cvc5---1.3.4.THM-Prf.s

%------------------------------------------------------------------------------
% File     : cvc5---1.3.4
% Problem  : ALG258^2 : TPTP v9.2.1. Bugfixed v5.2.0.
% Transfm  : none
% Format   : tptp:raw
% Command  : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM

% Computer : n023.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 : Wed Jun  3 08:05:40 AM UTC 2026

% Result   : Theorem 172.90s 173.27s
% Output   : Proof 172.90s
% Verified : 
% SZS Type : -

% Comments : 
%------------------------------------------------------------------------------
%----WARNING: Could not form TPTP format derivation
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13  % Problem  : ALG258^2 : TPTP v9.2.1. Bugfixed v5.2.0.
% 0.12/0.14  % Command  : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM
% 0.18/0.35  % Computer : n023.cluster.edu
% 0.18/0.35  % Model    : x86_64 x86_64
% 0.18/0.35  % CPU      : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.18/0.35  % Memory   : 8042.1875MB
% 0.18/0.35  % OS       : Linux 3.10.0-693.el7.x86_64
% 0.18/0.35  % CPULimit : 300
% 0.18/0.35  % WCLimit  : 300
% 0.18/0.35  % DateTime : Wed Jun  3 01:56:13 EDT 2026
% 0.18/0.35  % CPUTime  : 
% 0.38/0.56  %----Proving TH0
% 172.90/173.27  --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s...
% 172.90/173.27  --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --mbqi-enum-choice-grammar-all --no-cegqi --no-sygus-inst at 30s...
% 172.90/173.27  --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-mbqi-nested-check --no-cegqi --no-sygus-inst at 30s...
% 172.90/173.27  --- Run --ho-elim --full-saturate-quant at 18s...
% 172.90/173.27  --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s...
% 172.90/173.27  % SZS status Theorem
% 172.90/173.27  % SZS output start Proof
% 172.90/173.27  (
% 172.90/173.27  (declare-sort tptp.subst 0)
% 172.90/173.27  (declare-sort tptp.term 0)
% 172.90/173.27  (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst))
% 172.90/173.27  (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term))
% 172.90/173.27  (declare-const tptp.ap (-> tptp.term tptp.term tptp.term))
% 172.90/173.27  (declare-const tptp.one tptp.term)
% 172.90/173.27  (declare-const tptp.sh tptp.subst)
% 172.90/173.27  (declare-const tptp.lam (-> tptp.term tptp.term))
% 172.90/173.27  (declare-const tptp.var (-> tptp.term Bool))
% 172.90/173.27  (declare-const tptp.id tptp.subst)
% 172.90/173.27  (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_no_psi_cond Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lthm_3 Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_gthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3b_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3b_gthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3b Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3a_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3a_gthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3a Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3_gthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3 Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3aaa Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3aa_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3aa Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem2_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem2_gthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem2 Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem1_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem1_gthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem1 Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3v2a_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3v2a Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3v2_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3v2_gthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3v2 Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem3v2_f Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem2v2_gthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem2v2 Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem1v2_gthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem1v2 Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem0_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoasinduction_lem0 Bool)
% 172.90/173.27  (declare-const tptp.hoasapnotvar_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoasapnotvar_gthm Bool)
% 172.90/173.27  (declare-const tptp.hoasapnotvar Bool)
% 172.90/173.27  (declare-const tptp.hoaslamnotvar_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoaslamnotvar_gthm Bool)
% 172.90/173.27  (declare-const tptp.hoaslamnotvar Bool)
% 172.90/173.27  (declare-const tptp.hoaslamnotap_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoaslamnotap_gthm Bool)
% 172.90/173.27  (declare-const tptp.hoaslamnotap Bool)
% 172.90/173.27  (declare-const tptp.hoaslaminj_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoaslaminj_gthm Bool)
% 172.90/173.27  (declare-const tptp.hoaslaminj Bool)
% 172.90/173.27  (declare-const tptp.hoasapinj2_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoasapinj2_gthm Bool)
% 172.90/173.27  (declare-const tptp.hoasapinj2 Bool)
% 172.90/173.27  (declare-const tptp.pushprop_lem0_lthm Bool)
% 172.90/173.27  (declare-const tptp.axassoc Bool)
% 172.90/173.27  (declare-const tptp.pushprop_lem0_gthm Bool)
% 172.90/173.27  (declare-const tptp.axvarcons Bool)
% 172.90/173.27  (declare-const tptp.pushprop_lem0 Bool)
% 172.90/173.27  (declare-const tptp.apinj1 Bool)
% 172.90/173.27  (declare-const tptp.induction Bool)
% 172.90/173.27  (declare-const tptp.apnotvar Bool)
% 172.90/173.27  (declare-const tptp.laminj Bool)
% 172.90/173.27  (declare-const tptp.axvarshift Bool)
% 172.90/173.27  (declare-const tptp.ulamvarind Bool)
% 172.90/173.27  (declare-const tptp.pushprop_lem2v2_lthm Bool)
% 172.90/173.27  (declare-const tptp.ulamvarsh Bool)
% 172.90/173.27  (declare-const tptp.ulamvar1 Bool)
% 172.90/173.27  (declare-const tptp.axabs Bool)
% 172.90/173.27  (declare-const tptp.pushprop_lem1 Bool)
% 172.90/173.27  (declare-const tptp.shinj Bool)
% 172.90/173.27  (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst))
% 172.90/173.27  (declare-const tptp.apinj2 Bool)
% 172.90/173.27  (declare-const tptp.axvarid Bool)
% 172.90/173.27  (declare-const tptp.axidl Bool)
% 172.90/173.27  (declare-const tptp.axclos Bool)
% 172.90/173.27  (declare-const tptp.termmset Bool)
% 172.90/173.27  (declare-const tptp.axshiftcons Bool)
% 172.90/173.27  (declare-const tptp.lamnotap Bool)
% 172.90/173.27  (declare-const tptp.lamnotvar Bool)
% 172.90/173.27  (declare-const tptp.axapp Bool)
% 172.90/173.27  (declare-const tptp.axscons Bool)
% 172.90/173.27  (declare-const tptp.axmap Bool)
% 172.90/173.27  (declare-const tptp.axidr Bool)
% 172.90/173.27  (declare-const tptp.induction2lem Bool)
% 172.90/173.27  (declare-const tptp.pushprop_lem1_gthm Bool)
% 172.90/173.27  (declare-const tptp.hoasapinj1_lthm Bool)
% 172.90/173.27  (declare-const tptp.pushprop_lem1_lthm Bool)
% 172.90/173.27  (declare-const tptp.pushprop_lem1v2 Bool)
% 172.90/173.27  (declare-const tptp.pushprop_lem1v2_gthm Bool)
% 172.90/173.27  (declare-const tptp.induction2 Bool)
% 172.90/173.27  (declare-const tptp.pushprop_lem1v2_lthm Bool)
% 172.90/173.27  (declare-const tptp.pushprop_lem2v2 Bool)
% 172.90/173.27  (declare-const tptp.pushprop_lem2v2_gthm Bool)
% 172.90/173.27  (declare-const tptp.pushprop_lem3v2 Bool)
% 172.90/173.27  (declare-const tptp.pushprop_lem3v2_lthm Bool)
% 172.90/173.27  (declare-const tptp.pushprop Bool)
% 172.90/173.27  (declare-const tptp.pushprop_gthm Bool)
% 172.90/173.27  (declare-const tptp.hoasapinj1 Bool)
% 172.90/173.27  (declare-const tptp.pushprop_lthm_orig Bool)
% 172.90/173.27  (declare-const tptp.pushprop_lthm Bool)
% 172.90/173.27  (declare-const tptp.induction2lem_gthm Bool)
% 172.90/173.27  (declare-const tptp.induction2lem_lthm Bool)
% 172.90/173.27  (declare-const tptp.induction2_gthm Bool)
% 172.90/173.27  (declare-const tptp.induction2_lthm Bool)
% 172.90/173.27  (declare-const tptp.substmonoid Bool)
% 172.90/173.27  (declare-const tptp.substmonoid_gthm Bool)
% 172.90/173.27  (declare-const tptp.termmset_gthm Bool)
% 172.90/173.27  (declare-const tptp.substmonoid_lthm Bool)
% 172.90/173.27  (declare-const tptp.termmset_lthm Bool)
% 172.90/173.27  (declare-const tptp.hoasapinj1_gthm Bool)
% 172.90/173.27  (define tptp.pushprop_p_and_p_prime () (let ((_let_1 (@var "M" tptp.subst))) (let ((_let_2 (@var "A" tptp.term))) (let ((_let_3 (@var "X" tptp.term))) (let ((_let_4 (@var "P" (-> tptp.term Bool)))) (let ((_let_5 (@var "Q" (-> tptp.term Bool)))) (lambda (@list _let_2 _let_1 _let_4 _let_5) (forall (@list _let_3) (= (_ _let_5 _let_3) (_ _let_4 (_ (_ tptp.sub _let_3) (_ (_ tptp.push _let_2) _let_1))))))))))))
% 172.90/173.27  (define tptp.hoasap () (let ((_let_1 (@var "B" tptp.term))) (let ((_let_2 (@var "N" tptp.subst))) (let ((_let_3 (@var "A" tptp.term))) (lambda (@list (@var "M" tptp.subst) _let_3 _let_2 _let_1) (_ (_ tptp.ap (_ (_ tptp.sub _let_3) _let_2)) _let_1))))))
% 172.90/173.27  (define tptp.hoaslam () (let ((_let_1 (@var "F" (-> tptp.subst tptp.term tptp.term)))) (lambda (@list (@var "M" tptp.subst) _let_1) (_ tptp.lam (_ (_ _let_1 tptp.sh) tptp.one)))))
