%------------------------------------------------------------------------------
% File : Leo-III---1.8.0
% Problem : SEV660+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 : n004.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 12.00s 4.01s
% Output : Refutation 12.59s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 47
% Syntax : Number of formulae : 96 ( 27 unt; 0 typ; 0 def)
% Number of atoms : 402 ( 46 equ; 0 cnn)
% Maximal formula atoms : 16 ( 4 avg)
% Number of connectives : 1577 ( 2 ~; 0 |; 25 &;1269 @)
% ( 25 <=>; 256 =>; 0 <=; 0 <~>)
% Maximal formula depth : 25 ( 10 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 0 ( 0 >; 0 *; 0 +; 0 <<)
% Number of symbols : 46 ( 44 usr; 11 con; 0-7 aty)
% Number of variables : 369 ( 0 ^; 369 !; 0 ?; 369 :)
% 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(cmonads_2emon___24a2_decl,type,
cmonads_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(cmonads_2ebind___24a5_decl,type,
cmonads_2ebind___24a5: $i > $i > $i > $i > $i > $i ).
thf(cType___24t_decl,type,
cType___24t: $i > $o ).
thf(c_24__type__58___24t_decl,type,
c_24__type__58___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__203_decl,type,
c_24__lam__203: $i ).
thf(c_24__lam__203___24a6_decl,type,
c_24__lam__203___24a6: $i > $i > $i > $i > $i > $i > $i ).
thf(c_24__type__901___24t_decl,type,
c_24__type__901___24t: $i > $o ).
thf(cmonads_2emon_decl,type,
cmonads_2emon: $i ).
thf(c_24__type__376___24t_decl,type,
c_24__type__376___24t: $i > $i > $o ).
thf(c_24__type__8323___24t_decl,type,
c_24__type__8323___24t: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(cmonads_2eMonad___24t_decl,type,
cmonads_2eMonad___24t: $i > $o ).
thf(cmonads_2emon___24t_decl,type,
cmonads_2emon___24t: $i > $i > $i > $o ).
thf(c_24__type__172___24t_decl,type,
c_24__type__172___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__186___24t_decl,type,
c_24__type__186___24t: $i > $i > $i > $i > $i > $o ).
thf(c_24__type__172___24a3_decl,type,
c_24__type__172___24a3: $i > $i > $i > $i ).
thf(c_24__type__604___24t_decl,type,
c_24__type__604___24t: $i > $i > $o ).
thf(c_24__type__1___24t_decl,type,
c_24__type__1___24t: $i > $o ).
thf(c_24__type__1_decl,type,
c_24__type__1: $i ).
thf(c_24__type__433___24t_decl,type,
c_24__type__433___24t: $i > $o ).
thf(c_24__type__8351___24t_decl,type,
c_24__type__8351___24t: $i > $i > $i > $i > $i > $i > $i > $o ).
thf(c_24__lam__203___24a7_decl,type,
c_24__lam__203___24a7: $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_24__type__981___24t_decl,type,
c_24__type__981___24t: $i > $i > $o ).
thf(c_24__type__14909___24t_decl,type,
c_24__type__14909___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__846___24t_decl,type,
c_24__type__846___24t: $i > $i > $o ).
thf(c_24__type__2729___24t_decl,type,
c_24__type__2729___24t: $i > $i > $i > $o ).
thf(cmonads_2eret___24a3_decl,type,
cmonads_2eret___24a3: $i > $i > $i > $i ).
thf(cmonads_2eret___24a2_decl,type,
cmonads_2eret___24a2: $i > $i > $i ).
thf(c_24__type__15157___24t_decl,type,
c_24__type__15157___24t: $i > $i > $i > $o ).
thf(c_24__type__15180___24t_decl,type,
c_24__type__15180___24t: $i > $i > $i > $o ).
thf(c_24__type__74___24t_decl,type,
c_24__type__74___24t: $i > $o ).
thf(c_24__type__14917___24t_decl,type,
c_24__type__14917___24t: $i > $i > $i > $i > $o ).
