TSTP Solution File: ALG269^4 by cvc5-SAT---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5-SAT---1.0.5
% Problem : ALG269^4 : TPTP v8.1.2. Bugfixed v5.2.0.
% Transfm : none
% Format : tptp:raw
% Command : do_cvc5 %s %d
% Computer : n011.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 Nov 24 04:05:36 EST 2023
% Result : Unknown 2.35s 2.67s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.11/0.12 % Problem : ALG269^4 : TPTP v8.1.2. Bugfixed v5.2.0.
% 0.11/0.13 % Command : do_cvc5 %s %d
% 0.14/0.35 % Computer : n011.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 300
% 0.14/0.35 % DateTime : Thu Nov 23 00:54:35 EST 2023
% 0.14/0.35 % CPUTime :
% 2.35/2.67 ------- cvc5-thf for SAT : /export/starexec/sandbox2/tmp/tmp.3f0KZ4u9Br/cvc5---1.0.5_6253.p at 300...
% 2.35/2.67 --- Run --uf-ho --finite-model-find --ho-elim at 2...
% 2.35/2.67 --- Run --uf-ho --finite-model-find...
% 2.35/2.67 % SZS status GaveUp for cvc5---1.0.5_6253
% 2.35/2.67 % SZS output start CandidateFiniteModel for cvc5---1.0.5_6253
% 2.35/2.67 (
% 2.35/2.67 ; cardinality of $$unsorted is 1
% 2.35/2.67 ; rep: (as @$$unsorted_0 $$unsorted)
% 2.35/2.67 ; cardinality of tptp.term is 1
% 2.35/2.67 ; rep: (as @tptp.term_0 tptp.term)
% 2.35/2.67 ; cardinality of tptp.subst is 1
% 2.35/2.67 ; rep: (as @tptp.subst_0 tptp.subst)
% 2.35/2.67 (define-fun tptp.one () tptp.term (as @tptp.term_0 tptp.term))
% 2.35/2.67 (define-fun tptp.ap ((BOUND_VARIABLE_6773 tptp.term) (BOUND_VARIABLE_6775 tptp.term)) tptp.term (as @tptp.term_0 tptp.term))
% 2.35/2.67 (define-fun tptp.lam ((BOUND_VARIABLE_6778 tptp.term)) tptp.term (as @tptp.term_0 tptp.term))
% 2.35/2.67 (define-fun tptp.sub ((BOUND_VARIABLE_6782 tptp.term) (BOUND_VARIABLE_6784 tptp.subst)) tptp.term (as @tptp.term_0 tptp.term))
% 2.35/2.67 (define-fun tptp.id () tptp.subst (as @tptp.subst_0 tptp.subst))
% 2.35/2.67 (define-fun tptp.sh () tptp.subst (as @tptp.subst_0 tptp.subst))
% 2.35/2.67 (define-fun tptp.push ((BOUND_VARIABLE_6787 tptp.term) (BOUND_VARIABLE_6788 tptp.subst)) tptp.subst (as @tptp.subst_0 tptp.subst))
% 2.35/2.67 (define-fun tptp.comp ((BOUND_VARIABLE_6791 tptp.subst) (BOUND_VARIABLE_6792 tptp.subst)) tptp.subst (as @tptp.subst_0 tptp.subst))
% 2.35/2.67 (define-fun tptp.var ((BOUND_VARIABLE_6795 tptp.term)) Bool false)
% 2.35/2.67 (define-fun tptp.pushprop_lem1v2 () Bool (forall ((P (-> tptp.term Bool)) (Q (-> tptp.term Bool)) (A tptp.term) (M tptp.subst)) (or (not (@ P A)) (not (forall ((X tptp.term)) (= (@ P (@ (@ tptp.sub X) (@ (@ tptp.push A) M))) (@ Q X)))) (@ Q tptp.one))))
% 2.35/2.67 (define-fun tptp.pushprop_lem1_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.axmap () Bool true)
% 2.35/2.67 (define-fun tptp.pushprop_lem0_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.shinj () Bool (forall ((A tptp.term) (B tptp.term)) (or (not (= (@ (@ tptp.sub A) tptp.sh) (@ (@ tptp.sub B) tptp.sh))) (= A B))))
% 2.35/2.67 (define-fun tptp.hoasinduction_lem1v2 () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem1v2_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoasap ((BOUND_VARIABLE_7299 tptp.subst) (BOUND_VARIABLE_7301 tptp.term) (BOUND_VARIABLE_7303 tptp.subst) (BOUND_VARIABLE_7306 tptp.term)) tptp.term (as @tptp.term_0 tptp.term))