% 172.90/173.27  (define tptp.hoasvar () (let ((_let_1 (@var "N" tptp.subst))) (let ((_let_2 (@var "A" tptp.term))) (lambda (@list (@var "M" tptp.subst) _let_2 _let_1) (_ tptp.var (_ (_ tptp.sub _let_2) _let_1))))))
% 172.90/173.27  (define tptp.hoasinduction_p_and_p_prime () (let ((_let_1 (@var "X" tptp.term))) (let ((_let_2 (@var "P" (-> tptp.subst tptp.term tptp.subst Bool)))) (let ((_let_3 (@var "Q" (-> tptp.term Bool)))) (lambda (@list _let_2 _let_3) (forall (@list _let_1) (= (_ _let_3 _let_1) (_ (_ (_ _let_2 tptp.id) _let_1) tptp.id))))))))
% 172.90/173.27  (define @t1 () (@var "M" tptp.subst))
% 172.90/173.27  (define @t2 () (@var "B" tptp.term))
% 172.90/173.27  (define @t3 () (_ tptp.sub @t2))
% 172.90/173.27  (define @t4 () (_ @t3 @t1))
% 172.90/173.27  (define @t5 () (@var "A" tptp.term))
% 172.90/173.27  (define @t6 () (_ tptp.sub @t5))
% 172.90/173.27  (define @t7 () (_ @t6 @t1))
% 172.90/173.27  (define @t8 () (_ tptp.ap @t5))
% 172.90/173.27  (define @t9 () (_ @t8 @t2))
% 172.90/173.27  (define @t10 () (_ (_ tptp.push @t5) @t1))
% 172.90/173.27  (define @t11 () (_ tptp.sub tptp.one))
% 172.90/173.27  (define @t12 () (_ @t11 @t10))
% 172.90/173.27  (define @t13 () (@list @t5 @t1))
% 172.90/173.27  (define @t14 () (forall @t13 (= @t12 @t5)))
% 172.90/173.27  (define @t15 () (= tptp.axvarcons @t14))
% 172.90/173.27  (define @t16 () (@list @t5))
% 172.90/173.27  (define @t17 () (forall @t16 (= (_ @t6 tptp.id) @t5)))
% 172.90/173.27  (define @t18 () (_ tptp.comp @t1))
% 172.90/173.27  (define @t19 () (_ tptp.push tptp.one))
% 172.90/173.27  (define @t20 () (_ tptp.lam @t5))
% 172.90/173.27  (define @t21 () (@var "N" tptp.subst))
% 172.90/173.27  (define @t22 () (_ @t18 @t21))
% 172.90/173.27  (define @t23 () (@list @t5 @t1 @t21))
% 172.90/173.27  (define @t24 () (forall @t23 (= (_ (_ tptp.sub @t7) @t21) (_ @t6 @t22))))
% 172.90/173.27  (define @t25 () (@list @t1))
% 172.90/173.27  (define @t26 () (forall @t25 (= (_ (_ tptp.comp tptp.id) @t1) @t1)))
% 172.90/173.27  (define @t27 () (_ tptp.comp tptp.sh))
% 172.90/173.27  (define @t28 () (_ @t27 @t10))
% 172.90/173.27  (define @t29 () (forall @t13 (= @t28 @t1)))
% 172.90/173.27  (define @t30 () (= tptp.axshiftcons @t29))
% 172.90/173.27  (define @t31 () (@var "K" tptp.subst))
% 172.90/173.27  (define @t32 () (forall (@list @t1 @t21 @t31) (= (_ (_ tptp.comp @t22) @t31) (_ @t18 (_ (_ tptp.comp @t21) @t31)))))
% 172.90/173.27  (define @t33 () (_ @t6 @t21))
% 172.90/173.27  (define @t34 () (_ (_ tptp.push @t33) @t22))
% 172.90/173.27  (define @t35 () (forall @t25 (= (_ @t18 tptp.id) @t1)))
% 172.90/173.27  (define @t36 () (_ @t19 tptp.sh))
% 172.90/173.27  (define @t37 () (_ @t6 tptp.sh))
% 172.90/173.27  (define @t38 () (_ tptp.var @t5))
% 172.90/173.27  (define @t39 () (@var "P" (-> tptp.term Bool)))
% 172.90/173.27  (define @t40 () (_ @t39 @t5))
% 172.90/173.27  (define @t41 () (forall @t16 (=> @t38 @t40)))
% 172.90/173.27  (define @t42 () (@list @t39))
% 172.90/173.27  (define @t43 () (= @t5 @t2))
% 172.90/173.27  (define @t44 () (@var "D" tptp.term))
% 172.90/173.27  (define @t45 () (_ tptp.ap @t2))
% 172.90/173.27  (define @t46 () (@var "C" tptp.term))
% 172.90/173.27  (define @t47 () (= (_ @t8 @t46) (_ @t45 @t44)))
% 172.90/173.27  (define @t48 () (@list @t5 @t2 @t46 @t44))
% 172.90/173.27  (define @t49 () (= @t46 @t44))
% 172.90/173.27  (define @t50 () (_ tptp.lam @t2))
% 172.90/173.27  (define @t51 () (= @t20 @t50))
% 172.90/173.27  (define @t52 () (@list @t5 @t2))
% 172.90/173.27  (define @t53 () (forall @t52 (=> @t51 @t43)))
% 172.90/173.27  (define @t54 () (= tptp.laminj @t53))
% 172.90/173.27  (define @t55 () (forall @t16 @t40))
% 172.90/173.27  (define @t56 () (_ @t39 @t20))
% 172.90/173.27  (define @t57 () (_ @t39 @t2))
% 172.90/173.27  (define @t58 () (forall @t52 (=> @t40 (=> @t57 (_ @t39 @t9)))))
% 172.90/173.27  (define @t59 () (@var "Q" (-> tptp.term Bool)))
% 172.90/173.27  (define @t60 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t5) @t1) @t39) @t59))
% 172.90/173.27  (define @t61 () (@list @t59))
% 172.90/173.27  (define @t62 () (@list @t39 @t5 @t1))
% 172.90/173.27  (define @t63 () (_ tptp.push @t2))
% 172.90/173.27  (define @t64 () (@var "K" (-> tptp.term Bool)))
% 172.90/173.27  (define @t65 () (@list @t39 @t59 @t5 @t1))
% 172.90/173.27  (define @t66 () (_ tptp.sub @t46))
% 172.90/173.27  (define @t67 () (@list @t46))
% 172.90/173.27  (define @t68 () (_ tptp.var @t2))
% 172.90/173.27  (define @t69 () (@list @t2))
% 172.90/173.27  (define @t70 () (forall @t69 (=> @t68 (_ @t39 @t4))))
% 172.90/173.27  (define @t71 () (_ @t3 @t10))
% 172.90/173.27  (define @t72 () (forall @t69 (=> @t68 (_ @t39 @t71))))
% 172.90/173.27  (define @t73 () (_ @t59 @t2))
% 172.90/173.27  (define @t74 () (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop))))))
% 172.90/173.27  (define @t75 () (_ @t6 (_ @t63 tptp.id)))
% 172.90/173.27  (define @t76 () (forall @t16 (=> (forall @t69 (=> @t57 (_ @t39 @t75))) @t56)))
% 172.90/173.27  (define @t77 () (=> tptp.induction (=> tptp.pushprop tptp.induction2lem)))
% 172.90/173.27  (define @t78 () (=> tptp.induction2lem tptp.induction2))
% 172.90/173.27  (define @t79 () (_ tptp.hoasap tptp.id))
% 172.90/173.27  (define @t80 () (_ (_ @t79 @t5) tptp.id))
% 172.90/173.27  (define @t81 () (= (_ @t80 @t46) (_ (_ (_ @t79 @t2) tptp.id) @t44)))
% 172.90/173.27  (define @t82 () (@var "G" (-> tptp.subst tptp.term tptp.term)))
% 172.90/173.27  (define @t83 () (_ (_ @t82 @t1) @t5))
% 172.90/173.27  (define @t84 () (@var "F" (-> tptp.subst tptp.term tptp.term)))
% 172.90/173.27  (define @t85 () (_ @t84 @t1))
% 172.90/173.27  (define @t86 () (_ @t85 @t5))
% 172.90/173.27  (define @t87 () (= @t86 @t83))
% 172.90/173.27  (define @t88 () (@list @t1 @t5))
% 172.90/173.27  (define @t89 () (forall @t88 @t87))
% 172.90/173.27  (define @t90 () (lambda @t88 @t83))
% 172.90/173.27  (define @t91 () (_ tptp.hoaslam tptp.id))
% 172.90/173.27  (define @t92 () (lambda @t88 @t86))
% 172.90/173.27  (define @t93 () (_ @t91 @t92))
% 172.90/173.27  (define @t94 () (= @t93 (_ @t91 @t90)))
% 172.90/173.27  (define @t95 () (=> @t94 @t89))
% 172.90/173.27  (define @t96 () (_ (_ @t82 @t22) @t33))
% 172.90/173.27  (define @t97 () (_ (_ tptp.sub @t83) @t21))
% 172.90/173.27  (define @t98 () (= @t97 @t96))
% 172.90/173.27  (define @t99 () (@list @t1 @t5 @t21))
% 172.90/173.27  (define @t100 () (forall @t99 @t98))
% 172.90/173.27  (define @t101 () (=> @t100 @t95))
% 172.90/173.27  (define @t102 () (@list @t82))
% 172.90/173.27  (define @t103 () (forall @t102 @t101))
% 172.90/173.27  (define @t104 () (_ (_ @t84 @t22) @t33))
% 172.90/173.27  (define @t105 () (_ (_ tptp.sub @t86) @t21))
% 172.90/173.27  (define @t106 () (= @t105 @t104))
% 172.90/173.27  (define @t107 () (forall @t99 @t106))
% 172.90/173.27  (define @t108 () (=> @t107 @t103))
% 172.90/173.27  (define @t109 () (@list @t84))
% 172.90/173.27  (define @t110 () (forall @t109 @t108))
% 172.90/173.27  (define @t111 () (= tptp.hoaslaminj @t110))
% 172.90/173.27  (define @t112 () (=> tptp.laminj tptp.hoaslaminj))
% 172.90/173.27  (define @t113 () (=> tptp.axshiftcons @t112))
% 172.90/173.27  (define @t114 () (=> tptp.axvarcons @t113))
% 172.90/173.27  (define @t115 () (= tptp.hoaslaminj_lthm @t114))
% 172.90/173.27  (define @t116 () (_ @t80 @t2))
% 172.90/173.27  (define @t117 () (_ tptp.hoasvar tptp.id))
% 172.90/173.27  (define @t118 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool)))
% 172.90/173.27  (define @t119 () (_ (_ tptp.hoasinduction_p_and_p_prime @t118) @t59))
% 172.90/173.27  (define @t120 () (@list @t118))
% 172.90/173.27  (define @t121 () (_ @t59 @t5))
% 172.90/173.27  (define @t122 () (_ @t118 tptp.id))
% 172.90/173.27  (define @t123 () (_ (_ @t122 @t5) tptp.id))
% 172.90/173.27  (define @t124 () (forall @t16 (=> (_ (_ @t117 @t5) tptp.id) @t123)))
% 172.90/173.27  (define @t125 () (_ (_ (_ @t118 @t1) @t5) (_ (_ tptp.comp @t31) @t21)))
% 172.90/173.27  (define @t126 () (_ (_ (_ @t118 (_ @t18 @t31)) (_ @t6 @t31)) @t21))
% 172.90/173.27  (define @t127 () (@list @t1 @t5 @t21 @t31))
% 172.90/173.27  (define @t128 () (forall @t127 (=> @t126 @t125)))
% 172.90/173.27  (define @t129 () (forall @t127 (=> @t125 @t126)))
% 172.90/173.27  (define @t130 () (@list @t118 @t59))
% 172.90/173.27  (define @t131 () (_ (_ @t122 @t2) tptp.id))
% 172.90/173.27  (define @t132 () (forall @t52 (=> @t123 (=> @t131 (_ (_ @t122 @t116) tptp.id)))))
% 172.90/173.27  (define @t133 () (=> (forall @t16 (=> @t123 (_ (_ @t122 (_ (_ @t84 tptp.id) @t5)) tptp.id))) (_ (_ @t122 @t93) tptp.id)))
% 172.90/173.27  (define @t134 () (forall @t109 (=> @t107 @t133)))
% 172.90/173.27  (define @t135 () (=> @t134 (=> @t119 (forall @t16 (=> (forall @t69 (=> @t73 (_ @t59 @t75))) (_ @t59 @t20))))))
% 172.90/173.27  (define @t136 () (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1)))))))))))))))))))))))))))))))))))
% 172.90/173.27  (define @t137 () (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem2)))))))))))))))))))))))))))))))))))
% 172.90/173.27  (define @t138 () (forall @t69 (=> @t131 (_ (_ @t122 @t75) tptp.id))))
% 172.90/173.27  (define @t139 () (forall @t16 (=> @t138 (_ (_ @t122 (_ tptp.lam (_ @t6 @t36))) tptp.id))))
