%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : SEV028^5 : 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 : n004.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 09:40:06 AM UTC 2026
% Result : Theorem 1.84s 1.55s
% Output : Refutation 1.84s
% Verified :
% SZS Type : Refutation
% Derivation depth : 30
% Number of leaves : 17
% Syntax : Number of formulae : 79 ( 3 unt; 0 typ; 6 def)
% Number of atoms : 709 ( 234 equ; 0 cnn)
% Maximal formula atoms : 19 ( 8 avg)
% Number of connectives : 954 ( 144 ~; 143 |; 98 &; 512 @)
% ( 15 <=>; 42 =>; 0 <=; 0 <~>)
% Maximal formula depth : 18 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 31 ( 31 >; 0 *; 0 +; 0 <<)
% Number of symbols : 24 ( 21 usr; 14 con; 0-2 aty)
% Number of variables : 209 ( 0 ^; 127 !; 82 ?; 209 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_5,type,
a: $tType ).
thf(func_def_0,type,
a: $tType ).
thf(func_def_1,type,
cQ: a > a > $o ).
thf(func_def_5,type,
sK0: a > a > $o ).
thf(func_def_6,type,
sK1: a > a ).
thf(func_def_7,type,
sK2: ( a > $o ) > a ).
thf(func_def_8,type,
sK3: ( a > $o ) > a ).
thf(func_def_9,type,
sK4: ( a > $o ) > a ).
thf(func_def_10,type,
sK5: ( a > $o ) > a ).
thf(func_def_11,type,
sK6: ( a > $o ) > a ).
thf(func_def_12,type,
sK7: a ).
thf(func_def_13,type,
sK8: a ).
thf(func_def_14,type,
sK9: a ).
thf(func_def_15,type,
sK10: a ).
thf(func_def_16,type,
sK11: a ).
thf(func_def_17,type,
sK12: a ).
thf(func_def_20,type,
ph14:
!>[X0: $tType] : X0 ).
thf(f305,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f51,f56,f61,f62,f67,f68,f134,f181,f304]) ).
thf(f304,plain,
( ~ spl13_3
| spl13_4
| ~ spl13_6 ),
inference(avatar_contradiction_clause,[status(thm)],[f303]) ).
thf(f303,plain,
( $false
| ~ spl13_3
| spl13_4
| ~ spl13_6 ),
inference(subsumption_resolution,[status(thm)],[f289,f32]) ).
thf(f32,plain,
! [X0: a] :
( ( sK0 @ X0 @ X0 )
= $true ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f19,plain,
( ! [X0: a] :
( ( ( sK0 @ X0 @ X0 )
= $true )
& ! [X2: a] :
( ( ( sK0 @ X0 @ X2 )
!= $true )
| ! [X3: a] :
( ( cQ @ X2 @ X3 )
= ( sK0 @ X0 @ X3 ) ) )
& ( ( sK0 @ X0 @ ( sK1 @ X0 ) )
= $true )
& ! [X5: a > $o] :
( ! [X6: a] :
( ( X5 @ X6 )
!= $true )
| ( ( sK0 @ X0 )
= X5 )
| ( ( ( X5 @ ( sK2 @ X5 ) )
= $true )
& ( ( X5 @ ( sK3 @ X5 ) )
!= ( cQ @ ( sK2 @ X5 ) @ ( sK3 @ X5 ) ) ) )
| ( $true
!= ( X5 @ X0 ) ) ) )
& ! [X9: a > $o] :
( ( ( ( X9 @ ( sK5 @ X9 ) )
!= ( cQ @ ( sK4 @ X9 ) @ ( sK5 @ X9 ) ) )
& ( ( X9 @ ( sK4 @ X9 ) )
= $true ) )
| ! [X12: a] :
( $true
!= ( X9 @ X12 ) )
| ( ( X9 @ ( sK6 @ X9 ) )
= $true ) )
& ( ( ( ( cQ @ sK8 @ sK7 )
= $true )
& ( ( cQ @ sK8 @ sK9 )
!= $true )
& ( ( cQ @ sK7 @ sK9 )
= $true ) )
| ( ( ( cQ @ sK10 @ sK11 )
!= $true )
& ( ( cQ @ sK11 @ sK10 )
= $true ) )
| ( ( cQ @ sK12 @ sK12 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12])],[f8,f18,f17,f16,f15,f14,f13,f12,f11,f10,f9]) ).
thf(f9,plain,
! [X0: a] :
( ? [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
& ! [X2: a] :
( ( $true
!= ( X1 @ X2 ) )
| ! [X3: a] :
( ( cQ @ X2 @ X3 )
= ( X1 @ X3 ) ) )
& ? [X4: a] :
( ( X1 @ X4 )
= $true )
& ! [X5: a > $o] :
( ! [X6: a] :
( ( X5 @ X6 )
!= $true )
| ( X1 = X5 )
| ? [X7: a] :
( ( ( X5 @ X7 )
= $true )
& ? [X8: a] :
( ( cQ @ X7 @ X8 )
!= ( X5 @ X8 ) ) )
| ( $true
!= ( X5 @ X0 ) ) ) )
=> ( ( ( sK0 @ X0 @ X0 )
= $true )
& ! [X2: a] :
( ( ( sK0 @ X0 @ X2 )
!= $true )
| ! [X3: a] :
( ( cQ @ X2 @ X3 )
= ( sK0 @ X0 @ X3 ) ) )
& ? [X4: a] :
( $true
= ( sK0 @ X0 @ X4 ) )
& ! [X5: a > $o] :
( ! [X6: a] :
( ( X5 @ X6 )
!= $true )
| ( ( sK0 @ X0 )
= X5 )
| ? [X7: a] :
( ( ( X5 @ X7 )
= $true )
& ? [X8: a] :
( ( cQ @ X7 @ X8 )
!= ( X5 @ X8 ) ) )
| ( $true
!= ( X5 @ X0 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f10,plain,
! [X0: a] :
( ? [X4: a] :
( $true
= ( sK0 @ X0 @ X4 ) )
=> ( ( sK0 @ X0 @ ( sK1 @ X0 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f11,plain,
! [X5: a > $o] :
( ? [X7: a] :
( ( ( X5 @ X7 )
= $true )
& ? [X8: a] :
( ( cQ @ X7 @ X8 )
!= ( X5 @ X8 ) ) )
=> ( ( ( X5 @ ( sK2 @ X5 ) )
= $true )
& ? [X8: a] :
( ( X5 @ X8 )
!= ( cQ @ ( sK2 @ X5 ) @ X8 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f12,plain,
! [X5: a > $o] :
( ? [X8: a] :
( ( X5 @ X8 )
!= ( cQ @ ( sK2 @ X5 ) @ X8 ) )
=> ( ( X5 @ ( sK3 @ X5 ) )
!= ( cQ @ ( sK2 @ X5 ) @ ( sK3 @ X5 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X9: a > $o] :
( ? [X10: a] :
( ? [X11: a] :
( ( cQ @ X10 @ X11 )
!= ( X9 @ X11 ) )
& ( ( X9 @ X10 )
= $true ) )
=> ( ? [X11: a] :
( ( X9 @ X11 )
!= ( cQ @ ( sK4 @ X9 ) @ X11 ) )
& ( ( X9 @ ( sK4 @ X9 ) )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f14,plain,
! [X9: a > $o] :
( ? [X11: a] :
( ( X9 @ X11 )
!= ( cQ @ ( sK4 @ X9 ) @ X11 ) )
=> ( ( X9 @ ( sK5 @ X9 ) )
!= ( cQ @ ( sK4 @ X9 ) @ ( sK5 @ X9 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X9: a > $o] :
( ? [X13: a] :
( ( X9 @ X13 )
= $true )
=> ( ( X9 @ ( sK6 @ X9 ) )
= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
( ? [X14: a,X15: a,X16: a] :
( ( $true
= ( cQ @ X15 @ X14 ) )
& ( ( cQ @ X15 @ X16 )
!= $true )
& ( $true
= ( cQ @ X14 @ X16 ) ) )
=> ( ( ( cQ @ sK8 @ sK7 )
= $true )
& ( ( cQ @ sK8 @ sK9 )
!= $true )
& ( ( cQ @ sK7 @ sK9 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f17,plain,
( ? [X17: a,X18: a] :
( ( ( cQ @ X17 @ X18 )
!= $true )
& ( $true
= ( cQ @ X18 @ X17 ) ) )
=> ( ( ( cQ @ sK10 @ sK11 )
!= $true )
& ( ( cQ @ sK11 @ sK10 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
( ? [X19: a] :
( $true
!= ( cQ @ X19 @ X19 ) )
=> ( ( cQ @ sK12 @ sK12 )
!= $true ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f8,plain,
( ! [X0: a] :
? [X1: a > $o] :
( ( ( X1 @ X0 )
= $true )
& ! [X2: a] :
( ( $true
!= ( X1 @ X2 ) )
| ! [X3: a] :
( ( cQ @ X2 @ X3 )
= ( X1 @ X3 ) ) )
& ? [X4: a] :
( ( X1 @ X4 )
= $true )
& ! [X5: a > $o] :
( ! [X6: a] :
( ( X5 @ X6 )
!= $true )
| ( X1 = X5 )
| ? [X7: a] :
( ( ( X5 @ X7 )
= $true )
& ? [X8: a] :
( ( cQ @ X7 @ X8 )
!= ( X5 @ X8 ) ) )
| ( $true
!= ( X5 @ X0 ) ) ) )
& ! [X9: a > $o] :
( ? [X10: a] :
( ? [X11: a] :
( ( cQ @ X10 @ X11 )
!= ( X9 @ X11 ) )
& ( ( X9 @ X10 )
= $true ) )
| ! [X12: a] :
( $true
!= ( X9 @ X12 ) )
| ? [X13: a] :
( ( X9 @ X13 )
= $true ) )
& ( ? [X14: a,X15: a,X16: a] :
( ( $true
= ( cQ @ X15 @ X14 ) )
& ( ( cQ @ X15 @ X16 )
!= $true )
& ( $true
= ( cQ @ X14 @ X16 ) ) )
| ? [X17: a,X18: a] :
( ( ( cQ @ X17 @ X18 )
!= $true )
& ( $true
= ( cQ @ X18 @ X17 ) ) )
| ? [X19: a] :
( $true
!= ( cQ @ X19 @ X19 ) ) ) ),
inference(rectify,[status(thm)],[f7]) ).