% 2.35/2.67 (define-fun tptp.induction2lem () Bool (forall ((P (-> tptp.term Bool)) (BOUND_VARIABLE_3337 tptp.subst) (BOUND_VARIABLE_3335 tptp.term)) (or (not (forall ((A tptp.term) (B tptp.term)) (or (not (@ P A)) (not (@ P B)) (@ P (@ (@ tptp.ap A) B))))) (not (forall ((A tptp.term)) (or (not (forall ((B tptp.term)) (or (not (@ P B)) (@ P (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id)))))) (@ P (@ tptp.lam A))))) (not (forall ((B tptp.term)) (or (not (@ tptp.var B)) (@ P (@ (@ tptp.sub B) BOUND_VARIABLE_3337))))) (@ P (@ (@ tptp.sub BOUND_VARIABLE_3335) BOUND_VARIABLE_3337)))))
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3v2_f () Bool (forall ((B tptp.term)) (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (not (forall ((A tptp.term) (M tptp.subst)) (= (@ (@ F M) A) (@ (@ tptp.sub B) (@ (@ tptp.push A) M)))))))))
% 2.35/2.67 (define-fun tptp.axvarshift () Bool true)
% 2.35/2.67 (define-fun tptp.hoasapinj2 () Bool (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (or (not (= (@ (@ tptp.ap (@ (@ tptp.sub A) tptp.id)) C) (@ (@ tptp.ap (@ (@ tptp.sub B) tptp.id)) D))) (= C D))))
% 2.35/2.67 (define-fun tptp.hoasapnotvar_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoasapinj1 () Bool (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (or (not (= (@ (@ tptp.ap (@ (@ tptp.sub A) tptp.id)) C) (@ (@ tptp.ap (@ (@ tptp.sub B) tptp.id)) D))) (= A B))))
% 2.35/2.67 (define-fun tptp.ulamvar1 () Bool false)
% 2.35/2.67 (define-fun tptp.induction2lem_lthm () Bool (=> (forall ((A tptp.term) (M tptp.subst)) (= A (@ (@ tptp.sub tptp.one) (@ (@ tptp.push A) M)))) (=> (forall ((A tptp.term) (M tptp.subst)) (= M (@ (@ tptp.comp tptp.sh) (@ (@ tptp.push A) M)))) (=> (forall ((M tptp.subst)) (= M (@ (@ tptp.comp M) tptp.id))) (=> (forall ((P (-> tptp.term Bool)) (BOUND_VARIABLE_3181 tptp.term)) (or (not (forall ((A tptp.term)) (or (not (@ tptp.var A)) (@ P A)))) (not (forall ((A tptp.term) (B tptp.term)) (or (not (@ P A)) (not (@ P B)) (@ P (@ (@ tptp.ap A) B))))) (not (forall ((A tptp.term)) (or (not (@ P A)) (@ P (@ tptp.lam A))))) (@ P BOUND_VARIABLE_3181))) (forall ((P (-> tptp.term Bool)) (BOUND_VARIABLE_3337 tptp.subst) (BOUND_VARIABLE_3335 tptp.term)) (or (not (forall ((A tptp.term) (B tptp.term)) (or (not (@ P A)) (not (@ P B)) (@ P (@ (@ tptp.ap A) B))))) (not (forall ((A tptp.term)) (or (not (forall ((B tptp.term)) (or (not (@ P B)) (@ P (@ (@ tptp.sub A) (@ (@ tptp.push B) tptp.id)))))) (@ P (@ tptp.lam A))))) (not (forall ((B tptp.term)) (or (not (@ tptp.var B)) (@ P (@ (@ tptp.sub B) BOUND_VARIABLE_3337))))) (@ P (@ (@ tptp.sub BOUND_VARIABLE_3335) BOUND_VARIABLE_3337)))))))))
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3v2_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.apnotvar () Bool true)
% 2.35/2.67 (define-fun tptp.pushprop_lthm_orig () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3v2_f_lthm () Bool (forall ((B tptp.term)) (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (not (forall ((A tptp.term) (M tptp.subst)) (= (@ (@ F M) A) (@ (@ tptp.sub B) (@ (@ tptp.push A) M)))))))))
% 2.35/2.67 (define-fun tptp.hoasinduction_lthm () Bool (=> (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_3789 tptp.term) (BOUND_VARIABLE_3787 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((A tptp.term) (B tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (not (@ (@ (@ P tptp.id) B) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.ap (@ (@ tptp.sub A) tptp.id)) B)) tptp.id)))) (not (@ (@ (@ P tptp.id) BOUND_VARIABLE_3787) tptp.id)) (not (@ (@ (@ P tptp.id) BOUND_VARIABLE_3789) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.ap