% 172.90/173.27  (define @t140 () (=> @t134 (forall @t16 (=> @t138 (_ (_ @t122 @t20) tptp.id)))))
% 172.90/173.27  (define @t141 () (_ @t84 tptp.sh))
% 172.90/173.27  (define @t142 () (_ @t141 tptp.one))
% 172.90/173.27  (define @t143 () (=> @t132 (=> @t134 (forall @t16 @t123))))
% 172.90/173.27  (define @t144 () (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction))))
% 172.90/173.27  (define @t145 () (not tptp.hoaslaminj_lthm))
% 172.90/173.27  (define @t146 () (@var "X" tptp.term))
% 172.90/173.27  (define @t147 () (_ @t59 @t146))
% 172.90/173.27  (define @t148 () (@list @t146))
% 172.90/173.27  (define @t149 () (lambda (@list @t5 @t1 @t39 @t59) (forall @t148 (= @t147 (_ @t39 (_ (_ tptp.sub @t146) @t10))))))
% 172.90/173.27  (define @t150 () (lambda (@list @t1 @t5 @t21 @t2) (_ (_ tptp.ap @t33) @t2)))
% 172.90/173.27  (define @t151 () (_ tptp.lam @t142))
% 172.90/173.27  (define @t152 () (lambda (@list @t1 @t84) @t151))
% 172.90/173.27  (define @t153 () (lambda @t99 (_ tptp.var @t33)))
% 172.90/173.27  (define @t154 () (lambda @t130 (forall @t148 (= @t147 (_ (_ @t122 @t146) tptp.id)))))
% 172.90/173.27  (define @t155 () (@var "BOUND_VARIABLE_9581" tptp.term))
% 172.90/173.27  (define @t156 () (@var "BOUND_VARIABLE_9579" tptp.subst))
% 172.90/173.27  (define @t157 () (@var "BOUND_VARIABLE_11478" (@ho-elim-sort (-> tptp.subst tptp.term tptp.term))))
% 172.90/173.27  (define @t158 () (@const 0 (-> (@ho-elim-sort (-> tptp.subst tptp.term tptp.term)) tptp.subst (@ho-elim-sort (-> tptp.term tptp.term)))))
% 172.90/173.27  (define @t159 () (@const 1 (-> (@ho-elim-sort (-> tptp.term tptp.term)) tptp.term tptp.term)))
% 172.90/173.27  (define @t160 () (_ @t159 (_ @t158 @t157 @t156) @t155))
% 172.90/173.27  (define @t161 () (@var "BOUND_VARIABLE_11468" (@ho-elim-sort (-> tptp.subst tptp.term tptp.term))))
% 172.90/173.27  (define @t162 () (_ @t159 (_ @t158 @t161 @t156) @t155))
% 172.90/173.27  (define @t163 () (@const 2 (@ho-elim-sort (-> tptp.term tptp.term))))
% 172.90/173.27  (define @t164 () (_ @t159 @t163 (_ @t159 (_ @t158 @t157 tptp.sh) tptp.one)))
% 172.90/173.27  (define @t165 () (_ @t159 @t163 (_ @t159 (_ @t158 @t161 tptp.sh) tptp.one)))
% 172.90/173.27  (define @t166 () (not (= @t164 @t165)))
% 172.90/173.27  (define @t167 () (@const 3 (@ho-elim-sort (-> tptp.term tptp.subst tptp.term))))
% 172.90/173.27  (define @t168 () (@const 4 (-> (@ho-elim-sort (-> tptp.term tptp.subst tptp.term)) tptp.term (@ho-elim-sort (-> tptp.subst tptp.term)))))
% 172.90/173.27  (define @t169 () (@const 5 (-> (@ho-elim-sort (-> tptp.subst tptp.term)) tptp.subst tptp.term)))
% 172.90/173.27  (define @t170 () (_ @t169 (_ @t168 @t167 (_ @t159 (_ @t158 @t161 @t1) @t5)) @t21))
% 172.90/173.27  (define @t171 () (_ @t169 (_ @t168 @t167 @t5) @t21))
% 172.90/173.27  (define @t172 () (@const 6 (@ho-elim-sort (-> tptp.subst tptp.subst tptp.subst))))
% 172.90/173.27  (define @t173 () (@const 7 (-> (@ho-elim-sort (-> tptp.subst tptp.subst tptp.subst)) tptp.subst (@ho-elim-sort (-> tptp.subst tptp.subst)))))
% 172.90/173.27  (define @t174 () (@const 8 (-> (@ho-elim-sort (-> tptp.subst tptp.subst)) tptp.subst tptp.subst)))
% 172.90/173.27  (define @t175 () (_ @t174 (_ @t173 @t172 @t1) @t21))
% 172.90/173.27  (define @t176 () (_ @t159 (_ @t158 @t161 @t175) @t171))
% 172.90/173.27  (define @t177 () (forall @t99 (= @t170 @t176)))
% 172.90/173.27  (define @t178 () (not @t177))
% 172.90/173.27  (define @t179 () (_ @t169 (_ @t168 @t167 (_ @t159 (_ @t158 @t157 @t1) @t5)) @t21))
% 172.90/173.27  (define @t180 () (_ @t159 (_ @t158 @t157 @t175) @t171))
% 172.90/173.27  (define @t181 () (forall @t99 (= @t179 @t180)))
% 172.90/173.27  (define @t182 () (not @t181))
% 172.90/173.27  (define @t183 () (or @t182 @t178 @t166 (= @t160 @t162)))
% 172.90/173.27  (define @t184 () (@list @t157 @t161 @t156 @t155))
% 172.90/173.27  (define @t185 () (forall @t184 @t183))
% 172.90/173.27  (define @t186 () (_ @t159 @t163 @t5))
% 172.90/173.27  (define @t187 () (_ @t159 @t163 @t2))
% 172.90/173.27  (define @t188 () (not (= @t186 @t187)))
% 172.90/173.27  (define @t189 () (or @t188 @t43))
% 172.90/173.27  (define @t190 () (forall @t52 @t189))
% 172.90/173.27  (define @t191 () (=> @t190 @t185))
% 172.90/173.27  (define @t192 () (@const 9 (@ho-elim-sort (-> tptp.term tptp.subst tptp.subst))))
% 172.90/173.27  (define @t193 () (@const 10 (-> (@ho-elim-sort (-> tptp.term tptp.subst tptp.subst)) tptp.term (@ho-elim-sort (-> tptp.subst tptp.subst)))))
% 172.90/173.27  (define @t194 () (_ @t174 (_ @t193 @t192 @t5) @t1))
% 172.90/173.27  (define @t195 () (_ @t173 @t172 tptp.sh))
% 172.90/173.27  (define @t196 () (forall @t13 (= @t1 (_ @t174 @t195 @t194))))
% 172.90/173.27  (define @t197 () (=> @t196 @t191))
% 172.90/173.27  (define @t198 () (_ @t168 @t167 tptp.one))
% 172.90/173.27  (define @t199 () (forall @t13 (= @t5 (_ @t169 @t198 @t194))))
% 172.90/173.27  (define @t200 () (=> @t199 @t197))
% 172.90/173.27  (define @t201 () (not @t200))
% 172.90/173.27  (define @t202 () (@var "BOUND_VARIABLE_9577" (-> tptp.subst tptp.term tptp.term)))
% 172.90/173.27  (define @t203 () (= (_ @t84 @t156 @t155) (_ @t202 @t156 @t155)))
% 172.90/173.27  (define @t204 () (_ @t84 tptp.sh tptp.one))
% 172.90/173.27  (define @t205 () (tptp.lam @t204))
% 172.90/173.27  (define @t206 () (not (= @t205 (tptp.lam (_ @t202 tptp.sh tptp.one)))))
% 172.90/173.27  (define @t207 () (tptp.sub @t5 @t21))
% 172.90/173.27  (define @t208 () (tptp.comp @t1 @t21))
% 172.90/173.27  (define @t209 () (not (forall @t99 (= (tptp.sub (_ @t202 @t1 @t5) @t21) (_ @t202 @t208 @t207)))))
% 172.90/173.27  (define @t210 () (_ @t84 @t208 @t207))
% 172.90/173.27  (define @t211 () (_ @t84 @t1 @t5))
% 172.90/173.27  (define @t212 () (tptp.sub @t211 @t21))
% 172.90/173.27  (define @t213 () (forall @t99 (= @t212 @t210)))
% 172.90/173.27  (define @t214 () (not @t213))
% 172.90/173.27  (define @t215 () (or @t214 @t209 @t206 @t203))
% 172.90/173.27  (define @t216 () (@list @t84 @t202 @t156 @t155))
% 172.90/173.27  (define @t217 () (tptp.lam @t2))
% 172.90/173.27  (define @t218 () (tptp.lam @t5))
% 172.90/173.27  (define @t219 () (tptp.push @t5 @t1))
% 172.90/173.27  (define @t220 () (tptp.comp tptp.sh @t219))
% 172.90/173.27  (define @t221 () (tptp.sub tptp.one @t219))
% 172.90/173.27  (define @t222 () (or @t209 @t206 @t203))
% 172.90/173.27  (define @t223 () (or @t214 @t222))
% 172.90/173.27  (define @t224 () (forall @t216 @t223))
% 172.90/173.27  (define @t225 () (@list @t202 @t156 @t155))
% 172.90/173.27  (define @t226 () (forall @t225 @t223))
% 172.90/173.27  (define @t227 () (forall @t225 @t222))
% 172.90/173.27  (define @t228 () (@var "BOUND_VARIABLE_9564" tptp.term))
% 172.90/173.27  (define @t229 () (@var "BOUND_VARIABLE_9562" tptp.subst))
% 172.90/173.27  (define @t230 () (or @t214 @t227))
% 172.90/173.27  (define @t231 () (= (_ @t84 @t229 @t228) (_ @t82 @t229 @t228)))
% 172.90/173.27  (define @t232 () (_ @t82 tptp.sh tptp.one))
% 172.90/173.27  (define @t233 () (tptp.lam @t232))
% 172.90/173.27  (define @t234 () (not (= @t205 @t233)))
% 172.90/173.27  (define @t235 () (_ @t82 @t208 @t207))
% 172.90/173.27  (define @t236 () (_ @t82 @t1 @t5))
% 172.90/173.27  (define @t237 () (tptp.sub @t236 @t21))
% 172.90/173.27  (define @t238 () (forall @t99 (= @t237 @t235)))
% 172.90/173.27  (define @t239 () (not @t238))
% 172.90/173.27  (define @t240 () (or @t239 @t234 @t231))
% 172.90/173.27  (define @t241 () (forall (@list @t82 @t229 @t228) @t240))
% 172.90/173.27  (define @t242 () (@list @t229 @t228))
% 172.90/173.27  (define @t243 () (forall @t242 @t240))
% 172.90/173.27  (define @t244 () (forall @t242 @t231))
% 172.90/173.27  (define @t245 () (or @t239 @t234 @t244))
% 172.90/173.27  (define @t246 () (forall @t88 (= @t211 @t236)))
% 172.90/173.27  (define @t247 () (_ @t82 tptp.sh))
% 172.90/173.27  (define @t248 () (_ @t247 tptp.one))
% 172.90/173.27  (define @t249 () (_ tptp.lam @t248))
% 172.90/173.27  (define @t250 () (= @t151 @t249))
% 172.90/173.27  (define @t251 () (not @t250))
% 172.90/173.27  (define @t252 () (or @t239 @t251 @t246))
% 172.90/173.27  (define @t253 () (=> @t250 @t246))
% 172.90/173.27  (define @t254 () (lambda @t16 (_ @t247 @t5)))
% 172.90/173.27  (define @t255 () (_ @t90 tptp.sh))
% 172.90/173.27  (define @t256 () (lambda @t109 @t151))
% 172.90/173.27  (define @t257 () (_ @t152 tptp.id))
% 172.90/173.27  (define @t258 () (lambda @t16 (_ @t141 @t5)))
% 172.90/173.27  (define @t259 () (_ @t92 tptp.sh))
% 172.90/173.27  (define @t260 () (= (_ @t257 @t92) (_ @t257 @t90)))
% 172.90/173.27  (define @t261 () (=> @t260 @t89))
% 172.90/173.27  (define @t262 () (=> @t100 @t261))
% 172.90/173.27  (define @t263 () (forall @t102 @t262))
% 172.90/173.27  (define @t264 () (=> @t107 @t263))
% 172.90/173.27  (define @t265 () (forall @t109 @t264))
% 172.90/173.27  (define @t266 () (not @t51))
% 172.90/173.27  (define @t267 () (or @t266 @t43))
% 172.90/173.27  (define @t268 () (= @t1 @t28))
% 172.90/173.27  (define @t269 () (= @t5 @t12))
% 172.90/173.27  (define @t270 () (forall @t184 (or (not (forall @t99 (= @t180 @t179))) (not (forall @t99 (= @t176 @t170))) (not (= @t165 @t164)) (= @t162 @t160))))
% 172.90/173.27  (define @t271 () (@quantifiers_skolemize @t270 3))