thf(c_24__type__672___24t_decl,type,
c_24__type__672___24t: $i > $o ).
thf(cA___24t_decl,type,
cA___24t: $i > $o ).
thf(cmonads_2eextMonad___24a1_decl,type,
cmonads_2eextMonad___24a1: $i > $o ).
thf(9,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__8323___24t ) ) ) ) ) ) )
<=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_8323') ).
thf(88,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__8323___24t ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__8323___24t ) ) ) ) ) ) )
=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(36,axiom,
! [A: $i] :
( ( A @ c_24__type__672___24t )
<=> ! [B: $i] :
( ( B @ cmonads_2eMonad___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( C @ ( B @ cmonads_2emon___24t ) ) )
=> ! [F: $i] :
( ( F @ ( D @ ( C @ ( B @ c_24__type__172___24t ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ ( D @ ( B @ cmonads_2emon___24t ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_672') ).
thf(276,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cmonads_2eMonad___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( C @ ( B @ cmonads_2emon___24t ) ) )
=> ! [F: $i] :
( ( F @ ( D @ ( C @ ( B @ c_24__type__172___24t ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ ( D @ ( B @ cmonads_2emon___24t ) ) ) ) ) ) ) )
=> ( A @ c_24__type__672___24t ) )
& ( ( A @ c_24__type__672___24t )
=> ! [B: $i] :
( ( B @ cmonads_2eMonad___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( C @ ( B @ cmonads_2emon___24t ) ) )
=> ! [F: $i] :
( ( F @ ( D @ ( C @ ( B @ c_24__type__172___24t ) ) ) )
=> ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ ( D @ ( B @ cmonads_2emon___24t ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(3,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__58___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__58___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(56,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__58___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__58___24t ) ) )
=> ( ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) )
=> ( C = D ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__14909___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_14909') ).
thf(185,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__14909___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__14909___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(19,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(157,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)],[19]) ).
thf(8,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__376___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_376') ).
thf(78,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__376___24t ) ) )
& ( ( B @ ( A @ c_24__type__376___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)],[8]) ).
thf(26,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cmonads_2emon @ happ ) @ happ ) )
= ( B @ ( A @ cmonads_2emon___24a2 ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$adef_monads.mon_$a2') ).
thf(211,plain,
! [A: $i,B: $i] :
( ( B @ ( A @ ( cmonads_2emon @ happ ) @ happ ) )
= ( B @ ( A @ cmonads_2emon___24a2 ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(38,axiom,
cA @ cType___24t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_A') ).
thf(293,plain,
cA @ cType___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(33,axiom,
! [A: $i] :
( ( A @ c_24__type__74___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_74') ).
thf(252,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( B @ ( C @ t ) )
=> ( B @ ( C @ ( B @ ( A @ happ ) @ happ ) @ t ) ) ) )
=> ( A @ c_24__type__74___24t ) )
& ( ( A @ c_24__type__74___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)],[33]) ).
thf(14,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__604___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_604') ).
thf(118,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__604___24t ) ) )
& ( ( B @ ( A @ c_24__type__604___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)],[14]) ).
thf(29,axiom,
! [A: $i] :
( ( A @ cmonads_2eMonad___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( B @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( C @ ( B @ ( A @ c_24__type__172___24t ) ) ) )
=> ( ( E @ ( D @ ( B @ ( A @ cmonads_2eret___24a3 ) ) @ ( C @ ( B @ ( A @ cmonads_2ebind___24a5 ) ) ) ) )
= ( D @ ( E @ happ ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','monads.mon_lunit') ).
thf(230,plain,
! [A: $i] :
( ( A @ cmonads_2eMonad___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( B @ ( D @ t ) )
=> ! [E: $i] :
( ( E @ ( C @ ( B @ ( A @ c_24__type__172___24t ) ) ) )
=> ( ( E @ ( D @ ( B @ ( A @ cmonads_2eret___24a3 ) ) @ ( C @ ( B @ ( A @ cmonads_2ebind___24a5 ) ) ) ) )
= ( D @ ( E @ happ ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__172___24t ) ) ) )
<=> ( C @ ( B @ ( A @ c_24__type__172___24a3 ) ) @ ( D @ t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$tdef_$_type_172') ).