thf(f7,plain,
( ! [X5: a] :
? [X6: a > $o] :
( ( ( X6 @ X5 )
= $true )
& ! [X12: a] :
( ( $true
!= ( X6 @ X12 ) )
| ! [X13: a] :
( ( X6 @ X13 )
= ( cQ @ X12 @ X13 ) ) )
& ? [X7: a] :
( $true
= ( X6 @ X7 ) )
& ! [X8: a > $o] :
( ! [X11: a] :
( ( X8 @ X11 )
!= $true )
| ( X6 = X8 )
| ? [X9: a] :
( ( $true
= ( X8 @ X9 ) )
& ? [X10: a] :
( ( cQ @ X9 @ X10 )
!= ( X8 @ X10 ) ) )
| ( $true
!= ( X8 @ X5 ) ) ) )
& ! [X0: a > $o] :
( ? [X1: a] :
( ? [X2: a] :
( ( X0 @ X2 )
!= ( cQ @ X1 @ X2 ) )
& ( ( X0 @ X1 )
= $true ) )
| ! [X3: a] :
( ( X0 @ X3 )
!= $true )
| ? [X4: a] :
( ( X0 @ X4 )
= $true ) )
& ( ? [X16: a,X17: a,X18: a] :
( ( ( cQ @ X17 @ X16 )
= $true )
& ( ( cQ @ X17 @ X18 )
!= $true )
& ( $true
= ( cQ @ X16 @ X18 ) ) )
| ? [X14: a,X15: a] :
( ( $true
!= ( cQ @ X14 @ X15 ) )
& ( $true
= ( cQ @ X15 @ X14 ) ) )
| ? [X19: a] :
( $true
!= ( cQ @ X19 @ X19 ) ) ) ),
inference(flattening,[status(thm)],[f6]) ).
thf(f6,plain,
( ( ? [X14: a,X15: a] :
( ( $true
!= ( cQ @ X14 @ X15 ) )
& ( $true
= ( cQ @ X15 @ X14 ) ) )
| ? [X19: a] :
( $true
!= ( cQ @ X19 @ X19 ) )
| ? [X17: a,X18: a,X16: a] :
( ( ( cQ @ X17 @ X18 )
!= $true )
& ( ( cQ @ X17 @ X16 )
= $true )
& ( $true
= ( cQ @ X16 @ X18 ) ) ) )
& ! [X0: a > $o] :
( ? [X4: a] :
( ( X0 @ X4 )
= $true )
| ? [X1: a] :
( ? [X2: a] :
( ( X0 @ X2 )
!= ( cQ @ X1 @ X2 ) )
& ( ( X0 @ X1 )
= $true ) )
| ! [X3: a] :
( ( X0 @ X3 )
!= $true ) )
& ! [X5: a] :
? [X6: a > $o] :
( ? [X7: a] :
( $true
= ( X6 @ X7 ) )
& ! [X12: a] :
( ( $true
!= ( X6 @ X12 ) )
| ! [X13: a] :
( ( X6 @ X13 )
= ( cQ @ X12 @ X13 ) ) )
& ! [X8: a > $o] :
( ( X6 = X8 )
| ( $true
!= ( X8 @ X5 ) )
| ! [X11: a] :
( ( X8 @ X11 )
!= $true )
| ? [X9: a] :
( ( $true
= ( X8 @ X9 ) )
& ? [X10: a] :
( ( cQ @ X9 @ X10 )
!= ( X8 @ X10 ) ) ) )
& ( ( X6 @ X5 )
= $true ) ) ),
inference(ennf_transformation,[status(thm)],[f5]) ).
thf(f5,plain,
~ ( ( ! [X0: a > $o] :
( ( ! [X1: a] :
( ( ( X0 @ X1 )
= $true )
=> ! [X2: a] :
( ( X0 @ X2 )
= ( cQ @ X1 @ X2 ) ) )
& ? [X3: a] :
( ( X0 @ X3 )
= $true ) )
=> ? [X4: a] :
( ( X0 @ X4 )
= $true ) )
& ! [X5: a] :
? [X6: a > $o] :
( ? [X7: a] :
( $true
= ( X6 @ X7 ) )
& ! [X12: a] :
( ( $true
= ( X6 @ X12 ) )
=> ! [X13: a] :
( ( X6 @ X13 )
= ( cQ @ X12 @ X13 ) ) )
& ! [X8: a > $o] :
( ( ( $true
= ( X8 @ X5 ) )
& ? [X11: a] :
( ( X8 @ X11 )
= $true )
& ! [X9: a] :
( ( $true
= ( X8 @ X9 ) )
=> ! [X10: a] :
( ( cQ @ X9 @ X10 )
= ( X8 @ X10 ) ) ) )
=> ( X6 = X8 ) )
& ( ( X6 @ X5 )
= $true ) ) )
=> ( ! [X14: a,X15: a] :
( ( $true
= ( cQ @ X15 @ X14 ) )
=> ( $true
= ( cQ @ X14 @ X15 ) ) )
& ! [X19: a] :
( $true
= ( cQ @ X19 @ X19 ) )
& ! [X17: a,X18: a,X16: a] :
( ( ( ( cQ @ X17 @ X16 )
= $true )
& ( $true
= ( cQ @ X16 @ X18 ) ) )
=> ( ( cQ @ X17 @ X18 )
= $true ) ) ) ),
inference(fool_elimination,[status(thm)],[f4]) ).
thf(f4,plain,
~ ( ( ! [X0: a > $o] :
( ( ! [X1: a] :
( ( X0 @ X1 )
=> ! [X2: a] :
( ( X0 @ X2 )
<=> ( cQ @ X1 @ X2 ) ) )
& ? [X3: a] : ( X0 @ X3 ) )
=> ? [X4: a] : ( X0 @ X4 ) )
& ! [X5: a] :
? [X6: a > $o] :
( ? [X7: a] : ( X6 @ X7 )
& ! [X8: a > $o] :
( ( ( X8 @ X5 )
& ! [X9: a] :
( ( X8 @ X9 )
=> ! [X10: a] :
( ( cQ @ X9 @ X10 )
<=> ( X8 @ X10 ) ) )
& ? [X11: a] : ( X8 @ X11 ) )
=> ( X6 = X8 ) )
& ( X6 @ X5 )
& ! [X12: a] :
( ( X6 @ X12 )
=> ! [X13: a] :
( ( cQ @ X12 @ X13 )
<=> ( X6 @ X13 ) ) ) ) )
=> ( ! [X14: a,X15: a] :
( ( cQ @ X15 @ X14 )
=> ( cQ @ X14 @ X15 ) )
& ! [X16: a,X17: a,X18: a] :
( ( ( cQ @ X16 @ X18 )
& ( cQ @ X17 @ X16 ) )
=> ( cQ @ X17 @ X18 ) )
& ! [X19: a] : ( cQ @ X19 @ X19 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,negated_conjecture,
~ ( ( ! [X0: a > $o] :
( ( ! [X2: a] :
( ( X0 @ X2 )
=> ! [X3: a] :
( ( X0 @ X3 )
<=> ( cQ @ X2 @ X3 ) ) )
& ? [X1: a] : ( X0 @ X1 ) )
=> ? [X1: a] : ( X0 @ X1 ) )
& ! [X2: a] :
? [X0: a > $o] :
( ? [X1: a] : ( X0 @ X1 )
& ! [X5: a > $o] :
( ( ( X5 @ X2 )
& ! [X4: a] :
( ( X5 @ X4 )
=> ! [X3: a] :
( ( cQ @ X4 @ X3 )
<=> ( X5 @ X3 ) ) )
& ? [X1: a] : ( X5 @ X1 ) )
=> ( X0 = X5 ) )
& ( X0 @ X2 )
& ! [X4: a] :
( ( X0 @ X4 )
=> ! [X3: a] :
( ( cQ @ X4 @ X3 )
<=> ( X0 @ X3 ) ) ) ) )
=> ( ! [X3: a,X2: a] :
( ( cQ @ X2 @ X3 )
=> ( cQ @ X3 @ X2 ) )
& ! [X3: a,X2: a,X1: a] :
( ( ( cQ @ X3 @ X1 )
& ( cQ @ X2 @ X3 ) )
=> ( cQ @ X2 @ X1 ) )
& ! [X2: a] : ( cQ @ X2 @ X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f1]) ).
thf(f1,conjecture,
( ( ! [X0: a > $o] :
( ( ! [X2: a] :
( ( X0 @ X2 )
=> ! [X3: a] :
( ( X0 @ X3 )
<=> ( cQ @ X2 @ X3 ) ) )
& ? [X1: a] : ( X0 @ X1 ) )
=> ? [X1: a] : ( X0 @ X1 ) )
& ! [X2: a] :
? [X0: a > $o] :
( ? [X1: a] : ( X0 @ X1 )
& ! [X5: a > $o] :
( ( ( X5 @ X2 )
& ! [X4: a] :
( ( X5 @ X4 )
=> ! [X3: a] :
( ( cQ @ X4 @ X3 )
<=> ( X5 @ X3 ) ) )
& ? [X1: a] : ( X5 @ X1 ) )
=> ( X0 = X5 ) )
& ( X0 @ X2 )
& ! [X4: a] :
( ( X0 @ X4 )
=> ! [X3: a] :
( ( cQ @ X4 @ X3 )
<=> ( X0 @ X3 ) ) ) ) )
=> ( ! [X3: a,X2: a] :
( ( cQ @ X2 @ X3 )
=> ( cQ @ X3 @ X2 ) )
& ! [X3: a,X2: a,X1: a] :
( ( ( cQ @ X3 @ X1 )
& ( cQ @ X2 @ X3 ) )
=> ( cQ @ X2 @ X1 ) )
& ! [X2: a] : ( cQ @ X2 @ X2 ) ) ),
file('/export/starexec/sandbox/tmp/tmp.gggvNPM1jy/DTF2THF_5414.p',cTHM558_pme) ).
thf(f289,plain,
( ( $true
!= ( sK0 @ sK8 @ sK8 ) )
| ~ spl13_3
| spl13_4
| ~ spl13_6 ),
inference(trivial_inequality_removal,[status(thm)],[f286]) ).
thf(f286,plain,
( ( $true = $false )
| ( $true
!= ( sK0 @ sK8 @ sK8 ) )
| ~ spl13_3
| spl13_4
| ~ spl13_6 ),
inference(superposition,[status(thm)],[f50,f277]) ).
thf(f277,plain,
( ! [X0: a] :
( ( $false
= ( cQ @ X0 @ sK7 ) )
| ( ( sK0 @ sK8 @ X0 )
!= $true ) )
| spl13_4
| ~ spl13_6 ),
inference(trivial_inequality_removal,[status(thm)],[f271]) ).