BOUND_VARIABLE_3787) BOUND_VARIABLE_3789)) tptp.id))) (=> (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_4009 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ F tptp.sh) tptp.one))) tptp.id)))) (not (forall ((B tptp.term)) (or (not (@ (@ (@ P tptp.id) B) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.sub BOUND_VARIABLE_4009) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam BOUND_VARIABLE_4009)) tptp.id))) (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_4125 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((A tptp.term)) (or (not (@ tptp.var (@ (@ tptp.sub A) tptp.id))) (@ (@ (@ P tptp.id) A) tptp.id)))) (not (forall ((A tptp.term) (B tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (not (@ (@ (@ P tptp.id) B) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.ap (@ (@ tptp.sub A) tptp.id)) B)) tptp.id)))) (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ F tptp.sh) tptp.one))) tptp.id)))) (@ (@ (@ P tptp.id) BOUND_VARIABLE_4125) tptp.id))))))
% 2.35/2.67 (define-fun tptp.hoasinduction_no_psi_cond_lthm () Bool false)
% 2.35/2.67 (define-fun tptp.hoaslaminj () Bool (forall ((F (-> tptp.subst tptp.term tptp.term)) (BOUND_VARIABLE_3454 tptp.subst) (BOUND_VARIABLE_3452 tptp.term) (BOUND_VARIABLE_3450 (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ BOUND_VARIABLE_3450 M) A)) N) (@ (@ BOUND_VARIABLE_3450 (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (= (@ tptp.lam (@ (@ F tptp.sh) tptp.one)) (@ tptp.lam (@ (@ BOUND_VARIABLE_3450 tptp.sh) tptp.one)))) (= (@ (@ F BOUND_VARIABLE_3454) BOUND_VARIABLE_3452) (@ (@ BOUND_VARIABLE_3450 BOUND_VARIABLE_3454) BOUND_VARIABLE_3452)))))
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3aaa () Bool (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_3950 tptp.term)) (or (not (forall ((F (-> tptp.subst tptp.term tptp.term)) (BOUND_VARIABLE_3914 tptp.term)) (or (not (forall ((A tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ F tptp.sh) tptp.one))) tptp.id) (not (forall ((BOUND_VARIABLE_3856 tptp.subst) (BOUND_VARIABLE_3858 tptp.term) (BOUND_VARIABLE_3860 tptp.subst)) (= (@ (@ tptp.sub (@ (@ F BOUND_VARIABLE_3856) BOUND_VARIABLE_3858)) BOUND_VARIABLE_3860) (@ (@ tptp.sub (@ (@ tptp.sub BOUND_VARIABLE_3914) (@ (@ tptp.push BOUND_VARIABLE_3858) BOUND_VARIABLE_3856))) BOUND_VARIABLE_3860)))) (not (forall ((BOUND_VARIABLE_3874 tptp.subst) (BOUND_VARIABLE_3876 tptp.term) (BOUND_VARIABLE_3878 tptp.subst)) (= (@ (@ F (@ (@ tptp.comp BOUND_VARIABLE_3874) BOUND_VARIABLE_3878)) (@ (@ tptp.sub BOUND_VARIABLE_3876) BOUND_VARIABLE_3878)) (@ (@ tptp.sub BOUND_VARIABLE_3914) (@ (@ tptp.push (@ (@ tptp.sub BOUND_VARIABLE_3876) BOUND_VARIABLE_3878)) (@ (@ tptp.comp BOUND_VARIABLE_3874) BOUND_VARIABLE_3878))))))))) (not (forall ((B tptp.term)) (or (not (@ (@ (@ P tptp.id) B) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.sub BOUND_VARIABLE_3950) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ tptp.sub BOUND_VARIABLE_3950) (@ (@ tptp.push tptp.one) tptp.sh)))) tptp.id))))
% 2.35/2.67 (define-fun tptp.induction2lem_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3aa_lthm () Bool (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_3835 tptp.term)) (or (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ F tptp.sh) tptp.one))) tptp.id)))) (not (forall ((B tptp.term)) (or (not (@ (@ (@ P tptp.id) B) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.sub BOUND_VARIABLE_3835) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ tptp.sub BOUND_VARIABLE_3835) (@ (@ tptp.push tptp.one) tptp.sh)))) tptp.id))))