% 172.90/173.27  (define @t272 () (@quantifiers_skolemize @t270 2))
% 172.90/173.27  (define @t273 () (@quantifiers_skolemize @t270 0))
% 172.90/173.27  (define @t274 () (@quantifiers_skolemize @t270 1))
% 172.90/173.27  (define @t275 () (= (_ @t159 (_ @t158 @t274 @t272) @t271) (_ @t159 (_ @t158 @t273 @t272) @t271)))
% 172.90/173.27  (define @t276 () (_ @t159 (_ @t158 @t273 tptp.sh) tptp.one))
% 172.90/173.27  (define @t277 () (_ @t159 (_ @t158 @t274 tptp.sh) tptp.one))
% 172.90/173.27  (define @t278 () (= (_ @t159 @t163 @t277) (_ @t159 @t163 @t276)))
% 172.90/173.27  (define @t279 () (not @t278))
% 172.90/173.27  (define @t280 () (forall @t99 (= (_ @t159 (_ @t158 @t274 @t175) @t171) (_ @t169 (_ @t168 @t167 (_ @t159 (_ @t158 @t274 @t1) @t5)) @t21))))
% 172.90/173.27  (define @t281 () (not @t280))
% 172.90/173.27  (define @t282 () (forall @t99 (= (_ @t159 (_ @t158 @t273 @t175) @t171) (_ @t169 (_ @t168 @t167 (_ @t159 (_ @t158 @t273 @t1) @t5)) @t21))))
% 172.90/173.27  (define @t283 () (not @t282))
% 172.90/173.27  (define @t284 () (or @t283 @t281 @t279 @t275))
% 172.90/173.27  (define @t285 () (not @t275))
% 172.90/173.27  (define @t286 () (@list true))
% 172.90/173.27  (define @t287 () (@list @t284))
% 172.90/173.27  (define @t288 () (or @t279 (= @t276 @t277)))
% 172.90/173.27  (define @t289 () (forall @t52 (or (not (= @t187 @t186)) @t43)))
% 172.90/173.27  (define @t290 () (= @t277 @t276))
% 172.90/173.27  (define @t291 () (or @t279 @t290))
% 172.90/173.27  (define @t292 () (@list @t271 @t272))
% 172.90/173.27  (define @t293 () (_ @t174 (_ @t193 @t192 @t271) @t272))
% 172.90/173.27  (define @t294 () (@list tptp.sh tptp.one @t293))
% 172.90/173.27  (define @t295 () (_ @t168 @t167 @t276))
% 172.90/173.27  (define @t296 () (_ @t169 @t295 @t293))
% 172.90/173.27  (define @t297 () (_ @t169 @t198 @t293))
% 172.90/173.27  (define @t298 () (_ @t174 @t195 @t293))
% 172.90/173.27  (define @t299 () (_ @t158 @t273 @t298))
% 172.90/173.27  (define @t300 () (_ @t159 @t299 @t297))
% 172.90/173.27  (define @t301 () (= @t300 @t296))
% 172.90/173.27  (define @t302 () (not @t301))
% 172.90/173.27  (define @t303 () (_ @t158 @t274 @t298))
% 172.90/173.27  (define @t304 () (_ @t159 @t303 @t297))
% 172.90/173.27  (define @t305 () (= @t304 (_ @t169 (_ @t168 @t167 @t277) @t293)))
% 172.90/173.27  (define @t306 () (not @t305))
% 172.90/173.27  (define @t307 () (= @t272 @t298))
% 172.90/173.27  (define @t308 () (not @t307))
% 172.90/173.27  (define @t309 () (= @t271 @t297))
% 172.90/173.27  (define @t310 () (not @t309))
% 172.90/173.27  (define @t311 () (not @t290))
% 172.90/173.27  (define @t312 () (= @t296 @t300))
% 172.90/173.27  (define @t313 () (not @t312))
% 172.90/173.27  (define @t314 () (and @t301 @t302))
% 172.90/173.27  (assume @p1 (= tptp.axapp (forall (@list @t5 @t2 @t1) (= (_ (_ tptp.sub @t9) @t1) (_ (_ tptp.ap @t7) @t4)))))
% 172.90/173.27  (assume @p2 @t15)
% 172.90/173.27  (assume @p3 (= tptp.axvarid @t17))
% 172.90/173.27  (assume @p4 (= tptp.axabs (forall @t13 (= (_ (_ tptp.sub @t20) @t1) (_ tptp.lam (_ @t6 (_ @t19 (_ @t18 tptp.sh))))))))
% 172.90/173.27  (assume @p5 (= tptp.axclos @t24))
% 172.90/173.27  (assume @p6 (= tptp.axidl @t26))
% 172.90/173.27  (assume @p7 @t30)
% 172.90/173.27  (assume @p8 (= tptp.axassoc @t32))
% 172.90/173.27  (assume @p9 (= tptp.axmap (forall @t23 (= (_ (_ tptp.comp @t10) @t21) @t34))))
% 172.90/173.27  (assume @p10 (= tptp.axidr @t35))
% 172.90/173.27  (assume @p11 (= tptp.axvarshift (= @t36 tptp.id)))
% 172.90/173.27  (assume @p12 (= tptp.axscons (forall @t25 (= (_ (_ tptp.push (_ @t11 @t1)) (_ @t27 @t1)) @t1))))
% 172.90/173.27  (assume @p13 (= tptp.ulamvar1 (_ tptp.var tptp.one)))
% 172.90/173.27  (assume @p14 (= tptp.ulamvarsh (forall @t16 (=> @t38 (_ tptp.var @t37)))))
% 172.90/173.27  (assume @p15 (= tptp.ulamvarind (forall @t42 (=> (_ @t39 tptp.one) (=> (forall @t16 (=> @t38 (=> @t40 (_ @t39 @t37)))) @t41)))))
% 172.90/173.27  (assume @p16 (= tptp.apinj1 (forall @t48 (=> @t47 @t43))))
% 172.90/173.27  (assume @p17 (= tptp.apinj2 (forall @t48 (=> @t47 @t49))))
% 172.90/173.27  (assume @p18 @t54)
% 172.90/173.27  (assume @p19 (= tptp.shinj (forall @t52 (=> (= @t37 (_ @t3 tptp.sh)) @t43))))
% 172.90/173.27  (assume @p20 (= tptp.lamnotap (forall (@list @t5 @t2 @t46) (not (= @t20 (_ @t45 @t46))))))
% 172.90/173.27  (assume @p21 (= tptp.apnotvar (forall @t52 (not (_ tptp.var @t9)))))
% 172.90/173.27  (assume @p22 (= tptp.lamnotvar (forall @t16 (not (_ tptp.var @t20)))))
% 172.90/173.27  (assume @p23 (= tptp.induction (forall @t42 (=> @t41 (=> @t58 (=> (forall @t16 (=> @t40 @t56)) @t55))))))
% 172.90/173.27  (assume @p24 (= tptp.pushprop_lem0 (forall @t62 (exists @t61 @t60))))
% 172.90/173.27  (assume @p25 (= tptp.pushprop_lem0_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem0)))))))))))))))))))))))))
% 172.90/173.27  (assume @p26 (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0))
% 172.90/173.27  (assume @p27 (= tptp.pushprop_lem1 (forall (@list @t39 @t64 @t5 @t1 @t2) (=> @t40 (_ @t64 (_ @t6 (_ @t63 @t1)))))))
% 172.90/173.27  (assume @p28 (= tptp.pushprop_lem1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem1)))))))))))))))))))))))))
% 172.90/173.27  (assume @p29 (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1))))))
% 172.90/173.27  (assume @p30 (= tptp.pushprop_lem1v2 (forall @t65 (=> @t40 (=> @t60 (_ @t59 tptp.one))))))
% 172.90/173.27  (assume @p31 (= tptp.pushprop_lem1v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem1v2)))))))))))))))))))))))))
% 172.90/173.27  (assume @p32 (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2)))
% 172.90/173.27  (assume @p33 (= tptp.pushprop_lem2v2 (forall @t65 (=> @t60 (=> @t70 (forall @t67 (=> (_ tptp.var @t46) (=> (_ @t59 @t46) (_ @t59 (_ @t66 tptp.sh))))))))))
% 172.90/173.27  (assume @p34 (= tptp.pushprop_lem2v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop_lem2v2)))))))))))))))))))))))))
% 172.90/173.27  (assume @p35 (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2))))
% 172.90/173.27  (assume @p36 (= tptp.pushprop_lem3v2 (forall @t65 (=> @t60 (=> (forall @t69 (=> @t68 @t73)) @t72)))))
% 172.90/173.27  (assume @p37 (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2))
% 172.90/173.27  (assume @p38 (= tptp.pushprop (forall @t62 (=> @t70 (=> @t40 @t72)))))
% 172.90/173.27  (assume @p39 (= tptp.pushprop_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction tptp.pushprop)))))))))))))))))))))))))
% 172.90/173.27  (assume @p40 (= tptp.pushprop_lthm_orig @t74))
% 172.90/173.27  (assume @p41 (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 @t74)))
% 172.90/173.27  (assume @p42 (= tptp.induction2lem (forall @t42 (=> @t58 (=> @t76 (forall @t13 (=> @t70 (_ @t39 @t7))))))))
% 172.90/173.27  (assume @p43 (= tptp.induction2lem_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar @t77))))))))))))))))))))))))
% 172.90/173.27  (assume @p44 (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr @t77))))))))))
% 172.90/173.27  (assume @p45 (= tptp.induction2 (forall @t42 (=> @t41 (=> @t58 (=> @t76 @t55))))))
% 172.90/173.27  (assume @p46 (= tptp.induction2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop @t78))))))))))))))))))))))))))
% 172.90/173.27  (assume @p47 (= tptp.induction2_lthm (=> tptp.axvarid @t78)))
% 172.90/173.27  (assume @p48 (= tptp.substmonoid (and @t32 @t26 @t35)))
% 172.90/173.27  (assume @p49 (= tptp.substmonoid_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 tptp.substmonoid))))))))))))))))))))))))))))
% 172.90/173.27  (assume @p50 (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid)))))
% 172.90/173.27  (assume @p51 (= tptp.termmset (and @t24 @t17)))
% 172.90/173.27  (assume @p52 (= tptp.termmset_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid tptp.termmset)))))))))))))))))))))))))))))
% 172.90/173.27  (assume @p53 (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset))))
% 172.90/173.27  (assume @p54 (= tptp.hoasapinj1 (forall @t48 (=> @t81 @t43))))
% 172.90/173.27  (assume @p55 (= tptp.hoasapinj1_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset tptp.hoasapinj1))))))))))))))))))))))))))))))
% 172.90/173.27  (assume @p56 (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1))))
% 172.90/173.27  (assume @p57 (= tptp.hoasapinj2 (forall @t48 (=> @t81 @t49))))
% 172.90/173.27  (assume @p58 (= tptp.hoasapinj2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 tptp.hoasapinj2)))))))))))))))))))))))))))))))
% 172.90/173.27  (assume @p59 (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2)))
% 172.90/173.27  (assume @p60 @t111)
% 172.90/173.27  (assume @p61 (= tptp.hoaslaminj_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 tptp.hoaslaminj))))))))))))))))))))))))))))))))
% 172.90/173.27  (assume @p62 @t115)
% 172.90/173.27  (assume @p63 (= tptp.hoaslamnotap (forall @t109 (=> @t107 (forall @t52 (not (= (_ @t91 (lambda (@list @t1 @t46) (_ @t85 @t46))) @t116)))))))
% 172.90/173.27  (assume @p64 (= tptp.hoaslamnotap_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj tptp.hoaslamnotap)))))))))))))))))))))))))))))))))
% 172.90/173.27  (assume @p65 (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap)))
% 172.90/173.27  (assume @p66 (= tptp.hoaslamnotvar (forall @t109 (=> @t107 (not (_ (_ @t117 @t93) tptp.id))))))