thf(f271,plain,
( ! [X0: a] :
( ( $true != $true )
| ( ( sK0 @ sK8 @ X0 )
!= $true )
| ( $false
= ( cQ @ X0 @ sK7 ) ) )
| spl13_4
| ~ spl13_6 ),
inference(superposition,[status(thm)],[f269,f36]) ).
thf(f36,plain,
! [X2: a,X3: a,X0: a] :
( ( ( sK0 @ X0 @ X3 )
= $true )
| ( ( sK0 @ X0 @ X2 )
!= $true )
| ( ( cQ @ X2 @ X3 )
= $false ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f31,plain,
! [X2: a,X3: a,X0: a] :
( ( ( sK0 @ X0 @ X2 )
!= $true )
| ( ( cQ @ X2 @ X3 )
= ( sK0 @ X0 @ X3 ) ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f269,plain,
( ( ( sK0 @ sK8 @ sK7 )
!= $true )
| spl13_4
| ~ spl13_6 ),
inference(trivial_inequality_removal,[status(thm)],[f251]) ).
thf(f251,plain,
( ( ( sK0 @ sK8 @ sK7 )
!= $true )
| ( $true = $false )
| spl13_4
| ~ spl13_6 ),
inference(superposition,[status(thm)],[f234,f66]) ).
thf(f66,plain,
( ( ( cQ @ sK7 @ sK9 )
= $true )
| ~ spl13_6 ),
inference(avatar_component_clause,[status(thm)],[f64]) ).
thf(f64,definition,
( spl13_6
<=> ( ( cQ @ sK7 @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_6])],[avatar_definition]) ).
thf(f234,plain,
( ! [X0: a] :
( ( ( cQ @ X0 @ sK9 )
= $false )
| ( ( sK0 @ sK8 @ X0 )
!= $true ) )
| spl13_4 ),
inference(trivial_inequality_removal,[status(thm)],[f230]) ).
thf(f230,plain,
( ! [X0: a] :
( ( $true != $true )
| ( ( sK0 @ sK8 @ X0 )
!= $true )
| ( ( cQ @ X0 @ sK9 )
= $false ) )
| spl13_4 ),
inference(superposition,[status(thm)],[f223,f36]) ).
thf(f223,plain,
( ( ( sK0 @ sK8 @ sK9 )
!= $true )
| spl13_4 ),
inference(trivial_inequality_removal,[status(thm)],[f217]) ).
thf(f217,plain,
( ( ( sK0 @ sK8 @ sK9 )
!= $true )
| ( $true != $true )
| spl13_4 ),
inference(superposition,[status(thm)],[f214,f32]) ).
thf(f214,plain,
( ! [X0: a] :
( ( ( sK0 @ sK9 @ X0 )
!= $true )
| ( ( sK0 @ sK8 @ X0 )
!= $true ) )
| spl13_4 ),
inference(trivial_inequality_removal,[status(thm)],[f201]) ).
thf(f201,plain,
( ! [X0: a] :
( ( ( sK0 @ sK8 @ X0 )
!= $true )
| ( ( sK0 @ sK9 @ X0 )
!= $true )
| ( $true = $false ) )
| spl13_4 ),
inference(superposition,[status(thm)],[f197,f123]) ).
thf(f123,plain,
! [X0: a,X1: a] :
( ( ( cQ @ X1 @ X0 )
= $true )
| ( ( sK0 @ X0 @ X1 )
!= $true ) ),
inference(trivial_inequality_removal,[status(thm)],[f111]) ).
thf(f111,plain,
! [X0: a,X1: a] :
( ( ( cQ @ X1 @ X0 )
= $true )
| ( $true = $false )
| ( ( sK0 @ X0 @ X1 )
!= $true ) ),
inference(superposition,[status(thm)],[f35,f32]) ).
thf(f35,plain,
! [X2: a,X3: a,X0: a] :
( ( ( sK0 @ X0 @ X3 )
= $false )
| ( ( cQ @ X2 @ X3 )
= $true )
| ( ( sK0 @ X0 @ X2 )
!= $true ) ),
inference(binary_proxy_clausification,[status(thm)],[f31]) ).
thf(f197,plain,
( ! [X0: a] :
( ( ( cQ @ X0 @ sK8 )
= $false )
| ( ( sK0 @ sK9 @ X0 )
!= $true ) )
| spl13_4 ),
inference(trivial_inequality_removal,[status(thm)],[f191]) ).
thf(f191,plain,
( ! [X0: a] :
( ( $true != $true )
| ( ( sK0 @ sK9 @ X0 )
!= $true )
| ( ( cQ @ X0 @ sK8 )
= $false ) )
| spl13_4 ),
inference(superposition,[status(thm)],[f188,f36]) ).
thf(f188,plain,
( ( $true
!= ( sK0 @ sK9 @ sK8 ) )
| spl13_4 ),
inference(trivial_inequality_removal,[status(thm)],[f182]) ).
thf(f182,plain,
( ( $true
!= ( sK0 @ sK9 @ sK8 ) )
| ( $true != $true )
| spl13_4 ),
inference(superposition,[status(thm)],[f55,f123]) ).
thf(f55,plain,
( ( ( cQ @ sK8 @ sK9 )
!= $true )
| spl13_4 ),
inference(avatar_component_clause,[status(thm)],[f53]) ).
thf(f53,definition,
( spl13_4
<=> ( ( cQ @ sK8 @ sK9 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_4])],[avatar_definition]) ).
thf(f50,plain,
( ( ( cQ @ sK8 @ sK7 )
= $true )
| ~ spl13_3 ),
inference(avatar_component_clause,[status(thm)],[f48]) ).
thf(f48,definition,
( spl13_3
<=> ( ( cQ @ sK8 @ sK7 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_3])],[avatar_definition]) ).
thf(f181,plain,
( ~ spl13_1
| spl13_5 ),
inference(avatar_contradiction_clause,[status(thm)],[f180]) ).
thf(f180,plain,
( $false
| ~ spl13_1
| spl13_5 ),
inference(subsumption_resolution,[status(thm)],[f176,f32]) ).
thf(f176,plain,
( ( $true
!= ( sK0 @ sK11 @ sK11 ) )
| ~ spl13_1
| spl13_5 ),
inference(trivial_inequality_removal,[status(thm)],[f159]) ).
thf(f159,plain,
( ( $true = $false )
| ( $true
!= ( sK0 @ sK11 @ sK11 ) )
| ~ spl13_1
| spl13_5 ),
inference(superposition,[status(thm)],[f155,f42]) ).
thf(f42,plain,
( ( ( cQ @ sK11 @ sK10 )
= $true )
| ~ spl13_1 ),
inference(avatar_component_clause,[status(thm)],[f40]) ).
thf(f40,definition,
( spl13_1
<=> ( ( cQ @ sK11 @ sK10 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_1])],[avatar_definition]) ).
thf(f155,plain,
( ! [X0: a] :
( ( ( cQ @ X0 @ sK10 )
= $false )
| ( ( sK0 @ sK11 @ X0 )
!= $true ) )
| spl13_5 ),
inference(trivial_inequality_removal,[status(thm)],[f154]) ).
thf(f154,plain,
( ! [X0: a] :
( ( ( sK0 @ sK11 @ X0 )
!= $true )
| ( ( cQ @ X0 @ sK10 )
= $false )
| ( $true != $true ) )
| spl13_5 ),
inference(superposition,[status(thm)],[f138,f36]) ).
thf(f138,plain,
( ( $true
!= ( sK0 @ sK11 @ sK10 ) )
| spl13_5 ),
inference(trivial_inequality_removal,[status(thm)],[f135]) ).
thf(f135,plain,
( ( $true
!= ( sK0 @ sK11 @ sK10 ) )
| ( $true != $true )
| spl13_5 ),
inference(superposition,[status(thm)],[f60,f123]) ).
thf(f60,plain,
( ( ( cQ @ sK10 @ sK11 )
!= $true )
| spl13_5 ),
inference(avatar_component_clause,[status(thm)],[f58]) ).
thf(f58,definition,
( spl13_5
<=> ( ( cQ @ sK10 @ sK11 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_5])],[avatar_definition]) ).
thf(f134,plain,
spl13_2,
inference(avatar_contradiction_clause,[status(thm)],[f133]) ).
thf(f133,plain,
( $false
| spl13_2 ),
inference(subsumption_resolution,[status(thm)],[f132,f32]) ).
thf(f132,plain,
( ( ( sK0 @ sK12 @ sK12 )
!= $true )
| spl13_2 ),
inference(trivial_inequality_removal,[status(thm)],[f131]) ).
thf(f131,plain,
( ( ( sK0 @ sK12 @ sK12 )
!= $true )
| ( $true != $true )
| spl13_2 ),
inference(superposition,[status(thm)],[f46,f123]) ).
thf(f46,plain,
( ( ( cQ @ sK12 @ sK12 )
!= $true )
| spl13_2 ),
inference(avatar_component_clause,[status(thm)],[f44]) ).
thf(f44,definition,
( spl13_2
<=> ( ( cQ @ sK12 @ sK12 )
= $true ) ),
introduced(definition,[new_symbols(naming,[spl13_2])],[avatar_definition]) ).
thf(f68,plain,
( ~ spl13_5
| ~ spl13_2
| spl13_6 ),
inference(avatar_split_clause,[status(thm)],[f21,f64,f44,f58]) ).
thf(f21,plain,
( ( ( cQ @ sK12 @ sK12 )
!= $true )
| ( ( cQ @ sK7 @ sK9 )
= $true )
| ( ( cQ @ sK10 @ sK11 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f67,plain,
( ~ spl13_2
| spl13_1
| spl13_6 ),
inference(avatar_split_clause,[status(thm)],[f20,f64,f40,f44]) ).
thf(f20,plain,
( ( ( cQ @ sK12 @ sK12 )
!= $true )
| ( ( cQ @ sK11 @ sK10 )
= $true )
| ( ( cQ @ sK7 @ sK9 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f62,plain,
( ~ spl13_4
| ~ spl13_5
| ~ spl13_2 ),
inference(avatar_split_clause,[status(thm)],[f23,f44,f58,f53]) ).
thf(f23,plain,
( ( ( cQ @ sK10 @ sK11 )
!= $true )
| ( ( cQ @ sK12 @ sK12 )
!= $true )
| ( ( cQ @ sK8 @ sK9 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f61,plain,
( spl13_3
| ~ spl13_5
| ~ spl13_2 ),
inference(avatar_split_clause,[status(thm)],[f25,f44,f58,f48]) ).
