%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV666+1 : TPTP v9.3.1. Released v9.3.0.
% Transfm : none
% Format : tptp:raw
% Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% Computer : n020.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8046.5625MB
% OS : Linux 6.8.0-71-generic
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Sun Sep 27 08:48:19 AM UTC 2026
% Result : Theorem 13.77s 4.33s
% Output : Refutation 14.20s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 64
% Syntax : Number of formulae : 130 ( 45 unt; 0 typ; 0 def)
% Number of atoms : 553 ( 70 equ; 0 cnn)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 2412 ( 2 ~; 0 |; 32 &;1987 @)
% ( 32 <=>; 359 =>; 0 <=; 0 <~>)
% Maximal formula depth : 23 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 65 usr; 17 con; 0-7 aty)
% Number of variables : 575 ( 0 ^; 575 !; 0 ?; 575 :)
% Comments :
%------------------------------------------------------------------------------
thf(cm_decl,type,
cm: $i ).
thf(cn_decl,type,
cn: $i ).
thf(cQuicksortComplexity_2eutil_2eext__eq___24a4_decl,type,
cQuicksortComplexity_2eutil_2eext__eq___24a4: $i > $i > $i > $i > $o ).
thf(cA_decl,type,
cA: $i ).
thf(cQuicksortComplexity_2emonads_2emon___24a2_decl,type,
cQuicksortComplexity_2emonads_2emon___24a2: $i > $i > $i ).
thf(cM_decl,type,
cM: $i ).
thf(cB_decl,type,
cB: $i ).
thf(cf_decl,type,
cf: $i ).
thf(cg_decl,type,
cg: $i ).
thf(cQuicksortComplexity_2emonads_2ebind___24a5_decl,type,
cQuicksortComplexity_2emonads_2ebind___24a5: $i > $i > $i > $i > $i > $i ).
thf(cQuicksortComplexity_2emonads_2eMonad___24t_decl,type,
cQuicksortComplexity_2emonads_2eMonad___24t: $i > $o ).
thf(cType___24t_decl,type,
cType___24t: $i > $o ).
thf(cQuicksortComplexity_2emonads_2emon___24t_decl,type,
cQuicksortComplexity_2emonads_2emon___24t: $i > $i > $i > $o ).
thf(c_24__type__759___24t_decl,type,
c_24__type__759___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__2619___24t_decl,type,
c_24__type__2619___24t: $i > $i > $i > $i > $i > $o ).
thf(c_24__lam__2636___24a6_decl,type,
c_24__lam__2636___24a6: $i > $i > $i > $i > $i > $i > $i ).
thf(c_24__type__2726___24t_decl,type,
c_24__type__2726___24t: $i > $i > $i > $o ).
thf(t_decl,type,
t: $i > $i > $o ).
thf(happ_decl,type,
happ: $i > $i > $i ).
thf(c_24__lam__39635_decl,type,
c_24__lam__39635: $i ).
thf(c_24__lam__39635___24a6_decl,type,
c_24__lam__39635___24a6: $i > $i > $i > $i > $i > $i > $i ).
thf(cQuicksortComplexity_2emonads_2eliftM_decl,type,
cQuicksortComplexity_2emonads_2eliftM: $i ).
thf(cQuicksortComplexity_2emonads_2eliftM___24a5_decl,type,
cQuicksortComplexity_2emonads_2eliftM___24a5: $i > $i > $i > $i > $i > $i ).
thf(c_24__lam__7828_decl,type,
c_24__lam__7828: $i ).
thf(c_24__lam__7828___24a4_decl,type,
c_24__lam__7828___24a4: $i > $i > $i > $i > $i ).
thf(c_24__type__39762___24t_decl,type,
c_24__type__39762___24t: $i > $o ).
thf(cQuicksortComplexity_2emonads_2eextMonad___24a1_decl,type,
cQuicksortComplexity_2emonads_2eextMonad___24a1: $i > $o ).
thf(c_24__lam__8018_decl,type,
c_24__lam__8018: $i ).
thf(c_24__lam__8018___24a3_decl,type,
c_24__lam__8018___24a3: $i > $i > $i > $i ).
thf(c_24__type__225___24t_decl,type,
c_24__type__225___24t: $i > $i > $o ).
thf(c_24__type__176660___24t_decl,type,
c_24__type__176660___24t: $i > $o ).
thf(c_24__type__176660_decl,type,
c_24__type__176660: $i ).
thf(c_24__type__55245___24t_decl,type,
c_24__type__55245___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__39870___24t_decl,type,
c_24__type__39870___24t: $i > $i > $o ).
thf(c_24__lam__39622_decl,type,
c_24__lam__39622: $i ).
