%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG268^3 : TPTP v9.2.1. Bugfixed v5.2.0. % Transfm : none % Format : tptp:raw % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % Computer : n028.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 08:05:42 AM UTC 2026 % Result : Theorem 224.30s 224.50s % Output : Proof 224.30s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG268^3 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.12/0.14 % Command : /export/starexec/sandbox2/solver/bin/do_cvc5 /export/starexec/sandbox2/benchmark/theBenchmark.p 300 THM % 0.17/0.35 % Computer : n028.cluster.edu % 0.17/0.35 % Model : x86_64 x86_64 % 0.17/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.17/0.35 % Memory : 8042.1875MB % 0.17/0.35 % OS : Linux 3.10.0-693.el7.x86_64 % 0.17/0.35 % CPULimit : 300 % 0.17/0.35 % WCLimit : 300 % 0.17/0.35 % DateTime : Wed Jun 3 01:55:35 EDT 2026 % 0.17/0.35 % CPUTime : % 0.38/0.56 %----Proving TH0 % 224.30/224.50 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 224.30/224.50 --- 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... % 224.30/224.50 --- 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... % 224.30/224.50 --- Run --ho-elim --full-saturate-quant at 18s... % 224.30/224.50 --- Run --ho-elim --no-e-matching --full-saturate-quant at 12s... % 224.30/224.50 --- Run --ho-elim --no-e-matching --enum-inst-sum --full-saturate-quant at 12s... % 224.30/224.50 --- Run --ho-elim --finite-model-find --uf-ss=no-minimal at 9s... % 224.30/224.50 --- Run --no-ho-matching --finite-model-find --uf-ss=no-minimal at 6s... % 224.30/224.50 --- Run --no-ho-matching --full-saturate-quant --enum-inst-interleave --ho-elim-store-ax at 21s... % 224.30/224.50 --- Run --no-ho-matching --full-saturate-quant --macros-quant-mode=all at 18s... % 224.30/224.50 % SZS status Theorem % 224.30/224.50 % SZS output start Proof % 224.30/224.50 ( % 224.30/224.50 (declare-sort tptp.subst 0) % 224.30/224.50 (declare-sort tptp.term 0) % 224.30/224.50 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 224.30/224.50 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 224.30/224.50 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 224.30/224.50 (declare-const tptp.one tptp.term) % 224.30/224.50 (declare-const tptp.sh tptp.subst) % 224.30/224.50 (declare-const tptp.lam (-> tptp.term tptp.term)) % 224.30/224.50 (declare-const tptp.var (-> tptp.term Bool)) % 224.30/224.50 (declare-const tptp.id tptp.subst) % 224.30/224.50 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lthm_3 Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_gthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3b Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3a Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3 Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3aaa Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3aa Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem2 Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem1 Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3v2a Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3v2 Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem2v2 Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem1v2 Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 224.30/224.50 (declare-const tptp.hoasinduction_lem0 Bool) % 224.30/224.50 (declare-const tptp.hoasapnotvar_lthm Bool) % 224.30/224.50 (declare-const tptp.hoasapnotvar_gthm Bool) % 224.30/224.50 (declare-const tptp.hoasapnotvar Bool) % 224.30/224.50 (declare-const tptp.hoaslamnotvar_lthm Bool) % 224.30/224.50 (declare-const tptp.hoaslamnotvar_gthm Bool) % 224.30/224.50 (declare-const tptp.hoaslamnotvar Bool) % 224.30/224.50 (declare-const tptp.hoaslamnotap_lthm Bool) % 224.30/224.50 (declare-const tptp.hoaslamnotap_gthm Bool) % 224.30/224.50 (declare-const tptp.hoaslamnotap Bool) % 224.30/224.50 (declare-const tptp.hoaslaminj_lthm Bool) % 224.30/224.50 (declare-const tptp.hoaslaminj_gthm Bool) % 224.30/224.50 (declare-const tptp.hoaslaminj Bool) % 224.30/224.50 (declare-const tptp.hoasapinj2_lthm Bool) % 224.30/224.50 (declare-const tptp.hoasapinj2_gthm Bool) % 224.30/224.50 (declare-const tptp.hoasapinj2 Bool) % 224.30/224.50 (declare-const tptp.pushprop_lem0_lthm Bool) % 224.30/224.50 (declare-const tptp.axassoc Bool) % 224.30/224.50 (declare-const tptp.pushprop_lem0_gthm Bool) % 224.30/224.50 (declare-const tptp.axvarcons Bool) % 224.30/224.50 (declare-const tptp.pushprop_lem0 Bool) % 224.30/224.50 (declare-const tptp.apinj1 Bool) % 224.30/224.50 (declare-const tptp.induction Bool) % 224.30/224.50 (declare-const tptp.apnotvar Bool) % 224.30/224.50 (declare-const tptp.laminj Bool) % 224.30/224.50 (declare-const tptp.axvarshift Bool) % 224.30/224.50 (declare-const tptp.ulamvarind Bool) % 224.30/224.50 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 224.30/224.50 (declare-const tptp.ulamvarsh Bool) % 224.30/224.50 (declare-const tptp.ulamvar1 Bool) % 224.30/224.50 (declare-const tptp.axabs Bool) % 224.30/224.50 (declare-const tptp.pushprop_lem1 Bool) % 224.30/224.50 (declare-const tptp.shinj Bool) % 224.30/224.50 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 224.30/224.50 (declare-const tptp.apinj2 Bool) % 224.30/224.50 (declare-const tptp.axvarid Bool) % 224.30/224.50 (declare-const tptp.axidl Bool) % 224.30/224.50 (declare-const tptp.axclos Bool) % 224.30/224.50 (declare-const tptp.termmset Bool) % 224.30/224.50 (declare-const tptp.axshiftcons Bool) % 224.30/224.50 (declare-const tptp.lamnotap Bool) % 224.30/224.50 (declare-const tptp.lamnotvar Bool) % 224.30/224.50 (declare-const tptp.axapp Bool) % 224.30/224.50 (declare-const tptp.axscons Bool) % 224.30/224.50 (declare-const tptp.axmap Bool) % 224.30/224.50 (declare-const tptp.axidr Bool) % 224.30/224.50 (declare-const tptp.induction2lem Bool) % 224.30/224.50 (declare-const tptp.pushprop_lem1_gthm Bool) % 224.30/224.50 (declare-const tptp.hoasapinj1_lthm Bool) % 224.30/224.50 (declare-const tptp.pushprop_lem1_lthm Bool) % 224.30/224.50 (declare-const tptp.pushprop_lem1v2 Bool) % 224.30/224.50 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 224.30/224.50 (declare-const tptp.induction2 Bool) % 224.30/224.50 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 224.30/224.50 (declare-const tptp.pushprop_lem2v2 Bool) % 224.30/224.50 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 224.30/224.50 (declare-const tptp.pushprop_lem3v2 Bool) % 224.30/224.50 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 224.30/224.50 (declare-const tptp.pushprop Bool) % 224.30/224.50 (declare-const tptp.pushprop_gthm Bool) % 224.30/224.50 (declare-const tptp.hoasapinj1 Bool) % 224.30/224.50 (declare-const tptp.pushprop_lthm_orig Bool) % 224.30/224.50 (declare-const tptp.pushprop_lthm Bool) % 224.30/224.50 (declare-const tptp.induction2lem_gthm Bool) % 224.30/224.50 (declare-const tptp.induction2lem_lthm Bool) % 224.30/224.50 (declare-const