thf(f25,plain,
( ( ( cQ @ sK8 @ sK7 )
= $true )
| ( ( cQ @ sK12 @ sK12 )
!= $true )
| ( ( cQ @ sK10 @ sK11 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f56,plain,
( ~ spl13_2
| spl13_1
| ~ spl13_4 ),
inference(avatar_split_clause,[status(thm)],[f22,f53,f40,f44]) ).
thf(f22,plain,
( ( ( cQ @ sK11 @ sK10 )
= $true )
| ( ( cQ @ sK8 @ sK9 )
!= $true )
| ( ( cQ @ sK12 @ sK12 )
!= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
thf(f51,plain,
( spl13_1
| ~ spl13_2
| spl13_3 ),
inference(avatar_split_clause,[status(thm)],[f24,f48,f44,f40]) ).
thf(f24,plain,
( ( ( cQ @ sK11 @ sK10 )
= $true )
| ( ( cQ @ sK12 @ sK12 )
!= $true )
| ( ( cQ @ sK8 @ sK7 )
= $true ) ),
inference(cnf_transformation,[status(thm)],[f19]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : SEV028^5 : 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
% 0.17/0.34 % Computer : n004.cluster.edu
% 0.17/0.34 % Model : x86_64 x86_64
% 0.17/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.17/0.34 % Memory : 8042.1875MB
% 0.17/0.34 % OS : Linux 3.10.0-693.el7.x86_64
% 0.17/0.34 % CPULimit : 300
% 0.17/0.34 % WCLimit : 300
% 0.17/0.34 % DateTime : Tue Feb 24 12:38:41 EST 2026
% 0.17/0.35 % CPUTime :
% 0.17/0.35 Running /export/starexec/sandbox/solver/bin/run_DT2H2X /export/starexec/sandbox/benchmark/theBenchmark.p 300
% 0.20/0.48 ---- Original DTF file ---
% 0.20/0.48 thf(spec,logic,$$dhol).
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 % File : SEV028^5 : TPTP v9.2.1. Released v4.0.0.
% 0.20/0.48 % Domain : Set Theory (Relations)
% 0.20/0.48 % Problem : TPS problem from EQUIVALENCE-RELATIONS-THMS
% 0.20/0.48 % Version : Especial.
% 0.20/0.48 % English :
% 0.20/0.48
% 0.20/0.48 % Refs : [Bro09] Brown (2009), Email to Geoff Sutcliffe
% 0.20/0.48 % Source : [Bro09]
% 0.20/0.48 % Names : tps_1122 [Bro09]
% 0.20/0.48
% 0.20/0.48 % Status : Theorem
% 0.20/0.48 % Rating : 0.00 v9.0.0, 0.10 v8.2.0, 0.08 v8.1.0, 0.09 v7.5.0, 0.14 v7.4.0, 0.22 v7.2.0, 0.12 v7.1.0, 0.38 v7.0.0, 0.29 v6.4.0, 0.33 v6.3.0, 0.40 v6.2.0, 0.43 v5.5.0, 0.33 v5.4.0, 0.40 v5.1.0, 0.60 v5.0.0, 0.40 v4.1.0, 0.33 v4.0.1, 0.67 v4.0.0
% 0.20/0.48 % Syntax : Number of formulae : 3 ( 0 unt; 2 typ; 0 def)
% 0.20/0.48 % Number of atoms : 10 ( 1 equ; 0 cnn)
% 0.20/0.48 % Maximal formula atoms : 10 ( 10 avg)
% 0.20/0.48 % Number of connectives : 51 ( 0 ~; 0 |; 10 &; 30 @)
% 0.20/0.48 % ( 3 <=>; 8 =>; 0 <=; 0 <~>)
% 0.20/0.48 % Maximal formula depth : 18 ( 18 avg)
% 0.20/0.48 % Number of types : 2 ( 1 usr)
% 0.20/0.48 % Number of type conns : 5 ( 5 >; 0 *; 0 +; 0 <<)
% 0.20/0.48 % Number of symbols : 2 ( 1 usr; 0 con; 2-2 aty)
% 0.20/0.48 % Number of variables : 20 ( 0 ^; 15 !; 5 ?; 20 :)
% 0.20/0.48 % SPC : TH0_THM_EQU_NAR
% 0.20/0.48
% 0.20/0.48 % Comments : This problem is from the TPS library. Copyright (c) 2009 The TPS
% 0.20/0.48 % project in the Department of Mathematical Sciences at Carnegie
% 0.20/0.48 % Mellon University. Distributed under the Creative Commons copyleft
% 0.20/0.48 % license: http://creativecommons.org/licenses/by-sa/3.0/
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 thf(a_type,type,
% 0.20/0.48 a: $tType ).
% 0.20/0.48
% 0.20/0.48 thf(cQ,type,
% 0.20/0.48 cQ: a > a > $o ).
% 0.20/0.48
% 0.20/0.48 thf(cTHM558_pme,conjecture,
% 0.20/0.48 ( ( ! [Xp: a > $o] :
% 0.20/0.48 ( ( ? [Xz: a] : ( Xp @ Xz )
% 0.20/0.48 & ! [Xx: a] :
% 0.20/0.48 ( ( Xp @ Xx )
% 0.20/0.48 => ! [Xy: a] :
% 0.20/0.48 ( ( Xp @ Xy )
% 0.20/0.48 <=> ( cQ @ Xx @ Xy ) ) ) )
% 0.20/0.48 => ? [Xz: a] : ( Xp @ Xz ) )
% 0.20/0.48 & ! [Xx: a] :
% 0.20/0.48 ? [Xp: a > $o] :
% 0.20/0.48 ( ? [Xz: a] : ( Xp @ Xz )
% 0.20/0.48 & ! [Xx0: a] :
% 0.20/0.48 ( ( Xp @ Xx0 )
% 0.20/0.48 => ! [Xy: a] :
% 0.20/0.48 ( ( Xp @ Xy )
% 0.20/0.48 <=> ( cQ @ Xx0 @ Xy ) ) )
% 0.20/0.48 & ( Xp @ Xx )
% 0.20/0.48 & ! [Xq: a > $o] :
% 0.20/0.48 ( ( ? [Xz: a] : ( Xq @ Xz )
% 0.20/0.48 & ! [Xx0: a] :
% 0.20/0.48 ( ( Xq @ Xx0 )
% 0.20/0.48 => ! [Xy: a] :
% 0.20/0.48 ( ( Xq @ Xy )
% 0.20/0.48 <=> ( cQ @ Xx0 @ Xy ) ) )
% 0.20/0.48 & ( Xq @ Xx ) )
% 0.20/0.48 => ( Xq = Xp ) ) ) )
% 0.20/0.48 => ( ! [Xx: a] : ( cQ @ Xx @ Xx )
% 0.20/0.48 & ! [Xx: a,Xy: a] :
% 0.20/0.48 ( ( cQ @ Xx @ Xy )
% 0.20/0.48 => ( cQ @ Xy @ Xx ) )
% 0.20/0.48 & ! [Xx: a,Xy: a,Xz: a] :
% 0.20/0.48 ( ( ( cQ @ Xx @ Xy )
% 0.20/0.48 & ( cQ @ Xy @ Xz ) )
% 0.20/0.48 => ( cQ @ Xx @ Xz ) ) ) ) ).
% 0.20/0.48
% 0.20/0.48 %------------------------------------------------------------------------------
% 0.20/0.48 ------------------------
% 1.64/1.49 ---- Embedded in THF ---
% 1.64/1.49 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.64/1.49 %%% Generated on Tue Feb 24 12:38:42 EST 2026
% 1.64/1.49 %%% using '$$dhol' embedding, version 1.3.0.
% 1.64/1.49 %%% Logic specification used:
% 1.64/1.49 %%% thf(spec, logic, $$dhol).
% 1.64/1.49
% 1.64/1.49 % SZS output start ListOfTHF for /export/starexec/sandbox/tmp/tmp.gggvNPM1jy/DTF2DTF5414.p
% See solution above
% 1.64/1.49 ------------------------
% 1.84/1.50 ---- Cleaned THF ---
% 1.84/1.50 thf(a_type,type,
% 1.84/1.50 a: $tType ).
% 1.84/1.50
% 1.84/1.50 thf(cQ,type,
% 1.84/1.50 cQ: a > a > $o ).
% 1.84/1.50
% 1.84/1.50 thf(cTHM558_pme,conjecture,
% 1.84/1.50 ( ( ! [Xp: a > $o] :
% 1.84/1.50 ( ( ? [Xz: a] : ( Xp @ Xz )
% 1.84/1.50 & ! [Xx: a] :
% 1.84/1.50 ( ( Xp @ Xx )
% 1.84/1.50 => ! [Xy: a] :
% 1.84/1.50 ( ( Xp @ Xy )
% 1.84/1.50 <=> ( cQ @ Xx @ Xy ) ) ) )
% 1.84/1.50 => ? [Xz: a] : ( Xp @ Xz ) )
% 1.84/1.50 & ! [Xx: a] :
% 1.84/1.50 ? [Xp: a > $o] :
% 1.84/1.50 ( ? [Xz: a] : ( Xp @ Xz )
% 1.84/1.50 & ! [Xx0: a] :
% 1.84/1.50 ( ( Xp @ Xx0 )
% 1.84/1.50 => ! [Xy: a] :
% 1.84/1.50 ( ( Xp @ Xy )
% 1.84/1.50 <=> ( cQ @ Xx0 @ Xy ) ) )
% 1.84/1.50 & ( Xp @ Xx )
% 1.84/1.50 & ! [Xq: a > $o] :
% 1.84/1.50 ( ( ? [Xz: a] : ( Xq @ Xz )
% 1.84/1.50 & ! [Xx0: a] :
% 1.84/1.50 ( ( Xq @ Xx0 )
% 1.84/1.50 => ! [Xy: a] :
% 1.84/1.50 ( ( Xq @ Xy )
% 1.84/1.50 <=> ( cQ @ Xx0 @ Xy ) ) )
% 1.84/1.50 & ( Xq @ Xx ) )
% 1.84/1.50 => ( Xq = Xp ) ) ) )
% 1.84/1.50 => ( ! [Xx: a] : ( cQ @ Xx @ Xx )
% 1.84/1.50 & ! [Xx: a,Xy: a] :
% 1.84/1.50 ( ( cQ @ Xx @ Xy )
% 1.84/1.50 => ( cQ @ Xy @ Xx ) )
% 1.84/1.50 & ! [Xx: a,Xy: a,Xz: a] :
% 1.84/1.50 ( ( ( cQ @ Xx @ Xy )
% 1.84/1.50 & ( cQ @ Xy @ Xz ) )
% 1.84/1.50 => ( cQ @ Xx @ Xz ) ) ) ) ).