thf(112,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( C @ ( B @ ( A @ c_24__type__172___24a3 ) ) @ ( D @ t ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__172___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__172___24t ) ) ) )
=> ( C @ ( B @ ( A @ c_24__type__172___24a3 ) ) @ ( D @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(11,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(99,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)],[11]) ).
thf(21,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__981___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_981') ).
thf(171,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__981___24t ) ) )
& ( ( B @ ( A @ c_24__type__981___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)],[21]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__186___24t ) ) ) ) )
<=> ! [F: $i] :
( ( C @ ( F @ t ) )
=> ( F @ ( E @ happ ) @ ( D @ ( A @ cmonads_2emon___24t ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_186') ).
thf(214,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ! [F: $i] :
( ( C @ ( F @ t ) )
=> ( F @ ( E @ happ ) @ ( D @ ( A @ cmonads_2emon___24t ) ) ) )
=> ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__186___24t ) ) ) ) ) )
& ( ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__186___24t ) ) ) ) )
=> ! [F: $i] :
( ( C @ ( F @ t ) )
=> ( F @ ( E @ happ ) @ ( D @ ( A @ cmonads_2emon___24t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__58___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( B @ ( D @ ( C @ happ ) @ t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_58') ).
thf(62,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( B @ ( D @ ( C @ happ ) @ t ) ) )
=> ( C @ ( B @ ( A @ c_24__type__58___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__58___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( B @ ( D @ ( C @ happ ) @ t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(28,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__2729___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_2729') ).
thf(222,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) )
=> ( C @ ( B @ ( A @ c_24__type__2729___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__2729___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(45,axiom,
! [A: $i] :
( ( A @ c_24__type__1___24t )
<=> ! [B: $i] :
( ( B @ cA___24t )
=> ( B @ ( A @ happ ) @ ( cB @ ( cM @ cmonads_2emon___24t ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_1') ).
thf(307,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cA___24t )
=> ( B @ ( A @ happ ) @ ( cB @ ( cM @ cmonads_2emon___24t ) ) ) )
=> ( A @ c_24__type__1___24t ) )
& ( ( A @ c_24__type__1___24t )
=> ! [B: $i] :
( ( B @ cA___24t )
=> ( B @ ( A @ happ ) @ ( cB @ ( cM @ cmonads_2emon___24t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(37,axiom,
cf @ c_24__type__1___24t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_f') ).
thf(292,plain,
cf @ c_24__type__1___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(30,axiom,
! [A: $i] :
( ( A @ cmonads_2eMonad___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ cmonads_2emon___24t ) ) )
=> ( ( B @ ( A @ cmonads_2eret___24a2 ) @ ( C @ ( B @ ( B @ ( A @ cmonads_2ebind___24a5 ) ) ) ) )
= C ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','monads.mon_runit') ).
thf(233,plain,
! [A: $i] :
( ( A @ cmonads_2eMonad___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ cmonads_2emon___24t ) ) )
=> ( ( B @ ( A @ cmonads_2eret___24a2 ) @ ( C @ ( B @ ( B @ ( A @ cmonads_2ebind___24a5 ) ) ) ) )
= C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(25,axiom,
! [A: $i,B: $i] :
( ( B @ ( A @ c_24__type__846___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_846') ).
thf(201,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__846___24t ) ) )
& ( ( B @ ( A @ c_24__type__846___24t ) )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( C @ ( A @ happ ) @ ( D @ ( C @ ( B @ happ ) @ happ ) @ t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(40,axiom,
cM @ cmonads_2eMonad___24t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_M') ).
thf(297,plain,
cM @ cmonads_2eMonad___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__203 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__203___24a6 ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$adef_$_lam_203_$a6') ).
thf(70,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__203 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__203___24a6 ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(12,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__58___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__58___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(109,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__58___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__58___24t ) ) )
=> ( ( D @ ( C @ ( B @ ( A @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(7,axiom,
cmonads_2emon @ c_24__type__901___24t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_monads.mon') ).
