TSTP Solution File: SWW295+1 by Leo-III---1.7.7
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : Leo-III---1.7.7
% Problem : SWW295+1 : TPTP v8.1.2. Released v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : run_Leo-III %s %d
% Computer : n012.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 300s
% DateTime : Fri May 19 12:22:52 EDT 2023
% Result : Theorem 13.68s 4.39s
% Output : Refutation 14.34s
% Verified :
% SZS Type : Refutation
% Derivation depth : 3
% Number of leaves : 275
% Syntax : Number of formulae : 487 ( 227 unt; 65 typ; 0 def)
% Number of atoms : 911 ( 445 equ; 0 cnn)
% Maximal formula atoms : 12 ( 2 avg)
% Number of connectives : 5085 ( 226 ~; 21 |; 139 &;4370 @)
% ( 41 <=>; 288 =>; 0 <=; 0 <~>)
% Maximal formula depth : 19 ( 9 avg)
% Number of types : 2 ( 0 usr)
% Number of type conns : 158 ( 158 >; 0 *; 0 +; 0 <<)
% Number of symbols : 67 ( 65 usr; 12 con; 0-10 aty)
% Number of variables : 1921 ( 0 ^;1886 !; 35 ?;1921 :)
% Comments :
%------------------------------------------------------------------------------
thf(v_P_type,type,
v_P: $i > $i > $o ).
thf(c_Natural_Oevaln_type,type,
c_Natural_Oevaln: $i > $i > $i > $i > $o ).
thf(hAPP_type,type,
hAPP: $i > $i > $i ).
thf(c_Option_Othe_type,type,
c_Option_Othe: $i > $i ).
thf(tc_Com_Ocom_type,type,
tc_Com_Ocom: $i ).
thf(c_Com_Obody_type,type,
c_Com_Obody: $i ).
thf(v_pn_type,type,
v_pn: $i ).
thf(v_n_type,type,
v_n: $i ).
thf(v_Q_type,type,
v_Q: $i > $i > $o ).
thf(c_Com_Ocom_OBODY_type,type,
c_Com_Ocom_OBODY: $i > $i ).
thf(c_Nat_OSuc_type,type,
c_Nat_OSuc: $i ).
thf(c_Map_Omap__comp_type,type,
c_Map_Omap__comp: $i > $i > $i > $i > $i > $i > $i ).
thf(c_Option_Ooption_OSome_type,type,
c_Option_Ooption_OSome: $i > $i ).
thf(c_Option_Ooption_ONone_type,type,
c_Option_Ooption_ONone: $i > $i ).
thf(c_Com_Ocom_OWhile_type,type,
c_Com_Ocom_OWhile: $i > $i > $i ).
thf(c_Com_Ocom_OSemi_type,type,
c_Com_Ocom_OSemi: $i > $i > $i ).
thf(c_Com_Ocom_OLocal_type,type,
c_Com_Ocom_OLocal: $i > $i > $i > $i ).
thf(hBOOL_type,type,
hBOOL: $i > $o ).
thf(c_Natural_Oevalc_type,type,
c_Natural_Oevalc: $i > $i > $i > $o ).
thf(c_Com_Ocom_OCond_type,type,
c_Com_Ocom_OCond: $i > $i > $i > $i ).
thf(c_Com_OWT_type,type,
c_Com_OWT: $i ).
thf(c_Com_Ocom_OCall_type,type,
c_Com_Ocom_OCall: $i > $i > $i > $i ).
thf(c_Com_Ocom_OSKIP_type,type,
c_Com_Ocom_OSKIP: $i ).
thf(c_Com_Ocom_Ocom__rec_type,type,
c_Com_Ocom_Ocom__rec: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_Sum__Type_Osum_Osum__case_type,type,
c_Sum__Type_Osum_Osum__case: $i > $i > $i > $i > $i > $i ).
thf(c_Sum__Type_OInl_type,type,
c_Sum__Type_OInl: $i > $i > $i ).
thf(c_Product__Type_OPair_type,type,
c_Product__Type_OPair: $i > $i > $i ).
thf(c_Com_Ocom_OAss_type,type,
c_Com_Ocom_OAss: $i > $i > $i ).
thf(c_Sum__Type_OInr_type,type,
c_Sum__Type_OInr: $i > $i > $i ).
thf(c_Natural_Oupdate_type,type,
c_Natural_Oupdate: $i > $i > $i > $i ).
thf(c_List_Orotate1_type,type,
c_List_Orotate1: $i > $i ).
thf(c_List_Orotate_type,type,
c_List_Orotate: $i > $i > $i ).
thf(c_Nitpick_Opair__box_OPairBox_type,type,
c_Nitpick_Opair__box_OPairBox: $i > $i > $i > $i > $i ).
thf(c_Com_Ocom_Ocom__case_type,type,
c_Com_Ocom_Ocom__case: $i > $i > $i > $i > $i > $i > $i > $i > $i > $i > $i ).
thf(c_Com_OWT__bodies_type,type,
c_Com_OWT__bodies: $o ).
thf(c_New__Random__Sequence_Opos__empty_type,type,
c_New__Random__Sequence_Opos__empty: $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__empty_type,type,
c_New__DSequence_Opos__empty: $i > $i ).
thf(c_Finite__Set_Ofolding__one__idem_type,type,
c_Finite__Set_Ofolding__one__idem: $i > $i > $i > $o ).
thf(c_Typedef_Otype__definition_type,type,
c_Typedef_Otype__definition: $i > $i > $i > $i > $i > $o ).
thf(c_Sum__Type_OProjr_type,type,
c_Sum__Type_OProjr: $i > $i > $i > $i ).
thf(c_Nitpick_Opair__box_Opair__box__rec_type,type,
c_Nitpick_Opair__box_Opair__box__rec: $i > $i > $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Oneg__single_type,type,
c_New__Random__Sequence_Oneg__single: $i > $i ).
thf(c_New__DSequence_Oneg__single_type,type,
c_New__DSequence_Oneg__single: $i > $i > $i ).
thf(c_Lazy__Sequence_Ohb__single_type,type,
c_Lazy__Sequence_Ohb__single: $i > $i > $i ).
thf(c_FunDef_Oreduction__pair_type,type,
c_FunDef_Oreduction__pair: $i > $i > $o ).
thf(c_FunDef_Orp__inv__image_type,type,
c_FunDef_Orp__inv__image: $i > $i > $i ).
thf(c_Map_Omap__of_type,type,
c_Map_Omap__of: $i > $i > $i > $i ).
thf(tc_Com_Opname_type,type,
tc_Com_Opname: $i ).
thf(c_Com_Obodies_type,type,
c_Com_Obodies: $i ).
thf(c_Sum__Type_OProjl_type,type,
c_Sum__Type_OProjl: $i > $i > $i > $i ).
thf(c_Nitpick_Opair__box_Opair__box__case_type,type,
c_Nitpick_Opair__box_Opair__box__case: $i > $i > $i > $i > $i > $i ).
thf(c_Nat_Onat_Onat__rec_type,type,
c_Nat_Onat_Onat__rec: $i > $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__single_type,type,
c_New__Random__Sequence_Opos__single: $i > $i ).
thf(c_New__DSequence_Opos__single_type,type,
c_New__DSequence_Opos__single: $i > $i > $i ).
thf(c_Lazy__Sequence_Osingle_type,type,
c_Lazy__Sequence_Osingle: $i > $i > $i ).
thf(c_New__Random__Sequence_Opos__not__random__dseq_type,type,
c_New__Random__Sequence_Opos__not__random__dseq: $i > $i > $i > $i > $i ).
thf(c_New__DSequence_Opos__not__seq_type,type,
c_New__DSequence_Opos__not__seq: $i > $i ).
thf(c_Product__Type_Oprod_Oprod__rec_type,type,
c_Product__Type_Oprod_Oprod__rec: $i > $i > $i > $i > $i > $i ).
thf(c_Nat_Onat_Onat__case_type,type,
c_Nat_Onat_Onat__case: $i > $i > $i > $i > $i ).
thf(c_Int_ORep__Integ_type,type,
c_Int_ORep__Integ: $i ).
thf(c_Power_Opower_Opower_type,type,
c_Power_Opower_Opower: $i > $i > $i > $i ).
thf(c_Finite__Set_Ofolding__image__simple__idem_type,type,
c_Finite__Set_Ofolding__image__simple__idem: $i > $i > $i > $i > $i > $i > $o ).
thf(class_Rings_Osemiring__1_type,type,
class_Rings_Osemiring__1: $i > $o ).
thf(c_Nat_Osemiring__1__class_Oof__nat__aux_type,type,
c_Nat_Osemiring__1__class_Oof__nat__aux: $i > $i > $i > $i > $i ).
thf(c_Lazy__Sequence_Oempty_type,type,
c_Lazy__Sequence_Oempty: $i > $i ).
thf(111,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Com_Ocom_Ocom__rec @ K @ J @ I @ H @ G @ F @ E @ D @ C @ ( c_Com_Ocom_OAss @ B @ A ) )
= ( hAPP @ ( hAPP @ I @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I2_J) ).
thf(750,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Com_Ocom_Ocom__rec @ K @ J @ I @ H @ G @ F @ E @ D @ C @ ( c_Com_Ocom_OAss @ B @ A ) )
= ( hAPP @ ( hAPP @ I @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[111]) ).
thf(186,axiom,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__n__not__n) ).
thf(1031,plain,
! [A: $i] :
( ( hAPP @ c_Nat_OSuc @ A )
!= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[186]) ).
thf(5,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= ( c_Option_Ooption_ONone @ D ) )
=> ( ( c_Map_Omap__comp @ D @ C @ B @ A @ F @ E )
= ( c_Option_Ooption_ONone @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__simps_I1_J) ).
thf(234,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ F @ E )
= ( c_Option_Ooption_ONone @ D ) )
=> ( ( c_Map_Omap__comp @ D @ C @ B @ A @ F @ E )
= ( c_Option_Ooption_ONone @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[5]) ).
thf(207,axiom,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I18_J) ).
thf(1110,plain,
! [A: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[207]) ).
thf(178,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_prod_Orecs) ).
thf(1005,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Product__Type_Oprod_Oprod__rec @ F @ E @ D @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[178]) ).
thf(20,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCond @ F @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I56_J) ).
thf(276,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCond @ F @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[20]) ).
