%------------------------------------------------------------------------------ % File : cvc5---1.3.4 % Problem : ALG268^2 : 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 : n005.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 1.10s 1.34s % Output : Proof 1.10s % Verified : % SZS Type : - % Comments : %------------------------------------------------------------------------------ %----WARNING: Could not form TPTP format derivation %------------------------------------------------------------------------------ %----ORIGINAL SYSTEM OUTPUT % 0.00/0.12 % Problem : ALG268^2 : TPTP v9.2.1. Bugfixed v5.2.0. % 0.12/0.13 % Command : /export/starexec/sandbox/solver/bin/do_cvc5 /export/starexec/sandbox/benchmark/theBenchmark.p 300 THM % 0.18/0.34 % Computer : n005.cluster.edu % 0.18/0.34 % Model : x86_64 x86_64 % 0.18/0.34 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz % 0.18/0.34 % Memory : 8042.1875MB % 0.18/0.34 % OS : Linux 3.10.0-693.el7.x86_64 % 0.18/0.34 % CPULimit : 300 % 0.18/0.34 % WCLimit : 300 % 0.18/0.34 % DateTime : Wed Jun 3 01:55:18 EDT 2026 % 0.18/0.35 % CPUTime : % 0.38/0.58 %----Proving TH0 % 1.10/1.34 --- Run --mbqi --mbqi-enum --mbqi-enum-choice-grammar --mbqi-enum-global-syms-grammar --sygus-grammar-ho-partial --no-cegqi --no-sygus-inst at 90s... % 1.10/1.34 % SZS status Theorem % 1.10/1.34 % SZS output start Proof % 1.10/1.34 ( % 1.10/1.34 (declare-sort tptp.term 0) % 1.10/1.34 (declare-sort tptp.subst 0) % 1.10/1.34 (declare-const tptp.push (-> tptp.term tptp.subst tptp.subst)) % 1.10/1.34 (declare-const tptp.sub (-> tptp.term tptp.subst tptp.term)) % 1.10/1.34 (declare-const tptp.ap (-> tptp.term tptp.term tptp.term)) % 1.10/1.34 (declare-const tptp.one tptp.term) % 1.10/1.34 (declare-const tptp.sh tptp.subst) % 1.10/1.34 (declare-const tptp.lam (-> tptp.term tptp.term)) % 1.10/1.34 (declare-const tptp.var (-> tptp.term Bool)) % 1.10/1.34 (declare-const tptp.id tptp.subst) % 1.10/1.34 (declare-const tptp.hoasinduction_no_psi_cond_lthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_no_psi_cond Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lthm_3 Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_gthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3b_lthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3b_gthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3b Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3a_lthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3a_gthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3a Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3_lthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3_gthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3 Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3aaa Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3aa_lthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3aa Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem2_lthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem2_gthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem2 Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem1_lthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem1_gthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem1 Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3v2a_lthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3v2a Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3v2_lthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3v2_gthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3v2 Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3v2_f_lthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem3v2_f Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem2v2_gthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem2v2 Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem1v2_gthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem1v2 Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem0_lthm Bool) % 1.10/1.34 (declare-const tptp.hoasinduction_lem0 Bool) % 1.10/1.34 (declare-const tptp.hoasapnotvar_lthm Bool) % 1.10/1.34 (declare-const tptp.hoasapnotvar_gthm Bool) % 1.10/1.34 (declare-const tptp.hoasapnotvar Bool) % 1.10/1.34 (declare-const tptp.hoaslamnotvar_lthm Bool) % 1.10/1.34 (declare-const tptp.hoaslamnotvar_gthm Bool) % 1.10/1.34 (declare-const tptp.hoaslamnotvar Bool) % 1.10/1.34 (declare-const tptp.hoaslamnotap_lthm Bool) % 1.10/1.34 (declare-const tptp.hoaslamnotap_gthm Bool) % 1.10/1.34 (declare-const tptp.hoaslamnotap Bool) % 1.10/1.34 (declare-const tptp.hoaslaminj_lthm Bool) % 1.10/1.34 (declare-const tptp.hoaslaminj_gthm Bool) % 1.10/1.34 (declare-const tptp.hoaslaminj Bool) % 1.10/1.34 (declare-const tptp.hoasapinj2_lthm Bool) % 1.10/1.34 (declare-const tptp.hoasapinj2_gthm Bool) % 1.10/1.34 (declare-const tptp.hoasapinj2 Bool) % 1.10/1.34 (declare-const tptp.pushprop_lem0_lthm Bool) % 1.10/1.34 (declare-const tptp.axassoc Bool) % 1.10/1.34 (declare-const tptp.pushprop_lem0_gthm Bool) % 1.10/1.34 (declare-const tptp.axvarcons Bool) % 1.10/1.34 (declare-const tptp.pushprop_lem0 Bool) % 1.10/1.34 (declare-const tptp.apinj1 Bool) % 1.10/1.34 (declare-const tptp.induction Bool) % 1.10/1.34 (declare-const tptp.apnotvar Bool) % 1.10/1.34 (declare-const tptp.laminj Bool) % 1.10/1.34 (declare-const tptp.axvarshift Bool) % 1.10/1.34 (declare-const tptp.ulamvarind Bool) % 1.10/1.34 (declare-const tptp.pushprop_lem2v2_lthm Bool) % 1.10/1.34 (declare-const tptp.ulamvarsh Bool) % 1.10/1.34 (declare-const tptp.ulamvar1 Bool) % 1.10/1.34 (declare-const tptp.axabs Bool) % 1.10/1.34 (declare-const tptp.pushprop_lem1 Bool) % 1.10/1.34 (declare-const tptp.shinj Bool) % 1.10/1.34 (declare-const tptp.comp (-> tptp.subst tptp.subst tptp.subst)) % 1.10/1.34 (declare-const tptp.apinj2 Bool) % 1.10/1.34 (declare-const tptp.axvarid Bool) % 1.10/1.34 (declare-const