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3 () Bool (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_4009 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ F tptp.sh) tptp.one))) tptp.id)))) (not (forall ((B tptp.term)) (or (not (@ (@ (@ P tptp.id) B) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.sub BOUND_VARIABLE_4009) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam BOUND_VARIABLE_4009)) tptp.id))))
% 2.35/2.67 (define-fun tptp.hoasinduction_lem2 () Bool (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_3789 tptp.term) (BOUND_VARIABLE_3787 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((A tptp.term) (B tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (not (@ (@ (@ P tptp.id) B) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.ap (@ (@ tptp.sub A) tptp.id)) B)) tptp.id)))) (not (@ (@ (@ P tptp.id) BOUND_VARIABLE_3787) tptp.id)) (not (@ (@ (@ P tptp.id) BOUND_VARIABLE_3789) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.ap BOUND_VARIABLE_3787) BOUND_VARIABLE_3789)) tptp.id))))
% 2.35/2.67 (define-fun tptp.termmset_lthm () Bool (forall ((A tptp.term)) (= A (@ (@ tptp.sub A) tptp.id))))
% 2.35/2.67 (define-fun tptp.hoasinduction_lem1 () Bool true)
% 2.35/2.67 (define-fun tptp.hoaslamnotap_lthm () Bool true)
% 2.35/2.67 (define-fun tptp.pushprop_lem1v2_lthm () Bool (=> (forall ((A tptp.term) (M tptp.subst)) (= A (@ (@ tptp.sub tptp.one) (@ (@ tptp.push A) M)))) (forall ((P (-> tptp.term Bool)) (Q (-> tptp.term Bool)) (A tptp.term) (M tptp.subst)) (or (not (@ P A)) (not (forall ((X tptp.term)) (= (@ P (@ (@ tptp.sub X) (@ (@ tptp.push A) M))) (@ Q X)))) (@ Q tptp.one)))))
% 2.35/2.67 (define-fun tptp.hoasapnotvar () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem0 () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction () Bool (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_4125 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((A tptp.term)) (or (not (@ tptp.var (@ (@ tptp.sub A) tptp.id))) (@ (@ (@ P tptp.id) A) tptp.id)))) (not (forall ((A tptp.term) (B tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (not (@ (@ (@ P tptp.id) B) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.ap (@ (@ tptp.sub A) tptp.id)) B)) tptp.id)))) (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ F tptp.sh) tptp.one))) tptp.id)))) (@ (@ (@ P tptp.id) BOUND_VARIABLE_4125) tptp.id))))
% 2.35/2.67 (define-fun tptp.hoasinduction_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.axapp () Bool true)
% 2.35/2.67 (define-fun tptp.hoaslamnotvar_lthm () Bool true)
% 2.35/2.67 (define-fun tptp.pushprop_lem3v2_lthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3b_lthm () Bool (forall ((B tptp.term)) (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (not (= (@ (@ tptp.sub B) (@ (@ tptp.push tptp.one) tptp.sh)) (@ (@ F tptp.sh) tptp.one)))))))
% 2.35/2.67 (define-fun tptp.ulamvarind () Bool true)
% 2.35/2.67 (define-fun tptp.induction () Bool (forall ((P (-> tptp.term Bool)) (BOUND_VARIABLE_3181 tptp.term)) (or (not (forall ((A tptp.term)) (or (not (@ tptp.var A)) (@ P A)))) (not (forall ((A tptp.term) (B tptp.term)) (or (not (@ P A)) (not (@ P B)) (@ P (@ (@ tptp.ap A) B))))) (not (forall ((A tptp.term)) (or (not (@ P A)) (@ P (@ tptp.lam A))))) (@ P BOUND_VARIABLE_3181))))