thf(9,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OSemi @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I44_J) ).
thf(247,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OSemi @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[9]) ).
thf(138,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
!= ( hAPP @ ( c_Sum__Type_OInl @ C @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inr__not__Inl) ).
thf(861,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
!= ( hAPP @ ( c_Sum__Type_OInl @ C @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[138]) ).
thf(102,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCond @ E @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I27_J) ).
thf(715,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCond @ E @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[102]) ).
thf(126,axiom,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OAss @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I8_J) ).
thf(814,plain,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OAss @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[126]) ).
thf(73,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) @ B @ A )
<=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ D @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I6_J) ).
thf(538,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ D @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ C @ B @ A ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ D @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ C @ B @ A ) ) )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[73]) ).
thf(92,axiom,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I14_J) ).
thf(670,plain,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[92]) ).
thf(135,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ C @ B @ A )
<=> ( ( ( A = C )
& ~ ( hBOOL @ ( hAPP @ E @ C ) ) )
| ( ( hBOOL @ ( hAPP @ E @ C ) )
& ? [F: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ F )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ F @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I8_J) ).
thf(841,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ C @ B @ A )
=> ( ( ( A = C )
& ~ ( hBOOL @ ( hAPP @ E @ C ) ) )
| ( ( hBOOL @ ( hAPP @ E @ C ) )
& ? [F: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ F )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ F @ B @ A ) ) ) ) )
& ( ( ( ( A = C )
& ~ ( hBOOL @ ( hAPP @ E @ C ) ) )
| ( ( hBOOL @ ( hAPP @ E @ C ) )
& ? [F: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ F )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ F @ B @ A ) ) ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[135]) ).
thf(23,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inl__inject) ).
thf(288,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[23]) ).
thf(90,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I1_J) ).
thf(651,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[90]) ).
thf(104,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ( ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OSemi) ).
thf(724,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ( ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[104]) ).
thf(103,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
=> ~ ( c_Natural_Oevalc @ D @ B @ A ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
=> ~ ( c_Natural_Oevalc @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I5_J) ).
thf(719,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
=> ~ ( c_Natural_Oevalc @ D @ B @ A ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
=> ~ ( c_Natural_Oevalc @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[103]) ).
thf(119,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( c_Com_Ocom_Ocom__case @ L @ K @ J @ I @ H @ G @ F @ E @ D @ ( c_Com_Ocom_OCond @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ G @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I68_J) ).
thf(785,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( c_Com_Ocom_Ocom__case @ L @ K @ J @ I @ H @ G @ F @ E @ D @ ( c_Com_Ocom_OCond @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ G @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[119]) ).
thf(84,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Com_Ocom_OWhile @ D @ C )
= ( c_Com_Ocom_OWhile @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I5_J) ).
thf(619,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Com_Ocom_OWhile @ D @ C )
= ( c_Com_Ocom_OWhile @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Com_Ocom_OWhile @ D @ C )
= ( c_Com_Ocom_OWhile @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[84]) ).
thf(54,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OWhile @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I29_J) ).
thf(460,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OWhile @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[54]) ).
thf(22,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OLocal @ F @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I36_J) ).
thf(284,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OLocal @ F @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[22]) ).
thf(31,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OSemi @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I35_J) ).
thf(325,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OSemi @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[31]) ).
thf(205,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OSemi @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I48_J) ).
thf(1100,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OSemi @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[205]) ).
thf(14,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ C ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCall @ B @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OCall) ).
thf(261,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ C ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCall @ B @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[14]) ).
thf(63,axiom,
! [A: $i,B: $i] :
( ( c_Option_Ooption_ONone @ B )
!= ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I2_J) ).
thf(492,plain,
! [A: $i,B: $i] :
( ( c_Option_Ooption_ONone @ B )
!= ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[63]) ).
thf(51,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I2_J) ).
thf(443,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[51]) ).
thf(61,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OAss @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I32_J) ).
thf(485,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OAss @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[61]) ).
thf(128,axiom,
! [A: $i,B: $i] :
( ( c_Com_Ocom_OSemi @ B @ A )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I13_J) ).
thf(821,plain,
! [A: $i,B: $i] :
( ( c_Com_Ocom_OSemi @ B @ A )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[128]) ).
thf(150,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) ) )
<=> ? [B: $i] :
( ( hAPP @ c_Com_Obody @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Com_Ocom ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I7_J) ).
thf(905,plain,
! [A: $i] :
( ( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) ) )
=> ? [B: $i] :
( ( hAPP @ c_Com_Obody @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Com_Ocom ) @ B ) ) )
& ( ? [B: $i] :
( ( hAPP @ c_Com_Obody @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Com_Ocom ) @ B ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[150]) ).
thf(189,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ C ) @ B @ A )
=> ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I6_J) ).
thf(1040,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ C ) @ B @ A )
=> ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[189]) ).
thf(30,axiom,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I20_J) ).
thf(321,plain,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[30]) ).
thf(171,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ D @ C @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ B @ A ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ D @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__rec__Suc) ).
thf(981,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Nat_Onat_Onat__rec @ D @ C @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ B @ A ) @ ( hAPP @ ( c_Nat_Onat_Onat__rec @ D @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[171]) ).
thf(21,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OCall @ C @ B @ A )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I21_J) ).
thf(280,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OCall @ C @ B @ A )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[21]) ).
thf(86,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( B
!= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) )
<=> ( B
= ( c_Option_Ooption_ONone @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__Some__eq) ).
thf(634,plain,
! [A: $i,B: $i] :
( ( ! [C: $i] :
( B
!= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) )
=> ( B
= ( c_Option_Ooption_ONone @ A ) ) )
& ( ( B
= ( c_Option_Ooption_ONone @ A ) )
=> ! [C: $i] :
( B
!= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[86]) ).
thf(210,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Natural_Oevaln @ ( c_Com_Ocom_OAss @ D @ C ) @ B @ A @ ( c_Natural_Oupdate @ B @ D @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I2_J) ).
thf(1119,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Natural_Oevaln @ ( c_Com_Ocom_OAss @ D @ C ) @ B @ A @ ( c_Natural_Oupdate @ B @ D @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[210]) ).
thf(46,axiom,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I10_J) ).
thf(411,plain,
! [A: $i,B: $i,C: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[46]) ).
thf(49,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Com_Ocom_OLocal @ F @ E @ D )
= ( c_Com_Ocom_OLocal @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I2_J) ).
thf(428,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Com_Ocom_OLocal @ F @ E @ D )
= ( c_Com_Ocom_OLocal @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( c_Com_Ocom_OLocal @ F @ E @ D )
= ( c_Com_Ocom_OLocal @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[49]) ).
thf(206,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ E @ D ) @ C @ B @ A )
<=> ? [F: $i] :
( ( c_Natural_Oevaln @ E @ C @ B @ F )
& ( c_Natural_Oevaln @ D @ F @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I4_J) ).
thf(1104,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ E @ D ) @ C @ B @ A )
=> ? [F: $i] :
( ( c_Natural_Oevaln @ E @ C @ B @ F )
& ( c_Natural_Oevaln @ D @ F @ B @ A ) ) )
& ( ? [F: $i] :
( ( c_Natural_Oevaln @ E @ C @ B @ F )
& ( c_Natural_Oevaln @ D @ F @ B @ A ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ E @ D ) @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[206]) ).
thf(16,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ~ ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I4_J) ).
thf(265,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ~ ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[16]) ).
thf(27,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__inject) ).
thf(307,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[27]) ).
thf(24,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( c_Com_Ocom_Ocom__rec @ I @ H @ G @ F @ E @ D @ C @ B @ A @ c_Com_Ocom_OSKIP )
= H ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I1_J) ).
thf(292,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( c_Com_Ocom_Ocom__rec @ I @ H @ G @ F @ E @ D @ C @ B @ A @ c_Com_Ocom_OSKIP )
= H ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[24]) ).
thf(94,axiom,
! [A: $i,B: $i,C: $i] : ( c_Natural_Oevalc @ ( c_Com_Ocom_OAss @ C @ B ) @ A @ ( c_Natural_Oupdate @ A @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OAssign) ).
thf(678,plain,
! [A: $i,B: $i,C: $i] : ( c_Natural_Oevalc @ ( c_Com_Ocom_OAss @ C @ B ) @ A @ ( c_Natural_Oupdate @ A @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[94]) ).
thf(18,axiom,
! [A: $i,B: $i] :
( ( c_Com_Ocom_OWhile @ B @ A )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I17_J) ).
thf(270,plain,
! [A: $i,B: $i] :
( ( c_Com_Ocom_OWhile @ B @ A )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[18]) ).
thf(155,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OBODY @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I31_J) ).
thf(925,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OBODY @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[155]) ).
thf(41,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
& ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I4_J) ).
thf(381,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
& ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
& ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OSemi @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[41]) ).
thf(72,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OLocal @ E @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I38_J) ).
thf(534,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OLocal @ E @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[72]) ).
thf(192,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Int_ORep__Integ @ B )
= ( hAPP @ c_Int_ORep__Integ @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Rep__Integ__inject) ).
thf(1047,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Int_ORep__Integ @ B )
= ( hAPP @ c_Int_ORep__Integ @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_Int_ORep__Integ @ B )
= ( hAPP @ c_Int_ORep__Integ @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[192]) ).
thf(67,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
!= ( hAPP @ ( c_Sum__Type_OInr @ C @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inl__not__Inr) ).
thf(512,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
!= ( hAPP @ ( c_Sum__Type_OInr @ C @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[67]) ).
thf(161,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevalc @ C @ B @ A )
=> ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__evaln) ).
thf(942,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevalc @ C @ B @ A )
=> ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[161]) ).
thf(166,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat_Oinject) ).
thf(957,plain,
! [A: $i,B: $i] :
( ( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[166]) ).
thf(202,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ B @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ D ) @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OBody) ).
thf(1091,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ B @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ D ) @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[202]) ).
thf(129,axiom,
! [A: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I1_J) ).
thf(825,plain,
! [A: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[129]) ).
thf(190,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ F @ E @ D @ C )
=> ( ( c_Natural_Oevaln @ B @ C @ D @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ F @ B ) @ E @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OSemi) ).
thf(1042,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ F @ E @ D @ C )
=> ( ( c_Natural_Oevaln @ B @ C @ D @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ F @ B ) @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[190]) ).
thf(85,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCall @ E @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I51_J) ).
