%------------------------------------------------------------------------------
% File : DT2H2X---1.9.5
% Problem : NUN046^1 : TPTP v9.2.1. Released v7.0.0.
% Transfm : none
% Format : tptp:raw
% Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% Computer : n005.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 09:27:14 AM UTC 2026
% Result : Theorem 1.59s 1.38s
% Output : Refutation 1.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 16
% Number of leaves : 21
% Syntax : Number of formulae : 76 ( 21 unt; 0 typ; 5 def)
% Number of atoms : 318 ( 166 equ; 0 cnn)
% Maximal formula atoms : 12 ( 4 avg)
% Number of connectives : 1017 ( 94 ~; 72 |; 39 &; 793 @)
% ( 6 <=>; 13 =>; 0 <=; 0 <~>)
% Maximal formula depth : 12 ( 5 avg)
% Number of types : 2 ( 1 usr)
% Number of type conns : 40 ( 40 >; 0 *; 0 +; 0 <<)
% Number of symbols : 34 ( 31 usr; 17 con; 0-2 aty)
% Number of variables : 218 ( 0 ^; 138 !; 80 ?; 218 :)
% Comments :
%------------------------------------------------------------------------------
thf(type_def_6,type,
sK6: $tType ).
thf(func_def_0,type,
'const/trivia/I':
!>[X0: $tType] : ( X0 > X0 ) ).
thf(func_def_1,type,
'const/iterate/neutral':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_2,type,
'const/iterate/monoidal':
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > $o ) ).
thf(func_def_6,type,
sK0:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_7,type,
sK1:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_8,type,
sK2:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_9,type,
sK3:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_10,type,
sK4:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_11,type,
sK5:
!>[X0: $tType] : ( ( X0 > X0 > X0 ) > X0 ) ).
thf(func_def_12,type,
sK7: sK6 > sK6 > sK6 ).
thf(func_def_13,type,
sK8: sK6 ).
thf(func_def_14,type,
sK9: sK6 ).
thf(func_def_15,type,
sK10: sK6 ).
thf(func_def_16,type,
sK11: sK6 ).
thf(func_def_17,type,
sK12: sK6 ).
thf(func_def_18,type,
sK13: sK6 ).
thf(func_def_19,type,
sK14: sK6 ).
thf(func_def_20,type,
sK15: sK6 ).
thf(func_def_21,type,
sK16: sK6 ).
thf(func_def_22,type,
sK17: sK6 ).
thf(func_def_23,type,
sP18: sK6 > $o ).
thf(func_def_24,type,
sP19: sK6 > $o ).
thf(func_def_25,type,
sP20: sK6 > $o ).
thf(func_def_26,type,
sP21: sK6 > $o ).
thf(func_def_27,type,
sP22: sK6 > $o ).
thf(func_def_29,type,
ph24:
!>[X0: $tType] : X0 ).
thf(f109,plain,
$false,
inference(avatar_sat_refutation,[status(thm)],[f58,f85,f91,f98,f103,f108]) ).
thf(f108,plain,
~ spl23_1,
inference(avatar_contradiction_clause,[status(thm)],[f107]) ).
thf(f107,plain,
( $false
| ~ spl23_1 ),
inference(trivial_inequality_removal,[status(thm)],[f106]) ).
thf(f106,plain,
( ( $true = $false )
| ~ spl23_1 ),
inference(forward_demodulation,[status(thm)],[f41,f72]) ).
thf(f72,plain,
( $false
= ( sP20 @ sK14 ) ),
inference(backward_demodulation,[status(thm)],[f34,f68]) ).
thf(f68,plain,
! [X0: sK6] :
( ( sK7 @ X0 @ ( 'const/iterate/neutral' @ sK6 @ sK7 ) )
= X0 ),
inference(superposition,[status(thm)],[f63,f60]) ).
thf(f60,plain,
! [X0: sK6] :
( ( sK7 @ ( 'const/iterate/neutral' @ sK6 @ sK7 ) @ X0 )
= X0 ),
inference(trivial_inequality_removal,[status(thm)],[f59]) ).
thf(f59,plain,
! [X0: sK6] :
( ( ( sK7 @ ( 'const/iterate/neutral' @ sK6 @ sK7 ) @ X0 )
= X0 )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f27,f30]) ).
thf(f30,plain,
( ( 'const/iterate/monoidal' @ sK6 @ sK7 )
= $true ),
inference(cnf_transformation,[status(thm)],[f25]) ).
thf(f25,plain,
( ( ( ( sK7 @ sK9 @ ( sK7 @ sK8 @ sK10 ) )
!= ( sK7 @ sK8 @ ( sK7 @ sK9 @ sK10 ) ) )
| ( ( sK7 @ sK11 @ ( sK7 @ sK12 @ sK13 ) )
!= ( sK7 @ ( sK7 @ sK11 @ sK12 ) @ sK13 ) )
| ( sK14
!= ( sK7 @ sK14 @ ( 'const/iterate/neutral' @ sK6 @ sK7 ) ) )
| ( ( sK7 @ sK15 @ sK16 )
!= ( sK7 @ sK16 @ sK15 ) )
| ( sK17
!= ( sK7 @ ( 'const/iterate/neutral' @ sK6 @ sK7 ) @ sK17 ) ) )
& ( ( 'const/iterate/monoidal' @ sK6 @ sK7 )
= $true ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16,sK17])],[f18,f24,f23,f22,f21,f20,f19]) ).
thf(f19,plain,
( ? [X0: $tType,X1: X0 > X0 > X0] :
( ( ? [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ ( X1 @ X3 @ X4 ) )
!= ( X1 @ X3 @ ( X1 @ X2 @ X4 ) ) )
| ? [X5: X0,X6: X0,X7: X0] :
( ( X1 @ X5 @ ( X1 @ X6 @ X7 ) )
!= ( X1 @ ( X1 @ X5 @ X6 ) @ X7 ) )
| ? [X8: X0] :
( ( X1 @ X8 @ ( 'const/iterate/neutral' @ X0 @ X1 ) )
!= X8 )
| ? [X9: X0,X10: X0] :
( ( X1 @ X9 @ X10 )
!= ( X1 @ X10 @ X9 ) )
| ? [X11: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X11 )
!= X11 ) )
& ( ( 'const/iterate/monoidal' @ X0 @ X1 )
= $true ) )
=> ( ( ? [X4: sK6,X3: sK6,X2: sK6] :
( ( sK7 @ X3 @ ( sK7 @ X2 @ X4 ) )
!= ( sK7 @ X2 @ ( sK7 @ X3 @ X4 ) ) )
| ? [X7: sK6,X6: sK6,X5: sK6] :
( ( sK7 @ X5 @ ( sK7 @ X6 @ X7 ) )
!= ( sK7 @ ( sK7 @ X5 @ X6 ) @ X7 ) )
| ? [X8: sK6] :
( ( sK7 @ X8 @ ( 'const/iterate/neutral' @ sK6 @ sK7 ) )
!= X8 )
| ? [X10: sK6,X9: sK6] :
( ( sK7 @ X10 @ X9 )
!= ( sK7 @ X9 @ X10 ) )
| ? [X11: sK6] :
( ( sK7 @ ( 'const/iterate/neutral' @ sK6 @ sK7 ) @ X11 )
!= X11 ) )
& ( ( 'const/iterate/monoidal' @ sK6 @ sK7 )
= $true ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f20,plain,
( ? [X4: sK6,X3: sK6,X2: sK6] :
( ( sK7 @ X3 @ ( sK7 @ X2 @ X4 ) )
!= ( sK7 @ X2 @ ( sK7 @ X3 @ X4 ) ) )
=> ( ( sK7 @ sK9 @ ( sK7 @ sK8 @ sK10 ) )
!= ( sK7 @ sK8 @ ( sK7 @ sK9 @ sK10 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f21,plain,
( ? [X7: sK6,X6: sK6,X5: sK6] :
( ( sK7 @ X5 @ ( sK7 @ X6 @ X7 ) )
!= ( sK7 @ ( sK7 @ X5 @ X6 ) @ X7 ) )
=> ( ( sK7 @ sK11 @ ( sK7 @ sK12 @ sK13 ) )
!= ( sK7 @ ( sK7 @ sK11 @ sK12 ) @ sK13 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f22,plain,
( ? [X8: sK6] :
( ( sK7 @ X8 @ ( 'const/iterate/neutral' @ sK6 @ sK7 ) )
!= X8 )
=> ( sK14
!= ( sK7 @ sK14 @ ( 'const/iterate/neutral' @ sK6 @ sK7 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f23,plain,
( ? [X10: sK6,X9: sK6] :
( ( sK7 @ X10 @ X9 )
!= ( sK7 @ X9 @ X10 ) )
=> ( ( sK7 @ sK15 @ sK16 )
!= ( sK7 @ sK16 @ sK15 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f24,plain,
( ? [X11: sK6] :
( ( sK7 @ ( 'const/iterate/neutral' @ sK6 @ sK7 ) @ X11 )
!= X11 )
=> ( sK17
!= ( sK7 @ ( 'const/iterate/neutral' @ sK6 @ sK7 ) @ sK17 ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f18,plain,
? [X0: $tType,X1: X0 > X0 > X0] :
( ( ? [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ ( X1 @ X3 @ X4 ) )
!= ( X1 @ X3 @ ( X1 @ X2 @ X4 ) ) )
| ? [X5: X0,X6: X0,X7: X0] :
( ( X1 @ X5 @ ( X1 @ X6 @ X7 ) )
!= ( X1 @ ( X1 @ X5 @ X6 ) @ X7 ) )
| ? [X8: X0] :
( ( X1 @ X8 @ ( 'const/iterate/neutral' @ X0 @ X1 ) )
!= X8 )
| ? [X9: X0,X10: X0] :
( ( X1 @ X9 @ X10 )
!= ( X1 @ X10 @ X9 ) )
| ? [X11: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X11 )
!= X11 ) )
& ( ( 'const/iterate/monoidal' @ X0 @ X1 )
= $true ) ),
inference(rectify,[status(thm)],[f10]) ).
thf(f10,plain,
? [X0: $tType,X1: X0 > X0 > X0] :
( ( ? [X8: X0,X9: X0,X10: X0] :
( ( X1 @ X8 @ ( X1 @ X9 @ X10 ) )
!= ( X1 @ X9 @ ( X1 @ X8 @ X10 ) ) )
| ? [X5: X0,X6: X0,X7: X0] :
( ( X1 @ X5 @ ( X1 @ X6 @ X7 ) )
!= ( X1 @ ( X1 @ X5 @ X6 ) @ X7 ) )
| ? [X4: X0] :
( ( X1 @ X4 @ ( 'const/iterate/neutral' @ X0 @ X1 ) )
!= X4 )
| ? [X2: X0,X3: X0] :
( ( X1 @ X2 @ X3 )
!= ( X1 @ X3 @ X2 ) )
| ? [X11: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X11 )
!= X11 ) )
& ( ( 'const/iterate/monoidal' @ X0 @ X1 )
= $true ) ),
inference(ennf_transformation,[status(thm)],[f9]) ).
thf(f9,plain,
~ ! [X0: $tType,X1: X0 > X0 > X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X1 )
= $true )
=> ( ! [X4: X0] :
( ( X1 @ X4 @ ( 'const/iterate/neutral' @ X0 @ X1 ) )
= X4 )
& ! [X11: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X11 )
= X11 )
& ! [X2: X0,X3: X0] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) )
& ! [X5: X0,X6: X0,X7: X0] :
( ( X1 @ X5 @ ( X1 @ X6 @ X7 ) )
= ( X1 @ ( X1 @ X5 @ X6 ) @ X7 ) )
& ! [X8: X0,X9: X0,X10: X0] :
( ( X1 @ X8 @ ( X1 @ X9 @ X10 ) )
= ( X1 @ X9 @ ( X1 @ X8 @ X10 ) ) ) ) ),
inference(fool_elimination,[status(thm)],[f8]) ).