thf(c_24__lam__39622___24a6_decl,type,
c_24__lam__39622___24a6: $i > $i > $i > $i > $i > $i > $i ).
thf(c_24__type__987___24t_decl,type,
c_24__type__987___24t: $i > $o ).
thf(c_24__type__185961___24t_decl,type,
c_24__type__185961___24t: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__type__25186___24t_decl,type,
c_24__type__25186___24t: $i > $o ).
thf(cQuicksortComplexity_2emonads_2ebind__map_decl,type,
cQuicksortComplexity_2emonads_2ebind__map: $i ).
thf(cQuicksortComplexity_2emonads_2ebind__map___24a5_decl,type,
cQuicksortComplexity_2emonads_2ebind__map___24a5: $i > $i > $i > $i > $i > $i ).
thf(cQuicksortComplexity_2emonads_2eret___24a2_decl,type,
cQuicksortComplexity_2emonads_2eret___24a2: $i > $i > $i ).
thf(c_24__type__39805___24t_decl,type,
c_24__type__39805___24t: $i > $i > $o ).
thf(c_24__type__38959___24t_decl,type,
c_24__type__38959___24t: $i > $i > $i > $i > $i > $o ).
thf(c_24__type__55237___24t_decl,type,
c_24__type__55237___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__930___24t_decl,type,
c_24__type__930___24t: $i > $i > $o ).
thf(c_24__type__7897___24t_decl,type,
c_24__type__7897___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__38537___24t_decl,type,
c_24__type__38537___24t: $i > $i > $o ).
thf(c_24__lam__39622___24a7_decl,type,
c_24__lam__39622___24a7: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_24__type__460___24t_decl,type,
c_24__type__460___24t: $i > $i > $o ).
thf(c_24__type__25627___24t_decl,type,
c_24__type__25627___24t: $i > $i > $i > $o ).
thf(c_24__type__177004___24t_decl,type,
c_24__type__177004___24t: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__type__39774___24t_decl,type,
c_24__type__39774___24t: $i > $i > $o ).
thf(c_24__type__39727___24t_decl,type,
c_24__type__39727___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__10375___24t_decl,type,
c_24__type__10375___24t: $i > $i > $i > $o ).
thf(c_24__lam__39010_decl,type,
c_24__lam__39010: $i ).
thf(c_24__lam__39010___24a4_decl,type,
c_24__lam__39010___24a4: $i > $i > $i > $i > $i ).
thf(c_24__type__686___24t_decl,type,
c_24__type__686___24t: $i > $i > $o ).
thf(c_24__type__39835___24t_decl,type,
c_24__type__39835___24t: $i > $i > $o ).
thf(cQuicksortComplexity_2emonads_2eliftM2_decl,type,
cQuicksortComplexity_2emonads_2eliftM2: $i ).
thf(cQuicksortComplexity_2emonads_2eliftM2___24a7_decl,type,
cQuicksortComplexity_2emonads_2eliftM2___24a7: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_24__type__515___24t_decl,type,
c_24__type__515___24t: $i > $o ).
thf(c_24__type__25650___24t_decl,type,
c_24__type__25650___24t: $i > $i > $i > $o ).
thf(cA___24t_decl,type,
cA___24t: $i > $o ).
thf(cCoq_2eInit_2eDatatypes_2elist___24a1_decl,type,
cCoq_2eInit_2eDatatypes_2elist___24a1: $i > $i ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
<=> ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24a2 ) @ ( C @ t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$tdef_QuicksortComplexity.monads.mon') ).
thf(269,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24a2 ) @ ( C @ t ) )
=> ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) )
& ( ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24a2 ) @ ( C @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(45,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__686___24t ) )
<=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( C @ ( A @ happ ) @ ( D @ ( C @ ( B @ happ ) @ happ ) @ t ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_686') ).
thf(385,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( C @ ( A @ happ ) @ ( D @ ( C @ ( B @ happ ) @ happ ) @ t ) ) ) )
=> ( B @ ( A @ c_24__type__686___24t ) ) )
& ( ( B @ ( A @ c_24__type__686___24t ) )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( C @ ( A @ happ ) @ ( D @ ( C @ ( B @ happ ) @ happ ) @ t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(53,axiom,
cA @ cType___24t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_A') ).
thf(436,plain,
cA @ cType___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(59,axiom,
cf @ c_24__type__176660___24t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_f') ).
thf(460,plain,
cf @ c_24__type__176660___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(24,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2726___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2726___24t ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','QuicksortComplexity.util.ext_eq_rw') ).