% 172.90/173.27  (assume @p67 (= tptp.hoaslamnotvar_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap tptp.hoaslamnotvar))))))))))))))))))))))))))))))))))
% 172.90/173.27  (assume @p68 (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar))))
% 172.90/173.27  (assume @p69 (= tptp.hoasapnotvar (forall @t52 (not (_ (_ @t117 @t116) tptp.id)))))
% 172.90/173.27  (assume @p70 (= tptp.hoasapnotvar_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar tptp.hoasapnotvar)))))))))))))))))))))))))))))))))))
% 172.90/173.27  (assume @p71 (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar))))
% 172.90/173.27  (assume @p72 (= tptp.hoasinduction_lem0 (forall @t120 (exists @t61 @t119))))
% 172.90/173.27  (assume @p73 (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0))
% 172.90/173.27  (assume @p74 (= tptp.hoasinduction_lem1v2 (forall @t130 (=> @t129 (=> @t128 (=> @t124 (=> @t119 (forall @t16 (=> @t38 @t121)))))))))
% 172.90/173.27  (assume @p75 (= tptp.hoasinduction_lem1v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem1v2))))))))))))))))))))))))))))))))))))
% 172.90/173.27  (assume @p76 (= tptp.hoasinduction_lem2v2 (forall @t130 (=> @t129 (=> @t128 (=> @t132 (=> @t119 (forall @t52 (=> @t121 (=> @t73 (_ @t59 @t9)))))))))))
% 172.90/173.27  (assume @p77 (= tptp.hoasinduction_lem2v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem2v2))))))))))))))))))))))))))))))))))))
% 172.90/173.27  (assume @p78 (= tptp.hoasinduction_lem3v2_f (forall @t69 (exists @t109 (forall @t13 (= @t86 @t71))))))
% 172.90/173.27  (assume @p79 (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f))
% 172.90/173.27  (assume @p80 (= tptp.hoasinduction_lem3v2 (forall @t130 (=> @t129 (=> @t128 @t135)))))
% 172.90/173.27  (assume @p81 (= tptp.hoasinduction_lem3v2_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar tptp.hoasinduction_lem3v2))))))))))))))))))))))))))))))))))))
% 172.90/173.27  (assume @p82 (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2))))))
% 172.90/173.27  (assume @p83 (= tptp.hoasinduction_lem3v2a (forall @t130 @t135)))
% 172.90/173.27  (assume @p84 (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a)))))))
% 172.90/173.27  (assume @p85 (= tptp.hoasinduction_lem1 (forall @t120 (=> @t129 (=> @t128 (=> @t124 (forall @t16 (=> @t38 @t123))))))))
% 172.90/173.27  (assume @p86 (= tptp.hoasinduction_lem1_gthm @t136))
% 172.90/173.27  (assume @p87 (= tptp.hoasinduction_lem1_lthm @t136))
% 172.90/173.27  (assume @p88 (= tptp.hoasinduction_lem2 (forall @t120 (=> @t129 (=> @t128 (=> @t132 (forall @t52 (=> @t123 (=> @t131 (_ (_ @t122 @t9) tptp.id))))))))))
% 172.90/173.27  (assume @p89 (= tptp.hoasinduction_lem2_gthm @t137))
% 172.90/173.27  (assume @p90 (= tptp.hoasinduction_lem2_lthm @t137))
% 172.90/173.27  (assume @p91 (= tptp.hoasinduction_lem3aa (forall @t120 (=> @t134 @t139))))
% 172.90/173.27  (assume @p92 (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa))))
% 172.90/173.27  (assume @p93 (= tptp.hoasinduction_lem3aaa (forall @t120 (=> (forall @t109 (=> (exists @t67 (forall @t99 (and (= @t105 (_ (_ tptp.sub (_ @t66 @t10)) @t21)) (= (_ @t66 @t34) @t104)))) @t133)) @t139))))
% 172.90/173.27  (assume @p94 (= tptp.hoasinduction_lem3 (forall @t120 (=> @t129 (=> @t128 @t140)))))
% 172.90/173.27  (assume @p95 (= tptp.hoasinduction_lem3_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3))))))))))))))))))))))))))))))))))))))
% 172.90/173.27  (assume @p96 (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3)))))
% 172.90/173.27  (assume @p97 (= tptp.hoasinduction_lem3a (forall @t120 @t140)))
% 172.90/173.27  (assume @p98 (= tptp.hoasinduction_lem3a_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3a))))))))))))))))))))))))))))))))))))))
% 172.90/173.27  (assume @p99 (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a)))))
% 172.90/173.27  (assume @p100 (= tptp.hoasinduction_lem3b (forall @t69 (exists @t109 (= (_ @t3 @t36) @t142)))))
% 172.90/173.27  (assume @p101 (= tptp.hoasinduction_lem3b_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 tptp.hoasinduction_lem3b))))))))))))))))))))))))))))))))))))))
% 172.90/173.27  (assume @p102 (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b))
% 172.90/173.27  (assume @p103 (= tptp.hoasinduction (forall @t120 (=> @t129 (=> @t128 (=> @t124 @t143))))))
% 172.90/173.27  (assume @p104 (= tptp.hoasinduction_gthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axvarid (=> tptp.axabs (=> tptp.axclos (=> tptp.axidl (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr (=> tptp.axvarshift (=> tptp.axscons (=> tptp.ulamvar1 (=> tptp.ulamvarsh (=> tptp.ulamvarind (=> tptp.apinj1 (=> tptp.apinj2 (=> tptp.laminj (=> tptp.shinj (=> tptp.lamnotap (=> tptp.apnotvar (=> tptp.lamnotvar (=> tptp.induction (=> tptp.pushprop (=> tptp.induction2lem (=> tptp.induction2 (=> tptp.substmonoid (=> tptp.termmset (=> tptp.hoasapinj1 (=> tptp.hoasapinj2 (=> tptp.hoaslaminj (=> tptp.hoaslamnotap (=> tptp.hoaslamnotvar (=> tptp.hoasapnotvar @t144))))))))))))))))))))))))))))))))))))
% 172.90/173.27  (assume @p105 (= tptp.hoasinduction_lthm (=> tptp.induction2 @t144)))
% 172.90/173.27  (assume @p106 (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction))))))
% 172.90/173.27  (assume @p107 (= tptp.hoasinduction_no_psi_cond (forall @t120 @t143)))
% 172.90/173.27  (assume @p108 (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond))))))
% 172.90/173.27  (assume @p109 @t145)
% 172.90/173.27  (assume @p110 true)
% 172.90/173.27  (step @p111 (= tptp.pushprop_p_and_p_prime @t149) :rule refl :args (@t149))
% 172.90/173.27  (step @p112 (= tptp.hoasap @t150) :rule refl :args (@t150))
% 172.90/173.27  (step @p113 (= tptp.hoaslam @t152) :rule refl :args (@t152))
% 172.90/173.27  (step @p114 (= tptp.hoasvar @t153) :rule refl :args (@t153))
% 172.90/173.27  (step @p115 (= tptp.hoasinduction_p_and_p_prime @t154) :rule refl :args (@t154))
% 172.90/173.27  (step @p116 :rule eq-symm :args (@t160 @t162))
% 172.90/173.27  (step @p117 :rule eq-symm :args (@t164 @t165))
% 172.90/173.27  (step @p118 :rule cong :premises (@p117) :args (@t166))
% 172.90/173.27  (step @p119 :rule eq-symm :args (@t170 @t176))
% 172.90/173.27  (step @p120 :rule cong :premises (@p119) :args (@t177))
% 172.90/173.27  (step @p121 :rule cong :premises (@p120) :args (@t178))
% 172.90/173.27  (step @p122 :rule eq-symm :args (@t179 @t180))
% 172.90/173.27  (step @p123 :rule cong :premises (@p122) :args (@t181))
% 172.90/173.27  (step @p124 :rule cong :premises (@p123) :args (@t182))
% 172.90/173.27  (step @p125 :rule nary_cong :premises (@p124 @p121 @p118 @p116) :args (@t183))
% 172.90/173.27  (step @p126 :rule cong :premises (@p125) :args (@t185))
% 172.90/173.27  (step @p127 :rule refl :args (@t43))
% 172.90/173.27  (step @p128 :rule eq-symm :args (@t186 @t187))
% 172.90/173.27  (step @p129 :rule cong :premises (@p128) :args (@t188))
% 172.90/173.27  (step @p130 :rule nary_cong :premises (@p129 @p127) :args (@t189))
% 172.90/173.27  (step @p131 :rule cong :premises (@p130) :args (@t190))
% 172.90/173.27  (step @p132 :rule cong :premises (@p131 @p126) :args (@t191))
% 172.90/173.27  (step @p133 :rule refl :args (@t196))
% 172.90/173.27  (step @p134 :rule cong :premises (@p133 @p132) :args (@t197))
% 172.90/173.27  (step @p135 :rule refl :args (@t199))
% 172.90/173.27  (step @p136 :rule cong :premises (@p135 @p134) :args (@t200))
% 172.90/173.27  (step @p137 :rule cong :premises (@p136) :args (@t201))
% 172.90/173.27  ; WARNING: add trust step for TRUST
% 172.90/173.27  ; trust TRUST PREPROCESS_HO_ELIM
% 172.90/173.27  (step @p138 :rule trust :premises () :args ((= (not (=> (forall @t13 (= @t5 @t221)) (=> (forall @t13 (= @t1 @t220)) (=> (forall @t52 (or (not (= @t218 @t217)) @t43)) (forall @t216 @t215))))) @t201)))
% 172.90/173.27  (step @p139 :rule aci_norm :args ((= @t223 @t215)))
% 172.90/173.27  (step @p140 :rule cong :premises (@p139) :args (@t224))
% 172.90/173.27  (step @p141 :rule quant-merge-prenex :args ((= (forall @t109 @t226) @t224)))
% 172.90/173.27  (step @p142 :rule alpha_equiv :args (@t227 (@list @t202 @t156 @t155) (@list @t82 @t229 @t228)))
% 172.90/173.27  (step @p143 :rule refl :args (@t214))
% 172.90/173.27  (step @p144 :rule nary_cong :premises (@p143 @p142) :args (@t230))
% 172.90/173.27  (step @p145 :rule quant-miniscope-or :args ((= @t226 @t230)))
% 172.90/173.27  (step @p146 :rule trans :premises (@p145 @p144))
% 172.90/173.27  (step @p147 :rule symm :premises (@p146))
% 172.90/173.27  (step @p148 :rule cong :premises (@p147) :args ((forall @t109 (or @t214 @t241))))
% 172.90/173.27  (step @p149 :rule trans :premises (@p148 @p141))
% 172.90/173.27  (step @p150 :rule trans :premises (@p149 @p140))
% 172.90/173.27  (step @p151 :rule bool-impl-elim :args (@t213 @t241))
% 172.90/173.27  (step @p152 :rule cong :premises (@p151) :args ((forall @t109 (=> @t213 @t241))))
% 172.90/173.27  (step @p153 :rule trans :premises (@p152 @p150))
% 172.90/173.27  (step @p154 :rule quant-merge-prenex :args ((= (forall @t102 @t243) @t241)))
% 172.90/173.27  (step @p155 :rule alpha_equiv :args (@t244 (@list @t229 @t228) (@list @t1 @t5)))
% 172.90/173.27  (step @p156 :rule refl :args (@t234))