thf(f8,plain,
~ ! [X0: $tType,X1: X0 > X0 > X0] :
( ( 'const/iterate/monoidal' @ X0 @ X1 )
=> ( ! [X2: X0,X3: X0] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) )
& ! [X4: X0] :
( ( X1 @ X4 @ ( 'const/iterate/neutral' @ X0 @ X1 ) )
= X4 )
& ! [X5: X0,X6: X0,X7: X0] :
( ( X1 @ X5 @ ( X1 @ X6 @ X7 ) )
= ( X1 @ ( X1 @ X5 @ X6 ) @ X7 ) )
& ! [X8: X0,X9: X0,X10: X0] :
( ( X1 @ X8 @ ( X1 @ X9 @ X10 ) )
= ( X1 @ X9 @ ( X1 @ X8 @ X10 ) ) )
& ! [X11: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X11 )
= X11 ) ) ),
inference(rectify,[status(thm)],[f4]) ).
thf(f4,negated_conjecture,
~ ! [X0: $tType,X1: X0 > X0 > X0] :
( ( 'const/iterate/monoidal' @ X0 @ X1 )
=> ( ! [X2: X0,X3: X0] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) )
& ! [X2: X0] :
( ( X1 @ X2 @ ( 'const/iterate/neutral' @ X0 @ X1 ) )
= X2 )
& ! [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X1 @ X2 @ X3 ) @ X4 ) )
& ! [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ X3 @ ( X1 @ X2 @ X4 ) ) )
& ! [X2: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X2 )
= X2 ) ) ),
inference(negated_conjecture,[status(cth)],[f3]) ).
thf(f3,conjecture,
! [X0: $tType,X1: X0 > X0 > X0] :
( ( 'const/iterate/monoidal' @ X0 @ X1 )
=> ( ! [X2: X0,X3: X0] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) )
& ! [X2: X0] :
( ( X1 @ X2 @ ( 'const/iterate/neutral' @ X0 @ X1 ) )
= X2 )
& ! [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X1 @ X2 @ X3 ) @ X4 ) )
& ! [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ X3 @ ( X1 @ X2 @ X4 ) ) )
& ! [X2: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X2 )
= X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pXFn3AYXRd/DTF2THF_19330.p','thm/iterate/MONOIDAL_AC_') ).
thf(f27,plain,
! [X0: $tType,X10: X0,X1: X0 > X0 > X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X1 )
!= $true )
| ( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X10 )
= X10 ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f17,plain,
! [X0: $tType,X1: X0 > X0 > X0] :
( ( ( ( 'const/iterate/monoidal' @ X0 @ X1 )
= $true )
| ( ( X1 @ ( sK0 @ X0 @ X1 ) @ ( sK1 @ X0 @ X1 ) )
!= ( X1 @ ( sK1 @ X0 @ X1 ) @ ( sK0 @ X0 @ X1 ) ) )
| ( ( sK2 @ X0 @ X1 )
!= ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ ( sK2 @ X0 @ X1 ) ) )
| ( ( X1 @ ( X1 @ ( sK3 @ X0 @ X1 ) @ ( sK4 @ X0 @ X1 ) ) @ ( sK5 @ X0 @ X1 ) )
!= ( X1 @ ( sK3 @ X0 @ X1 ) @ ( X1 @ ( sK4 @ X0 @ X1 ) @ ( sK5 @ X0 @ X1 ) ) ) ) )
& ( ( ! [X8: X0,X9: X0] :
( ( X1 @ X9 @ X8 )
= ( X1 @ X8 @ X9 ) )
& ! [X10: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X10 )
= X10 )
& ! [X11: X0,X12: X0,X13: X0] :
( ( X1 @ ( X1 @ X11 @ X12 ) @ X13 )
= ( X1 @ X11 @ ( X1 @ X12 @ X13 ) ) ) )
| ( ( 'const/iterate/monoidal' @ X0 @ X1 )
!= $true ) ) ),
inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f13,f16,f15,f14]) ).
thf(f14,plain,
! [X0: $tType,X1: X0 > X0 > X0] :
( ? [X2: X0,X3: X0] :
( ( X1 @ X2 @ X3 )
!= ( X1 @ X3 @ X2 ) )
=> ( ( X1 @ ( sK0 @ X0 @ X1 ) @ ( sK1 @ X0 @ X1 ) )
!= ( X1 @ ( sK1 @ X0 @ X1 ) @ ( sK0 @ X0 @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f15,plain,
! [X0: $tType,X1: X0 > X0 > X0] :
( ? [X4: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X4 )
!= X4 )
=> ( ( sK2 @ X0 @ X1 )
!= ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ ( sK2 @ X0 @ X1 ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f16,plain,
! [X0: $tType,X1: X0 > X0 > X0] :
( ? [X5: X0,X6: X0,X7: X0] :
( ( X1 @ X5 @ ( X1 @ X6 @ X7 ) )
!= ( X1 @ ( X1 @ X5 @ X6 ) @ X7 ) )
=> ( ( X1 @ ( X1 @ ( sK3 @ X0 @ X1 ) @ ( sK4 @ X0 @ X1 ) ) @ ( sK5 @ X0 @ X1 ) )
!= ( X1 @ ( sK3 @ X0 @ X1 ) @ ( X1 @ ( sK4 @ X0 @ X1 ) @ ( sK5 @ X0 @ X1 ) ) ) ) ),
introduced(definition,[],[choice_axiom]) ).
thf(f13,plain,
! [X0: $tType,X1: X0 > X0 > X0] :
( ( ( ( 'const/iterate/monoidal' @ X0 @ X1 )
= $true )
| ? [X2: X0,X3: X0] :
( ( X1 @ X2 @ X3 )
!= ( X1 @ X3 @ X2 ) )
| ? [X4: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X4 )
!= X4 )
| ? [X5: X0,X6: X0,X7: X0] :
( ( X1 @ X5 @ ( X1 @ X6 @ X7 ) )
!= ( X1 @ ( X1 @ X5 @ X6 ) @ X7 ) ) )
& ( ( ! [X8: X0,X9: X0] :
( ( X1 @ X9 @ X8 )
= ( X1 @ X8 @ X9 ) )
& ! [X10: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X10 )
= X10 )
& ! [X11: X0,X12: X0,X13: X0] :
( ( X1 @ ( X1 @ X11 @ X12 ) @ X13 )
= ( X1 @ X11 @ ( X1 @ X12 @ X13 ) ) ) )
| ( ( 'const/iterate/monoidal' @ X0 @ X1 )
!= $true ) ) ),
inference(rectify,[status(thm)],[f12]) ).
thf(f12,plain,
! [X0: $tType,X1: X0 > X0 > X0] :
( ( ( ( 'const/iterate/monoidal' @ X0 @ X1 )
= $true )
| ? [X6: X0,X7: X0] :
( ( X1 @ X6 @ X7 )
!= ( X1 @ X7 @ X6 ) )
| ? [X5: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X5 )
!= X5 )
| ? [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ ( X1 @ X3 @ X4 ) )
!= ( X1 @ ( X1 @ X2 @ X3 ) @ X4 ) ) )
& ( ( ! [X6: X0,X7: X0] :
( ( X1 @ X6 @ X7 )
= ( X1 @ X7 @ X6 ) )
& ! [X5: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X5 )
= X5 )
& ! [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X1 @ X2 @ X3 ) @ X4 ) ) )
| ( ( 'const/iterate/monoidal' @ X0 @ X1 )
!= $true ) ) ),
inference(flattening,[status(thm)],[f11]) ).
thf(f11,plain,
! [X0: $tType,X1: X0 > X0 > X0] :
( ( ( ( 'const/iterate/monoidal' @ X0 @ X1 )
= $true )
| ? [X6: X0,X7: X0] :
( ( X1 @ X6 @ X7 )
!= ( X1 @ X7 @ X6 ) )
| ? [X5: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X5 )
!= X5 )
| ? [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ ( X1 @ X3 @ X4 ) )
!= ( X1 @ ( X1 @ X2 @ X3 ) @ X4 ) ) )
& ( ( ! [X6: X0,X7: X0] :
( ( X1 @ X6 @ X7 )
= ( X1 @ X7 @ X6 ) )
& ! [X5: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X5 )
= X5 )
& ! [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X1 @ X2 @ X3 ) @ X4 ) ) )
| ( ( 'const/iterate/monoidal' @ X0 @ X1 )
!= $true ) ) ),
inference(nnf_transformation,[status(thm)],[f7]) ).
thf(f7,plain,
! [X0: $tType,X1: X0 > X0 > X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X1 )
= $true )
<=> ( ! [X6: X0,X7: X0] :
( ( X1 @ X6 @ X7 )
= ( X1 @ X7 @ X6 ) )
& ! [X5: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X5 )
= X5 )
& ! [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X1 @ X2 @ X3 ) @ X4 ) ) ) ),
inference(fool_elimination,[status(thm)],[f6]) ).
thf(f6,plain,
! [X0: $tType,X1: X0 > X0 > X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X1 )
= ( ! [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X1 @ X2 @ X3 ) @ X4 ) ) ) )
& ! [X5: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X5 )
= X5 )
& ! [X6: X0,X7: X0] :
( ( X1 @ X6 @ X7 )
= ( X1 @ X7 @ X6 ) ) ),
inference(rectify,[status(thm)],[f2]) ).
thf(f2,axiom,
! [X0: $tType,X1: X0 > X0 > X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X1 )
= ( ! [X2: X0,X3: X0,X4: X0] :
( ( X1 @ X2 @ ( X1 @ X3 @ X4 ) )
= ( X1 @ ( X1 @ X2 @ X3 ) @ X4 ) ) ) )
& ! [X2: X0] :
( ( X1 @ ( 'const/iterate/neutral' @ X0 @ X1 ) @ X2 )
= X2 )
& ! [X2: X0,X3: X0] :
( ( X1 @ X2 @ X3 )
= ( X1 @ X3 @ X2 ) ) ),
file('/export/starexec/sandbox2/tmp/tmp.pXFn3AYXRd/DTF2THF_19330.p','thm/iterate/monoidal_') ).
thf(f63,plain,
! [X0: sK6,X1: sK6] :
( ( sK7 @ X1 @ X0 )
= ( sK7 @ X0 @ X1 ) ),
inference(trivial_inequality_removal,[status(thm)],[f62]) ).
thf(f62,plain,
! [X0: sK6,X1: sK6] :
( ( ( sK7 @ X1 @ X0 )
= ( sK7 @ X0 @ X1 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f28,f30]) ).
thf(f28,plain,
! [X0: $tType,X1: X0 > X0 > X0,X8: X0,X9: X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X1 )
!= $true )
| ( ( X1 @ X9 @ X8 )
= ( X1 @ X8 @ X9 ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f34,plain,
( $false
= ( sP20 @ ( sK7 @ sK14 @ ( 'const/iterate/neutral' @ sK6 @ sK7 ) ) ) ),
introduced(definition,[new_symbols(naming,[sP20])],[inequality_splitting_name_introduction]) ).
thf(f41,plain,
( ( $true
= ( sP20 @ sK14 ) )
| ~ spl23_1 ),
inference(avatar_component_clause,[status(thm)],[f39]) ).
thf(f39,definition,
( spl23_1
<=> ( $true
= ( sP20 @ sK14 ) ) ),
introduced(definition,[new_symbols(naming,[spl23_1])],[avatar_definition]) ).
thf(f103,plain,
~ spl23_5,
inference(avatar_contradiction_clause,[status(thm)],[f102]) ).
thf(f102,plain,
( $false
| ~ spl23_5 ),
inference(trivial_inequality_removal,[status(thm)],[f101]) ).
thf(f101,plain,
( ( $true = $false )
| ~ spl23_5 ),
inference(forward_demodulation,[status(thm)],[f100,f35]) ).
thf(f35,plain,
( ( sP21 @ ( sK7 @ sK15 @ sK16 ) )
= $false ),
introduced(definition,[new_symbols(naming,[sP21])],[inequality_splitting_name_introduction]) ).
thf(f100,plain,
( ( ( sP21 @ ( sK7 @ sK15 @ sK16 ) )
= $true )
| ~ spl23_5 ),
inference(forward_demodulation,[status(thm)],[f57,f63]) ).
thf(f57,plain,
( ( $true
= ( sP21 @ ( sK7 @ sK16 @ sK15 ) ) )
| ~ spl23_5 ),
inference(avatar_component_clause,[status(thm)],[f55]) ).
thf(f55,definition,
( spl23_5
<=> ( $true
= ( sP21 @ ( sK7 @ sK16 @ sK15 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl23_5])],[avatar_definition]) ).