tptp.axidl Bool) % 1.10/1.34 (declare-const tptp.axclos Bool) % 1.10/1.34 (declare-const tptp.termmset Bool) % 1.10/1.34 (declare-const tptp.axshiftcons Bool) % 1.10/1.34 (declare-const tptp.lamnotap Bool) % 1.10/1.34 (declare-const tptp.lamnotvar Bool) % 1.10/1.34 (declare-const tptp.axapp Bool) % 1.10/1.34 (declare-const tptp.axscons Bool) % 1.10/1.34 (declare-const tptp.axmap Bool) % 1.10/1.34 (declare-const tptp.axidr Bool) % 1.10/1.34 (declare-const tptp.induction2lem Bool) % 1.10/1.34 (declare-const tptp.pushprop_lem1_gthm Bool) % 1.10/1.34 (declare-const tptp.hoasapinj1_lthm Bool) % 1.10/1.34 (declare-const tptp.pushprop_lem1_lthm Bool) % 1.10/1.34 (declare-const tptp.pushprop_lem1v2 Bool) % 1.10/1.34 (declare-const tptp.pushprop_lem1v2_gthm Bool) % 1.10/1.34 (declare-const tptp.induction2 Bool) % 1.10/1.34 (declare-const tptp.pushprop_lem1v2_lthm Bool) % 1.10/1.34 (declare-const tptp.pushprop_lem2v2 Bool) % 1.10/1.34 (declare-const tptp.pushprop_lem2v2_gthm Bool) % 1.10/1.34 (declare-const tptp.pushprop_lem3v2 Bool) % 1.10/1.34 (declare-const tptp.pushprop_lem3v2_lthm Bool) % 1.10/1.34 (declare-const tptp.pushprop Bool) % 1.10/1.34 (declare-const tptp.pushprop_gthm Bool) % 1.10/1.34 (declare-const tptp.hoasapinj1 Bool) % 1.10/1.34 (declare-const tptp.pushprop_lthm_orig Bool) % 1.10/1.34 (declare-const tptp.pushprop_lthm Bool) % 1.10/1.34 (declare-const tptp.induction2lem_gthm Bool) % 1.10/1.34 (declare-const tptp.induction2lem_lthm Bool) % 1.10/1.34 (declare-const tptp.induction2_gthm Bool) % 1.10/1.34 (declare-const tptp.induction2_lthm Bool) % 1.10/1.34 (declare-const tptp.substmonoid Bool) % 1.10/1.34 (declare-const tptp.substmonoid_gthm Bool) % 1.10/1.34 (declare-const tptp.termmset_gthm Bool) % 1.10/1.34 (declare-const tptp.substmonoid_lthm Bool) % 1.10/1.34 (declare-const tptp.termmset_lthm Bool) % 1.10/1.34 (declare-const tptp.hoasapinj1_gthm Bool) % 1.10/1.34 (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)))))))))))) % 1.10/1.34 (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)))))) % 1.10/1.34 (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))))) % 1.10/1.34 (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)))))) % 1.10/1.34 (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)))))))) % 1.10/1.34 (define @t1 () (@var "M" tptp.subst)) % 1.10/1.34 (define @t2 () (@var "B" tptp.term)) % 1.10/1.34 (define @t3 () (_ tptp.sub @t2)) % 1.10/1.34 (define @t4 () (_ @t3 @t1)) % 1.10/1.34 (define @t5 () (@var "A" tptp.term)) % 1.10/1.34 (define @t6 () (_ tptp.sub @t5)) % 1.10/1.34 (define @t7 () (_ @t6 @t1)) % 1.10/1.34 (define @t8 () (_ tptp.ap @t5)) % 1.10/1.34 (define @t9 () (_ @t8 @t2)) % 1.10/1.34 (define @t10 () (_ (_ tptp.push @t5) @t1)) % 1.10/1.34 (define @t11 () (_ tptp.sub tptp.one)) % 1.10/1.34 (define @t12 () (@list @t5 @t1)) % 1.10/1.34 (define @t13 () (_ @t6 tptp.id)) % 1.10/1.34 (define @t14 () (@list @t5)) % 1.10/1.34 (define @t15 () (forall @t14 (= @t13 @t5))) % 1.10/1.34 (define @t16 () (= tptp.axvarid @t15)) % 1.10/1.34 (define @t17 () (_ tptp.comp @t1)) % 1.10/1.34 (define @t18 () (_ tptp.push tptp.one)) % 1.10/1.34 (define @t19 () (_ tptp.lam @t5)) % 1.10/1.34 (define @t20 () (@var "N" tptp.subst)) % 1.10/1.34 (define @t21 () (_ @t17 @t20)) % 1.10/1.34 (define @t22 () (@list @t5 @t1 @t20)) % 1.10/1.34 (define @t23 () (forall @t22 (= (_ (_ tptp.sub @t7) @t20) (_ @t6 @t21)))) % 1.10/1.34 (define @t24 () (@list @t1)) % 1.10/1.34 (define @t25 () (forall @t24 (= (_ (_ tptp.comp tptp.id) @t1) @t1))) % 1.10/1.34 (define @t26 () (_ tptp.comp tptp.sh)) % 1.10/1.34 (define @t27 () (@var "K" tptp.subst)) % 1.10/1.34 (define @t28 () (forall (@list @t1 @t20 @t27) (= (_ (_ tptp.comp @t21) @t27) (_ @t17 (_ (_ tptp.comp @t20) @t27))))) % 1.10/1.34 (define @t29 () (_ @t6 @t20)) % 1.10/1.34 (define @t30 () (_ (_ tptp.push @t29) @t21)) % 1.10/1.34 (define @t31 () (forall @t24 (= (_ @t17 tptp.id) @t1))) % 1.10/1.34 (define @t32 () (_ @t18 tptp.sh)) % 1.10/1.34 (define @t33 () (= tptp.axvarshift (= @t32 tptp.id))) % 1.10/1.34 (define @t34 () (_ @t6 tptp.sh)) % 1.10/1.34 (define @t35 () (_ tptp.var @t5)) % 1.10/1.34 (define @t36 () (@var "P" (-> tptp.term Bool))) % 1.10/1.34 (define @t37 () (_ @t36 @t5)) % 1.10/1.34 (define @t38 () (forall @t14 (=> @t35 @t37))) % 1.10/1.34 (define @t39 () (@list @t36)) % 1.10/1.34 (define @t40 () (= @t5 @t2)) % 1.10/1.34 (define @t41 () (@var "D" tptp.term)) % 1.10/1.34 (define @t42 () (_ tptp.ap @t2)) % 1.10/1.34 (define @t43 () (@var "C" tptp.term)) % 1.10/1.34 (define @t44 () (= (_ @t8 @t43) (_ @t42 @t41))) % 1.10/1.34 (define @t45 () (@list @t5 @t2 @t43 @t41)) % 1.10/1.34 (define @t46 () (= @t43 @t41)) % 1.10/1.34 (define @t47 () (@list @t5 @t2)) % 1.10/1.34 (define @t48 () (forall @t14 @t37)) % 1.10/1.34 (define @t49 () (_ @t36 @t19)) % 1.10/1.34 (define @t50 () (_ @t36 @t2)) % 1.10/1.34 (define @t51 () (forall @t47 (=> @t37 (=> @t50 (_ @t36 @t9))))) % 1.10/1.34 (define @t52 () (@var "Q" (-> tptp.term Bool))) % 1.10/1.34 (define @t53 () (_ (_ (_ (_ tptp.pushprop_p_and_p_prime @t5) @t1) @t36) @t52)) % 1.10/1.34 (define @t54 () (@list @t52)) % 1.10/1.34 (define @t55 () (@list @t36 @t5 @t1)) % 1.10/1.34 (define @t56 () (_ tptp.push @t2)) % 1.10/1.34 (define @t57 () (@var "K" (-> tptp.term Bool))) % 1.10/1.34 (define @t58 () (@list @t36 @t52 @t5 @t1)) % 1.10/1.34 (define @t59 () (_ tptp.sub @t43)) % 1.10/1.34 (define @t60 () (@list @t43)) % 1.10/1.34 (define @t61 () (_ tptp.var @t2)) % 1.10/1.34 (define @t62 () (@list @t2)) % 1.10/1.34 (define @t63 () (forall @t62 (=> @t61 (_ @t36 @t4)))) % 1.10/1.34 (define @t64 () (_ @t3 @t10)) % 1.10/1.34 (define @t65 () (forall @t62 (=> @t61 (_ @t36 @t64)))) % 1.10/1.34 (define @t66 () (_ @t52 @t2)) % 1.10/1.34 (define @t67 () (=> tptp.ulamvar1 (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop)))))) % 1.10/1.34 (define @t68 () (_ @t56 tptp.id)) % 1.10/1.34 (define @t69 () (_ @t6 @t68)) % 1.10/1.34 (define @t70 () (forall @t14 (=> (forall @t62 (=> @t50 (_ @t36 @t69))) @t49))) % 1.10/1.34 (define @t71 () (=> tptp.induction (=> tptp.pushprop tptp.induction2lem))) % 1.10/1.34 (define @t72 () (=> tptp.induction2lem tptp.induction2)) % 1.10/1.34 (define @t73 () (_ tptp.hoasap tptp.id)) % 1.10/1.34 (define @t74 () (_ (_ @t73 @t5) tptp.id)) % 1.10/1.34 (define @t75 () (= (_ @t74 @t43) (_ (_ (_ @t73 @t2) tptp.id) @t41))) % 1.10/1.34 (define @t76 () (@var "G" (-> tptp.subst tptp.term tptp.term))) % 1.10/1.34 (define @t77 () (_ (_ @t76 @t1) @t5)) % 1.10/1.34 (define @t78 () (@var "F" (-> tptp.subst tptp.term tptp.term))) % 1.10/1.34 (define @t79 () (_ @t78 @t1)) % 1.10/1.34 (define @t80 () (_ @t79 @t5)) % 1.10/1.34 (define @t81 () (@list @t1 @t5)) % 1.10/1.34 (define @t82 () (_ tptp.hoaslam tptp.id)) % 1.10/1.34 (define @t83 () (lambda @t81 @t80)) % 1.10/1.34 (define @t84 () (_ @t82 @t83)) % 1.10/1.34 (define @t85 () (@list @t1 @t5 @t20)) % 1.10/1.34 (define @t86 () (_ (_ @t78 @t21) @t29)) % 1.10/1.34 (define @t87 () (_ (_ tptp.sub @t80) @t20)) % 1.10/1.34 (define @t88 () (= @t87 @t86)) % 1.10/1.34 (define @t89 () (forall @t85 @t88)) % 1.10/1.34 (define @t90 () (@list @t78)) % 1.10/1.34 (define @t91 () (_ @t74 @t2)) % 1.10/1.34 (define @t92 () (_ tptp.hoasvar tptp.id)) % 1.10/1.34 (define @t93 () (@var "P" (-> tptp.subst tptp.term tptp.subst Bool))) % 1.10/1.34 (define @t94 () (_ (_ tptp.hoasinduction_p_and_p_prime @t93) @t52)) % 1.10/1.34 (define @t95 () (@list @t93)) % 1.10/1.34 (define @t96 () (_ @t52 @t5)) % 1.10/1.34 (define @t97 () (_ @t93 tptp.id)) % 1.10/1.34 (define @t98 () (_ (_ @t97 @t5) tptp.id)) % 1.10/1.34 (define @t99 () (forall @t14 (=> (_ (_ @t92 @t5) tptp.id) @t98))) % 1.10/1.34 (define @t100 () (_ (_ tptp.comp @t27) @t20)) % 1.10/1.34 (define @t101 () (_ (_ @t93 @t1) @t5)) % 1.10/1.34 (define @t102 () (_ @t101 @t100)) % 1.10/1.34 (define @t103 () (_ @t6 @t27)) % 1.10/1.34 (define @t104 () (_ @t17 @t27)) % 1.10/1.34 (define @t105 () (_ (_ (_ @t93 @t104) @t103) @t20)) % 1.10/1.34 (define @t106 () (@list @t1 @t5 @t20 @t27)) % 1.10/1.34 (define @t107 () (forall @t106 (=> @t105 @t102))) % 1.10/1.34 (define @t108 () (forall @t106 (=> @t102 @t105))) % 1.10/1.34 (define @t109 () (@list @t93 @t52)) % 1.10/1.34 (define @t110 () (_ (_ @t97 @t2) tptp.id)) % 1.10/1.34 (define @t111 () (forall @t47 (=> @t98 (=> @t110 (_ (_ @t97 @t91) tptp.id))))) % 1.10/1.34 (define @t112 () (_ (_ @t78 tptp.id) @t5)) % 1.10/1.34 (define @t113 () (_ (_ @t97 @t112) tptp.id)) % 1.10/1.34 (define @t114 () (forall @t14 (=> @t98 @t113))) % 1.10/1.34 (define @t115 () (=> @t114 (_ (_ @t97 @t84) tptp.id))) % 1.10/1.34 (define @t116 () (=> @t89 @t115)) % 1.10/1.34 (define @t117 () (forall @t90 @t116)) % 1.10/1.34 (define @t118 () (=> @t117 (=> @t94 (forall @t14 (=> (forall @t62 (=> @t66 (_ @t52 @t69))) (_ @t52 @t19)))))) % 1.10/1.34 (define @t119 () (=> 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))))))))))))))))))))))))))))))))))) % 1.10/1.34 (define @t120 () (=> 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))))))))))))))))))))))))))))))))))) % 1.10/1.34 (define @t121 () (_ @t6 @t32)) % 1.10/1.34 (define @t122 () (_ tptp.lam @t121)) % 1.10/1.34 (define @t123 () (_ (_ @t97 @t122) tptp.id)) % 1.10/1.34 (define @t124 () (_ (_ @t97 @t69) tptp.id)) % 1.10/1.34 (define @t125 () (forall @t62 (=> @t110 @t124))) % 1.10/1.34 (define @t126 () (=> @t125 @t123)) % 1.10/1.34 (define @t127 () (forall @t14 @t126)) % 1.10/1.34 (define @t128 () (=> @t117 @t127)) % 1.10/1.34 (define @t129 () (forall @t95 @t128)) % 1.10/1.34 (define @t130 () (= tptp.hoasinduction_lem3aa @t129)) % 1.10/1.34 (define @t131 () (_ (_ @t97 @t19) tptp.id)) % 1.10/1.34 (define @t132 () (=> @t125 @t131)) % 1.10/1.34 (define @t133 () (forall @t14 @t132)) % 1.10/1.34 (define @t134 () (=> @t117 @t133)) % 1.10/1.34 (define @t135 () (=> @t107 @t134)) % 1.10/1.34 (define @t136 () (=> @t108 @t135)) % 1.10/1.34 (define @t137 () (forall @t95 @t136)) % 1.10/1.34 (define @t138 () (= tptp.hoasinduction_lem3 @t137)) % 1.10/1.34 (define @t139 () (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3)) % 1.10/1.34 (define @t140 () (=> tptp.axvarshift @t139)) % 1.10/1.34 (define @t141 () (=> tptp.axvarid @t140)) % 1.10/1.34 (define @t142 () (= tptp.hoasinduction_lem3_lthm @t141)) % 1.10/1.34 (define @t143 () (_ @t78 tptp.sh)) % 1.10/1.34 (define @t144 () (_ @t143 tptp.one)) % 1.10/1.34 (define @t145 () (=> @t111 (=> @t117 (forall @t14 @t98)))) % 1.10/1.34 (define @t146 () (=> tptp.hoasinduction_lem1 (=> tptp.hoasinduction_lem2 (=> tptp.hoasinduction_lem3 tptp.hoasinduction)))) % 1.10/1.34 (define @t147 () (not tptp.hoasinduction_lem3_lthm)) % 1.10/1.34 (define @t148 () (@var "X" tptp.term)) % 1.10/1.34 (define @t149 () (_ @t52 @t148)) % 1.10/1.34 (define @t150 () (@list @t148)) % 1.10/1.34 (define @t151 () (lambda (@list @t5 @t1 @t36 @t52) (forall @t150 (= @t149 (_ @t36 (_ (_ tptp.sub @t148) @t10)))))) % 1.10/1.34 (define @t152 () (lambda (@list @t1 @t5 @t20 @t2) (_ (_ tptp.ap @t29) @t2))) % 1.10/1.34 (define @t153 () (_ tptp.lam @t144)) % 1.10/1.34 (define @t154 () (lambda (@list @t1 @t78) @t153)) % 1.10/1.34 (define @t155 () (lambda @t85 (_ tptp.var @t29))) % 1.10/1.34 (define @t156 () (lambda @t109 (forall @t150 (= @t149 (_ (_ @t97 @t148) tptp.id))))) % 1.10/1.34 (define @t157 () (tptp.push tptp.one tptp.sh)) % 1.10/1.34 (define @t158 () (@var "BOUND_VARIABLE_10239" tptp.term)) % 1.10/1.34 (define @t159 () (tptp.lam @t158)) % 1.10/1.34 (define @t160 () (tptp.push @t2 @t157)) % 1.10/1.34 (define @t161 () (not (_ @t93 @t157 @t2 @t157))) % 1.10/1.34 (define @t162 () (not (forall @t62 (or @t161 (_ @t93 @t157 (tptp.sub @t158 @t160) @t157))))) % 1.10/1.34 (define @t163 () (_ @t78 tptp.sh tptp.one)) % 1.10/1.34 (define @t164 () (tptp.lam @t163)) % 1.10/1.34 (define @t165 () (_ @t78 @t157 @t5)) % 1.10/1.34 (define @t166 () (not (forall @t14 (or (not (_ @t93 @t157 @t5 @t157)) (_ @t93 @t157 @t165 @t157))))) % 1.10/1.34 (define @t167 () (tptp.sub @t5 @t20)) % 1.10/1.34 (define @t168 () (tptp.comp @t1 @t20)) % 1.10/1.34 (define @t169 () (_ @t78 @t168 @t167)) % 1.10/1.34 (define @t170 () (_ @t78 @t1 @t5)) % 1.10/1.34 (define @t171 () (tptp.sub @t170 @t20)) % 1.10/1.34 (define @t172 () (forall @t85 (= @t171 @t169))) % 1.10/1.34 (define @t173 () (not @t172)) % 1.10/1.34 (define @t174 () (not (forall @t90 (or @t173 @t166 (_ @t93 @t157 @t164 @t157))))) % 1.10/1.34 (define @t175 () (tptp.comp @t27 @t20)) % 1.10/1.34 (define @t176 () (_ @t93 @t1 @t5 @t175)) % 1.10/1.34 (define @t177 () (tptp.sub @t5 @t27)) % 1.10/1.34 (define @t178 () (tptp.comp @t1 @t27)) % 1.10/1.34 (define @t179 () (_ @t93 @t178 @t177 @t20)) % 1.10/1.34 (define @t180 () (forall @t106 (or (not @t179) @t176))) % 1.10/1.34 (define @t181 () (not @t180)) % 1.10/1.34 (define @t182 () (forall @t106 (or (not @t176) @t179))) % 1.10/1.34 (define @t183 () (not @t182)) % 1.10/1.34 (define @t184 () (@list @t93 @t158)) % 1.10/1.34 (define @t185 () (forall @t184 (or @t183 @t181 @t174 @t162 (_ @t93 @t157 @t159 @t157)))) % 1.10/1.34 (define @t186 () (@var "BOUND_VARIABLE_10074" tptp.term)) % 1.10/1.34 (define @t187 () (tptp.lam (tptp.sub @t186 @t157))) % 1.10/1.34 (define @t188 () (not (forall @t62 (or @t161 (_ @t93 @t157 (tptp.sub @t186 @t160) @t157))))) % 1.10/1.34 (define @t189 () (@list @t93 @t186)) % 1.10/1.34 (define @t190 () (forall @t189 (or @t174 @t188 (_ @t93 @t157 @t187 @t157)))) % 1.10/1.34 (define @t191 () (_ @t93 @t32 @t159 @t32)) % 1.10/1.34 (define @t192 () (or @t183 @t181 @t174 @t162 @t191)) % 1.10/1.34 (define @t193 () (tptp.push @t2 @t32)) % 1.10/1.34 (define @t194 () (tptp.sub @t158 @t193)) % 1.10/1.34 (define @t195 () (_ @t93 @t32 @t194 @t32)) % 1.10/1.34 (define @t196 () (_ @t93 @t32 @t2 @t32)) % 1.10/1.34 (define @t197 () (not @t196)) % 1.10/1.34 (define @t198 () (or @t197 @t195)) % 1.10/1.34 (define @t199 () (forall @t62 @t198)) % 1.10/1.34 (define @t200 () (not @t199)) % 1.10/1.34 (define @t201 () (_ @t93 @t32 @t164 @t32)) % 1.10/1.34 (define @t202 () (or @t173 @t166 @t201)) % 1.10/1.34 (define @t203 () (_ @t78 @t32 @t5)) % 1.10/1.34 (define @t204 () (_ @t93 @t32 @t203 @t32)) % 1.10/1.34 (define @t205 () (_ @t93 @t32 @t5 @t32)) % 1.10/1.34 (define @t206 () (not @t205)) % 1.10/1.34 (define @t207 () (or @t206 @t204)) % 1.10/1.34 (define @t208 () (forall @t14 @t207)) % 1.10/1.34 (define @t209 () (not @t208)) % 1.10/1.34 (define @t210 () (or @t173 @t209 @t201)) % 1.10/1.34 (define @t211 () (forall @t90 @t210)) % 1.10/1.34 (define @t212 () (not @t211)) % 1.10/1.34 (define @t213 () (or @t183 @t181 @t212 @t200 @t191)) % 1.10/1.34 (define @t214 () (forall @t184 @t213)) % 1.10/1.34 (define @t215 () (_ @t93 @t32 @t187 @t32)) % 1.10/1.34 (define @t216 () (or @t174 @t188 @t215)) % 1.10/1.34 (define @t217 () (tptp.sub @t186 @t193)) % 1.10/1.34 (define @t218 () (_ @t93 @t32 @t217 @t32)) % 1.10/1.34 (define @t219 () (or @t197 @t218)) % 1.10/1.34 (define @t220 () (forall @t62 @t219)) % 1.10/1.34 (define @t221 () (not @t220)) % 1.10/1.34 (define @t222 () (or @t212 @t221 @t215)) % 1.10/1.34 (define @t223 () (forall @t189 @t222)) % 1.10/1.34 (define @t224 () (=> @t223 @t214)) % 1.10/1.34 (define @t225 () (=> (= @t32 @t32) @t224)) % 1.10/1.34 (define @t226 () (tptp.sub @t5 @t32)) % 1.10/1.34 (define @t227 () (= @t5 @t226)) % 1.10/1.34 (define @t228 () (forall @t14 @t227)) % 1.10/1.34 (define @t229 () (=> @t228 @t225)) % 1.10/1.34 (define @t230 () (_ @t93 tptp.id @t159 tptp.id)) % 1.10/1.34 (define @t231 () (tptp.push @t2 tptp.id)) % 1.10/1.34 (define @t232 () (tptp.sub @t158 @t231)) % 1.10/1.34 (define @t233 () (_ @t93 tptp.id @t232 tptp.id)) % 1.10/1.34 (define @t234 () (_ @t93 tptp.id @t2 tptp.id)) % 1.10/1.34 (define @t235 () (not @t234)) % 1.10/1.34 (define @t236 () (or @t235 @t233)) % 1.10/1.34 (define @t237 () (forall @t62 @t236)) % 1.10/1.34 (define @t238 () (not @t237)) % 1.10/1.34 (define @t239 () (_ @t93 tptp.id @t164 tptp.id)) % 1.10/1.34 (define @t240 () (_ @t78 tptp.id @t5)) % 1.10/1.34 (define @t241 () (_ @t93 tptp.id @t240 tptp.id)) % 1.10/1.34 (define @t242 () (_ @t93 tptp.id @t5 tptp.id)) % 1.10/1.34 (define @t243 () (not @t242)) % 1.10/1.34 (define @t244 () (or @t243 @t241)) % 1.10/1.34 (define @t245 () (forall @t14 @t244)) % 1.10/1.34 (define @t246 () (not @t245)) % 1.10/1.34 (define @t247 () (or @t173 @t246 @t239)) % 1.10/1.34 (define @t248 () (forall @t90 @t247)) % 1.10/1.34 (define @t249 () (not @t248)) % 1.10/1.34 (define @t250 () (or @t183 @t181 @t249 @t238 @t230)) % 1.10/1.34 (define @t251 () (forall @t184 @t250)) % 1.10/1.34 (define @t252 () (_ @t93 tptp.id @t187 tptp.id)) % 1.10/1.34 (define @t253 () (tptp.sub @t186 @t231)) % 1.10/1.34 (define @t254 () (_ @t93 tptp.id @t253 tptp.id)) % 1.10/1.34 (define @t255 () (or @t235 @t254)) % 1.10/1.34 (define @t256 () (forall @t62 @t255)) % 1.10/1.34 (define @t257 () (not @t256)) % 1.10/1.34 (define @t258 () (or @t249 @t257 @t252)) % 1.10/1.34 (define @t259 () (forall @t189 @t258)) % 1.10/1.34 (define @t260 () (=> @t259 @t251)) % 1.10/1.34 (define @t261 () (= tptp.id @t32)) % 1.10/1.34 (define @t262 () (=> @t261 @t260)) % 1.10/1.34 (define @t263 () (tptp.sub @t5 tptp.id)) % 1.10/1.34 (define @t264 () (= @t5 @t263)) % 1.10/1.34 (define @t265 () (forall @t14 @t264)) % 1.10/1.34 (define @t266 () (or @t238 @t230)) % 1.10/1.34 (define @t267 () (or @t183 @t181 @t249 @t266)) % 1.10/1.34 (define @t268 () (forall @t184 @t267)) % 1.10/1.34 (define @t269 () (@list @t158)) % 1.10/1.34 (define @t270 () (forall @t269 @t267)) % 1.10/1.34 (define @t271 () (forall @t269 @t266)) % 1.10/1.34 (define @t272 () (@list @t5)) % 1.10/1.34 (define @t273 () (or @t183 @t181 @t249 @t271)) % 1.10/1.34 (define @t274 () (tptp.lam @t5)) % 1.10/1.34 (define @t275 () (_ @t93 tptp.id @t274 tptp.id)) % 1.10/1.34 (define @t276 () (tptp.sub @t5 @t231)) % 1.10/1.34 (define @t277 () (_ @t93 tptp.id @t276 tptp.id)) % 1.10/1.34 (define @t278 () (forall @t62 (or @t235 @t277))) % 1.10/1.34 (define @t279 () (not @t278)) % 1.10/1.34 (define @t280 () (forall @t14 (or @t279 @t275))) % 1.10/1.34 (define @t281 () (or @t183 @t181 @t249 @t280)) % 1.10/1.34 (define @t282 () (or @t181 @t249 @t280)) % 1.10/1.34 (define @t283 () (=> @t248 @t280)) % 1.10/1.34 (define @t284 () (=> @t180 @t283)) % 1.10/1.34 (define @t285 () (or @t279 @t131)) % 1.10/1.34 (define @t286 () (not @t110)) % 1.10/1.34 (define @t287 () (or @t286 @t124)) % 1.10/1.34 (define @t288 () (_ (_ @t97 @t153) tptp.id)) % 1.10/1.34 (define @t289 () (or @t173 @t246 @t288)) % 1.10/1.34 (define @t290 () (=> @t245 @t288)) % 1.10/1.34 (define @t291 () (lambda @t14 (_ @t143 @t5))) % 1.10/1.34 (define @t292 () (_ @t83 tptp.sh)) % 1.10/1.34 (define @t293 () (lambda @t90 @t153)) % 1.10/1.34 (define @t294 () (_ @t154 tptp.id)) % 1.10/1.34 (define @t295 () (not @t98)) % 1.10/1.34 (define @t296 () (or @t295 @t113)) % 1.10/1.34 (define @t297 () (=> @t114 (_ (_ @t97 (_ @t294 @t83)) tptp.id))) % 1.10/1.34 (define @t298 () (=> @t89 @t297)) % 1.10/1.34 (define @t299 () (forall @t90 @t298)) % 1.10/1.34 (define @t300 () (=> @t299 @t133)) % 1.10/1.34 (define @t301 () (not @t105)) % 1.10/1.34 (define @t302 () (or @t301 @t102)) % 1.10/1.34 (define @t303 () (=> @t107 @t300)) % 1.10/1.34 (define @t304 () (not @t102)) % 1.10/1.34 (define @t305 () (or @t304 @t105)) % 1.10/1.34 (define @t306 () (=> @t108 @t303)) % 1.10/1.34 (define @t307 () (forall @t95 @t306)) % 1.10/1.34 (define @t308 () (or @t257 @t252)) % 1.10/1.34 (define @t309 () (or @t249 @t308)) % 1.10/1.34 (define @t310 () (forall @t189 @t309)) % 1.10/1.34 (define @t311 () (@list @t186)) % 1.10/1.34 (define @t312 () (forall @t311 @t309)) % 1.10/1.34 (define @t313 () (forall @t311 @t308)) % 1.10/1.34 (define @t314 () (or @t249 @t313)) % 1.10/1.34 (define @t315 () (tptp.sub @t5 @t157)) % 1.10/1.34 (define @t316 () (tptp.lam @t315)) % 1.10/1.34 (define @t317 () (_ @t93 tptp.id @t316 tptp.id)) % 1.10/1.34 (define @t318 () (forall @t14 (or @t279 @t317))) % 1.10/1.34 (define @t319 () (or @t279 @t123)) % 1.10/1.34 (define @t320 () (=> @t299 @t127)) % 1.10/1.34 (define @t321 () (forall @t95 @t320)) % 1.10/1.34 (define @t322 () (= @t5 @t13)) % 1.10/1.34 (define @t323 () (@quantifiers_skolemize @t185 1)) % 1.10/1.34 (define @t324 () (@quantifiers_skolemize @t185 0)) % 1.10/1.34 (define @t325 () (_ @t324 @t157 (tptp.lam @t323) @t157)) % 1.10/1.34 (define @t326 () (tptp.sub @t323 @t160)) % 1.10/1.34 (define @t327 () (_ @t324 @t157 @t326 @t157)) % 1.10/1.34 (define @t328 () (_ @t324 @t157 @t2 @t157)) % 1.10/1.34 (define @t329 () (forall @t62 (or (not @t328) @t327))) % 1.10/1.34 (define @t330 () (not @t329)) % 1.10/1.34 (define @t331 () (_ @t324 @t157 @t164 @t157)) % 1.10/1.34 (define @t332 () (_ @t324 @t157 @t165 @t157)) % 1.10/1.34 (define @t333 () (_ @t324 @t157 @t5 @t157)) % 1.10/1.34 (define @t334 () (forall @t90 (or @t173 (not (forall @t14 (or (not @t333) @t332))) @t331))) % 1.10/1.34 (define @t335 () (not @t334)) % 1.10/1.34 (define @t336 () (_ @t324 @t1 @t5 @t175)) % 1.10/1.34 (define @t337 () (_ @t324 @t178 @t177 @t20)) % 1.10/1.34 (define @t338 () (or (not (forall @t106 (or (not @t336) @t337))) (not (forall @t106 (or (not @t337) @t336))) @t335 @t330 @t325)) % 1.10/1.34 (define @t339 () (@list true)) % 1.10/1.34 (define @t340 () (@list @t338)) % 1.10/1.34 (define @t341 () (tptp.lam (tptp.sub @t323 @t157))) % 1.10/1.34 (define @t342 () (_ @t324 @t157 @t341 @t157)) % 1.10/1.34 (define @t343 () (or @t335 @t330 @t342)) % 1.10/1.34 (define @t344 () (not @t343)) % 1.10/1.34 (define @t345 () (@var "BOUND_VARIABLE_12667" tptp.subst)) % 1.10/1.34 (define @t346 () (@var "BOUND_VARIABLE_12668" tptp.term)) % 1.10/1.34 (define @t347 () (lambda (@list @t345 @t346 (@var "BOUND_VARIABLE_12669" tptp.subst)) (_ @t324 @t345 @t346 @t345))) % 1.10/1.34 (define @t348 () (_ @t347 @t157 @t341 @t157)) % 1.10/1.34 (define @t349 () (_ @t347 @t157 @t326 @t157)) % 1.10/1.34 (define @t350 () (_ @t347 @t157 @t2 @t157)) % 1.10/1.34 (define @t351 () (not @t350)) % 1.10/1.34 (define @t352 () (or @t351 @t349)) % 1.10/1.34 (define @t353 () (forall @t62 @t352)) % 1.10/1.34 (define @t354 () (not @t353)) % 1.10/1.34 (define @t355 () (_ @t347 @t157 @t164 @t157)) % 1.10/1.34 (define @t356 () (_ @t347 @t157 @t165 @t157)) % 1.10/1.34 (define @t357 () (_ @t347 @t157 @t5 @t157)) % 1.10/1.34 (define @t358 () (not @t357)) % 1.10/1.34 (define @t359 () (or @t358 @t356)) % 1.10/1.34 (define @t360 () (forall @t14 @t359)) % 1.10/1.34 (define @t361 () (not @t360)) % 1.10/1.34 (define @t362 () (or @t173 @t361 @t355)) % 1.10/1.34 (define @t363 () (forall @t90 @t362)) % 1.10/1.34 (define @t364 () (not @t363)) % 1.10/1.34 (define @t365 () (or @t364 @t354 @t348)) % 1.10/1.34 (assume @p1 (= tptp.axapp (forall (@list @t5 @t2 @t1) (= (_ (_ tptp.sub @t9) @t1) (_ (_ tptp.ap @t7) @t4))))) % 1.10/1.34 (assume @p2 (= tptp.axvarcons (forall @t12 (= (_ @t11 @t10) @t5)))) % 1.10/1.34 (assume @p3 @t16) % 1.10/1.34 (assume @p4 (= tptp.axabs (forall @t12 (= (_ (_ tptp.sub @t19) @t1) (_ tptp.lam (_ @t6 (_ @t18 (_ @t17 tptp.sh)))))))) % 1.10/1.34 (assume @p5 (= tptp.axclos @t23)) % 1.10/1.34 (assume @p6 (= tptp.axidl @t25)) % 1.10/1.34 (assume @p7 (= tptp.axshiftcons (forall @t12 (= (_ @t26 @t10) @t1)))) % 1.10/1.34 (assume @p8 (= tptp.axassoc @t28)) % 1.10/1.34 (assume @p9 (= tptp.axmap (forall @t22 (= (_ (_ tptp.comp @t10) @t20) @t30)))) % 1.10/1.34 (assume @p10 (= tptp.axidr @t31)) % 1.10/1.34 (assume @p11 @t33) % 1.10/1.34 (assume @p12 (= tptp.axscons (forall @t24 (= (_ (_ tptp.push (_ @t11 @t1)) (_ @t26 @t1)) @t1)))) % 