| ( ( X30 @ sK3 )
= $true )
| ( ( ~ ( X30 @ ( sK10 @ X30 ) ) )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f335]) ).
thf(f335,plain,
! [X30: a > $o] :
( ( $false
= ( ~ ( X30 @ sK3 ) ) )
| ( ( ~ ( X30 @ ( sK10 @ X30 ) ) )
= $false )
| ( ( ~ ( X30 @ ( sK11 @ X30 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f334]) ).
thf(f334,plain,
! [X30: a > $o] :
( ( ( ~ ( X30 @ ( sK11 @ X30 ) ) )
= $true )
| ( $false
= ( ~ ( X30 @ sK3 ) ) )
| ( ( ~ ( X30
@ ( sK10
@ ^ [Y0: a] : ( X30 @ Y0 ) ) ) )
= $false ) ),
inference(boolean_simplification,[status(thm)],[f333]) ).
thf(f333,plain,
! [X30: a > $o] :
( ( $false
= ( ~ ( X30 @ sK3 ) ) )
| ( ( ~ ( X30
@ ( sK10
@ ^ [Y0: a] :
~ ~ ( X30 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( X30 @ ( sK11 @ X30 ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f332]) ).
thf(f332,plain,
! [X30: a > $o] :
( ( ( ~ ( X30
@ ( sK10
@ ^ [Y0: a] :
~ ~ ( X30 @ Y0 ) ) ) )
= $false )
| ( ( ~ ( X30
@ ( sK11
@ ^ [Y0: a] : ( X30 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ~ ( X30 @ sK3 ) ) ) ),
inference(boolean_simplification,[status(thm)],[f331]) ).
thf(f331,plain,
! [X30: a > $o] :
( ( ( ~ ( X30
@ ( sK11
@ ^ [Y0: a] :
~ ~ ( X30 @ Y0 ) ) ) )
= $true )
| ( $false
= ( ~ ( X30 @ sK3 ) ) )
| ( ( ~ ( X30
@ ( sK10
@ ^ [Y0: a] :
~ ~ ( X30 @ Y0 ) ) ) )
= $false ) ),
inference(beta_eta_normalization,[status(thm)],[f311]) ).
thf(f311,plain,
! [X30: a > $o] :
( ( ( ^ [Y0: a] :
~ ( X30 @ Y0 )
@ ( sK10
@ ^ [Y0: a] :
~ ( ^ [Y1: a] :
~ ( X30 @ Y1 )
@ Y0 ) ) )
= $false )
| ( ( ^ [Y0: a] :
~ ( X30 @ Y0 )
@ ( sK11
@ ^ [Y0: a] :
~ ( ^ [Y1: a] :
~ ( X30 @ Y1 )
@ Y0 ) ) )
= $true )
| ( $false
= ( ^ [Y0: a] :
~ ( X30 @ Y0 )
@ sK3 ) ) ),
inference(primitive_instantiation,[status(thm)],[f43]) ).
thf(f43,plain,
! [X27: a > $o] :
( ( ( X27
@ ( sK11
@ ^ [Y0: a] :
~ ( X27 @ Y0 ) ) )
= $true )
| ( ( X27
@ ( sK10
@ ^ [Y0: a] :
~ ( X27 @ Y0 ) ) )
= $false )
| ( ( X27 @ sK3 )
= $false ) ),
inference(not_proxy_clausification,[status(thm)],[f42]) ).
thf(f42,plain,
! [X27: a > $o] :
( ( ( X27
@ ( sK10
@ ^ [Y0: a] :
~ ( X27 @ Y0 ) ) )
= $false )
| ( ( ~ ( X27 @ sK3 ) )
= $true )
| ( ( X27
@ ( sK11
@ ^ [Y0: a] :
~ ( X27 @ Y0 ) ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f41]) ).
thf(f41,plain,
! [X27: a > $o] :
( ( ( X27
@ ( sK11
@ ^ [Y0: a] :
~ ( X27 @ Y0 ) ) )
= $true )
| ( ( ~ ( X27
@ ( sK10
@ ^ [Y0: a] :
~ ( X27 @ Y0 ) ) ) )
= $true )
| ( ( ~ ( X27 @ sK3 ) )
= $true ) ),
inference(not_proxy_clausification,[status(thm)],[f40]) ).
thf(f40,plain,
! [X27: a > $o] :
( ( ( ~ ( X27
@ ( sK11
@ ^ [Y0: a] :
~ ( X27 @ Y0 ) ) ) )
!= $true )
| ( ( ~ ( X27 @ sK3 ) )
= $true )
| ( ( ~ ( X27
@ ( sK10
@ ^ [Y0: a] :
~ ( X27 @ Y0 ) ) ) )
= $true ) ),
inference(beta_eta_normalization,[status(thm)],[f39]) ).
thf(f39,plain,
! [X27: a > $o] :
( ( ( ^ [Y0: a] :
~ ( X27 @ Y0 )
@ ( sK10
@ ^ [Y0: a] :
~ ( X27 @ Y0 ) ) )
= $true )
| ( ( ^ [Y0: a] :
~ ( X27 @ Y0 )
@ sK3 )
= $true )
| ( ( ^ [Y0: a] :
~ ( X27 @ Y0 )
@ ( sK11
@ ^ [Y0: a] :
~ ( X27 @ Y0 ) ) )
!= $true ) ),
inference(primitive_instantiation,[status(thm)],[f18]) ).
thf(f18,plain,
! [X24: a > $o] :
( ( ( X24 @ ( sK10 @ X24 ) )
= $true )
| ( ( X24 @ ( sK11 @ X24 ) )
!= $true )
| ( ( X24 @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f161,plain,
! [X0: a > $o] :
( ( ( sK4 @ ( sK11 @ X0 ) )
= $true )
| ( ( X0 @ ( sK10 @ X0 ) )
= $true )
| ( ( X0 @ sK3 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f160,f95]) ).
thf(f160,plain,
! [X0: a > $o] :
( ( ( X0 @ sK3 )
= $true )
| ( ( sK4 @ ( sK11 @ X0 ) )
= $true )
| ( ( X0 @ ( sK10 @ X0 ) )
= $true )
| ( ( sK0 @ sK1 @ ( sK11 @ X0 ) )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f147]) ).
thf(f147,plain,
! [X0: a > $o] :
( ( ( X0 @ sK3 )
= $true )
| ( ( sK0 @ sK1 @ ( sK11 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK11 @ X0 ) )
= $true )
| ( ( X0 @ ( sK10 @ X0 ) )
= $true )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f75,f19]) ).
thf(f19,plain,
! [X24: a > $o] :
( ( ( sK2 @ sK1 @ ( sK11 @ X24 ) )
= $true )
| ( ( X24 @ ( sK10 @ X24 ) )
= $true )
| ( ( X24 @ sK3 )
= $true )
| ( ( sK0 @ sK1 @ ( sK11 @ X24 ) )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f210,plain,
spl12_14,
inference(avatar_split_clause,[status(thm)],[f209,f202]) ).
thf(f209,plain,
! [X0: a > $o] :
( ( ( X0 @ ( sK9 @ X0 ) )
!= $true )
| ( ( sK4 @ ( sK11 @ X0 ) )
= $true )
| ( ( X0 @ sK3 )
= $true ) ),
inference(subsumption_resolution,[status(thm)],[f186,f95]) ).
thf(f186,plain,
! [X0: a > $o] :
( ( ( sK0 @ sK1 @ ( sK11 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK11 @ X0 ) )
= $true )
| ( ( X0 @ ( sK9 @ X0 ) )
!= $true )
| ( ( X0 @ sK3 )
= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f183]) ).
thf(f183,plain,
! [X0: a > $o] :
( ( ( sK0 @ sK1 @ ( sK11 @ X0 ) )
= $true )
| ( ( sK4 @ ( sK11 @ X0 ) )
= $true )
| ( ( X0 @ ( sK9 @ X0 ) )
!= $true )
| ( $true != $true )
| ( ( X0 @ sK3 )
= $true ) ),
inference(superposition,[status(thm)],[f75,f23]) ).
thf(f23,plain,
! [X24: a > $o] :
( ( ( sK2 @ sK1 @ ( sK11 @ X24 ) )
= $true )
| ( ( sK0 @ sK1 @ ( sK11 @ X24 ) )
= $true )
| ( ( X24 @ ( sK9 @ X24 ) )
!= $true )
| ( ( X24 @ sK3 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV149^5 : TPTP v9.2.1. Released v4.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n020.cluster.edu
% 0.16/0.34 % Model : x86_64 x86_64
% 0.16/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.34 % Memory : 8042.1875MB
% 0.16/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.34 % CPULimit : 300
% 0.16/0.34 % WCLimit : 300
% 0.16/0.34 % DateTime : Tue Feb 24 12:41:12 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.19/0.47 ---- Original DTF file ---
% 0.19/0.47 thf(spec,logic,$$dhol).
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 % File : SEV149^5 : TPTP v9.2.1. Released v4.0.0.
% 0.19/0.47 % Domain : Set Theory (Relations)
% 0.19/0.47 % Problem : TPS problem from TRANSITIVE-CLOSURE
% 0.19/0.47 % Version : Especial.
% 0.19/0.47 % English :
% 0.19/0.47
% 0.19/0.47 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.19/0.47 % Source : [Bro09]
% 0.19/0.47 % Names : tps_1187 [Bro09]
% 0.19/0.47
% 0.19/0.47 % Status : Theorem
% 0.19/0.47 % Rating : 0.08 v9.1.0, 0.12 v9.0.0, 0.08 v8.2.0, 0.09 v8.1.0, 0.17 v7.4.0, 0.11 v7.3.0, 0.20 v7.2.0, 0.12 v7.1.0, 0.14 v7.0.0, 0.12 v6.4.0, 0.14 v6.3.0, 0.17 v6.0.0, 0.00 v5.2.0, 0.50 v5.1.0, 0.75 v5.0.0, 0.25 v4.1.0, 0.33 v4.0.0
% 0.19/0.47 % Syntax : Number of formulae : 2 ( 0 unt; 1 typ; 0 def)
% 0.19/0.47 % Number of atoms : 0 ( 0 equ; 0 cnn)
% 0.19/0.47 % Maximal formula atoms : 0 ( 0 avg)
% 0.19/0.47 % Number of connectives : 83 ( 0 ~; 4 |; 12 &; 48 @)
% 0.19/0.47 % ( 0 <=>; 19 =>; 0 <=; 0 <~>)
% 0.19/0.47 % Maximal formula depth : 23 ( 23 avg)
% 0.19/0.47 % Number of types : 2 ( 1 usr)
% 0.19/0.47 % Number of type conns : 10 ( 10 >; 0 *; 0 +; 0 <<)
% 0.19/0.47 % Number of symbols : 0 ( 0 usr; 0 con; --- aty)
% 0.19/0.47 % Number of variables : 28 ( 0 ^; 28 !; 0 ?; 28 :)
% 0.19/0.47 % SPC : TH0_THM_NEQ_NAR
% 0.19/0.47
% 0.19/0.47 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.19/0.47 % project in the Department of Mathematical Sciences at Carnegie
% 0.19/0.47 % Mellon University. Distributed under the Creative Commons copyleft
% 0.19/0.47 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 thf(a_type,type,
% 0.19/0.47 a: $tType ).