thf(f98,plain,
~ spl23_4,
inference(avatar_contradiction_clause,[status(thm)],[f97]) ).
thf(f97,plain,
( $false
| ~ spl23_4 ),
inference(trivial_inequality_removal,[status(thm)],[f96]) ).
thf(f96,plain,
( ( $true = $false )
| ~ spl23_4 ),
inference(forward_demodulation,[status(thm)],[f53,f61]) ).
thf(f61,plain,
( ( sP22 @ sK17 )
= $false ),
inference(backward_demodulation,[status(thm)],[f36,f60]) ).
thf(f36,plain,
( $false
= ( sP22 @ ( sK7 @ ( 'const/iterate/neutral' @ sK6 @ sK7 ) @ sK17 ) ) ),
introduced(definition,[new_symbols(naming,[sP22])],[inequality_splitting_name_introduction]) ).
thf(f53,plain,
( ( $true
= ( sP22 @ sK17 ) )
| ~ spl23_4 ),
inference(avatar_component_clause,[status(thm)],[f51]) ).
thf(f51,definition,
( spl23_4
<=> ( $true
= ( sP22 @ sK17 ) ) ),
introduced(definition,[new_symbols(naming,[spl23_4])],[avatar_definition]) ).
thf(f91,plain,
~ spl23_3,
inference(avatar_contradiction_clause,[status(thm)],[f90]) ).
thf(f90,plain,
( $false
| ~ spl23_3 ),
inference(trivial_inequality_removal,[status(thm)],[f89]) ).
thf(f89,plain,
( ( $true = $false )
| ~ spl23_3 ),
inference(forward_demodulation,[status(thm)],[f88,f33]) ).
thf(f33,plain,
( ( sP19 @ ( sK7 @ sK11 @ ( sK7 @ sK12 @ sK13 ) ) )
= $false ),
introduced(definition,[new_symbols(naming,[sP19])],[inequality_splitting_name_introduction]) ).
thf(f88,plain,
( ( ( sP19 @ ( sK7 @ sK11 @ ( sK7 @ sK12 @ sK13 ) ) )
= $true )
| ~ spl23_3 ),
inference(forward_demodulation,[status(thm)],[f87,f77]) ).
thf(f77,plain,
! [X2: sK6,X0: sK6,X1: sK6] :
( ( sK7 @ X0 @ ( sK7 @ X1 @ X2 ) )
= ( sK7 @ X2 @ ( sK7 @ X0 @ X1 ) ) ),
inference(superposition,[status(thm)],[f65,f63]) ).
thf(f65,plain,
! [X2: sK6,X0: sK6,X1: sK6] :
( ( sK7 @ X0 @ ( sK7 @ X1 @ X2 ) )
= ( sK7 @ ( sK7 @ X0 @ X1 ) @ X2 ) ),
inference(trivial_inequality_removal,[status(thm)],[f64]) ).
thf(f64,plain,
! [X2: sK6,X0: sK6,X1: sK6] :
( ( ( sK7 @ X0 @ ( sK7 @ X1 @ X2 ) )
= ( sK7 @ ( sK7 @ X0 @ X1 ) @ X2 ) )
| ( $true != $true ) ),
inference(superposition,[status(thm)],[f26,f30]) ).
thf(f26,plain,
! [X0: $tType,X11: X0,X1: X0 > X0 > X0,X12: X0,X13: X0] :
( ( ( 'const/iterate/monoidal' @ X0 @ X1 )
!= $true )
| ( ( X1 @ ( X1 @ X11 @ X12 ) @ X13 )
= ( X1 @ X11 @ ( X1 @ X12 @ X13 ) ) ) ),
inference(cnf_transformation,[status(thm)],[f17]) ).
thf(f87,plain,
( ( $true
= ( sP19 @ ( sK7 @ sK13 @ ( sK7 @ sK11 @ sK12 ) ) ) )
| ~ spl23_3 ),
inference(forward_demodulation,[status(thm)],[f49,f63]) ).
thf(f49,plain,
( ( $true
= ( sP19 @ ( sK7 @ ( sK7 @ sK11 @ sK12 ) @ sK13 ) ) )
| ~ spl23_3 ),
inference(avatar_component_clause,[status(thm)],[f47]) ).
thf(f47,definition,
( spl23_3
<=> ( $true
= ( sP19 @ ( sK7 @ ( sK7 @ sK11 @ sK12 ) @ sK13 ) ) ) ),
introduced(definition,[new_symbols(naming,[spl23_3])],[avatar_definition]) ).
thf(f85,plain,
~ spl23_2,
inference(avatar_contradiction_clause,[status(thm)],[f84]) ).
thf(f84,plain,
( $false
| ~ spl23_2 ),
inference(trivial_inequality_removal,[status(thm)],[f83]) ).
thf(f83,plain,
( ( $true = $false )
| ~ spl23_2 ),
inference(backward_demodulation,[status(thm)],[f45,f82]) ).
thf(f82,plain,
( ( sP18 @ ( sK7 @ sK8 @ ( sK7 @ sK9 @ sK10 ) ) )
= $false ),
inference(forward_demodulation,[status(thm)],[f81,f63]) ).
thf(f81,plain,
( $false
= ( sP18 @ ( sK7 @ sK8 @ ( sK7 @ sK10 @ sK9 ) ) ) ),
inference(backward_demodulation,[status(thm)],[f32,f77]) ).
thf(f32,plain,
( ( sP18 @ ( sK7 @ sK9 @ ( sK7 @ sK8 @ sK10 ) ) )
= $false ),
introduced(definition,[new_symbols(naming,[sP18])],[inequality_splitting_name_introduction]) ).
thf(f45,plain,
( ( $true
= ( sP18 @ ( sK7 @ sK8 @ ( sK7 @ sK9 @ sK10 ) ) ) )
| ~ spl23_2 ),
inference(avatar_component_clause,[status(thm)],[f43]) ).
thf(f43,definition,
( spl23_2
<=> ( $true
= ( sP18 @ ( sK7 @ sK8 @ ( sK7 @ sK9 @ sK10 ) ) ) ) ),
introduced(definition,[new_symbols(naming,[spl23_2])],[avatar_definition]) ).
thf(f58,plain,
( spl23_1
| spl23_2
| spl23_3
| spl23_4
| spl23_5 ),
inference(avatar_split_clause,[status(thm)],[f37,f55,f51,f47,f43,f39]) ).
thf(f37,plain,
( ( $true
= ( sP19 @ ( sK7 @ ( sK7 @ sK11 @ sK12 ) @ sK13 ) ) )
| ( $true
= ( sP20 @ sK14 ) )
| ( $true
= ( sP18 @ ( sK7 @ sK8 @ ( sK7 @ sK9 @ sK10 ) ) ) )
| ( $true
= ( sP22 @ sK17 ) )
| ( $true
= ( sP21 @ ( sK7 @ sK16 @ sK15 ) ) ) ),
inference(inequality_splitting,[status(thm)],[f31,f36,f35,f34,f33,f32]) ).
thf(f31,plain,
( ( ( sK7 @ sK9 @ ( sK7 @ sK8 @ sK10 ) )
!= ( sK7 @ sK8 @ ( sK7 @ sK9 @ sK10 ) ) )
| ( ( sK7 @ sK11 @ ( sK7 @ sK12 @ sK13 ) )
!= ( sK7 @ ( sK7 @ sK11 @ sK12 ) @ sK13 ) )
| ( sK14
!= ( sK7 @ sK14 @ ( 'const/iterate/neutral' @ sK6 @ sK7 ) ) )
| ( ( sK7 @ sK15 @ sK16 )
!= ( sK7 @ sK16 @ sK15 ) )
| ( sK17
!= ( sK7 @ ( 'const/iterate/neutral' @ sK6 @ sK7 ) @ sK17 ) ) ),
inference(cnf_transformation,[status(thm)],[f25]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.12 % Problem : NUN046^1 : TPTP v9.2.1. Released v7.0.0.
% 0.12/0.13 % Command : /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.16/0.34 % Computer : n005.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 11:19:44 EST 2026
% 0.16/0.34 % CPUTime :
% 0.16/0.34 Running /export/starexec/sandbox2/solver/bin/run_DT2H2X /export/starexec/sandbox2/benchmark/theBenchmark.p 300
% 0.26/0.46 ---- Original DTF file ---
% 0.26/0.46 thf(spec,logic,$$dhol).
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 % File : NUN046^1 : TPTP v9.2.1. Released v7.0.0.
% 0.26/0.46 % Domain : Number theory
% 0.26/0.46 % Problem : MONOIDAL_AC
% 0.26/0.46 % Version : Especial.
% 0.26/0.46 % English :
% 0.26/0.46
% 0.26/0.46 % Refs : [Kal16] Kalisyk (2016), Email to Geoff Sutcliffe
% 0.26/0.46 % Source : [Kal16]
% 0.26/0.46 % Names : MONOIDAL_AC_.p [Kal16]
% 0.26/0.46
% 0.26/0.46 % Status : ContradictoryAxioms
% 0.26/0.46 % Rating : 0.00 v7.1.0
% 0.26/0.46 % Syntax : Number of formulae : 6 ( 2 unt; 3 typ; 0 def)
% 0.26/0.46 % Number of atoms : 12 ( 10 equ; 0 cnn)
% 0.26/0.46 % Maximal formula atoms : 6 ( 4 avg)
% 0.26/0.46 % Number of connectives : 57 ( 0 ~; 0 |; 6 &; 50 @)
% 0.26/0.46 % ( 0 <=>; 1 =>; 0 <=; 0 <~>)
% 0.26/0.46 % Maximal formula depth : 11 ( 6 avg)
% 0.26/0.46 % Number of types : 1 ( 0 usr)
% 0.26/0.46 % Number of type conns : 11 ( 11 >; 0 *; 0 +; 0 <<)
% 0.26/0.46 % Number of symbols : 4 ( 3 usr; 0 con; 2-2 aty)
% 0.26/0.46 % Number of variables : 25 ( 0 ^; 22 !; 0 ?; 25 :)
% 0.26/0.46 % ( 3 !>; 0 ?*; 0 @-; 0 @+)
% 0.26/0.46 % SPC : TH1_CAX_EQU_NAR
% 0.26/0.46
% 0.26/0.46 % Comments : Exported from core HOL Light.
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 thf('thf_const_const/trivia/I',type,
% 0.26/0.46 'const/trivia/I':
% 0.26/0.46 !>[A: $tType] : ( A > A ) ).
% 0.26/0.46
% 0.26/0.46 thf('thf_const_const/iterate/neutral',type,
% 0.26/0.46 'const/iterate/neutral':
% 0.26/0.46 !>[A: $tType] : ( ( A > A > A ) > A ) ).
% 0.26/0.46
% 0.26/0.46 thf('thf_const_const/iterate/monoidal',type,
% 0.26/0.46 'const/iterate/monoidal':
% 0.26/0.46 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 0.26/0.46
% 0.26/0.46 thf('thm/trivia/I_THM_',axiom,
% 0.26/0.46 ! [A: $tType,A0: A] :
% 0.26/0.46 ( ( 'const/trivia/I' @ A @ A0 )
% 0.26/0.46 = A0 ) ).
% 0.26/0.46
% 0.26/0.46 thf('thm/iterate/monoidal_',axiom,
% 0.26/0.46 ! [A: $tType,A0: A > A > A] :
% 0.26/0.46 ( ( 'const/iterate/monoidal' @ A @ A0 )
% 0.26/0.46 = ( ! [A1: A,A2: A] :
% 0.26/0.46 ( ( A0 @ A1 @ A2 )
% 0.26/0.46 = ( A0 @ A2 @ A1 ) )
% 0.26/0.46 & ! [A1: A,A2: A,A3: A] :
% 0.26/0.46 ( ( A0 @ A1 @ ( A0 @ A2 @ A3 ) )
% 0.26/0.46 = ( A0 @ ( A0 @ A1 @ A2 ) @ A3 ) )
% 0.26/0.46 & ! [A1: A] :
% 0.26/0.46 ( ( A0 @ ( 'const/iterate/neutral' @ A @ A0 ) @ A1 )
% 0.26/0.46 = A1 ) ) ) ).