thf(228,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2726___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2726___24t ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(35,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__38537___24t ) )
<=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( C @ ( A @ happ ) @ ( D @ ( C @ ( B @ happ ) @ happ ) @ t ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_38537') ).
thf(307,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( C @ ( A @ happ ) @ ( D @ ( C @ ( B @ happ ) @ happ ) @ t ) ) ) )
=> ( B @ ( A @ c_24__type__38537___24t ) ) )
& ( ( B @ ( A @ c_24__type__38537___24t ) )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( C @ ( A @ happ ) @ ( D @ ( C @ ( B @ happ ) @ happ ) @ t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( A @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ! [E: $i] :
( ( E @ ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ! [F: $i] :
( ( F @ ( C @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ! [G: $i] :
( ( G @ ( C @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ( ( D = E )
=> ( ( G @ ( F @ ( C @ ( A @ cQuicksortComplexity_2emonads_2emon___24a2 ) @ ( B @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ( ( F @ ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) )
= ( G @ ( E @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','QuicksortComplexity.monads.bind_eqq') ).
thf(317,plain,
! [A: $i] :
( ( A @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( A @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ! [E: $i] :
( ( E @ ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ! [F: $i] :
( ( F @ ( C @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ! [G: $i] :
( ( G @ ( C @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ( ( D = E )
=> ( ( G @ ( F @ ( C @ ( A @ cQuicksortComplexity_2emonads_2emon___24a2 ) @ ( B @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ( ( F @ ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) )
= ( G @ ( E @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2eliftM___24a5 ) ) ) ) )
= ( D @ ( C @ ( B @ ( A @ c_24__lam__7828___24a4 ) ) ) @ ( E @ ( B @ ( A @ ( D @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_def_QuicksortComplexity.monads.liftM') ).
thf(457,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2eliftM___24a5 ) ) ) ) )
= ( D @ ( C @ ( B @ ( A @ c_24__lam__7828___24a4 ) ) ) @ ( E @ ( B @ ( A @ ( D @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__38959___24t ) ) ) ) )
<=> ! [F: $i] :
( ( B @ ( F @ t ) )
=> ! [G: $i] :
( ( C @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ ( D @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_38959') ).
thf(259,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( B @ ( F @ t ) )
=> ! [G: $i] :
( ( C @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ ( D @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__38959___24t ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__38959___24t ) ) ) ) )
=> ! [F: $i] :
( ( B @ ( F @ t ) )
=> ! [G: $i] :
( ( C @ ( G @ t ) )
=> ( G @ ( F @ ( E @ happ ) @ happ ) @ ( D @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( cQuicksortComplexity_2emonads_2eliftM2 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2eliftM2___24a7 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$adef_QuicksortComplexity.monads.liftM2_$a7') ).
thf(409,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( cQuicksortComplexity_2emonads_2eliftM2 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2eliftM2___24a7 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(65,axiom,
cB @ cType___24t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_B') ).
thf(470,plain,
cB @ cType___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(33,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__930___24t ) )
<=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( C @ ( A @ happ ) @ ( D @ ( C @ ( B @ happ ) @ happ ) @ t ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_930') ).
thf(287,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( C @ ( A @ happ ) @ ( D @ ( C @ ( B @ happ ) @ happ ) @ t ) ) ) )
=> ( B @ ( A @ c_24__type__930___24t ) ) )
& ( ( B @ ( A @ c_24__type__930___24t ) )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( C @ ( A @ happ ) @ ( D @ ( C @ ( B @ happ ) @ happ ) @ t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(63,axiom,
cM @ cQuicksortComplexity_2emonads_2eextMonad___24a1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
thf(468,plain,
cM @ cQuicksortComplexity_2emonads_2eextMonad___24a1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(26,axiom,
! [A: $i] :
( ( A @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( ( B @ ( A @ cQuicksortComplexity_2emonads_2eret___24a2 ) @ ( C @ ( B @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','QuicksortComplexity.monads.mon_runit') ).
thf(234,plain,
! [A: $i] :
( ( A @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( ( B @ ( A @ cQuicksortComplexity_2emonads_2eret___24a2 ) @ ( C @ ( B @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2726___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2726___24t ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) )
=> ( C = D ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Coq.Logic.FunctionalExtensionality.functional_extensionality') ).
thf(88,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2726___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2726___24t ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(55,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__39622___24a7 ) ) ) ) ) ) )
= ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__39635___24a6 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( E @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_lam_39622') ).
thf(443,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__39622___24a7 ) ) ) ) ) ) )
= ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__39635___24a6 ) ) ) ) ) @ ( F @ ( C @ ( B @ ( E @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__39622 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__39622___24a7 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$adef_$_lam_39622_$a7') ).
