%------------------------------------------------------------------------------
% File     : cvc5---1.0.5
% Problem  : LCL808-1 : TPTP v8.1.2. Released v4.1.0.
% Transfm  : none
% Format   : tptp
% Command  : do_cvc5 %s %d

% Computer : n014.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 : Thu Aug 31 07:03:48 EDT 2023

% Result   : Unsatisfiable 0.22s 0.56s
% Output   : Proof 0.22s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.00/0.14  % Problem    : LCL808-1 : TPTP v8.1.2. Released v4.1.0.
% 0.00/0.15  % Command    : do_cvc5 %s %d
% 0.19/0.36  % Computer : n014.cluster.edu
% 0.19/0.36  % Model    : x86_64 x86_64
% 0.19/0.36  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.19/0.36  % Memory   : 8042.1875MB
% 0.19/0.36  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.19/0.36  % CPULimit   : 300
% 0.19/0.36  % WCLimit    : 300
% 0.19/0.36  % DateTime   : Thu Aug 24 17:31:03 EDT 2023
% 0.19/0.36  % CPUTime    : 
% 0.22/0.50  %----Proving TF0_NAR, FOF, or CNF
% 0.22/0.51  ------- convert to smt2 : /export/starexec/sandbox/tmp/tmp.knKCQSNyuV/cvc5---1.0.5_32097.p...
% 0.22/0.52  ------- get file name : TPTP file name is LCL808-1
% 0.22/0.53  ------- cvc5-fof : /export/starexec/sandbox/solver/bin/cvc5---1.0.5_32097.smt2...
% 0.22/0.53  --- Run --decision=internal --simplification=none --no-inst-no-entail --no-cbqi --full-saturate-quant at 10...
% 0.22/0.56  % SZS status Unsatisfiable for LCL808-1
% 0.22/0.56  % SZS output start Proof for LCL808-1
% 0.22/0.57  (
% 0.22/0.57  (let ((_let_1 (tptp.c_InductTermi_OIT (tptp.c_Lambda_Osubst tptp.v_b____ tptp.v_u____ tptp.v_i____)))) (let ((_let_2 (not _let_1))) (let ((_let_3 (tptp.c_Type_Otyping tptp.v_e____ tptp.v_u____ tptp.v_T____))) (let ((_let_4 (tptp.c_InductTermi_OIT tptp.v_u____))) (let ((_let_5 (forall ((V_ua $$unsorted) (V_ia $$unsorted) (V_ea $$unsorted) (V_T_H $$unsorted)) (or (tptp.c_InductTermi_OIT (tptp.c_Lambda_Osubst tptp.v_b____ V_ua V_ia)) (not (tptp.c_Type_Otyping V_ea V_ua tptp.v_T____)) (not (tptp.c_InductTermi_OIT V_ua)) (not (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_ea V_ia tptp.v_T____ tptp.tc_Type_Otype) tptp.v_b____ V_T_H)))))) (let ((_let_6 (tptp.c_Type_Otyping (tptp.c_Type_Oshift tptp.v_e____ tptp.v_i____ tptp.v_T____ tptp.tc_Type_Otype) tptp.v_b____ tptp.v_Ua____))) (let ((_let_7 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (let ((_let_8 (not _let_6))) (let ((_let_9 (not _let_4))) (let ((_let_10 (not _let_3))) (let ((_let_11 (or _let_1 _let_10 _let_9 _let_8))) (let ((_let_12 (_let_5))) (let ((_let_13 (ASSUME :args _let_12))) (let ((_let_14 (not _let_11))) (SCOPE (SCOPE (MACRO_RESOLUTION_TRUST (IMPLIES_ELIM (SCOPE (INSTANTIATE _let_13 :args (tptp.v_u____ tptp.v_i____ tptp.v_e____ tptp.v_Ua____ QUANTIFIERS_INST_E_MATCHING ((not (= (tptp.c_Type_Otyping V_ea V_ua tptp.v_T____) false)) (not (= (tptp.c_Type_Otyping (tptp.c_Type_Oshift V_ea V_ia tptp.v_T____ tptp.tc_Type_Otype) tptp.v_b____ V_T_H) false))))) :args _let_12)) (MACRO_RESOLUTION_TRUST (REORDERING (CNF_OR_POS :args (_let_11)) :args ((or _let_1 _let_9 _let_8 _let_10 _let_14))) (ASSUME :args (_let_2)) (ASSUME :args (_let_4)) (ASSUME :args (_let_6)) (ASSUME :args (_let_3)) :args (_let_14 true _let_1 false _let_4 false _let_6 false _let_3)) _let_13 :args (false true _let_11 false _let_5)) :args ((forall ((T_a $$unsorted) (V_m $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_HOL_Ozero__class_Ozero T_a) T_a)))) (forall ((T_a $$unsorted)) (or (not (tptp.class_Ring__and__Field_Osemiring__1 T_a)) (= (tptp.c_Nat_Osemiring__1__class_Oof__nat (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) T_a) (tptp.c_HOL_Ozero__class_Ozero T_a)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Nat_Osemiring__char__0 T_a)) (not (= (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a))) (= V_m V_n))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_m $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_Nat_Osemiring__1__class_Oof__nat V_m T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_b $$unsorted) (V_a $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((T_a $$unsorted) (V_a $$unsorted) (V_b $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_a V_b T_a)) (not (tptp.c_HOL_Oord__class_Oless V_b V_a T_a)))) (not (tptp.c_HOL_Oord__class_Oless _let_7 _let_7 tptp.tc_nat)) (forall ((V_n $$unsorted)) (let ((_let_1 (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat))) (or (tptp.c_HOL_Oord__class_Oless _let_1 V_n tptp.tc_nat) (= V_n _let_1)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a)))) (forall ((T_a $$unsorted) (V_n $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__semidom T_a)) (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero T_a) (tptp.c_Nat_Osemiring__1__class_Oof__nat V_n T_a) T_a) (not (tptp.c_HOL_Oord__class_Oless (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) V_n tptp.tc_nat)))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((V_y $$unsorted) (V_x $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_y V_x tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_x V_y tptp.tc_nat) (= V_x V_y))) (forall ((V_n $$unsorted) (V_m $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_n V_m tptp.tc_nat) (tptp.c_HOL_Oord__class_Oless V_m V_n tptp.tc_nat) (= V_m V_n))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (= V_x V_y) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a))) (forall ((T_a $$unsorted) (V_y $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Ring__and__Field_Oordered__idom T_a)) (tptp.c_HOL_Oord__class_Oless V_y V_x T_a) (tptp.c_HOL_Oord__class_Oless V_x V_y T_a) (= V_x V_y))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Olinorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((T_a $$unsorted) (V_x $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x T_a)))) (forall ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n V_n tptp.tc_nat))) (forall ((V_x $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat))) (forall ((T_a $$unsorted) (V_x $$unsorted) (V_z $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Opreorder T_a)) (tptp.c_HOL_Oord__class_Oless V_x V_z T_a) (not (tptp.c_HOL_Oord__class_Oless V_y V_z T_a)) (not (tptp.c_HOL_Oord__class_Oless V_x V_y T_a)))) (forall ((T_a $$unsorted) (V_z $$unsorted) (V_x $$unsorted) (V_y $$unsorted)) (or (not (tptp.class_Orderings_Oorder