% 0.26/0.46
% 0.26/0.46 thf('thm/iterate/MONOIDAL_AC_',conjecture,
% 0.26/0.46 ! [A: $tType,A0: A > A > A] :
% 0.26/0.46 ( ( 'const/iterate/monoidal' @ A @ A0 )
% 0.26/0.46 => ( ! [A1: A] :
% 0.26/0.46 ( ( A0 @ ( 'const/iterate/neutral' @ A @ A0 ) @ A1 )
% 0.26/0.46 = A1 )
% 0.26/0.46 & ! [A1: A] :
% 0.26/0.46 ( ( A0 @ A1 @ ( 'const/iterate/neutral' @ A @ A0 ) )
% 0.26/0.46 = A1 )
% 0.26/0.46 & ! [A1: A,A2: A] :
% 0.26/0.46 ( ( A0 @ A1 @ A2 )
% 0.26/0.46 = ( A0 @ A2 @ A1 ) )
% 0.26/0.46 & ! [A1: A,A2: A,A3: A] :
% 0.26/0.46 ( ( A0 @ ( A0 @ A1 @ A2 ) @ A3 )
% 0.26/0.46 = ( A0 @ A1 @ ( A0 @ A2 @ A3 ) ) )
% 0.26/0.46 & ! [A1: A,A2: A,A3: A] :
% 0.26/0.46 ( ( A0 @ A1 @ ( A0 @ A2 @ A3 ) )
% 0.26/0.46 = ( A0 @ A2 @ ( A0 @ A1 @ A3 ) ) ) ) ) ).
% 0.26/0.46
% 0.26/0.46 %------------------------------------------------------------------------------
% 0.26/0.46 ------------------------
% 1.53/1.21 ---- Embedded in THF ---
% 1.53/1.21 %%% This output was generated by embedproblem, version 1.9.5 (library version 1.9).
% 1.53/1.21 %%% Generated on Tue Feb 24 11:19:45 EST 2026
% 1.53/1.21 %%% using '$$dhol' embedding, version 1.3.0.
% 1.53/1.21 %%% Logic specification used:
% 1.53/1.21 %%% thf(spec, logic, $$dhol).
% 1.53/1.21
% 1.53/1.21 % SZS output start ListOfTHF for /export/starexec/sandbox2/tmp/tmp.pXFn3AYXRd/DTF2DTF19330.p
% See solution above
% 1.53/1.21 ------------------------
% 1.53/1.22 ---- Cleaned THF ---
% 1.53/1.23 thf('thf_const_const/trivia/I',type,
% 1.53/1.23 'const/trivia/I':
% 1.53/1.23 !>[A: $tType] : ( A > A ) ).
% 1.53/1.23
% 1.53/1.23 thf('thf_const_const/iterate/neutral',type,
% 1.53/1.23 'const/iterate/neutral':
% 1.53/1.23 !>[A: $tType] : ( ( A > A > A ) > A ) ).
% 1.53/1.23
% 1.53/1.23 thf('thf_const_const/iterate/monoidal',type,
% 1.53/1.23 'const/iterate/monoidal':
% 1.53/1.23 !>[A: $tType] : ( ( A > A > A ) > $o ) ).
% 1.53/1.23
% 1.53/1.23 thf('thm/trivia/I_THM_',axiom,
% 1.53/1.23 ! [A: $tType,A0: A] :
% 1.53/1.23 ( ( 'const/trivia/I' @ A @ A0 )
% 1.53/1.23 = A0 ) ).
% 1.53/1.23
% 1.53/1.23 thf('thm/iterate/monoidal_',axiom,
% 1.53/1.23 ! [A: $tType,A0: A > A > A] :
% 1.53/1.23 ( ( 'const/iterate/monoidal' @ A @ A0 )
% 1.53/1.23 = ( ! [A1: A,A2: A] :
% 1.53/1.23 ( ( A0 @ A1 @ A2 )
% 1.53/1.23 = ( A0 @ A2 @ A1 ) )
% 1.53/1.23 & ! [A1: A,A2: A,A3: A] :
% 1.53/1.23 ( ( A0 @ A1 @ ( A0 @ A2 @ A3 ) )
% 1.53/1.23 = ( A0 @ ( A0 @ A1 @ A2 ) @ A3 ) )
% 1.53/1.23 & ! [A1: A] :
% 1.53/1.23 ( ( A0 @ ( 'const/iterate/neutral' @ A @ A0 ) @ A1 )
% 1.53/1.23 = A1 ) ) ) ).
% 1.53/1.23
% 1.53/1.23 thf('thm/iterate/MONOIDAL_AC_',conjecture,
% 1.53/1.23 ! [A: $tType,A0: A > A > A] :
% 1.53/1.23 ( ( 'const/iterate/monoidal' @ A @ A0 )
% 1.53/1.23 => ( ! [A1: A] :
% 1.53/1.23 ( ( A0 @ ( 'const/iterate/neutral' @ A @ A0 ) @ A1 )
% 1.53/1.23 = A1 )
% 1.53/1.23 & ! [A1: A] :
% 1.53/1.23 ( ( A0 @ A1 @ ( 'const/iterate/neutral' @ A @ A0 ) )
% 1.53/1.23 = A1 )
% 1.53/1.23 & ! [A1: A,A2: A] :
% 1.53/1.23 ( ( A0 @ A1 @ A2 )
% 1.53/1.23 = ( A0 @ A2 @ A1 ) )
% 1.53/1.23 & ! [A1: A,A2: A,A3: A] :
% 1.53/1.23 ( ( A0 @ ( A0 @ A1 @ A2 ) @ A3 )
% 1.53/1.23 = ( A0 @ A1 @ ( A0 @ A2 @ A3 ) ) )
% 1.53/1.23 & ! [A1: A,A2: A,A3: A] :
% 1.53/1.23 ( ( A0 @ A1 @ ( A0 @ A2 @ A3 ) )
% 1.53/1.23 = ( A0 @ A2 @ ( A0 @ A1 @ A3 ) ) ) ) ) ).
% 1.53/1.23 ------------------------
% 1.53/1.24 % (19619)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_19330 for (2999ds/27Mi)
% 1.53/1.24 % (19622)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_19330 for (2999ds/275Mi)
% 1.53/1.25 % (19620)lrs+10_1:1_au=on:inj=on:i=2:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/2Mi)
% 1.53/1.25 % (19617)lrs+1002_1:8_bd=off:fd=off:hud=10:tnu=1:i=183:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/183Mi)
% 1.53/1.25 % (19618)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_19330 for (2999ds/4Mi)
% 1.53/1.25 % (19621)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_19330 for (2999ds/2Mi)
% 1.53/1.25 % (19623)lrs+1004_1:128_cond=on:e2e=on:sp=weighted_frequency:i=18:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/18Mi)
% 1.53/1.25 % (19620)Instruction limit reached!
% 1.53/1.25 % (19620)------------------------------
% 1.53/1.25 % (19620)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.25 % (19620)Termination reason: Unknown
% 1.53/1.25 % (19620)Termination phase: Preprocessing 3
% 1.53/1.25
% 1.53/1.25 % (19620)Memory used [KB]: 1023
% 1.53/1.25 % (19620)Time elapsed: 0.003 s
% 1.53/1.25 % (19620)Instructions burned: 2 (million)
% 1.53/1.25 % (19620)------------------------------
% 1.53/1.25 % (19620)------------------------------
% 1.53/1.25 % (19621)Instruction limit reached!
% 1.53/1.25 % (19621)------------------------------
% 1.53/1.25 % (19621)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.25 % (19621)Termination reason: Unknown
% 1.53/1.25 % (19621)Termination phase: shuffling
% 1.53/1.25
% 1.53/1.25 % (19621)Memory used [KB]: 895
% 1.53/1.25 % (19621)Time elapsed: 0.003 s
% 1.53/1.25 % (19621)Instructions burned: 2 (million)
% 1.53/1.25 % (19621)------------------------------
% 1.53/1.25 % (19621)------------------------------
% 1.53/1.25 % (19619)Instruction limit reached!
% 1.53/1.25 % (19619)------------------------------
% 1.53/1.25 % (19619)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.25 % (19619)Termination reason: Unknown
% 1.53/1.25 % (19619)Termination phase: Saturation
% 1.53/1.25
% 1.53/1.25 % (19619)Memory used [KB]: 5628
% 1.53/1.25 % (19619)Time elapsed: 0.011 s
% 1.53/1.25 % (19619)Instructions burned: 28 (million)
% 1.53/1.25 % (19619)------------------------------
% 1.53/1.25 % (19619)------------------------------
% 1.53/1.25 % (19618)Instruction limit reached!
% 1.53/1.25 % (19618)------------------------------
% 1.53/1.25 % (19618)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.25 % (19618)Termination reason: Unknown
% 1.53/1.25 % (19618)Termination phase: Saturation
% 1.53/1.25
% 1.53/1.25 % (19618)Memory used [KB]: 5500
% 1.53/1.25 % (19618)Time elapsed: 0.005 s
% 1.53/1.25 % (19618)Instructions burned: 4 (million)
% 1.53/1.25 % (19618)------------------------------
% 1.53/1.25 % (19618)------------------------------
% 1.53/1.26 % (19626)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_19330 for (2999ds/15Mi)
% 1.53/1.26 % (19623)Instruction limit reached!
% 1.53/1.26 % (19623)------------------------------
% 1.53/1.26 % (19623)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.26 % (19623)Termination reason: Unknown
% 1.53/1.26 % (19623)Termination phase: Saturation
% 1.53/1.26
% 1.53/1.26 % (19623)Memory used [KB]: 5628
% 1.53/1.26 % (19623)Time elapsed: 0.014 s
% 1.53/1.26 % (19623)Instructions burned: 18 (million)
% 1.53/1.26 % (19623)------------------------------
% 1.53/1.26 % (19623)------------------------------
% 1.53/1.26 % (19624)lrs+10_1:1_bet=on:cnfonf=off:fd=off:hud=5:inj=on:i=3:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/3Mi)
% 1.53/1.27 % (19626)Instruction limit reached!
% 1.53/1.27 % (19626)------------------------------
% 1.53/1.27 % (19626)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.27 % (19626)Termination reason: Unknown
% 1.53/1.27 % (19626)Termination phase: Saturation
% 1.53/1.27
% 1.53/1.27 % (19626)Memory used [KB]: 5628
% 1.53/1.27 % (19626)Time elapsed: 0.007 s
% 1.53/1.27 % (19626)Instructions burned: 16 (million)
% 1.53/1.27 % (19626)------------------------------
% 1.53/1.27 % (19626)------------------------------
% 1.53/1.27 % (19624)Instruction limit reached!
% 1.53/1.27 % (19624)------------------------------
% 1.53/1.27 % (19624)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.27 % (19624)Termination reason: Unknown
% 1.53/1.27 % (19624)Termination phase: Saturation
% 1.53/1.27
% 1.53/1.27 % (19624)Memory used [KB]: 5500
% 1.53/1.27 % (19624)Time elapsed: 0.003 s
% 1.53/1.27 % (19624)Instructions burned: 3 (million)
% 1.53/1.27 % (19624)------------------------------
% 1.53/1.27 % (19624)------------------------------
% 1.53/1.27 % (19625)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_19330 for (2999ds/37Mi)
% 1.53/1.27 % Exception at run slice level
% 1.53/1.27 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.53/1.27 % (19627)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_19330 for (2999ds/3Mi)
% 1.53/1.27 % (19627)Instruction limit reached!
% 1.53/1.27 % (19627)------------------------------
% 1.53/1.27 % (19627)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.27 % (19627)Termination reason: Unknown
% 1.53/1.27 % (19627)Termination phase: Saturation
% 1.53/1.27
% 1.53/1.27 % (19627)Memory used [KB]: 5500
% 1.53/1.27 % (19627)Time elapsed: 0.004 s
% 1.53/1.27 % (19627)Instructions burned: 3 (million)
% 1.53/1.27 % (19627)------------------------------
% 1.53/1.27 % (19627)------------------------------
% 1.53/1.27 % (19629)lrs+10_1:1_av=off:chr=on:plsq=on:slsq=on:i=7:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/7Mi)
% 1.53/1.28 % (19630)lrs+10_1:1_acc=on:amm=sco:cs=on:tgt=full:i=16:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/16Mi)
% 1.53/1.28 % (19629)Instruction limit reached!