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3a_lthm () Bool (=> (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_3835 tptp.term)) (or (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ F tptp.sh) tptp.one))) tptp.id)))) (not (forall ((B tptp.term)) (or (not (@ (@ (@ P tptp.id) B) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.sub BOUND_VARIABLE_3835) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ tptp.sub BOUND_VARIABLE_3835) (@ (@ tptp.push tptp.one) tptp.sh)))) tptp.id))) (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_4055 tptp.term)) (or (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ F tptp.sh) tptp.one))) tptp.id)))) (not (forall ((B tptp.term)) (or (not (@ (@ (@ P tptp.id) B) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.sub BOUND_VARIABLE_4055) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam BOUND_VARIABLE_4055)) tptp.id)))))
% 2.35/2.67 (define-fun tptp.termmset_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3aa () Bool (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_3835 tptp.term)) (or (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ F tptp.sh) tptp.one))) tptp.id)))) (not (forall ((B tptp.term)) (or (not (@ (@ (@ P tptp.id) B) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.sub BOUND_VARIABLE_3835) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ tptp.sub BOUND_VARIABLE_3835) (@ (@ tptp.push tptp.one) tptp.sh)))) tptp.id))))
% 2.35/2.67 (define-fun tptp.pushprop_lem1v2_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoaslamnotap_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoaslamnotvar_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3b_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.pushprop_lem2v2 () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3a_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.axclos () Bool true)
% 2.35/2.67 (define-fun tptp.axassoc () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem2v2 () Bool (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool)) (BOUND_VARIABLE_3592 tptp.term) (BOUND_VARIABLE_3590 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((A tptp.term) (B tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (not (@ (@ (@ P tptp.id) B) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.ap (@ (@ tptp.sub A) tptp.id)) B)) tptp.id)))) (not (forall ((X tptp.term)) (= (@ (@ (@ P tptp.id) X) tptp.id) (@ Q X)))) (not (@ Q BOUND_VARIABLE_3590)) (not (@ Q BOUND_VARIABLE_3592)) (@ Q (@ (@ tptp.ap BOUND_VARIABLE_3590) BOUND_VARIABLE_3592)))))
% 2.35/2.67 (define-fun tptp.pushprop_lthm () Bool true)
% 2.35/2.67 (define-fun tptp.apinj2 () Bool (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (or (not (= (@ (@ tptp.ap A) C) (@ (@ tptp.ap B) D))) (= C D))))
% 2.35/2.67 (define-fun tptp.apinj1 () Bool (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (or (not (= (@ (@ tptp.ap A) C) (@ (@ tptp.ap B) D))) (= A B))))
% 2.35/2.67 (define-fun tptp.hoasapinj2_lthm () Bool (=> (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (or (not (= (@ (@ tptp.ap A) C) (@ (@ tptp.ap B) D))) (= C D))) (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (or (not (= (@ (@ tptp.ap (@ (@ tptp.sub A) tptp.id)) C) (@ (@ tptp.ap (@ (@ tptp.sub B) tptp.id)) D))) (= C D)))))
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3v2a () Bool true)