tptp.induction2_gthm Bool) % 224.30/224.50 (declare-const tptp.induction2_lthm Bool) % 224.30/224.50 (declare-const tptp.substmonoid Bool) % 224.30/224.50 (declare-const tptp.substmonoid_gthm Bool) % 224.30/224.50 (declare-const tptp.termmset_gthm Bool) % 224.30/224.50 (declare-const tptp.substmonoid_lthm Bool) % 224.30/224.50 (declare-const tptp.termmset_lthm Bool) % 224.30/224.50 (declare-const tptp.hoasapinj1_gthm Bool) % 224.30/224.50 (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)))))))))))) % 224.30/224.50 (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)))))) % 224.30/224.50 (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))))) % 224.30/224.50 (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)))))) % 224.30/224.50 (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)))))))) % 224.30/224.50 (define @t1 () (@var "M" tptp.subst)) % 224.30/224.50 (define @t2 () (@var "B" tptp.term)) % 224.30/224.50 (define @t3 () (_ tptp.sub @t2)) % 224.30/224.50 (define @t4 () (_ @t3 @t1)) % 224.30/224.50 (define @t5 () (@var "A" tptp.term)) % 224.30/224.50 (define @t6 () (_ tptp.sub @t5)) % 224.30/224.50 (define @t7 () (_ @t6 @t1)) % 224.30/224.50 (define @t8 () (_ tptp.ap @t5)) % 224.30/224.50 (define @t9 () (_ @t8 @t2)) % 224.30/224.50 (define @t10 () (_ (_ tptp.push @t5) @t1)) % 224.30/224.50 (define @t11 () (_ tptp.sub tptp.one)) % 224.30/224.50 (define @t12 () (@list @t5 @t1)) % 224.30/224.50 (define @t13 () (_ @t6 tptp.id)) % 224.30/224.50 (define @t14 () (@list @t5)) % 224.30/224.50 (define @t15 () (forall @t14 (= @t13 @t5))) % 224.30/224.50 (define @t16 () (= tptp.axvarid @t15)) % 224.30/224.50 (define @t17 () (_ tptp.comp @t1)) % 224.30/224.50 (define @t18 () (_ tptp.push tptp.one)) % 224.30/224.50 (define @t19 () (_ tptp.lam @t5)) % 224.30/224.50 (define @t20 () (@var "N" tptp.subst)) % 224.30/224.50 (define @t21 () (_ @t17 @t20)) % 224.30/224.50 (define @t22 () (_ @t6 @t21)) % 224.30/224.50 (define @t23 () (_ (_ tptp.sub @t7) @t20)) % 224.30/224.50 (define @t24 () (= @t23 @t22)) % 224.30/224.50 (define @t25 () (@list @t5 @t1 @t20)) % 224.30/224.50 (define @t26 () (forall @t25 @t24)) % 224.30/224.50 (define @t27 () (= tptp.axclos @t26)) % 224.30/224.50 (define @t28 () (@list @t1)) % 224.30/224.50 (define @t29 () (forall @t28 (= (_ (_ tptp.comp tptp.id) @t1) @t1))) % 224.30/224.50 (define @t30 () (_ tptp.comp tptp.sh)) % 224.30/224.50 (define @t31 () (@var "K" tptp.subst)) % 224.30/224.50 (define @t32 () (forall (@list @t1 @t20 @t31) (= (_ (_ tptp.comp @t21) @t31) (_ @t17 (_ (_ tptp.comp @t20) @t31))))) % 224.30/224.50 (define @t33 () (_ @t6 @t20)) % 224.30/224.50 (define @t34 () (_ (_ tptp.push @t33) @t21)) % 224.30/224.50 (define @t35 () (_ (_ tptp.comp @t10) @t20)) % 224.30/224.50 (define @t36 () (= @t35 @t34)) % 224.30/224.50 (define @t37 () (forall @t25 @t36)) % 224.30/224.50 (define @t38 () (= tptp.axmap @t37)) % 224.30/224.50 (define @t39 () (forall @t28 (= (_ @t17 tptp.id) @t1))) % 224.30/224.50 (define @t40 () (_ @t18 tptp.sh)) % 224.30/224.50 (define @t41 () (= tptp.axvarshift (= @t40 tptp.id))) % 224.30/224.50 (define @t42 () (_ @t6 tptp.sh)) % 224.30/224.50 (define @t43 () (_ tptp.var @t5)) % 224.30/224.50 (define @t44 () (@var "P" (-> tptp.term Bool))) % 224.30/224.50 (define @t45 () (_ @t44 @t5)) % 224.30/224.50 (define @t46 () (forall @t14 (=> @t43 @t45))) % 224.30/224.50 (define @t47 () (@list @t44)) % 224.30/224.50 (define @t48 () (= @t5 @t2)) % 224.30/224.50 (define @t49 () (@var "D" tptp.term)) % 224.30/224.50 (define @t50 () (_ tptp.ap @t2)) % 224.30/224.50 (define @t51 () (@var "C" tptp.term)) % 224.30/224.50 (define @t52 () (= (_ @t8 @t51) (_ @t50 @t49))) % 224.30/224.50 (define @t53 () (@list @t5 @t2 @t51 @t49)) % 224.30/224.50 (define @t54 () (= @t51 @t49)) % 224.30/224.50 (define @t55 () (@list @t5 @t2)) % 224.30/224.50 (define @t56 () (forall @t14 @t45)) % 224.30/224.50 (define @t57 () (_ @t44 @t19)) % 224.30/224.50 (define @t58 () (_ @t44 @t2)) % 224.30/224.50 (define @t59 () (forall @t55 (=> @t45 (=> @t58 (_ @t44 @t9))))) % 224.30/224.50 (define @t60 () (@var "Q" (-> tptp.term Bool))) % 224.30/224.50 (define @t61 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t5) @t1) @t44) @t60)) % 224.30/224.50 (define @t62 () (@list @t60)) % 224.30/224.50 (define @t63 () (@list @t44 @t5 @t1)) % 224.30/224.50 (define @t64 () (_ tptp.push @t2)) % 224.30/224.50 (define @t65 () (@var "K" (-> tptp.term Bool))) % 224.30/224.50 (define @t66 () (@list @t44 @t60 @t5 @t1)) % 224.30/224.50 (define @t67 () (_ tptp.sub @t51)) % 224.30/224.50 (define @t68 () (@list @t51)) % 224.30/224.50 (define @t69 () (_ tptp.var @t2)) % 224.30/224.50 (define @t70 () (@list @t2)) % 224.30/224.50 (define @t71 () (forall @t70 (=> @t69 (_ @t44 @t4)))) % 224.30/224.50 (define @t72 () (_ @t3 @t10)) % 224.30/224.50 (define @t73 () (forall @t70 (=> @t69 (_ @t44 @t72)))) % 224.30/224.50 (define @t74 () (_ @t60 @t2)) % 224.30/224.50 (define @t75 () (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop)))))) % 224.30/224.50 (define @t76 () (_ @t64 tptp.id)) % 224.30/224.50 (define @t77 () (_ @t6 @t76)) % 224.30/224.50 (define @t78 () (forall @t14 (=> (forall @t70 (=> @t58 (_ @t44 @t77))) @t57))) % 224.30/224.50 (define @t79 () (=> tptp.induction (=> tptp.pushprop tptp.induction2lem))) % 224.30/224.50 (define @t80 () (=> tptp.induction2lem tptp.induction2)) % 224.30/224.50 (define @t81 () (_ tptp.hoasap tptp.id)) % 224.30/224.50 (define @t82 () (_ (_ @t81 @t5) tptp.id)) % 224.30/224.50 (define @t83 () (= (_ @t82 @t51) (_ (_ (_ @t81 @t2) tptp.id) @t49))) % 224.30/224.50 (define @t84 () (@var "G" (-> tptp.subst tptp.term tptp.term))) % 224.30/224.50 (define @t85 () (_ (_ @t84 @t1) @t5)) % 224.30/224.50 (define @t86 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 224.30/224.50 (define @t87 () (_ @t86 @t1)) % 224.30/224.50 (define @t88 () (_ @t87 @t5)) % 224.30/224.50 (define @t89 () (@list @t1 @t5)) % 224.30/224.50 (define @t90 () (_ tptp.hoaslam tptp.id)) % 224.30/224.50 (define @t91 () (lambda @t89 @t88)) % 224.30/224.50 (define @t92 () (_ @t90 @t91)) % 224.30/224.50 (define @t93 () (@list @t1 @t5 @t20)) % 224.30/224.50 (define @t94 () (_ (_ @t86 @t21) @t33)) % 224.30/224.50 (define @t95 () (_ (_ tptp.sub @t88) @t20)) % 224.30/224.50 (define @t96 () (= @t95 @t94)) % 224.30/224.50 (define @t97 () (forall @t93 @t96)) % 224.30/224.50 (define @t98 () (@list @t86)) % 224.30/224.50 (define @t99 () (_ @t82 @t2)) % 224.30/224.50 (define @t100 () (_ tptp.hoasvar tptp.id)) % 224.30/224.50 (define @t101 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 224.30/224.50 (define @t102 () (_ (_ tptp.hoasinduction_p_and_p_prime @t101) @t60)) % 224.30/224.50 (define @t103 () (@list @t101)) % 224.30/224.50 (define @t104 () (_ @t60 @t5)) % 224.30/224.50 (define @t105 () (_ @t101 tptp.id)) % 224.30/224.50 (define @t106 () (_ (_ @t105 @t5) tptp.id)) % 224.30/224.50 (define @t107 () (forall @t14 (=> (_ (_ @t100 @t5) tptp.id) @t106))) % 224.30/224.50 (define @t108 () (_ (_ (_ @t101 @t1) @t5) (_ (_ tptp.comp @t31) @t20))) % 224.30/224.50 (define @t109 () (_ (_ (_ @t101 (_ @t17 @t31)) (_ @t6 @t31)) @t20)) % 224.30/224.50 (define @t110 () (@list @t1 @t5 @t20 @t31)) % 224.30/224.50 (define @t111 () (forall @t110 (=> @t109 @t108))) % 224.30/224.50 (define @t112 () (forall @t110 (=> @t108 @t109))) % 224.30/224.50 (define @t113 () (@list @t101 @t60)) % 224.30/224.50 (define @t114 () (_ (_ @t105 @t2) tptp.id)) % 224.30/224.50 (define @t115 () (forall @t55 (=> @t106 (=> @t114 (_ (_ @t105 @t99) tptp.id))))) % 224.30/224.50 (define @t116 () (forall @t12 (= @t88 @t72))) % 224.30/224.50 (define @t117 () (exists @t98 @t116)) % 224.30/224.50 (define @t118 () (forall @t70 @t117)) % 224.30/224.50 (define @t119 () (= tptp.hoasinduction_lem3v2_f @t118)) % 224.30/224.50 (define @t120 () (_ @t60 @t19)) % 224.30/224.50 (define @t121 () (_ @t60 @t77)) % 224.30/224.50 (define @t122 () (forall @t70 (=> @t74 @t121))) % 224.30/224.50 (define @t123 () (=> @t122 @t120)) % 224.30/224.50 (define @t124 () (forall @t14 @t123)) % 224.30/224.50 (define @t125 () (=> @t102 @t124)) % 224.30/224.50 (define @t126 () (_ (_ @t86 tptp.id) @t5)) % 224.30/224.50 (define @t127 () (_ (_ @t105 @t126) tptp.id)) % 224.30/224.50 (define @t128 () (forall @t14 (=> @t106 @t127))) % 224.30/224.50 (define @t129 () (=> @t128 (_ (_ @t105 @t92) tptp.id))) % 224.30/224.50 (define @t130 () (=> @t97 @t129)) % 224.30/224.50 (define @t131 () (forall @t98 @t130)) % 224.30/224.50 (define @t132 () (=> @t131 @t125)) % 224.30/224.50 (define @t133 () (forall @t113 @t132)) % 224.30/224.50 (define @t134 () (= tptp.hoasinduction_lem3v2a @t133)) % 224.30/224.50 (define @t135 () (=> tptp.axmap tptp.hoasinduction_lem3v2a)) % 224.30/224.50 (define @t136 () (=> tptp.axclos @t135)) % 224.30/224.50 (define @t137 () (=> tptp.axvarshift @t136)) % 224.30/224.50 (define @t138 () (=> tptp.axvarid @t137)) % 224.30/224.50 (define @t139 () (=> tptp.hoasinduction_lem3v2_f @t138)) % 224.30/224.50 (define @t140 () (= tptp.hoasinduction_lem3v2a_lthm @t139)) % 224.30/224.50 (define @t141 () (=> 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))))))))))))))))))))))))))))))))))) % 224.30/224.50 (define @t142 () (=> 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))))))))))))))))))))))))))))))))))) % 224.30/224.50 (define @t143 () (forall @t70 (=> @t114 (_ (_ @t105 @t77) tptp.id)))) % 224.30/224.50 (define @t144 () (forall @t14 (=> @t143 (_ (_ @t105 (_ tptp.lam (_ @t6 @t40))) tptp.id)))) % 224.30/224.50 (define @t145 () (=> @t131 (forall @t14 (=> @t143 (_ (_ @t105 @t19) tptp.id))))) % 224.30/224.50 (define @t146 () (_ @t86 tptp.sh)) % 224.30/224.50 (define @t147 () (_ @t146 tptp.one)) % 224.30/224.50 (define @t148 () (=> @t115 (=> @t131 (forall @t14 @t106)))) % 224.30/224.50 (define @t149 () (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction)))) % 224.30/224.50 (define @t150 () (not tptp.hoasinduction_lem3v2a_lthm)) % 224.30/224.50 (define @t151 () (@var "X" tptp.term)) % 224.30/224.50 (define @t152 () (_ @t60 @t151)) % 224.30/224.50 (define @t153 () (@list @t151)) % 224.30/224.50 (define @t154 () (lambda (@list @t5 @t1 @t44 @t60) (forall @t153 (= @t152 (_ @t44 (_ (_ tptp.sub @t151) @t10)))))) % 224.30/224.50 (define @t155 () (lambda (@list @t1 @t5 @t20 @t2) (_ (_ tptp.ap @t33) @t2))) % 224.30/224.50 (define @t156 () (_ tptp.lam @t147)) % 224.30/224.50 (define @t157 () (lambda (@list @t1 @t86) @t156)) % 224.30/224.50 (define @t158 () (lambda @t93 (_ tptp.var @t33))) % 224.30/224.50 (define @t159 () (_ (_ @t105 @t151) tptp.id)) % 224.30/224.50 (define @t160 () (= @t152 @t159)) % 224.30/224.50 (define @t161 () (forall @t153 @t160)) % 224.30/224.50 (define @t162 () (lambda @t113 @t161)) % 224.30/224.50 (define @t163 () (@var "BOUND_VARIABLE_9960" tptp.term)) % 224.30/224.50 (define @t164 () (_ @t60 (tptp.lam @t163))) % 224.30/224.50 (define @t165 () (tptp.push tptp.one tptp.sh)) % 224.30/224.50 (define @t166 () (tptp.push @t2 @t165)) % 224.30/224.50 (define @t167 () (_ @t60 @t2)) % 224.30/224.50 (define @t168 () (not @t167)) % 224.30/224.50 (define @t169 () (_ @t60 @t151)) % 224.30/224.50 (define @t170 () (_ @t86 tptp.sh tptp.one)) % 224.30/224.50 (define @t171 () (tptp.lam @t170)) % 224.30/224.50 (define @t172 () (_ @t86 @t165 @t5)) % 224.30/224.50 (define @t173 () (not (forall @t14 (or (not (_ @t101 @t165 @t5 @t165)) (_ @t101 @t165 @t172 @t165))))) % 224.30/224.50 (define @t174 () (tptp.sub @t5 @t20)) % 224.30/224.50 (define @t175 () (tptp.comp @t1 @t20)) % 224.30/224.50 (define @t176 () (_ @t86 @t175 @t174)) % 224.30/224.50 (define @t177 () (_ @t86 @t1 @t5)) % 224.30/224.50 (define @t178 () (tptp.sub @t177 @t20)) % 224.30/224.50 (define @t179 () (forall @t93 (= @t178 @t176))) % 224.30/224.50 (define @t180 () (not @t179)) % 224.30/224.50 (define @t181 () (@list @t101 @t60 @t163)) % 224.30/224.50 (define @t182 () (forall @t181 (or (not (forall @t98 (or @t180 @t173 (_ @t101 @t165 @t171 @t165)))) (not (forall @t153 (= @t169 (_ @t101 @t165 @t151 @t165)))) (not (forall @t70 (or @t168 (_ @t60 (tptp.sub @t163 @t166))))) @t164))) % 224.30/224.50 (define @t183 () (tptp.push @t174 @t175)) % 224.30/224.50 (define @t184 () (tptp.push @t5 @t1)) % 224.30/224.50 (define @t185 () (tptp.comp @t184 @t20)) % 224.30/224.50 (define @t186 () (forall @t25 (= @t185 @t183))) % 224.30/224.50 (define @t187 () (tptp.sub @t5 @t175)) % 224.30/224.50 (define @t188 () (tptp.sub @t5 @t1)) % 224.30/224.50 (define @t189 () (tptp.sub @t188 @t20)) % 224.30/224.50 (define @t190 () (forall @t25 (= @t189 @t187))) % 224.30/224.50 (define @t191 () (tptp.push @t2 @t40)) % 224.30/224.50 (define @t192 () (tptp.sub @t163 @t191)) % 224.30/224.50 (define @t193 () (_ @t60 @t192)) % 224.30/224.50 (define @t194 () (or @t168 @t193)) % 224.30/224.50 (define @t195 () (forall @t70 @t194)) % 224.30/224.50 (define @t196 () (not @t195)) % 224.30/224.50 (define @t197 () (_ @t101 @t40 @t151 @t40)) % 224.30/224.50 (define @t198 () (= @t169 @t197)) % 224.30/224.50 (define @t199 () (forall @t153 @t198)) % 224.30/224.50 (define @t200 () (not @t199)) % 224.30/224.50 (define @t201 () (_ @t101 @t40 @t171 @t40)) % 224.30/224.50 (define @t202 () (or @t180 @t173 @t201)) % 224.30/224.50 (define @t203 () (_ @t86 @t40 @t5)) % 224.30/224.50 (define @t204 () (_ @t101 @t40 @t203 @t40)) % 224.30/224.50 (define @t205 () (_ @t101 @t40 @t5 @t40)) % 224.30/224.50 (define @t206 () (not @t205)) % 224.30/224.50 (define @t207 () (or @t206 @t204)) % 224.30/224.50 (define @t208 () (forall @t14 @t207)) % 224.30/224.50 (define @t209 () (not @t208)) % 224.30/224.50 (define @t210 () (or @t180 @t209 @t201)) % 224.30/224.50 (define @t211 () (forall @t98 @t210)) % 224.30/224.50 (define @t212 () (not @t211)) % 224.30/224.50 (define @t213 () (or @t212 @t200 @t196 @t164)) % 224.30/224.50 (define @t214 () (forall @t181 @t213)) % 224.30/224.50 (define @t215 () (=> @t186 @t214)) % 224.30/224.50 (define @t216 () (=> @t190 @t215)) % 224.30/224.50 (define @t217 () (=> (= @t40 @t40) @t216)) % 224.30/224.50 (define @t218 () (tptp.sub @t5 @t40)) % 224.30/224.50 (define @t219 () (= @t5 @t218)) % 224.30/224.50 (define @t220 () (forall @t14 @t219)) % 224.30/224.50 (define @t221 () (=> @t220 @t217)) % 224.30/224.50 (define @t222 () (tptp.sub @t2 @t184)) % 224.30/224.50 (define @t223 () (forall @t12 (= @t222 @t177))) % 224.30/224.50 (define @t224 () (not (forall @t98 (not @t223)))) % 224.30/224.50 (define @t225 () (forall @t70 @t224)) % 224.30/224.50 (define @t226 () (=> @t225 @t221)) % 224.30/224.50 (define @t227 () (tptp.push @t2 tptp.id)) % 224.30/224.50 (define @t228 () (tptp.sub @t163 @t227)) % 224.30/224.50 (define @t229 () (_ @t60 @t228)) % 224.30/224.50 (define @t230 () (or @t168 @t229)) % 224.30/224.50 (define @t231 () (forall @t70 @t230)) % 224.30/224.50 (define @t232 () (not @t231)) % 224.30/224.50 (define @t233 () (_ @t101 tptp.id @t151 tptp.id)) % 224.30/224.50 (define @t234 () (= @t169 @t233)) % 224.30/224.50 (define @t235 () (forall @t153 @t234)) % 224.30/224.50 (define @t236 () (not @t235)) % 224.30/224.50 (define @t237 () (_ @t101 tptp.id @t171 tptp.id)) % 224.30/224.50 (define @t238 () (_ @t86 tptp.id @t5)) % 224.30/224.50 (define @t239 () (_ @t101 tptp.id @t238 tptp.id)) % 224.30/224.50 (define @t240 () (_ @t101 tptp.id @t5 tptp.id)) % 224.30/224.50 (define @t241 () (not @t240)) % 224.30/224.50 (define @t242 () (or @t241 @t239)) % 224.30/224.50 (define @t243 () (forall @t14 @t242)) % 224.30/224.50 (define @t244 () (not @t243)) % 224.30/224.50 (define @t245 () (or @t180 @t244 @t237)) % 224.30/224.50 (define @t246 () (forall @t98 @t245)) % 224.30/224.50 (define @t247 () (not @t246)) % 224.30/224.50 (define @t248 () (or @t247 @t236 @t232 @t164)) % 224.30/224.50 (define @t249 () (forall @t181 @t248)) % 224.30/224.50 (define @t250 () (=> @t186 @t249)) % 224.30/224.50 (define @t251 () (=> @t190 @t250)) % 224.30/224.50 (define @t252 () (= tptp.id @t40)) % 224.30/224.50 (define @t253 () (=> @t252 @t251)) % 224.30/224.50 (define @t254 () (tptp.sub @t5 tptp.id)) % 224.30/224.50 (define @t255 () (= @t5 @t254)) % 224.30/224.50 (define @t256 () (forall @t14 @t255)) % 224.30/224.50 (define @t257 () (=> @t256 @t253)) % 224.30/224.50 (define @t258 () (or @t232 @t164)) % 224.30/224.50 (define @t259 () (or @t247 @t236 @t258)) % 224.30/224.50 (define @t260 () (forall @t181 @t259)) % 224.30/224.50 (define @t261 () (@list @t163)) % 224.30/224.50 (define @t262 () (forall @t261 @t259)) % 224.30/224.50 (define @t263 () (forall @t261 @t258)) % 224.30/224.50 (define @t264 () (or @t247 @t236 @t263)) % 224.30/224.50 (define @t265 () (tptp.lam @t5)) % 224.30/224.50 (define @t266 () (_ @t60 @t265)) % 224.30/224.50 (define @t267 () (tptp.sub @t5 @t227)) % 224.30/224.50 (define @t268 () (_ @t60 @t267)) % 224.30/224.50 (define @t269 () (forall @t70 (or @t168 @t268))) % 224.30/224.50 (define @t270 () (not @t269)) % 224.30/224.50 (define @t271 () (forall @t14 (or @t270 @t266))) % 224.30/224.50 (define @t272 () (or @t247 @t236 @t271)) % 224.30/224.50 (define @t273 () (=> @t235 @t271)) % 224.30/224.50 (define @t274 () (or @t270 @t120)) % 224.30/224.50 (define @t275 () (not @t74)) % 224.30/224.50 (define @t276 () (or @t275 @t121)) % 224.30/224.50 (define @t277 () (lambda @t62 @t235)) % 224.30/224.50 (define @t278 () (_ (lambda @t113 @t235) @t101)) % 224.30/224.50 (define @t279 () (=> (_ @t278 @t60) @t124)) % 224.30/224.50 (define @t280 () (_ (_ @t105 @t156) tptp.id)) % 224.30/224.50 (define @t281 () (or @t180 @t244 @t280)) % 224.30/224.50 (define @t282 () (=> @t243 @t280)) % 224.30/224.50 (define @t283 () (lambda @t14 (_ @t146 @t5))) % 224.30/224.50 (define @t284 () (_ @t91 tptp.sh)) % 224.30/224.50 (define @t285 () (lambda @t98 @t156)) % 224.30/224.50 (define @t286 () (_ @t157 tptp.id)) % 224.30/224.50 (define @t287 () (not @t106)) % 224.30/224.50 (define @t288 () (or @t287 @t127)) % 224.30/224.50 (define @t289 () (=> @t128 (_ (_ @t105 (_ @t286 @t91)) tptp.id))) % 224.30/224.50 (define @t290 () (=> @t97 @t289)) % 224.30/224.50 (define @t291 () (forall @t98 @t290)) % 224.30/224.50 (define @t292 () (=> @t291 @t279)) % 224.30/224.50 (define @t293 () (forall @t113 @t292)) % 224.30/224.50 (define @t294 () (= @t5 @t13)) % 224.30/224.50 (define @t295 () (= @t72 @t88)) % 224.30/224.50 (define @t296 () (@quantifiers_skolemize @t182 2)) % 224.30/224.50 (define @t297 () (tptp.sub @t296 @t184)) % 224.30/224.50 (define @t298 () (forall @t12 (= @t297 @t177))) % 224.30/224.50 (define @t299 () (not @t298)) % 224.30/224.50 (define @t300 () (forall @t98 @t299)) % 224.30/224.50 (define @t301 () (not @t300)) % 224.30/224.50 (define @t302 () (@list @t296)) % 224.30/224.50 (define @t303 () (forall @t98 (not (forall @t12 (= @t177 @t297))))) % 224.30/224.50 (define @t304 () (not @t303)) % 224.30/224.50 (define @t305 () (@list false)) % 224.30/224.50 (define @t306 () (@quantifiers_skolemize @t303 0)) % 224.30/224.50 (define @t307 () (_ @t306 @t1 @t5)) % 224.30/224.50 (define @t308 () (forall @t12 (= @t297 @t307))) % 224.30/224.50 (define @t309 () (forall @t12 (= @t307 @t297))) % 224.30/224.50 (define @t310 () (not (not @t309))) % 224.30/224.50 (define @t311 () (@list true)) % 224.30/224.50 (define @t312 () (@quantifiers_skolemize @t182 0)) % 224.30/224.50 (define @t313 () (not (_ @t312 @t165 @t5 @t165))) % 224.30/224.50 (define @t314 () (forall @t14 (or @t313 (_ @t312 @t165 (_ @t306 @t165 @t5) @t165)))) % 224.30/224.50 (define @t315 () (@quantifiers_skolemize @t314 0)) % 224.30/224.50 (define @t316 () (tptp.sub @t296 (tptp.push @t315 @t165))) % 224.30/224.50 (define @t317 () (_ @t306 @t165 @t315)) % 224.30/224.50 (define @t318 () (= @t316 @t317)) % 224.30/224.50 (define @t319 () (= @t317 @t316)) % 224.30/224.50 (define @t320 () (@list @t308)) % 224.30/224.50 (define @t321 () (@quantifiers_skolemize @t182 1)) % 224.30/224.50 (define @t322 () (forall @t153 (= (_ @t321 @t151) (_ @t312 @t165 @t151 @t165)))) % 224.30/224.50 (define @t323 () (tptp.lam @t296)) % 224.30/224.50 (define @t324 () (_ @t321 @t323)) % 224.30/224.50 (define @t325 () (forall @t70 (or (not (_ @t321 @t2)) (_ @t321 (tptp.sub @t296 @t166))))) % 224.30/224.50 (define @t326 () (not @t325)) % 224.30/224.50 (define @t327 () (not @t322)) % 224.30/224.50 (define @t328 () (forall @t98 (or @t180 (not (forall @t14 (or @t313 (_ @t312 @t165 @t172 @t165)))) (_ @t312 @t165 @t171 @t165)))) % 224.30/224.50 (define @t329 () (not @t328)) % 224.30/224.50 (define @t330 () (or @t329 @t327 @t326 @t324)) % 224.30/224.50 (define @t331 () (@list @t330)) % 224.30/224.50 (define @t332 () (_ @t321 @t317)) % 224.30/224.50 (define @t333 () (_ @t312 @t165 @t317 @t165)) % 224.30/224.50 (define @t334 () (= @t332 @t333)) % 224.30/224.50 (define @t335 () (= @t333 @t332)) % 224.30/224.50 (define @t336 () (@list @t322)) % 224.30/224.50 (define @t337 () (_ @t312 @t165 @t323 @t165)) % 224.30/224.50 (define @t338 () (= @t324 @t337)) % 