1.10/1.34 (assume @p13 (= tptp.ulamvar1 (_ tptp.var tptp.one))) % 1.10/1.34 (assume @p14 (= tptp.ulamvarsh (forall @t14 (=> @t35 (_ tptp.var @t34))))) % 1.10/1.34 (assume @p15 (= tptp.ulamvarind (forall @t39 (=> (_ @t36 tptp.one) (=> (forall @t14 (=> @t35 (=> @t37 (_ @t36 @t34)))) @t38))))) % 1.10/1.34 (assume @p16 (= tptp.apinj1 (forall @t45 (=> @t44 @t40)))) % 1.10/1.34 (assume @p17 (= tptp.apinj2 (forall @t45 (=> @t44 @t46)))) % 1.10/1.34 (assume @p18 (= tptp.laminj (forall @t47 (=> (= @t19 (_ tptp.lam @t2)) @t40)))) % 1.10/1.34 (assume @p19 (= tptp.shinj (forall @t47 (=> (= @t34 (_ @t3 tptp.sh)) @t40)))) % 1.10/1.34 (assume @p20 (= tptp.lamnotap (forall (@list @t5 @t2 @t43) (not (= @t19 (_ @t42 @t43)))))) % 1.10/1.34 (assume @p21 (= tptp.apnotvar (forall @t47 (not (_ tptp.var @t9))))) % 1.10/1.34 (assume @p22 (= tptp.lamnotvar (forall @t14 (not (_ tptp.var @t19))))) % 1.10/1.34 (assume @p23 (= tptp.induction (forall @t39 (=> @t38 (=> @t51 (=> (forall @t14 (=> @t37 @t49)) @t48)))))) % 1.10/1.34 (assume @p24 (= tptp.pushprop_lem0 (forall @t55 (exists @t54 @t53)))) % 1.10/1.34 (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))))))))))))))))))))))))) % 1.10/1.34 (assume @p26 (= tptp.pushprop_lem0_lthm tptp.pushprop_lem0)) % 1.10/1.34 (assume @p27 (= tptp.pushprop_lem1 (forall (@list @t36 @t57 @t5 @t1 @t2) (=> @t37 (_ @t57 (_ @t6 (_ @t56 @t1))))))) % 1.10/1.34 (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))))))))))))))))))))))))) % 1.10/1.34 (assume @p29 (= tptp.pushprop_lem1_lthm (=> tptp.axvarcons (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.ulamvarind tptp.pushprop_lem1)))))) % 1.10/1.34 (assume @p30 (= tptp.pushprop_lem1v2 (forall @t58 (=> @t37 (=> @t53 (_ @t52 tptp.one)))))) % 1.10/1.34 (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))))))))))))))))))))))))) % 1.10/1.34 (assume @p32 (= tptp.pushprop_lem1v2_lthm (=> tptp.axvarcons tptp.pushprop_lem1v2))) % 1.10/1.34 (assume @p33 (= tptp.pushprop_lem2v2 (forall @t58 (=> @t53 (=> @t63 (forall @t60 (=> (_ tptp.var @t43) (=> (_ @t52 @t43) (_ @t52 (_ @t59 tptp.sh)))))))))) % 1.10/1.34 (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))))))))))))))))))))))))) % 1.10/1.34 (assume @p35 (= tptp.pushprop_lem2v2_lthm (=> tptp.axclos (=> tptp.axshiftcons tptp.pushprop_lem2v2)))) % 1.10/1.34 (assume @p36 (= tptp.pushprop_lem3v2 (forall @t58 (=> @t53 (=> (forall @t62 (=> @t61 @t66)) @t65))))) % 1.10/1.34 (assume @p37 (= tptp.pushprop_lem3v2_lthm tptp.pushprop_lem3v2)) % 1.10/1.34 (assume @p38 (= tptp.pushprop (forall @t55 (=> @t63 (=> @t37 @t65))))) % 1.10/1.34 (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))))))))))))))))))))))))) % 1.10/1.34 (assume @p40 (= tptp.pushprop_lthm_orig @t67)) % 1.10/1.34 (assume @p41 (= tptp.pushprop_lthm (=> tptp.pushprop_lem0 @t67))) % 1.10/1.34 (assume @p42 (= tptp.induction2lem (forall @t39 (=> @t51 (=> @t70 (forall @t12 (=> @t63 (_ @t36 @t7)))))))) % 1.10/1.34 (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 @t71)))))))))))))))))))))))) % 1.10/1.34 (assume @p44 (= tptp.induction2lem_lthm (=> tptp.axapp (=> tptp.axvarcons (=> tptp.axabs (=> tptp.axclos (=> tptp.axshiftcons (=> tptp.axassoc (=> tptp.axmap (=> tptp.axidr @t71)))))))))) % 1.10/1.34 (assume @p45 (= tptp.induction2 (forall @t39 (=> @t38 (=> @t51 (=> @t70 @t48)))))) % 1.10/1.34 (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 @t72)))))))))))))))))))))))))) % 1.10/1.34 (assume @p47 (= tptp.induction2_lthm (=> tptp.axvarid @t72))) % 1.10/1.34 (assume @p48 (= tptp.substmonoid (and @t28 @t25 @t31))) % 1.10/1.34 (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)))))))))))))))))))))))))))) % 1.10/1.34 (assume @p50 (= tptp.substmonoid_lthm (=> tptp.axidl (=> tptp.axassoc (=> tptp.axidr tptp.substmonoid))))) % 1.10/1.34 (assume @p51 (= tptp.termmset (and @t23 @t15))) % 1.10/1.34 (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))))))))))))))))))))))))))))) % 1.10/1.34 (assume @p53 (= tptp.termmset_lthm (=> tptp.axvarid (=> tptp.axclos tptp.termmset)))) % 1.10/1.34 (assume @p54 (= tptp.hoasapinj1 (forall @t45 (=> @t75 @t40)))) % 1.10/1.34 (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)))))))))))))))))))))))))))))) % 1.10/1.34 (assume @p56 (= tptp.hoasapinj1_lthm (=> tptp.axvarid (=> tptp.apinj1 tptp.hoasapinj1)))) % 1.10/1.34 (assume @p57 (= tptp.hoasapinj2 (forall @t45 (=> @t75 @t46)))) % 1.10/1.34 (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))))))))))))))))))))))))))))))) % 1.10/1.34 (assume @p59 (= tptp.hoasapinj2_lthm (=> tptp.apinj2 tptp.hoasapinj2))) % 1.10/1.34 (assume @p60 (= tptp.hoaslaminj (forall @t90 (=> @t89 (forall (@list @t76) (=> (forall @t85 (= (_ (_ tptp.sub @t77) @t20) (_ (_ @t76 @t21) @t29))) (=> (= @t84 (_ @t82 (lambda @t81 @t77))) (forall @t81 (= @t80 @t77))))))))) % 1.10/1.34 (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)))))))))))))))))))))))))))))))) % 1.10/1.34 (assume @p62 (= tptp.hoaslaminj_lthm (=> tptp.axvarcons (=> tptp.axshiftcons (=> tptp.laminj tptp.hoaslaminj))))) % 1.10/1.34 (assume @p63 (= tptp.hoaslamnotap (forall @t90 (=> @t89 (forall @t47 (not (= (_ @t82 (lambda (@list @t1 @t43) (_ @t79 @t43))) @t91))))))) % 1.10/1.34 (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))))))))))))))))))))))))))))))))) % 1.10/1.34 (assume @p65 (= tptp.hoaslamnotap_lthm (=> tptp.lamnotap tptp.hoaslamnotap))) % 1.10/1.34 (assume @p66 (= tptp.hoaslamnotvar (forall @t90 (=> @t89 (not (_ (_ @t92 @t84) tptp.id)))))) % 1.10/1.34 (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)))))))))))))))))))))))))))))))))) % 1.10/1.34 (assume @p68 (= tptp.hoaslamnotvar_lthm (=> tptp.axvarid (=> tptp.lamnotvar tptp.hoaslamnotvar)))) % 1.10/1.34 (assume @p69 (= tptp.hoasapnotvar (forall @t47 (not (_ (_ @t92 @t91) tptp.id))))) % 1.10/1.34 (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))))))))))))))))))))))))))))))))))) % 