% 1.84/1.50 ------------------------
% 1.84/1.52 % (5515)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_5414 for (2999ds/2Mi)
% 1.84/1.52 % (5513)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_5414 for (2999ds/27Mi)
% 1.84/1.52 % (5514)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_5414 for (2999ds/2Mi)
% 1.84/1.52 % (5517)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_5414 for (2999ds/18Mi)
% 1.84/1.52 % (5511)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_5414 for (2999ds/183Mi)
% 1.84/1.52 % (5512)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_5414 for (2999ds/4Mi)
% 1.84/1.52 % (5515)Instruction limit reached!
% 1.84/1.52 % (5515)------------------------------
% 1.84/1.52 % (5515)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.52 % (5515)Termination reason: Unknown
% 1.84/1.52 % (5515)Termination phase: shuffling
% 1.84/1.52
% 1.84/1.52 % (5515)Memory used [KB]: 895
% 1.84/1.52 % (5515)Time elapsed: 0.002 s
% 1.84/1.52 % (5515)Instructions burned: 2 (million)
% 1.84/1.52 % (5515)------------------------------
% 1.84/1.52 % (5515)------------------------------
% 1.84/1.52 % (5514)Instruction limit reached!
% 1.84/1.52 % (5514)------------------------------
% 1.84/1.52 % (5514)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.52 % (5514)Termination reason: Unknown
% 1.84/1.52 % (5514)Termination phase: Saturation
% 1.84/1.52
% 1.84/1.52 % (5514)Memory used [KB]: 5500
% 1.84/1.52 % (5514)Time elapsed: 0.003 s
% 1.84/1.52 % (5514)Instructions burned: 3 (million)
% 1.84/1.52 % (5514)------------------------------
% 1.84/1.52 % (5514)------------------------------
% 1.84/1.52 % (5516)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_5414 for (2999ds/275Mi)
% 1.84/1.52 % (5512)Instruction limit reached!
% 1.84/1.52 % (5512)------------------------------
% 1.84/1.52 % (5512)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.52 % (5512)Termination reason: Unknown
% 1.84/1.52 % (5512)Termination phase: Saturation
% 1.84/1.52
% 1.84/1.52 % (5512)Memory used [KB]: 5500
% 1.84/1.52 % (5512)Time elapsed: 0.004 s
% 1.84/1.52 % (5512)Instructions burned: 4 (million)
% 1.84/1.52 % (5512)------------------------------
% 1.84/1.52 % (5512)------------------------------
% 1.84/1.53 % (5517)Instruction limit reached!
% 1.84/1.53 % (5517)------------------------------
% 1.84/1.53 % (5517)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.53 % (5517)Termination reason: Unknown
% 1.84/1.53 % (5517)Termination phase: Saturation
% 1.84/1.53
% 1.84/1.53 % (5517)Memory used [KB]: 5628
% 1.84/1.53 % (5517)Time elapsed: 0.012 s
% 1.84/1.53 % (5517)Instructions burned: 19 (million)
% 1.84/1.53 % (5517)------------------------------
% 1.84/1.53 % (5517)------------------------------
% 1.84/1.54 % (5513)Instruction limit reached!
% 1.84/1.54 % (5513)------------------------------
% 1.84/1.54 % (5513)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.54 % (5513)Termination reason: Unknown
% 1.84/1.54 % (5513)Termination phase: Saturation
% 1.84/1.54
% 1.84/1.54 % (5513)Memory used [KB]: 5628
% 1.84/1.54 % (5513)Time elapsed: 0.016 s
% 1.84/1.54 % (5513)Instructions burned: 27 (million)
% 1.84/1.54 % (5513)------------------------------
% 1.84/1.54 % (5513)------------------------------
% 1.84/1.54 % (5518)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_5414 for (2999ds/3Mi)
% 1.84/1.54 % (5519)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_5414 for (2999ds/37Mi)
% 1.84/1.54 % (5518)Instruction limit reached!
% 1.84/1.54 % (5518)------------------------------
% 1.84/1.54 % (5518)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.54 % (5518)Termination reason: Unknown
% 1.84/1.54 % (5518)Termination phase: Saturation
% 1.84/1.54
% 1.84/1.54 % (5518)Memory used [KB]: 5500
% 1.84/1.54 % (5518)Time elapsed: 0.004 s
% 1.84/1.54 % (5518)Instructions burned: 3 (million)
% 1.84/1.54 % (5518)------------------------------
% 1.84/1.54 % (5518)------------------------------
% 1.84/1.54 % (5520)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_5414 for (2999ds/15Mi)
% 1.84/1.55 % (5511)First to succeed.
% 1.84/1.55 % (5521)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_5414 for (2999ds/3Mi)
% 1.84/1.55 % (5521)Instruction limit reached!
% 1.84/1.55 % (5521)------------------------------
% 1.84/1.55 % (5521)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.55 % (5521)Termination reason: Unknown
% 1.84/1.55 % (5521)Termination phase: Saturation
% 1.84/1.55
% 1.84/1.55 % (5521)Memory used [KB]: 5500
% 1.84/1.55 % (5521)Time elapsed: 0.004 s
% 1.84/1.55 % (5521)Instructions burned: 3 (million)
% 1.84/1.55 % (5521)------------------------------
% 1.84/1.55 % (5521)------------------------------
% 1.84/1.55 % (5520)Instruction limit reached!
% 1.84/1.55 % (5520)------------------------------
% 1.84/1.55 % (5520)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.55 % (5520)Termination reason: Unknown
% 1.84/1.55 % (5520)Termination phase: Saturation
% 1.84/1.55
% 1.84/1.55 % (5520)Memory used [KB]: 5628
% 1.84/1.55 % (5520)Time elapsed: 0.011 s
% 1.84/1.55 % (5520)Instructions burned: 15 (million)
% 1.84/1.55 % (5520)------------------------------
% 1.84/1.55 % (5520)------------------------------
% 1.84/1.55 % (5511)Refutation found. Thanks to Tanya!
% 1.84/1.55 % SZS status Theorem for DTF2THF_5414
% 1.84/1.55 % SZS output start Proof for DTF2THF_5414
% 1.84/1.55 thf(type_def_5, type, a: $tType).
% 1.84/1.55 thf(func_def_0, type, a: $tType).
% 1.84/1.55 thf(func_def_1, type, cQ: a > a > $o).
% 1.84/1.55 thf(func_def_5, type, sK0: a > a > $o).
% 1.84/1.55 thf(func_def_6, type, sK1: a > a).
% 1.84/1.55 thf(func_def_7, type, sK2: (a > $o) > a).
% 1.84/1.55 thf(func_def_8, type, sK3: (a > $o) > a).
% 1.84/1.55 thf(func_def_9, type, sK4: (a > $o) > a).
% 1.84/1.55 thf(func_def_10, type, sK5: (a > $o) > a).
% 1.84/1.55 thf(func_def_11, type, sK6: (a > $o) > a).
% 1.84/1.55 thf(func_def_12, type, sK7: a).
% 1.84/1.55 thf(func_def_13, type, sK8: a).
% 1.84/1.55 thf(func_def_14, type, sK9: a).
% 1.84/1.55 thf(func_def_15, type, sK10: a).
% 1.84/1.55 thf(func_def_16, type, sK11: a).
% 1.84/1.55 thf(func_def_17, type, sK12: a).
% 1.84/1.55 thf(func_def_20, type, ph14: !>[X0: $tType]:(X0)).
% 1.84/1.55 thf(f305,plain,(
% 1.84/1.55 $false),
% 1.84/1.55 inference(avatar_sat_refutation,[status(thm)],[f51,f56,f61,f62,f67,f68,f134,f181,f304])).
% 1.84/1.55 thf(f304,plain,(
% 1.84/1.55 ~spl13_3 | spl13_4 | ~spl13_6),
% 1.84/1.55 inference(avatar_contradiction_clause,[status(thm)],[f303])).
% 1.84/1.55 thf(f303,plain,(
% 1.84/1.55 $false | (~spl13_3 | spl13_4 | ~spl13_6)),
% 1.84/1.55 inference(subsumption_resolution,[status(thm)],[f289,f32])).
% 1.84/1.55 thf(f32,plain,(
% 1.84/1.55 ( ! [X0 : a] : (((sK0 @ X0 @ X0) = $true)) )),
% 1.84/1.55 inference(cnf_transformation,[status(thm)],[f19])).
% 1.84/1.55 thf(f19,plain,(
% 1.84/1.55 ! [X0 : a] : (((sK0 @ X0 @ X0) = $true) & ! [X2 : a] : (((sK0 @ X0 @ X2) != $true) | ! [X3 : a] : ((cQ @ X2 @ X3) = (sK0 @ X0 @ X3))) & ((sK0 @ X0 @ (sK1 @ X0)) = $true) & ! [X5 : a > $o] : (! [X6 : a] : ((X5 @ X6) != $true) | ((sK0 @ X0) = X5) | (((X5 @ (sK2 @ X5)) = $true) & ((X5 @ (sK3 @ X5)) != (cQ @ (sK2 @ X5) @ (sK3 @ X5)))) | ($true != (X5 @ X0)))) & ! [X9 : a > $o] : ((((X9 @ (sK5 @ X9)) != (cQ @ (sK4 @ X9) @ (sK5 @ X9))) & ((X9 @ (sK4 @ X9)) = $true)) | ! [X12 : a] : ($true != (X9 @ X12)) | ((X9 @ (sK6 @ X9)) = $true)) & ((((cQ @ sK8 @ sK7) = $true) & ((cQ @ sK8 @ sK9) != $true) & ((cQ @ sK7 @ sK9) = $true)) | (((cQ @ sK10 @ sK11) != $true) & ((cQ @ sK11 @ sK10) = $true)) | ((cQ @ sK12 @ sK12) != $true))),
% 1.84/1.55 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5,sK6,sK7,sK8,sK9,sK10,sK11,sK12])],[f8,f18,f17,f16,f15,f14,f13,f12,f11,f10,f9])).