thf(321,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__39622 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__39622___24a7 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(5,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2726___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2726___24t ) ) )
=> ( ( C = D )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Coq.Logic.FunctionalExtensionality.equal_f') ).
thf(84,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2726___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__2726___24t ) ) )
=> ( ( C = D )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__55245___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_55245') ).
thf(132,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cType___24t ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__55245___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__55245___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(12,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__225___24t ) )
<=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( C @ ( A @ happ ) @ ( D @ ( C @ ( B @ happ ) @ happ ) @ t ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_225') ).
thf(116,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( C @ ( A @ happ ) @ ( D @ ( C @ ( B @ happ ) @ happ ) @ t ) ) ) )
=> ( B @ ( A @ c_24__type__225___24t ) ) )
& ( ( B @ ( A @ c_24__type__225___24t ) )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( C @ ( A @ happ ) @ ( D @ ( C @ ( B @ happ ) @ happ ) @ t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__25627___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_25627') ).
thf(334,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) )
=> ( C @ ( B @ ( A @ c_24__type__25627___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__25627___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__7897___24t ) ) ) )
<=> ! [E: $i] :
( ( B @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ ( A @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_7897') ).
thf(297,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( B @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ ( A @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__7897___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__7897___24t ) ) ) )
=> ! [E: $i] :
( ( B @ ( E @ t ) )
=> ! [F: $i] :
( ( A @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ ( A @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__55237___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_55237') ).
thf(275,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cType___24t ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__55237___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__55237___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(52,axiom,
cg @ c_24__type__176660___24t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_g') ).
thf(435,plain,
cg @ c_24__type__176660___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( cQuicksortComplexity_2emonads_2eliftM @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2eliftM___24a5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$adef_QuicksortComplexity.monads.liftM_$a5') ).
thf(97,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( cQuicksortComplexity_2emonads_2eliftM @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2eliftM___24a5 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(60,axiom,
cm @ ( cA @ ( cM @ cQuicksortComplexity_2emonads_2emon___24t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_m') ).
thf(461,plain,
cm @ ( cA @ ( cM @ cQuicksortComplexity_2emonads_2emon___24t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(38,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__460___24t ) )
<=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( C @ ( A @ happ ) @ ( D @ ( C @ ( B @ happ ) @ happ ) @ t ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_460') ).
thf(324,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( C @ ( A @ happ ) @ ( D @ ( C @ ( B @ happ ) @ happ ) @ t ) ) ) )
=> ( B @ ( A @ c_24__type__460___24t ) ) )
& ( ( B @ ( A @ c_24__type__460___24t ) )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( C @ ( A @ happ ) @ ( D @ ( C @ ( B @ happ ) @ happ ) @ t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ! [F: $i] :
( ( F @ ( C @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ! [G: $i] :
( ( G @ ( D @ ( C @ ( B @ ( A @ c_24__type__2619___24t ) ) ) ) )
=> ( ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) @ ( D @ ( C @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) )
= ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ c_24__lam__2636___24a6 ) ) ) ) ) @ ( E @ ( D @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','QuicksortComplexity.monads.mon_assoc') ).
thf(73,plain,
! [A: $i] :
( ( A @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ! [F: $i] :
( ( F @ ( C @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ! [G: $i] :
( ( G @ ( D @ ( C @ ( B @ ( A @ c_24__type__2619___24t ) ) ) ) )
=> ( ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) @ ( D @ ( C @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) )
= ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ c_24__lam__2636___24a6 ) ) ) ) ) @ ( E @ ( D @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(27,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__39805___24t ) )
<=> ! [C: $i] :
( ( C @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( C @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( D @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ ( D @ ( C @ ( A @ happ ) @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_39805') ).
thf(237,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( C @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( D @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ ( D @ ( C @ ( A @ happ ) @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) )
=> ( B @ ( A @ c_24__type__39805___24t ) ) )
& ( ( B @ ( A @ c_24__type__39805___24t ) )
=> ! [C: $i] :
( ( C @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( C @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( D @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ ( D @ ( C @ ( A @ happ ) @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(48,axiom,
! [A: $i] :
( ( A @ c_24__type__515___24t )
<=> ! [B: $i] :
( ( B @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cType___24t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_515') ).
thf(412,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cType___24t ) ) )
=> ( A @ c_24__type__515___24t ) )
& ( ( A @ c_24__type__515___24t )
=> ! [B: $i] :
( ( B @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cType___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__39870___24t ) )
<=> ! [C: $i] :
( ( C @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( C @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( D @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ ( D @ ( C @ ( A @ happ ) @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_39870') ).