thf(630,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCall @ E @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[85]) ).
thf(120,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__empty @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__empty @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__empty__def) ).
thf(788,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__empty @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__empty @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[120]) ).
thf(152,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Sum__Type_OProjr @ C @ B @ ( hAPP @ ( c_Sum__Type_OInr @ B @ C ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Projr_Osimps) ).
thf(916,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Sum__Type_OProjr @ C @ B @ ( hAPP @ ( c_Sum__Type_OInr @ B @ C ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[152]) ).
thf(143,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__one__idem_Oidem) ).
thf(879,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Finite__Set_Ofolding__one__idem @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ C @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[143]) ).
thf(32,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OWhile @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_While) ).
thf(329,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OWhile @ A @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[32]) ).
thf(131,axiom,
! [A: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ A @ A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OSkip) ).
thf(830,plain,
! [A: $i] : ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ A @ A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[131]) ).
thf(113,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) @ B @ A )
<=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ D @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I5_J) ).
thf(757,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ D @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ C @ B @ A ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ D @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ E @ B ) )
& ( c_Natural_Oevalc @ C @ B @ A ) ) )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ D @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[113]) ).
thf(96,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OSemi @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I50_J) ).
thf(682,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OSemi @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[96]) ).
thf(101,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) @ C @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
=> ~ ( c_Natural_Oevaln @ E @ C @ B @ A ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
=> ~ ( c_Natural_Oevaln @ D @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I5_J) ).
thf(710,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) @ C @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
=> ~ ( c_Natural_Oevaln @ E @ C @ B @ A ) )
=> ~ ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
=> ~ ( c_Natural_Oevaln @ D @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[101]) ).
thf(53,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCond @ C @ B @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ~ ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I5_J) ).
thf(456,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCond @ C @ B @ A ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ~ ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[53]) ).
thf(29,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Inr__inject) ).
thf(317,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
= ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[29]) ).
thf(211,axiom,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_ext) ).
thf(1121,plain,
! [A: $i,B: $i] :
( ! [C: $i] :
( ( hAPP @ B @ C )
= ( hAPP @ A @ C ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[211]) ).
thf(204,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OBODY @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I62_J) ).
thf(1096,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OBODY @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[204]) ).
thf(118,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ C ) )
=> ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCond @ A @ C @ B ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OIf) ).
thf(783,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ C ) )
=> ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCond @ A @ C @ B ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[118]) ).
thf(137,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OLocal @ E @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I34_J) ).
thf(857,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OLocal @ E @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[137]) ).
thf(185,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Nat_Onat_Onat__case @ D @ C @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_nat__case__Suc) ).
thf(1028,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Nat_Onat_Onat__case @ D @ C @ B @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[185]) ).
thf(35,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCond @ E @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I52_J) ).
thf(339,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCond @ E @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[35]) ).
thf(157,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Oneg__single @ C @ B ) @ A )
= ( c_Lazy__Sequence_Ohb__single @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Oneg__single__def) ).
thf(933,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Oneg__single @ C @ B ) @ A )
= ( c_Lazy__Sequence_Ohb__single @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[157]) ).
thf(112,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OAss @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I26_J) ).
thf(753,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OAss @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[112]) ).
thf(62,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Orotate1 @ C ) @ ( hAPP @ ( c_List_Orotate @ C @ B ) @ A ) )
= ( hAPP @ ( c_List_Orotate @ C @ B ) @ ( hAPP @ ( c_List_Orotate1 @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate1__rotate__swap) ).
thf(489,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Orotate1 @ C ) @ ( hAPP @ ( c_List_Orotate @ C @ B ) @ A ) )
= ( hAPP @ ( c_List_Orotate @ C @ B ) @ ( hAPP @ ( c_List_Orotate1 @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[62]) ).
thf(181,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ C @ B @ A )
=> ( A = C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I1_J) ).
thf(1016,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ C @ B @ A )
=> ( A = C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[181]) ).
thf(149,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OBODY @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I49_J) ).
thf(901,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OBODY @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[149]) ).
thf(97,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCall @ E @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I33_J) ).
thf(686,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCall @ E @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[97]) ).
thf(1,conjecture,
( ! [A: $i,B: $i] :
( ( v_P @ A @ B )
=> ! [C: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ B @ v_n @ C )
=> ( v_Q @ A @ C ) ) )
<=> ! [A: $i,B: $i] :
( ( v_P @ A @ B )
=> ! [C: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ B @ ( hAPP @ c_Nat_OSuc @ v_n ) @ C )
=> ( v_Q @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',conj_0) ).
thf(2,negated_conjecture,
~ ( ! [A: $i,B: $i] :
( ( v_P @ A @ B )
=> ! [C: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ B @ v_n @ C )
=> ( v_Q @ A @ C ) ) )
<=> ! [A: $i,B: $i] :
( ( v_P @ A @ B )
=> ! [C: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ B @ ( hAPP @ c_Nat_OSuc @ v_n ) @ C )
=> ( v_Q @ A @ C ) ) ) ),
inference(neg_conjecture,[status(cth)],[1]) ).
thf(212,plain,
~ ( ( ! [A: $i,B: $i] :
( ( v_P @ A @ B )
=> ! [C: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ B @ v_n @ C )
=> ( v_Q @ A @ C ) ) )
=> ! [A: $i,B: $i] :
( ( v_P @ A @ B )
=> ! [C: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ B @ ( hAPP @ c_Nat_OSuc @ v_n ) @ C )
=> ( v_Q @ A @ C ) ) ) )
& ( ! [A: $i,B: $i] :
( ( v_P @ A @ B )
=> ! [C: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ v_pn ) @ B @ ( hAPP @ c_Nat_OSuc @ v_n ) @ C )
=> ( v_Q @ A @ C ) ) )
=> ! [A: $i,B: $i] :
( ( v_P @ A @ B )
=> ! [C: $i] :
( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ v_pn ) ) @ B @ v_n @ C )
=> ( v_Q @ A @ C ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[2]) ).
thf(100,axiom,
! [A: $i,B: $i] :
( c_Com_OWT__bodies
=> ( ( ( hAPP @ c_Com_Obody @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Com_Ocom ) @ A ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT__bodiesD) ).
thf(706,plain,
! [A: $i,B: $i] :
( c_Com_OWT__bodies
=> ( ( ( hAPP @ c_Com_Obody @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Com_Ocom ) @ A ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[100]) ).
thf(208,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__empty @ B ) @ A )
= ( c_Lazy__Sequence_Oempty @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__empty__def) ).
thf(1114,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__empty @ B ) @ A )
= ( c_Lazy__Sequence_Oempty @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[208]) ).
thf(108,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OLocal @ C @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I3_J) ).
thf(738,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OLocal @ C @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) )
& ( ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OLocal @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[108]) ).
thf(172,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Opos__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Opos__single @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__single__def) ).
thf(984,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Opos__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Opos__single @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[172]) ).
thf(177,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__not__random__dseq @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__not__seq @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pos__not__random__dseq__def) ).
thf(1002,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_New__Random__Sequence_Opos__not__random__dseq @ D @ C @ B @ A )
= ( c_New__DSequence_Opos__not__seq @ ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[177]) ).
thf(117,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OWhile @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I60_J) ).
thf(779,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OWhile @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[117]) ).
thf(159,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FunDef_Oreduction__pair @ D @ C )
=> ( c_FunDef_Oreduction__pair @ B @ ( hAPP @ ( hAPP @ ( c_FunDef_Orp__inv__image @ D @ B ) @ C ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rp__inv__image__rp) ).
thf(938,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_FunDef_Oreduction__pair @ D @ C )
=> ( c_FunDef_Oreduction__pair @ B @ ( hAPP @ ( hAPP @ ( c_FunDef_Orp__inv__image @ D @ B ) @ C ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[159]) ).
thf(193,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ D ) @ C @ B @ A )
=> ~ ! [E: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ E ) )
=> ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ E @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I6_J) ).
thf(1054,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ D ) @ C @ B @ A )
=> ~ ! [E: $i] :
( ( B
= ( hAPP @ c_Nat_OSuc @ E ) )
=> ~ ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[193]) ).
thf(187,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ B @ A )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ C ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OBody) ).
thf(1035,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ B @ A )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ C ) @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[187]) ).
thf(93,axiom,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I16_J) ).
thf(674,plain,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[93]) ).
thf(184,axiom,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Natural_Oevaln @ ( c_Com_Ocom_OAss @ D @ C ) @ B @ A @ ( c_Natural_Oupdate @ B @ D @ ( hAPP @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OAssign) ).
thf(1026,plain,
! [A: $i,B: $i,C: $i,D: $i] : ( c_Natural_Oevaln @ ( c_Com_Ocom_OAss @ D @ C ) @ B @ A @ ( c_Natural_Oupdate @ B @ D @ ( hAPP @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[184]) ).
thf(122,axiom,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ C @ B ) )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ A ) @ B @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OWhileFalse) ).
thf(794,plain,
! [A: $i,B: $i,C: $i] :
( ~ ( hBOOL @ ( hAPP @ C @ B ) )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ A ) @ B @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[122]) ).
thf(36,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ D @ C ) @ B @ A )
=> ~ ! [E: $i] :
( ( c_Natural_Oevalc @ D @ B @ E )
=> ~ ( c_Natural_Oevalc @ C @ E @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I4_J) ).
thf(343,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ D @ C ) @ B @ A )
=> ~ ! [E: $i] :
( ( c_Natural_Oevalc @ D @ B @ E )
=> ~ ( c_Natural_Oevalc @ C @ E @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[36]) ).
thf(6,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OWhile @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I47_J) ).
thf(237,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OWhile @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[6]) ).
thf(107,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ D @ C ) @ B @ A )
<=> ? [E: $i] :
( ( c_Natural_Oevalc @ D @ B @ E )
& ( c_Natural_Oevalc @ C @ E @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I4_J) ).
thf(732,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ D @ C ) @ B @ A )
=> ? [E: $i] :
( ( c_Natural_Oevalc @ D @ B @ E )
& ( c_Natural_Oevalc @ C @ E @ A ) ) )
& ( ? [E: $i] :
( ( c_Natural_Oevalc @ D @ B @ E )
& ( c_Natural_Oevalc @ C @ E @ A ) )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ D @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[107]) ).
thf(109,axiom,
! [A: $i,B: $i,C: $i] :
( ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
<=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ E ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_split__paired__All) ).