% 1.84/1.55 thf(f9,plain,(
% 1.84/1.55 ! [X0 : a] : (? [X1 : a > $o] : (((X1 @ X0) = $true) & ! [X2 : a] : (($true != (X1 @ X2)) | ! [X3 : a] : ((cQ @ X2 @ X3) = (X1 @ X3))) & ? [X4 : a] : ((X1 @ X4) = $true) & ! [X5 : a > $o] : (! [X6 : a] : ((X5 @ X6) != $true) | (X1 = X5) | ? [X7 : a] : (((X5 @ X7) = $true) & ? [X8 : a] : ((cQ @ X7 @ X8) != (X5 @ X8))) | ($true != (X5 @ X0)))) => (((sK0 @ X0 @ X0) = $true) & ! [X2 : a] : (((sK0 @ X0 @ X2) != $true) | ! [X3 : a] : ((cQ @ X2 @ X3) = (sK0 @ X0 @ X3))) & ? [X4 : a] : ($true = (sK0 @ X0 @ X4)) & ! [X5 : a > $o] : (! [X6 : a] : ((X5 @ X6) != $true) | ((sK0 @ X0) = X5) | ? [X7 : a] : (((X5 @ X7) = $true) & ? [X8 : a] : ((cQ @ X7 @ X8) != (X5 @ X8))) | ($true != (X5 @ X0)))))),
% 1.84/1.55 introduced(definition,[],[choice_axiom])).
% 1.84/1.55 thf(f10,plain,(
% 1.84/1.55 ! [X0 : a] : (? [X4 : a] : ($true = (sK0 @ X0 @ X4)) => ((sK0 @ X0 @ (sK1 @ X0)) = $true))),
% 1.84/1.55 introduced(definition,[],[choice_axiom])).
% 1.84/1.55 thf(f11,plain,(
% 1.84/1.55 ! [X5 : a > $o] : (? [X7 : a] : (((X5 @ X7) = $true) & ? [X8 : a] : ((cQ @ X7 @ X8) != (X5 @ X8))) => (((X5 @ (sK2 @ X5)) = $true) & ? [X8 : a] : ((X5 @ X8) != (cQ @ (sK2 @ X5) @ X8))))),
% 1.84/1.55 introduced(definition,[],[choice_axiom])).
% 1.84/1.55 thf(f12,plain,(
% 1.84/1.55 ! [X5 : a > $o] : (? [X8 : a] : ((X5 @ X8) != (cQ @ (sK2 @ X5) @ X8)) => ((X5 @ (sK3 @ X5)) != (cQ @ (sK2 @ X5) @ (sK3 @ X5))))),
% 1.84/1.55 introduced(definition,[],[choice_axiom])).
% 1.84/1.55 thf(f13,plain,(
% 1.84/1.55 ! [X9 : a > $o] : (? [X10 : a] : (? [X11 : a] : ((cQ @ X10 @ X11) != (X9 @ X11)) & ((X9 @ X10) = $true)) => (? [X11 : a] : ((X9 @ X11) != (cQ @ (sK4 @ X9) @ X11)) & ((X9 @ (sK4 @ X9)) = $true)))),
% 1.84/1.55 introduced(definition,[],[choice_axiom])).
% 1.84/1.55 thf(f14,plain,(
% 1.84/1.55 ! [X9 : a > $o] : (? [X11 : a] : ((X9 @ X11) != (cQ @ (sK4 @ X9) @ X11)) => ((X9 @ (sK5 @ X9)) != (cQ @ (sK4 @ X9) @ (sK5 @ X9))))),
% 1.84/1.55 introduced(definition,[],[choice_axiom])).
% 1.84/1.55 thf(f15,plain,(
% 1.84/1.55 ! [X9 : a > $o] : (? [X13 : a] : ((X9 @ X13) = $true) => ((X9 @ (sK6 @ X9)) = $true))),
% 1.84/1.55 introduced(definition,[],[choice_axiom])).
% 1.84/1.55 thf(f16,plain,(
% 1.84/1.55 ? [X14 : a,X15 : a,X16 : a] : (($true = (cQ @ X15 @ X14)) & ((cQ @ X15 @ X16) != $true) & ($true = (cQ @ X14 @ X16))) => (((cQ @ sK8 @ sK7) = $true) & ((cQ @ sK8 @ sK9) != $true) & ((cQ @ sK7 @ sK9) = $true))),
% 1.84/1.55 introduced(definition,[],[choice_axiom])).
% 1.84/1.55 thf(f17,plain,(
% 1.84/1.55 ? [X17 : a,X18 : a] : (((cQ @ X17 @ X18) != $true) & ($true = (cQ @ X18 @ X17))) => (((cQ @ sK10 @ sK11) != $true) & ((cQ @ sK11 @ sK10) = $true))),
% 1.84/1.55 introduced(definition,[],[choice_axiom])).
% 1.84/1.55 thf(f18,plain,(
% 1.84/1.55 ? [X19 : a] : ($true != (cQ @ X19 @ X19)) => ((cQ @ sK12 @ sK12) != $true)),
% 1.84/1.55 introduced(definition,[],[choice_axiom])).
% 1.84/1.55 thf(f8,plain,(
% 1.84/1.55 ! [X0 : a] : ? [X1 : a > $o] : (((X1 @ X0) = $true) & ! [X2 : a] : (($true != (X1 @ X2)) | ! [X3 : a] : ((cQ @ X2 @ X3) = (X1 @ X3))) & ? [X4 : a] : ((X1 @ X4) = $true) & ! [X5 : a > $o] : (! [X6 : a] : ((X5 @ X6) != $true) | (X1 = X5) | ? [X7 : a] : (((X5 @ X7) = $true) & ? [X8 : a] : ((cQ @ X7 @ X8) != (X5 @ X8))) | ($true != (X5 @ X0)))) & ! [X9 : a > $o] : (? [X10 : a] : (? [X11 : a] : ((cQ @ X10 @ X11) != (X9 @ X11)) & ((X9 @ X10) = $true)) | ! [X12 : a] : ($true != (X9 @ X12)) | ? [X13 : a] : ((X9 @ X13) = $true)) & (? [X14 : a,X15 : a,X16 : a] : (($true = (cQ @ X15 @ X14)) & ((cQ @ X15 @ X16) != $true) & ($true = (cQ @ X14 @ X16))) | ? [X17 : a,X18 : a] : (((cQ @ X17 @ X18) != $true) & ($true = (cQ @ X18 @ X17))) | ? [X19 : a] : ($true != (cQ @ X19 @ X19)))),
% 1.84/1.55 inference(rectify,[status(thm)],[f7])).
% 1.84/1.55 thf(f7,plain,(
% 1.84/1.55 ! [X5 : a] : ? [X6 : a > $o] : (((X6 @ X5) = $true) & ! [X12 : a] : (($true != (X6 @ X12)) | ! [X13 : a] : ((X6 @ X13) = (cQ @ X12 @ X13))) & ? [X7 : a] : ($true = (X6 @ X7)) & ! [X8 : a > $o] : (! [X11 : a] : ((X8 @ X11) != $true) | (X6 = X8) | ? [X9 : a] : (($true = (X8 @ X9)) & ? [X10 : a] : ((cQ @ X9 @ X10) != (X8 @ X10))) | ($true != (X8 @ X5)))) & ! [X0 : a > $o] : (? [X1 : a] : (? [X2 : a] : ((X0 @ X2) != (cQ @ X1 @ X2)) & ((X0 @ X1) = $true)) | ! [X3 : a] : ((X0 @ X3) != $true) | ? [X4 : a] : ((X0 @ X4) = $true)) & (? [X16 : a,X17 : a,X18 : a] : (((cQ @ X17 @ X16) = $true) & ((cQ @ X17 @ X18) != $true) & ($true = (cQ @ X16 @ X18))) | ? [X14 : a,X15 : a] : (($true != (cQ @ X14 @ X15)) & ($true = (cQ @ X15 @ X14))) | ? [X19 : a] : ($true != (cQ @ X19 @ X19)))),
% 1.84/1.55 inference(flattening,[status(thm)],[f6])).
% 1.84/1.55 thf(f6,plain,(
% 1.84/1.55 (? [X14 : a,X15 : a] : (($true != (cQ @ X14 @ X15)) & ($true = (cQ @ X15 @ X14))) | ? [X19 : a] : ($true != (cQ @ X19 @ X19)) | ? [X17 : a,X18 : a,X16 : a] : (((cQ @ X17 @ X18) != $true) & (((cQ @ X17 @ X16) = $true) & ($true = (cQ @ X16 @ X18))))) & (! [X0 : a > $o] : (? [X4 : a] : ((X0 @ X4) = $true) | (? [X1 : a] : (? [X2 : a] : ((X0 @ X2) != (cQ @ X1 @ X2)) & ((X0 @ X1) = $true)) | ! [X3 : a] : ((X0 @ X3) != $true))) & ! [X5 : a] : ? [X6 : a > $o] : (? [X7 : a] : ($true = (X6 @ X7)) & ! [X12 : a] : (($true != (X6 @ X12)) | ! [X13 : a] : ((X6 @ X13) = (cQ @ X12 @ X13))) & ! [X8 : a > $o] : ((X6 = X8) | (($true != (X8 @ X5)) | ! [X11 : a] : ((X8 @ X11) != $true) | ? [X9 : a] : (($true = (X8 @ X9)) & ? [X10 : a] : ((cQ @ X9 @ X10) != (X8 @ X10))))) & ((X6 @ X5) = $true)))),
% 1.84/1.55 inference(ennf_transformation,[status(thm)],[f5])).
% 1.84/1.55 thf(f5,plain,(
% 1.84/1.55 ~((! [X0 : a > $o] : ((! [X1 : a] : (((X0 @ X1) = $true) => ! [X2 : a] : ((X0 @ X2) = (cQ @ X1 @ X2))) & ? [X3 : a] : ((X0 @ X3) = $true)) => ? [X4 : a] : ((X0 @ X4) = $true)) & ! [X5 : a] : ? [X6 : a > $o] : (? [X7 : a] : ($true = (X6 @ X7)) & ! [X12 : a] : (($true = (X6 @ X12)) => ! [X13 : a] : ((X6 @ X13) = (cQ @ X12 @ X13))) & ! [X8 : a > $o] : ((($true = (X8 @ X5)) & ? [X11 : a] : ((X8 @ X11) = $true) & ! [X9 : a] : (($true = (X8 @ X9)) => ! [X10 : a] : ((cQ @ X9 @ X10) = (X8 @ X10)))) => (X6 = X8)) & ((X6 @ X5) = $true))) => (! [X14 : a,X15 : a] : (($true = (cQ @ X15 @ X14)) => ($true = (cQ @ X14 @ X15))) & ! [X19 : a] : ($true = (cQ @ X19 @ X19)) & ! [X17 : a,X18 : a,X16 : a] : ((((cQ @ X17 @ X16) = $true) & ($true = (cQ @ X16 @ X18))) => ((cQ @ X17 @ X18) = $true))))),
% 1.84/1.55 inference(fool_elimination,[status(thm)],[f4])).