thf(161,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( C @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( D @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ ( D @ ( C @ ( A @ happ ) @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) )
=> ( B @ ( A @ c_24__type__39870___24t ) ) )
& ( ( B @ ( A @ c_24__type__39870___24t ) )
=> ! [C: $i] :
( ( C @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( C @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( D @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ ( D @ ( C @ ( A @ happ ) @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( c_24__lam__39010 @ happ ) @ happ ) @ happ ) @ happ ) )
= ( D @ ( C @ ( B @ ( A @ c_24__lam__39010___24a4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$adef_$_lam_39010_$a4') ).
thf(382,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( c_24__lam__39010 @ happ ) @ happ ) @ happ ) @ happ ) )
= ( D @ ( C @ ( B @ ( A @ c_24__lam__39010___24a4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__39774___24t ) )
<=> ! [C: $i] :
( ( C @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( C @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( D @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ ( D @ ( C @ ( A @ happ ) @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_39774') ).
thf(350,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( C @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( D @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ ( D @ ( C @ ( A @ happ ) @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) )
=> ( B @ ( A @ c_24__type__39774___24t ) ) )
& ( ( B @ ( A @ c_24__type__39774___24t ) )
=> ! [C: $i] :
( ( C @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( C @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( D @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ ( D @ ( C @ ( A @ happ ) @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(11,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( c_24__lam__8018 @ happ ) @ happ ) @ happ ) )
= ( C @ ( B @ ( A @ c_24__lam__8018___24a3 ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$adef_$_lam_8018_$a3') ).
thf(113,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ ( c_24__lam__8018 @ happ ) @ happ ) @ happ ) )
= ( C @ ( B @ ( A @ c_24__lam__8018___24a3 ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2726___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( B @ ( D @ ( C @ happ ) @ t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_2726') ).
thf(76,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( B @ ( D @ ( C @ happ ) @ t ) ) )
=> ( C @ ( B @ ( A @ c_24__type__2726___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__2726___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( B @ ( D @ ( C @ happ ) @ t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(51,axiom,
cn @ ( cA @ ( cM @ cQuicksortComplexity_2emonads_2emon___24t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_n') ).
thf(434,plain,
cn @ ( cA @ ( cM @ cQuicksortComplexity_2emonads_2emon___24t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(23,axiom,
! [A: $i] :
( ( A @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
<=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ! [E: $i] :
( ( E @ ( C @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ( ( E @ ( D @ ( C @ ( A @ cQuicksortComplexity_2emonads_2emon___24a2 ) @ ( B @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ! [F: $i] :
( ( F @ ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( ( D @ ( F @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) )
= ( E @ ( F @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_def_QuicksortComplexity.monads.extMonad') ).
thf(208,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ! [E: $i] :
( ( E @ ( C @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ( ( E @ ( D @ ( C @ ( A @ cQuicksortComplexity_2emonads_2emon___24a2 ) @ ( B @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ! [F: $i] :
( ( F @ ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( ( D @ ( F @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) )
= ( E @ ( F @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ) ) ) ) ) ) )
=> ( A @ cQuicksortComplexity_2emonads_2eextMonad___24a1 ) )
& ( ( A @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ! [E: $i] :
( ( E @ ( C @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ( ( E @ ( D @ ( C @ ( A @ cQuicksortComplexity_2emonads_2emon___24a2 ) @ ( B @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ! [F: $i] :
( ( F @ ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( ( D @ ( F @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) )
= ( E @ ( F @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ c_24__type__39762___24t )
<=> ! [B: $i] :
( ( B @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( B @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ( B @ ( A @ happ ) @ cQuicksortComplexity_2emonads_2eMonad___24t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_39762') ).
thf(103,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( B @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ( B @ ( A @ happ ) @ cQuicksortComplexity_2emonads_2eMonad___24t ) ) )
=> ( A @ c_24__type__39762___24t ) )
& ( ( A @ c_24__type__39762___24t )
=> ! [B: $i] :
( ( B @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( B @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ( B @ ( A @ happ ) @ cQuicksortComplexity_2emonads_2eMonad___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( A @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( D @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ! [F: $i] :
( ( F @ ( D @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ( ( F @ ( E @ ( D @ ( A @ cQuicksortComplexity_2emonads_2emon___24a2 ) @ ( B @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ( ( E @ ( C @ ( D @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) )
= ( F @ ( C @ ( D @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','QuicksortComplexity.monads.extFlipped') ).