% 2.35/2.67 (define-fun tptp.hoasapinj1_lthm () Bool (=> (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (or (not (= (@ (@ tptp.ap A) C) (@ (@ tptp.ap B) D))) (= A B))) (forall ((A tptp.term) (B tptp.term) (C tptp.term) (D tptp.term)) (or (not (= (@ (@ tptp.ap (@ (@ tptp.sub A) tptp.id)) C) (@ (@ tptp.ap (@ (@ tptp.sub B) tptp.id)) D))) (= A B)))))
% 2.35/2.67 (define-fun tptp.hoaslaminj_lthm () Bool (=> (forall ((A tptp.term) (M tptp.subst)) (= A (@ (@ tptp.sub tptp.one) (@ (@ tptp.push A) M)))) (=> (forall ((A tptp.term) (M tptp.subst)) (= M (@ (@ tptp.comp tptp.sh) (@ (@ tptp.push A) M)))) (=> (forall ((A tptp.term) (B tptp.term)) (or (not (= (@ tptp.lam A) (@ tptp.lam B))) (= A B))) (forall ((F (-> tptp.subst tptp.term tptp.term)) (BOUND_VARIABLE_3454 tptp.subst) (BOUND_VARIABLE_3452 tptp.term) (BOUND_VARIABLE_3450 (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ BOUND_VARIABLE_3450 M) A)) N) (@ (@ BOUND_VARIABLE_3450 (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (= (@ tptp.lam (@ (@ F tptp.sh) tptp.one)) (@ tptp.lam (@ (@ BOUND_VARIABLE_3450 tptp.sh) tptp.one)))) (= (@ (@ F BOUND_VARIABLE_3454) BOUND_VARIABLE_3452) (@ (@ BOUND_VARIABLE_3450 BOUND_VARIABLE_3454) BOUND_VARIABLE_3452))))))))
% 2.35/2.67 (define-fun tptp.axvarcons () Bool (forall ((A tptp.term) (M tptp.subst)) (= A (@ (@ tptp.sub tptp.one) (@ (@ tptp.push A) M)))))
% 2.35/2.67 (define-fun tptp.hoaslam ((BOUND_VARIABLE_8107 tptp.subst) (BOUND_VARIABLE_8109 (-> tptp.subst tptp.term tptp.term))) tptp.term (as @tptp.term_0 tptp.term))
% 2.35/2.67 (define-fun tptp.axscons () Bool (forall ((M tptp.subst)) (= M (@ (@ tptp.push (@ (@ tptp.sub tptp.one) M)) (@ (@ tptp.comp tptp.sh) M)))))
% 2.35/2.67 (define-fun tptp.hoasinduction_lem2v2_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.axidr () Bool (forall ((M tptp.subst)) (= M (@ (@ tptp.comp M) tptp.id))))
% 2.35/2.67 (define-fun tptp.pushprop_lem1 () Bool (forall ((P (-> tptp.term Bool)) (K (-> tptp.term Bool)) (A tptp.term) (M tptp.subst) (B tptp.term)) (or (not (@ P A)) (@ K (@ (@ tptp.sub A) (@ (@ tptp.push B) M))))))
% 2.35/2.67 (define-fun tptp.laminj () Bool (forall ((A tptp.term) (B tptp.term)) (or (not (= (@ tptp.lam A) (@ tptp.lam B))) (= A B))))
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3_lthm () Bool (=> (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_3835 tptp.term)) (or (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ F tptp.sh) tptp.one))) tptp.id)))) (not (forall ((B tptp.term)) (or (not (@ (@ (@ P tptp.id) B) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.sub BOUND_VARIABLE_3835) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ tptp.sub BOUND_VARIABLE_3835) (@ (@ tptp.push tptp.one) tptp.sh)))) tptp.id))) (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_4009 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ F tptp.sh) tptp.one))) tptp.id)))) (not (forall ((B tptp.term)) (or (not (@ (@ (@ P tptp.id) B) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.sub BOUND_VARIABLE_4009) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam BOUND_VARIABLE_4009)) tptp.id)))))
% 2.35/2.67 (define-fun tptp.pushprop_lem0 () Bool (forall ((P (-> tptp.term Bool)) (A tptp.term) (M tptp.subst)) (not (forall ((Q (-> tptp.term Bool))) (not (forall ((X tptp.term)) (= (@ P (@ (@ tptp.sub X) (@ (@ tptp.push A) M))) (@ Q X))))))))