% 172.90/173.27  (step @p157 :rule refl :args (@t239))
% 172.90/173.27  (step @p158 :rule nary_cong :premises (@p157 @p156 @p155) :args (@t245))
% 172.90/173.27  (step @p159 :rule quant-miniscope-or :args ((= @t243 @t245)))
% 172.90/173.27  (step @p160 :rule trans :premises (@p159 @p158))
% 172.90/173.27  (step @p161 :rule symm :premises (@p160))
% 172.90/173.27  (step @p162 :rule cong :premises (@p161) :args ((forall @t102 (or @t239 @t234 @t246))))
% 172.90/173.27  (step @p163 :rule trans :premises (@p162 @p154))
% 172.90/173.27  (step @p164 :rule refl :args (@t246))
% 172.90/173.27  (step @p165 :rule refl :args ((tptp.lam @t248)))
% 172.90/173.27  (step @p166 :rule refl :args (@t232))
% 172.90/173.27  (step @p167 :rule cong :premises (@p166) :args (@t233))
% 172.90/173.27  (step @p168 :rule trans :premises (@p167 @p165))
% 172.90/173.27  (step @p169 :rule refl :args (tptp.lam))
% 172.90/173.27  (step @p170 :rule ho_cong :premises (@p169 @p166))
% 172.90/173.27  (step @p171 :rule cong :premises (@p170 @p168) :args ((= (_ tptp.lam @t232) @t233)))
% 172.90/173.27  (step @p172 :rule symm :premises (@p171))
% 172.90/173.27  (step @p173 :rule refl :args (@t249))
% 172.90/173.27  (step @p174 :rule eq_resolve :premises (@p173 @p172))
% 172.90/173.27  (step @p175 :rule refl :args (@t248))
% 172.90/173.27  (step @p176 :rule cong :premises (@p175 @p166) :args ((= @t248 @t232)))
% 172.90/173.27  (step @p177 :rule symm :premises (@p176))
% 172.90/173.27  (step @p178 :rule eq_resolve :premises (@p175 @p177))
% 172.90/173.27  (step @p179 :rule ho_cong :premises (@p169 @p178))
% 172.90/173.27  (step @p180 :rule trans :premises (@p179 @p174))
% 172.90/173.27  (step @p181 :rule refl :args ((tptp.lam @t142)))
% 172.90/173.27  (step @p182 :rule refl :args (@t204))
% 172.90/173.27  (step @p183 :rule cong :premises (@p182) :args (@t205))
% 172.90/173.27  (step @p184 :rule trans :premises (@p183 @p181))
% 172.90/173.27  (step @p185 :rule ho_cong :premises (@p169 @p182))
% 172.90/173.27  (step @p186 :rule cong :premises (@p185 @p184) :args ((= (_ tptp.lam @t204) @t205)))
% 172.90/173.27  (step @p187 :rule symm :premises (@p186))
% 172.90/173.27  (step @p188 :rule refl :args (@t151))
% 172.90/173.27  (step @p189 :rule eq_resolve :premises (@p188 @p187))
% 172.90/173.27  (step @p190 :rule refl :args (@t142))
% 172.90/173.27  (step @p191 :rule cong :premises (@p190 @p182) :args ((= @t142 @t204)))
% 172.90/173.27  (step @p192 :rule symm :premises (@p191))
% 172.90/173.27  (step @p193 :rule eq_resolve :premises (@p190 @p192))
% 172.90/173.27  (step @p194 :rule ho_cong :premises (@p169 @p193))
% 172.90/173.27  (step @p195 :rule trans :premises (@p194 @p189))
% 172.90/173.27  (step @p196 :rule cong :premises (@p195 @p180) :args (@t250))
% 172.90/173.27  (step @p197 :rule cong :premises (@p196) :args (@t251))
% 172.90/173.27  (step @p198 :rule nary_cong :premises (@p157 @p197 @p164) :args (@t252))
% 172.90/173.27  (step @p199 :rule cong :premises (@p198) :args ((forall @t102 @t252)))
% 172.90/173.27  (step @p200 :rule trans :premises (@p199 @p163))
% 172.90/173.27  (step @p201 :rule aci_norm :args ((= (or @t239 (or @t251 @t246)) @t252)))
% 172.90/173.27  (step @p202 :rule bool-impl-elim :args (@t250 @t246))
% 172.90/173.27  (step @p203 :rule nary_cong :premises (@p157 @p202) :args ((or @t239 @t253)))
% 172.90/173.27  (step @p204 :rule trans :premises (@p203 @p201))
% 172.90/173.27  (step @p205 :rule bool-impl-elim :args (@t238 @t253))
% 172.90/173.27  (step @p206 :rule trans :premises (@p205 @p204))
% 172.90/173.27  (step @p207 :rule cong :premises (@p206) :args ((forall @t102 (=> @t238 @t253))))
% 172.90/173.27  (step @p208 :rule trans :premises (@p207 @p200))
% 172.90/173.27  (step @p209 :rule refl :args (@t236))
% 172.90/173.27  (step @p210 :rule refl :args (@t83))
% 172.90/173.27  (step @p211 :rule cong :premises (@p210 @p209) :args ((= @t83 @t236)))
% 172.90/173.27  (step @p212 :rule symm :premises (@p211))
% 172.90/173.27  (step @p213 :rule eq_resolve :premises (@p210 @p212))
% 172.90/173.27  (step @p214 :rule refl :args (@t211))
% 172.90/173.27  (step @p215 :rule refl :args (@t86))
% 172.90/173.27  (step @p216 :rule cong :premises (@p215 @p214) :args ((= @t86 @t211)))
% 172.90/173.27  (step @p217 :rule symm :premises (@p216))
% 172.90/173.27  (step @p218 :rule eq_resolve :premises (@p215 @p217))
% 172.90/173.27  (step @p219 :rule cong :premises (@p218 @p213) :args (@t87))
% 172.90/173.27  (step @p220 :rule cong :premises (@p219) :args (@t89))
% 172.90/173.27  (step @p221 :rule beta-reduce :args ((= (_ @t254 tptp.one) @t248)))
% 172.90/173.27  (step @p222 :rule refl :args (tptp.one))
% 172.90/173.27  (step @p223 :rule beta-reduce :args ((= @t255 @t254)))
% 172.90/173.27  (step @p224 :rule ho_cong :premises (@p223 @p222))
% 172.90/173.27  (step @p225 :rule trans :premises (@p224 @p221))
% 172.90/173.27  (step @p226 :rule refl :args (tptp.lam))
% 172.90/173.27  (step @p227 :rule ho_cong :premises (@p226 @p225))
% 172.90/173.27  (step @p228 :rule beta-reduce :args ((= (_ @t256 @t90) (_ tptp.lam (_ @t255 tptp.one)))))
% 172.90/173.27  (step @p229 :rule trans :premises (@p228 @p227))
% 172.90/173.27  (step @p230 :rule refl :args (@t90))
% 172.90/173.27  (step @p231 :rule beta-reduce :args ((= @t257 @t256)))
% 172.90/173.27  (step @p232 :rule ho_cong :premises (@p231 @p230))
% 172.90/173.27  (step @p233 :rule trans :premises (@p232 @p229))
% 172.90/173.27  (step @p234 :rule beta-reduce :args ((= (_ @t258 tptp.one) @t142)))
% 172.90/173.27  (step @p235 :rule beta-reduce :args ((= @t259 @t258)))
% 172.90/173.27  (step @p236 :rule ho_cong :premises (@p235 @p222))
% 172.90/173.27  (step @p237 :rule trans :premises (@p236 @p234))
% 172.90/173.27  (step @p238 :rule ho_cong :premises (@p226 @p237))
% 172.90/173.27  (step @p239 :rule beta-reduce :args ((= (_ @t256 @t92) (_ tptp.lam (_ @t259 tptp.one)))))
% 172.90/173.27  (step @p240 :rule trans :premises (@p239 @p238))
% 172.90/173.27  (step @p241 :rule refl :args (@t92))
% 172.90/173.27  (step @p242 :rule ho_cong :premises (@p231 @p241))
% 172.90/173.27  (step @p243 :rule trans :premises (@p242 @p240))
% 172.90/173.27  (step @p244 :rule cong :premises (@p243 @p233) :args (@t260))
% 172.90/173.27  (step @p245 :rule cong :premises (@p244 @p220) :args (@t261))
% 172.90/173.27  (step @p246 :rule refl :args ((_ @t82 @t22 @t33)))
% 172.90/173.27  (step @p247 :rule refl :args (@t207))
% 172.90/173.27  (step @p248 :rule refl :args (@t208))
% 172.90/173.27  (step @p249 :rule cong :premises (@p248 @p247) :args (@t235))
% 172.90/173.27  (step @p250 :rule trans :premises (@p249 @p246))
% 172.90/173.27  (step @p251 :rule refl :args (@t82))
% 172.90/173.27  (step @p252 :rule ho_cong :premises (@p251 @p248))
% 172.90/173.27  (step @p253 :rule ho_cong :premises (@p252 @p247))
% 172.90/173.27  (step @p254 :rule cong :premises (@p253 @p250) :args ((= (_ (_ @t82 @t208) @t207) @t235)))
% 172.90/173.27  (step @p255 :rule symm :premises (@p254))
% 172.90/173.27  (step @p256 :rule refl :args (@t96))
% 172.90/173.27  (step @p257 :rule eq_resolve :premises (@p256 @p255))
% 172.90/173.27  (step @p258 :rule refl :args (@t33))
% 172.90/173.27  (step @p259 :rule cong :premises (@p258 @p247) :args ((= @t33 @t207)))
% 172.90/173.27  (step @p260 :rule symm :premises (@p259))
% 172.90/173.27  (step @p261 :rule eq_resolve :premises (@p258 @p260))
% 172.90/173.27  (step @p262 :rule refl :args (@t22))
% 172.90/173.27  (step @p263 :rule cong :premises (@p262 @p248) :args ((= @t22 @t208)))
% 172.90/173.27  (step @p264 :rule symm :premises (@p263))
% 172.90/173.27  (step @p265 :rule eq_resolve :premises (@p262 @p264))
% 172.90/173.27  (step @p266 :rule ho_cong :premises (@p251 @p265))
% 172.90/173.27  (step @p267 :rule ho_cong :premises (@p266 @p261))
% 172.90/173.27  (step @p268 :rule trans :premises (@p267 @p257))
% 172.90/173.27  (step @p269 :rule refl :args ((tptp.sub @t83 @t21)))
% 172.90/173.27  (step @p270 :rule refl :args (@t21))
% 172.90/173.27  (step @p271 :rule cong :premises (@p209 @p270) :args (@t237))
% 172.90/173.27  (step @p272 :rule trans :premises (@p271 @p269))
% 172.90/173.27  (step @p273 :rule refl :args (tptp.sub))
% 172.90/173.27  (step @p274 :rule ho_cong :premises (@p273 @p209))
% 172.90/173.27  (step @p275 :rule ho_cong :premises (@p274 @p270))
% 172.90/173.27  (step @p276 :rule cong :premises (@p275 @p272) :args ((= (_ (_ tptp.sub @t236) @t21) @t237)))
% 172.90/173.27  (step @p277 :rule symm :premises (@p276))
% 172.90/173.27  (step @p278 :rule refl :args (@t97))
% 172.90/173.27  (step @p279 :rule eq_resolve :premises (@p278 @p277))
% 172.90/173.27  (step @p280 :rule ho_cong :premises (@p273 @p213))
% 172.90/173.27  (step @p281 :rule ho_cong :premises (@p280 @p270))
% 172.90/173.27  (step @p282 :rule trans :premises (@p281 @p279))
% 172.90/173.27  (step @p283 :rule cong :premises (@p282 @p268) :args (@t98))
% 172.90/173.27  (step @p284 :rule cong :premises (@p283) :args (@t100))
% 172.90/173.27  (step @p285 :rule cong :premises (@p284 @p245) :args (@t262))
% 172.90/173.27  (step @p286 :rule cong :premises (@p285) :args (@t263))
% 172.90/173.27  (step @p287 :rule trans :premises (@p286 @p208))
% 172.90/173.27  (step @p288 :rule refl :args ((_ @t84 @t22 @t33)))