% 0.19/0.47
% 0.19/0.47 thf(cTHM251B_pme,conjecture,
% 0.19/0.47 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 0.19/0.47 ( ! [Xq: a > $o] :
% 0.19/0.47 ( ( ! [Xw: a] :
% 0.19/0.47 ( ( ( R @ Xx @ Xw )
% 0.19/0.47 | ( S @ Xx @ Xw ) )
% 0.19/0.47 => ( Xq @ Xw ) )
% 0.19/0.47 & ! [Xu: a,Xv: a] :
% 0.19/0.47 ( ( ( Xq @ Xu )
% 0.19/0.47 & ( ( R @ Xu @ Xv )
% 0.19/0.47 | ( S @ Xu @ Xv ) ) )
% 0.19/0.47 => ( Xq @ Xv ) ) )
% 0.19/0.47 => ( Xq @ Xy ) )
% 0.19/0.47 => ! [Xq: a > $o] :
% 0.19/0.47 ( ( ! [Xw: a] :
% 0.19/0.47 ( ( ! [Xq0: a > $o] :
% 0.19/0.47 ( ( ! [Xw0: a] :
% 0.19/0.47 ( ( R @ Xx @ Xw0 )
% 0.19/0.47 => ( Xq0 @ Xw0 ) )
% 0.19/0.47 & ! [Xu: a,Xv: a] :
% 0.19/0.47 ( ( ( Xq0 @ Xu )
% 0.19/0.47 & ( R @ Xu @ Xv ) )
% 0.19/0.47 => ( Xq0 @ Xv ) ) )
% 0.19/0.47 => ( Xq0 @ Xw ) )
% 0.19/0.47 | ! [Xq0: a > $o] :
% 0.19/0.47 ( ( ! [Xw0: a] :
% 0.19/0.47 ( ( S @ Xx @ Xw0 )
% 0.19/0.47 => ( Xq0 @ Xw0 ) )
% 0.19/0.47 & ! [Xu: a,Xv: a] :
% 0.19/0.47 ( ( ( Xq0 @ Xu )
% 0.19/0.47 & ( S @ Xu @ Xv ) )
% 0.19/0.47 => ( Xq0 @ Xv ) ) )
% 0.19/0.47 => ( Xq0 @ Xw ) ) )
% 0.19/0.47 => ( Xq @ Xw ) )
% 0.19/0.47 & ! [Xu: a,Xv: a] :
% 0.19/0.47 ( ( ( Xq @ Xu )
% 0.19/0.47 & ( ! [Xq0: a > $o] :
% 0.19/0.47 ( ( ! [Xw: a] :
% 0.19/0.47 ( ( R @ Xu @ Xw )
% 0.19/0.47 => ( Xq0 @ Xw ) )
% 0.19/0.47 & ! [Xu0: a,Xv0: a] :
% 0.19/0.47 ( ( ( Xq0 @ Xu0 )
% 0.19/0.47 & ( R @ Xu0 @ Xv0 ) )
% 0.19/0.47 => ( Xq0 @ Xv0 ) ) )
% 0.19/0.47 => ( Xq0 @ Xv ) )
% 0.19/0.47 | ! [Xq0: a > $o] :
% 0.19/0.47 ( ( ! [Xw: a] :
% 0.19/0.47 ( ( S @ Xu @ Xw )
% 0.19/0.47 => ( Xq0 @ Xw ) )
% 0.19/0.47 & ! [Xu0: a,Xv0: a] :
% 0.19/0.47 ( ( ( Xq0 @ Xu0 )
% 0.19/0.47 & ( S @ Xu0 @ Xv0 ) )
% 0.19/0.47 => ( Xq0 @ Xv0 ) ) )
% 0.19/0.47 => ( Xq0 @ Xv ) ) ) )
% 0.19/0.47 => ( Xq @ Xv ) ) )
% 0.19/0.47 => ( Xq @ Xy ) ) ) ).
% 0.19/0.47
% 0.19/0.47 %------------------------------------------------------------------------------
% 0.19/0.47 ------------------------
% 1.51/1.27 ---- Embedded in THF ---
% 1.51/1.28 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.51/1.28 %%% Generated on Tue Feb 24 12:41:13 EST 2026
% 1.51/1.28 %%% using '$$dhol' embedding, version 1.3.0.
% 1.51/1.28 %%% Logic specification used:
% 1.51/1.28 %%% thf(spec, logic, $$dhol).
% 1.51/1.28
% 1.51/1.28 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.Ma74ZRMDgU/DTF2DTF9795.p
% See solution above
% 1.51/1.28 ------------------------
% 1.51/1.29 ---- Cleaned THF ---
% 1.51/1.29 thf(a_type,type,
% 1.51/1.29 a: $tType ).
% 1.51/1.29
% 1.51/1.29 thf(cTHM251B_pme,conjecture,
% 1.51/1.29 ! [R: a > a > $o,S: a > a > $o,Xx: a,Xy: a] :
% 1.51/1.29 ( ! [Xq: a > $o] :
% 1.51/1.29 ( ( ! [Xw: a] :
% 1.51/1.29 ( ( ( R @ Xx @ Xw )
% 1.51/1.29 | ( S @ Xx @ Xw ) )
% 1.51/1.29 => ( Xq @ Xw ) )
% 1.51/1.29 & ! [Xu: a,Xv: a] :
% 1.51/1.29 ( ( ( Xq @ Xu )
% 1.51/1.29 & ( ( R @ Xu @ Xv )
% 1.51/1.29 | ( S @ Xu @ Xv ) ) )
% 1.51/1.29 => ( Xq @ Xv ) ) )
% 1.51/1.29 => ( Xq @ Xy ) )
% 1.51/1.29 => ! [Xq: a > $o] :
% 1.51/1.29 ( ( ! [Xw: a] :
% 1.51/1.29 ( ( ! [Xq0: a > $o] :
% 1.51/1.29 ( ( ! [Xw0: a] :
% 1.51/1.29 ( ( R @ Xx @ Xw0 )
% 1.51/1.29 => ( Xq0 @ Xw0 ) )
% 1.51/1.29 & ! [Xu: a,Xv: a] :
% 1.51/1.29 ( ( ( Xq0 @ Xu )
% 1.51/1.29 & ( R @ Xu @ Xv ) )
% 1.51/1.29 => ( Xq0 @ Xv ) ) )
% 1.51/1.29 => ( Xq0 @ Xw ) )
% 1.51/1.29 | ! [Xq0: a > $o] :
% 1.51/1.29 ( ( ! [Xw0: a] :
% 1.51/1.29 ( ( S @ Xx @ Xw0 )
% 1.51/1.29 => ( Xq0 @ Xw0 ) )
% 1.51/1.29 & ! [Xu: a,Xv: a] :
% 1.51/1.29 ( ( ( Xq0 @ Xu )
% 1.51/1.29 & ( S @ Xu @ Xv ) )
% 1.51/1.29 => ( Xq0 @ Xv ) ) )
% 1.51/1.29 => ( Xq0 @ Xw ) ) )
% 1.51/1.29 => ( Xq @ Xw ) )
% 1.51/1.29 & ! [Xu: a,Xv: a] :
% 1.51/1.29 ( ( ( Xq @ Xu )
% 1.51/1.29 & ( ! [Xq0: a > $o] :
% 1.51/1.29 ( ( ! [Xw: a] :
% 1.51/1.29 ( ( R @ Xu @ Xw )
% 1.51/1.29 => ( Xq0 @ Xw ) )
% 1.51/1.29 & ! [Xu0: a,Xv0: a] :
% 1.51/1.29 ( ( ( Xq0 @ Xu0 )
% 1.51/1.29 & ( R @ Xu0 @ Xv0 ) )
% 1.51/1.29 => ( Xq0 @ Xv0 ) ) )
% 1.51/1.29 => ( Xq0 @ Xv ) )
% 1.51/1.29 | ! [Xq0: a > $o] :
% 1.51/1.29 ( ( ! [Xw: a] :
% 1.51/1.29 ( ( S @ Xu @ Xw )
% 1.51/1.29 => ( Xq0 @ Xw ) )
% 1.51/1.29 & ! [Xu0: a,Xv0: a] :
% 1.51/1.29 ( ( ( Xq0 @ Xu0 )
% 1.51/1.29 & ( S @ Xu0 @ Xv0 ) )
% 1.51/1.29 => ( Xq0 @ Xv0 ) ) )
% 1.51/1.29 => ( Xq0 @ Xv ) ) ) )
% 1.51/1.29 => ( Xq @ Xv ) ) )
% 1.51/1.29 => ( Xq @ Xy ) ) ) ).
% 1.51/1.29 ------------------------
% 1.69/1.30 % (9985)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_9795 for (2999ds/27Mi)
% 1.69/1.31 % (9984)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_9795 for (2999ds/4Mi)
% 1.69/1.31 % (9986)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/2Mi)
% 1.69/1.31 % (9983)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/183Mi)
% 1.69/1.31 % (9989)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/18Mi)
% 1.69/1.31 % (9986)Instruction limit reached!
% 1.69/1.31 % (9986)------------------------------
% 1.69/1.31 % (9986)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.31 % (9986)Termination reason: Unknown
% 1.69/1.31 % (9986)Termination phase: shuffling
% 1.69/1.31
% 1.69/1.31 % (9986)Memory used [KB]: 1023
% 1.69/1.31 % (9986)Time elapsed: 0.003 s
% 1.69/1.31 % (9986)Instructions burned: 2 (million)
% 1.69/1.31 % (9986)------------------------------
% 1.69/1.31 % (9986)------------------------------
% 1.69/1.32 % (9984)Instruction limit reached!
% 1.69/1.32 % (9984)------------------------------
% 1.69/1.32 % (9984)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (9984)Termination reason: Unknown
% 1.69/1.32 % (9984)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (9984)Memory used [KB]: 5500
% 1.69/1.32 % (9984)Time elapsed: 0.005 s
% 1.69/1.32 % (9984)Instructions burned: 5 (million)
% 1.69/1.32 % (9984)------------------------------
% 1.69/1.32 % (9984)------------------------------
% 1.69/1.32 % (9988)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_9795 for (2999ds/275Mi)
% 1.69/1.32 % (9989)Instruction limit reached!
% 1.69/1.32 % (9989)------------------------------
% 1.69/1.32 % (9989)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.32 % (9989)Termination reason: Unknown
% 1.69/1.32 % (9989)Termination phase: Saturation
% 1.69/1.32
% 1.69/1.32 % (9989)Memory used [KB]: 5628
% 1.69/1.32 % (9989)Time elapsed: 0.013 s
% 1.69/1.32 % (9989)Instructions burned: 18 (million)
% 1.69/1.32 % (9989)------------------------------
% 1.69/1.32 % (9989)------------------------------
% 1.69/1.33 % (9985)Instruction limit reached!
% 1.69/1.33 % (9985)------------------------------
% 1.69/1.33 % (9985)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (9985)Termination reason: Unknown
% 1.69/1.33 % (9985)Termination phase: Saturation
% 1.69/1.33
% 1.69/1.33 % (9985)Memory used [KB]: 5756
% 1.69/1.33 % (9985)Time elapsed: 0.016 s
% 1.69/1.33 % (9985)Instructions burned: 27 (million)
% 1.69/1.33 % (9985)------------------------------
% 1.69/1.33 % (9985)------------------------------
% 1.69/1.33 % (9987)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_9795 for (2999ds/2Mi)
% 1.69/1.33 % (9990)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/3Mi)
% 1.69/1.33 % (9987)Instruction limit reached!
% 1.69/1.33 % (9987)------------------------------
% 1.69/1.33 % (9987)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (9987)Termination reason: Unknown
% 1.69/1.33 % (9987)Termination phase: shuffling
% 1.69/1.33
% 1.69/1.33 % (9987)Memory used [KB]: 1023
% 1.69/1.33 % (9987)Time elapsed: 0.004 s
% 1.69/1.33 % (9987)Instructions burned: 2 (million)
% 1.69/1.33 % (9987)------------------------------
% 1.69/1.33 % (9987)------------------------------
% 1.69/1.33 % (9991)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_9795 for (2999ds/37Mi)
% 1.69/1.33 % (9990)Instruction limit reached!