thf(743,plain,
! [A: $i,B: $i,C: $i] :
( ( ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) )
=> ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ E ) ) ) )
& ( ! [D: $i,E: $i] : ( hBOOL @ ( hAPP @ C @ ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ B @ A ) @ D ) @ E ) ) )
=> ! [D: $i] : ( hBOOL @ ( hAPP @ C @ D ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[109]) ).
thf(142,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OCond @ D @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I54_J) ).
thf(875,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OCond @ D @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[142]) ).
thf(78,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OAss @ D @ C ) @ B @ A )
=> ( A
= ( c_Natural_Oupdate @ B @ D @ ( hAPP @ C @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I2_J) ).
thf(577,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OAss @ D @ C ) @ B @ A )
=> ( A
= ( c_Natural_Oupdate @ B @ D @ ( hAPP @ C @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[78]) ).
thf(87,axiom,
! [A: $i,B: $i] :
( ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ B @ A )
=> ( A = B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__elim__cases_I1_J) ).
thf(641,plain,
! [A: $i,B: $i] :
( ( c_Natural_Oevalc @ c_Com_Ocom_OSKIP @ B @ A )
=> ( A = B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[87]) ).
thf(158,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ A )
=> ( c_Natural_Oevaln @ D @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__Suc) ).
thf(936,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ A )
=> ( c_Natural_Oevaln @ D @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[158]) ).
thf(28,axiom,
! [A: $i,B: $i] :
( ( c_Com_Ocom_OAss @ B @ A )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I9_J) ).
thf(313,plain,
! [A: $i,B: $i] :
( ( c_Com_Ocom_OAss @ B @ A )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[28]) ).
thf(194,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_power_Opower_Opower__Suc) ).
thf(1058,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ ( hAPP @ ( hAPP @ ( c_Power_Opower_Opower @ E @ D @ C ) @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[194]) ).
thf(56,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCond @ E @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I45_J) ).
thf(466,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCond @ E @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[56]) ).
thf(34,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OLocal @ C @ B @ A )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I11_J) ).
thf(335,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OLocal @ C @ B @ A )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[34]) ).
thf(163,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Option_Othe @ B ) @ ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_the_Osimps) ).
thf(947,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Option_Othe @ B ) @ ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[163]) ).
thf(38,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Pair__eq) ).
thf(350,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ D ) @ C )
= ( hAPP @ ( hAPP @ ( c_Product__Type_OPair @ F @ E ) @ B ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[38]) ).
thf(153,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__rec @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Orecs) ).
thf(919,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__rec @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[153]) ).
thf(125,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) @ C @ B @ A )
<=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ E @ C @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ D @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I5_J) ).
thf(804,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) @ C @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ E @ C @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ D @ C @ B @ A ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ E @ C @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ D @ C @ B @ A ) ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[125]) ).
thf(81,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) @ A @ A )
<=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ? [D: $i] :
( ( c_Natural_Oevalc @ B @ A @ D )
& ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I7_J) ).
thf(604,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) @ A @ A )
=> ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ? [D: $i] :
( ( c_Natural_Oevalc @ B @ A @ D )
& ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) @ D @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ C @ A ) )
=> ? [D: $i] :
( ( c_Natural_Oevalc @ B @ A @ D )
& ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) @ D @ A ) ) )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ C @ B ) @ A @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[81]) ).
thf(19,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( c_Natural_Oevaln @ D @ E @ C @ B )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ A @ D ) @ E @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OIfFalse) ).
thf(274,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ~ ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( c_Natural_Oevaln @ D @ E @ C @ B )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ A @ D ) @ E @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[19]) ).
thf(209,axiom,
! [A: $i,B: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ B @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I1_J) ).
thf(1117,plain,
! [A: $i,B: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ B @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[209]) ).
thf(180,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ C ) @ B @ A )
<=> ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I9_J) ).
thf(1011,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ C ) @ B @ A )
=> ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ B @ A ) )
& ( ( c_Natural_Oevalc @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ C ) ) @ B @ A )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OBODY @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[180]) ).
thf(174,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hAPP @ E @ F )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ D @ C @ B ) @ F ) )
=> ( ( hAPP @ E @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ B @ A ) @ ( hAPP @ E @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_def__nat__rec__Suc) ).
thf(990,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ! [F: $i] :
( ( hAPP @ E @ F )
= ( hAPP @ ( c_Nat_Onat_Onat__rec @ D @ C @ B ) @ F ) )
=> ( ( hAPP @ E @ ( hAPP @ c_Nat_OSuc @ A ) )
= ( hAPP @ ( hAPP @ B @ A ) @ ( hAPP @ E @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[174]) ).
thf(77,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A )
=> ( ( ( A = B )
=> ( hBOOL @ ( hAPP @ D @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ! [E: $i] :
( ( c_Natural_Oevalc @ C @ B @ E )
=> ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc__WHILE__case) ).
thf(567,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A )
=> ( ( ( A = B )
=> ( hBOOL @ ( hAPP @ D @ B ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ! [E: $i] :
( ( c_Natural_Oevalc @ C @ B @ E )
=> ~ ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[77]) ).
thf(8,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( c_Natural_Oevalc @ C @ D @ B )
=> ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ E @ C ) @ B @ A )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ E @ C ) @ D @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OWhileTrue) ).
thf(245,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( c_Natural_Oevalc @ C @ D @ B )
=> ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ E @ C ) @ B @ A )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ E @ C ) @ D @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[8]) ).
thf(66,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( c_Com_Ocom_Ocom__rec @ L @ K @ J @ I @ H @ G @ F @ E @ D @ ( c_Com_Ocom_OCond @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ G @ C ) @ B ) @ A ) @ ( c_Com_Ocom_Ocom__rec @ L @ K @ J @ I @ H @ G @ F @ E @ D @ B ) ) @ ( c_Com_Ocom_Ocom__rec @ L @ K @ J @ I @ H @ G @ F @ E @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I5_J) ).
thf(509,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( c_Com_Ocom_Ocom__rec @ L @ K @ J @ I @ H @ G @ F @ E @ D @ ( c_Com_Ocom_OCond @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ G @ C ) @ B ) @ A ) @ ( c_Com_Ocom_Ocom__rec @ L @ K @ J @ I @ H @ G @ F @ E @ D @ B ) ) @ ( c_Com_Ocom_Ocom__rec @ L @ K @ J @ I @ H @ G @ F @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[66]) ).
thf(83,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OLocal @ C @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I3_J) ).
thf(616,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OLocal @ C @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[83]) ).
thf(146,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Natural_Oevalc @ C @ B @ A )
<=> ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_eval__eq) ).
thf(890,plain,
! [A: $i,B: $i,C: $i] :
( ( ( c_Natural_Oevalc @ C @ B @ A )
=> ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A ) )
& ( ? [D: $i] : ( c_Natural_Oevaln @ C @ B @ D @ A )
=> ( c_Natural_Oevalc @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[146]) ).
thf(42,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_Option_Ooption_ONone @ A ) )
<=> ? [C: $i] :
( B
= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_not__None__eq) ).
thf(387,plain,
! [A: $i,B: $i] :
( ( ( B
!= ( c_Option_Ooption_ONone @ A ) )
=> ? [C: $i] :
( B
= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) ) )
& ( ? [C: $i] :
( B
= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) )
=> ( B
!= ( c_Option_Ooption_ONone @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[42]) ).
thf(199,axiom,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) ) )
=> ~ ! [B: $i] :
( ( hAPP @ c_Com_Obody @ A )
!= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Com_Ocom ) @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I7_J) ).
thf(1080,plain,
! [A: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) ) )
=> ~ ! [B: $i] :
( ( hAPP @ c_Com_Obody @ A )
!= ( hAPP @ ( c_Option_Ooption_OSome @ tc_Com_Ocom ) @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[199]) ).
thf(75,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Nitpick_Opair__box_OPairBox @ F @ E @ D @ C )
= ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Oinject) ).
thf(552,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Nitpick_Opair__box_OPairBox @ F @ E @ D @ C )
= ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Nitpick_Opair__box_OPairBox @ F @ E @ D @ C )
= ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[75]) ).
thf(80,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) @ C @ B @ A )
<=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ E @ C @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ D @ C @ B @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I6_J) ).
thf(594,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) @ C @ B @ A )
=> ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ E @ C @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ D @ C @ B @ A ) ) ) )
& ( ( ( ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ E @ C @ B @ A ) )
| ( ~ ( hBOOL @ ( hAPP @ F @ C ) )
& ( c_Natural_Oevaln @ D @ C @ B @ A ) ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ E @ D ) @ C @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[80]) ).
thf(105,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( c_Natural_Oevaln @ D @ E @ C @ B )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ D @ A ) @ E @ C @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OIfTrue) ).
thf(726,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( c_Natural_Oevaln @ D @ E @ C @ B )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OCond @ F @ D @ A ) @ E @ C @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[105]) ).
thf(60,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ B ) @ C @ A @ C ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OWhileFalse) ).
thf(483,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ~ ( hBOOL @ ( hAPP @ D @ C ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ B ) @ C @ A @ C ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[60]) ).
thf(69,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OAss @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I28_J) ).
thf(520,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OAss @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[69]) ).
thf(10,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCall @ C @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I8_J) ).
thf(251,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCall @ C @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ B ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[10]) ).
thf(147,axiom,
! [A: $i,B: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ B @ A @ B ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OSkip) ).
thf(895,plain,
! [A: $i,B: $i] : ( c_Natural_Oevaln @ c_Com_Ocom_OSKIP @ B @ A @ B ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[147]) ).
thf(167,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OBODY @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I41_J) ).
thf(964,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OBODY @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[167]) ).
thf(195,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OLocal @ D @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I40_J) ).
thf(1061,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OLocal @ D @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[195]) ).
thf(151,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( ( hAPP @ C @ ( hAPP @ D @ A ) )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inverse) ).
thf(912,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Typedef_Otype__definition @ F @ E @ D @ C @ B )
=> ( ( hAPP @ C @ ( hAPP @ D @ A ) )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[151]) ).
thf(130,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevalc @ D @ C @ B )
=> ( ( c_Natural_Oevalc @ D @ C @ A )
=> ( A = B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com__det) ).
thf(827,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevalc @ D @ C @ B )
=> ( ( c_Natural_Oevalc @ D @ C @ A )
=> ( A = B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[130]) ).