thf(77,plain,
cmonads_2emon @ c_24__type__901___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__172___24t ) ) ) )
<=> ! [E: $i] :
( ( B @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ ( C @ ( A @ cmonads_2emon___24t ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_172') ).
thf(193,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ! [E: $i] :
( ( B @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ ( C @ ( A @ cmonads_2emon___24t ) ) ) )
=> ( D @ ( C @ ( B @ ( A @ c_24__type__172___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__172___24t ) ) ) )
=> ! [E: $i] :
( ( B @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ ( C @ ( A @ cmonads_2emon___24t ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(10,axiom,
! [A: $i] :
( ( A @ cmonads_2eMonad___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( B @ ( A @ cmonads_2emon___24t ) ) )
=> ! [F: $i] :
( ( F @ ( C @ ( B @ ( A @ c_24__type__172___24t ) ) ) )
=> ! [G: $i] :
( ( G @ ( D @ ( C @ ( B @ ( A @ c_24__type__186___24t ) ) ) ) )
=> ( ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ cmonads_2ebind___24a5 ) ) ) ) @ ( D @ ( C @ ( A @ cmonads_2ebind___24a5 ) ) ) ) )
= ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ c_24__lam__203___24a6 ) ) ) ) ) @ ( E @ ( D @ ( B @ ( A @ cmonads_2ebind___24a5 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','monads.mon_assoc') ).
thf(96,plain,
! [A: $i] :
( ( A @ cmonads_2eMonad___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( D @ cType___24t )
=> ! [E: $i] :
( ( E @ ( B @ ( A @ cmonads_2emon___24t ) ) )
=> ! [F: $i] :
( ( F @ ( C @ ( B @ ( A @ c_24__type__172___24t ) ) ) )
=> ! [G: $i] :
( ( G @ ( D @ ( C @ ( B @ ( A @ c_24__type__186___24t ) ) ) ) )
=> ( ( G @ ( F @ ( E @ ( C @ ( B @ ( A @ cmonads_2ebind___24a5 ) ) ) ) @ ( D @ ( C @ ( A @ cmonads_2ebind___24a5 ) ) ) ) )
= ( G @ ( F @ ( D @ ( C @ ( B @ ( A @ c_24__lam__203___24a6 ) ) ) ) ) @ ( E @ ( D @ ( B @ ( A @ cmonads_2ebind___24a5 ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(16,axiom,
! [A: $i] :
( ( A @ c_24__type__433___24t )
<=> ! [B: $i] :
( ( B @ cmonads_2eMonad___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( C @ ( B @ cmonads_2emon___24t ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_433') ).
thf(134,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cmonads_2eMonad___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( C @ ( B @ cmonads_2emon___24t ) ) ) ) ) )
=> ( A @ c_24__type__433___24t ) )
& ( ( A @ c_24__type__433___24t )
=> ! [B: $i] :
( ( B @ cmonads_2eMonad___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( C @ ( D @ t ) )
=> ( D @ ( C @ ( B @ ( A @ happ ) @ happ ) @ happ ) @ ( C @ ( B @ cmonads_2emon___24t ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(6,axiom,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__58___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__58___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(73,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ ( B @ ( A @ c_24__type__58___24t ) ) )
=> ! [D: $i] :
( ( D @ ( B @ ( A @ c_24__type__58___24t ) ) )
=> ( ( C = D )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( ( E @ ( C @ happ ) )
= ( E @ ( D @ happ ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(15,axiom,
! [A: $i] :
( ( A @ c_24__type__1___24t )
<=> ( c_24__type__1 @ ( A @ t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$tdef_$_type_1') ).
thf(128,plain,
! [A: $i] :
( ( ( c_24__type__1 @ ( A @ t ) )
=> ( A @ c_24__type__1___24t ) )
& ( ( A @ c_24__type__1___24t )
=> ( c_24__type__1 @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(32,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__15180___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_15180') ).