% 1.69/1.33 % (9990)------------------------------
% 1.69/1.33 % (9990)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.33 % (9990)Termination reason: Unknown
% 1.69/1.33 % (9990)Termination phase: Property scanning
% 1.69/1.33
% 1.69/1.33 % (9990)Memory used [KB]: 1023
% 1.69/1.33 % (9990)Time elapsed: 0.004 s
% 1.69/1.33 % (9990)Instructions burned: 4 (million)
% 1.69/1.33 % (9990)------------------------------
% 1.69/1.33 % (9990)------------------------------
% 1.69/1.34 % (9992)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_9795 for (2999ds/15Mi)
% 1.69/1.34 % (9993)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_9795 for (2999ds/3Mi)
% 1.69/1.35 % (9993)Instruction limit reached!
% 1.69/1.35 % (9993)------------------------------
% 1.69/1.35 % (9993)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (9993)Termination reason: Unknown
% 1.69/1.35 % (9993)Termination phase: Property scanning
% 1.69/1.35
% 1.69/1.35 % (9993)Memory used [KB]: 1023
% 1.69/1.35 % (9993)Time elapsed: 0.003 s
% 1.69/1.35 % (9993)Instructions burned: 4 (million)
% 1.69/1.35 % (9993)------------------------------
% 1.69/1.35 % (9993)------------------------------
% 1.69/1.35 % (9994)lrs+1002_1:1_aac=none:au=on:cnfonf=lazy_gen:plsq=on:plsqc=1:plsqr=4203469,65536:i=1041:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/1041Mi)
% 1.69/1.35 % (9992)Instruction limit reached!
% 1.69/1.35 % (9992)------------------------------
% 1.69/1.35 % (9992)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (9992)Termination reason: Unknown
% 1.69/1.35 % (9992)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (9992)Memory used [KB]: 5628
% 1.69/1.35 % (9992)Time elapsed: 0.011 s
% 1.69/1.35 % (9992)Instructions burned: 15 (million)
% 1.69/1.35 % (9992)------------------------------
% 1.69/1.35 % (9992)------------------------------
% 1.69/1.35 % (9991)Instruction limit reached!
% 1.69/1.35 % (9991)------------------------------
% 1.69/1.35 % (9991)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.35 % (9991)Termination reason: Unknown
% 1.69/1.35 % (9991)Termination phase: Saturation
% 1.69/1.35
% 1.69/1.35 % (9991)Memory used [KB]: 5628
% 1.69/1.35 % (9991)Time elapsed: 0.022 s
% 1.69/1.35 % (9991)Instructions burned: 37 (million)
% 1.69/1.35 % (9991)------------------------------
% 1.69/1.35 % (9991)------------------------------
% 1.69/1.36 % (9996)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/16Mi)
% 1.69/1.36 % (9995)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/7Mi)
% 1.69/1.36 % (9996)Instruction limit reached!
% 1.69/1.36 % (9996)------------------------------
% 1.69/1.36 % (9996)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.36 % (9996)Termination reason: Unknown
% 1.69/1.36 % (9996)Termination phase: Saturation
% 1.69/1.36
% 1.69/1.36 % (9996)Memory used [KB]: 5628
% 1.69/1.36 % (9996)Time elapsed: 0.007 s
% 1.69/1.36 % (9996)Instructions burned: 16 (million)
% 1.69/1.36 % (9996)------------------------------
% 1.69/1.36 % (9996)------------------------------
% 1.69/1.37 % (9995)Instruction limit reached!
% 1.69/1.37 % (9995)------------------------------
% 1.69/1.37 % (9995)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (9995)Termination reason: Unknown
% 1.69/1.37 % (9995)Termination phase: Saturation
% 1.69/1.37
% 1.69/1.37 % (9995)Memory used [KB]: 1151
% 1.69/1.37 % (9995)Time elapsed: 0.008 s
% 1.69/1.37 % (9995)Instructions burned: 8 (million)
% 1.69/1.37 % (9995)------------------------------
% 1.69/1.37 % (9995)------------------------------
% 1.69/1.37 % (9997)lrs+21_1:1_au=on:cnfonf=off:fd=preordered:fe=off:fsr=off:hud=11:inj=on:kws=precedence:s2pl=no:sp=weighted_frequency:tgt=full:i=3:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/3Mi)
% 1.69/1.37 % (9997)Instruction limit reached!
% 1.69/1.37 % (9997)------------------------------
% 1.69/1.37 % (9997)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (9997)Termination reason: Unknown
% 1.69/1.37 % (9997)Termination phase: Preprocessing 3
% 1.69/1.37
% 1.69/1.37 % (9997)Memory used [KB]: 1023
% 1.69/1.37 % (9997)Time elapsed: 0.004 s
% 1.69/1.37 % (9997)Instructions burned: 3 (million)
% 1.69/1.37 % (9997)------------------------------
% 1.69/1.37 % (9997)------------------------------
% 1.69/1.37 % (9998)lrs+2_1:1_apa=on:au=on:bd=preordered:cnfonf=off:cs=on:ixr=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/3Mi)
% 1.69/1.37 % (9998)Instruction limit reached!
% 1.69/1.37 % (9998)------------------------------
% 1.69/1.37 % (9998)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.37 % (9998)Termination reason: Unknown
% 1.69/1.37 % (9998)Termination phase: Preprocessing 3
% 1.69/1.37
% 1.69/1.37 % (9998)Memory used [KB]: 1023
% 1.69/1.37 % (9998)Time elapsed: 0.004 s
% 1.69/1.37 % (9998)Instructions burned: 3 (million)
% 1.69/1.37 % (9998)------------------------------
% 1.69/1.37 % (9998)------------------------------
% 1.69/1.37 % (9999)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/7Mi)
% 1.69/1.38 % (9999)Instruction limit reached!
% 1.69/1.38 % (9999)------------------------------
% 1.69/1.38 % (9999)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.38 % (9999)Termination reason: Unknown
% 1.69/1.38 % (9999)Termination phase: Saturation
% 1.69/1.38
% 1.69/1.38 % (9999)Memory used [KB]: 5628
% 1.69/1.38 % (9999)Time elapsed: 0.004 s
% 1.69/1.38 % (9999)Instructions burned: 9 (million)
% 1.69/1.38 % (9999)------------------------------
% 1.69/1.38 % (9999)------------------------------
% 1.69/1.39 % (10003)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/710Mi)
% 1.69/1.39 % (10001)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/4Mi)
% 1.69/1.39 % (10000)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/3Mi)
% 1.69/1.39 % (10001)Instruction limit reached!
% 1.69/1.39 % (10001)------------------------------
% 1.69/1.39 % (10001)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (10001)Termination reason: Unknown
% 1.69/1.39 % (10001)Termination phase: Preprocessing 3
% 1.69/1.39
% 1.69/1.39 % (10001)Memory used [KB]: 1023
% 1.69/1.39 % (10001)Time elapsed: 0.003 s
% 1.69/1.39 % (10001)Instructions burned: 4 (million)
% 1.69/1.39 % (10001)------------------------------
% 1.69/1.39 % (10001)------------------------------
% 1.69/1.39 % (10000)Instruction limit reached!
% 1.69/1.39 % (10000)------------------------------
% 1.69/1.39 % (10000)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.39 % (10000)Termination reason: Unknown
% 1.69/1.39 % (10000)Termination phase: Property scanning
% 1.69/1.39
% 1.69/1.39 % (10000)Memory used [KB]: 1023
% 1.69/1.39 % (10000)Time elapsed: 0.005 s
% 1.69/1.39 % (10000)Instructions burned: 3 (million)
% 1.69/1.39 % (10000)------------------------------
% 1.69/1.39 % (10000)------------------------------
% 1.69/1.40 % (9988)First to succeed.
% 1.69/1.40 % (10002)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/18Mi)
% 1.69/1.40 % (10004)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_9795 for (2999ds/6Mi)
% 1.69/1.40 % (9988)Refutation found. Thanks to Tanya!
% 1.69/1.40 % SZS status Theorem for DTF2THF_9795
% 1.69/1.40 % SZS output start Proof for DTF2THF_9795
% 1.69/1.40 thf(type_def_5, type, a: $tType).
% 1.69/1.40 thf(func_def_0, type, a: $tType).
% 1.69/1.40 thf(func_def_4, type, sK0: a > a > $o).
% 1.69/1.40 thf(func_def_5, type, sK1: a).
% 1.69/1.40 thf(func_def_6, type, sK2: a > a > $o).
% 1.69/1.40 thf(func_def_7, type, sK3: a).
% 1.69/1.40 thf(func_def_8, type, sK4: a > $o).
% 1.69/1.40 thf(func_def_9, type, sK5: a > a > $o).
% 1.69/1.40 thf(func_def_10, type, sK6: a > a > $o).
% 1.69/1.40 thf(func_def_11, type, sK7: a > a > a > $o).
% 1.69/1.40 thf(func_def_12, type, sK8: a > a > a > $o).
% 1.69/1.40 thf(func_def_13, type, sK9: (a > $o) > a).
% 1.69/1.40 thf(func_def_14, type, sK10: (a > $o) > a).
% 1.69/1.40 thf(func_def_15, type, sK11: (a > $o) > a).
% 1.69/1.40 thf(func_def_18, type, ph13: !>[X0: $tType]:(X0)).
% 1.69/1.40 thf(f1246,plain,(
% 1.69/1.40 $false),
% 1.69/1.40 inference(avatar_sat_refutation,[status(thm)],[f210,f779,f1192,f1229,f1245])).
% 1.69/1.40 thf(f1245,plain,(
% 1.69/1.40 ~spl12_14 | ~spl12_42),
% 1.69/1.40 inference(avatar_contradiction_clause,[status(thm)],[f1244])).
% 1.69/1.40 thf(f1244,plain,(
% 1.69/1.40 $false | (~spl12_14 | ~spl12_42)),
% 1.69/1.40 inference(subsumption_resolution,[status(thm)],[f1243,f36])).
% 1.69/1.40 thf(f36,plain,(
% 1.69/1.40 ((sK4 @ sK3) != $true)),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.40 thf(f17,plain,(
% 1.69/1.40 (((sK4 @ sK3) != $true) & ! [X5 : a] : (((sK4 @ X5) = $true) | ((! [X7 : a,X8 : a] : (((sK5 @ X5 @ X7) = $true) | ((sK0 @ X8 @ X7) != $true) | ((sK5 @ X5 @ X8) != $true)) & ((sK5 @ X5 @ X5) != $true) & ! [X9 : a] : (($true != (sK0 @ sK1 @ X9)) | ((sK5 @ X5 @ X9) = $true))) & (((sK6 @ X5 @ X5) != $true) & ! [X11 : a,X12 : a] : (((sK2 @ X11 @ X12) != $true) | ((sK6 @ X5 @ X12) = $true) | ((sK6 @ X5 @ X11) != $true)) & ! [X13 : a] : (((sK6 @ X5 @ X13) = $true) | ((sK2 @ sK1 @ X13) != $true))))) & ! [X14 : a,X15 : a] : (((sK4 @ X14) != $true) | ((! [X17 : a] : (((sK7 @ X15 @ X14 @ X17) = $true) | ((sK2 @ X14 @ X17) != $true)) & ! [X18 : a,X19 : a] : (((sK2 @ X19 @ X18) != $true) | ((sK7 @ X15 @ X14 @ X19) != $true) | ((sK7 @ X15 @ X14 @ X18) = $true)) & ((sK7 @ X15 @ X14 @ X15) != $true)) & (((sK8 @ X15 @ X14 @ X15) != $true) & ! [X21 : a,X22 : a] : (((sK8 @ X15 @ X14 @ X21) = $true) | ((sK0 @ X22 @ X21) != $true) | ((sK8 @ X15 @ X14 @ X22) != $true)) & ! [X23 : a] : (((sK0 @ X14 @ X23) != $true) | ((sK8 @ X15 @ X14 @ X23) = $true)))) | ((sK4 @ X15) = $true))) & ! [X24 : a > $o] : (((X24 @ sK3) = $true) | (((X24 @ (sK9 @ X24)) != $true) & (((sK2 @ (sK10 @ X24) @ (sK9 @ X24)) = $true) | ((sK0 @ (sK10 @ X24) @ (sK9 @ X24)) = $true)) & ((X24 @ (sK10 @ X24)) = $true)) | ((((sK0 @ sK1 @ (sK11 @ X24)) = $true) | ((sK2 @ sK1 @ (sK11 @ X24)) = $true)) & ((X24 @ (sK11 @ X24)) != $true)))),
% 1.69/1.40 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11])],[f8,f16,f15,f14,f13,f12,f11,f10,f9])).