% 172.90/173.27  (step @p289 :rule cong :premises (@p248 @p247) :args (@t210))
% 172.90/173.27  (step @p290 :rule trans :premises (@p289 @p288))
% 172.90/173.27  (step @p291 :rule refl :args (@t84))
% 172.90/173.27  (step @p292 :rule ho_cong :premises (@p291 @p248))
% 172.90/173.27  (step @p293 :rule ho_cong :premises (@p292 @p247))
% 172.90/173.27  (step @p294 :rule cong :premises (@p293 @p290) :args ((= (_ (_ @t84 @t208) @t207) @t210)))
% 172.90/173.27  (step @p295 :rule symm :premises (@p294))
% 172.90/173.27  (step @p296 :rule refl :args (@t104))
% 172.90/173.27  (step @p297 :rule eq_resolve :premises (@p296 @p295))
% 172.90/173.27  (step @p298 :rule ho_cong :premises (@p291 @p265))
% 172.90/173.27  (step @p299 :rule ho_cong :premises (@p298 @p261))
% 172.90/173.27  (step @p300 :rule trans :premises (@p299 @p297))
% 172.90/173.27  (step @p301 :rule refl :args ((tptp.sub @t86 @t21)))
% 172.90/173.27  (step @p302 :rule cong :premises (@p214 @p270) :args (@t212))
% 172.90/173.27  (step @p303 :rule trans :premises (@p302 @p301))
% 172.90/173.27  (step @p304 :rule ho_cong :premises (@p273 @p214))
% 172.90/173.27  (step @p305 :rule ho_cong :premises (@p304 @p270))
% 172.90/173.27  (step @p306 :rule cong :premises (@p305 @p303) :args ((= (_ (_ tptp.sub @t211) @t21) @t212)))
% 172.90/173.27  (step @p307 :rule symm :premises (@p306))
% 172.90/173.27  (step @p308 :rule refl :args (@t105))
% 172.90/173.27  (step @p309 :rule eq_resolve :premises (@p308 @p307))
% 172.90/173.27  (step @p310 :rule ho_cong :premises (@p273 @p218))
% 172.90/173.27  (step @p311 :rule ho_cong :premises (@p310 @p270))
% 172.90/173.27  (step @p312 :rule trans :premises (@p311 @p309))
% 172.90/173.27  (step @p313 :rule cong :premises (@p312 @p300) :args (@t106))
% 172.90/173.27  (step @p314 :rule cong :premises (@p313) :args (@t107))
% 172.90/173.27  (step @p315 :rule cong :premises (@p314 @p287) :args (@t264))
% 172.90/173.27  (step @p316 :rule cong :premises (@p315) :args (@t265))
% 172.90/173.27  (step @p317 :rule trans :premises (@p316 @p153))
% 172.90/173.27  (step @p318 :rule refl :args (tptp.hoaslaminj))
% 172.90/173.27  (step @p319 :rule cong :premises (@p318 @p317) :args ((= tptp.hoaslaminj @t265)))
% 172.90/173.27  (step @p320 :rule refl :args (@t89))
% 172.90/173.27  (step @p321 :rule refl :args (tptp.id))
% 172.90/173.27  (step @p322 :rule ho_cong :premises (@p113 @p321))
% 172.90/173.27  (step @p323 :rule ho_cong :premises (@p322 @p230))
% 172.90/173.27  (step @p324 :rule ho_cong :premises (@p322 @p241))
% 172.90/173.27  (step @p325 :rule cong :premises (@p324 @p323) :args (@t94))
% 172.90/173.27  (step @p326 :rule cong :premises (@p325 @p320) :args (@t95))
% 172.90/173.27  (step @p327 :rule refl :args (@t100))
% 172.90/173.27  (step @p328 :rule cong :premises (@p327 @p326) :args (@t101))
% 172.90/173.27  (step @p329 :rule cong :premises (@p328) :args (@t103))
% 172.90/173.27  (step @p330 :rule refl :args (@t107))
% 172.90/173.27  (step @p331 :rule cong :premises (@p330 @p329) :args (@t108))
% 172.90/173.27  (step @p332 :rule cong :premises (@p331) :args (@t110))
% 172.90/173.27  (step @p333 :rule cong :premises (@p318 @p332) :args (@t111))
% 172.90/173.27  (step @p334 :rule trans :premises (@p333 @p319))
% 172.90/173.27  (step @p335 :rule eq_resolve :premises (@p60 @p334))
% 172.90/173.27  (step @p336 :rule refl :args (@t43))
% 172.90/173.27  (step @p337 :rule refl :args (@t217))
% 172.90/173.27  (step @p338 :rule refl :args (@t50))
% 172.90/173.27  (step @p339 :rule cong :premises (@p338 @p337) :args ((= @t50 @t217)))
% 172.90/173.27  (step @p340 :rule symm :premises (@p339))
% 172.90/173.27  (step @p341 :rule eq_resolve :premises (@p338 @p340))
% 172.90/173.27  (step @p342 :rule refl :args (@t218))
% 172.90/173.27  (step @p343 :rule refl :args (@t20))
% 172.90/173.27  (step @p344 :rule cong :premises (@p343 @p342) :args ((= @t20 @t218)))
% 172.90/173.27  (step @p345 :rule symm :premises (@p344))
% 172.90/173.27  (step @p346 :rule eq_resolve :premises (@p343 @p345))
% 172.90/173.27  (step @p347 :rule cong :premises (@p346 @p341) :args (@t51))
% 172.90/173.27  (step @p348 :rule cong :premises (@p347) :args (@t266))
% 172.90/173.27  (step @p349 :rule nary_cong :premises (@p348 @p336) :args (@t267))
% 172.90/173.27  (step @p350 :rule cong :premises (@p349) :args ((forall @t52 @t267)))
% 172.90/173.27  (step @p351 :rule bool-impl-elim :args (@t51 @t43))
% 172.90/173.27  (step @p352 :rule cong :premises (@p351) :args (@t53))
% 172.90/173.27  (step @p353 :rule trans :premises (@p352 @p350))
% 172.90/173.27  (step @p354 :rule refl :args (tptp.laminj))
% 172.90/173.27  (step @p355 :rule cong :premises (@p354 @p353) :args (@t54))
% 172.90/173.27  (step @p356 :rule eq_resolve :premises (@p18 @p355))
% 172.90/173.27  (step @p357 :rule cong :premises (@p356 @p335) :args (@t112))
% 172.90/173.27  (step @p358 :rule refl :args ((tptp.comp tptp.sh @t10)))
% 172.90/173.27  (step @p359 :rule refl :args (@t219))
% 172.90/173.27  (step @p360 :rule refl :args (tptp.sh))
% 172.90/173.27  (step @p361 :rule cong :premises (@p360 @p359) :args (@t220))
% 172.90/173.27  (step @p362 :rule trans :premises (@p361 @p358))
% 172.90/173.27  (step @p363 :rule refl :args (@t27))
% 172.90/173.27  (step @p364 :rule ho_cong :premises (@p363 @p359))
% 172.90/173.27  (step @p365 :rule cong :premises (@p364 @p362) :args ((= (_ @t27 @t219) @t220)))
% 172.90/173.27  (step @p366 :rule symm :premises (@p365))
% 172.90/173.27  (step @p367 :rule refl :args (@t28))
% 172.90/173.27  (step @p368 :rule eq_resolve :premises (@p367 @p366))
% 172.90/173.27  (step @p369 :rule refl :args (@t10))
% 172.90/173.27  (step @p370 :rule cong :premises (@p369 @p359) :args ((= @t10 @t219)))
% 172.90/173.27  (step @p371 :rule symm :premises (@p370))
% 172.90/173.27  (step @p372 :rule eq_resolve :premises (@p369 @p371))
% 172.90/173.27  (step @p373 :rule ho_cong :premises (@p363 @p372))
% 172.90/173.27  (step @p374 :rule trans :premises (@p373 @p368))
% 172.90/173.27  (step @p375 :rule refl :args (@t1))
% 172.90/173.27  (step @p376 :rule cong :premises (@p375 @p374) :args (@t268))
% 172.90/173.27  (step @p377 :rule cong :premises (@p376) :args ((forall @t13 @t268)))
% 172.90/173.27  (step @p378 :rule eq-symm :args (@t28 @t1))
% 172.90/173.27  (step @p379 :rule cong :premises (@p378) :args (@t29))
% 172.90/173.27  (step @p380 :rule trans :premises (@p379 @p377))
% 172.90/173.27  (step @p381 :rule refl :args (tptp.axshiftcons))
% 172.90/173.27  (step @p382 :rule cong :premises (@p381 @p380) :args (@t30))
% 172.90/173.27  (step @p383 :rule eq_resolve :premises (@p7 @p382))
% 172.90/173.27  (step @p384 :rule cong :premises (@p383 @p357) :args (@t113))
% 172.90/173.27  (step @p385 :rule refl :args ((tptp.sub tptp.one @t10)))
% 172.90/173.27  (step @p386 :rule refl :args (tptp.one))
% 172.90/173.27  (step @p387 :rule cong :premises (@p386 @p359) :args (@t221))
% 172.90/173.27  (step @p388 :rule trans :premises (@p387 @p385))
% 172.90/173.27  (step @p389 :rule refl :args (@t11))
% 172.90/173.27  (step @p390 :rule ho_cong :premises (@p389 @p359))
% 172.90/173.27  (step @p391 :rule cong :premises (@p390 @p388) :args ((= (_ @t11 @t219) @t221)))
% 172.90/173.27  (step @p392 :rule symm :premises (@p391))
% 172.90/173.27  (step @p393 :rule refl :args (@t12))
% 172.90/173.27  (step @p394 :rule eq_resolve :premises (@p393 @p392))
% 172.90/173.27  (step @p395 :rule ho_cong :premises (@p389 @p372))
% 172.90/173.27  (step @p396 :rule trans :premises (@p395 @p394))
% 172.90/173.27  (step @p397 :rule refl :args (@t5))
% 172.90/173.27  (step @p398 :rule cong :premises (@p397 @p396) :args (@t269))
% 172.90/173.27  (step @p399 :rule cong :premises (@p398) :args ((forall @t13 @t269)))
% 172.90/173.27  (step @p400 :rule eq-symm :args (@t12 @t5))
% 172.90/173.27  (step @p401 :rule cong :premises (@p400) :args (@t14))
% 172.90/173.27  (step @p402 :rule trans :premises (@p401 @p399))
% 172.90/173.27  (step @p403 :rule refl :args (tptp.axvarcons))
% 172.90/173.27  (step @p404 :rule cong :premises (@p403 @p402) :args (@t15))
% 172.90/173.27  (step @p405 :rule eq_resolve :premises (@p2 @p404))
% 172.90/173.27  (step @p406 :rule cong :premises (@p405 @p384) :args (@t114))
% 172.90/173.27  (step @p407 :rule refl :args (tptp.hoaslaminj_lthm))
% 172.90/173.27  (step @p408 :rule cong :premises (@p407 @p406) :args (@t115))
% 172.90/173.27  (step @p409 :rule eq_resolve :premises (@p62 @p408))
% 172.90/173.27  (step @p410 :rule cong :premises (@p409) :args (@t145))
% 172.90/173.27  (step @p411 :rule trans :premises (@p410 @p138 @p137))
% 172.90/173.27  (step @p412 :rule eq_resolve :premises (@p109 @p411))
% 172.90/173.27  (step @p413 :rule not_implies_elim2 :premises (@p412))
% 172.90/173.27  (step @p414 :rule not_implies_elim2 :premises (@p413))
% 172.90/173.27  (step @p415 :rule not_implies_elim2 :premises (@p414))
% 172.90/173.27  (step @p416 :rule skolemize :premises (@p415))
% 172.90/173.27  (step @p417 :rule cnf_or_neg :args (@t284 3))
% 172.90/173.27  (step @p418 :rule chain_m_resolution :premises (@p417 @p416) :args (@t285 @t286 @t287))
% 172.90/173.27  (step @p419 :rule not_implies_elim1 :premises (@p414))
% 172.90/173.27  (step @p420 :rule eq-symm :args (@t276 @t277))
% 172.90/173.27  (step @p421 :rule refl :args (@t279))