thf(244,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) )
=> ( C @ ( B @ ( A @ c_24__type__15180___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__15180___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(41,axiom,
cg @ c_24__type__1___24t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_g') ).
thf(298,plain,
cg @ c_24__type__1___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(20,axiom,
! [A: $i] :
( ( A @ c_24__type__901___24t )
<=> ! [B: $i] :
( ( B @ cmonads_2eMonad___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cType___24t ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_901') ).
thf(161,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cmonads_2eMonad___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cType___24t ) ) )
=> ( A @ c_24__type__901___24t ) )
& ( ( A @ c_24__type__901___24t )
=> ! [B: $i] :
( ( B @ cmonads_2eMonad___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ( C @ ( B @ ( A @ happ ) @ happ ) @ cType___24t ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(1,conjecture,
( ( cm = cn )
=> ( ( cg @ ( cf @ ( cB @ ( cM @ cmonads_2emon___24a2 ) @ ( cA @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ( ( cf @ ( cm @ ( cB @ ( cA @ ( cM @ cmonads_2ebind___24a5 ) ) ) ) )
= ( cg @ ( cn @ ( cB @ ( cA @ ( cM @ cmonads_2ebind___24a5 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','_HAMMER_GOAL') ).
thf(2,negated_conjecture,
~ ( ( cm = cn )
=> ( ( cg @ ( cf @ ( cB @ ( cM @ cmonads_2emon___24a2 ) @ ( cA @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ( ( cf @ ( cm @ ( cB @ ( cA @ ( cM @ cmonads_2ebind___24a5 ) ) ) ) )
= ( cg @ ( cn @ ( cB @ ( cA @ ( cM @ cmonads_2ebind___24a5 ) ) ) ) ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(49,plain,
~ ( ( cm = cn )
=> ( ( cg @ ( cf @ ( cB @ ( cM @ cmonads_2emon___24a2 ) @ ( cA @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ( ( cf @ ( cm @ ( cB @ ( cA @ ( cM @ cmonads_2ebind___24a5 ) ) ) ) )
= ( cg @ ( cn @ ( cB @ ( cA @ ( cM @ cmonads_2ebind___24a5 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(47,axiom,
cM @ cmonads_2eextMonad___24a1,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p',e) ).
thf(335,plain,
cM @ cmonads_2eextMonad___24a1,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ c_24__type__15157___24t ) ) )
<=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_15157') ).
thf(236,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) )
=> ( C @ ( B @ ( A @ c_24__type__15157___24t ) ) ) )
& ( ( C @ ( B @ ( A @ c_24__type__15157___24t ) ) )
=> ! [D: $i] :
( ( A @ ( D @ t ) )
=> ( D @ ( C @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(22,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(181,plain,
! [A: $i] :
( ( A @ cType___24t )
=> ! [B: $i] :
( ( A @ ( B @ t ) )
=> ! [C: $i] :
( ( A @ ( C @ t ) )
=> ( ( B = C )
=> ( C = B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(44,axiom,
cm @ ( cA @ ( cM @ cmonads_2emon___24t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_m') ).
thf(306,plain,
cm @ ( cA @ ( cM @ cmonads_2emon___24t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(42,axiom,
cn @ ( cA @ ( cM @ cmonads_2emon___24t ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_n') ).
thf(299,plain,
cn @ ( cA @ ( cM @ cmonads_2emon___24t ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(48,axiom,
cB @ cType___24t,
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_typeof_B') ).
thf(336,plain,
cB @ cType___24t,
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(18,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ ( c_24__lam__203 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__203___24a7 ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$adef_$_lam_203_$a7') ).
thf(154,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__203 @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) @ happ ) )
= ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__203___24a7 ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(43,axiom,
! [A: $i] :
( ( A @ cA___24t )
<=> ( cA @ ( A @ t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$tdef_A') ).