thf(191,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OAss @ E @ D ) @ C @ B @ A )
=> ( A
= ( c_Natural_Oupdate @ C @ E @ ( hAPP @ D @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I2_J) ).
thf(1044,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OAss @ E @ D ) @ C @ B @ A )
=> ( A
= ( c_Natural_Oupdate @ C @ E @ ( hAPP @ D @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[191]) ).
thf(140,axiom,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A )
!= ( c_Option_Ooption_ONone @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Osimps_I3_J) ).
thf(868,plain,
! [A: $i,B: $i] :
( ( hAPP @ ( c_Option_Ooption_OSome @ B ) @ A )
!= ( c_Option_Ooption_ONone @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[140]) ).
thf(144,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G = F )
=> ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ E @ D @ C @ B @ A ) @ G )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ E @ D @ C @ B @ A ) @ F ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__case__weak__cong) ).
thf(883,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( G = F )
=> ( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ E @ D @ C @ B @ A ) @ G )
= ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ E @ D @ C @ B @ A ) @ F ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[144]) ).
thf(43,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Com_Ocom_OAss @ D @ C )
= ( c_Com_Ocom_OAss @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I1_J) ).
thf(394,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Com_Ocom_OAss @ D @ C )
= ( c_Com_Ocom_OAss @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Com_Ocom_OAss @ D @ C )
= ( c_Com_Ocom_OAss @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[43]) ).
thf(76,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OSemi @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I25_J) ).
thf(563,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OSemi @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[76]) ).
thf(176,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ A )
=> ( c_Natural_Oevalc @ D @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__evalc) ).
thf(1000,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ A )
=> ( c_Natural_Oevalc @ D @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[176]) ).
thf(26,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( c_Sum__Type_Osum_Osum__case @ G @ F @ E @ D @ C )
= ( c_Sum__Type_Osum_Osum__case @ G @ F @ E @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum__case__inject) ).
thf(299,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( c_Sum__Type_Osum_Osum__case @ G @ F @ E @ D @ C )
= ( c_Sum__Type_Osum_Osum__case @ G @ F @ E @ B @ A ) )
=> ~ ( ( D = B )
=> ( C != A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[26]) ).
thf(7,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OWhile @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I39_J) ).
thf(241,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OWhile @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[7]) ).
thf(154,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Oneg__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Oneg__single @ E @ D ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_neg__single__def) ).
thf(922,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ ( c_New__Random__Sequence_Oneg__single @ E ) @ D ) @ C ) @ B ) @ A )
= ( c_New__DSequence_Oneg__single @ E @ D ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[154]) ).
thf(91,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Map_Omap__comp @ F @ E @ D @ C @ B @ A )
= ( c_Option_Ooption_ONone @ E ) )
<=> ( ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ F ) )
| ? [G: $i] :
( ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ G ) )
& ( ( hAPP @ C @ G )
= ( c_Option_Ooption_ONone @ E ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__None__iff) ).
thf(658,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Map_Omap__comp @ F @ E @ D @ C @ B @ A )
= ( c_Option_Ooption_ONone @ E ) )
=> ( ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ F ) )
| ? [G: $i] :
( ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ G ) )
& ( ( hAPP @ C @ G )
= ( c_Option_Ooption_ONone @ E ) ) ) ) )
& ( ( ( ( hAPP @ B @ A )
= ( c_Option_Ooption_ONone @ F ) )
| ? [G: $i] :
( ( ( hAPP @ B @ A )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ G ) )
& ( ( hAPP @ C @ G )
= ( c_Option_Ooption_ONone @ E ) ) ) )
=> ( ( c_Map_Omap__comp @ F @ E @ D @ C @ B @ A )
= ( c_Option_Ooption_ONone @ E ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[91]) ).
thf(58,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCall @ C @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I8_J) ).
thf(473,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCall @ C @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ B ) ) ) )
& ( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ B ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCall @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[58]) ).
thf(48,axiom,
! [A: $i,B: $i,C: $i] : ( c_Natural_Oevalc @ ( c_Com_Ocom_OAss @ C @ B ) @ A @ ( c_Natural_Oupdate @ A @ C @ ( hAPP @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I2_J) ).
thf(426,plain,
! [A: $i,B: $i,C: $i] : ( c_Natural_Oevalc @ ( c_Com_Ocom_OAss @ C @ B ) @ A @ ( c_Natural_Oupdate @ A @ C @ ( hAPP @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[48]) ).
thf(95,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OAss @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I2_J) ).
thf(680,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OAss @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[95]) ).
thf(74,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OAss @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I24_J) ).
thf(548,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OAss @ D @ C )
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[74]) ).
thf(12,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( c_Com_Ocom_Ocom__rec @ L @ K @ J @ I @ H @ G @ F @ E @ D @ ( c_Com_Ocom_OCall @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I8_J) ).
thf(255,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( c_Com_Ocom_Ocom__rec @ L @ K @ J @ I @ H @ G @ F @ E @ D @ ( c_Com_Ocom_OCall @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[12]) ).
thf(89,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Com_Ocom_Ocom__rec @ K @ J @ I @ H @ G @ F @ E @ D @ C @ ( c_Com_Ocom_OWhile @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ E @ B ) @ A ) @ ( c_Com_Ocom_Ocom__rec @ K @ J @ I @ H @ G @ F @ E @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I6_J) ).
thf(648,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Com_Ocom_Ocom__rec @ K @ J @ I @ H @ G @ F @ E @ D @ C @ ( c_Com_Ocom_OWhile @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ E @ B ) @ A ) @ ( c_Com_Ocom_Ocom__rec @ K @ J @ I @ H @ G @ F @ E @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[89]) ).
thf(68,axiom,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I12_J) ).
thf(516,plain,
! [A: $i,B: $i] :
( c_Com_Ocom_OSKIP
!= ( c_Com_Ocom_OSemi @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[68]) ).
thf(168,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OAss @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I30_J) ).
thf(968,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OAss @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[168]) ).
thf(133,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Com_Ocom_Ocom__case @ K @ J @ I @ H @ G @ F @ E @ D @ C @ ( c_Com_Ocom_OAss @ B @ A ) )
= ( hAPP @ ( hAPP @ I @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I65_J) ).
thf(836,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Com_Ocom_Ocom__case @ K @ J @ I @ H @ G @ F @ E @ D @ C @ ( c_Com_Ocom_OAss @ B @ A ) )
= ( hAPP @ ( hAPP @ I @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[133]) ).
thf(71,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ F @ E @ D @ C @ B ) @ ( hAPP @ ( c_Sum__Type_OInr @ D @ F ) @ A ) )
= ( hAPP @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I6_J) ).
thf(531,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ F @ E @ D @ C @ B ) @ ( hAPP @ ( c_Sum__Type_OInr @ D @ F ) @ A ) )
= ( hAPP @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[71]) ).
thf(162,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Sum__Type_OProjl @ C @ B @ ( hAPP @ ( c_Sum__Type_OInl @ C @ B ) @ A ) )
= A ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Projl_Osimps) ).
thf(944,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Sum__Type_OProjl @ C @ B @ ( hAPP @ ( c_Sum__Type_OInl @ C @ B ) @ A ) )
= A ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[162]) ).
thf(79,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Com_Ocom_OCall @ F @ E @ D )
= ( c_Com_Ocom_OCall @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I7_J) ).
thf(580,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Com_Ocom_OCall @ F @ E @ D )
= ( c_Com_Ocom_OCall @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( c_Com_Ocom_OCall @ F @ E @ D )
= ( c_Com_Ocom_OCall @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[79]) ).
thf(98,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A )
<=> ( ( ( A = B )
& ~ ( hBOOL @ ( hAPP @ D @ B ) ) )
| ( ( hBOOL @ ( hAPP @ D @ B ) )
& ? [E: $i] :
( ( c_Natural_Oevalc @ C @ B @ E )
& ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_Oequations_I8_J) ).
thf(690,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A )
=> ( ( ( A = B )
& ~ ( hBOOL @ ( hAPP @ D @ B ) ) )
| ( ( hBOOL @ ( hAPP @ D @ B ) )
& ? [E: $i] :
( ( c_Natural_Oevalc @ C @ B @ E )
& ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A ) ) ) ) )
& ( ( ( ( A = B )
& ~ ( hBOOL @ ( hAPP @ D @ B ) ) )
| ( ( hBOOL @ ( hAPP @ D @ B ) )
& ? [E: $i] :
( ( c_Natural_Oevalc @ C @ B @ E )
& ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A ) ) ) )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[98]) ).
thf(25,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OWhile @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I53_J) ).
thf(295,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OWhile @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[25]) ).
thf(141,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( c_Com_Ocom_Ocom__case @ I @ H @ G @ F @ E @ D @ C @ B @ A @ c_Com_Ocom_OSKIP )
= H ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I64_J) ).
thf(872,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i] :
( ( c_Com_Ocom_Ocom__case @ I @ H @ G @ F @ E @ D @ C @ B @ A @ c_Com_Ocom_OSKIP )
= H ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[141]) ).
thf(145,axiom,
! [A: $i] :
( ( ( hAPP @ c_Com_Obody @ A )
!= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OBody) ).
thf(887,plain,
! [A: $i] :
( ( ( hAPP @ c_Com_Obody @ A )
!= ( c_Option_Ooption_ONone @ tc_Com_Ocom ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OBODY @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[145]) ).
thf(165,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__case @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_pair__box_Osimps_I2_J) ).
thf(954,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Nitpick_Opair__box_Opair__box__case @ F @ E @ D @ C @ ( c_Nitpick_Opair__box_OPairBox @ F @ E @ B @ A ) )
= ( hAPP @ ( hAPP @ C @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[165]) ).
thf(45,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( c_Natural_Oevalc @ C @ D @ B )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ A @ C ) @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OIfFalse) ).
thf(409,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ~ ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( c_Natural_Oevalc @ C @ D @ B )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ A @ C ) @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[45]) ).
thf(15,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ C ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OLocal @ B @ A @ C ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OLocal) ).
thf(263,plain,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ C ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OLocal @ B @ A @ C ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[15]) ).
thf(175,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( ( hAPP @ E @ B )
= ( hAPP @ E @ A ) )
<=> ( B = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_type__definition_ORep__inject) ).