% 1.84/1.55 thf(f4,plain,(
% 1.84/1.55 ~((! [X0 : a > $o] : ((! [X1 : a] : ((X0 @ X1) => ! [X2 : a] : ((X0 @ X2) <=> (cQ @ X1 @ X2))) & ? [X3 : a] : (X0 @ X3)) => ? [X4 : a] : (X0 @ X4)) & ! [X5 : a] : ? [X6 : a > $o] : (? [X7 : a] : (X6 @ X7) & ! [X8 : a > $o] : (((X8 @ X5) & ! [X9 : a] : ((X8 @ X9) => ! [X10 : a] : ((cQ @ X9 @ X10) <=> (X8 @ X10))) & ? [X11 : a] : (X8 @ X11)) => (X6 = X8)) & (X6 @ X5) & ! [X12 : a] : ((X6 @ X12) => ! [X13 : a] : ((cQ @ X12 @ X13) <=> (X6 @ X13))))) => (! [X14 : a,X15 : a] : ((cQ @ X15 @ X14) => (cQ @ X14 @ X15)) & ! [X16 : a,X17 : a,X18 : a] : (((cQ @ X16 @ X18) & (cQ @ X17 @ X16)) => (cQ @ X17 @ X18)) & ! [X19 : a] : (cQ @ X19 @ X19)))),
% 1.84/1.55 inference(rectify,[status(thm)],[f2])).
% 1.84/1.55 thf(f2,negated_conjecture,(
% 1.84/1.55 ~((! [X0 : a > $o] : ((! [X2 : a] : ((X0 @ X2) => ! [X3 : a] : ((X0 @ X3) <=> (cQ @ X2 @ X3))) & ? [X1 : a] : (X0 @ X1)) => ? [X1 : a] : (X0 @ X1)) & ! [X2 : a] : ? [X0 : a > $o] : (? [X1 : a] : (X0 @ X1) & ! [X5 : a > $o] : (((X5 @ X2) & ! [X4 : a] : ((X5 @ X4) => ! [X3 : a] : ((cQ @ X4 @ X3) <=> (X5 @ X3))) & ? [X1 : a] : (X5 @ X1)) => (X0 = X5)) & (X0 @ X2) & ! [X4 : a] : ((X0 @ X4) => ! [X3 : a] : ((cQ @ X4 @ X3) <=> (X0 @ X3))))) => (! [X3 : a,X2 : a] : ((cQ @ X2 @ X3) => (cQ @ X3 @ X2)) & ! [X3 : a,X2 : a,X1 : a] : (((cQ @ X3 @ X1) & (cQ @ X2 @ X3)) => (cQ @ X2 @ X1)) & ! [X2 : a] : (cQ @ X2 @ X2)))),
% 1.84/1.55 inference(negated_conjecture,[status(cth)],[f1])).
% 1.84/1.55 thf(f1,conjecture,(
% 1.84/1.55 (! [X0 : a > $o] : ((! [X2 : a] : ((X0 @ X2) => ! [X3 : a] : ((X0 @ X3) <=> (cQ @ X2 @ X3))) & ? [X1 : a] : (X0 @ X1)) => ? [X1 : a] : (X0 @ X1)) & ! [X2 : a] : ? [X0 : a > $o] : (? [X1 : a] : (X0 @ X1) & ! [X5 : a > $o] : (((X5 @ X2) & ! [X4 : a] : ((X5 @ X4) => ! [X3 : a] : ((cQ @ X4 @ X3) <=> (X5 @ X3))) & ? [X1 : a] : (X5 @ X1)) => (X0 = X5)) & (X0 @ X2) & ! [X4 : a] : ((X0 @ X4) => ! [X3 : a] : ((cQ @ X4 @ X3) <=> (X0 @ X3))))) => (! [X3 : a,X2 : a] : ((cQ @ X2 @ X3) => (cQ @ X3 @ X2)) & ! [X3 : a,X2 : a,X1 : a] : (((cQ @ X3 @ X1) & (cQ @ X2 @ X3)) => (cQ @ X2 @ X1)) & ! [X2 : a] : (cQ @ X2 @ X2))),
% 1.84/1.55 file('/export/starexec/sandbox/tmp/tmp.gggvNPM1jy/DTF2THF_5414.p',cTHM558_pme)).
% 1.84/1.55 thf(f289,plain,(
% 1.84/1.55 ($true != (sK0 @ sK8 @ sK8)) | (~spl13_3 | spl13_4 | ~spl13_6)),
% 1.84/1.55 inference(trivial_inequality_removal,[status(thm)],[f286])).
% 1.84/1.55 thf(f286,plain,(
% 1.84/1.55 ($true = $false) | ($true != (sK0 @ sK8 @ sK8)) | (~spl13_3 | spl13_4 | ~spl13_6)),
% 1.84/1.55 inference(superposition,[status(thm)],[f50,f277])).
% 1.84/1.55 thf(f277,plain,(
% 1.84/1.55 ( ! [X0 : a] : (($false = (cQ @ X0 @ sK7)) | ((sK0 @ sK8 @ X0) != $true)) ) | (spl13_4 | ~spl13_6)),
% 1.84/1.55 inference(trivial_inequality_removal,[status(thm)],[f271])).
% 1.84/1.55 thf(f271,plain,(
% 1.84/1.55 ( ! [X0 : a] : (($true != $true) | ((sK0 @ sK8 @ X0) != $true) | ($false = (cQ @ X0 @ sK7))) ) | (spl13_4 | ~spl13_6)),
% 1.84/1.55 inference(superposition,[status(thm)],[f269,f36])).
% 1.84/1.55 thf(f36,plain,(
% 1.84/1.55 ( ! [X2 : a,X3 : a,X0 : a] : (((sK0 @ X0 @ X3) = $true) | ((sK0 @ X0 @ X2) != $true) | ((cQ @ X2 @ X3) = $false)) )),
% 1.84/1.55 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.84/1.55 thf(f31,plain,(
% 1.84/1.55 ( ! [X2 : a,X3 : a,X0 : a] : (((sK0 @ X0 @ X2) != $true) | ((cQ @ X2 @ X3) = (sK0 @ X0 @ X3))) )),
% 1.84/1.55 inference(cnf_transformation,[status(thm)],[f19])).
% 1.84/1.55 thf(f269,plain,(
% 1.84/1.55 ((sK0 @ sK8 @ sK7) != $true) | (spl13_4 | ~spl13_6)),
% 1.84/1.55 inference(trivial_inequality_removal,[status(thm)],[f251])).
% 1.84/1.55 thf(f251,plain,(
% 1.84/1.55 ((sK0 @ sK8 @ sK7) != $true) | ($true = $false) | (spl13_4 | ~spl13_6)),
% 1.84/1.55 inference(superposition,[status(thm)],[f234,f66])).
% 1.84/1.55 thf(f66,plain,(
% 1.84/1.55 ((cQ @ sK7 @ sK9) = $true) | ~spl13_6),
% 1.84/1.55 inference(avatar_component_clause,[status(thm)],[f64])).
% 1.84/1.55 thf(f64,definition,(
% 1.84/1.55 spl13_6 <=> ((cQ @ sK7 @ sK9) = $true)),
% 1.84/1.55 introduced(definition,[new_symbols(naming,[spl13_6])],[avatar_definition])).
% 1.84/1.55 thf(f234,plain,(
% 1.84/1.55 ( ! [X0 : a] : (((cQ @ X0 @ sK9) = $false) | ((sK0 @ sK8 @ X0) != $true)) ) | spl13_4),
% 1.84/1.55 inference(trivial_inequality_removal,[status(thm)],[f230])).
% 1.84/1.55 thf(f230,plain,(
% 1.84/1.55 ( ! [X0 : a] : (($true != $true) | ((sK0 @ sK8 @ X0) != $true) | ((cQ @ X0 @ sK9) = $false)) ) | spl13_4),
% 1.84/1.55 inference(superposition,[status(thm)],[f223,f36])).
% 1.84/1.55 thf(f223,plain,(
% 1.84/1.55 ((sK0 @ sK8 @ sK9) != $true) | spl13_4),
% 1.84/1.55 inference(trivial_inequality_removal,[status(thm)],[f217])).
% 1.84/1.55 thf(f217,plain,(
% 1.84/1.55 ((sK0 @ sK8 @ sK9) != $true) | ($true != $true) | spl13_4),
% 1.84/1.55 inference(superposition,[status(thm)],[f214,f32])).
% 1.84/1.55 thf(f214,plain,(
% 1.84/1.55 ( ! [X0 : a] : (((sK0 @ sK9 @ X0) != $true) | ((sK0 @ sK8 @ X0) != $true)) ) | spl13_4),
% 1.84/1.55 inference(trivial_inequality_removal,[status(thm)],[f201])).
% 1.84/1.55 thf(f201,plain,(
% 1.84/1.55 ( ! [X0 : a] : (((sK0 @ sK8 @ X0) != $true) | ((sK0 @ sK9 @ X0) != $true) | ($true = $false)) ) | spl13_4),
% 1.84/1.55 inference(superposition,[status(thm)],[f197,f123])).
% 1.84/1.55 thf(f123,plain,(
% 1.84/1.55 ( ! [X0 : a,X1 : a] : (((cQ @ X1 @ X0) = $true) | ((sK0 @ X0 @ X1) != $true)) )),
% 1.84/1.55 inference(trivial_inequality_removal,[status(thm)],[f111])).
% 1.84/1.55 thf(f111,plain,(
% 1.84/1.55 ( ! [X0 : a,X1 : a] : (((cQ @ X1 @ X0) = $true) | ($true = $false) | ((sK0 @ X0 @ X1) != $true)) )),
% 1.84/1.55 inference(superposition,[status(thm)],[f35,f32])).
% 1.84/1.55 thf(f35,plain,(
% 1.84/1.55 ( ! [X2 : a,X3 : a,X0 : a] : (((sK0 @ X0 @ X3) = $false) | ((cQ @ X2 @ X3) = $true) | ((sK0 @ X0 @ X2) != $true)) )),
% 1.84/1.55 inference(binary_proxy_clausification,[status(thm)],[f31])).
% 1.84/1.55 thf(f197,plain,(
% 1.84/1.55 ( ! [X0 : a] : (((cQ @ X0 @ sK8) = $false) | ((sK0 @ sK9 @ X0) != $true)) ) | spl13_4),
% 1.84/1.55 inference(trivial_inequality_removal,[status(thm)],[f191])).