224.30/224.50 (define @t339 () (not @t337)) % 224.30/224.50 (define @t340 () (@list true false)) % 224.30/224.50 (define @t341 () (tptp.lam (_ @t306 tptp.sh tptp.one))) % 224.30/224.50 (define @t342 () (_ @t312 @t165 @t341 @t165)) % 224.30/224.50 (define @t343 () (forall @t93 (= (tptp.sub @t307 @t20) (_ @t306 @t175 @t174)))) % 224.30/224.50 (define @t344 () (@quantifiers_skolemize @t343 2)) % 224.30/224.50 (define @t345 () (@quantifiers_skolemize @t343 0)) % 224.30/224.50 (define @t346 () (tptp.comp @t345 @t344)) % 224.30/224.50 (define @t347 () (@quantifiers_skolemize @t343 1)) % 224.30/224.50 (define @t348 () (tptp.sub @t347 @t344)) % 224.30/224.50 (define @t349 () (tptp.push @t347 @t345)) % 224.30/224.50 (define @t350 () (tptp.sub @t296 @t349)) % 224.30/224.50 (define @t351 () (_ @t306 @t345 @t347)) % 224.30/224.50 (define @t352 () (= @t350 @t351)) % 224.30/224.50 (define @t353 () (tptp.sub @t351 @t344)) % 224.30/224.50 (define @t354 () (= @t353 (_ @t306 @t346 @t348))) % 224.30/224.50 (define @t355 () (not @t354)) % 224.30/224.50 (define @t356 () (not @t343)) % 224.30/224.50 (define @t357 () (not @t314)) % 224.30/224.50 (define @t358 () (or @t356 @t357 @t342)) % 224.30/224.50 (define @t359 () (@list false true false)) % 224.30/224.50 (define @t360 () (_ @t312 @t165 @t315 @t165)) % 224.30/224.50 (define @t361 () (not @t360)) % 224.30/224.50 (define @t362 () (or @t361 @t333)) % 224.30/224.50 (define @t363 () (not @t362)) % 224.30/224.50 (define @t364 () (@list @t362)) % 224.30/224.50 (define @t365 () (not @t332)) % 224.30/224.50 (define @t366 () (@list @t315)) % 224.30/224.50 (define @t367 () (_ @t321 @t315)) % 224.30/224.50 (define @t368 () (= @t367 @t360)) % 224.30/224.50 (define @t369 () (= @t360 @t367)) % 224.30/224.50 (define @t370 () (@list false false)) % 224.30/224.50 (define @t371 () (_ @t321 @t316)) % 224.30/224.50 (define @t372 () (not @t367)) % 224.30/224.50 (define @t373 () (or @t372 @t371)) % 224.30/224.50 (define @t374 () (not @t371)) % 224.30/224.50 (define @t375 () (not @t319)) % 224.30/224.50 (define @t376 () (and @t371 @t319 @t365)) % 224.30/224.50 (assume @p1 (= tptp.axapp (forall (@list @t5 @t2 @t1) (= (_ (_ tptp.sub @t9) @t1) (_ (_ tptp.ap @t7) @t4))))) % 224.30/224.50 (assume @p2 (= tptp.axvarcons (forall @t12 (= (_ @t11 @t10) @t5)))) % 224.30/224.50 (assume @p3 @t16) % 224.30/224.50 (assume @p4 (= tptp.axabs (forall @t12 (= (_ (_ tptp.sub @t19) @t1) (_ tptp.lam (_ @t6 (_ @t18 (_ @t17 tptp.sh)))))))) % 224.30/224.50 (assume @p5 @t27) % 224.30/224.50 (assume @p6 (= tptp.axidl @t29)) % 224.30/224.50 (assume @p7 (= tptp.axshiftcons (forall @t12 (= (_ @t30 @t10) @t1)))) % 224.30/224.50 (assume @p8 (= tptp.axassoc @t32)) % 224.30/224.50 (assume @p9 @t38) % 224.30/224.50 (assume @p10 (= tptp.axidr @t39)) % 224.30/224.50 (assume @p11 @t41) % 224.30/224.50 (assume @p12 (= tptp.axscons (forall @t28 (= (_ (_ tptp.push (_ @t11 @t1)) (_ @t30 @t1)) @t1)))) % 224.30/224.50 (assume @p13 (= tptp.ulamvar1 (_ tptp.var tptp.one))) % 224.30/224.50 (assume @p14 (= tptp.ulamvarsh (forall @t14 (=> @t43 (_ tptp.var @t42))))) % 224.30/224.50 (assume @p15 (= tptp.ulamvarind (forall @t47 (=> (_ @t44 tptp.one) (=> (forall @t14 (=> @t43 (=> @t45 (_ @t44 @t42)))) @t46))))) % 224.30/224.50 (assume @p16 (= tptp.apinj1 (forall @t53 (=> @t52 @t48)))) % 224.30/224.50 (assume @p17 (= tptp.apinj2 (forall @t53 (=> @t52 @t54)))) % 224.30/224.50 (assume @p18 (= tptp.laminj (forall @t55 (=> (= @t19 (_ tptp.lam @t2)) @t48)))) % 224.30/224.50 (assume @p19 (= tptp.shinj (forall @t55 (=> (= @t42 (_ @t3 tptp.sh)) @t48)))) % 224.30/224.50 (assume @p20 (= tptp.lamnotap (forall (@list @t5 @t2 @t51) (not (= @t19 (_ @t50 @t51)))))) % 224.30/224.50 (assume @p21 (= tptp.apnotvar (forall @t55 (not (_ tptp.var @t9))))) % 224.30/224.50 (assume @p22 (= tptp.lamnotvar (forall @t14 (not (_ tptp.var @t19))))) % 224.30/224.50 (assume @p23 (= tptp.induction (forall @t47 (=> @t46 (=> @t59 (=> (forall @t14 (=> @t45 @t57)) @t56)))))) % 224.30/224.50 (assume @p24 (= tptp.pushprop_lem0 (forall @t63 (exists @t62 @t61)))) % 224.30/224.50 (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))))))))))))))))))))))))) % 224.30/224.50 (assume @p26 (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0)) % 224.30/224.50 (assume @p27 (= tptp.pushprop_lem1 (forall (@list @t44 @t65 @t5 @t1 @t2) (=> @t45 (_ @t65 (_ @t6 (_ @t64 @t1))))))) % 224.30/224.50 (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))))))))))))))))))))))))) % 224.30/224.50 (assume @p29 (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1)))))) % 224.30/224.50 (assume @p30 (= tptp.pushprop_lem1v2 (forall @t66 (=> @t45 (=> @t61 (_ @t60 tptp.one)))))) % 224.30/224.50 (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))))))))))))))))))))))))) % 224.30/224.50 (assume @p32 (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2))) % 224.30/224.50 (assume @p33 (= tptp.pushprop_lem2v2 (forall @t66 (=> @t61 (=> @t71 (forall @t68 (=> (_ tptp.var @t51) (=> (_ @t60 @t51) (_ @t60 (_ @t67 tptp.sh)))))))))) % 224.30/224.50 (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))))))))))))))))))))))))) % 224.30/224.50 (assume @p35 (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2)))) % 224.30/224.50 (assume @p36 (= tptp.pushprop_lem3v2 (forall @t66 (=> @t61 (=> (forall @t70 (=> @t69 @t74)) @t73))))) % 224.30/224.50 (assume @p37 (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2)) % 224.30/224.50 (assume @p38 (= tptp.pushprop (forall @t63 (=> @t71 (=> @t45 @t73))))) % 224.30/224.50 (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))))))))))))))))))))))))) % 224.30/224.50 (assume @p40 (= tptp.pushprop_lthm_orig @t75)) % 224.30/224.50 (assume @p41 (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 @t75))) % 224.30/224.50 (assume @p42 (= tptp.induction2lem (forall @t47 (=> @t59 (=> @t78 (forall @t12 (=> @t71 (_ @t44 @t7)))))))) % 224.30/224.50 (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 @t79)))))))))))))))))))))))) % 224.30/224.50 (assume @p44 (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr @t79)))))))))) % 224.30/224.50 (assume @p45 (= tptp.induction2 (forall @t47 (=> @t46 (=> @t59 (=> @t78 @t56)))))) % 224.30/224.50 (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 @t80)))))))))))))))))))))))))) % 224.30/224.50 (assume @p47 (= tptp.induction2_lthm (=> tptp.axvarid @t80))) % 224.30/224.50 (assume @p48 (= tptp.substmonoid (and @t32 @t29 @t39))) % 224.30/224.50 (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)))))))))))))))))))))))))))) % 224.30/224.50 (assume @p50 (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid))))) % 224.30/224.50 (assume @p51 (= tptp.termmset (and @t26 @t15))) % 224.30/224.50 (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))))))))))))))))))))))))))))) % 224.30/224.50 (assume @p53 (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset)))) % 224.30/224.50 (assume @p54 (= tptp.hoasapinj1 (forall @t53 (=> @t83 @t48)))) % 224.30/224.50 (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)))))))))))))))))))))))))))))) % 224.30/224.50 (assume @p56 (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1)))) % 224.30/224.50 (assume @p57 (= tptp.hoasapinj2 (forall @t53 (=> @t83 @t54)))) % 224.30/224.50 (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))))))))))))))))))))))))))))))) % 224.30/224.50 (assume @p59 (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2))) % 224.30/224.50 (assume @p60 (= tptp.hoaslaminj (forall @t98 (=> @t97 (forall (@list @t84) (=> (forall @t93 (= (_ (_ tptp.sub @t85) @t20) (_ (_ @t84 @t21) @t33))) (=> (= @t92 (_ @t90 (lambda @t89 @t85))) (forall @t89 (= @t88 @t85))))))))) % 224.30/224.50 (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)))))))))))))))))))))))))))))))) % 224.30/224.50 (assume @p62 (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj))))) % 224.30/224.50 (assume @p63 (= tptp.hoaslamnotap (forall @t98 (=> @t97 (forall @t55 (not (= (_ @t90 (lambda (@list @t1 @t51) (_ @t87 @t51))) @t99))))))) % 224.30/224.50 (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))))))))))))))))))))))))))))))))) % 224.30/224.50 (assume @p65 (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap))) % 224.30/224.50 (assume @p66 (= tptp.hoaslamnotvar (forall @t98 (=> @t97 (not (_ (_ @t100 @t92) tptp.id)))))) % 224.30/224.50 (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)))))))))))))))))))))))))))))))))) % 224.30/224.50 (assume @p68 (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar)))) % 224.30/224.50 (assume @p69 (= tptp.hoasapnotvar (forall @t55 (not (_ (_ @t100 @t99) tptp.id))))) % 224.30/224.50 (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))))))))))))))))))))))))))))))))))) % 224.30/224.50 (assume @p71 (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar)))) % 224.30/224.50 (assume @p72 (= tptp.hoasinduction_lem0 (forall @t103 (exists @t62 @t102)))) % 224.30/224.50 (assume @p73 (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0)) % 224.30/224.50 (assume @p74 (= tptp.hoasinduction_lem1v2 (forall @t113 (=> @t112 (=> @t111 (=> @t107 (=> @t102 (forall @t14 (=> @t43 @t104))))))))) % 224.30/224.50 (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)))))))))))))))))))))))))))))))))))) % 224.30/224.50 (assume @p76 (= tptp.hoasinduction_lem2v2 (forall @t113 (=> @t112 (=> @t111 (=> @t115 (=> @t102 (forall @t55 (=> @t104 (=> @t74 (_ @t60 @t9))))))))))) % 224.30/224.50 (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)))))))))))))))))))))))))))))))))))) % 224.30/224.50 (assume @p78 @t119) % 224.30/224.50 (assume @p79 (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f)) % 224.30/224.50 (assume @p80 (= tptp.hoasinduction_lem3v2 (forall @t113 (=> @t112 (=> @t111 @t132))))) % 224.30/224.50 (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)))))))))))))))))))))))))))))))))))) % 224.30/224.50 (assume @p82 (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2)))))) % 224.30/224.50 (assume @p83 @t134) % 224.30/224.50 (assume @p84 @t140) % 224.30/224.50 (assume @p85 (= tptp.hoasinduction_lem1 (forall @t103 (=> @t112 (=> @t111 (=> @t107 (forall @t14 (=> @t43 @t106)))))))) % 224.30/224.50 (assume @p86 (= tptp.hoasinduction_lem1_gthm @t141)) % 224.30/224.50 (assume @p87 (= tptp.hoasinduction_lem1_lthm @t141)) % 224.30/224.50 (assume @p88 (= tptp.hoasinduction_lem2 (forall @t103 (=> @t112 (=> @t111 (=> @t115 (forall @t55 (=> @t106 (=> @t114 (_ (_ @t105 @t9) tptp.id)))))))))) % 224.30/224.50 (assume @p89 (= tptp.hoasinduction_lem2_gthm @t142)) % 224.30/224.50 (assume @p90 (= tptp.hoasinduction_lem2_lthm @t142)) % 224.30/224.50 (assume @p91 (= tptp.hoasinduction_lem3aa (forall @t103 (=> @t131 @t144)))) % 224.30/224.50 (assume @p92 (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa)))) % 224.30/224.50 (assume @p93 (= tptp.hoasinduction_lem3aaa (forall @t103 (=> (forall @t98 (=> (exists @t68 (forall @t93 (and (= @t95 (_ (_ tptp.sub (_ @t67 @t10)) @t20)) (= (_ @t67 @t34) @t94)))) @t129)) @t144)))) % 224.30/224.50 (assume @p94 (= tptp.hoasinduction_lem3 (forall @t103 (=> @t112 (=> @t111 @t145))))) % 224.30/224.50 (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)))))))))))))))))))))))))))))))))))))) % 224.30/224.50 (assume @p96 (= tptp.hoasinduction_lem3_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3))))) % 224.30/224.50 (assume @p97 (= tptp.hoasinduction_lem3a (forall @t103 @t145))) % 224.30/224.50 (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)))))))))))))))))))))))))))))))))))))) % 224.30/224.50 (assume @p99 (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a))))) % 224.30/224.50 (assume @p100 (= tptp.hoasinduction_lem3b (forall @t70 (exists @t98 (= (_ @t3 @t40) @t147))))) % 224.30/224.50 (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)))))))))))))))))))))))))))))))))))))) % 224.30/224.50 (assume @p102 (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b)) % 224.30/224.50 (assume @p103 (= tptp.hoasinduction (forall @t103 (=> @t112 (=> @t111 (=> @t107 @t148)))))) % 224.30/224.50 (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 @t149)))))))))))))))))))))))))))))))))))) % 224.30/224.50 (assume @p105 (= tptp.hoasinduction_lthm (=> tptp.induction2 @t149))) % 224.30/224.50 (assume @p106 (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction)))))) % 224.30/224.50 (assume @p107 (= tptp.hoasinduction_no_psi_cond (forall @t103 @t148))) % 224.30/224.50 (assume @p108 (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond)))))) % 224.30/224.50 (assume @p109 @t150) % 224.30/224.50 (assume @p110 true) % 224.30/224.50 (step @p111 (= tptp.pushprop_p_and_p_prime @t154) :rule refl :args (@t154)) % 224.30/224.50 (step @p112 (= tptp.hoasap @t155) :rule refl :args (@t155)) % 224.30/224.50 (step @p113 (= tptp.hoaslam @t157) :rule refl :args (@t157)) % 224.30/224.50 (step @p114 (= tptp.hoasvar @t158) :rule refl :args (@t158)) % 224.30/224.50 (step @p115 (= tptp.hoasinduction_p_and_p_prime @t162) :rule refl :args (@t162)) % 224.30/224.50 (step @p116 :rule bool-impl-true2 :args ((=> @t190 (=> @t186 @t182)))) % 224.30/224.50 (step @p117 :rule refl :args (@t164)) % 224.30/224.50 (step @p118 :rule refl :args (@t165)) % 224.30/224.50 (step @p119 :rule refl :args (@t40)) % 224.30/224.50 (step @p120 :rule cong :premises (@p119 @p118) :args ((= @t40 @t165))) % 224.30/224.50 (step @p121 :rule symm :premises (@p120)) % 224.30/224.50 (step @p122 :rule eq_resolve :premises (@p119 @p121)) % 224.30/224.50 (step @p123 :rule refl :args (@t2)) % 224.30/224.50 (step @p124 :rule cong :premises (@p123 @p122) :args (@t191)) % 224.30/224.50 (step @p125 :rule refl :args (@t163)) % 224.30/224.50 (step @p126 :rule cong :premises (@p125 @p124) :args (@t192)) % 224.30/224.50 (step @p127 :rule cong :premises (@p126) :args (@t193)) % 224.30/224.50 (step @p128 :rule refl :args (@t168)) % 224.30/224.50 (step @p129 :rule nary_cong :premises (@p128 @p127) :args (@t194)) % 