thf(993,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Typedef_Otype__definition @ G @ F @ E @ D @ C )
=> ( ( ( ( hAPP @ E @ B )
= ( hAPP @ E @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ E @ B )
= ( hAPP @ E @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[175]) ).
thf(121,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Com_Ocom_Ocom__case @ K @ J @ I @ H @ G @ F @ E @ D @ C @ ( c_Com_Ocom_OWhile @ B @ A ) )
= ( hAPP @ ( hAPP @ E @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I69_J) ).
thf(791,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Com_Ocom_Ocom__case @ K @ J @ I @ H @ G @ F @ E @ D @ C @ ( c_Com_Ocom_OWhile @ B @ A ) )
= ( hAPP @ ( hAPP @ E @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[121]) ).
thf(33,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OLocal @ F @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I42_J) ).
thf(331,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OLocal @ F @ E @ D )
!= ( c_Com_Ocom_OCall @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[33]) ).
thf(57,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( c_Com_Ocom_Ocom__rec @ L @ K @ J @ I @ H @ G @ F @ E @ D @ ( c_Com_Ocom_OLocal @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ I @ C ) @ B ) @ A ) @ ( c_Com_Ocom_Ocom__rec @ L @ K @ J @ I @ H @ G @ F @ E @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I3_J) ).
thf(470,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( c_Com_Ocom_Ocom__rec @ L @ K @ J @ I @ H @ G @ F @ E @ D @ ( c_Com_Ocom_OLocal @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ I @ C ) @ B ) @ A ) @ ( c_Com_Ocom_Ocom__rec @ L @ K @ J @ I @ H @ G @ F @ E @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[57]) ).
thf(39,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( c_Com_Ocom_OCond @ F @ E @ D )
= ( c_Com_Ocom_OCond @ C @ B @ A ) )
<=> ( ( F = C )
& ( E = B )
& ( D = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I4_J) ).
thf(359,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( ( ( c_Com_Ocom_OCond @ F @ E @ D )
= ( c_Com_Ocom_OCond @ C @ B @ A ) )
=> ( ( F = C )
& ( E = B )
& ( D = A ) ) )
& ( ( ( F = C )
& ( E = B )
& ( D = A ) )
=> ( ( c_Com_Ocom_OCond @ F @ E @ D )
= ( c_Com_Ocom_OCond @ C @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[39]) ).
thf(99,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( c_Com_Ocom_Ocom__case @ L @ K @ J @ I @ H @ G @ F @ E @ D @ ( c_Com_Ocom_OLocal @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ I @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I66_J) ).
thf(703,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( c_Com_Ocom_Ocom__case @ L @ K @ J @ I @ H @ G @ F @ E @ D @ ( c_Com_Ocom_OLocal @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ I @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[99]) ).
thf(183,axiom,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_Suc__inject) ).
thf(1023,plain,
! [A: $i,B: $i] :
( ( ( hAPP @ c_Nat_OSuc @ B )
= ( hAPP @ c_Nat_OSuc @ A ) )
=> ( B = A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[183]) ).
thf(179,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Orotate @ C @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( c_List_Orotate1 @ C ) @ ( hAPP @ ( c_List_Orotate @ C @ B ) @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_rotate__Suc) ).
thf(1008,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_List_Orotate @ C @ ( hAPP @ c_Nat_OSuc @ B ) ) @ A )
= ( hAPP @ ( c_List_Orotate1 @ C ) @ ( hAPP @ ( c_List_Orotate @ C @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[179]) ).
thf(82,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
!= ( hAPP @ ( c_Sum__Type_OInl @ C @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I4_J) ).
thf(612,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Sum__Type_OInr @ D @ C ) @ B )
!= ( hAPP @ ( c_Sum__Type_OInl @ C @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[82]) ).
thf(4,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ G @ F )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ D ) )
=> ( ( c_Map_Omap__comp @ E @ C @ B @ A @ G @ F )
= ( hAPP @ A @ D ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__simps_I2_J) ).
thf(231,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( hAPP @ G @ F )
= ( hAPP @ ( c_Option_Ooption_OSome @ E ) @ D ) )
=> ( ( c_Map_Omap__comp @ E @ C @ B @ A @ G @ F )
= ( hAPP @ A @ D ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[4]) ).
thf(170,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ D ) @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
<=> ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I9_J) ).
thf(976,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ D ) @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
=> ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ B @ A ) )
& ( ( c_Natural_Oevaln @ ( hAPP @ ( c_Option_Othe @ tc_Com_Ocom ) @ ( hAPP @ c_Com_Obody @ D ) ) @ C @ B @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OBODY @ D ) @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[170]) ).
thf(70,axiom,
! [A: $i,B: $i,C: $i] :
( ( ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Oinject) ).
thf(524,plain,
! [A: $i,B: $i,C: $i] :
( ( ( ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ C ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[70]) ).
thf(115,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OCond @ C @ B @ A )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I15_J) ).
thf(771,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OCond @ C @ B @ A )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[115]) ).
thf(52,axiom,
! [A: $i,B: $i,C: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCond @ C @ B @ A ) ) )
<=> ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
& ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I5_J) ).
thf(450,plain,
! [A: $i,B: $i,C: $i] :
( ( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCond @ C @ B @ A ) ) )
=> ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
& ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ c_Com_OWT @ B ) )
& ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OCond @ C @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[52]) ).
thf(200,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OBODY @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I55_J) ).
thf(1084,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OBODY @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[200]) ).
thf(110,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( c_Natural_Oevalc @ C @ D @ B )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ C @ A ) @ D @ B ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OIfTrue) ).
thf(748,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( hBOOL @ ( hAPP @ E @ D ) )
=> ( ( c_Natural_Oevalc @ C @ D @ B )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OCond @ E @ C @ A ) @ D @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[110]) ).
thf(13,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ F @ E @ D @ C @ B ) @ ( hAPP @ ( c_Sum__Type_OInl @ F @ D ) @ A ) )
= ( hAPP @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I5_J) ).
thf(258,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hAPP @ ( c_Sum__Type_Osum_Osum__case @ F @ E @ D @ C @ B ) @ ( hAPP @ ( c_Sum__Type_OInl @ F @ D ) @ A ) )
= ( hAPP @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[13]) ).
thf(156,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OBODY @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I59_J) ).
thf(929,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OBODY @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[156]) ).
thf(132,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCall @ F @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I57_J) ).
thf(832,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCall @ F @ E @ D )
!= ( c_Com_Ocom_OCond @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[132]) ).
thf(37,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCall @ E @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I61_J) ).
thf(346,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OCall @ E @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[37]) ).
thf(124,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCall @ F @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I43_J) ).
thf(800,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCall @ F @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[124]) ).
thf(198,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( c_Com_Ocom_Ocom__case @ J @ I @ H @ G @ F @ E @ D @ C @ B @ ( c_Com_Ocom_OBODY @ A ) )
= ( hAPP @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I70_J) ).
thf(1077,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( c_Com_Ocom_Ocom__case @ J @ I @ H @ G @ F @ E @ D @ C @ B @ ( c_Com_Ocom_OBODY @ A ) )
= ( hAPP @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[198]) ).
thf(59,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OWhile @ B @ A ) ) )
<=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I6_J) ).
thf(478,plain,
! [A: $i,B: $i] :
( ( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OWhile @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) )
& ( ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OWhile @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[59]) ).
thf(164,axiom,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_n__not__Suc__n) ).
thf(950,plain,
! [A: $i] :
( A
!= ( hAPP @ c_Nat_OSuc @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[164]) ).
thf(127,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( c_Com_Ocom_Ocom__case @ L @ K @ J @ I @ H @ G @ F @ E @ D @ ( c_Com_Ocom_OCall @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I71_J) ).
thf(818,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i,L: $i] :
( ( c_Com_Ocom_Ocom__case @ L @ K @ J @ I @ H @ G @ F @ E @ D @ ( c_Com_Ocom_OCall @ C @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ D @ C ) @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[127]) ).
thf(44,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCond @ F @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I37_J) ).
thf(405,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( c_Com_Ocom_OCond @ F @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[44]) ).
thf(136,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Com_Ocom_Ocom__rec @ K @ J @ I @ H @ G @ F @ E @ D @ C @ ( c_Com_Ocom_OSemi @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ G @ B ) @ A ) @ ( c_Com_Ocom_Ocom__rec @ K @ J @ I @ H @ G @ F @ E @ D @ C @ B ) ) @ ( c_Com_Ocom_Ocom__rec @ K @ J @ I @ H @ G @ F @ E @ D @ C @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I4_J) ).
thf(854,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Com_Ocom_Ocom__rec @ K @ J @ I @ H @ G @ F @ E @ D @ C @ ( c_Com_Ocom_OSemi @ B @ A ) )
= ( hAPP @ ( hAPP @ ( hAPP @ ( hAPP @ G @ B ) @ A ) @ ( c_Com_Ocom_Ocom__rec @ K @ J @ I @ H @ G @ F @ E @ D @ C @ B ) ) @ ( c_Com_Ocom_Ocom__rec @ K @ J @ I @ H @ G @ F @ E @ D @ C @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[136]) ).
thf(139,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Com_Ocom_Ocom__case @ K @ J @ I @ H @ G @ F @ E @ D @ C @ ( c_Com_Ocom_OSemi @ B @ A ) )
= ( hAPP @ ( hAPP @ G @ B ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I67_J) ).
thf(865,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i,K: $i] :
( ( c_Com_Ocom_Ocom__case @ K @ J @ I @ H @ G @ F @ E @ D @ C @ ( c_Com_Ocom_OSemi @ B @ A ) )
= ( hAPP @ ( hAPP @ G @ B ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[139]) ).
thf(40,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A @ B )
<=> ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ? [E: $i] :
( ( c_Natural_Oevaln @ C @ B @ A @ E )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A @ B ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_Oequations_I7_J) ).
thf(373,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A @ B )
=> ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ? [E: $i] :
( ( c_Natural_Oevaln @ C @ B @ A @ E )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A @ B ) ) ) )
& ( ( ( hBOOL @ ( hAPP @ D @ B ) )
=> ? [E: $i] :
( ( c_Natural_Oevaln @ C @ B @ A @ E )
& ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ E @ A @ B ) ) )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ D @ C ) @ B @ A @ B ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[40]) ).
thf(196,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ G @ F @ E @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ E @ A ) @ A )
= A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_folding__image__simple__idem_Oidem) ).