% 2.35/2.67 (define-fun tptp.pushprop_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.axabs () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3v2a_lthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem2_lthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoasapinj2_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_p_and_p_prime ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool))) Bool (forall ((X tptp.term)) (= (@ Q X) (@ (@ (@ P tptp.id) X) tptp.id))))
% 2.35/2.67 (define-fun tptp.hoasinduction_lem1_lthm () Bool true)
% 2.35/2.67 (define-fun tptp.lamnotap () Bool false)
% 2.35/2.67 (define-fun tptp.hoasapinj1_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoaslamnotvar () Bool true)
% 2.35/2.67 (define-fun tptp.axidl () Bool (forall ((M tptp.subst)) (= M (@ (@ tptp.comp tptp.id) M))))
% 2.35/2.67 (define-fun tptp.hoaslaminj_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.induction2_lthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem0_lthm () Bool true)
% 2.35/2.67 (define-fun tptp.substmonoid_lthm () Bool (=> (forall ((M tptp.subst)) (= M (@ (@ tptp.comp tptp.id) M))) (=> (forall ((M tptp.subst)) (= M (@ (@ tptp.comp M) tptp.id))) (and (forall ((M tptp.subst)) (= M (@ (@ tptp.comp tptp.id) M))) (forall ((M tptp.subst)) (= M (@ (@ tptp.comp M) tptp.id)))))))
% 2.35/2.67 (define-fun tptp.pushprop () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem2_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3b () Bool (forall ((B tptp.term)) (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (not (= (@ (@ tptp.sub B) (@ (@ tptp.push tptp.one) tptp.sh)) (@ (@ F tptp.sh) tptp.one)))))))
% 2.35/2.67 (define-fun tptp.substmonoid () Bool (and (forall ((M tptp.subst)) (= M (@ (@ tptp.comp tptp.id) M))) (forall ((M tptp.subst)) (= M (@ (@ tptp.comp M) tptp.id)))))
% 2.35/2.67 (define-fun tptp.lamnotvar () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3a () Bool (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_4055 tptp.term)) (or (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ F tptp.sh) tptp.one))) tptp.id)))) (not (forall ((B tptp.term)) (or (not (@ (@ (@ P tptp.id) B) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.sub BOUND_VARIABLE_4055) (@ (@ tptp.push B) tptp.id))) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam BOUND_VARIABLE_4055)) tptp.id))))
% 2.35/2.67 (define-fun tptp.hoasinduction_lem1_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_no_psi_cond () Bool false)
% 2.35/2.67 (define-fun tptp.induction2_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.pushprop_lem2v2_lthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoasvar ((BOUND_VARIABLE_8191 tptp.subst) (BOUND_VARIABLE_8193 tptp.term) (BOUND_VARIABLE_8195 tptp.subst)) Bool false)
% 2.35/2.67 (define-fun tptp.hoaslamnotap () Bool (forall ((F (-> tptp.subst tptp.term tptp.term)) (BOUND_VARIABLE_3492 tptp.term) (BOUND_VARIABLE_3490 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (= (@ tptp.lam (@ (@ F tptp.sh) tptp.one)) (@ (@ tptp.ap (@ (@ tptp.sub BOUND_VARIABLE_3490) tptp.id)) BOUND_VARIABLE_3492))))))
% 2.35/2.67 (define-fun tptp.substmonoid_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.ulamvarsh () Bool true)
% 2.35/2.67 (define-fun tptp.induction2 () Bool true)
% 2.35/2.67 (define-fun tptp.pushprop_lem3v2 () Bool true)
% 2.35/2.67 (define-fun tptp.pushprop_lem2v2_gthm () Bool true)