% 1.69/1.40 thf(f9,plain,(
% 1.69/1.40 ? [X0 : a > a > $o,X1 : a,X2 : a > a > $o,X3 : a] : (? [X4 : a > $o] : (((X4 @ X3) != $true) & ! [X5 : a] : (((X4 @ X5) = $true) | (? [X6 : a > $o] : (! [X7 : a,X8 : a] : (((X6 @ X7) = $true) | ((X0 @ X8 @ X7) != $true) | ((X6 @ X8) != $true)) & ((X6 @ X5) != $true) & ! [X9 : a] : (((X0 @ X1 @ X9) != $true) | ((X6 @ X9) = $true))) & ? [X10 : a > $o] : (((X10 @ X5) != $true) & ! [X11 : a,X12 : a] : (((X2 @ X11 @ X12) != $true) | ($true = (X10 @ X12)) | ($true != (X10 @ X11))) & ! [X13 : a] : (((X10 @ X13) = $true) | ((X2 @ X1 @ X13) != $true))))) & ! [X14 : a,X15 : a] : (((X4 @ X14) != $true) | (? [X16 : a > $o] : (! [X17 : a] : (((X16 @ X17) = $true) | ((X2 @ X14 @ X17) != $true)) & ! [X18 : a,X19 : a] : (((X2 @ X19 @ X18) != $true) | ((X16 @ X19) != $true) | ((X16 @ X18) = $true)) & ((X16 @ X15) != $true)) & ? [X20 : a > $o] : (((X20 @ X15) != $true) & ! [X21 : a,X22 : a] : (((X20 @ X21) = $true) | ((X0 @ X22 @ X21) != $true) | ((X20 @ X22) != $true)) & ! [X23 : a] : (((X0 @ X14 @ X23) != $true) | ((X20 @ X23) = $true)))) | ((X4 @ X15) = $true))) & ! [X24 : a > $o] : (((X24 @ X3) = $true) | ? [X25 : a,X26 : a] : (((X24 @ X25) != $true) & (((X2 @ X26 @ X25) = $true) | ((X0 @ X26 @ X25) = $true)) & ((X24 @ X26) = $true)) | ? [X27 : a] : ((((X0 @ X1 @ X27) = $true) | ((X2 @ X1 @ X27) = $true)) & ((X24 @ X27) != $true)))) => (? [X4 : a > $o] : (((X4 @ sK3) != $true) & ! [X5 : a] : (((X4 @ X5) = $true) | (? [X6 : a > $o] : (! [X8 : a,X7 : a] : (((X6 @ X7) = $true) | ((sK0 @ X8 @ X7) != $true) | ((X6 @ X8) != $true)) & ((X6 @ X5) != $true) & ! [X9 : a] : (($true != (sK0 @ sK1 @ X9)) | ((X6 @ X9) = $true))) & ? [X10 : a > $o] : (((X10 @ X5) != $true) & ! [X12 : a,X11 : a] : (((sK2 @ X11 @ X12) != $true) | ($true = (X10 @ X12)) | ($true != (X10 @ X11))) & ! [X13 : a] : (((X10 @ X13) = $true) | ((sK2 @ sK1 @ X13) != $true))))) & ! [X15 : a,X14 : a] : (((X4 @ X14) != $true) | (? [X16 : a > $o] : (! [X17 : a] : (((X16 @ X17) = $true) | ((sK2 @ X14 @ X17) != $true)) & ! [X19 : a,X18 : a] : (((sK2 @ X19 @ X18) != $true) | ((X16 @ X19) != $true) | ((X16 @ X18) = $true)) & ((X16 @ X15) != $true)) & ? [X20 : a > $o] : (((X20 @ X15) != $true) & ! [X22 : a,X21 : a] : (((X20 @ X21) = $true) | ((sK0 @ X22 @ X21) != $true) | ((X20 @ X22) != $true)) & ! [X23 : a] : (((sK0 @ X14 @ X23) != $true) | ((X20 @ X23) = $true)))) | ((X4 @ X15) = $true))) & ! [X24 : a > $o] : (((X24 @ sK3) = $true) | ? [X26 : a,X25 : a] : (((X24 @ X25) != $true) & (((sK2 @ X26 @ X25) = $true) | ((sK0 @ X26 @ X25) = $true)) & ((X24 @ X26) = $true)) | ? [X27 : a] : ((((sK0 @ sK1 @ X27) = $true) | ($true = (sK2 @ sK1 @ X27))) & ((X24 @ X27) != $true))))),
% 1.69/1.40 introduced(definition,[],[choice_axiom])).
% 1.69/1.40 thf(f10,plain,(
% 1.69/1.40 ? [X4 : a > $o] : (((X4 @ sK3) != $true) & ! [X5 : a] : (((X4 @ X5) = $true) | (? [X6 : a > $o] : (! [X8 : a,X7 : a] : (((X6 @ X7) = $true) | ((sK0 @ X8 @ X7) != $true) | ((X6 @ X8) != $true)) & ((X6 @ X5) != $true) & ! [X9 : a] : (($true != (sK0 @ sK1 @ X9)) | ((X6 @ X9) = $true))) & ? [X10 : a > $o] : (((X10 @ X5) != $true) & ! [X12 : a,X11 : a] : (((sK2 @ X11 @ X12) != $true) | ($true = (X10 @ X12)) | ($true != (X10 @ X11))) & ! [X13 : a] : (((X10 @ X13) = $true) | ((sK2 @ sK1 @ X13) != $true))))) & ! [X15 : a,X14 : a] : (((X4 @ X14) != $true) | (? [X16 : a > $o] : (! [X17 : a] : (((X16 @ X17) = $true) | ((sK2 @ X14 @ X17) != $true)) & ! [X19 : a,X18 : a] : (((sK2 @ X19 @ X18) != $true) | ((X16 @ X19) != $true) | ((X16 @ X18) = $true)) & ((X16 @ X15) != $true)) & ? [X20 : a > $o] : (((X20 @ X15) != $true) & ! [X22 : a,X21 : a] : (((X20 @ X21) = $true) | ((sK0 @ X22 @ X21) != $true) | ((X20 @ X22) != $true)) & ! [X23 : a] : (((sK0 @ X14 @ X23) != $true) | ((X20 @ X23) = $true)))) | ((X4 @ X15) = $true))) => (((sK4 @ sK3) != $true) & ! [X5 : a] : (((sK4 @ X5) = $true) | (? [X6 : a > $o] : (! [X8 : a,X7 : a] : (((X6 @ X7) = $true) | ((sK0 @ X8 @ X7) != $true) | ((X6 @ X8) != $true)) & ((X6 @ X5) != $true) & ! [X9 : a] : (($true != (sK0 @ sK1 @ X9)) | ((X6 @ X9) = $true))) & ? [X10 : a > $o] : (((X10 @ X5) != $true) & ! [X12 : a,X11 : a] : (((sK2 @ X11 @ X12) != $true) | ($true = (X10 @ X12)) | ($true != (X10 @ X11))) & ! [X13 : a] : (((X10 @ X13) = $true) | ((sK2 @ sK1 @ X13) != $true))))) & ! [X15 : a,X14 : a] : (((sK4 @ X14) != $true) | (? [X16 : a > $o] : (! [X17 : a] : (((X16 @ X17) = $true) | ((sK2 @ X14 @ X17) != $true)) & ! [X19 : a,X18 : a] : (((sK2 @ X19 @ X18) != $true) | ((X16 @ X19) != $true) | ((X16 @ X18) = $true)) & ((X16 @ X15) != $true)) & ? [X20 : a > $o] : (((X20 @ X15) != $true) & ! [X22 : a,X21 : a] : (((X20 @ X21) = $true) | ((sK0 @ X22 @ X21) != $true) | ((X20 @ X22) != $true)) & ! [X23 : a] : (((sK0 @ X14 @ X23) != $true) | ((X20 @ X23) = $true)))) | ((sK4 @ X15) = $true)))),
% 1.69/1.40 introduced(definition,[],[choice_axiom])).
% 1.69/1.40 thf(f11,plain,(
% 1.69/1.40 ! [X5 : a] : (? [X6 : a > $o] : (! [X8 : a,X7 : a] : (((X6 @ X7) = $true) | ((sK0 @ X8 @ X7) != $true) | ((X6 @ X8) != $true)) & ((X6 @ X5) != $true) & ! [X9 : a] : (($true != (sK0 @ sK1 @ X9)) | ((X6 @ X9) = $true))) => (! [X8 : a,X7 : a] : (((sK5 @ X5 @ X7) = $true) | ((sK0 @ X8 @ X7) != $true) | ((sK5 @ X5 @ X8) != $true)) & ((sK5 @ X5 @ X5) != $true) & ! [X9 : a] : (($true != (sK0 @ sK1 @ X9)) | ((sK5 @ X5 @ X9) = $true))))),
% 1.69/1.40 introduced(definition,[],[choice_axiom])).
% 1.69/1.40 thf(f12,plain,(
% 1.69/1.40 ! [X5 : a] : (? [X10 : a > $o] : (((X10 @ X5) != $true) & ! [X12 : a,X11 : a] : (((sK2 @ X11 @ X12) != $true) | ($true = (X10 @ X12)) | ($true != (X10 @ X11))) & ! [X13 : a] : (((X10 @ X13) = $true) | ((sK2 @ sK1 @ X13) != $true))) => (((sK6 @ X5 @ X5) != $true) & ! [X12 : a,X11 : a] : (((sK2 @ X11 @ X12) != $true) | ((sK6 @ X5 @ X12) = $true) | ((sK6 @ X5 @ X11) != $true)) & ! [X13 : a] : (((sK6 @ X5 @ X13) = $true) | ((sK2 @ sK1 @ X13) != $true))))),
% 1.69/1.40 introduced(definition,[],[choice_axiom])).
% 1.69/1.40 thf(f13,plain,(
% 1.69/1.40 ! [X14 : a,X15 : a] : (? [X16 : a > $o] : (! [X17 : a] : (((X16 @ X17) = $true) | ((sK2 @ X14 @ X17) != $true)) & ! [X19 : a,X18 : a] : (((sK2 @ X19 @ X18) != $true) | ((X16 @ X19) != $true) | ((X16 @ X18) = $true)) & ((X16 @ X15) != $true)) => (! [X17 : a] : (((sK7 @ X15 @ X14 @ X17) = $true) | ((sK2 @ X14 @ X17) != $true)) & ! [X19 : a,X18 : a] : (((sK2 @ X19 @ X18) != $true) | ((sK7 @ X15 @ X14 @ X19) != $true) | ((sK7 @ X15 @ X14 @ X18) = $true)) & ((sK7 @ X15 @ X14 @ X15) != $true)))),
% 1.69/1.40 introduced(definition,[],[choice_axiom])).