% 172.90/173.27  (step @p422 :rule nary_cong :premises (@p421 @p420) :args (@t288))
% 172.90/173.27  (step @p423 :rule refl :args (@t289))
% 172.90/173.27  (step @p424 :rule cong :premises (@p423 @p422) :args ((=> @t289 @t288)))
% 172.90/173.27  (assume-push @p524 @t289)
% 172.90/173.27  (step @p426 :rule instantiate :premises (@p419) :args ((@list @t276 @t277)))
% 172.90/173.27  (step-pop @p525 :rule scope :premises (@p426))
% 172.90/173.27  (step @p427 :rule process_scope :premises (@p525) :args (@t288))
% 172.90/173.27  (step @p429 :rule eq_resolve :premises (@p427 @p424))
% 172.90/173.27  (step @p430 :rule implies_elim :premises (@p429))
% 172.90/173.27  (step @p431 :rule chain_m_resolution :premises (@p430 @p419) :args (@t291 (@list false) (@list @t289)))
% 172.90/173.27  (step @p432 :rule bool-double-not-elim :args (@t278))
% 172.90/173.27  (step @p433 :rule refl :args (@t284))
% 172.90/173.27  (step @p434 :rule nary_cong :premises (@p433 @p432) :args ((or @t284 (not @t279))))
% 172.90/173.27  (step @p435 :rule cnf_or_neg :args (@t284 2))
% 172.90/173.27  (step @p436 :rule eq_resolve :premises (@p435 @p434))
% 172.90/173.27  (step @p437 :rule reordering :premises (@p436) :args ((or @t278 @t284)))
% 172.90/173.27  (step @p438 :rule chain_m_resolution :premises (@p437 @p416) :args (@t278 @t286 @t287))
% 172.90/173.27  (step @p439 :rule cnf_or_pos :args (@t291))
% 172.90/173.27  (step @p440 :rule reordering :premises (@p439) :args ((or @t279 @t290 (not @t291))))
% 172.90/173.27  (step @p441 :rule chain_m_resolution :premises (@p440 @p438 @p431) :args (@t290 (@list false false) (@list @t278 @t291)))
% 172.90/173.27  (step @p442 :rule not_implies_elim1 :premises (@p412))
% 172.90/173.27  (step @p443 :rule instantiate :premises (@p442) :args (@t292))
% 172.90/173.27  (step @p444 :rule not_implies_elim1 :premises (@p413))
% 172.90/173.27  (step @p445 :rule instantiate :premises (@p444) :args (@t292))
% 172.90/173.27  (step @p446 :rule bool-double-not-elim :args (@t280))
% 172.90/173.27  (step @p447 :rule nary_cong :premises (@p433 @p446) :args ((or @t284 (not @t281))))
% 172.90/173.27  (step @p448 :rule cnf_or_neg :args (@t284 1))
% 172.90/173.27  (step @p449 :rule eq_resolve :premises (@p448 @p447))
% 172.90/173.27  (step @p450 :rule reordering :premises (@p449) :args ((or @t280 @t284)))
% 172.90/173.27  (step @p451 :rule chain_m_resolution :premises (@p450 @p416) :args (@t280 @t286 @t287))
% 172.90/173.27  (step @p452 :rule instantiate :premises (@p451) :args (@t294))
% 172.90/173.27  (step @p453 :rule bool-double-not-elim :args (@t282))
% 172.90/173.27  (step @p454 :rule nary_cong :premises (@p433 @p453) :args ((or @t284 (not @t283))))
% 172.90/173.27  (step @p455 :rule cnf_or_neg :args (@t284 0))
% 172.90/173.27  (step @p456 :rule eq_resolve :premises (@p455 @p454))
% 172.90/173.27  (step @p457 :rule reordering :premises (@p456) :args ((or @t282 @t284)))
% 172.90/173.27  (step @p458 :rule chain_m_resolution :premises (@p457 @p416) :args (@t282 @t286 @t287))
% 172.90/173.27  (step @p459 :rule instantiate :premises (@p458) :args (@t294))
% 172.90/173.27  (step @p460 :rule refl :args (@t302))
% 172.90/173.27  (step @p461 :rule refl :args (@t306))
% 172.90/173.27  (step @p462 :rule refl :args (@t308))
% 172.90/173.27  (step @p463 :rule refl :args (@t310))
% 172.90/173.27  (step @p464 :rule refl :args (@t311))
% 172.90/173.27  (step @p465 :rule bool-double-not-elim :args (@t275))
% 172.90/173.27  (step @p466 :rule nary_cong :premises (@p465 @p464 @p463 @p462 @p461 @p460) :args ((or (not @t285) @t311 @t310 @t308 @t306 @t302)))
% 172.90/173.27  (assume-push @p526 @t301)
% 172.90/173.27  (assume-push @p527 @t302)
% 172.90/173.27  (step @p469 :rule evaluate :args ((= false true)))
% 172.90/173.28  (step @p470 :rule true_intro :premises (@p459))
% 172.90/173.28  (step @p471 :rule bool-eq-false :args (@t301))
% 172.90/173.28  (step @p472 :rule symm :premises (@p471))
% 172.90/173.28  (step @p473 :rule eq-symm :args (@t296 @t300))
% 172.90/173.28  (step @p474 :rule cong :premises (@p473) :args (@t313))
% 172.90/173.28  (step @p475 :rule bool-eq-false :args (@t312))
% 172.90/173.28  (step @p476 :rule trans :premises (@p475 @p474))
% 172.90/173.28  (step @p477 :rule trans :premises (@p476 @p472))
% 172.90/173.28  (step @p478 :rule false_intro :premises (@p418))
% 172.90/173.28  (step @p479 :rule symm :premises (@p443))
% 172.90/173.28  (step @p480 :rule symm :premises (@p445))
% 172.90/173.28  (step @p481 :rule refl :args (@t273))
% 172.90/173.28  (step @p482 :rule cong :premises (@p481 @p480) :args (@t299))
% 172.90/173.28  (step @p483 :rule cong :premises (@p482 @p479) :args (@t300))
% 172.90/173.28  (step @p484 :rule refl :args (@t274))
% 172.90/173.28  (step @p485 :rule cong :premises (@p484 @p480) :args (@t303))
% 172.90/173.28  (step @p486 :rule cong :premises (@p485 @p479) :args (@t304))
% 172.90/173.28  (step @p487 :rule symm :premises (@p452))
% 172.90/173.28  (step @p488 :rule refl :args (@t293))
% 172.90/173.28  (step @p489 :rule symm :premises (@p441))
% 172.90/173.28  (step @p490 :rule refl :args (@t167))
% 172.90/173.28  (step @p491 :rule cong :premises (@p490 @p489) :args (@t295))
% 172.90/173.28  (step @p492 :rule cong :premises (@p491 @p488) :args (@t296))
% 172.90/173.28  (step @p493 :rule trans :premises (@p492 @p487 @p486))
% 172.90/173.28  (step @p494 :rule cong :premises (@p493 @p483) :args (@t312))
% 172.90/173.28  (step @p495 :rule trans :premises (@p494 @p478))
% 172.90/173.28  (step @p496 :rule eq_resolve :premises (@p495 @p477))
% 172.90/173.28  (step @p497 :rule symm :premises (@p496))
% 172.90/173.28  (step @p498 :rule trans :premises (@p497 @p470))
% 172.90/173.28  (step @p499 false :rule eq_resolve :premises (@p498 @p469))
% 172.90/173.28  (step-pop @p528 :rule scope :premises (@p499))
% 172.90/173.28  (step-pop @p529 :rule scope :premises (@p528))
% 172.90/173.28  (step @p500 :rule process_scope :premises (@p529) :args (false))
% 172.90/173.28  (assume-push @p530 @t285)
% 172.90/173.28  (assume-push @p531 @t290)
% 172.90/173.28  (assume-push @p532 @t309)
% 172.90/173.28  (assume-push @p533 @t307)
% 172.90/173.28  (assume-push @p534 @t305)
% 172.90/173.28  (assume-push @p535 @t301)
% 172.90/173.28  (step @p471 :rule bool-eq-false :args (@t301))
% 172.90/173.28  (step @p472 :rule symm :premises (@p471))
% 172.90/173.28  (step @p473 :rule eq-symm :args (@t296 @t300))
% 172.90/173.28  (step @p474 :rule cong :premises (@p473) :args (@t313))
% 172.90/173.28  (step @p475 :rule bool-eq-false :args (@t312))
% 172.90/173.28  (step @p476 :rule trans :premises (@p475 @p474))
% 172.90/173.28  (step @p477 :rule trans :premises (@p476 @p472))
% 172.90/173.28  (step @p478 :rule false_intro :premises (@p418))
% 172.90/173.28  (step @p479 :rule symm :premises (@p443))
% 172.90/173.28  (step @p480 :rule symm :premises (@p445))
% 172.90/173.28  (step @p481 :rule refl :args (@t273))
% 172.90/173.28  (step @p482 :rule cong :premises (@p481 @p480) :args (@t299))
% 172.90/173.28  (step @p483 :rule cong :premises (@p482 @p479) :args (@t300))
% 172.90/173.28  (step @p484 :rule refl :args (@t274))
% 172.90/173.28  (step @p485 :rule cong :premises (@p484 @p480) :args (@t303))
% 172.90/173.28  (step @p486 :rule cong :premises (@p485 @p479) :args (@t304))
% 172.90/173.28  (step @p487 :rule symm :premises (@p452))
% 172.90/173.28  (step @p488 :rule refl :args (@t293))
% 172.90/173.28  (step @p489 :rule symm :premises (@p441))
% 172.90/173.28  (step @p490 :rule refl :args (@t167))
% 172.90/173.28  (step @p491 :rule cong :premises (@p490 @p489) :args (@t295))
% 172.90/173.28  (step @p492 :rule cong :premises (@p491 @p488) :args (@t296))
% 172.90/173.28  (step @p493 :rule trans :premises (@p492 @p487 @p486))
% 172.90/173.28  (step @p494 :rule cong :premises (@p493 @p483) :args (@t312))
% 172.90/173.28  (step @p495 :rule trans :premises (@p494 @p478))
% 172.90/173.28  (step @p509 :rule eq_resolve :premises (@p495 @p477))
% 172.90/173.28  (step @p510 :rule false_elim :premises (@p509))
% 172.90/173.28  (step @p511 :rule and_intro :premises (@p459 @p510))
% 172.90/173.28  (step-pop @p536 :rule scope :premises (@p511))
% 172.90/173.28  (step-pop @p537 :rule scope :premises (@p536))
% 172.90/173.28  (step-pop @p538 :rule scope :premises (@p537))
% 172.90/173.28  (step-pop @p539 :rule scope :premises (@p538))
% 172.90/173.28  (step-pop @p540 :rule scope :premises (@p539))
% 172.90/173.28  (step-pop @p541 :rule scope :premises (@p540))
% 172.90/173.28  (step @p512 :rule process_scope :premises (@p541) :args (@t314))
% 172.90/173.28  (step @p519 :rule implies_elim :premises (@p512))
% 172.90/173.28  (step @p520 :rule resolution :premises (@p519 @p500) :args (true @t314))
% 172.90/173.28  (step @p521 :rule not_and :premises (@p520))
% 172.90/173.28  (step @p522 :rule eq_resolve :premises (@p521 @p466))
% 172.90/173.28  (step @p523 false :rule chain_m_resolution :premises (@p522 @p459 @p452 @p445 @p443 @p441 @p418) :args (false (@list false false false false false true) (@list @t301 @t305 @t307 @t309 @t290 @t275)))
% 172.90/173.28  )
% 172.90/173.28  % SZS output end Proof
% 172.90/173.28  % cvc5 exiting
%------------------------------------------------------------------------------