% 1.84/1.55 thf(f191,plain,(
% 1.84/1.55 ( ! [X0 : a] : (($true != $true) | ((sK0 @ sK9 @ X0) != $true) | ((cQ @ X0 @ sK8) = $false)) ) | spl13_4),
% 1.84/1.55 inference(superposition,[status(thm)],[f188,f36])).
% 1.84/1.55 thf(f188,plain,(
% 1.84/1.55 ($true != (sK0 @ sK9 @ sK8)) | spl13_4),
% 1.84/1.55 inference(trivial_inequality_removal,[status(thm)],[f182])).
% 1.84/1.55 thf(f182,plain,(
% 1.84/1.55 ($true != (sK0 @ sK9 @ sK8)) | ($true != $true) | spl13_4),
% 1.84/1.55 inference(superposition,[status(thm)],[f55,f123])).
% 1.84/1.55 thf(f55,plain,(
% 1.84/1.55 ((cQ @ sK8 @ sK9) != $true) | spl13_4),
% 1.84/1.55 inference(avatar_component_clause,[status(thm)],[f53])).
% 1.84/1.55 thf(f53,definition,(
% 1.84/1.55 spl13_4 <=> ((cQ @ sK8 @ sK9) = $true)),
% 1.84/1.55 introduced(definition,[new_symbols(naming,[spl13_4])],[avatar_definition])).
% 1.84/1.55 thf(f50,plain,(
% 1.84/1.55 ((cQ @ sK8 @ sK7) = $true) | ~spl13_3),
% 1.84/1.55 inference(avatar_component_clause,[status(thm)],[f48])).
% 1.84/1.55 thf(f48,definition,(
% 1.84/1.55 spl13_3 <=> ((cQ @ sK8 @ sK7) = $true)),
% 1.84/1.55 introduced(definition,[new_symbols(naming,[spl13_3])],[avatar_definition])).
% 1.84/1.55 thf(f181,plain,(
% 1.84/1.55 ~spl13_1 | spl13_5),
% 1.84/1.55 inference(avatar_contradiction_clause,[status(thm)],[f180])).
% 1.84/1.55 thf(f180,plain,(
% 1.84/1.55 $false | (~spl13_1 | spl13_5)),
% 1.84/1.55 inference(subsumption_resolution,[status(thm)],[f176,f32])).
% 1.84/1.55 thf(f176,plain,(
% 1.84/1.55 ($true != (sK0 @ sK11 @ sK11)) | (~spl13_1 | spl13_5)),
% 1.84/1.55 inference(trivial_inequality_removal,[status(thm)],[f159])).
% 1.84/1.55 thf(f159,plain,(
% 1.84/1.55 ($true = $false) | ($true != (sK0 @ sK11 @ sK11)) | (~spl13_1 | spl13_5)),
% 1.84/1.55 inference(superposition,[status(thm)],[f155,f42])).
% 1.84/1.55 thf(f42,plain,(
% 1.84/1.55 ((cQ @ sK11 @ sK10) = $true) | ~spl13_1),
% 1.84/1.55 inference(avatar_component_clause,[status(thm)],[f40])).
% 1.84/1.55 thf(f40,definition,(
% 1.84/1.55 spl13_1 <=> ((cQ @ sK11 @ sK10) = $true)),
% 1.84/1.55 introduced(definition,[new_symbols(naming,[spl13_1])],[avatar_definition])).
% 1.84/1.55 thf(f155,plain,(
% 1.84/1.55 ( ! [X0 : a] : (((cQ @ X0 @ sK10) = $false) | ((sK0 @ sK11 @ X0) != $true)) ) | spl13_5),
% 1.84/1.55 inference(trivial_inequality_removal,[status(thm)],[f154])).
% 1.84/1.55 thf(f154,plain,(
% 1.84/1.55 ( ! [X0 : a] : (((sK0 @ sK11 @ X0) != $true) | ((cQ @ X0 @ sK10) = $false) | ($true != $true)) ) | spl13_5),
% 1.84/1.55 inference(superposition,[status(thm)],[f138,f36])).
% 1.84/1.55 thf(f138,plain,(
% 1.84/1.55 ($true != (sK0 @ sK11 @ sK10)) | spl13_5),
% 1.84/1.55 inference(trivial_inequality_removal,[status(thm)],[f135])).
% 1.84/1.55 thf(f135,plain,(
% 1.84/1.55 ($true != (sK0 @ sK11 @ sK10)) | ($true != $true) | spl13_5),
% 1.84/1.55 inference(superposition,[status(thm)],[f60,f123])).
% 1.84/1.55 thf(f60,plain,(
% 1.84/1.55 ((cQ @ sK10 @ sK11) != $true) | spl13_5),
% 1.84/1.55 inference(avatar_component_clause,[status(thm)],[f58])).
% 1.84/1.55 thf(f58,definition,(
% 1.84/1.55 spl13_5 <=> ((cQ @ sK10 @ sK11) = $true)),
% 1.84/1.55 introduced(definition,[new_symbols(naming,[spl13_5])],[avatar_definition])).
% 1.84/1.55 thf(f134,plain,(
% 1.84/1.55 spl13_2),
% 1.84/1.55 inference(avatar_contradiction_clause,[status(thm)],[f133])).
% 1.84/1.55 thf(f133,plain,(
% 1.84/1.55 $false | spl13_2),
% 1.84/1.55 inference(subsumption_resolution,[status(thm)],[f132,f32])).
% 1.84/1.55 thf(f132,plain,(
% 1.84/1.55 ((sK0 @ sK12 @ sK12) != $true) | spl13_2),
% 1.84/1.55 inference(trivial_inequality_removal,[status(thm)],[f131])).
% 1.84/1.55 thf(f131,plain,(
% 1.84/1.55 ((sK0 @ sK12 @ sK12) != $true) | ($true != $true) | spl13_2),
% 1.84/1.55 inference(superposition,[status(thm)],[f46,f123])).
% 1.84/1.55 thf(f46,plain,(
% 1.84/1.55 ((cQ @ sK12 @ sK12) != $true) | spl13_2),
% 1.84/1.55 inference(avatar_component_clause,[status(thm)],[f44])).
% 1.84/1.55 thf(f44,definition,(
% 1.84/1.55 spl13_2 <=> ((cQ @ sK12 @ sK12) = $true)),
% 1.84/1.55 introduced(definition,[new_symbols(naming,[spl13_2])],[avatar_definition])).
% 1.84/1.55 thf(f68,plain,(
% 1.84/1.55 ~spl13_5 | ~spl13_2 | spl13_6),
% 1.84/1.55 inference(avatar_split_clause,[status(thm)],[f21,f64,f44,f58])).
% 1.84/1.55 thf(f21,plain,(
% 1.84/1.55 ((cQ @ sK12 @ sK12) != $true) | ((cQ @ sK7 @ sK9) = $true) | ((cQ @ sK10 @ sK11) != $true)),
% 1.84/1.55 inference(cnf_transformation,[status(thm)],[f19])).
% 1.84/1.55 thf(f67,plain,(
% 1.84/1.55 ~spl13_2 | spl13_1 | spl13_6),
% 1.84/1.55 inference(avatar_split_clause,[status(thm)],[f20,f64,f40,f44])).
% 1.84/1.55 thf(f20,plain,(
% 1.84/1.55 ((cQ @ sK12 @ sK12) != $true) | ((cQ @ sK11 @ sK10) = $true) | ((cQ @ sK7 @ sK9) = $true)),
% 1.84/1.55 inference(cnf_transformation,[status(thm)],[f19])).
% 1.84/1.55 thf(f62,plain,(
% 1.84/1.55 ~spl13_4 | ~spl13_5 | ~spl13_2),
% 1.84/1.55 inference(avatar_split_clause,[status(thm)],[f23,f44,f58,f53])).
% 1.84/1.55 thf(f23,plain,(
% 1.84/1.55 ((cQ @ sK10 @ sK11) != $true) | ((cQ @ sK12 @ sK12) != $true) | ((cQ @ sK8 @ sK9) != $true)),
% 1.84/1.55 inference(cnf_transformation,[status(thm)],[f19])).
% 1.84/1.55 thf(f61,plain,(
% 1.84/1.55 spl13_3 | ~spl13_5 | ~spl13_2),
% 1.84/1.55 inference(avatar_split_clause,[status(thm)],[f25,f44,f58,f48])).
% 1.84/1.55 thf(f25,plain,(
% 1.84/1.55 ((cQ @ sK8 @ sK7) = $true) | ((cQ @ sK12 @ sK12) != $true) | ((cQ @ sK10 @ sK11) != $true)),
% 1.84/1.55 inference(cnf_transformation,[status(thm)],[f19])).
% 1.84/1.55 thf(f56,plain,(
% 1.84/1.55 ~spl13_2 | spl13_1 | ~spl13_4),
% 1.84/1.55 inference(avatar_split_clause,[status(thm)],[f22,f53,f40,f44])).
% 1.84/1.55 thf(f22,plain,(
% 1.84/1.55 ((cQ @ sK11 @ sK10) = $true) | ((cQ @ sK8 @ sK9) != $true) | ((cQ @ sK12 @ sK12) != $true)),
% 1.84/1.55 inference(cnf_transformation,[status(thm)],[f19])).
% 1.84/1.55 thf(f51,plain,(
% 1.84/1.55 spl13_1 | ~spl13_2 | spl13_3),
% 1.84/1.55 inference(avatar_split_clause,[status(thm)],[f24,f48,f44,f40])).
% 1.84/1.55 thf(f24,plain,(
% 1.84/1.55 ((cQ @ sK11 @ sK10) = $true) | ((cQ @ sK12 @ sK12) != $true) | ((cQ @ sK8 @ sK7) = $true)),
% 1.84/1.55 inference(cnf_transformation,[status(thm)],[f19])).
% 1.84/1.55 % SZS output end Proof for DTF2THF_5414
% 1.84/1.55 % (5511)------------------------------
% 1.84/1.55 % (5511)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.84/1.55 % (5511)Termination reason: Refutation
% 1.84/1.55
% 1.84/1.55 % (5511)Memory used [KB]: 6012
% 1.84/1.55 % (5511)Time elapsed: 0.029 s
% 1.84/1.55 % (5511)Instructions burned: 47 (million)
% 1.84/1.55 % (5511)------------------------------
% 1.84/1.55 % (5511)------------------------------
% 1.84/1.55 % (5510)Success in time 0.04 s
%------------------------------------------------------------------------------