% 1.69/1.40 thf(f14,plain,(
% 1.69/1.40 ! [X14 : a,X15 : a] : (? [X20 : a > $o] : (((X20 @ X15) != $true) & ! [X22 : a,X21 : a] : (((X20 @ X21) = $true) | ((sK0 @ X22 @ X21) != $true) | ((X20 @ X22) != $true)) & ! [X23 : a] : (((sK0 @ X14 @ X23) != $true) | ((X20 @ X23) = $true))) => (((sK8 @ X15 @ X14 @ X15) != $true) & ! [X22 : a,X21 : a] : (((sK8 @ X15 @ X14 @ X21) = $true) | ((sK0 @ X22 @ X21) != $true) | ((sK8 @ X15 @ X14 @ X22) != $true)) & ! [X23 : a] : (((sK0 @ X14 @ X23) != $true) | ((sK8 @ X15 @ X14 @ X23) = $true))))),
% 1.69/1.40 introduced(definition,[],[choice_axiom])).
% 1.69/1.40 thf(f15,plain,(
% 1.69/1.40 ! [X24 : a > $o] : (? [X26 : a,X25 : a] : (((X24 @ X25) != $true) & (((sK2 @ X26 @ X25) = $true) | ((sK0 @ X26 @ X25) = $true)) & ((X24 @ X26) = $true)) => (((X24 @ (sK9 @ X24)) != $true) & (((sK2 @ (sK10 @ X24) @ (sK9 @ X24)) = $true) | ((sK0 @ (sK10 @ X24) @ (sK9 @ X24)) = $true)) & ((X24 @ (sK10 @ X24)) = $true)))),
% 1.69/1.40 introduced(definition,[],[choice_axiom])).
% 1.69/1.40 thf(f16,plain,(
% 1.69/1.40 ! [X24 : a > $o] : (? [X27 : a] : ((((sK0 @ sK1 @ X27) = $true) | ($true = (sK2 @ sK1 @ X27))) & ((X24 @ X27) != $true)) => ((((sK0 @ sK1 @ (sK11 @ X24)) = $true) | ((sK2 @ sK1 @ (sK11 @ X24)) = $true)) & ((X24 @ (sK11 @ X24)) != $true)))),
% 1.69/1.40 introduced(definition,[],[choice_axiom])).
% 1.69/1.40 thf(f8,plain,(
% 1.69/1.40 ? [X0 : a > a > $o,X1 : a,X2 : a > a > $o,X3 : a] : (? [X4 : a > $o] : (((X4 @ X3) != $true) & ! [X5 : a] : (((X4 @ X5) = $true) | (? [X6 : a > $o] : (! [X7 : a,X8 : a] : (((X6 @ X7) = $true) | ((X0 @ X8 @ X7) != $true) | ((X6 @ X8) != $true)) & ((X6 @ X5) != $true) & ! [X9 : a] : (((X0 @ X1 @ X9) != $true) | ((X6 @ X9) = $true))) & ? [X10 : a > $o] : (((X10 @ X5) != $true) & ! [X11 : a,X12 : a] : (((X2 @ X11 @ X12) != $true) | ($true = (X10 @ X12)) | ($true != (X10 @ X11))) & ! [X13 : a] : (((X10 @ X13) = $true) | ((X2 @ X1 @ X13) != $true))))) & ! [X14 : a,X15 : a] : (((X4 @ X14) != $true) | (? [X16 : a > $o] : (! [X17 : a] : (((X16 @ X17) = $true) | ((X2 @ X14 @ X17) != $true)) & ! [X18 : a,X19 : a] : (((X2 @ X19 @ X18) != $true) | ((X16 @ X19) != $true) | ((X16 @ X18) = $true)) & ((X16 @ X15) != $true)) & ? [X20 : a > $o] : (((X20 @ X15) != $true) & ! [X21 : a,X22 : a] : (((X20 @ X21) = $true) | ((X0 @ X22 @ X21) != $true) | ((X20 @ X22) != $true)) & ! [X23 : a] : (((X0 @ X14 @ X23) != $true) | ((X20 @ X23) = $true)))) | ((X4 @ X15) = $true))) & ! [X24 : a > $o] : (((X24 @ X3) = $true) | ? [X25 : a,X26 : a] : (((X24 @ X25) != $true) & (((X2 @ X26 @ X25) = $true) | ((X0 @ X26 @ X25) = $true)) & ((X24 @ X26) = $true)) | ? [X27 : a] : ((((X0 @ X1 @ X27) = $true) | ((X2 @ X1 @ X27) = $true)) & ((X24 @ X27) != $true))))),
% 1.69/1.40 inference(rectify,[status(thm)],[f7])).
% 1.69/1.40 thf(f7,plain,(
% 1.69/1.40 ? [X0 : a > a > $o,X2 : a,X1 : a > a > $o,X3 : a] : (? [X8 : a > $o] : (((X8 @ X3) != $true) & ! [X19 : a] : (((X8 @ X19) = $true) | (? [X24 : a > $o] : (! [X26 : a,X25 : a] : (((X24 @ X26) = $true) | ((X0 @ X25 @ X26) != $true) | ((X24 @ X25) != $true)) & ((X24 @ X19) != $true) & ! [X27 : a] : (((X0 @ X2 @ X27) != $true) | ((X24 @ X27) = $true))) & ? [X20 : a > $o] : (((X20 @ X19) != $true) & ! [X22 : a,X21 : a] : (((X1 @ X22 @ X21) != $true) | ((X20 @ X21) = $true) | ((X20 @ X22) != $true)) & ! [X23 : a] : (((X20 @ X23) = $true) | ((X1 @ X2 @ X23) != $true))))) & ! [X9 : a,X10 : a] : (((X8 @ X9) != $true) | (? [X11 : a > $o] : (! [X12 : a] : (((X11 @ X12) = $true) | ((X1 @ X9 @ X12) != $true)) & ! [X13 : a,X14 : a] : (((X1 @ X14 @ X13) != $true) | ((X11 @ X14) != $true) | ((X11 @ X13) = $true)) & ($true != (X11 @ X10))) & ? [X15 : a > $o] : (((X15 @ X10) != $true) & ! [X17 : a,X16 : a] : (((X15 @ X17) = $true) | ((X0 @ X16 @ X17) != $true) | ((X15 @ X16) != $true)) & ! [X18 : a] : (((X0 @ X9 @ X18) != $true) | ((X15 @ X18) = $true)))) | ((X8 @ X10) = $true))) & ! [X4 : a > $o] : (((X4 @ X3) = $true) | ? [X6 : a,X5 : a] : (((X4 @ X6) != $true) & (((X1 @ X5 @ X6) = $true) | ((X0 @ X5 @ X6) = $true)) & ((X4 @ X5) = $true)) | ? [X7 : a] : ((((X0 @ X2 @ X7) = $true) | ((X1 @ X2 @ X7) = $true)) & ((X4 @ X7) != $true))))),
% 1.69/1.40 inference(flattening,[status(thm)],[f6])).
% 1.69/1.40 thf(f6,plain,(
% 1.69/1.40 ? [X2 : a,X0 : a > a > $o,X3 : a,X1 : a > a > $o] : (? [X8 : a > $o] : (((X8 @ X3) != $true) & (! [X19 : a] : (((X8 @ X19) = $true) | (? [X24 : a > $o] : (((X24 @ X19) != $true) & (! [X27 : a] : (((X0 @ X2 @ X27) != $true) | ((X24 @ X27) = $true)) & ! [X26 : a,X25 : a] : (((X24 @ X26) = $true) | (((X24 @ X25) != $true) | ((X0 @ X25 @ X26) != $true))))) & ? [X20 : a > $o] : (((X20 @ X19) != $true) & (! [X23 : a] : (((X20 @ X23) = $true) | ((X1 @ X2 @ X23) != $true)) & ! [X21 : a,X22 : a] : (((X20 @ X21) = $true) | (((X20 @ X22) != $true) | ((X1 @ X22 @ X21) != $true))))))) & ! [X10 : a,X9 : a] : (((X8 @ X10) = $true) | (((X8 @ X9) != $true) | (? [X15 : a > $o] : (((X15 @ X10) != $true) & (! [X18 : a] : (((X0 @ X9 @ X18) != $true) | ((X15 @ X18) = $true)) & ! [X16 : a,X17 : a] : (((X15 @ X17) = $true) | (((X15 @ X16) != $true) | ((X0 @ X16 @ X17) != $true))))) & ? [X11 : a > $o] : (($true != (X11 @ X10)) & (! [X14 : a,X13 : a] : (((X11 @ X13) = $true) | (((X11 @ X14) != $true) | ((X1 @ X14 @ X13) != $true))) & ! [X12 : a] : (((X11 @ X12) = $true) | ((X1 @ X9 @ X12) != $true))))))))) & ! [X4 : a > $o] : (((X4 @ X3) = $true) | (? [X7 : a] : ((((X0 @ X2 @ X7) = $true) | ((X1 @ X2 @ X7) = $true)) & ((X4 @ X7) != $true)) | ? [X6 : a,X5 : a] : (((X4 @ X6) != $true) & (((X4 @ X5) = $true) & (((X1 @ X5 @ X6) = $true) | ((X0 @ X5 @ X6) = $true)))))))),
% 1.69/1.40 inference(ennf_transformation,[status(thm)],[f5])).
% 1.69/1.40 thf(f5,plain,(
% 1.69/1.40 ~! [X2 : a,X0 : a > a > $o,X3 : a,X1 : a > a > $o] : (! [X4 : a > $o] : ((! [X7 : a] : ((((X0 @ X2 @ X7) = $true) | ((X1 @ X2 @ X7) = $true)) => ((X4 @ X7) = $true)) & ! [X6 : a,X5 : a] : ((((X4 @ X5) = $true) & (((X1 @ X5 @ X6) = $true) | ((X0 @ X5 @ X6) = $true))) => ((X4 @ X6) = $true))) => ((X4 @ X3) = $true)) => ! [X8 : a > $o] : ((! [X19 : a] : ((! [X24 : a > $o] : ((! [X27 : a] : (((X0 @ X2 @ X27) = $true) => ((X24 @ X27) = $true)) & ! [X26 : a,X25 : a] : ((((X24 @ X25) = $true) & ((X0 @ X25 @ X26) = $true)) => ((X24 @ X26) = $true))) => ((X24 @ X19) = $true)) | ! [X20 : a > $o] : ((! [X23 : a] : (((X1 @ X2 @ X23) = $true) => ((X20 @ X23) = $true)) & ! [X21 : a,X22 : a] : ((((X20 @ X22) = $true) & ((X1 @ X22 @ X21) = $true)) => ((X20 @ X21) = $true))) => ((X20 @ X19) = $true))) => ((X8 @ X19) = $true)) & ! [X10 : a,X9 : a] : ((((X8 @ X9) = $true) & (! [X15 : a > $o] : ((! [X18 : a] : (((X0 @ X9 @ X18) = $true) => ((X15 @ X18) = $true)) & ! [X16 : a,X17 : a] : ((((X15 @ X16) = $true) & ((X0 @ X16 @ X17) = $true)) => ((X15 @ X17) = $true))) => ((X15 @ X10) = $true)) | ! [X11 : a > $o] : ((! [X14 : a,X13 : a] : ((((X11 @ X14) = $true) & ((X1 @ X14 @ X13) = $true)) => ((X11 @ X13) = $true)) & ! [X12 : a] : (((X1 @ X9 @ X12) = $true) => ((X11 @ X12) = $true))) => ($true = (X11 @ X10))))) => ((X8 @ X10) = $true))) => ((X8 @ X3) = $true)))),
% 1.69/1.40 inference(fool_elimination,[status(thm)],[f4])).