T_a)) (tptp.c_HOL_Oord__class_Oless V_z V_x T_a) (not (tptp.c_HOL_Oord__class_Oless V_z V_y T_a)) (not (tptp.c_HOL_Oord__class_Oless V_y V_x T_a)))) (forall ((V_m $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_m (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_n $$unsorted)) (not (tptp.c_HOL_Oord__class_Oless V_n (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat) tptp.tc_nat))) (forall ((V_dB1_H $$unsorted) (V_dB2_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Lambda_OdB_OApp V_dB1_H V_dB2_H) (tptp.c_Lambda_OdB_OVar V_nat)))) (forall ((V_s $$unsorted) (V_t $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OAbs V_s) (tptp.c_Lambda_OdB_OAbs V_t)) (not (tptp.c_Lambda_Obeta V_s V_t)))) (forall ((V_s $$unsorted) (V_r $$unsorted)) (or (= V_s (tptp.c_Lambda_OdB_OAbs (tptp.c_Lambda_Osko__Lambda__Xbeta__cases__2__1 V_r V_s))) (not (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OAbs V_r) V_s)))) (forall ((V_t $$unsorted) (V_i $$unsorted)) (or (tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OApp V_t (tptp.c_Lambda_OdB_OVar V_i))) (not (tptp.c_InductTermi_OIT V_t)))) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.c_Lambda_Olift V_r V_i) (tptp.c_Lambda_Olift V_s V_i)) (not (tptp.c_Lambda_Obeta V_r V_s)))) (forall ((V_i $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.c_Lambda_Olift _let_1 V_k) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_i V_k tptp.tc_nat))))) (forall ((V_s $$unsorted) (V_u $$unsorted) (V_t $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OApp V_s V_u) (tptp.c_Lambda_OdB_OApp V_t V_u)) (not (tptp.c_Lambda_Obeta V_s V_t)))) (forall ((V_u $$unsorted) (V_s $$unsorted) (V_t $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OApp V_u V_s) (tptp.c_Lambda_OdB_OApp V_u V_t)) (not (tptp.c_Lambda_Obeta V_s V_t)))) (forall ((V_x $$unsorted) (V_s $$unsorted)) (or (tptp.c_HOL_Oord__class_Oless V_x V_x tptp.tc_nat) (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar V_x) V_s V_x) V_s))) (forall ((V_i $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_i))) (or (= (tptp.c_Lambda_Osubst _let_1 V_s V_k) _let_1) (= V_i V_k) (tptp.c_HOL_Oord__class_Oless V_k V_i tptp.tc_nat)))) (forall ((V_s $$unsorted) (V_t $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Olift (tptp.c_Lambda_OdB_OApp V_s V_t) V_k) (tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Olift V_s V_k) (tptp.c_Lambda_Olift V_t V_k)))) (forall ((V_nat $$unsorted) (V_dB_H $$unsorted)) (not (= (tptp.c_Lambda_OdB_OVar V_nat) (tptp.c_Lambda_OdB_OAbs V_dB_H)))) (forall ((V_dB $$unsorted) (V_dB_H $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OAbs V_dB) (tptp.c_Lambda_OdB_OAbs V_dB_H))) (= V_dB V_dB_H))) (forall ((V_nat $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (not (= (tptp.c_Lambda_OdB_OVar V_nat) (tptp.c_Lambda_OdB_OApp V_dB1_H V_dB2_H)))) (forall ((V_s $$unsorted) (V_t $$unsorted)) (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_OdB_OAbs V_s) V_t) (tptp.c_Lambda_Osubst V_s V_t (tptp.c_HOL_Ozero__class_Ozero tptp.tc_nat)))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OApp V_dB1 V_dB2) (tptp.c_Lambda_OdB_OApp V_dB1_H V_dB2_H))) (= V_dB2 