% 1.53/1.28 % (19629)------------------------------
% 1.53/1.28 % (19629)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (19629)Termination reason: Unknown
% 1.53/1.28 % (19629)Termination phase: Saturation
% 1.53/1.28
% 1.53/1.28 % (19629)Memory used [KB]: 1023
% 1.53/1.28 % (19629)Time elapsed: 0.004 s
% 1.53/1.28 % (19629)Instructions burned: 9 (million)
% 1.53/1.28 % (19629)------------------------------
% 1.53/1.28 % (19629)------------------------------
% 1.53/1.28 % (19628)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_19330 for (2999ds/1041Mi)
% 1.53/1.28 % Exception at run slice level
% 1.53/1.28 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.53/1.28 % (19630)Instruction limit reached!
% 1.53/1.28 % (19630)------------------------------
% 1.53/1.28 % (19630)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.28 % (19630)Termination reason: Unknown
% 1.53/1.28 % (19630)Termination phase: Saturation
% 1.53/1.28
% 1.53/1.28 % (19630)Memory used [KB]: 5628
% 1.53/1.28 % (19630)Time elapsed: 0.007 s
% 1.53/1.28 % (19630)Instructions burned: 17 (million)
% 1.53/1.28 % (19630)------------------------------
% 1.53/1.28 % (19630)------------------------------
% 1.53/1.29 % (19631)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_19330 for (2999ds/3Mi)
% 1.53/1.29 % (19633)lrs+10_1:1_cnfonf=off:cs=on:hud=3:prag=on:sup=off:i=7:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/7Mi)
% 1.53/1.29 % (19631)Instruction limit reached!
% 1.53/1.29 % (19631)------------------------------
% 1.53/1.29 % (19631)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (19631)Termination reason: Unknown
% 1.53/1.29 % (19631)Termination phase: Property scanning
% 1.53/1.29
% 1.53/1.29 % (19631)Memory used [KB]: 1023
% 1.53/1.29 % (19631)Time elapsed: 0.004 s
% 1.53/1.29 % (19631)Instructions burned: 4 (million)
% 1.53/1.29 % (19631)------------------------------
% 1.53/1.29 % (19631)------------------------------
% 1.53/1.29 % (19632)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_19330 for (2999ds/3Mi)
% 1.53/1.29 % (19632)Instruction limit reached!
% 1.53/1.29 % (19632)------------------------------
% 1.53/1.29 % (19632)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (19632)Termination reason: Unknown
% 1.53/1.29 % (19632)Termination phase: Saturation
% 1.53/1.29
% 1.53/1.29 % (19632)Memory used [KB]: 1023
% 1.53/1.29 % (19632)Time elapsed: 0.004 s
% 1.53/1.29 % (19632)Instructions burned: 4 (million)
% 1.53/1.29 % (19632)------------------------------
% 1.53/1.29 % (19632)------------------------------
% 1.53/1.29 % (19633)Instruction limit reached!
% 1.53/1.29 % (19633)------------------------------
% 1.53/1.29 % (19633)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (19633)Termination reason: Unknown
% 1.53/1.29 % (19633)Termination phase: Saturation
% 1.53/1.29
% 1.53/1.29 % (19633)Memory used [KB]: 5500
% 1.53/1.29 % (19633)Time elapsed: 0.004 s
% 1.53/1.29 % (19633)Instructions burned: 10 (million)
% 1.53/1.29 % (19633)------------------------------
% 1.53/1.29 % (19633)------------------------------
% 1.53/1.29 % (19635)dis+1004_1:1_cha=on:cs=on:fe=off:hud=1:i=4:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/4Mi)
% 1.53/1.29 % (19635)Instruction limit reached!
% 1.53/1.29 % (19635)------------------------------
% 1.53/1.29 % (19635)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.53/1.29 % (19635)Termination reason: Unknown
% 1.53/1.29 % (19635)Termination phase: Saturation
% 1.53/1.29
% 1.53/1.29 % (19635)Memory used [KB]: 5500
% 1.53/1.29 % (19635)Time elapsed: 0.003 s
% 1.53/1.29 % (19635)Instructions burned: 4 (million)
% 1.53/1.29 % (19635)------------------------------
% 1.53/1.29 % (19635)------------------------------
% 1.53/1.30 % (19634)dis+1002_1:1_add=large:cnfonf=lazy_pi_sigma_gen:fe=off:prag=on:i=3:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/3Mi)
% 1.59/1.30 % Exception at run slice level
% 1.59/1.30 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.59/1.30 % (19638)lrs+1004_1:1_chr=on:prag=on:i=6:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/6Mi)
% 1.59/1.30 % (19638)Instruction limit reached!
% 1.59/1.30 % (19638)------------------------------
% 1.59/1.30 % (19638)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (19638)Termination reason: Unknown
% 1.59/1.30 % (19638)Termination phase: Saturation
% 1.59/1.30
% 1.59/1.30 % (19638)Memory used [KB]: 5500
% 1.59/1.30 % (19638)Time elapsed: 0.003 s
% 1.59/1.30 % (19638)Instructions burned: 6 (million)
% 1.59/1.30 % (19638)------------------------------
% 1.59/1.30 % (19638)------------------------------
% 1.59/1.30 % (19639)dis+1002_5:1_au=on:bd=off:e2e=on:fde=none:fs=off:fsr=off:sos=on:i=902:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/902Mi)
% 1.59/1.30 % (19639)Refutation not found, incomplete strategy
% 1.59/1.30 % (19639)------------------------------
% 1.59/1.30 % (19639)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.30 % (19639)Termination reason: Refutation not found, incomplete strategy
% 1.59/1.30
% 1.59/1.30
% 1.59/1.30 % (19639)Memory used [KB]: 5500
% 1.59/1.30 % (19639)Time elapsed: 0.003 s
% 1.59/1.30 % (19639)Instructions burned: 4 (million)
% 1.59/1.30 % (19639)------------------------------
% 1.59/1.30 % (19639)------------------------------
% 1.59/1.30 % (19636)lrs+1002_1:1_anc=all_dependent:au=on:cbe=off:fde=unused:ntd=on:i=18:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/18Mi)
% 1.59/1.31 % (19637)lrs+10_1:1_e2e=on:sd=1:sgt=8:ss=axioms:i=710:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/710Mi)
% 1.59/1.31 % (19641)dis+10_1:1_cnfonf=lazy_gen:fe=off:i=5:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/5Mi)
% 1.59/1.31 % Exception at run slice level
% 1.59/1.31 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.59/1.31 % (19642)lrs+2_1:1_cnfonf=lazy_not_gen_be_off:cs=on:fe=off:hud=10:inj=on:ins=3:plsq=on:plsqc=1:sd=10:ss=axioms:tnu=1:i=6:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/6Mi)
% 1.59/1.31 % (19640)dis+21_1:8_apa=on:cnfonf=off:fd=off:fsr=off:hud=0:ins=1:kws=inv_frequency:nwc=10.0:ss=axioms:st=5.0:i=21:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/21Mi)
% 1.59/1.31 % Exception at run slice level
% 1.59/1.31 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.59/1.32 % (19636)Instruction limit reached!
% 1.59/1.32 % (19636)------------------------------
% 1.59/1.32 % (19636)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.32 % (19636)Termination reason: Unknown
% 1.59/1.32 % (19636)Termination phase: Saturation
% 1.59/1.32
% 1.59/1.32 % (19636)Memory used [KB]: 5628
% 1.59/1.32 % (19636)Time elapsed: 0.013 s
% 1.59/1.32 % (19636)Instructions burned: 18 (million)
% 1.59/1.32 % (19636)------------------------------
% 1.59/1.32 % (19636)------------------------------
% 1.59/1.32 % (19643)lrs+1002_1:128_au=on:c=on:fsr=off:piset=equals:i=377:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/377Mi)
% 1.59/1.32 % (19644)dis+1010_1:4_atotf=0.2:c=on:cbe=off:cnfonf=lazy_simp:fe=off:ins=2:ntd=on:s2a=on:s2at=5.0:sgt=5:ss=axioms:st=1.5:i=779:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/779Mi)
% 1.59/1.33 % Exception at run slice level
% 1.59/1.33 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.59/1.33 % (19640)Instruction limit reached!
% 1.59/1.33 % (19640)------------------------------
% 1.59/1.33 % (19640)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.33 % (19640)Termination reason: Unknown
% 1.59/1.33 % (19640)Termination phase: Saturation
% 1.59/1.33
% 1.59/1.33 % (19640)Memory used [KB]: 5628
% 1.59/1.33 % (19640)Time elapsed: 0.016 s
% 1.59/1.33 % (19640)Instructions burned: 21 (million)
% 1.59/1.33 % (19640)------------------------------
% 1.59/1.33 % (19640)------------------------------
% 1.59/1.33 % (19622)Instruction limit reached!
% 1.59/1.33 % (19622)------------------------------
% 1.59/1.33 % (19622)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.33 % (19622)Termination reason: Unknown
% 1.59/1.33 % (19622)Termination phase: Saturation
% 1.59/1.33
% 1.59/1.33 % (19622)Memory used [KB]: 6012
% 1.59/1.33 % (19622)Time elapsed: 0.089 s
% 1.59/1.33 % (19622)Instructions burned: 277 (million)
% 1.59/1.33 % (19622)------------------------------
% 1.59/1.33 % (19622)------------------------------
% 1.59/1.33 % (19645)lrs+10_1:1_cnfonf=lazy_not_be_gen:ntd=on:sp=const_min:ss=axioms:sup=off:i=19:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/19Mi)
% 1.59/1.33 % Exception at run slice level
% 1.59/1.33 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.59/1.34 % (19646)lrs+1010_1:1_au=on:s2a=on:sd=1:sgt=50:ss=axioms:i=879:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/879Mi)
% 1.59/1.34 % (19648)ott+21_1:1_apa=on:au=on:cnfonf=off:sos=on:i=3:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/3Mi)
% 1.59/1.34 % (19648)Instruction limit reached!
% 1.59/1.34 % (19648)------------------------------
% 1.59/1.34 % (19648)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.34 % (19648)Termination reason: Unknown
% 1.59/1.34 % (19648)Termination phase: Saturation
% 1.59/1.34
% 1.59/1.34 % (19648)Memory used [KB]: 1023
% 1.59/1.34 % (19648)Time elapsed: 0.003 s
% 1.59/1.34 % (19648)Instructions burned: 4 (million)
% 1.59/1.34 % (19648)------------------------------
% 1.59/1.34 % (19648)------------------------------
% 1.59/1.35 % (19617)Instruction limit reached!
% 1.59/1.35 % (19617)------------------------------
% 1.59/1.35 % (19617)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.35 % (19617)Termination reason: Unknown
% 1.59/1.35 % (19617)Termination phase: Saturation
% 1.59/1.35
% 1.59/1.35 % (19617)Memory used [KB]: 6908
% 1.59/1.35 % (19617)Time elapsed: 0.100 s
% 1.59/1.35 % (19617)Instructions burned: 184 (million)
% 1.59/1.35 % (19617)------------------------------
% 1.59/1.35 % (19617)------------------------------
% 1.59/1.35 % (19647)dis+1002_1:128_acc=on:er=filter:i=17:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/17Mi)
% 1.59/1.35 % (19649)lrs+1010_1:8_cnfonf=off:hud=1:inj=on:tnu=5:i=30:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/30Mi)
% 1.59/1.35 % (19650)dis+10_1:1_ixr=off:plsq=on:plsqc=1:plsqr=32,1:s2a=on:i=127:si=on:rtra=on_0 on DTF2THF_19330 for (2999ds/127Mi)
% 1.59/1.36 % (19647)Instruction limit reached!
% 1.59/1.36 % (19647)------------------------------
% 1.59/1.36 % (19647)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (19647)Termination reason: Unknown
% 1.59/1.36 % (19647)Termination phase: Saturation
% 1.59/1.36
% 1.59/1.36 % (19647)Memory used [KB]: 5628
% 1.59/1.36 % (19647)Time elapsed: 0.012 s
% 1.59/1.36 % (19647)Instructions burned: 17 (million)
% 1.59/1.36 % (19647)------------------------------
% 1.59/1.36 % (19647)------------------------------
% 1.59/1.36 % (19651)lrs+1002_1:1_au=on:cbe=off:cnfonf=conj_eager:cond=on:hi=on:i=100:si=on:rtra=on_0 on DTF2THF_19330 for (2998ds/100Mi)
% 1.59/1.36 % (19649)Instruction limit reached!