thf(300,plain,
! [A: $i] :
( ( ( cA @ ( A @ t ) )
=> ( A @ cA___24t ) )
& ( ( A @ cA___24t )
=> ( cA @ ( A @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(46,axiom,
! [A: $i] :
( ( A @ cmonads_2eextMonad___24a1 )
<=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__172___24t ) ) ) )
=> ! [E: $i] :
( ( E @ ( C @ ( B @ ( A @ c_24__type__172___24t ) ) ) )
=> ( ( E @ ( D @ ( C @ ( A @ cmonads_2emon___24a2 ) @ ( B @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ! [F: $i] :
( ( F @ ( B @ ( A @ cmonads_2emon___24t ) ) )
=> ( ( D @ ( F @ ( C @ ( B @ ( A @ cmonads_2ebind___24a5 ) ) ) ) )
= ( E @ ( F @ ( C @ ( B @ ( A @ cmonads_2ebind___24a5 ) ) ) ) ) ) ) ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_def_monads.extMonad') ).
thf(315,plain,
! [A: $i] :
( ( ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__172___24t ) ) ) )
=> ! [E: $i] :
( ( E @ ( C @ ( B @ ( A @ c_24__type__172___24t ) ) ) )
=> ( ( E @ ( D @ ( C @ ( A @ cmonads_2emon___24a2 ) @ ( B @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ! [F: $i] :
( ( F @ ( B @ ( A @ cmonads_2emon___24t ) ) )
=> ( ( D @ ( F @ ( C @ ( B @ ( A @ cmonads_2ebind___24a5 ) ) ) ) )
= ( E @ ( F @ ( C @ ( B @ ( A @ cmonads_2ebind___24a5 ) ) ) ) ) ) ) ) ) ) ) )
=> ( A @ cmonads_2eextMonad___24a1 ) )
& ( ( A @ cmonads_2eextMonad___24a1 )
=> ! [B: $i] :
( ( B @ cType___24t )
=> ! [C: $i] :
( ( C @ cType___24t )
=> ! [D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__172___24t ) ) ) )
=> ! [E: $i] :
( ( E @ ( C @ ( B @ ( A @ c_24__type__172___24t ) ) ) )
=> ( ( E @ ( D @ ( C @ ( A @ cmonads_2emon___24a2 ) @ ( B @ cQuicksortComplexity_2eutil_2eext__eq___24a4 ) ) ) )
=> ! [F: $i] :
( ( F @ ( B @ ( A @ cmonads_2emon___24t ) ) )
=> ( ( D @ ( F @ ( C @ ( B @ ( A @ cmonads_2ebind___24a5 ) ) ) ) )
= ( E @ ( F @ ( C @ ( B @ ( A @ cmonads_2ebind___24a5 ) ) ) ) ) ) ) ) ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( C @ ( B @ ( A @ cmonads_2emon___24t ) ) )
<=> ( B @ ( A @ cmonads_2emon___24a2 ) @ ( C @ t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$tdef_monads.mon') ).
thf(262,plain,
! [A: $i,B: $i,C: $i] :
( ( ( B @ ( A @ cmonads_2emon___24a2 ) @ ( C @ t ) )
=> ( C @ ( B @ ( A @ cmonads_2emon___24t ) ) ) )
& ( ( C @ ( B @ ( A @ cmonads_2emon___24t ) ) )
=> ( B @ ( A @ cmonads_2emon___24a2 ) @ ( C @ t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(17,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__8351___24t ) ) ) ) ) ) )
<=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_8351') ).
thf(146,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__8351___24t ) ) ) ) ) ) ) )
& ( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__type__8351___24t ) ) ) ) ) ) )
=> ! [H: $i] :
( ( A @ ( H @ t ) )
=> ( H @ ( G @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G @ ( F @ ( E @ ( D @ ( C @ ( B @ ( A @ c_24__lam__203___24a7 ) ) ) ) ) ) )
= ( F @ ( G @ ( E @ happ ) @ ( D @ ( C @ ( A @ cmonads_2ebind___24a5 ) ) ) ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_lam_203') ).
thf(294,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__203___24a7 ) ) ) ) ) ) )
= ( F @ ( G @ ( E @ happ ) @ ( D @ ( C @ ( A @ cmonads_2ebind___24a5 ) ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( D @ ( C @ ( B @ ( A @ c_24__type__14917___24t ) ) ) )
<=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cType___24t ) ) ),
file('/export/starexec/sandbox2/benchmark/theBenchmark.p','$_type_14917') ).