thf(1065,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( c_Finite__Set_Ofolding__image__simple__idem @ G @ F @ E @ D @ C @ B )
=> ( ( hAPP @ ( hAPP @ E @ A ) @ A )
= A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[196]) ).
thf(123,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OAss @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I22_J) ).
thf(796,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OAss @ E @ D )
!= ( c_Com_Ocom_OLocal @ C @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[123]) ).
thf(47,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( c_Com_Ocom_OSemi @ D @ C )
= ( c_Com_Ocom_OSemi @ B @ A ) )
<=> ( ( D = B )
& ( C = A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I3_J) ).
thf(415,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( ( ( c_Com_Ocom_OSemi @ D @ C )
= ( c_Com_Ocom_OSemi @ B @ A ) )
=> ( ( D = B )
& ( C = A ) ) )
& ( ( ( D = B )
& ( C = A ) )
=> ( ( c_Com_Ocom_OSemi @ D @ C )
= ( c_Com_Ocom_OSemi @ B @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[47]) ).
thf(65,axiom,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OWhile @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WTs__elim__cases_I6_J) ).
thf(506,plain,
! [A: $i,B: $i] :
( ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OWhile @ B @ A ) ) )
=> ( hBOOL @ ( hAPP @ c_Com_OWT @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[65]) ).
thf(17,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevalc @ E @ D @ C )
=> ( ( c_Natural_Oevalc @ B @ C @ A )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ E @ B ) @ D @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evalc_OSemi) ).
thf(268,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevalc @ E @ D @ C )
=> ( ( c_Natural_Oevalc @ B @ C @ A )
=> ( c_Natural_Oevalc @ ( c_Com_Ocom_OSemi @ E @ B ) @ D @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[17]) ).
thf(148,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OCall @ D @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I63_J) ).
thf(897,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OCall @ D @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[148]) ).
thf(114,axiom,
! [A: $i,B: $i] :
( ( B
!= ( c_Option_Ooption_ONone @ A ) )
=> ~ ! [C: $i] :
( B
!= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_option_Oexhaust) ).
thf(767,plain,
! [A: $i,B: $i] :
( ( B
!= ( c_Option_Ooption_ONone @ A ) )
=> ~ ! [C: $i] :
( B
!= ( hAPP @ ( c_Option_Ooption_OSome @ A ) @ C ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[114]) ).
thf(106,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
!= ( hAPP @ ( c_Sum__Type_OInr @ C @ D ) @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_sum_Osimps_I3_J) ).
thf(728,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( hAPP @ ( c_Sum__Type_OInl @ D @ C ) @ B )
!= ( hAPP @ ( c_Sum__Type_OInr @ C @ D ) @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[106]) ).
thf(173,axiom,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__single @ C @ B ) @ A )
= ( c_Lazy__Sequence_Osingle @ C @ B ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_New__DSequence_Opos__single__def) ).
thf(987,plain,
! [A: $i,B: $i,C: $i] :
( ( hAPP @ ( c_New__DSequence_Opos__single @ C @ B ) @ A )
= ( c_Lazy__Sequence_Osingle @ C @ B ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[173]) ).
thf(55,axiom,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OAss @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OAssign) ).
thf(464,plain,
! [A: $i,B: $i] : ( hBOOL @ ( hAPP @ c_Com_OWT @ ( c_Com_Ocom_OAss @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[55]) ).
thf(182,axiom,
! [A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I19_J) ).
thf(1019,plain,
! [A: $i] :
( ( c_Com_Ocom_OBODY @ A )
!= c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[182]) ).
thf(88,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OSemi @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I46_J) ).
thf(644,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( c_Com_Ocom_OSemi @ D @ C )
!= ( c_Com_Ocom_OWhile @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[88]) ).
thf(50,axiom,
hBOOL @ ( hAPP @ c_Com_OWT @ c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_OSkip) ).
thf(442,plain,
hBOOL @ ( hAPP @ c_Com_OWT @ c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[50]) ).
thf(203,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ E @ D ) @ C @ B @ A )
=> ~ ! [F: $i] :
( ( c_Natural_Oevaln @ E @ C @ B @ F )
=> ~ ( c_Natural_Oevaln @ D @ F @ B @ A ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__elim__cases_I4_J) ).
thf(1093,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OSemi @ E @ D ) @ C @ B @ A )
=> ~ ! [F: $i] :
( ( c_Natural_Oevaln @ E @ C @ B @ F )
=> ~ ( c_Natural_Oevaln @ D @ F @ B @ A ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[203]) ).
thf(134,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( c_Natural_Oevaln @ D @ E @ C @ B )
=> ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ F @ D ) @ B @ C @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ F @ D ) @ E @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln_OWhileTrue) ).
thf(839,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i] :
( ( hBOOL @ ( hAPP @ F @ E ) )
=> ( ( c_Natural_Oevaln @ D @ E @ C @ B )
=> ( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ F @ D ) @ B @ C @ A )
=> ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ F @ D ) @ E @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[134]) ).
thf(11,axiom,
hBOOL @ ( hAPP @ c_Com_OWT @ c_Com_Ocom_OSKIP ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_WT_Oequations_I1_J) ).
thf(254,plain,
hBOOL @ ( hAPP @ c_Com_OWT @ c_Com_Ocom_OSKIP ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[11]) ).
thf(160,axiom,
( c_Com_Obody
= ( c_Map_Omap__of @ tc_Com_Opname @ tc_Com_Ocom @ c_Com_Obodies ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_body__def) ).
thf(940,plain,
( c_Com_Obody
= ( c_Map_Omap__of @ tc_Com_Opname @ tc_Com_Ocom @ c_Com_Obodies ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[160]) ).
thf(201,axiom,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Osemiring__1 @ D )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat__aux @ D @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_Nat_Osemiring__1__class_Oof__nat__aux @ D @ C @ B @ ( hAPP @ C @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_of__nat__aux_Osimps_I2_J) ).
thf(1088,plain,
! [A: $i,B: $i,C: $i,D: $i] :
( ( class_Rings_Osemiring__1 @ D )
=> ( ( c_Nat_Osemiring__1__class_Oof__nat__aux @ D @ C @ ( hAPP @ c_Nat_OSuc @ B ) @ A )
= ( c_Nat_Osemiring__1__class_Oof__nat__aux @ D @ C @ B @ ( hAPP @ C @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[201]) ).
thf(3,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( c_Map_Omap__comp @ G @ F @ E @ D @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) )
<=> ? [H: $i] :
( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ G ) @ H ) )
& ( ( hAPP @ D @ H )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_map__comp__Some__iff) ).
thf(222,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i] :
( ( ( ( c_Map_Omap__comp @ G @ F @ E @ D @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) )
=> ? [H: $i] :
( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ G ) @ H ) )
& ( ( hAPP @ D @ H )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) )
& ( ? [H: $i] :
( ( ( hAPP @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ G ) @ H ) )
& ( ( hAPP @ D @ H )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) )
=> ( ( c_Map_Omap__comp @ G @ F @ E @ D @ C @ B )
= ( hAPP @ ( c_Option_Ooption_OSome @ F ) @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[3]) ).
thf(169,axiom,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OWhile @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I58_J) ).
thf(972,plain,
! [A: $i,B: $i,C: $i] :
( ( c_Com_Ocom_OWhile @ C @ B )
!= ( c_Com_Ocom_OBODY @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[169]) ).
thf(188,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( c_Com_Ocom_Ocom__rec @ J @ I @ H @ G @ F @ E @ D @ C @ B @ ( c_Com_Ocom_OBODY @ A ) )
= ( hAPP @ C @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Orecs_I7_J) ).
thf(1037,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i,F: $i,G: $i,H: $i,I: $i,J: $i] :
( ( c_Com_Ocom_Ocom__rec @ J @ I @ H @ G @ F @ E @ D @ C @ B @ ( c_Com_Ocom_OBODY @ A ) )
= ( hAPP @ C @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[188]) ).
thf(116,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OLocal @ E @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I23_J) ).
thf(775,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Com_Ocom_OLocal @ E @ D @ C )
!= ( c_Com_Ocom_OAss @ B @ A ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[116]) ).
thf(64,axiom,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ C @ B @ A )
=> ( ( ( A = C )
=> ( hBOOL @ ( hAPP @ E @ C ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ E @ C ) )
=> ! [F: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ F )
=> ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ F @ B @ A ) ) ) ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_evaln__WHILE__case) ).
thf(496,plain,
! [A: $i,B: $i,C: $i,D: $i,E: $i] :
( ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ C @ B @ A )
=> ( ( ( A = C )
=> ( hBOOL @ ( hAPP @ E @ C ) ) )
=> ~ ( ( hBOOL @ ( hAPP @ E @ C ) )
=> ! [F: $i] :
( ( c_Natural_Oevaln @ D @ C @ B @ F )
=> ~ ( c_Natural_Oevaln @ ( c_Com_Ocom_OWhile @ E @ D ) @ F @ B @ A ) ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[64]) ).
thf(197,axiom,
! [A: $i,B: $i] :
( ( ( c_Com_Ocom_OBODY @ B )
= ( c_Com_Ocom_OBODY @ A ) )
<=> ( B = A ) ),
file('/export/starexec/sandbox/benchmark/theBenchmark.p',fact_com_Osimps_I6_J) ).
thf(1069,plain,
! [A: $i,B: $i] :
( ( ( ( c_Com_Ocom_OBODY @ B )
= ( c_Com_Ocom_OBODY @ A ) )
=> ( B = A ) )
& ( ( B = A )
=> ( ( c_Com_Ocom_OBODY @ B )
= ( c_Com_Ocom_OBODY @ A ) ) ) ),
inference(defexp_and_simp_and_etaexpand,[status(thm)],[197]) ).
thf(1132,plain,
$false,
inference(cvc4,[status(thm)],[750,1031,234,1110,1005,276,247,861,715,814,538,670,841,288,651,724,719,785,619,460,284,325,1100,261,492,443,485,821,905,1040,321,981,280,634,1119,411,428,1104,265,307,292,678,270,925,381,534,1047,512,942,957,1091,825,1042,630,788,916,879,329,830,757,682,710,456,317,1121,1096,783,857,1028,339,933,753,489,1016,901,686,212,706,1114,738,984,1002,779,938,1054,1035,674,1026,794,343,237,732,743,875,577,641,936,313,1058,466,335,947,350,919,804,604,274,1117,1011,990,567,245,509,616,890,387,1080,552,594,726,483,520,251,895,964,1061,912,827,1044,868,883,394,563,1000,299,241,922,658,473,426,680,548,255,648,516,968,836,531,944,580,690,295,872,887,954,409,263,993,791,331,470,359,703,1023,1008,612,231,976,524,771,450,1084,748,258,929,832,346,800,1077,478,950,818,405,854,865,373,1065,796,415,506,268,897,767,728,987,464,1019,644,442,1093,839,254,940,1088,222,972,1037,775,496,1069]) ).