thf(140,plain,
! [A: $i] :
( ( A @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( A @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( D @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ! [F: $i] :
( ( F @ ( D @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ( ( F @ ( E @ ( D @ ( A @ cQuicksortComplexity_2emonads_2emon___24a2 ) @ ( B @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ( ( E @ ( C @ ( D @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) )
= ( F @ ( C @ ( D @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(1,conjecture,
( ( cm = cn )
=> ( ( cg @ ( cf @ ( cB @ ( cM @ cQuicksortComplexity_2emonads_2emon___24a2 ) @ ( cA @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ( ( cf @ ( cm @ ( cB @ ( cA @ ( cM @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) )
= ( cg @ ( cn @ ( cB @ ( cA @ ( cM @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
thf(2,negated_conjecture,
~ ( ( cm = cn )
=> ( ( cg @ ( cf @ ( cB @ ( cM @ cQuicksortComplexity_2emonads_2emon___24a2 ) @ ( cA @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ( ( cf @ ( cm @ ( cB @ ( cA @ ( cM @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) )
= ( cg @ ( cn @ ( cB @ ( cA @ ( cM @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(66,plain,
~ ( ( cm = cn )
=> ( ( cg @ ( cf @ ( cB @ ( cM @ cQuicksortComplexity_2emonads_2emon___24a2 ) @ ( cA @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ( ( cf @ ( cm @ ( cB @ ( cA @ ( cM @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) )
= ( cg @ ( cn @ ( cB @ ( cA @ ( cM @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__2619___24t ) ) ) ) )
<=> ! [F: $i] :
( ( C @ ( F @ t ) )
=> ( F @ ( E @ happ ) @ ( D @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_2619') ).
thf(251,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( C @ ( F @ t ) )
=> ( F @ ( E @ happ ) @ ( D @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__2619___24t ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__2619___24t ) ) ) ) )
=> ! [F: $i] :
( ( C @ ( F @ t ) )
=> ( F @ ( E @ happ ) @ ( D @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(22,axiom,
! [A: $i] :
( ( A @ c_24__type__25186___24t )
<=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ( B @ ( C @ ( B @ ( A @ happ ) @ happ ) @ t ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_25186') ).
thf(198,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ( B @ ( C @ ( B @ ( A @ happ ) @ happ ) @ t ) ) ) )
=> ( A @ c_24__type__25186___24t ) )
& ( ( A @ c_24__type__25186___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ( B @ ( C @ ( B @ ( A @ happ ) @ happ ) @ t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2eliftM2___24a7 ) ) ) ) ) ) )
= ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__39622___24a6 ) ) ) ) ) @ ( F @ ( C @ ( A @ ( E @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_def_QuicksortComplexity.monads.liftM2') ).
thf(462,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2eliftM2___24a7 ) ) ) ) ) ) )
= ( G @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__39622___24a6 ) ) ) ) ) @ ( F @ ( C @ ( A @ ( E @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(50,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__25650___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_25650') ).
thf(426,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) )
=> ( C @ ( B @ ( A @ c_24__type__25650___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__25650___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__10375___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_10375') ).
thf(374,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) )
=> ( C @ ( B @ ( A @ c_24__type__10375___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__10375___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__177004___24t ) ) ) ) ) ) )
<=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_177004') ).
thf(342,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ happ ) @ cType___24t ) )
=> ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__177004___24t ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__177004___24t ) ) ) ) ) ) )
=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__39622 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__39622___24a6 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$adef_$_lam_39622_$a6') ).
thf(175,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__39622 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__39622___24a6 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(56,axiom,
! [A: $i] :
( ( A @ c_24__type__176660___24t )
<=> ! [B: $i] :
( ( B @ cA___24t )
=> ( B @ ( A @ happ ) @ ( cB @ ( cM @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_176660') ).
thf(446,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cA___24t )
=> ( B @ ( A @ happ ) @ ( cB @ ( cM @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) )
=> ( A @ c_24__type__176660___24t ) )
& ( ( A @ c_24__type__176660___24t )
=> ! [B: $i] :
( ( B @ cA___24t )
=> ( B @ ( A @ happ ) @ ( cB @ ( cM @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(16,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
<=> ! [E: $i] :
( ( B @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ ( C @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_759') ).
thf(143,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( B @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ ( C @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__759___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__759___24t ) ) ) )
=> ! [E: $i] :
( ( B @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ ( C @ ( A @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__lam__8018___24a3 ) ) )
= ( B @ cCoq_2eInit_2eDatatypes_2elist___24a1 @ ( A @ cQuicksortComplexity_2emonads_2emon___24a2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_lam_8018') ).
thf(465,plain,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__lam__8018___24a3 ) ) )
= ( B @ cCoq_2eInit_2eDatatypes_2elist___24a1 @ ( A @ cQuicksortComplexity_2emonads_2emon___24a2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( cQuicksortComplexity_2emonads_2ebind__map @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind__map___24a5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$adef_QuicksortComplexity.monads.bind_map_$a5') ).