1.10/1.34 (assume @p71 (= tptp.hoasapnotvar_lthm (=> tptp.axvarid (=> tptp.apnotvar tptp.hoasapnotvar)))) % 1.10/1.34 (assume @p72 (= tptp.hoasinduction_lem0 (forall @t95 (exists @t54 @t94)))) % 1.10/1.34 (assume @p73 (= tptp.hoasinduction_lem0_lthm tptp.hoasinduction_lem0)) % 1.10/1.34 (assume @p74 (= tptp.hoasinduction_lem1v2 (forall @t109 (=> @t108 (=> @t107 (=> @t99 (=> @t94 (forall @t14 (=> @t35 @t96))))))))) % 1.10/1.34 (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)))))))))))))))))))))))))))))))))))) % 1.10/1.34 (assume @p76 (= tptp.hoasinduction_lem2v2 (forall @t109 (=> @t108 (=> @t107 (=> @t111 (=> @t94 (forall @t47 (=> @t96 (=> @t66 (_ @t52 @t9))))))))))) % 1.10/1.34 (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)))))))))))))))))))))))))))))))))))) % 1.10/1.34 (assume @p78 (= tptp.hoasinduction_lem3v2_f (forall @t62 (exists @t90 (forall @t12 (= @t80 @t64)))))) % 1.10/1.34 (assume @p79 (= tptp.hoasinduction_lem3v2_f_lthm tptp.hoasinduction_lem3v2_f)) % 1.10/1.34 (assume @p80 (= tptp.hoasinduction_lem3v2 (forall @t109 (=> @t108 (=> @t107 @t118))))) % 1.10/1.34 (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)))))))))))))))))))))))))))))))))))) % 1.10/1.34 (assume @p82 (= tptp.hoasinduction_lem3v2_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2)))))) % 1.10/1.34 (assume @p83 (= tptp.hoasinduction_lem3v2a (forall @t109 @t118))) % 1.10/1.34 (assume @p84 (= tptp.hoasinduction_lem3v2a_lthm (=> tptp.hoasinduction_lem3v2_f (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3v2a))))))) % 1.10/1.34 (assume @p85 (= tptp.hoasinduction_lem1 (forall @t95 (=> @t108 (=> @t107 (=> @t99 (forall @t14 (=> @t35 @t98)))))))) % 1.10/1.34 (assume @p86 (= tptp.hoasinduction_lem1_gthm @t119)) % 1.10/1.34 (assume @p87 (= tptp.hoasinduction_lem1_lthm @t119)) % 1.10/1.34 (assume @p88 (= tptp.hoasinduction_lem2 (forall @t95 (=> @t108 (=> @t107 (=> @t111 (forall @t47 (=> @t98 (=> @t110 (_ (_ @t97 @t9) tptp.id)))))))))) % 1.10/1.34 (assume @p89 (= tptp.hoasinduction_lem2_gthm @t120)) % 1.10/1.34 (assume @p90 (= tptp.hoasinduction_lem2_lthm @t120)) % 1.10/1.34 (assume @p91 @t130) % 1.10/1.34 (assume @p92 (= tptp.hoasinduction_lem3aa_lthm (=> tptp.axclos (=> tptp.axmap tptp.hoasinduction_lem3aa)))) % 1.10/1.34 (assume @p93 (= tptp.hoasinduction_lem3aaa (forall @t95 (=> (forall @t90 (=> (exists @t60 (forall @t85 (and (= @t87 (_ (_ tptp.sub (_ @t59 @t10)) @t20)) (= (_ @t59 @t30) @t86)))) @t115)) @t127)))) % 1.10/1.34 (assume @p94 @t138) % 1.10/1.34 (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)))))))))))))))))))))))))))))))))))))) % 1.10/1.34 (assume @p96 @t142) % 1.10/1.34 (assume @p97 (= tptp.hoasinduction_lem3a (forall @t95 @t134))) % 1.10/1.34 (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)))))))))))))))))))))))))))))))))))))) % 1.10/1.34 (assume @p99 (= tptp.hoasinduction_lem3a_lthm (=> tptp.axvarid (=> tptp.axvarshift (=> tptp.hoasinduction_lem3aa tptp.hoasinduction_lem3a))))) % 1.10/1.34 (assume @p100 (= tptp.hoasinduction_lem3b (forall @t62 (exists @t90 (= (_ @t3 @t32) @t144))))) % 1.10/1.34 (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)))))))))))))))))))))))))))))))))))))) % 1.10/1.34 (assume @p102 (= tptp.hoasinduction_lem3b_lthm tptp.hoasinduction_lem3b)) % 1.10/1.34 (assume @p103 (= tptp.hoasinduction (forall @t95 (=> @t108 (=> @t107 (=> @t99 @t145)))))) % 1.10/1.34 (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 @t146)))))))))))))))))))))))))))))))))))) % 1.10/1.34 (assume @p105 (= tptp.hoasinduction_lthm (=> tptp.induction2 @t146))) % 1.10/1.34 (assume @p106 (= tptp.hoasinduction_lthm_3 (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction)))))) % 1.10/1.34 (assume @p107 (= tptp.hoasinduction_no_psi_cond (forall @t95 @t145))) % 1.10/1.34 (assume @p108 (= tptp.hoasinduction_no_psi_cond_lthm (=> tptp.hoasinduction_lem0 (=> tptp.induction2 (=> tptp.axvarid (=> tptp.hoasinduction_lem3v2a tptp.hoasinduction_no_psi_cond)))))) % 1.10/1.34 (assume @p109 @t147) % 1.10/1.34 (assume @p110 true) % 1.10/1.34 (step @p111 (= tptp.pushprop_p_and_p_prime @t151) :rule refl :args (@t151)) % 1.10/1.34 (step @p112 (= tptp.hoasap @t152) :rule refl :args (@t152)) % 1.10/1.34 (step @p113 (= tptp.hoaslam @t154) :rule refl :args (@t154)) % 1.10/1.34 (step @p114 (= tptp.hoasvar @t155) :rule refl :args (@t155)) % 1.10/1.34 (step @p115 (= tptp.hoasinduction_p_and_p_prime @t156) :rule refl :args (@t156)) % 1.10/1.34 (step @p116 :rule bool-impl-true2 :args ((=> @t190 @t185))) % 1.10/1.34 (step @p117 :rule refl :args (@t157)) % 1.10/1.34 (step @p118 :rule refl :args (@t32)) % 1.10/1.34 (step @p119 :rule cong :premises (@p118 @p117) :args ((= @t32 @t157))) % 1.10/1.34 (step @p120 :rule symm :premises (@p119)) % 1.10/1.34 (step @p121 :rule eq_resolve :premises (@p118 @p120)) % 1.10/1.34 (step @p122 :rule refl :args (@t159)) % 1.10/1.34 (step @p123 :rule cong :premises (@p121 @p122 @p121) :args (@t191)) % 1.10/1.34 (step @p124 :rule refl :args (@t162)) % 1.10/1.34 (step @p125 :rule refl :args (@t174)) % 1.10/1.34 (step @p126 :rule refl :args (@t181)) % 1.10/1.34 (step @p127 :rule refl :args (@t183)) % 1.10/1.34 (step @p128 :rule nary_cong :premises (@p127 @p126 @p125 @p124 @p123) :args (@t192)) % 1.10/1.34 (step @p129 :rule cong :premises (@p128) :args ((forall @t184 @t192))) % 1.10/1.34 (step @p130 :rule refl :args (@t191)) % 1.10/1.34 (step @p131 :rule refl :args (@t2)) % 1.10/1.34 (step @p132 :rule cong :premises (@p131 @p121) :args (@t193)) % 1.10/1.34 (step @p133 :rule refl :args (@t158)) % 1.10/1.34 (step @p134 :rule cong :premises (@p133 @p132) :args (@t194)) % 1.10/1.34 (step @p135 :rule cong :premises (@p121 @p134 @p121) :args (@t195)) % 1.10/1.34 (step @p136 :rule cong :premises (@p121 @p131 @p121) :args (@t196)) % 1.10/1.34 (step @p137 :rule cong :premises (@p136) :args (@t197)) % 