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.03/0.12 % Problem : SWW295+1 : TPTP v8.1.2. Released v5.2.0.
% 0.15/0.15 % Command : run_Leo-III %s %d
% 0.16/0.36 % Computer : n012.cluster.edu
% 0.16/0.36 % Model : x86_64 x86_64
% 0.16/0.36 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.16/0.36 % Memory : 8042.1875MB
% 0.16/0.36 % OS : Linux 3.10.0-693.el7.x86_64
% 0.16/0.36 % CPULimit : 300
% 0.16/0.36 % WCLimit : 300
% 0.16/0.36 % DateTime : Thu May 18 22:41:32 EDT 2023
% 0.16/0.37 % CPUTime :
% 0.98/0.90 % [INFO] Parsing problem /export/starexec/sandbox/benchmark/theBenchmark.p ...
% 2.75/1.42 % [INFO] Parsing done (517ms).
% 2.75/1.43 % [INFO] Running in sequential loop mode.
% 3.09/1.63 % [INFO] eprover registered as external prover.
% 3.09/1.63 % [INFO] cvc4 registered as external prover.
% 3.09/1.63 % [INFO] Scanning for conjecture ...
% 4.67/2.02 % [INFO] Found a conjecture and 5204 axioms. Running axiom selection ...
% 6.06/2.52 % [INFO] Axiom selection finished. Selected 209 axioms (removed 4995 axioms).
% 6.55/2.68 % [INFO] Problem is first-order (TPTP FOF).
% 6.55/2.70 % [INFO] Type checking passed.
% 6.55/2.70 % [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 ...
% 13.68/4.39 % External prover 'cvc4' found a proof!
% 13.68/4.39 % [INFO] Killing All external provers ...
% 13.68/4.39 % Time passed: 3869ms (effective reasoning time: 2951ms)
% 13.68/4.39 % 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)>
% 13.68/4.39 % Axioms used in derivation (209): fact_WT_OLocal, fact_com_Osimps_I58_J, fact_While, fact_sum_Osimps_I5_J, fact_com_Osimps_I56_J, fact_evalc__evaln, fact_evalc_Oequations_I8_J, fact_com__det, fact_com_Osimps_I8_J, fact_com_Osimps_I71_J, fact_evalc_OIfFalse, fact_evaln__elim__cases_I5_J, fact_nat__rec__Suc, fact_com_Osimps_I17_J, fact_sum__case__weak__cong, fact_com_Osimps_I50_J, fact_Inr__not__Inl, fact_prod_Orecs, fact_com_Osimps_I22_J, fact_com_Osimps_I31_J, fact_com_Osimps_I37_J, fact_WT_Oequations_I5_J, fact_pair__box_Oinject, fact_com_Osimps_I40_J, fact_WTs__elim__cases_I3_J, fact_com_Osimps_I69_J, fact_evalc__elim__cases_I1_J, fact_com_Osimps_I10_J, fact_option_Osimps_I2_J, fact_com_Osimps_I24_J, fact_com_Osimps_I46_J, fact_evalc__elim__cases_I4_J, fact_evalc_Oequations_I1_J, fact_com_Osimps_I2_J, fact_WTs__elim__cases_I8_J, fact_com_Osimps_I60_J, fact_evaln_OAssign, fact_Projl_Osimps, fact_option_Oexhaust, fact_com_Osimps_I27_J, fact_sum_Osimps_I3_J, fact_neg__single__def, fact_com_Osimps_I59_J, fact_evalc__elim__cases_I6_J, fact_evaln__Suc, fact_com_Orecs_I1_J, fact_split__paired__All, fact_com_Orecs_I4_J, fact_evalc__elim__cases_I2_J, fact_com_Osimps_I62_J, fact_com_Osimps_I14_J, fact_WT_Oequations_I2_J, fact_com_Osimps_I55_J, fact_com_Osimps_I53_J, fact_nat_Oinject, fact_option_Osimps_I3_J, fact_com_Osimps_I3_J, fact_com_Osimps_I20_J, fact_com_Osimps_I5_J, fact_com_Osimps_I66_J, fact_evaln_Oequations_I2_J, fact_evalc_OIfTrue, fact_pos__empty__def, fact_Rep__Integ__inject, fact_com_Osimps_I23_J, fact_WT__bodiesD, fact_com_Osimps_I13_J, fact_com_Osimps_I41_J, fact_WT_Oequations_I7_J, fact_WT_OAssign, fact_com_Orecs_I7_J, fact_evalc_Oequations_I4_J, fact_Inr__inject, fact_WT_OSemi, fact_evaln_OBody, fact_com_Osimps_I30_J, fact_com_Osimps_I57_J, fact_evaln_OWhileFalse, fact_com_Osimps_I47_J, fact_com_Osimps_I63_J, fact_New__DSequence_Oneg__single__def, fact_com_Osimps_I35_J, fact_evaln_Oequations_I7_J, fact_com_Osimps_I18_J, fact_evaln_OSkip, fact_evaln_OIfTrue, fact_evaln_OSemi, fact_sum_Osimps_I6_J, fact_com_Orecs_I2_J, fact_com_Osimps_I12_J, fact_evalc_OSemi, fact_evalc_OSkip, fact_folding__one__idem_Oidem, fact_com_Osimps_I7_J, fact_of__nat__aux_Osimps_I2_J, fact_com_Orecs_I6_J, fact_WTs__elim__cases_I4_J, fact_body__def, fact_com_Osimps_I45_J, fact_com_Osimps_I28_J, fact_com_Orecs_I3_J, fact_pos__single__def, fact_evalc__WHILE__case, fact_rp__inv__image__rp, fact_WT_OBody, fact_com_Osimps_I32_J, fact_pair__box_Orecs, fact_WT_OSkip, fact_not__Some__eq, fact_WT_Oequations_I3_J, fact_com_Osimps_I6_J, fact_WT_Oequations_I4_J, fact_evalc_Oequations_I9_J, fact_com_Osimps_I21_J, fact_not__None__eq, fact_com_Osimps_I26_J, fact_com_Orecs_I8_J, fact_Pair__inject, fact_evaln_OIfFalse, fact_Suc__inject, fact_ext, fact_com_Osimps_I42_J, fact_com_Osimps_I54_J, fact_evaln__WHILE__case, fact_com_Osimps_I33_J, fact_com_Osimps_I67_J, fact_com_Osimps_I48_J, fact_com_Osimps_I68_J, fact_map__comp__None__iff, fact_n__not__Suc__n, fact_com_Osimps_I64_J, fact_evaln_Oequations_I5_J, fact_WTs__elim__cases_I6_J, fact_com_Osimps_I34_J, fact_Inl__inject, fact_WT_Oequations_I8_J, fact_WT_OCall, fact_evaln_Oequations_I6_J, fact_evalc_OBody, fact_com_Osimps_I36_J, fact_WTs__elim__cases_I5_J, fact_evalc_OWhileFalse, fact_com_Orecs_I5_J, fact_com_Osimps_I38_J, fact_map__comp__simps_I1_J, fact_map__comp__simps_I2_J, fact_com_Osimps_I16_J, fact_evaln__elim__cases_I2_J, fact_evalc_OWhileTrue, fact_sum_Osimps_I4_J, fact_New__DSequence_Opos__empty__def, fact_com_Osimps_I11_J, fact_sum_Osimps_I1_J, fact_evaln__elim__cases_I4_J, fact_com_Osimps_I9_J, fact_nat__case__Suc, fact_rotate__Suc, fact_com_Osimps_I44_J, fact_power_Opower_Opower__Suc, fact_evaln_OWhileTrue, fact_map__comp__Some__iff, fact_evalc_Oequations_I5_J, fact_evaln__elim__cases_I6_J, fact_com_Osimps_I29_J, fact_Pair__eq, fact_Projr_Osimps, fact_com_Osimps_I39_J, fact_com_Osimps_I25_J, fact_com_Osimps_I19_J, fact_evalc__elim__cases_I5_J, fact_com_Osimps_I1_J, fact_option_Oinject, fact_sum__case__inject, fact_evaln_Oequations_I4_J, fact_evaln_Oequations_I9_J, fact_com_Osimps_I61_J, fact_WT_Oequations_I1_J, fact_type__definition_ORep__inject, fact_WT_OIf, fact_New__DSequence_Opos__single__def, fact_com_Osimps_I49_J, fact_com_Osimps_I43_J, fact_evalc_Oequations_I2_J, fact_the_Osimps, fact_pair__box_Osimps_I2_J, fact_com_Osimps_I52_J, fact_Suc__n__not__n, fact_pos__not__random__dseq__def, fact_com_Osimps_I15_J, fact_evaln_Oequations_I8_J, fact_com_Osimps_I70_J, fact_sum_Osimps_I2_J, fact_evalc_Oequations_I6_J, fact_WT_Oequations_I6_J, fact_com_Osimps_I4_J, fact_type__definition_ORep__inverse, fact_WTs__elim__cases_I7_J, fact_evalc_OAssign, fact_folding__image__simple__idem_Oidem, fact_com_Osimps_I51_J, fact_eval__eq, fact_com_Osimps_I65_J, fact_evaln__evalc, fact_evalc_Oequations_I7_J, fact_def__nat__rec__Suc, fact_rotate1__rotate__swap, fact_evaln__elim__cases_I1_J, fact_evaln_Oequations_I1_J, fact_Inl__not__Inr
% 13.68/4.39 % No. of inferences in proof: 422
% 13.68/4.39 % SZS status Theorem for /export/starexec/sandbox/benchmark/theBenchmark.p : 3869 ms resp. 2951 ms w/o parsing
% 14.34/4.51 % SZS output start Refutation for /export/starexec/sandbox/benchmark/theBenchmark.p
% See solution above
% 14.34/4.51 % [INFO] Killing All external provers ...
%------------------------------------------------------------------------------