V_dB2_H))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB1_H $$unsorted) (V_dB2_H $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OApp V_dB1 V_dB2) (tptp.c_Lambda_OdB_OApp V_dB1_H V_dB2_H))) (= V_dB1 V_dB1_H))) (forall ((V_i $$unsorted) (V_t $$unsorted)) (not (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OVar V_i) V_t))) (forall ((V_r $$unsorted) (V_s $$unsorted)) (or (tptp.c_Lambda_Obeta V_r (tptp.c_Lambda_Osko__Lambda__Xbeta__cases__2__1 V_r V_s)) (not (tptp.c_Lambda_Obeta (tptp.c_Lambda_OdB_OAbs V_r) V_s)))) (forall ((V_j $$unsorted) (V_u $$unsorted) (V_i $$unsorted)) (let ((_let_1 (tptp.c_Lambda_OdB_OVar V_j))) (or (= (tptp.c_Lambda_Osubst _let_1 V_u V_i) _let_1) (not (tptp.c_HOL_Oord__class_Oless V_j V_i tptp.tc_nat))))) (forall ((V_dB_H $$unsorted) (V_dB1 $$unsorted) (V_dB2 $$unsorted)) (not (= (tptp.c_Lambda_OdB_OAbs V_dB_H) (tptp.c_Lambda_OdB_OApp V_dB1 V_dB2)))) (forall ((V_nat $$unsorted) (V_nat_H $$unsorted)) (or (not (= (tptp.c_Lambda_OdB_OVar V_nat) (tptp.c_Lambda_OdB_OVar V_nat_H))) (= V_nat V_nat_H))) (forall ((V_dB1 $$unsorted) (V_dB2 $$unsorted) (V_dB_H $$unsorted)) (not (= (tptp.c_Lambda_OdB_OApp V_dB1 V_dB2) (tptp.c_Lambda_OdB_OAbs V_dB_H)))) (forall ((V_dB_H $$unsorted) (V_nat $$unsorted)) (not (= (tptp.c_Lambda_OdB_OAbs V_dB_H) (tptp.c_Lambda_OdB_OVar V_nat)))) (forall ((V_t $$unsorted) (V_u $$unsorted) (V_s $$unsorted) (V_k $$unsorted)) (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OApp V_t V_u) V_s V_k) (tptp.c_Lambda_OdB_OApp (tptp.c_Lambda_Osubst V_t V_s V_k) (tptp.c_Lambda_Osubst V_u V_s V_k)))) (forall ((V_k $$unsorted) (V_u $$unsorted)) (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_OdB_OVar V_k) V_u V_k) V_u)) (forall ((V_r $$unsorted) (V_i $$unsorted) (V_j $$unsorted)) (or (tptp.c_InductTermi_OIT (tptp.c_Lambda_Osubst V_r (tptp.c_Lambda_OdB_OVar V_i) V_j)) (not (tptp.c_InductTermi_OIT V_r)))) (forall ((V_t $$unsorted) (V_i $$unsorted)) (or (tptp.c_InductTermi_OIT (tptp.c_Lambda_Olift V_t V_i)) (not (tptp.c_InductTermi_OIT V_t)))) (= tptp.v_n____ tptp.v_i____) (forall ((V_n $$unsorted)) (tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OVar V_n))) (forall ((V_r $$unsorted) (V_t $$unsorted) (V_i $$unsorted) (V_s $$unsorted)) (or (tptp.c_Lambda_Obeta (tptp.c_Lambda_Osubst V_r V_t V_i) (tptp.c_Lambda_Osubst V_s V_t V_i)) (not (tptp.c_Lambda_Obeta V_r V_s)))) (tptp.c_InductTermi_OIT tptp.v_ua______) (forall ((V_r $$unsorted)) (or (tptp.c_InductTermi_OIT (tptp.c_Lambda_OdB_OAbs V_r)) (not (tptp.c_InductTermi_OIT V_r)))) _let_4 (forall ((V_t $$unsorted) (V_k $$unsorted) (V_s $$unsorted)) (= (tptp.c_Lambda_Osubst (tptp.c_Lambda_Olift V_t V_k) V_s V_k) V_t)) _let_6 _let_5 _let_4 _let_3 _let_2 (tptp.class_Ring__and__Field_Oordered__semidom tptp.tc_nat) (tptp.class_Ring__and__Field_Osemiring__1 tptp.tc_nat) (tptp.class_Nat_Osemiring__char__0 tptp.tc_nat) (tptp.class_Orderings_Opreorder tptp.tc_nat) (tptp.class_Orderings_Olinorder tptp.tc_nat) (tptp.class_Orderings_Oorder tptp.tc_nat))))))))))))))))))
% 0.22/0.57  )
% 0.22/0.57  % SZS output end Proof for LCL808-1
% 0.22/0.57  % cvc5---1.0.5 exiting
% 0.22/0.57  % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------