% 2.35/2.67 (define-fun tptp.pushprop_lem1_lthm () Bool (=> (forall ((A tptp.term) (M tptp.subst)) (= A (@ (@ tptp.sub tptp.one) (@ (@ tptp.push A) M)))) (=> (forall ((A tptp.term) (M tptp.subst)) (= M (@ (@ tptp.comp tptp.sh) (@ (@ tptp.push A) M)))) (forall ((P (-> tptp.term Bool)) (K (-> tptp.term Bool)) (A tptp.term) (M tptp.subst) (B tptp.term)) (or (not (@ P A)) (@ K (@ (@ tptp.sub A) (@ (@ tptp.push B) M))))))))
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3v2 () Bool (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool)) (BOUND_VARIABLE_3658 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ F tptp.sh) tptp.one))) tptp.id)))) (not (forall ((X tptp.term)) (= (@ (@ (@ P tptp.id) X) tptp.id) (@ Q X)))) (not (forall ((B tptp.term)) (or (not (@ Q B)) (@ Q (@ (@ tptp.sub BOUND_VARIABLE_3658) (@ (@ tptp.push B) tptp.id)))))) (@ Q (@ tptp.lam BOUND_VARIABLE_3658)))))
% 2.35/2.67 (define-fun tptp.axshiftcons () Bool (forall ((A tptp.term) (M tptp.subst)) (= M (@ (@ tptp.comp tptp.sh) (@ (@ tptp.push A) M)))))
% 2.35/2.67 (define-fun tptp.termmset () Bool (forall ((A tptp.term)) (= A (@ (@ tptp.sub A) tptp.id))))
% 2.35/2.67 (define-fun tptp.pushprop_lem0_lthm () Bool (forall ((P (-> tptp.term Bool)) (A tptp.term) (M tptp.subst)) (not (forall ((Q (-> tptp.term Bool))) (not (forall ((X tptp.term)) (= (@ P (@ (@ tptp.sub X) (@ (@ tptp.push A) M))) (@ Q X))))))))
% 2.35/2.67 (define-fun tptp.hoasapnotvar_lthm () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lem3v2_lthm () Bool (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (Q (-> tptp.term Bool)) (BOUND_VARIABLE_3658 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ F tptp.sh) tptp.one))) tptp.id)))) (not (forall ((X tptp.term)) (= (@ (@ (@ P tptp.id) X) tptp.id) (@ Q X)))) (not (forall ((B tptp.term)) (or (not (@ Q B)) (@ Q (@ (@ tptp.sub BOUND_VARIABLE_3658) (@ (@ tptp.push B) tptp.id)))))) (@ Q (@ tptp.lam BOUND_VARIABLE_3658)))))
% 2.35/2.67 (define-fun tptp.pushprop_p_and_p_prime ((A tptp.term) (M tptp.subst) (P (-> tptp.term Bool)) (Q (-> tptp.term Bool))) Bool (forall ((X tptp.term)) (= (@ Q X) (@ P (@ (@ tptp.sub X) (@ (@ tptp.push A) M))))))
% 2.35/2.67 (define-fun tptp.axvarid () Bool true)
% 2.35/2.67 (define-fun tptp.hoasinduction_lthm_3 () Bool (forall ((P (-> tptp.subst tptp.term tptp.subst Bool)) (BOUND_VARIABLE_4125 tptp.term)) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))) (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)))) (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst) (K tptp.subst)) (or (not (@ (@ (@ P (@ (@ tptp.comp M) K)) (@ (@ tptp.sub A) K)) N)) (@ (@ (@ P M) A) (@ (@ tptp.comp K) N))))) (not (forall ((A tptp.term)) (or (not (@ tptp.var (@ (@ tptp.sub A) tptp.id))) (@ (@ (@ P tptp.id) A) tptp.id)))) (not (forall ((A tptp.term) (B tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (not (@ (@ (@ P tptp.id) B) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ tptp.ap (@ (@ tptp.sub A) tptp.id)) B)) tptp.id)))) (not (forall ((F (-> tptp.subst tptp.term tptp.term))) (or (not (forall ((M tptp.subst) (A tptp.term) (N tptp.subst)) (= (@ (@ tptp.sub (@ (@ F M) A)) N) (@ (@ F (@ (@ tptp.comp M) N)) (@ (@ tptp.sub A) N))))) (not (forall ((A tptp.term)) (or (not (@ (@ (@ P tptp.id) A) tptp.id)) (@ (@ (@ P tptp.id) (@ (@ F tptp.id) A)) tptp.id)))) (@ (@ (@ P tptp.id) (@ tptp.lam (@ (@ F tptp.sh) tptp.one))) tptp.id)))) (@ (@ (@ P tptp.id) BOUND_VARIABLE_4125) tptp.id))))
% 2.35/2.67 )
% 2.35/2.67 % SZS output end CandidateFiniteModel for cvc5---1.0.5_6253
% 2.35/2.67 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------