224.30/224.50 (step @p130 :rule cong :premises (@p129) :args (@t195)) % 224.30/224.50 (step @p131 :rule cong :premises (@p130) :args (@t196)) % 224.30/224.50 (step @p132 :rule refl :args (@t151)) % 224.30/224.50 (step @p133 :rule cong :premises (@p122 @p132 @p122) :args (@t197)) % 224.30/224.50 (step @p134 :rule refl :args (@t169)) % 224.30/224.50 (step @p135 :rule cong :premises (@p134 @p133) :args (@t198)) % 224.30/224.50 (step @p136 :rule cong :premises (@p135) :args (@t199)) % 224.30/224.50 (step @p137 :rule cong :premises (@p136) :args (@t200)) % 224.30/224.50 (step @p138 :rule refl :args (@t171)) % 224.30/224.50 (step @p139 :rule cong :premises (@p122 @p138 @p122) :args (@t201)) % 224.30/224.50 (step @p140 :rule refl :args (@t173)) % 224.30/224.50 (step @p141 :rule refl :args (@t180)) % 224.30/224.50 (step @p142 :rule nary_cong :premises (@p141 @p140 @p139) :args (@t202)) % 224.30/224.50 (step @p143 :rule cong :premises (@p142) :args ((forall @t98 @t202))) % 224.30/224.50 (step @p144 :rule refl :args (@t201)) % 224.30/224.50 (step @p145 :rule refl :args (@t5)) % 224.30/224.50 (step @p146 :rule cong :premises (@p122 @p145) :args (@t203)) % 224.30/224.50 (step @p147 :rule cong :premises (@p122 @p146 @p122) :args (@t204)) % 224.30/224.50 (step @p148 :rule cong :premises (@p122 @p145 @p122) :args (@t205)) % 224.30/224.50 (step @p149 :rule cong :premises (@p148) :args (@t206)) % 224.30/224.50 (step @p150 :rule nary_cong :premises (@p149 @p147) :args (@t207)) % 224.30/224.50 (step @p151 :rule cong :premises (@p150) :args (@t208)) % 224.30/224.50 (step @p152 :rule cong :premises (@p151) :args (@t209)) % 224.30/224.50 (step @p153 :rule refl :args (@t180)) % 224.30/224.50 (step @p154 :rule nary_cong :premises (@p153 @p152 @p144) :args (@t210)) % 224.30/224.50 (step @p155 :rule cong :premises (@p154) :args (@t211)) % 224.30/224.50 (step @p156 :rule trans :premises (@p155 @p143)) % 224.30/224.50 (step @p157 :rule cong :premises (@p156) :args (@t212)) % 224.30/224.50 (step @p158 :rule nary_cong :premises (@p157 @p137 @p131 @p117) :args (@t213)) % 224.30/224.50 (step @p159 :rule cong :premises (@p158) :args (@t214)) % 224.30/224.50 (step @p160 :rule refl :args (@t186)) % 224.30/224.50 (step @p161 :rule cong :premises (@p160 @p159) :args (@t215)) % 224.30/224.50 (step @p162 :rule refl :args (@t190)) % 224.30/224.50 (step @p163 :rule cong :premises (@p162 @p161) :args (@t216)) % 224.30/224.50 (step @p164 :rule eq-refl :args (@t40)) % 224.30/224.50 (step @p165 :rule cong :premises (@p164 @p163) :args (@t217)) % 224.30/224.50 (step @p166 :rule trans :premises (@p165 @p116)) % 224.30/224.50 (step @p167 :rule cong :premises (@p145 @p122) :args (@t218)) % 224.30/224.50 (step @p168 :rule cong :premises (@p145 @p167) :args (@t219)) % 224.30/224.50 (step @p169 :rule cong :premises (@p168) :args (@t220)) % 224.30/224.50 (step @p170 :rule cong :premises (@p169 @p166) :args (@t221)) % 224.30/224.50 (step @p171 :rule refl :args (@t225)) % 224.30/224.50 (step @p172 :rule cong :premises (@p171 @p170) :args (@t226)) % 224.30/224.50 (step @p173 :rule cong :premises (@p172) :args ((not @t226))) % 224.30/224.50 (step @p174 :rule eq-symm :args (@t40 tptp.id)) % 224.30/224.50 (step @p175 :rule refl :args (tptp.axvarshift)) % 224.30/224.50 (step @p176 :rule cong :premises (@p175 @p174) :args (@t41)) % 224.30/224.50 (step @p177 :rule eq_resolve :premises (@p11 @p176)) % 224.30/224.50 (step @p178 :rule equiv_elim2 :premises (@p84)) % 224.30/224.50 (step @p179 :rule resolution :premises (@p178 @p109) :args (true tptp.hoasinduction_lem3v2a_lthm)) % 224.30/224.50 (step @p180 :rule not_implies_elim2 :premises (@p179)) % 224.30/224.50 (step @p181 :rule not_implies_elim2 :premises (@p180)) % 224.30/224.50 (step @p182 :rule not_implies_elim1 :premises (@p181)) % 224.30/224.50 (step @p183 :rule eq_resolve :premises (@p182 @p177)) % 224.30/224.50 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@t330))) % 224.30/224.50 (step @p669 :rule chain_m_resolution :premises (@p668 @p646) :args (@t328 @t311 @t331)) % 224.30/224.50 (step @p670 :rule instantiate :premises (@p669) :args ((@list @t306))) % 224.30/224.50 (step @p671 :rule instantiate :premises (@p653) :args ((@list @t323))) % 224.30/224.50 (step @p672 :rule cnf_or_neg :args (@t330 3)) % 224.30/224.50 (step @p673 :rule chain_m_resolution :premises (@p672 @p646) :args ((not @t324) @t311 @t331)) % 224.30/224.50 (step @p674 :rule cnf_equiv_pos2 :args (@t338)) % 224.30/224.50 (step @p675 :rule reordering :premises (@p674) :args ((or @t324 @t339 (not @t338)))) % 224.30/224.50 (step @p676 :rule chain_m_resolution :premises (@p675 @p673 @p671) :args (@t339 @t340 (@list @t324 @t338))) % 224.30/224.50 (step @p677 :rule false_intro :premises (@p676)) % 224.30/224.50 (step @p678 :rule refl :args (@t165)) % 224.30/224.50 (step @p679 :rule not_implies_elim1 :premises (@p642)) % 224.30/224.50 (step @p680 :rule instantiate :premises (@p679) :args (@t302)) % 224.30/224.50 (step @p681 :rule symm :premises (@p680)) % 224.30/224.50 (step @p682 :rule instantiate :premises (@p632) :args ((@list tptp.one tptp.sh))) % 224.30/224.50 (step @p683 :rule symm :premises (@p682)) % 224.30/224.50 (step @p684 :rule trans :premises (@p683 @p681)) % 224.30/224.50 (step @p685 :rule cong :premises (@p684) :args (@t341)) % 224.30/224.50 (step @p686 :rule cong :premises (@p678 @p685 @p678) :args (@t342)) % 224.30/224.50 (step @p687 :rule trans :premises (@p686 @p677)) % 224.30/224.50 (step @p688 :rule false_elim :premises (@p687)) % 224.30/224.50 (step @p689 :rule instantiate :premises (@p632) :args ((@list @t348 @t346))) % 224.30/224.50 (step @p690 :rule not_implies_elim1 :premises (@p644)) % 224.30/224.50 (step @p691 :rule instantiate :premises (@p690) :args ((@list @t347 @t345 @t344))) % 224.30/224.50 (step @p692 :rule refl :args (@t296)) % 224.30/224.50 (step @p693 :rule cong :premises (@p692 @p691) :args ((tptp.sub @t296 (tptp.comp @t349 @t344)))) % 224.30/224.50 (step @p694 :rule not_implies_elim1 :premises (@p643)) % 224.30/224.50 (step @p695 :rule instantiate :premises (@p694) :args ((@list @t296 @t349 @t344))) % 224.30/224.50 (step @p696 :rule refl :args (@t344)) % 224.30/224.50 (step @p697 :rule eq-symm :args (@t350 @t351)) % 224.30/224.50 (step @p698 :rule cong :premises (@p616 @p697) :args ((=> @t308 @t352))) % 224.30/224.50 (assume-push @p805 @t308) % 224.30/224.50 (step @p700 :rule instantiate :premises (@p632) :args ((@list @t347 @t345))) % 224.30/224.50 (step-pop @p806 :rule scope :premises (@p700)) % 224.30/224.50 (step @p701 :rule process_scope :premises (@p806) :args (@t352)) % 224.30/224.50 (step @p703 :rule eq_resolve :premises (@p701 @p698)) % 224.30/224.50 (step @p704 :rule implies_elim :premises (@p703)) % 224.30/224.50 (step @p705 :rule chain_m_resolution :premises (@p704 @p632) :args ((= @t351 @t350) @t305 @t320)) % 224.30/224.50 (step @p706 :rule cong :premises (@p705 @p696) :args (@t353)) % 224.30/224.50 (step @p707 :rule trans :premises (@p706 @p695 @p693 @p689)) % 224.30/224.50 (step @p708 :rule refl :args (@t355)) % 224.30/224.50 (step @p709 :rule bool-double-not-elim :args (@t343)) % 224.30/224.50 (step @p710 :rule nary_cong :premises (@p709 @p708) :args ((or (not @t356) @t355))) % 224.30/224.50 (assume-push @p807 @t356) % 224.30/224.50 (step @p712 :rule skolemize :premises (@p807)) % 224.30/224.50 (step-pop @p808 :rule scope :premises (@p712)) % 224.30/224.50 (step @p713 :rule process_scope :premises (@p808) :args (@t355)) % 224.30/224.50 (step @p715 :rule implies_elim :premises (@p713)) % 224.30/224.50 (step @p716 :rule eq_resolve :premises (@p715 @p710)) % 224.30/224.50 (step @p717 :rule chain_m_resolution :premises (@p716 @p707) :args (@t343 @t305 (@list @t354))) % 224.30/224.50 (step @p718 :rule cnf_or_pos :args (@t358)) % 224.30/224.50 (step @p719 :rule reordering :premises (@p718) :args ((or @t356 @t357 @t342 (not @t358)))) % 224.30/224.50 (step @p720 :rule chain_m_resolution :premises (@p719 @p717 @p688 @p670) :args (@t357 @t359 (@list @t343 @t342 @t358))) % 224.30/224.50 (step @p721 :rule refl :args (@t363)) % 224.30/224.50 (step @p722 :rule bool-double-not-elim :args (@t314)) % 224.30/224.50 (step @p723 :rule nary_cong :premises (@p722 @p721) :args ((or (not @t357) @t363))) % 224.30/224.50 (assume-push @p809 @t357) % 224.30/224.50 (step @p725 :rule skolemize :premises (@p809)) % 224.30/224.50 (step-pop @p810 :rule scope :premises (@p725)) % 224.30/224.50 (step @p726 :rule process_scope :premises (@p810) :args (@t363)) % 224.30/224.50 (step @p728 :rule implies_elim :premises (@p726)) % 224.30/224.50 (step @p729 :rule eq_resolve :premises (@p728 @p723)) % 224.30/224.50 (step @p730 :rule chain_m_resolution :premises (@p729 @p720) :args (@t363 @t311 (@list @t314))) % 224.30/224.50 (step @p731 :rule cnf_or_neg :args (@t362 1)) % 224.30/224.50 (step @p732 :rule chain_m_resolution :premises (@p731 @p730) :args ((not @t333) @t311 @t364)) % 224.30/224.50 (step @p733 :rule cnf_equiv_pos2 :args (@t335)) % 224.30/224.50 (step @p734 :rule reordering :premises (@p733) :args ((or @t333 @t365 (not @t335)))) % 224.30/224.50 (step @p735 :rule chain_m_resolution :premises (@p734 @p732 @p663) :args (@t365 @t340 (@list @t333 @t335))) % 224.30/224.50 (step @p736 :rule bool-double-not-elim :args (@t325)) % 224.30/224.50 (step @p737 :rule nary_cong :premises (@p648 @p736) :args ((or @t330 (not @t326)))) % 224.30/224.50 (step @p738 :rule cnf_or_neg :args (@t330 2)) % 224.30/224.50 (step @p739 :rule eq_resolve :premises (@p738 @p737)) % 224.30/224.50 (step @p740 :rule reordering :premises (@p739) :args ((or @t325 @t330))) % 224.30/224.50 (step @p741 :rule chain_m_resolution :premises (@p740 @p646) :args (@t325 @t311 @t331)) % 224.30/224.50 (step @p742 :rule instantiate :premises (@p741) :args (@t366)) % 224.30/224.50 (step @p743 :rule eq-symm :args (@t367 @t360)) % 224.30/224.50 (step @p744 :rule cong :premises (@p655 @p743) :args ((=> @t322 @t368))) % 224.30/224.50 (assume-push @p811 @t322) % 224.30/224.50 (step @p746 :rule instantiate :premises (@p653) :args (@t366)) % 224.30/224.50 (step-pop @p812 :rule scope :premises (@p746)) % 224.30/224.50 (step @p747 :rule process_scope :premises (@p812) :args (@t368)) % 224.30/224.50 (step @p749 :rule eq_resolve :premises (@p747 @p744)) % 224.30/224.50 (step @p750 :rule implies_elim :premises (@p749)) % 224.30/224.50 (step @p751 :rule chain_m_resolution :premises (@p750 @p653) :args (@t369 @t305 @t336)) % 224.30/224.50 (step @p752 :rule bool-double-not-elim :args (@t360)) % 224.30/224.50 (step @p753 :rule refl :args (@t362)) % 224.30/224.50 (step @p754 :rule nary_cong :premises (@p753 @p752) :args ((or @t362 (not @t361)))) % 224.30/224.50 (step @p755 :rule cnf_or_neg :args (@t362 0)) % 224.30/224.50 (step @p756 :rule eq_resolve :premises (@p755 @p754)) % 224.30/224.50 (step @p757 :rule reordering :premises (@p756) :args ((or @t360 @t362))) % 224.30/224.50 (step @p758 :rule chain_m_resolution :premises (@p757 @p730) :args (@t360 @t311 @t364)) % 224.30/224.50 (step @p759 :rule cnf_equiv_pos1 :args (@t369)) % 224.30/224.50 (step @p760 :rule reordering :premises (@p759) :args ((or @t361 @t367 (not @t369)))) % 224.30/224.50 (step @p761 :rule chain_m_resolution :premises (@p760 @p758 @p751) :args (@t367 @t370 (@list @t360 @t369))) % 224.30/224.50 (step @p762 :rule cnf_or_pos :args (@t373)) % 224.30/224.50 (step @p763 :rule reordering :premises (@p762) :args ((or @t372 @t371 (not @t373)))) % 224.30/224.50 (step @p764 :rule chain_m_resolution :premises (@p763 @p761 @p742) :args (@t371 @t370 (@list @t367 @t373))) % 224.30/224.50 (step @p765 :rule refl :args (@t374)) % 224.30/224.50 (step @p766 :rule bool-double-not-elim :args (@t332)) % 224.30/224.50 (step @p767 :rule refl :args (@t375)) % 224.30/224.50 (step @p768 :rule nary_cong :premises (@p767 @p766 @p765) :args ((or @t375 (not @t365) @t374))) % 224.30/224.50 (assume-push @p813 @t371) % 224.30/224.50 (assume-push @p814 @t319) % 224.30/224.50 (assume-push @p815 @t365) % 224.30/224.50 (step @p772 :rule evaluate :args ((= false true))) % 224.30/224.50 (step @p773 :rule true_intro :premises (@p813)) % 224.30/224.50 (step @p774 :rule cong :premises (@p641) :args (@t332)) % 224.30/224.50 (step @p775 :rule false_intro :premises (@p815)) % 224.30/224.50 (step @p776 :rule symm :premises (@p775)) % 224.30/224.50 (step @p777 :rule trans :premises (@p776 @p774 @p773)) % 224.30/224.50 (step @p778 false :rule eq_resolve :premises (@p777 @p772)) % 224.30/224.50 (step-pop @p816 :rule scope :premises (@p778)) % 224.30/224.50 (step-pop @p817 :rule scope :premises (@p816)) % 224.30/224.50 (step-pop @p818 :rule scope :premises (@p817)) % 224.30/224.50 (step @p779 :rule process_scope :premises (@p818) :args (false)) % 224.30/224.50 (assume-push @p819 @t319) % 224.30/224.50 (assume-push @p820 @t365) % 224.30/224.50 (assume-push @p821 @t371) % 224.30/224.50 (step @p786 :rule and_intro :premises (@p821 @p641 @p820)) % 224.30/224.50 (step-pop @p822 :rule scope :premises (@p786)) % 224.30/224.50 (step-pop @p823 :rule scope :premises (@p822)) % 224.30/224.50 (step-pop @p824 :rule scope :premises (@p823)) % 224.30/224.50 (step @p787 :rule process_scope :premises (@p824) :args (@t376)) % 224.30/224.50 (step @p791 :rule implies_elim :premises (@p787)) % 224.30/224.50 (step @p792 :rule resolution :premises (@p791 @p779) :args (true @t376)) % 224.30/224.50 (step @p793 :rule not_and :premises (@p792)) % 224.30/224.50 (step @p794 :rule eq_resolve :premises (@p793 @p768)) % 224.30/224.50 (step @p795 :rule reordering :premises (@p794) :args ((or @t332 @t375 @t374))) % 224.30/224.50 (step @p796 false :rule chain_m_resolution :premises (@p795 @p764 @p735 @p641) :args (false @t359 (@list @t371 @t332 @t319))) % 224.30/224.50 ) % 224.30/224.50 % SZS output end Proof % 224.30/224.50 % cvc5 exiting %------------------------------------------------------------------------------