% 1.69/1.40 thf(f4,plain,(
% 1.69/1.40 ~! [X0 : a > a > $o,X1 : a > a > $o,X2 : a,X3 : a] : (! [X4 : a > $o] : ((! [X5 : a,X6 : a] : ((((X0 @ X5 @ X6) | (X1 @ X5 @ X6)) & (X4 @ X5)) => (X4 @ X6)) & ! [X7 : a] : (((X0 @ X2 @ X7) | (X1 @ X2 @ X7)) => (X4 @ X7))) => (X4 @ X3)) => ! [X8 : a > $o] : ((! [X9 : a,X10 : a] : (((! [X11 : a > $o] : ((! [X12 : a] : ((X1 @ X9 @ X12) => (X11 @ X12)) & ! [X13 : a,X14 : a] : (((X11 @ X14) & (X1 @ X14 @ X13)) => (X11 @ X13))) => (X11 @ X10)) | ! [X15 : a > $o] : ((! [X16 : a,X17 : a] : (((X15 @ X16) & (X0 @ X16 @ X17)) => (X15 @ X17)) & ! [X18 : a] : ((X0 @ X9 @ X18) => (X15 @ X18))) => (X15 @ X10))) & (X8 @ X9)) => (X8 @ X10)) & ! [X19 : a] : ((! [X20 : a > $o] : ((! [X21 : a,X22 : a] : (((X1 @ X22 @ X21) & (X20 @ X22)) => (X20 @ X21)) & ! [X23 : a] : ((X1 @ X2 @ X23) => (X20 @ X23))) => (X20 @ X19)) | ! [X24 : a > $o] : ((! [X25 : a,X26 : a] : (((X24 @ X25) & (X0 @ X25 @ X26)) => (X24 @ X26)) & ! [X27 : a] : ((X0 @ X2 @ X27) => (X24 @ X27))) => (X24 @ X19))) => (X8 @ X19))) => (X8 @ X3)))),
% 1.69/1.40 inference(rectify,[status(thm)],[f2])).
% 1.69/1.40 thf(f2,negated_conjecture,(
% 1.69/1.40 ~! [X0 : a > a > $o,X1 : a > a > $o,X2 : a,X3 : a] : (! [X4 : a > $o] : ((! [X6 : a,X7 : a] : ((((X0 @ X6 @ X7) | (X1 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : (((X0 @ X2 @ X5) | (X1 @ X2 @ X5)) => (X4 @ X5))) => (X4 @ X3)) => ! [X4 : a > $o] : ((! [X6 : a,X7 : a] : (((! [X8 : a > $o] : ((! [X5 : a] : ((X1 @ X6 @ X5) => (X8 @ X5)) & ! [X11 : a,X10 : a] : (((X8 @ X10) & (X1 @ X10 @ X11)) => (X8 @ X11))) => (X8 @ X7)) | ! [X8 : a > $o] : ((! [X10 : a,X11 : a] : (((X8 @ X10) & (X0 @ X10 @ X11)) => (X8 @ X11)) & ! [X5 : a] : ((X0 @ X6 @ X5) => (X8 @ X5))) => (X8 @ X7))) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : ((! [X8 : a > $o] : ((! [X7 : a,X6 : a] : (((X1 @ X6 @ X7) & (X8 @ X6)) => (X8 @ X7)) & ! [X9 : a] : ((X1 @ X2 @ X9) => (X8 @ X9))) => (X8 @ X5)) | ! [X8 : a > $o] : ((! [X6 : a,X7 : a] : (((X8 @ X6) & (X0 @ X6 @ X7)) => (X8 @ X7)) & ! [X9 : a] : ((X0 @ X2 @ X9) => (X8 @ X9))) => (X8 @ X5))) => (X4 @ X5))) => (X4 @ X3)))),
% 1.69/1.40 inference(negated_conjecture,[status(cth)],[f1])).
% 1.69/1.40 thf(f1,conjecture,(
% 1.69/1.40 ! [X0 : a > a > $o,X1 : a > a > $o,X2 : a,X3 : a] : (! [X4 : a > $o] : ((! [X6 : a,X7 : a] : ((((X0 @ X6 @ X7) | (X1 @ X6 @ X7)) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : (((X0 @ X2 @ X5) | (X1 @ X2 @ X5)) => (X4 @ X5))) => (X4 @ X3)) => ! [X4 : a > $o] : ((! [X6 : a,X7 : a] : (((! [X8 : a > $o] : ((! [X5 : a] : ((X1 @ X6 @ X5) => (X8 @ X5)) & ! [X11 : a,X10 : a] : (((X8 @ X10) & (X1 @ X10 @ X11)) => (X8 @ X11))) => (X8 @ X7)) | ! [X8 : a > $o] : ((! [X10 : a,X11 : a] : (((X8 @ X10) & (X0 @ X10 @ X11)) => (X8 @ X11)) & ! [X5 : a] : ((X0 @ X6 @ X5) => (X8 @ X5))) => (X8 @ X7))) & (X4 @ X6)) => (X4 @ X7)) & ! [X5 : a] : ((! [X8 : a > $o] : ((! [X7 : a,X6 : a] : (((X1 @ X6 @ X7) & (X8 @ X6)) => (X8 @ X7)) & ! [X9 : a] : ((X1 @ X2 @ X9) => (X8 @ X9))) => (X8 @ X5)) | ! [X8 : a > $o] : ((! [X6 : a,X7 : a] : (((X8 @ X6) & (X0 @ X6 @ X7)) => (X8 @ X7)) & ! [X9 : a] : ((X0 @ X2 @ X9) => (X8 @ X9))) => (X8 @ X5))) => (X4 @ X5))) => (X4 @ X3)))),
% 1.69/1.40 file('/export/starexec/sandbox/tmp/tmp.Ma74ZRMDgU/DTF2THF_9795.p',cTHM251B_pme)).
% 1.69/1.40 thf(f1243,plain,(
% 1.69/1.40 ((sK4 @ sK3) = $true) | (~spl12_14 | ~spl12_42)),
% 1.69/1.40 inference(subsumption_resolution,[status(thm)],[f607,f596])).
% 1.69/1.40 thf(f596,plain,(
% 1.69/1.40 ((sK4 @ (sK9 @ sK4)) = $true) | ~spl12_42),
% 1.69/1.40 inference(avatar_component_clause,[status(thm)],[f595])).
% 1.69/1.40 thf(f595,definition,(
% 1.69/1.40 spl12_42 <=> ((sK4 @ (sK9 @ sK4)) = $true)),
% 1.69/1.40 introduced(definition,[new_symbols(naming,[spl12_42])],[avatar_definition])).
% 1.69/1.40 thf(f607,plain,(
% 1.69/1.40 ((sK4 @ (sK9 @ sK4)) != $true) | ((sK4 @ sK3) = $true) | ~spl12_14),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f606])).
% 1.69/1.40 thf(f606,plain,(
% 1.69/1.40 ((sK4 @ sK3) = $true) | ((sK4 @ (sK9 @ sK4)) != $true) | ($true != $true) | ~spl12_14),
% 1.69/1.40 inference(duplicate_literal_removal,[status(thm)],[f605])).
% 1.69/1.40 thf(f605,plain,(
% 1.69/1.40 ((sK4 @ (sK9 @ sK4)) != $true) | ((sK4 @ sK3) = $true) | ((sK4 @ (sK9 @ sK4)) != $true) | ($true != $true) | ((sK4 @ sK3) = $true) | ~spl12_14),
% 1.69/1.40 inference(superposition,[status(thm)],[f22,f203])).
% 1.69/1.40 thf(f203,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (((sK4 @ (sK11 @ X0)) = $true) | ((X0 @ (sK9 @ X0)) != $true) | ((X0 @ sK3) = $true)) ) | ~spl12_14),
% 1.69/1.40 inference(avatar_component_clause,[status(thm)],[f202])).
% 1.69/1.40 thf(f202,definition,(
% 1.69/1.40 spl12_14 <=> ! [X0 : a > $o] : (((X0 @ sK3) = $true) | ((X0 @ (sK9 @ X0)) != $true) | ((sK4 @ (sK11 @ X0)) = $true))),
% 1.69/1.40 introduced(definition,[new_symbols(naming,[spl12_14])],[avatar_definition])).
% 1.69/1.40 thf(f22,plain,(
% 1.69/1.40 ( ! [X24 : a > $o] : (((X24 @ (sK11 @ X24)) != $true) | ((X24 @ sK3) = $true) | ((X24 @ (sK9 @ X24)) != $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.40 thf(f1229,plain,(
% 1.69/1.40 spl12_42 | ~spl12_43 | ~spl12_62),
% 1.69/1.40 inference(avatar_contradiction_clause,[status(thm)],[f1228])).
% 1.69/1.40 thf(f1228,plain,(
% 1.69/1.40 $false | (spl12_42 | ~spl12_43 | ~spl12_62)),
% 1.69/1.40 inference(subsumption_resolution,[status(thm)],[f1227,f597])).
% 1.69/1.40 thf(f597,plain,(
% 1.69/1.40 ((sK4 @ (sK9 @ sK4)) != $true) | spl12_42),
% 1.69/1.40 inference(avatar_component_clause,[status(thm)],[f595])).
% 1.69/1.40 thf(f1227,plain,(
% 1.69/1.40 ((sK4 @ (sK9 @ sK4)) = $true) | (spl12_42 | ~spl12_43 | ~spl12_62)),
% 1.69/1.40 inference(subsumption_resolution,[status(thm)],[f1226,f36])).
% 1.69/1.40 thf(f1226,plain,(
% 1.69/1.40 ((sK4 @ sK3) = $true) | ((sK4 @ (sK9 @ sK4)) = $true) | (spl12_42 | ~spl12_43 | ~spl12_62)),
% 1.69/1.40 inference(subsumption_resolution,[status(thm)],[f1211,f601])).
% 1.69/1.40 thf(f601,plain,(
% 1.69/1.40 ((sK4 @ (sK10 @ sK4)) = $true) | ~spl12_43),
% 1.69/1.40 inference(avatar_component_clause,[status(thm)],[f599])).
% 1.69/1.40 thf(f599,definition,(
% 1.69/1.40 spl12_43 <=> ((sK4 @ (sK10 @ sK4)) = $true)),
% 1.69/1.40 introduced(definition,[new_symbols(naming,[spl12_43])],[avatar_definition])).
% 1.69/1.40 thf(f1211,plain,(
% 1.69/1.40 ((sK4 @ (sK10 @ sK4)) != $true) | ((sK4 @ sK3) = $true) | ((sK4 @ (sK9 @ sK4)) = $true) | (spl12_42 | ~spl12_43 | ~spl12_62)),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f1207])).
% 1.69/1.40 thf(f1207,plain,(
% 1.69/1.40 ((sK4 @ (sK10 @ sK4)) != $true) | ($true != $true) | ((sK4 @ (sK9 @ sK4)) = $true) | ((sK4 @ sK3) = $true) | (spl12_42 | ~spl12_43 | ~spl12_62)),
% 1.69/1.40 inference(superposition,[status(thm)],[f963,f1184])).
% 1.69/1.40 thf(f1184,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (((sK4 @ (sK11 @ X0)) = $true) | ((sK4 @ (sK9 @ X0)) = $true) | ((X0 @ sK3) = $true) | ((sK4 @ (sK10 @ X0)) != $true)) ) | ~spl12_62),
% 1.69/1.40 inference(avatar_component_clause,[status(thm)],[f1183])).
% 1.69/1.40 thf(f1183,definition,(
% 1.69/1.40 spl12_62 <=> ! [X0 : a > $o] : (((sK4 @ (sK10 @ X0)) != $true) | ((X0 @ sK3) = $true) | ((sK4 @ (sK9 @ X0)) = $true) | ((sK4 @ (sK11 @ X0)) = $true))),
% 1.69/1.40 introduced(definition,[new_symbols(naming,[spl12_62])],[avatar_definition])).
% 1.69/1.40 thf(f963,plain,(
% 1.69/1.40 ((sK4 @ (sK11 @ sK4)) != $true) | (spl12_42 | ~spl12_43)),
% 1.69/1.40 inference(subsumption_resolution,[status(thm)],[f962,f36])).