% 1.59/1.36 % (19649)------------------------------
% 1.59/1.36 % (19649)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.36 % (19649)Termination reason: Unknown
% 1.59/1.36 % (19649)Termination phase: Saturation
% 1.59/1.36
% 1.59/1.36 % (19649)Memory used [KB]: 5628
% 1.59/1.36 % (19649)Time elapsed: 0.016 s
% 1.59/1.36 % (19649)Instructions burned: 31 (million)
% 1.59/1.36 % (19649)------------------------------
% 1.59/1.36 % (19649)------------------------------
% 1.59/1.37 % (19652)dis+10_1:1_anc=none:cnfonf=lazy_gen:fd=preordered:fe=off:hud=10:ins=3:ixr=off:nwc=5.0:plsq=on:plsqc=1:plsqr=32,1:sp=const_frequency:uhcvi=on:i=3:si=on:rtra=on_0 on DTF2THF_19330 for (2998ds/3Mi)
% 1.59/1.37 % Exception at run slice level
% 1.59/1.37 User error: Vampire does not support full TH1. This benchmark is either outside of the TH1 fragment, or outside of the fragment supported by Vampire
% 1.59/1.37 % (19653)lrs+10_8:1_au=on:avsq=on:e2e=on:ins=3:s2a=on:s2at=3.0:ss=axioms:i=20:si=on:rtra=on_0 on DTF2THF_19330 for (2998ds/20Mi)
% 1.59/1.38 % (19654)dis+1002_1:1_cbe=off:hud=5:nm=4:plsq=on:plsqr=7,1:prag=on:sp=const_max:tnu=1:i=86:si=on:rtra=on_0 on DTF2THF_19330 for (2998ds/86Mi)
% 1.59/1.38 % (19653)First to succeed.
% 1.59/1.38 % (19653)Refutation found. Thanks to Tanya!
% 1.59/1.38 % SZS status Theorem for DTF2THF_19330
% 1.59/1.38 % SZS output start Proof for DTF2THF_19330
% 1.59/1.38 thf(type_def_6, type, sK6: $tType).
% 1.59/1.38 thf(func_def_0, type, 'const/trivia/I': !>[X0: $tType]:(X0 > X0)).
% 1.59/1.38 thf(func_def_1, type, 'const/iterate/neutral': !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.59/1.38 thf(func_def_2, type, 'const/iterate/monoidal': !>[X0: $tType]:((X0 > X0 > X0) > $o)).
% 1.59/1.38 thf(func_def_6, type, sK0: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.59/1.38 thf(func_def_7, type, sK1: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.59/1.38 thf(func_def_8, type, sK2: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.59/1.38 thf(func_def_9, type, sK3: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.59/1.38 thf(func_def_10, type, sK4: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.59/1.38 thf(func_def_11, type, sK5: !>[X0: $tType]:((X0 > X0 > X0) > X0)).
% 1.59/1.38 thf(func_def_12, type, sK7: sK6 > sK6 > sK6).
% 1.59/1.38 thf(func_def_13, type, sK8: sK6).
% 1.59/1.38 thf(func_def_14, type, sK9: sK6).
% 1.59/1.38 thf(func_def_15, type, sK10: sK6).
% 1.59/1.38 thf(func_def_16, type, sK11: sK6).
% 1.59/1.38 thf(func_def_17, type, sK12: sK6).
% 1.59/1.38 thf(func_def_18, type, sK13: sK6).
% 1.59/1.38 thf(func_def_19, type, sK14: sK6).
% 1.59/1.38 thf(func_def_20, type, sK15: sK6).
% 1.59/1.38 thf(func_def_21, type, sK16: sK6).
% 1.59/1.38 thf(func_def_22, type, sK17: sK6).
% 1.59/1.38 thf(func_def_23, type, sP18: sK6 > $o).
% 1.59/1.38 thf(func_def_24, type, sP19: sK6 > $o).
% 1.59/1.38 thf(func_def_25, type, sP20: sK6 > $o).
% 1.59/1.38 thf(func_def_26, type, sP21: sK6 > $o).
% 1.59/1.38 thf(func_def_27, type, sP22: sK6 > $o).
% 1.59/1.38 thf(func_def_29, type, ph24: !>[X0: $tType]:(X0)).
% 1.59/1.38 thf(f109,plain,(
% 1.59/1.38 $false),
% 1.59/1.38 inference(avatar_sat_refutation,[status(thm)],[f58,f85,f91,f98,f103,f108])).
% 1.59/1.38 thf(f108,plain,(
% 1.59/1.38 ~spl23_1),
% 1.59/1.38 inference(avatar_contradiction_clause,[status(thm)],[f107])).
% 1.59/1.38 thf(f107,plain,(
% 1.59/1.38 $false | ~spl23_1),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f106])).
% 1.59/1.38 thf(f106,plain,(
% 1.59/1.38 ($true = $false) | ~spl23_1),
% 1.59/1.38 inference(forward_demodulation,[status(thm)],[f41,f72])).
% 1.59/1.38 thf(f72,plain,(
% 1.59/1.38 ($false = (sP20 @ sK14))),
% 1.59/1.38 inference(backward_demodulation,[status(thm)],[f34,f68])).
% 1.59/1.38 thf(f68,plain,(
% 1.59/1.38 ( ! [X0 : sK6] : (((sK7 @ X0 @ ('const/iterate/neutral' @ sK6 @ sK7)) = X0)) )),
% 1.59/1.38 inference(superposition,[status(thm)],[f63,f60])).
% 1.59/1.38 thf(f60,plain,(
% 1.59/1.38 ( ! [X0 : sK6] : (((sK7 @ ('const/iterate/neutral' @ sK6 @ sK7) @ X0) = X0)) )),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f59])).
% 1.59/1.38 thf(f59,plain,(
% 1.59/1.38 ( ! [X0 : sK6] : (((sK7 @ ('const/iterate/neutral' @ sK6 @ sK7) @ X0) = X0) | ($true != $true)) )),
% 1.59/1.38 inference(superposition,[status(thm)],[f27,f30])).
% 1.59/1.38 thf(f30,plain,(
% 1.59/1.38 (('const/iterate/monoidal' @ sK6 @ sK7) = $true)),
% 1.59/1.38 inference(cnf_transformation,[status(thm)],[f25])).
% 1.59/1.38 thf(f25,plain,(
% 1.59/1.38 (((sK7 @ sK9 @ (sK7 @ sK8 @ sK10)) != (sK7 @ sK8 @ (sK7 @ sK9 @ sK10))) | ((sK7 @ sK11 @ (sK7 @ sK12 @ sK13)) != (sK7 @ (sK7 @ sK11 @ sK12) @ sK13)) | (sK14 != (sK7 @ sK14 @ ('const/iterate/neutral' @ sK6 @ sK7))) | ((sK7 @ sK15 @ sK16) != (sK7 @ sK16 @ sK15)) | (sK17 != (sK7 @ ('const/iterate/neutral' @ sK6 @ sK7) @ sK17))) & (('const/iterate/monoidal' @ sK6 @ sK7) = $true)),
% 1.59/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK6,sK7,sK8,sK9,sK10,sK11,sK12,sK13,sK14,sK15,sK16,sK17])],[f18,f24,f23,f22,f21,f20,f19])).
% 1.59/1.38 thf(f19,plain,(
% 1.59/1.38 ? [X0 : $tType,X1 : X0 > X0 > X0] : ((? [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ (X1 @ X3 @ X4)) != (X1 @ X3 @ (X1 @ X2 @ X4))) | ? [X5 : X0,X6 : X0,X7 : X0] : ((X1 @ X5 @ (X1 @ X6 @ X7)) != (X1 @ (X1 @ X5 @ X6) @ X7)) | ? [X8 : X0] : ((X1 @ X8 @ ('const/iterate/neutral' @ X0 @ X1)) != X8) | ? [X9 : X0,X10 : X0] : ((X1 @ X9 @ X10) != (X1 @ X10 @ X9)) | ? [X11 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X11) != X11)) & (('const/iterate/monoidal' @ X0 @ X1) = $true)) => ((? [X4 : sK6,X3 : sK6,X2 : sK6] : ((sK7 @ X3 @ (sK7 @ X2 @ X4)) != (sK7 @ X2 @ (sK7 @ X3 @ X4))) | ? [X7 : sK6,X6 : sK6,X5 : sK6] : ((sK7 @ X5 @ (sK7 @ X6 @ X7)) != (sK7 @ (sK7 @ X5 @ X6) @ X7)) | ? [X8 : sK6] : ((sK7 @ X8 @ ('const/iterate/neutral' @ sK6 @ sK7)) != X8) | ? [X10 : sK6,X9 : sK6] : ((sK7 @ X10 @ X9) != (sK7 @ X9 @ X10)) | ? [X11 : sK6] : ((sK7 @ ('const/iterate/neutral' @ sK6 @ sK7) @ X11) != X11)) & (('const/iterate/monoidal' @ sK6 @ sK7) = $true))),
% 1.59/1.38 introduced(definition,[],[choice_axiom])).
% 1.59/1.38 thf(f20,plain,(
% 1.59/1.38 ? [X4 : sK6,X3 : sK6,X2 : sK6] : ((sK7 @ X3 @ (sK7 @ X2 @ X4)) != (sK7 @ X2 @ (sK7 @ X3 @ X4))) => ((sK7 @ sK9 @ (sK7 @ sK8 @ sK10)) != (sK7 @ sK8 @ (sK7 @ sK9 @ sK10)))),
% 1.59/1.38 introduced(definition,[],[choice_axiom])).
% 1.59/1.38 thf(f21,plain,(
% 1.59/1.38 ? [X7 : sK6,X6 : sK6,X5 : sK6] : ((sK7 @ X5 @ (sK7 @ X6 @ X7)) != (sK7 @ (sK7 @ X5 @ X6) @ X7)) => ((sK7 @ sK11 @ (sK7 @ sK12 @ sK13)) != (sK7 @ (sK7 @ sK11 @ sK12) @ sK13))),
% 1.59/1.38 introduced(definition,[],[choice_axiom])).
% 1.59/1.38 thf(f22,plain,(
% 1.59/1.38 ? [X8 : sK6] : ((sK7 @ X8 @ ('const/iterate/neutral' @ sK6 @ sK7)) != X8) => (sK14 != (sK7 @ sK14 @ ('const/iterate/neutral' @ sK6 @ sK7)))),
% 1.59/1.38 introduced(definition,[],[choice_axiom])).
% 1.59/1.38 thf(f23,plain,(
% 1.59/1.38 ? [X10 : sK6,X9 : sK6] : ((sK7 @ X10 @ X9) != (sK7 @ X9 @ X10)) => ((sK7 @ sK15 @ sK16) != (sK7 @ sK16 @ sK15))),
% 1.59/1.38 introduced(definition,[],[choice_axiom])).
% 1.59/1.38 thf(f24,plain,(
% 1.59/1.38 ? [X11 : sK6] : ((sK7 @ ('const/iterate/neutral' @ sK6 @ sK7) @ X11) != X11) => (sK17 != (sK7 @ ('const/iterate/neutral' @ sK6 @ sK7) @ sK17))),
% 1.59/1.38 introduced(definition,[],[choice_axiom])).
% 1.59/1.38 thf(f18,plain,(
% 1.59/1.38 ? [X0 : $tType,X1 : X0 > X0 > X0] : ((? [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ (X1 @ X3 @ X4)) != (X1 @ X3 @ (X1 @ X2 @ X4))) | ? [X5 : X0,X6 : X0,X7 : X0] : ((X1 @ X5 @ (X1 @ X6 @ X7)) != (X1 @ (X1 @ X5 @ X6) @ X7)) | ? [X8 : X0] : ((X1 @ X8 @ ('const/iterate/neutral' @ X0 @ X1)) != X8) | ? [X9 : X0,X10 : X0] : ((X1 @ X9 @ X10) != (X1 @ X10 @ X9)) | ? [X11 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X11) != X11)) & (('const/iterate/monoidal' @ X0 @ X1) = $true))),
% 1.59/1.38 inference(rectify,[status(thm)],[f10])).