1.10/1.34 (step @p138 :rule nary_cong :premises (@p137 @p135) :args (@t198)) % 1.10/1.34 (step @p139 :rule cong :premises (@p138) :args (@t199)) % 1.10/1.34 (step @p140 :rule cong :premises (@p139) :args (@t200)) % 1.10/1.34 (step @p141 :rule refl :args (@t164)) % 1.10/1.34 (step @p142 :rule cong :premises (@p121 @p141 @p121) :args (@t201)) % 1.10/1.34 (step @p143 :rule refl :args (@t166)) % 1.10/1.34 (step @p144 :rule refl :args (@t173)) % 1.10/1.34 (step @p145 :rule nary_cong :premises (@p144 @p143 @p142) :args (@t202)) % 1.10/1.34 (step @p146 :rule cong :premises (@p145) :args ((forall @t90 @t202))) % 1.10/1.34 (step @p147 :rule refl :args (@t201)) % 1.10/1.34 (step @p148 :rule refl :args (@t5)) % 1.10/1.34 (step @p149 :rule cong :premises (@p121 @p148) :args (@t203)) % 1.10/1.34 (step @p150 :rule cong :premises (@p121 @p149 @p121) :args (@t204)) % 1.10/1.34 (step @p151 :rule cong :premises (@p121 @p148 @p121) :args (@t205)) % 1.10/1.34 (step @p152 :rule cong :premises (@p151) :args (@t206)) % 1.10/1.34 (step @p153 :rule nary_cong :premises (@p152 @p150) :args (@t207)) % 1.10/1.34 (step @p154 :rule cong :premises (@p153) :args (@t208)) % 1.10/1.34 (step @p155 :rule cong :premises (@p154) :args (@t209)) % 1.10/1.34 (step @p156 :rule refl :args (@t173)) % 1.10/1.34 (step @p157 :rule nary_cong :premises (@p156 @p155 @p147) :args (@t210)) % 1.10/1.34 (step @p158 :rule cong :premises (@p157) :args (@t211)) % 1.10/1.34 (step @p159 :rule trans :premises (@p158 @p146)) % 1.10/1.34 (step @p160 :rule cong :premises (@p159) :args (@t212)) % 1.10/1.34 (step @p161 :rule refl :args (@t181)) % 1.10/1.34 (step @p162 :rule refl :args (@t183)) % 1.10/1.34 (step @p163 :rule nary_cong :premises (@p162 @p161 @p160 @p140 @p130) :args (@t213)) % 1.10/1.34 (step @p164 :rule cong :premises (@p163) :args (@t214)) % 1.10/1.34 (step @p165 :rule trans :premises (@p164 @p129)) % 1.10/1.34 (step @p166 :rule refl :args (@t187)) % 1.10/1.34 (step @p167 :rule cong :premises (@p121 @p166 @p121) :args (@t215)) % 1.10/1.34 (step @p168 :rule refl :args (@t188)) % 1.10/1.34 (step @p169 :rule nary_cong :premises (@p125 @p168 @p167) :args (@t216)) % 1.10/1.34 (step @p170 :rule cong :premises (@p169) :args ((forall @t189 @t216))) % 1.10/1.34 (step @p171 :rule refl :args (@t215)) % 1.10/1.34 (step @p172 :rule refl :args (@t186)) % 1.10/1.34 (step @p173 :rule cong :premises (@p172 @p132) :args (@t217)) % 1.10/1.34 (step @p174 :rule cong :premises (@p121 @p173 @p121) :args (@t218)) % 1.10/1.34 (step @p175 :rule nary_cong :premises (@p137 @p174) :args (@t219)) % 1.10/1.34 (step @p176 :rule cong :premises (@p175) :args (@t220)) % 1.10/1.34 (step @p177 :rule cong :premises (@p176) :args (@t221)) % 1.10/1.34 (step @p178 :rule nary_cong :premises (@p160 @p177 @p171) :args (@t222)) % 1.10/1.34 (step @p179 :rule cong :premises (@p178) :args (@t223)) % 1.10/1.34 (step @p180 :rule trans :premises (@p179 @p170)) % 1.10/1.34 (step @p181 :rule cong :premises (@p180 @p165) :args (@t224)) % 1.10/1.34 (step @p182 :rule eq-refl :args (@t32)) % 1.10/1.34 (step @p183 :rule cong :premises (@p182 @p181) :args (@t225)) % 1.10/1.34 (step @p184 :rule trans :premises (@p183 @p116)) % 1.10/1.34 (step @p185 :rule cong :premises (@p148 @p121) :args (@t226)) % 1.10/1.34 (step @p186 :rule cong :premises (@p148 @p185) :args (@t227)) % 1.10/1.34 (step @p187 :rule cong :premises (@p186) :args (@t228)) % 1.10/1.35 (step @p188 :rule cong :premises (@p187 @p184) :args (@t229)) % 1.10/1.35 (step @p189 :rule cong :premises (@p188) :args ((not @t229))) % 1.10/1.35 (step @p190 :rule eq-symm :args (@t32 tptp.id)) % 1.10/1.35 (step @p191 :rule refl :args (tptp.axvarshift)) % 1.10/1.35 (step @p192 :rule cong :premises (@p191 @p190) :args (@t33)) % 1.10/1.35 (step @p193 :rule eq_resolve :premises (@p11 @p192)) % 1.10/1.35 (step @p194 :rule equiv_elim2 :premises (@p96)) % 1.10/1.35 (step @p195 :rule resolution :premises (@p194 @p109) :args (true tptp.hoasinduction_lem3_lthm)) % 1.10/1.35 (step @p196 :rule not_implies_elim2 :premises (@p195)) % 1.10/1.35 (step @p197 :rule not_implies_elim1 :premises (@p196)) % 1.10/1.35 (step @p198 :rule eq_resolve :premises (@p197 @p193)) % 1.10/1.35 (step @p199 :rule refl :args (@t159)) % 1.10/1.35 (step @p200 :rule cong :premises (@p198 @p199 @p198) :args (@t230)) % 1.10/1.35 (step 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1.10/1.35 (step @p678 :rule beta-reduce :args ((= @t357 @t333))) % 1.10/1.35 (step @p679 :rule cong :premises (@p678) :args (@t358)) % 1.10/1.35 (step @p680 :rule nary_cong :premises (@p679 @p677) :args (@t359)) % 1.10/1.35 (step @p681 :rule cong :premises (@p680) :args (@t360)) % 1.10/1.35 (step @p682 :rule cong :premises (@p681) :args (@t361)) % 1.10/1.35 (step @p683 :rule nary_cong :premises (@p156 @p682 @p676) :args (@t362)) % 1.10/1.35 (step @p684 :rule cong :premises (@p683) :args (@t363)) % 1.10/1.35 (step @p685 :rule cong :premises (@p684) :args (@t364)) % 1.10/1.35 (step @p686 :rule nary_cong :premises (@p685 @p675 @p669) :args (@t365)) % 1.10/1.35 (step @p687 :rule refl :args (@t190)) % 1.10/1.35 (step @p688 :rule cong :premises (@p687 @p686) :args ((=> @t190 @t365))) % 1.10/1.35 (assume-push @p696 @t190) % 1.10/1.35 (step @p690 :rule instantiate :premises (@p639) :args ((@list @t347 @t323))) % 1.10/1.35 (step-pop @p697 :rule scope :premises (@p690)) % 1.10/1.35 (step @p691 :rule process_scope :premises (@p697) :args (@t365)) % 1.10/1.35 (step @p693 :rule eq_resolve :premises (@p691 @p688)) % 1.10/1.35 (step @p694 :rule implies_elim :premises (@p693)) % 1.10/1.35 (step @p695 false :rule chain_m_resolution :premises (@p694 @p668 @p639) :args (false (@list true false) (@list @t343 @t190))) % 1.10/1.35 ) % 1.10/1.35 % SZS output end Proof % 1.10/1.35 % cvc5 exiting %------------------------------------------------------------------------------