% 1.69/1.40 thf(f962,plain,(
% 1.69/1.40 ((sK4 @ (sK11 @ sK4)) != $true) | ((sK4 @ sK3) = $true) | (spl12_42 | ~spl12_43)),
% 1.69/1.40 inference(subsumption_resolution,[status(thm)],[f955,f601])).
% 1.69/1.40 thf(f955,plain,(
% 1.69/1.40 ((sK4 @ (sK10 @ sK4)) != $true) | ((sK4 @ (sK11 @ sK4)) != $true) | ((sK4 @ sK3) = $true) | spl12_42),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f954])).
% 1.69/1.40 thf(f954,plain,(
% 1.69/1.40 ((sK4 @ (sK11 @ sK4)) != $true) | ((sK4 @ (sK10 @ sK4)) != $true) | ($true != $true) | ((sK4 @ sK3) = $true) | spl12_42),
% 1.69/1.40 inference(superposition,[status(thm)],[f597,f240])).
% 1.69/1.40 thf(f240,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (((sK4 @ (sK9 @ X0)) = $true) | ((X0 @ sK3) = $true) | ((sK4 @ (sK10 @ X0)) != $true) | ((X0 @ (sK11 @ X0)) != $true)) )),
% 1.69/1.40 inference(subsumption_resolution,[status(thm)],[f239,f135])).
% 1.69/1.40 thf(f135,plain,(
% 1.69/1.40 ( ! [X0 : a,X1 : a] : (((sK0 @ X1 @ X0) != $true) | ((sK4 @ X0) = $true) | ((sK4 @ X1) != $true)) )),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f134])).
% 1.69/1.40 thf(f134,plain,(
% 1.69/1.40 ( ! [X0 : a,X1 : a] : (((sK0 @ X1 @ X0) != $true) | ((sK4 @ X0) = $true) | ($true != $true) | ((sK4 @ X1) != $true)) )),
% 1.69/1.40 inference(duplicate_literal_removal,[status(thm)],[f131])).
% 1.69/1.40 thf(f131,plain,(
% 1.69/1.40 ( ! [X0 : a,X1 : a] : (((sK4 @ X0) = $true) | ($true != $true) | ((sK4 @ X1) != $true) | ((sK0 @ X1 @ X0) != $true) | ((sK4 @ X0) = $true) | ((sK4 @ X1) != $true)) )),
% 1.69/1.40 inference(superposition,[status(thm)],[f26,f24])).
% 1.69/1.40 thf(f24,plain,(
% 1.69/1.40 ( ! [X14 : a,X15 : a,X23 : a] : (((sK8 @ X15 @ X14 @ X23) = $true) | ((sK4 @ X15) = $true) | ((sK0 @ X14 @ X23) != $true) | ((sK4 @ X14) != $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.40 thf(f26,plain,(
% 1.69/1.40 ( ! [X14 : a,X15 : a] : (((sK8 @ X15 @ X14 @ X15) != $true) | ((sK4 @ X14) != $true) | ((sK4 @ X15) = $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.40 thf(f239,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (((X0 @ (sK11 @ X0)) != $true) | ((sK0 @ (sK10 @ X0) @ (sK9 @ X0)) = $true) | ((X0 @ sK3) = $true) | ((sK4 @ (sK10 @ X0)) != $true) | ((sK4 @ (sK9 @ X0)) = $true)) )),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f238])).
% 1.69/1.40 thf(f238,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (((X0 @ (sK11 @ X0)) != $true) | ((X0 @ sK3) = $true) | ((sK0 @ (sK10 @ X0) @ (sK9 @ X0)) = $true) | ($true != $true) | ((sK4 @ (sK10 @ X0)) != $true) | ((sK4 @ (sK9 @ X0)) = $true)) )),
% 1.69/1.40 inference(superposition,[status(thm)],[f141,f20])).
% 1.69/1.40 thf(f20,plain,(
% 1.69/1.40 ( ! [X24 : a > $o] : (((sK2 @ (sK10 @ X24) @ (sK9 @ X24)) = $true) | ((X24 @ (sK11 @ X24)) != $true) | ((X24 @ sK3) = $true) | ((sK0 @ (sK10 @ X24) @ (sK9 @ X24)) = $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.40 thf(f141,plain,(
% 1.69/1.40 ( ! [X0 : a,X1 : a] : (((sK2 @ X1 @ X0) != $true) | ((sK4 @ X1) != $true) | ((sK4 @ X0) = $true)) )),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f140])).
% 1.69/1.40 thf(f140,plain,(
% 1.69/1.40 ( ! [X0 : a,X1 : a] : (((sK4 @ X0) = $true) | ((sK2 @ X1 @ X0) != $true) | ($true != $true) | ((sK4 @ X1) != $true)) )),
% 1.69/1.40 inference(duplicate_literal_removal,[status(thm)],[f138])).
% 1.69/1.40 thf(f138,plain,(
% 1.69/1.40 ( ! [X0 : a,X1 : a] : (((sK4 @ X0) = $true) | ((sK4 @ X1) != $true) | ((sK4 @ X1) != $true) | ($true != $true) | ((sK4 @ X0) = $true) | ((sK2 @ X1 @ X0) != $true)) )),
% 1.69/1.40 inference(superposition,[status(thm)],[f27,f29])).
% 1.69/1.40 thf(f29,plain,(
% 1.69/1.40 ( ! [X14 : a,X17 : a,X15 : a] : (((sK7 @ X15 @ X14 @ X17) = $true) | ((sK4 @ X14) != $true) | ((sK2 @ X14 @ X17) != $true) | ((sK4 @ X15) = $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.40 thf(f27,plain,(
% 1.69/1.40 ( ! [X14 : a,X15 : a] : (((sK7 @ X15 @ X14 @ X15) != $true) | ((sK4 @ X15) = $true) | ((sK4 @ X14) != $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.40 thf(f1192,plain,(
% 1.69/1.40 spl12_62),
% 1.69/1.40 inference(avatar_split_clause,[status(thm)],[f1191,f1183])).
% 1.69/1.40 thf(f1191,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (((sK4 @ (sK11 @ X0)) = $true) | ((sK4 @ (sK9 @ X0)) = $true) | ((sK4 @ (sK10 @ X0)) != $true) | ((X0 @ sK3) = $true)) )),
% 1.69/1.40 inference(subsumption_resolution,[status(thm)],[f1169,f95])).
% 1.69/1.40 thf(f95,plain,(
% 1.69/1.40 ( ! [X0 : a] : (((sK0 @ sK1 @ X0) != $true) | ((sK4 @ X0) = $true)) )),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f94])).
% 1.69/1.40 thf(f94,plain,(
% 1.69/1.40 ( ! [X0 : a] : (((sK4 @ X0) = $true) | ((sK0 @ sK1 @ X0) != $true) | ($true != $true)) )),
% 1.69/1.40 inference(duplicate_literal_removal,[status(thm)],[f92])).
% 1.69/1.40 thf(f92,plain,(
% 1.69/1.40 ( ! [X0 : a] : (((sK0 @ sK1 @ X0) != $true) | ((sK4 @ X0) = $true) | ($true != $true) | ((sK4 @ X0) = $true)) )),
% 1.69/1.40 inference(superposition,[status(thm)],[f34,f33])).
% 1.69/1.40 thf(f33,plain,(
% 1.69/1.40 ( ! [X9 : a,X5 : a] : (((sK5 @ X5 @ X9) = $true) | ($true != (sK0 @ sK1 @ X9)) | ((sK4 @ X5) = $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.40 thf(f34,plain,(
% 1.69/1.40 ( ! [X5 : a] : (((sK5 @ X5 @ X5) != $true) | ((sK4 @ X5) = $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.40 thf(f1169,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (((sK4 @ (sK9 @ X0)) = $true) | ((sK4 @ (sK10 @ X0)) != $true) | ((sK4 @ (sK11 @ X0)) = $true) | ((X0 @ sK3) = $true) | ((sK0 @ sK1 @ (sK11 @ X0)) = $true)) )),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f1152])).
% 1.69/1.40 thf(f1152,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (((X0 @ sK3) = $true) | ((sK4 @ (sK11 @ X0)) = $true) | ((sK4 @ (sK9 @ X0)) = $true) | ((sK0 @ sK1 @ (sK11 @ X0)) = $true) | ((sK4 @ (sK10 @ X0)) != $true) | ($true != $true)) )),
% 1.69/1.40 inference(superposition,[status(thm)],[f75,f243])).
% 1.69/1.40 thf(f243,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (((sK2 @ sK1 @ (sK11 @ X0)) = $true) | ((sK0 @ sK1 @ (sK11 @ X0)) = $true) | ((sK4 @ (sK9 @ X0)) = $true) | ((sK4 @ (sK10 @ X0)) != $true) | ((X0 @ sK3) = $true)) )),
% 1.69/1.40 inference(subsumption_resolution,[status(thm)],[f242,f135])).
% 1.69/1.40 thf(f242,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (((X0 @ sK3) = $true) | ((sK2 @ sK1 @ (sK11 @ X0)) = $true) | ((sK0 @ (sK10 @ X0) @ (sK9 @ X0)) = $true) | ((sK4 @ (sK10 @ X0)) != $true) | ((sK4 @ (sK9 @ X0)) = $true) | ((sK0 @ sK1 @ (sK11 @ X0)) = $true)) )),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f241])).
% 1.69/1.40 thf(f241,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (($true != $true) | ((sK0 @ sK1 @ (sK11 @ X0)) = $true) | ((sK4 @ (sK10 @ X0)) != $true) | ((sK0 @ (sK10 @ X0) @ (sK9 @ X0)) = $true) | ((sK2 @ sK1 @ (sK11 @ X0)) = $true) | ((sK4 @ (sK9 @ X0)) = $true) | ((X0 @ sK3) = $true)) )),
% 1.69/1.40 inference(superposition,[status(thm)],[f141,f21])).
% 1.69/1.40 thf(f21,plain,(
% 1.69/1.40 ( ! [X24 : a > $o] : (((sK2 @ (sK10 @ X24) @ (sK9 @ X24)) = $true) | ((sK0 @ sK1 @ (sK11 @ X24)) = $true) | ((sK2 @ sK1 @ (sK11 @ X24)) = $true) | ((X24 @ sK3) = $true) | ((sK0 @ (sK10 @ X24) @ (sK9 @ X24)) = $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.40 thf(f75,plain,(
% 1.69/1.40 ( ! [X0 : a] : (((sK2 @ sK1 @ X0) != $true) | ((sK4 @ X0) = $true)) )),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f74])).
% 1.69/1.40 thf(f74,plain,(
% 1.69/1.40 ( ! [X0 : a] : (((sK2 @ sK1 @ X0) != $true) | ((sK4 @ X0) = $true) | ($true != $true)) )),
% 1.69/1.40 inference(duplicate_literal_removal,[status(thm)],[f72])).
% 1.69/1.40 thf(f72,plain,(
% 1.69/1.40 ( ! [X0 : a] : (($true != $true) | ((sK4 @ X0) = $true) | ((sK2 @ sK1 @ X0) != $true) | ((sK4 @ X0) = $true)) )),
% 1.69/1.40 inference(superposition,[status(thm)],[f32,f30])).
% 1.69/1.40 thf(f30,plain,(
% 1.69/1.40 ( ! [X5 : a,X13 : a] : (((sK6 @ X5 @ X13) = $true) | ((sK2 @ sK1 @ X13) != $true) | ((sK4 @ X5) = $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.40 thf(f32,plain,(
% 1.69/1.40 ( ! [X5 : a] : (((sK6 @ X5 @ X5) != $true) | ((sK4 @ X5) = $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.40 thf(f779,plain,(
% 1.69/1.40 spl12_43),
% 1.69/1.40 inference(avatar_split_clause,[status(thm)],[f778,f599])).