% 1.59/1.38 thf(f10,plain,(
% 1.59/1.38 ? [X0 : $tType,X1 : X0 > X0 > X0] : ((? [X8 : X0,X9 : X0,X10 : X0] : ((X1 @ X8 @ (X1 @ X9 @ X10)) != (X1 @ X9 @ (X1 @ X8 @ X10))) | ? [X5 : X0,X6 : X0,X7 : X0] : ((X1 @ X5 @ (X1 @ X6 @ X7)) != (X1 @ (X1 @ X5 @ X6) @ X7)) | ? [X4 : X0] : ((X1 @ X4 @ ('const/iterate/neutral' @ X0 @ X1)) != X4) | ? [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) != (X1 @ X3 @ X2)) | ? [X11 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X11) != X11)) & (('const/iterate/monoidal' @ X0 @ X1) = $true))),
% 1.59/1.38 inference(ennf_transformation,[status(thm)],[f9])).
% 1.59/1.38 thf(f9,plain,(
% 1.59/1.38 ~! [X0 : $tType,X1 : X0 > X0 > X0] : ((('const/iterate/monoidal' @ X0 @ X1) = $true) => (! [X4 : X0] : ((X1 @ X4 @ ('const/iterate/neutral' @ X0 @ X1)) = X4) & ! [X11 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X11) = X11) & ! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) = (X1 @ X3 @ X2)) & ! [X5 : X0,X6 : X0,X7 : X0] : ((X1 @ X5 @ (X1 @ X6 @ X7)) = (X1 @ (X1 @ X5 @ X6) @ X7)) & ! [X8 : X0,X9 : X0,X10 : X0] : ((X1 @ X8 @ (X1 @ X9 @ X10)) = (X1 @ X9 @ (X1 @ X8 @ X10)))))),
% 1.59/1.38 inference(fool_elimination,[status(thm)],[f8])).
% 1.59/1.38 thf(f8,plain,(
% 1.59/1.38 ~! [X0 : $tType,X1 : X0 > X0 > X0] : (('const/iterate/monoidal' @ X0 @ X1) => (! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) = (X1 @ X3 @ X2)) & ! [X4 : X0] : ((X1 @ X4 @ ('const/iterate/neutral' @ X0 @ X1)) = X4) & ! [X5 : X0,X6 : X0,X7 : X0] : ((X1 @ X5 @ (X1 @ X6 @ X7)) = (X1 @ (X1 @ X5 @ X6) @ X7)) & ! [X8 : X0,X9 : X0,X10 : X0] : ((X1 @ X8 @ (X1 @ X9 @ X10)) = (X1 @ X9 @ (X1 @ X8 @ X10))) & ! [X11 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X11) = X11)))),
% 1.59/1.38 inference(rectify,[status(thm)],[f4])).
% 1.59/1.38 thf(f4,negated_conjecture,(
% 1.59/1.38 ~! [X0 : $tType,X1 : X0 > X0 > X0] : (('const/iterate/monoidal' @ X0 @ X1) => (! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) = (X1 @ X3 @ X2)) & ! [X2 : X0] : ((X1 @ X2 @ ('const/iterate/neutral' @ X0 @ X1)) = X2) & ! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ (X1 @ X2 @ X3) @ X4)) & ! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ X3 @ (X1 @ X2 @ X4))) & ! [X2 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X2) = X2)))),
% 1.59/1.38 inference(negated_conjecture,[status(cth)],[f3])).
% 1.59/1.38 thf(f3,conjecture,(
% 1.59/1.38 ! [X0 : $tType,X1 : X0 > X0 > X0] : (('const/iterate/monoidal' @ X0 @ X1) => (! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) = (X1 @ X3 @ X2)) & ! [X2 : X0] : ((X1 @ X2 @ ('const/iterate/neutral' @ X0 @ X1)) = X2) & ! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ (X1 @ X2 @ X3) @ X4)) & ! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ X3 @ (X1 @ X2 @ X4))) & ! [X2 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X2) = X2)))),
% 1.59/1.38 file('/export/starexec/sandbox2/tmp/tmp.pXFn3AYXRd/DTF2THF_19330.p','thm/iterate/MONOIDAL_AC_')).
% 1.59/1.38 thf(f27,plain,(
% 1.59/1.38 ( ! [X0 : $tType,X10 : X0,X1 : X0 > X0 > X0] : ((('const/iterate/monoidal' @ X0 @ X1) != $true) | ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X10) = X10)) )),
% 1.59/1.38 inference(cnf_transformation,[status(thm)],[f17])).
% 1.59/1.38 thf(f17,plain,(
% 1.59/1.38 ! [X0 : $tType,X1 : X0 > X0 > X0] : (((('const/iterate/monoidal' @ X0 @ X1) = $true) | ((X1 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1)) != (X1 @ (sK1 @ X0 @ X1) @ (sK0 @ X0 @ X1))) | ((sK2 @ X0 @ X1) != (X1 @ ('const/iterate/neutral' @ X0 @ X1) @ (sK2 @ X0 @ X1))) | ((X1 @ (X1 @ (sK3 @ X0 @ X1) @ (sK4 @ X0 @ X1)) @ (sK5 @ X0 @ X1)) != (X1 @ (sK3 @ X0 @ X1) @ (X1 @ (sK4 @ X0 @ X1) @ (sK5 @ X0 @ X1))))) & ((! [X8 : X0,X9 : X0] : ((X1 @ X9 @ X8) = (X1 @ X8 @ X9)) & ! [X10 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X10) = X10) & ! [X11 : X0,X12 : X0,X13 : X0] : ((X1 @ (X1 @ X11 @ X12) @ X13) = (X1 @ X11 @ (X1 @ X12 @ X13)))) | (('const/iterate/monoidal' @ X0 @ X1) != $true)))),
% 1.59/1.38 inference(skolemisation,[status(esa),new_symbols(skolem,[sK0,sK1,sK2,sK3,sK4,sK5])],[f13,f16,f15,f14])).
% 1.59/1.38 thf(f14,plain,(
% 1.59/1.38 ! [X0 : $tType,X1 : X0 > X0 > X0] : (? [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) != (X1 @ X3 @ X2)) => ((X1 @ (sK0 @ X0 @ X1) @ (sK1 @ X0 @ X1)) != (X1 @ (sK1 @ X0 @ X1) @ (sK0 @ X0 @ X1))))),
% 1.59/1.38 introduced(definition,[],[choice_axiom])).
% 1.59/1.38 thf(f15,plain,(
% 1.59/1.38 ! [X0 : $tType,X1 : X0 > X0 > X0] : (? [X4 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X4) != X4) => ((sK2 @ X0 @ X1) != (X1 @ ('const/iterate/neutral' @ X0 @ X1) @ (sK2 @ X0 @ X1))))),
% 1.59/1.38 introduced(definition,[],[choice_axiom])).
% 1.59/1.38 thf(f16,plain,(
% 1.59/1.38 ! [X0 : $tType,X1 : X0 > X0 > X0] : (? [X5 : X0,X6 : X0,X7 : X0] : ((X1 @ X5 @ (X1 @ X6 @ X7)) != (X1 @ (X1 @ X5 @ X6) @ X7)) => ((X1 @ (X1 @ (sK3 @ X0 @ X1) @ (sK4 @ X0 @ X1)) @ (sK5 @ X0 @ X1)) != (X1 @ (sK3 @ X0 @ X1) @ (X1 @ (sK4 @ X0 @ X1) @ (sK5 @ X0 @ X1)))))),
% 1.59/1.38 introduced(definition,[],[choice_axiom])).
% 1.59/1.38 thf(f13,plain,(
% 1.59/1.38 ! [X0 : $tType,X1 : X0 > X0 > X0] : (((('const/iterate/monoidal' @ X0 @ X1) = $true) | ? [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) != (X1 @ X3 @ X2)) | ? [X4 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X4) != X4) | ? [X5 : X0,X6 : X0,X7 : X0] : ((X1 @ X5 @ (X1 @ X6 @ X7)) != (X1 @ (X1 @ X5 @ X6) @ X7))) & ((! [X8 : X0,X9 : X0] : ((X1 @ X9 @ X8) = (X1 @ X8 @ X9)) & ! [X10 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X10) = X10) & ! [X11 : X0,X12 : X0,X13 : X0] : ((X1 @ (X1 @ X11 @ X12) @ X13) = (X1 @ X11 @ (X1 @ X12 @ X13)))) | (('const/iterate/monoidal' @ X0 @ X1) != $true)))),
% 1.59/1.38 inference(rectify,[status(thm)],[f12])).
% 1.59/1.38 thf(f12,plain,(
% 1.59/1.38 ! [X0 : $tType,X1 : X0 > X0 > X0] : (((('const/iterate/monoidal' @ X0 @ X1) = $true) | ? [X6 : X0,X7 : X0] : ((X1 @ X6 @ X7) != (X1 @ X7 @ X6)) | ? [X5 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X5) != X5) | ? [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ (X1 @ X3 @ X4)) != (X1 @ (X1 @ X2 @ X3) @ X4))) & ((! [X6 : X0,X7 : X0] : ((X1 @ X6 @ X7) = (X1 @ X7 @ X6)) & ! [X5 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X5) = X5) & ! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ (X1 @ X2 @ X3) @ X4))) | (('const/iterate/monoidal' @ X0 @ X1) != $true)))),
% 1.59/1.38 inference(flattening,[status(thm)],[f11])).
% 1.59/1.38 thf(f11,plain,(
% 1.59/1.38 ! [X0 : $tType,X1 : X0 > X0 > X0] : (((('const/iterate/monoidal' @ X0 @ X1) = $true) | (? [X6 : X0,X7 : X0] : ((X1 @ X6 @ X7) != (X1 @ X7 @ X6)) | ? [X5 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X5) != X5) | ? [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ (X1 @ X3 @ X4)) != (X1 @ (X1 @ X2 @ X3) @ X4)))) & ((! [X6 : X0,X7 : X0] : ((X1 @ X6 @ X7) = (X1 @ X7 @ X6)) & ! [X5 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X5) = X5) & ! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ (X1 @ X2 @ X3) @ X4))) | (('const/iterate/monoidal' @ X0 @ X1) != $true)))),
% 1.59/1.38 inference(nnf_transformation,[status(thm)],[f7])).
% 1.59/1.38 thf(f7,plain,(
% 1.59/1.38 ! [X0 : $tType,X1 : X0 > X0 > X0] : ((('const/iterate/monoidal' @ X0 @ X1) = $true) <=> (! [X6 : X0,X7 : X0] : ((X1 @ X6 @ X7) = (X1 @ X7 @ X6)) & ! [X5 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X5) = X5) & ! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ (X1 @ X2 @ X3) @ X4))))),
% 1.59/1.38 inference(fool_elimination,[status(thm)],[f6])).
% 1.59/1.38 thf(f6,plain,(
% 1.59/1.38 ! [X0 : $tType,X1 : X0 > X0 > X0] : (('const/iterate/monoidal' @ X0 @ X1) = ! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ (X1 @ X2 @ X3) @ X4)) & ! [X5 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X5) = X5) & ! [X6 : X0,X7 : X0] : ((X1 @ X6 @ X7) = (X1 @ X7 @ X6)))),
% 1.59/1.38 inference(rectify,[status(thm)],[f2])).
% 1.59/1.38 thf(f2,axiom,(
% 1.59/1.38 ! [X0 : $tType,X1 : X0 > X0 > X0] : (('const/iterate/monoidal' @ X0 @ X1) = ! [X2 : X0,X3 : X0,X4 : X0] : ((X1 @ X2 @ (X1 @ X3 @ X4)) = (X1 @ (X1 @ X2 @ X3) @ X4)) & ! [X2 : X0] : ((X1 @ ('const/iterate/neutral' @ X0 @ X1) @ X2) = X2) & ! [X2 : X0,X3 : X0] : ((X1 @ X2 @ X3) = (X1 @ X3 @ X2)))),
% 1.59/1.38 file('/export/starexec/sandbox2/tmp/tmp.pXFn3AYXRd/DTF2THF_19330.p','thm/iterate/monoidal_')).
% 1.59/1.38 thf(f63,plain,(
% 1.59/1.38 ( ! [X0 : sK6,X1 : sK6] : (((sK7 @ X1 @ X0) = (sK7 @ X0 @ X1))) )),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f62])).