thf(231,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ ( cQuicksortComplexity_2emonads_2ebind__map @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( E @ ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind__map___24a5 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_def_QuicksortComplexity.util.ext_eq') ).
thf(151,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__185961___24t ) ) ) ) ) ) )
<=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_185961') ).
thf(190,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ happ ) @ cType___24t ) )
=> ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__185961___24t ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__185961___24t ) ) ) ) ) ) )
=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(49,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( ( B = C )
=> ( C = B ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','Coq.Logic.EqdepFacts.internal_eq_sym_internal') ).
thf(422,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( ( B = C )
=> ( C = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(13,axiom,
! [A: $i] :
( ( A @ c_24__type__176660___24t )
<=> ( c_24__type__176660 @ ( A @ t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$tdef_$_type_176660') ).
thf(126,plain,
! [A: $i] :
( ( ( c_24__type__176660 @ ( A @ t ) )
=> ( A @ c_24__type__176660___24t ) )
& ( ( A @ c_24__type__176660___24t )
=> ( c_24__type__176660 @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(54,axiom,
! [A: $i] :
( ( A @ cA___24t )
<=> ( cA @ ( A @ t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$tdef_A') ).
thf(437,plain,
! [A: $i] :
( ( ( cA @ ( A @ t ) )
=> ( A @ cA___24t ) )
& ( ( A @ cA___24t )
=> ( cA @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__39635 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__39635___24a6 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$adef_$_lam_39635_$a6') ).
thf(94,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__39635 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__39635___24a6 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(32,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( B = C )
=> ( ( C = D )
=> ( B = D ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','QuicksortComplexity.util.eq_trans') ).
thf(283,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( ( B = C )
=> ( ( C = D )
=> ( B = D ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(46,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__39835___24t ) )
<=> ! [C: $i] :
( ( C @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( C @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( D @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ ( D @ ( C @ ( A @ happ ) @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_39835') ).
thf(395,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( ( C @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( C @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( D @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ ( D @ ( C @ ( A @ happ ) @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) )
=> ( B @ ( A @ c_24__type__39835___24t ) ) )
& ( ( B @ ( A @ c_24__type__39835___24t ) )
=> ! [C: $i] :
( ( C @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ( ( C @ cQuicksortComplexity_2emonads_2eextMonad___24a1 )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( D @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) )
=> ( E @ ( D @ ( C @ ( B @ happ ) @ happ ) @ happ ) @ ( D @ ( C @ ( A @ happ ) @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ c_24__type__987___24t )
<=> ! [B: $i] :
( ( B @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( C @ ( B @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_987') ).
thf(178,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( C @ ( B @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) )
=> ( A @ c_24__type__987___24t ) )
& ( ( A @ c_24__type__987___24t )
=> ! [B: $i] :
( ( B @ cQuicksortComplexity_2emonads_2eMonad___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( C @ ( B @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(64,axiom,
cM @ cQuicksortComplexity_2emonads_2eMonad___24t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_M') ).
thf(469,plain,
cM @ cQuicksortComplexity_2emonads_2eMonad___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind__map___24a5 ) ) ) ) )
= ( D @ ( C @ ( B @ ( A @ c_24__lam__39010___24a4 ) ) ) @ ( E @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_def_QuicksortComplexity.monads.bind_map') ).
thf(454,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind__map___24a5 ) ) ) ) )
= ( D @ ( C @ ( B @ ( A @ c_24__lam__39010___24a4 ) ) ) @ ( E @ ( C @ ( B @ ( A @ cQuicksortComplexity_2emonads_2ebind___24a5 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(42,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__39727___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( B @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ ( A @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_39727') ).
thf(364,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( B @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ ( A @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__39727___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__39727___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ! [F: $i] :
( ( B @ ( F @ t ) )
=> ( F @ ( E @ ( D @ happ ) @ happ ) @ ( A @ ( C @ cQuicksortComplexity_2emonads_2emon___24t ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( c_24__lam__7828 @ happ ) @ happ ) @ happ ) @ happ ) )
= ( D @ ( C @ ( B @ ( A @ c_24__lam__7828___24a4 ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$adef_$_lam_7828_$a4') ).
thf(100,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ ( c_24__lam__7828 @ happ ) @ happ ) @ happ ) @ happ ) )
= ( D @ ( C @ ( B @ ( A @ c_24__lam__7828___24a4 ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(510,plain,
$false,
inference(e,[status(thm)],[269,385,436,460,228,307,317,457,259,409,470,287,468,234,88,443,321,84,132,116,334,297,275,435,97,461,324,73,237,412,161,382,350,113,76,434,208,103,140,66,251,198,462,426,374,342,175,446,143,465,231,151,190,422,126,437,94,283,395,178,469,454,364,100]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV666+1 : TPTP v9.3.1. Released v9.3.0.