% 1.69/1.40 thf(f778,plain,(
% 1.69/1.40 ((sK4 @ (sK10 @ sK4)) = $true)),
% 1.69/1.40 inference(subsumption_resolution,[status(thm)],[f728,f36])).
% 1.69/1.40 thf(f728,plain,(
% 1.69/1.40 ((sK4 @ (sK10 @ sK4)) = $true) | ((sK4 @ sK3) = $true)),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f727])).
% 1.69/1.40 thf(f727,plain,(
% 1.69/1.40 ($false = $true) | ((sK4 @ (sK10 @ sK4)) = $true) | ((sK4 @ sK3) = $true)),
% 1.69/1.40 inference(duplicate_literal_removal,[status(thm)],[f704])).
% 1.69/1.40 thf(f704,plain,(
% 1.69/1.40 ($false = $true) | ((sK4 @ (sK10 @ sK4)) = $true) | ((sK4 @ sK3) = $true) | ((sK4 @ (sK10 @ sK4)) = $true) | ((sK4 @ sK3) = $true)),
% 1.69/1.40 inference(superposition,[status(thm)],[f161,f338])).
% 1.69/1.40 thf(f338,plain,(
% 1.69/1.40 ( ! [X30 : a > $o] : (((X30 @ (sK11 @ X30)) = $false) | ((X30 @ (sK10 @ X30)) = $true) | ((X30 @ sK3) = $true)) )),
% 1.69/1.40 inference(not_proxy_clausification,[status(thm)],[f337])).
% 1.69/1.40 thf(f337,plain,(
% 1.69/1.40 ( ! [X30 : a > $o] : (((X30 @ sK3) = $true) | ((~ (X30 @ (sK10 @ X30))) = $false) | ((X30 @ (sK11 @ X30)) = $false)) )),
% 1.69/1.40 inference(not_proxy_clausification,[status(thm)],[f336])).
% 1.69/1.40 thf(f336,plain,(
% 1.69/1.40 ( ! [X30 : a > $o] : (((~ (X30 @ (sK11 @ X30))) = $true) | ((X30 @ sK3) = $true) | ((~ (X30 @ (sK10 @ X30))) = $false)) )),
% 1.69/1.40 inference(not_proxy_clausification,[status(thm)],[f335])).
% 1.69/1.40 thf(f335,plain,(
% 1.69/1.40 ( ! [X30 : a > $o] : (($false = (~ (X30 @ sK3))) | ((~ (X30 @ (sK10 @ X30))) = $false) | ((~ (X30 @ (sK11 @ X30))) = $true)) )),
% 1.69/1.40 inference(beta_eta_normalization,[status(thm)],[f334])).
% 1.69/1.40 thf(f334,plain,(
% 1.69/1.40 ( ! [X30 : a > $o] : (((~ (X30 @ (sK11 @ X30))) = $true) | ($false = (~ (X30 @ sK3))) | ((~ (X30 @ (sK10 @ (^[Y0 : a]: (X30 @ Y0))))) = $false)) )),
% 1.69/1.40 inference(boolean_simplification,[status(thm)],[f333])).
% 1.69/1.40 thf(f333,plain,(
% 1.69/1.40 ( ! [X30 : a > $o] : (($false = (~ (X30 @ sK3))) | ((~ (X30 @ (sK10 @ (^[Y0 : a]: (~ (~ (X30 @ Y0))))))) = $false) | ((~ (X30 @ (sK11 @ X30))) = $true)) )),
% 1.69/1.40 inference(beta_eta_normalization,[status(thm)],[f332])).
% 1.69/1.40 thf(f332,plain,(
% 1.69/1.40 ( ! [X30 : a > $o] : (((~ (X30 @ (sK10 @ (^[Y0 : a]: (~ (~ (X30 @ Y0))))))) = $false) | ((~ (X30 @ (sK11 @ (^[Y0 : a]: (X30 @ Y0))))) = $true) | ($false = (~ (X30 @ sK3)))) )),
% 1.69/1.40 inference(boolean_simplification,[status(thm)],[f331])).
% 1.69/1.40 thf(f331,plain,(
% 1.69/1.40 ( ! [X30 : a > $o] : (((~ (X30 @ (sK11 @ (^[Y0 : a]: (~ (~ (X30 @ Y0))))))) = $true) | ($false = (~ (X30 @ sK3))) | ((~ (X30 @ (sK10 @ (^[Y0 : a]: (~ (~ (X30 @ Y0))))))) = $false)) )),
% 1.69/1.40 inference(beta_eta_normalization,[status(thm)],[f311])).
% 1.69/1.40 thf(f311,plain,(
% 1.69/1.40 ( ! [X30 : a > $o] : ((((^[Y0 : a]: (~ (X30 @ Y0))) @ (sK10 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (~ (X30 @ Y1))) @ Y0))))) = $false) | (((^[Y0 : a]: (~ (X30 @ Y0))) @ (sK11 @ (^[Y0 : a]: (~ ((^[Y1 : a]: (~ (X30 @ Y1))) @ Y0))))) = $true) | ($false = ((^[Y0 : a]: (~ (X30 @ Y0))) @ sK3))) )),
% 1.69/1.40 inference(primitive_instantiation,[status(thm)],[f43])).
% 1.69/1.40 thf(f43,plain,(
% 1.69/1.40 ( ! [X27 : a > $o] : (((X27 @ (sK11 @ (^[Y0 : a]: (~ (X27 @ Y0))))) = $true) | ((X27 @ (sK10 @ (^[Y0 : a]: (~ (X27 @ Y0))))) = $false) | ((X27 @ sK3) = $false)) )),
% 1.69/1.40 inference(not_proxy_clausification,[status(thm)],[f42])).
% 1.69/1.40 thf(f42,plain,(
% 1.69/1.40 ( ! [X27 : a > $o] : (((X27 @ (sK10 @ (^[Y0 : a]: (~ (X27 @ Y0))))) = $false) | ((~ (X27 @ sK3)) = $true) | ((X27 @ (sK11 @ (^[Y0 : a]: (~ (X27 @ Y0))))) = $true)) )),
% 1.69/1.40 inference(not_proxy_clausification,[status(thm)],[f41])).
% 1.69/1.40 thf(f41,plain,(
% 1.69/1.40 ( ! [X27 : a > $o] : (((X27 @ (sK11 @ (^[Y0 : a]: (~ (X27 @ Y0))))) = $true) | ((~ (X27 @ (sK10 @ (^[Y0 : a]: (~ (X27 @ Y0)))))) = $true) | ((~ (X27 @ sK3)) = $true)) )),
% 1.69/1.40 inference(not_proxy_clausification,[status(thm)],[f40])).
% 1.69/1.40 thf(f40,plain,(
% 1.69/1.40 ( ! [X27 : a > $o] : (((~ (X27 @ (sK11 @ (^[Y0 : a]: (~ (X27 @ Y0)))))) != $true) | ((~ (X27 @ sK3)) = $true) | ((~ (X27 @ (sK10 @ (^[Y0 : a]: (~ (X27 @ Y0)))))) = $true)) )),
% 1.69/1.40 inference(beta_eta_normalization,[status(thm)],[f39])).
% 1.69/1.40 thf(f39,plain,(
% 1.69/1.40 ( ! [X27 : a > $o] : ((((^[Y0 : a]: (~ (X27 @ Y0))) @ (sK10 @ (^[Y0 : a]: (~ (X27 @ Y0))))) = $true) | (((^[Y0 : a]: (~ (X27 @ Y0))) @ sK3) = $true) | (((^[Y0 : a]: (~ (X27 @ Y0))) @ (sK11 @ (^[Y0 : a]: (~ (X27 @ Y0))))) != $true)) )),
% 1.69/1.40 inference(primitive_instantiation,[status(thm)],[f18])).
% 1.69/1.40 thf(f18,plain,(
% 1.69/1.40 ( ! [X24 : a > $o] : (((X24 @ (sK10 @ X24)) = $true) | ((X24 @ (sK11 @ X24)) != $true) | ((X24 @ sK3) = $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.40 thf(f161,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (((sK4 @ (sK11 @ X0)) = $true) | ((X0 @ (sK10 @ X0)) = $true) | ((X0 @ sK3) = $true)) )),
% 1.69/1.40 inference(subsumption_resolution,[status(thm)],[f160,f95])).
% 1.69/1.40 thf(f160,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (((X0 @ sK3) = $true) | ((sK4 @ (sK11 @ X0)) = $true) | ((X0 @ (sK10 @ X0)) = $true) | ((sK0 @ sK1 @ (sK11 @ X0)) = $true)) )),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f147])).
% 1.69/1.40 thf(f147,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (((X0 @ sK3) = $true) | ((sK0 @ sK1 @ (sK11 @ X0)) = $true) | ((sK4 @ (sK11 @ X0)) = $true) | ((X0 @ (sK10 @ X0)) = $true) | ($true != $true)) )),
% 1.69/1.40 inference(superposition,[status(thm)],[f75,f19])).
% 1.69/1.40 thf(f19,plain,(
% 1.69/1.40 ( ! [X24 : a > $o] : (((sK2 @ sK1 @ (sK11 @ X24)) = $true) | ((X24 @ (sK10 @ X24)) = $true) | ((X24 @ sK3) = $true) | ((sK0 @ sK1 @ (sK11 @ X24)) = $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.40 thf(f210,plain,(
% 1.69/1.40 spl12_14),
% 1.69/1.40 inference(avatar_split_clause,[status(thm)],[f209,f202])).
% 1.69/1.40 thf(f209,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (((X0 @ (sK9 @ X0)) != $true) | ((sK4 @ (sK11 @ X0)) = $true) | ((X0 @ sK3) = $true)) )),
% 1.69/1.40 inference(subsumption_resolution,[status(thm)],[f186,f95])).
% 1.69/1.40 thf(f186,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (((sK0 @ sK1 @ (sK11 @ X0)) = $true) | ((sK4 @ (sK11 @ X0)) = $true) | ((X0 @ (sK9 @ X0)) != $true) | ((X0 @ sK3) = $true)) )),
% 1.69/1.40 inference(trivial_inequality_removal,[status(thm)],[f183])).
% 1.69/1.40 thf(f183,plain,(
% 1.69/1.40 ( ! [X0 : a > $o] : (((sK0 @ sK1 @ (sK11 @ X0)) = $true) | ((sK4 @ (sK11 @ X0)) = $true) | ((X0 @ (sK9 @ X0)) != $true) | ($true != $true) | ((X0 @ sK3) = $true)) )),
% 1.69/1.40 inference(superposition,[status(thm)],[f75,f23])).
% 1.69/1.40 thf(f23,plain,(
% 1.69/1.40 ( ! [X24 : a > $o] : (((sK2 @ sK1 @ (sK11 @ X24)) = $true) | ((sK0 @ sK1 @ (sK11 @ X24)) = $true) | ((X24 @ (sK9 @ X24)) != $true) | ((X24 @ sK3) = $true)) )),
% 1.69/1.40 inference(cnf_transformation,[status(thm)],[f17])).
% 1.69/1.40 % SZS output end Proof for DTF2THF_9795
% 1.69/1.40 % (9988)------------------------------
% 1.69/1.40 % (9988)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.69/1.40 % (9988)Termination reason: Refutation
% 1.69/1.40
% 1.69/1.40 % (9988)Memory used [KB]: 6268
% 1.69/1.40 % (9988)Time elapsed: 0.084 s
% 1.69/1.40 % (9988)Instructions burned: 223 (million)
% 1.69/1.40 % (9988)------------------------------
% 1.69/1.40 % (9988)------------------------------
% 1.69/1.40 % (9982)Success in time 0.104 s
%------------------------------------------------------------------------------