% 1.59/1.38 thf(f62,plain,(
% 1.59/1.38 ( ! [X0 : sK6,X1 : sK6] : (((sK7 @ X1 @ X0) = (sK7 @ X0 @ X1)) | ($true != $true)) )),
% 1.59/1.38 inference(superposition,[status(thm)],[f28,f30])).
% 1.59/1.38 thf(f28,plain,(
% 1.59/1.38 ( ! [X0 : $tType,X1 : X0 > X0 > X0,X8 : X0,X9 : X0] : ((('const/iterate/monoidal' @ X0 @ X1) != $true) | ((X1 @ X9 @ X8) = (X1 @ X8 @ X9))) )),
% 1.59/1.38 inference(cnf_transformation,[status(thm)],[f17])).
% 1.59/1.38 thf(f34,plain,(
% 1.59/1.38 ($false = (sP20 @ (sK7 @ sK14 @ ('const/iterate/neutral' @ sK6 @ sK7))))),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[sP20])],[inequality_splitting_name_introduction])).
% 1.59/1.38 thf(f41,plain,(
% 1.59/1.38 ($true = (sP20 @ sK14)) | ~spl23_1),
% 1.59/1.38 inference(avatar_component_clause,[status(thm)],[f39])).
% 1.59/1.38 thf(f39,definition,(
% 1.59/1.38 spl23_1 <=> ($true = (sP20 @ sK14))),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[spl23_1])],[avatar_definition])).
% 1.59/1.38 thf(f103,plain,(
% 1.59/1.38 ~spl23_5),
% 1.59/1.38 inference(avatar_contradiction_clause,[status(thm)],[f102])).
% 1.59/1.38 thf(f102,plain,(
% 1.59/1.38 $false | ~spl23_5),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f101])).
% 1.59/1.38 thf(f101,plain,(
% 1.59/1.38 ($true = $false) | ~spl23_5),
% 1.59/1.38 inference(forward_demodulation,[status(thm)],[f100,f35])).
% 1.59/1.38 thf(f35,plain,(
% 1.59/1.38 ((sP21 @ (sK7 @ sK15 @ sK16)) = $false)),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[sP21])],[inequality_splitting_name_introduction])).
% 1.59/1.38 thf(f100,plain,(
% 1.59/1.38 ((sP21 @ (sK7 @ sK15 @ sK16)) = $true) | ~spl23_5),
% 1.59/1.38 inference(forward_demodulation,[status(thm)],[f57,f63])).
% 1.59/1.38 thf(f57,plain,(
% 1.59/1.38 ($true = (sP21 @ (sK7 @ sK16 @ sK15))) | ~spl23_5),
% 1.59/1.38 inference(avatar_component_clause,[status(thm)],[f55])).
% 1.59/1.38 thf(f55,definition,(
% 1.59/1.38 spl23_5 <=> ($true = (sP21 @ (sK7 @ sK16 @ sK15)))),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[spl23_5])],[avatar_definition])).
% 1.59/1.38 thf(f98,plain,(
% 1.59/1.38 ~spl23_4),
% 1.59/1.38 inference(avatar_contradiction_clause,[status(thm)],[f97])).
% 1.59/1.38 thf(f97,plain,(
% 1.59/1.38 $false | ~spl23_4),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f96])).
% 1.59/1.38 thf(f96,plain,(
% 1.59/1.38 ($true = $false) | ~spl23_4),
% 1.59/1.38 inference(forward_demodulation,[status(thm)],[f53,f61])).
% 1.59/1.38 thf(f61,plain,(
% 1.59/1.38 ((sP22 @ sK17) = $false)),
% 1.59/1.38 inference(backward_demodulation,[status(thm)],[f36,f60])).
% 1.59/1.38 thf(f36,plain,(
% 1.59/1.38 ($false = (sP22 @ (sK7 @ ('const/iterate/neutral' @ sK6 @ sK7) @ sK17)))),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[sP22])],[inequality_splitting_name_introduction])).
% 1.59/1.38 thf(f53,plain,(
% 1.59/1.38 ($true = (sP22 @ sK17)) | ~spl23_4),
% 1.59/1.38 inference(avatar_component_clause,[status(thm)],[f51])).
% 1.59/1.38 thf(f51,definition,(
% 1.59/1.38 spl23_4 <=> ($true = (sP22 @ sK17))),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[spl23_4])],[avatar_definition])).
% 1.59/1.38 thf(f91,plain,(
% 1.59/1.38 ~spl23_3),
% 1.59/1.38 inference(avatar_contradiction_clause,[status(thm)],[f90])).
% 1.59/1.38 thf(f90,plain,(
% 1.59/1.38 $false | ~spl23_3),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f89])).
% 1.59/1.38 thf(f89,plain,(
% 1.59/1.38 ($true = $false) | ~spl23_3),
% 1.59/1.38 inference(forward_demodulation,[status(thm)],[f88,f33])).
% 1.59/1.38 thf(f33,plain,(
% 1.59/1.38 ((sP19 @ (sK7 @ sK11 @ (sK7 @ sK12 @ sK13))) = $false)),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[sP19])],[inequality_splitting_name_introduction])).
% 1.59/1.38 thf(f88,plain,(
% 1.59/1.38 ((sP19 @ (sK7 @ sK11 @ (sK7 @ sK12 @ sK13))) = $true) | ~spl23_3),
% 1.59/1.38 inference(forward_demodulation,[status(thm)],[f87,f77])).
% 1.59/1.38 thf(f77,plain,(
% 1.59/1.38 ( ! [X2 : sK6,X0 : sK6,X1 : sK6] : (((sK7 @ X0 @ (sK7 @ X1 @ X2)) = (sK7 @ X2 @ (sK7 @ X0 @ X1)))) )),
% 1.59/1.38 inference(superposition,[status(thm)],[f65,f63])).
% 1.59/1.38 thf(f65,plain,(
% 1.59/1.38 ( ! [X2 : sK6,X0 : sK6,X1 : sK6] : (((sK7 @ X0 @ (sK7 @ X1 @ X2)) = (sK7 @ (sK7 @ X0 @ X1) @ X2))) )),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f64])).
% 1.59/1.38 thf(f64,plain,(
% 1.59/1.38 ( ! [X2 : sK6,X0 : sK6,X1 : sK6] : (((sK7 @ X0 @ (sK7 @ X1 @ X2)) = (sK7 @ (sK7 @ X0 @ X1) @ X2)) | ($true != $true)) )),
% 1.59/1.38 inference(superposition,[status(thm)],[f26,f30])).
% 1.59/1.38 thf(f26,plain,(
% 1.59/1.38 ( ! [X0 : $tType,X11 : X0,X1 : X0 > X0 > X0,X12 : X0,X13 : X0] : ((('const/iterate/monoidal' @ X0 @ X1) != $true) | ((X1 @ (X1 @ X11 @ X12) @ X13) = (X1 @ X11 @ (X1 @ X12 @ X13)))) )),
% 1.59/1.38 inference(cnf_transformation,[status(thm)],[f17])).
% 1.59/1.38 thf(f87,plain,(
% 1.59/1.38 ($true = (sP19 @ (sK7 @ sK13 @ (sK7 @ sK11 @ sK12)))) | ~spl23_3),
% 1.59/1.38 inference(forward_demodulation,[status(thm)],[f49,f63])).
% 1.59/1.38 thf(f49,plain,(
% 1.59/1.38 ($true = (sP19 @ (sK7 @ (sK7 @ sK11 @ sK12) @ sK13))) | ~spl23_3),
% 1.59/1.38 inference(avatar_component_clause,[status(thm)],[f47])).
% 1.59/1.38 thf(f47,definition,(
% 1.59/1.38 spl23_3 <=> ($true = (sP19 @ (sK7 @ (sK7 @ sK11 @ sK12) @ sK13)))),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[spl23_3])],[avatar_definition])).
% 1.59/1.38 thf(f85,plain,(
% 1.59/1.38 ~spl23_2),
% 1.59/1.38 inference(avatar_contradiction_clause,[status(thm)],[f84])).
% 1.59/1.38 thf(f84,plain,(
% 1.59/1.38 $false | ~spl23_2),
% 1.59/1.38 inference(trivial_inequality_removal,[status(thm)],[f83])).
% 1.59/1.38 thf(f83,plain,(
% 1.59/1.38 ($true = $false) | ~spl23_2),
% 1.59/1.38 inference(backward_demodulation,[status(thm)],[f45,f82])).
% 1.59/1.38 thf(f82,plain,(
% 1.59/1.38 ((sP18 @ (sK7 @ sK8 @ (sK7 @ sK9 @ sK10))) = $false)),
% 1.59/1.38 inference(forward_demodulation,[status(thm)],[f81,f63])).
% 1.59/1.38 thf(f81,plain,(
% 1.59/1.38 ($false = (sP18 @ (sK7 @ sK8 @ (sK7 @ sK10 @ sK9))))),
% 1.59/1.38 inference(backward_demodulation,[status(thm)],[f32,f77])).
% 1.59/1.38 thf(f32,plain,(
% 1.59/1.38 ((sP18 @ (sK7 @ sK9 @ (sK7 @ sK8 @ sK10))) = $false)),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[sP18])],[inequality_splitting_name_introduction])).
% 1.59/1.38 thf(f45,plain,(
% 1.59/1.38 ($true = (sP18 @ (sK7 @ sK8 @ (sK7 @ sK9 @ sK10)))) | ~spl23_2),
% 1.59/1.38 inference(avatar_component_clause,[status(thm)],[f43])).
% 1.59/1.38 thf(f43,definition,(
% 1.59/1.38 spl23_2 <=> ($true = (sP18 @ (sK7 @ sK8 @ (sK7 @ sK9 @ sK10))))),
% 1.59/1.38 introduced(definition,[new_symbols(naming,[spl23_2])],[avatar_definition])).
% 1.59/1.38 thf(f58,plain,(
% 1.59/1.38 spl23_1 | spl23_2 | spl23_3 | spl23_4 | spl23_5),
% 1.59/1.38 inference(avatar_split_clause,[status(thm)],[f37,f55,f51,f47,f43,f39])).
% 1.59/1.38 thf(f37,plain,(
% 1.59/1.38 ($true = (sP19 @ (sK7 @ (sK7 @ sK11 @ sK12) @ sK13))) | ($true = (sP20 @ sK14)) | ($true = (sP18 @ (sK7 @ sK8 @ (sK7 @ sK9 @ sK10)))) | ($true = (sP22 @ sK17)) | ($true = (sP21 @ (sK7 @ sK16 @ sK15)))),
% 1.59/1.38 inference(inequality_splitting,[status(thm)],[f31,f36,f35,f34,f33,f32])).
% 1.59/1.38 thf(f31,plain,(
% 1.59/1.38 ((sK7 @ sK9 @ (sK7 @ sK8 @ sK10)) != (sK7 @ sK8 @ (sK7 @ sK9 @ sK10))) | ((sK7 @ sK11 @ (sK7 @ sK12 @ sK13)) != (sK7 @ (sK7 @ sK11 @ sK12) @ sK13)) | (sK14 != (sK7 @ sK14 @ ('const/iterate/neutral' @ sK6 @ sK7))) | ((sK7 @ sK15 @ sK16) != (sK7 @ sK16 @ sK15)) | (sK17 != (sK7 @ ('const/iterate/neutral' @ sK6 @ sK7) @ sK17))),
% 1.59/1.38 inference(cnf_transformation,[status(thm)],[f25])).
% 1.59/1.38 % SZS output end Proof for DTF2THF_19330
% 1.59/1.38 % (19653)------------------------------
% 1.59/1.38 % (19653)Version: Vampire 4.8 (commit 7b44b1c2f on 2025-07-15 09:50:17 +0100)
% 1.59/1.38 % (19653)Termination reason: Refutation
% 1.59/1.38
% 1.59/1.38 % (19653)Memory used [KB]: 5628
% 1.59/1.38 % (19653)Time elapsed: 0.009 s
% 1.59/1.38 % (19653)Instructions burned: 14 (million)
% 1.59/1.38 % (19653)------------------------------
% 1.59/1.38 % (19653)------------------------------
% 1.59/1.38 % (19616)Success in time 0.137 s
%------------------------------------------------------------------------------