% 0.00/0.08 % Command : java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.15/0.41 % Computer : n020.cluster.edu
% 0.15/0.41 % Model : x86_64 x86_64
% 0.15/0.41 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.15/0.41 % Memory : 8046.5625MB
% 0.15/0.41 % OS : Linux 6.8.0-71-generic
% 0.15/0.41 % CPULimit : 300
% 0.15/0.41 % WCLimit : 300
% 0.15/0.41 % DateTime : Sat Sep 26 11:35:18 UTC 2026
% 0.15/0.42 % CPUTime :
% 0.15/0.42 Running java -Xss128m -Xmx2g -Xms1g -jar /export/starexec/sandbox2/solver/bin/leo3.jar /export/starexec/sandbox2/benchmark/theBenchmark.p -t 300 -p --atp eprover=/export/starexec/sandbox2/solver/bin/externals/eprover --instantiate 39
% 0.86/0.99 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 3.66/1.78 % [INFO] Parsing done (787ms).
% 3.66/1.79 % [INFO] Running in sequential loop mode.
% 4.85/2.19 % [INFO] eprover registered as external prover.
% 4.85/2.19 % [INFO] Scanning for conjecture ...
% 6.06/2.54 % [INFO] Found a conjecture (or negated_conjecture) and 3535 axioms. Running axiom selection ...
% 7.39/2.82 % [INFO] Axiom selection finished. Selected 63 axioms (removed 3472 axioms).
% 7.87/2.98 % [INFO] Problem is first-order (TPTP FOF).
% 7.87/3.00 % [INFO] Type checking passed.
% 7.87/3.01 % [CONFIG] Using configuration: timeout(300) with strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>. Searching for refutation ...
% 13.77/4.32 % External prover 'e' found a proof!
% 13.77/4.32 % [INFO] Killing All external provers ...
% 13.77/4.32 % Time passed: 3766ms (effective reasoning time: 2524ms)
% 13.77/4.32 % Solved by strategy<name(default),share(1.0),primSubst(3),sos(false),unifierCount(4),uniDepth(8),boolExt(true),choice(true),renaming(true),funcspec(false), domConstr(0),specialInstances(39),restrictUniAttempts(true),termOrdering(CPO)>
% 13.77/4.33 % Axioms used in derivation (63): $adef_$_lam_39622_$a7, $_typeof_B, $adef_QuicksortComplexity.monads.liftM_$a5, $_type_686, $_type_176660, $_type_515, $_type_55237, QuicksortComplexity.monads.mon_runit, $_typeof_m, $_type_38537, $_typeof_f, $_type_10375, e, Coq.Logic.FunctionalExtensionality.functional_extensionality, $_def_QuicksortComplexity.util.ext_eq, QuicksortComplexity.monads.mon_assoc, $_type_39774, $_type_39835, $_def_QuicksortComplexity.monads.bind_map, $adef_$_lam_39635_$a6, $_type_987, $_type_39805, $_typeof_g, $adef_$_lam_39010_$a4, $_def_QuicksortComplexity.monads.liftM2, $_lam_39622, $_type_7897, $_type_39727, $_def_QuicksortComplexity.monads.liftM, $_type_225, QuicksortComplexity.util.ext_eq_rw, $_type_185961, $adef_$_lam_39622_$a6, $_type_460, $tdef_$_type_176660, $_type_38959, $tdef_A, $adef_$_lam_8018_$a3, $_lam_8018, $_type_25650, $_typeof_A, $_type_2619, $adef_QuicksortComplexity.monads.bind_map_$a5, $_typeof_n, $_type_930, $_type_25627, QuicksortComplexity.util.eq_trans, Coq.Logic.FunctionalExtensionality.equal_f, $_type_759, $_typeof_M, Coq.Logic.EqdepFacts.internal_eq_sym_internal, $_type_39762, $_type_25186, QuicksortComplexity.monads.extFlipped, $_def_QuicksortComplexity.monads.extMonad, $_type_39870, QuicksortComplexity.monads.bind_eqq, $adef_$_lam_7828_$a4, $adef_QuicksortComplexity.monads.liftM2_$a7, $_type_2726, $_type_177004, $tdef_QuicksortComplexity.monads.mon, $_type_55245
% 13.77/4.33 % No. of inferences in proof: 130
% 13.77/4.33 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3766 ms resp. 2524 ms w/o parsing
% 14.20/4.46 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 14.20/4.46 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------