thf(268,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__14917___24t ) ) ) ) )
& ( ( D @ ( C @ ( B @ ( A @ c_24__type__14917___24t ) ) ) )
=> ! [E: $i] :
( ( A @ ( E @ t ) )
=> ( E @ ( D @ happ ) @ cType___24t ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(454,plain,
$false,
inference(e,[status(thm)],[88,276,56,185,157,78,211,293,252,118,230,112,99,171,214,62,222,307,292,233,201,297,70,109,77,193,96,134,73,128,244,298,161,49,335,236,181,306,299,336,154,300,315,262,146,294,268]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.03 % Problem : SEV660+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
% 0.14/0.55 % Computer : n004.cluster.edu
% 0.14/0.55 % Model : x86_64 x86_64
% 0.14/0.55 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.55 % Memory : 8046.5625MB
% 0.14/0.55 % OS : Linux 6.8.0-71-generic
% 0.14/0.55 % CPULimit : 300
% 0.14/0.55 % WCLimit : 300
% 0.14/0.55 % DateTime : Sat Sep 26 11:32:54 UTC 2026
% 0.14/0.56 % CPUTime :
% 0.14/0.56 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
% 0.18/0.85 % [INFO] Parsing problem /export/starexec/sandbox2/benchmark/theBenchmark.p ...
% 2.14/1.27 % [INFO] Parsing done (420ms).
% 2.14/1.29 % [INFO] Running in sequential loop mode.
% 3.83/1.70 % [INFO] eprover registered as external prover.
% 3.83/1.71 % [INFO] Scanning for conjecture ...
% 4.54/2.00 % [INFO] Found a conjecture (or negated_conjecture) and 2689 axioms. Running axiom selection ...
% 5.90/2.25 % [INFO] Axiom selection finished. Selected 46 axioms (removed 2643 axioms).
% 6.36/2.38 % [INFO] Problem is first-order (TPTP FOF).
% 6.36/2.39 % [INFO] Type checking passed.
% 6.82/2.40 % [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 ...
% 12.00/4.00 % External prover 'e' found a proof!
% 12.00/4.00 % [INFO] Killing All external provers ...
% 12.00/4.00 % Time passed: 3349ms (effective reasoning time: 2705ms)
% 12.00/4.00 % 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)>
% 12.00/4.00 % Axioms used in derivation (46): $_type_14917, $_typeof_B, $_def_QuicksortComplexity.util.ext_eq, $_typeof_g, $tdef_$_type_1, $_type_1, $tdef_A, $tdef_$_type_172, $_type_15157, $_type_846, e, Coq.Logic.FunctionalExtensionality.functional_extensionality, $_def_monads.extMonad, $_type_8323, QuicksortComplexity.util.ext_eq_rw, $_type_433, $tdef_monads.mon, $_type_8351, $_type_604, monads.mon_lunit, $_type_901, $_lam_203, $_typeof_A, $_typeof_n, monads.mon_assoc, $_type_172, QuicksortComplexity.util.eq_trans, Coq.Logic.FunctionalExtensionality.equal_f, $_type_981, $_type_15180, $_type_74, $_typeof_M, Coq.Logic.EqdepFacts.internal_eq_sym_internal, $adef_$_lam_203_$a6, $_type_14909, $adef_monads.mon_$a2, $_type_672, $_typeof_m, monads.mon_runit, $_type_2729, $_typeof_monads.mon, $_type_58, $_type_186, $_type_376, $_typeof_f, $adef_$_lam_203_$a7
% 12.00/4.00 % No. of inferences in proof: 96
% 12.00/4.01 % SZS status Theorem for /export/starexec/sandbox2/benchmark/theBenchmark.p : 3349 ms resp. 2705 ms w/o parsing
% 12.59/4.10 % SZS output start Refutation for /export/starexec/sandbox2/benchmark/theBenchmark.p
% See solution above
% 12.59/4.10 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------